Encyclopedia of Physical Science and Technology (3Rd Ed 2001 Academic Press) - Astronomy

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Encyclopedia of Physical Science and Technology EN001H-05-32 May 26, 2001 14:47

AstrochemistrySteven N. ShoreIndiana University South Bend

I. IntroductionII. Physical ProcessesIII. DustIV. Molecular EnvironmentsV. Chemical Processes

VI. Cosmological ChemistryVII. Conclusion

GLOSSARY

Astrochemistry The theoretical study of chemical pro-cesses in cosmic environments and the observationaldetermination of physical parameters through the studyof abundances of molecular species. This review con-centrates on the recent results concerning circumstellarenvelopes and the interstellar medium. The field deals,however, with synthesis of molecules in cometarynuclei and planetary atmospheres, as well as stellarphotospheres.

Fractionation Process by which isotopes are included inmolecules, either by the process of direct transfer or bycharge exchange.

Large-velocity gradient approximation (also calledSobolev approximation) the assumption that the linewidth due to thermal broadening is small comparedwith the large-scale velocity field in a medium. It isbasic to the assumption that the optical depth of a linedepends only on the velocity gradient.

Molecular cloud The densest phase of the interstellar

medium. Clouds have large size (of order 1–10 pc)and high densities (≥103 cm−3).

Polycyclic aromatic hydrocarbons (PAHs) Hydrocar-bons in complex chains and agglomerated rings thoughtto be responsible for the diffuse emission lines observedin dust nebulae in the near-infrared. These moleculesform the lowest-mass end of the dust distribution andare responsible for ubiquitous diffuse emission in the1- to 25-µm galactic background radiation.

Units Parsec (pc), 3.1 × 1018 cm; solar mass (M�), 2 ×1033 g; Jansky (Jy), 10−23 erg−1 cm−2 Hz−1.

Vibronic Transition Molecular transition involvingstates which are split by rotation that is induced throughrotation–vibrational coupling; the fine-structure statesof electronic transitions.

I. INTRODUCTION

Astrochemistry is a field that spans virtually all cosmicenvironments, from comets and planetary atmospheres to

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666 Astrochemistry

the interstellar medium. As such, it is more concerned withprocesses and what they reveal about the physical natureof the medium than with the specific arena in which theseprocesses occur. It is one of the few astrophysical fields inwhich laboratory work is possible, and in which conditionssimilar to those studied astronomically can be simulated.In this review, we shall concentrate on the most recentwork, concerned mainly with stellar mass outflows andthe interstellar medium. For want of space, planets andstellar photospheres have been excluded.

Observational astrochemistry is accomplished primar-ily with infrared (IR) and millimeter techniques, areas oftechnology which have been seen explosive expansion inthe past decade. With the improvement of superconductingdetectors and the development of interferometric arrays,this field is one which will surely change significantly inthe next decade.

We will begin by examining the physical processesneeded to diagnose the conditions in astrochemical en-vironments and then examine some of the chemical prod-ucts thus detected. It is important to keep in mind that,with the exception of solar system objects, astrochemi-cal analyses are quintessentially remote sensing, studiedby observations of spectral lines emanating from distantsources through the applications of radiative transfer the-ory and molecular line formation.

II. PHYSICAL PROCESSES

A. Basic Molecular Spectroscopy

1. Electronic Transitions

The electronic states in a molecule, analogs of the atomicstates and characterized by total electronic angular mo-mentum and spin, are generally separated in energy byabout the same order of magnitude as for isolated atoms,usually several electron volts (eV). Thus the transitionsfrom molecular electronic states, which also correspondto different potentials, are best observed in the ultraviolet(UV) region. Excitation depends on the presence of UVradiation, and electronic transitions are usually seen in ab-sorption, as in the 1∑+

g state of H2. The strength of thetransition depends on the dipole (heteronuclear moleculesand ions) or the quadrupole (homonuclear) moments. Vi-brational states dominate the optical and infrared, and ro-tational states are best observed in the millimeter and cen-timeter portions of the spectrum.

For diatomic molecules, these states are classified by theprojection of the electronic angular momentum along theinternuclear axis, �, and the projected combined spin

∑and are grouped into multiplets according to the couplingbetween these states and the rotational angular momen-tum J . For � �= 0, the states are split by � = � + ∑

into fine-structure levels, called �-doubling. Interactionwith nuclear spins produces hyperfine splitting of the ro-tational levels, with quantum number F . These hyperfinetransitions in OH are responsible for the observed maseremission.

2. Rotational Transitions

The nuclei, which are the massive components of mole-cules, are free to rotate and precess about the center ofmass. Thus, a molecule with a moment of inertia, I , hasa rotational angular momentum J which is quantized andthus takes on only discrete values. The energies of thesestates can be shown to be

EJ = h

4πIJ (J + 1) ≡ Bv J (J + 1), (1)

so that transitions between states of unequal J show a step-ladder pattern in the separation of lines of the same series.Because of the large value of the moments of inertia, dueto the mass of the nucleus, the separation of these states issmall, of order 0.01 eV, increasing with increasing J . Thesimple representation that has just been used, however, isonly appropriate for diatomic species, which have only onerotational axis that is degenerate in the two axes orthogonalto the internuclear axis about the center of mass.

If the molecule is more complex, for example, H2O,then two or three axes are needed to fully describe the ro-tation. Each of these has an associated moment of inertia,depending on the details of the electronic states and theinternuclear distances and masses. The projection of therotation along the body axis, K , now appears in the termsfor the rotational splitting. For instance, for a symmetrictop molecule line CH3,

F|v| = B|v| J (J + 1) + (B|v| − A|v|

)K 2 ± 2A|v|ζ K , (2)

where ζ describes the coupling of the vibrations and therotations (vibronic states) and splits the otherwise degen-erate K levels. The constants A and B are the momentsof inertia about the parallel and perpendicular axes of ro-tation, relative to the body axis. The rotational lines willbe distributed in a way that depends on the ratio of themoments of inertia of the principal axes of the molecule.Thus there will be multiplets for lines which are closelyspaced in energy and which can be strongly radiativelycoupled (see discussion of masers).

3. Vibrational Transitions

Vibrational states distribute as those of a harmonic oscil-lator, with

Ev = hν0(v + 1

2

), (3)



Astrochemistry 667

where ν0 is the vibrational frequency of the ground state.Polyatomic molecules have additional vibrational statesdue to the multiple modes presented by different config-urations. For instance, bending modes in water are statesfor which the O moves and the H remains fixed, whileothers have both the O and H moving oppositely (the so-called ν2 and ν3 modes), in addition to the fundamental ν1

mode which involves the O–H bond stretch. Vibrationalcoupling produces an angular momentum which splits ro-tational states, as mentioned above under vibronic transi-tions.

Coupling of vibrational and electronic states—that is,between � and v—produces an angular momentum K ,which for polyatomic molecules depends on the axis aboutwhich the rotation is executed. For instance, in H2O thereis a prolate and oblate rotational axis for the molecule, sothat a state J is split by two values of K and labeled byJK+ K− . More complex states are possible, depending onthe complexity of the molecule. For example, inversiontransitions of molecules such as NH3, which occur at cen-timeter wavelengths, result from small perturbations ofrotational states by vibrational transition between mirrormolecular conformations.

B. Radiative Transfer: ObservationalAstrochemistry

1. Line Radiative Transfer

Molecular observations are almost always concerned withspecific discrete transitions. These are generally observedat millimeter or centimeter wavelengths. The intensity ofa source is determined by the rate of collisional versusradiative transitions between levels. Because of the ex-tremely low densities usually associated with molecularenvironments, whether in a circumstellar envelope or amolecular cloud, pressure broadening is unimportant. In-stead, the molecule radiates at its local velocity into theline of sight. This dispersion of velocity may be due strictlyto the thermal motions of the particles, or it may be due tothe presence of turbulence or large-scale chaotic motionswithin the medium. Either way, the local profile, φ(ν) is aGaussian with a finite width in frequency.

The absorption coefficient for a state can be written as

κν = (n1 B12 − n2 B21)φ(ν), (4)

where n j is the population of the upper (n2) or lower (n1)state, and B12 and B21 are the Einstein transition probabil-ities for stimulated transitions. The emission coefficient,due to spontaneous transitions, is given by

jν = n2 A21φ(ν), (5)

where A21 is the Einstein spontaneous transition prob-ability and φν is the line profile function that describesthe frequency dependence of the line. In its most generalform, φν is the convolution of the intrinsic line profile dueto radiative and collisional broadening of the upper andlower states (usually a Lorentzian profile) and the extrinsicbroadening due to the random motions of the molecules (aGaussian profile whose width depends on the thermal andturbulent velocities added quadratically). The equation ofradiative transfer is

d Iνdl

= −κν Iν + jν, (6)

where I is the intensity and l is the path length through themedium. Collisions dominate most molecular excitation,and if the emission rate is low, as usually occurs in molec-ular clouds, then the populations can be assumed to be inlocal thermal equilibrium, hence given by the Boltzmanndistribution:

N2

N1= g2

g1e−E12/kTex , (7)

where Tex is the excitation temperature, which is assumedto be of the order of the kinetic temperature of the excit-ing particles, and g is the statistical weight of the states,which are separated by E12. The optical depth for a lineis proportional to the path length through the medium, sothat

κndl = κndv

/(dv

dl

)= c

νκ0n

�ν

dv/dl, (8)

where �ν is the line width in frequency, κ0 is the opac-ity at line center, n is the number density, and dv/dl isthe velocity gradient along the line of sight. The so-calledlarge velocity gradient or Sobolev approximation (alsocalled the “on the spot” approximation because the emis-sion and/or absorption is assumed to depend on only thelocal conditions) assumes that this gradient is larger thanthe thermal speeds so that the optical depth of the mediumis small. For molecular clouds, observed line widths areusually a few kilometers per second, while the thermalspeed is about 0.1 km s−1, so this approximation seems tobe valid for all but the most abundant species.

Like their atomic counterparts, molecular lines satu-rate when the populations have reached the values asso-ciated with strict equilibrium with the incoming radia-tion. This occurs first at the line center. Any motion in themedium, ordered or random, will broaden the line and thusthe molecules will “see” radiation at other wavelengthsagainst which they can absorb, or into which they canemit. If the medium is optically thick at line center butthe velocity dispersion is large, the overall optical depthcan be considerably reduced by spreading out the line infrequency.



668 Astrochemistry

The most abundant molecules, because of the low ve-locities observed in the clouds and high column densities,cannot be interpreted by simple optically thin models. ForCO (any isotope), the ratio of the (2 → 1) to (1 → 0) tran-sitions should be 3:1 in strength, if completely opticallythin, because of the ratio of the statistical weights and tran-sition probabilities and the temperature known to exist inthe clouds. However, 12C16O (1 → 0) is often observed toshow flat-topped profiles, not the Gaussian form whichwould be typical of a randomly moving optically thinmolecular gas. Also, the intensity ratio of the transitions isoften seen to depart from that expected for such a medium.The implication is that 12CO is optically thick, and thatthe densest parts of the cloud may not be observable in theground-state transition. Lower-abundance species (for in-stance, the isotopes 13CO and 12C18O, or more highly ex-cited states of 12C16O (such as 3 → 2) may, however, probedenser parts of the cloud. Further, the higher transitionsrequire higher densities for excitation, so there is a delicateinterplay between chemistry and radiative transfer whichenters into the interpretation of abundances. This is crucialto the understanding of the formation of the molecules.

The abundance of a species is related to the observedline intensity by the antenna temperature, the temperaturewhich an equivalent blackbody radiator would have tohave at the line frequency to equal the observed lineintensity:

Iline =∫ ∞

0

TA

ν2dν, (9)

which is integrated over the velocity width of the line. Thecolumn density, by number, in the lower level is definedas

Nl = 4π3/2

(ln 2)1/2

kν

hc2

(2Jl + 1)

(2Ju + 1)

1

Aul

∫line

TB dv, (10)

where k is the Boltzmann constant and v is the velocitywidth of the line. Then the total column density of thespecies is found using the Boltzmann distribution for thelevels:

Ntot = NlQ(T )

(2Jl + 1)exp

(El

kT

), (11)

where Q(T ) is the molecular partition function, the sumover the population probabilities for all of the rotationallevels,

Q(T ) =∑J,K

gJ,K e−E J K /kT , (12)

which can often be found in closed form. For instance, fora symmetric top molecule,

Q(T ) =(

π

Av B2v

)1/2(kT

hc

)3/2

exp

(Bvhc

4kT

), (13)

where Bv = Cv and Av are the moments of inertia forthe rotational states and El = hc[Bv J (J + 1) + (Av −Bv)K 2]. In the optically thin, LVG approximation, this suf-fices to determine the abundance of the species of interest.It assumes that all emission is due to thermal equilibriumprevailing due to collisions among the levels.

2. Masers

Because of the low densities, molecules in cosmic envi-ronments can show populations of many levels which areinverted. That is, the higher levels sometimes have higherpopulations than the lower ones. The primary reason forthis is that transitions take place between high states whichare only weakly collisionally coupled to lower levels, andfor which radiative transitions are long. If there is a strongbackground radiation field at shorter wavelength than thetransition of interest, upper states of the molecule maybe radiatively excited with subsequent overpopulation ofsome of the lower states by radiative and collisional deex-citation. Thus, for masers to occur, more than two statesmust be involved in strongly coupled transitions.

Masers also serve as a warning that the intensity ofa spectral line is not necessarily a direct measure of itsabundance. Population inversions enhance the brightnesstemperatures, leading to overestimates of excitation andabundance in those species in which masing occurs. Be-cause not all molecules undergo maser amplification, theassumption of thermal equilibrium is usually not bad, butshould be employed with caution.

The emission and absorption coefficients for the systemcan be defined as before. Now assume that there are a totalof n levels, and that they are coupled via collisions andradiation to the levels 1 and 2. Then the time-dependentpopulations of 1 and 2 are given by

dn1

dt= P1(n − n1 − n2) − (n1 B12 − n2 B21)

�

4πI

− n1C12 − n1�; (14)

dn2

dt= P2(n − n1 − n2) − (n2 B21 − n1 B12)

�

4πI

− n2(A21 − C21) − n2�. (15)

Here P1 and P2 are the pump rates from the higher-lyinglevels through radiation and collisions, � is the solidangle, and � is the rate at which the masing levels aredepopulated.

For molecular masers, it can be assumed that the twomasing levels have the same statistical weight. Thus,B12 = B21 = B. The number of levels involved in the par-ticular population inversion is small. This implies strongradiative coupling between states which, for some rea-son, are selectively pumped by the external sources of



Astrochemistry 669

radiation. The OH molecule is an excellent example ofthis behavior.

If the absorption coefficient is negative, in other words,if the populations are sufficiently inverted, the radiationin the 2 → 1 transition will amplify along its path untilthe maser saturates, that is, until the populations do notchange along the path length. The amplification selectsout the line center, and the line gradually narrows as aresult of increasing path length. This behavior is of greatimportance, because the brightness temperature increasesas the line gets narrower. Further, the radiation has a finiteamplification length; the maser can saturate. In the absenceof collisions and in steady state, � can be replaced by� = 2BI (�/4π ), so that the brightness temperature of asaturated maser is given by

TB,s = hν

2k

�

A

�

4π(16)

This makes masers very intense radiation sources, sincethe pump radiation at higher frequency has been convertedboth to lower frequency and narrower bandwidth by theamplification process. The emission is also highly polar-ized, since it is coherent.

Masing depends on the presence of a strong radiationfield for excitation and maintenance. Such radiation, usu-ally infrared, is significant in several environments, no-tably in circumstellar envelopes (CSEs) and in molecularclouds. In CSEs, far-infrared radiation is converted to cen-timeter radiation by OH, which has transitions centeredaround 1665 MHz. Ammonia, water, HCN, and SiO, arealso important stellar maser sources. Water masers are alsoassociated with regions of active star formation, where IRfrom the protostellar cores can excite the millimeter ra-diation in the densest parts of the cloud. Because theyare strongly amplifying, the masing sites are easily dis-tinguished from the background and their proper motionscan be directly measured using VLBI techniques. Theirtime variability is also well observed, although it is stillnot fully understood theoretically.

III. DUST

A fundamental constituent of the atmospheres of thecoolest stars (whether red giants or brown dwarfs) andof the interstellar medium is the solid material that has be-come known as dust. Although dust was recognized andcharacterized more than 50 years ago, many of its basicproperties are still debated. In large measure, this is dueto the very indirect way in which information about thecomposition and structure of the dust is obtained.

The spectral signature of dust is the presence of sev-eral very broad features in the infrared and the ultraviolet,

whose strength correlates well with the extinction of vis-ible starlight. The UV feature, near 2175 A, is likely dueto some form of solid carbon, something like graphite oran amorphous state of carbon. Its strength and shape arevariable throughout the galactic plane, although not en-tirely absent along most lines of sight through the plane,and these also are variable from one galaxy to another.The identification of the infrared band at 10 µm is moresecure, being due to silicates and at 11 µm due to SiC.Dust is normally virtually transparent at this wavelengthbecause of the size of the grains, and in the diffuse in-terstellar medium the column densities are insufficient toproduce appreciable absorption in the IR band; it is seenin the atmospheres of highly evolved red supergiants. Inthese stars, because of the low emission from the envelopeas a whole and the large spatial extent of the outer stellarlayers, the feature is often seen in emission. Unless the starhappens to be sufficiently cold that the outer atmosphereis emitting significantly at these wavelengths, the featurewill always be seen in emission; a few very dense shellsshow absorption at the same wavelength.

The presence of silicates in both the interstellar medium(ISM) and stellar envelopes is certain, but the precise phys-ical state of the silicate is not well known. As is typical ofsolids, most of the detailed information about the internalstructure of the radiating species is lost due to the com-plexity of the lattice structure and the effects of nearest-neighbor perturbations to the energy states. These resultin broad diffuse absorption or emission bands.

Other IR features in the 3- to 10-µm region have beenidentified with both water ice (near 3.2 µm) and withpolycyclic aromatic hydrocarbons (PAHs) (several bands,especially near 3.3, 6.2, 7.7, 8.6, and 11.3 µm). Theyare identified with C–H and C–C bending and stretch-ing modes of complex organic molecules, although spe-cific identifications are insecure. The water is presumedto condense onto the grains in dense environments, likemolecular clouds. The PAHs are more like small grainsthan molecules, but are likely associated with the forma-tion and destruction of dust, forming the small particleend of the size spectrum. Because they are nearly molec-ular, they are not in equilibrium with the radiation field—that is, they do not radiate like blackbodies. Instead, theydeexcite from UV radiative absorption from the diffuseinterstellar radiation field (DIRF) via vibronic transitionsin the near-IR. This means that their emission requiressome UV excitation, which is supported by their presencein photodissociation regions at the boundaries of molec-ular clouds and planetary nebulae. The observed IR dif-fuse bands, which have optical analogs seen in absorptionagainst background sources, are likely due to the C–Hbond stretch, the analog of the Si–O vibration responsiblefor the 10-µm feature.



670 Astrochemistry

Dust radiates in the infrared. By Kirchhoff’s law, solidmaterial in thermal equilibrium radiates like a blackbody.Most of the incident energy falling on the grain is scat-tered, hence the blueness of reflection nebulae and thereddening of starlight. The absorbed photons are reradi-ated at a rate approximated by jν = κν Bν(T ), where κν

is the monochromatic absorption coefficient and Bν(T )is the Planck function at temperature T . The equilibriumtemperature of the grain depends, therefore, on its size andcomposition. Carbon grains absorb effectively in the UVdue to the diffuse 2175-A band, but radiate inefficientlyin the IR, so they are hotter than silicates, for which thereverse holds. The PAHs are distinguished by two effects.They show a much higher color temperature than the largergrains and, in addition to their lines, they cannot be in ther-mal equilibrium since their specific heats are temperaturedependent (see below).

Grains provide a solid surface on which chemical re-actions take place. In fact, they are the primary site forH2 synthesis. In addition, metallic ions deplete onto thegrains. This is evident from the lower-than-stellar abun-dances observed for the heavy metals, such as iron andcalcium, in the diffuse interstellar medium. It appears thatmost of the heavy metals in the diffuse and molecularcloud phases of the ISM may be tied up in the grains,which nonetheless constitute only about 10−6, by num-ber, of the ISM. CO and H2O may also stick to the grainsurfaces, and models and laboratory simulations show ahost of complex organic molecules can be synthesized inthe resultant mantle. It remains to be determined whetherthese simulations are relevant for interstellar conditions;they do seem to mimic many of the reaction products ob-served in situ in comet Halley.

An important problem in dust chemistry is the precisedetermination of both the formation mechanism and sizespectrum of the grains. At the smallest-particle end, thegrains behave like large molecules. The PAHs are sta-ble against UV radiation and also can be cleaved from thelarger graphite grains. The signature of small grains is thatthey cannot come into equilibrium with the UV radiationfield, and do not radiate like blackbodies. Instead, theirspecific heats depend explicitly on the number of avail-able modes, N , proportional to the number of constituentmolecules. They radiate with an excitation temperaturedepending on the incident photon energy as T = hν/NC .Hence, they have color temperatures which are of order1000 K in the presence of the DIRF, in spite of the fact thatthey are never in equilibrium and so have no true kinetictemperature. The resulting emission bands are vibrationaltransitions which redistribute the incident UV radiation onshort time scales.

IV. MOLECULAR ENVIRONMENTS

A. Circumstellar Envelopes

Molecules are frequently observed in the outer envelopesof red supergiants with surface temperatures less thanabout 5000 K. These stars have strong stellar winds, oforder 10−7 to 10−6 M� yr−1, with velocities typically lessthan 50 km s−1. A few hotter stars, such as 89 Herculis andHD 161796, have also been found to show CO emission;these and related stars are proto-planetary nebula objectsin the process of becoming white dwarf stars. For somevery highly evolved dusty stars, strong far-IR emission, in-dicative of dust, is accompanied by maser emission. Theseare the so-called OH/IR stars, which are most frequentlyMira variables. Some evolved stars also show SiO masers.A few stars, such as the extreme supergiant IRC + 10216,are veritable chemical factories, displaying almost all ofthe molecular species observed in comets and in denseinterstellar molecular clouds.

B. The Environment of the Interstellar Medium

The interstellar medium is a very inhomogeneous, disequi-librated place. The diffuse medium has densities of 0.01 to1 cm−3 in the ionized phase and about 1 to 103 cm−3 for thecooler neutral phase. The medium is heated by supernovastellar wind shocks, and has a sufficiently long coolingtime that it never becomes any colder than about 106 K.This is because the atoms are very inefficient coolants. Indenser regions, the temperature is reduced to about 106

K, and cooling due to neutral hydrogen recombinationbecomes efficient. For lower temperature, the cooling in-creases dramatically, first due to hydrogen line emission,which reduces the temperature to 104 K, and then fromatomic fine-structure transitions, which reduce the tem-perature to several hundreds of degrees. To lower this tem-perature further takes two additions to the medium—dustgrains and molecules.

In diffuse regions, the dust will always be colder thanthe gas, primarily because of the larger number of modesavailable for the redistribution of the energy. In fact, thetemperature, or equivalently the excitation, of the dust issensitive more to the spectrum of the radiation incident onit than to its dilution. The cooling of the dust is strictlyradiative, efficiently absorbing in the UV and radiatingin the IR. The harder the UV radiation which is incidenton the grain, the warmer the grain will be, regardless ofthe intensity of the radiation. The grains are the criticalshield for the cloud material from background radiativeheating. The presence of dust also effectively cools the gas



Astrochemistry 671

because of surface atom interactions which promote theformation of molecules, especially H2. Molecular coolingis due to collisional excitation of abundant species, whichthen reradiate their energy in the far-IR and millimeterwavelengths, at which the grains are optically thin. Deepin the cores of molecular clouds, the situation is reversed.Here the grains are warmer than the gas, and actually heatthe gas through collisions of the particles with the grainsurface. As such, they serve as the fuel for the chemistry.Collisions of molecular hydrogen with, for instance, COexcite the latter, which radiates its energy from the cloud atthe expense of the gas kinetic energy. Thus, the IR whichpenetrates the cloud and heats the grains can be transferredto the excitation of the various chemical constituents of themedium effectively, serving to power the reactions whichbuild complex molecular species.

V. CHEMICAL PROCESSES

A. Surface Chemistry: Formationof Molecular Hydrogen

The basic problem in the study of the interstellar mediumis the formation of molecular hydrogen, H2. This is of pri-mary importance because, at the low temperatures charac-teristic of the cloud environments, this molecule is respon-sible for the excitation of CO. One might initially expectreactions of the form

2H → H2 + γ, (17)

where γ is an emitted photon. This process, the so-calledradiative association mechanism, is important for the for-mation process. The rate is, alas, many orders of mag-nitude short of that required to produce the molecule. Infact, it appears that the formation of H2 can only proceedvia one of two possible avenues: (1) if there is a sufficientabundance of free electrons,

H + e → H− (18)

H− + 2H → H−3 (19)

→ H∗2 + H−; (20)

or (2) via some form of surface interaction where radia-tive association is replaced by reaction on a solid surfaceof two neutral atoms in the presence of a UV radiationfield which is capable of exceeding the appropriate bind-ing energy of the molecule to the grain surface. The first ofthese is independent of the abundance of metals, while thelatter is critically dependent on the existence of interstel-lar grains on which the reactions can take place. Becauseit appears that the solid lattice is far more efficient, andbecause it exists in the interstellar environment that now

is observed in molecular clouds, we shall concentrate onthe second mechanism. The first type of mechanism hasbeen implicated in star formation processes in the earlyuniverse.

Assume that the grain consists of a simple lattice, likegraphite. Should an atom of neutral hydrogen strike thesurface, there is a sticking probability, S, such that the atomwill become bound to the surface rather than be reflectedback into the diffuse medium. The rate of impact on thesurface of hydrogen atoms is given by the mean collisiontime of a H atom with a grain having a geometric crosssection

∑. The velocity dispersion in the gas isvth ∼ T 1/2,

so that

dn

dt= nH ng Sπa2

gvth (21)

and the rate of hopping, or migration, among lattice sites istmig. Then, if KHH is the reaction rate, the rate of formationof H2 is approximately given by

nH2 ≈ KHHnHg S∑

σ tmigβ−1, (22)

where β is the rate of release of H2 from trapping sitesback into the medium. An empirical rate for H2 formationis

dn(H2)

dt≈ 3 × 10−17cm3 s−1 n2

H. (23)

Here nH is the ambient gas density, with the grains scal-ing as a fixed fraction of nH. There is, however, reasonto believe that at the lowest neutral hydrogen densities,the formation process depends on the random rate of ar-rival of molecules on the surface and there is an expo-nential threshold for the molecular formation (see Caselliet al., 1998). Grains are a prerequisite for the formation ofmolecular hydrogen in the present galaxy, but gas-phasereactions in the dense regions that are typical of molecularclouds will otherwise produce all of the species which areobserved. Therefore, in what follows, we shall concentrateon the work which done in the 1990s on the problem ofgas-phase chemistry.

B. Gas-Phase Chemistry

The first observations of diatomic species in the diffuse in-terstellar medium several decades ago posed serious chal-lenges for theorists because of the extremely low densitieswhich are found there. Radiative association seemed un-able to produce any of the observed species, most impor-tantly CH, and this meant that exotic mechanisms were ini-tially held responsible for the presence of such molecules.Work on the abundance of H2, following the observation ofthe molecule in the diffuse medium in the ultraviolet by theCopernicus satellite in the mid-1970s, and the discovery of



672 Astrochemistry

elemental depletion along many lines of sight in the inter-stellar medium, led to the suggestion that grains were alsothe fundamental site for the chemistry required to produceeven the simplest diatoms. The Fuse mission, launched in1999, covers the same spectral range (900–1200 A) asdid Copernicus, but with significantly higher sensitivityand resolution, and is now being used to study more thor-oughly the molecular hydrogen component of the galaxy.In addition, the ISO mission detected large abundances ofH2 in the far-IR even from regions that have very low COabundances.

The discovery of large, cold molecular cloud complexesdramatically altered this view, providing the necessaryconditions for low-temperature, high-density gas-phasereactions to occur. The development of many computa-tional schema for handling enormous reaction networks,often involving thousands of reactions and hundreds of re-acting species, also spurred theoretical work on this sub-ject. This section is meant only to serve as a guide to thesecalculations. The basic physical input is really quite sim-ple; it is the computational complexity that makes for thedifferences found among various workers in the field.

The chemistry of gas-phase reactions, either in the in-terstellar medium or in stellar atmospheres, is mediatedby the abundance of ions. These can be formed in severalways: by cosmic-ray ionization, or by the direct photo-ionization of the atoms involved in the reactions with sub-sequent charge transfer to the molecules. Ionic reactionsare generally exothermic and so occur efficiently at lowtemperature. In the presence of an ion, a neutral moleculeor atom develops an induced dipole which increases itscapture cross section. Thus the reactions occur quickly andlead to stable states, in addition to allowing the moleculeto form in a radiatively unstable excited state which, upondecaying, radiates the energy of formation away from thesite of the reaction.

1. Reaction Rates

In general, reactions depend on two factors, the activationenergy � and the temperature. Cross sections can be ob-served directly in the laboratory at some controlled tem-perature, usually near room temperature (about 300 K),and then scaled to the temperatures found in clouds. Theycan also be deduced from first principles. Generally, thesereactions have the form K =〈σv〉 where the average ofthe cross section, σ , is taken over the velocity distribu-tion of the interacting particles where the relative velocityis v. For this reason, assuming the reacting particles arethermalized, the rates depend on temperature. For ionicreactions, where the potential is the coulomb interaction,the so-called Langevin approximation applies, and it canbe shown that the rates are approximately constant. Thus

measurements at room temperature suffice for the deter-mination of the rate coefficients, K = k, where usually k,the reaction constant, is of order 10−8 to 10−13 cm3 s−1.Most ionic reactions have little or no potential barriers, be-ing generally exothermic. Hence there is usually a simpleconstant volumetric rate which is assumed to be a con-stant. Neutral reactions are most likely to involve substan-tial activation energies which greatly inhibit their rates offormation. If a neutral channel is important in a networkof reactions, it will likely be a bottleneck for the forma-tion of the product species. These have strong tempera-ture dependences because of their activation energies andusually are several orders of magnitude slower than theion-neutral channels. Electronic recombination reactionstypically scale as T −1/2.

Before proceeding with a discussion of specific results,one point should be emphasized. In many of the reactionnetworks, among all of the rates which must be tabulatedand all of the reactions which must be tracked, many ofthe rates have to be approximated by guesses or simplefits to laboratory data. Few measurements (except on theSpace Shuttle) at interstellar conditions are available, andthis is a very significant challenge for future laboratoryastrophysics. In many of the networks, perhaps as few as10% of the rates are known to within a factor of 50%,and perhaps as many as half are bald guesses and may beuncertain to a factor of 10. This is a field still in its infancy,where only the dominant channels are well understood, butmany of the details are still extremely important becauseof the physical conditions that can be probed by tracespecies.

2. Ionization

Ionization in the densest parts of molecular clouds de-pends on the penetration of cosmic rays and UV radiation,as well as the presence of shocks generated by such pro-cesses as cloud–cloud collisions and internal star forma-tion. In order to probe the electron density in the clouds, itis important to be able to account for the presence of com-plex polyatomic molecules, whose formation requires iongas-phase reactions.

The rate for cosmic-ray (CR) ionization, ζCR, is about(3 ± 1) × 10−17 s−1. This is an integral over the collisionalionization cross section for low (MeV)-energy CR pro-tons, but it is approximately a constant for most of thespecies of interest. An obstacle in our understanding ofthe detailed structure of molecular clouds is our igno-rance of the precise specification of this rate. The low-energy end of the cosmic-ray spectrum is difficult to de-termine empirically from terrestrial observation, becausethese particles propagate diffusively through the interplan-etary medium, scattering off of turbulence in the solar



Astrochemistry 673

wind; their spectrum cannot be observed directly , evenwith in situ measurements from the Voyager and Ulyssesspacecraft, and must be inferred from models for their mo-tion through the heliosphere. The more easily observedcosmic ray protons and electrons, in the GeV and higherrange, have little or no effect on the ionization of the in-terstellar medium because of the small interaction crosssections for atoms at such high energies.

In molecular clouds, atomic species with ionization en-ergies greater than 13.6 eV must be predominantly neutralbecause of the shielding effects of neutral hydrogen. It ismainly the heavier elements, such as C, N, and O, whichare observed in the peripheral portions of the clouds to bein the partially ionized state. For circumstellar envelopes,cosmic rays lose out to photo processes and the chemistryis mediated by the input of stellar photospheric radiation(in the hotter stars and in novae and supernovae) and fromthe diffuse interstellar radiation field.

The basic equations for two body interactions can bewritten in the form

d Ni

dt=

∑j,k �=i

Ki jk N j Nk −∑

j

K ′i j Ni N j , (24)

where Ki jk is the formation rate for the i th molecularspecies, while K ′

i j is the destruction rate for the molecule.The inclusion of UV photo processes is accomplished bythe photodissociation rate:

Rpd =∫ ∞

ν0

κν Fνe−τνdν

hν, (25)

where Fν is the incident photon flux, τν is the opacity ofthe ambient medium (presumed to be from dust), κν isthe continuous absorption coefficient for the dissociativecontinuum, and the dissociation energy is hν0.

An aspect in which circumstellar environments dif-fer from interstellar is the net mass advection throughthe medium. Abundances become time dependent—andhence space dependent—in the envelope, due both to theimplicit time dependence of the reactions and to the trans-port of matter through different radii via stellar wind flow.The atomic abundances are fixed at stellar photosphere,rather than having to be assumed for some mixture ofphysical parameters of temperature and pressure as theymust for molecular clouds. It is then essentially an initial-value problem to compute the abundances which will bea function of radius in the envelope. For a steady-statewind, the abundances become strictly a function of ra-dius. Also, unlike a molecular cloud, the density profileof the envelope is specified from the assumption of steadymass loss at the terminal velocity for the wind, so thatρ(r ) = M/(4πr2v∞), where M is the mass loss rate andv∞ is the terminal velocity of the wind.

An interesting aspect of stellar envelopes is that theymay have two different sources of UV radiation, inter-nal and external. Work on the envelope of two extreme,low-temperature, evolved supergiants, IRC + 10216 andα Ori, showed that the outer limit of the molecular en-velope is determined by the DIRF, which destroys theoutermost molecular species by photodissociation, whilethe inner boundary is set by both the temperature and UVemission from the stellar chromospheres. In this respect,since the dynamics can be probed in exquisite detail forseveral of the nearer supergiants through molecular ob-servations, and since the input abundances are known andatomic in nature, it is possible to use these stars as verywell-conditioned laboratories for the study of the sameprocesses which must be involved in at least some aspectsof molecular cloud chemistry. For the densest envelopes,which are completely optically thick and hence very sim-ilar to molecular clouds, cosmic rays are significant ingoverning the ion fractions but can be neglected in thinenvelopes (low mass loss rates).

3. Cooling Processes

Chemistry also feeds back into the thermal balance ofthe clouds. Molecules radiate in portions of the spec-trum where the medium is usually optically thin. Sincethis radiation can escape from the cloud, it is the primarymeans whereby the clouds cool. Star formation requiresthat otherwise hydrostatic clouds become gravitationallyunstable, a process which can be affected by the rate ofenergy loss as well as by external perturbations. Thus time-dependent processes, those which cause the stability of theclouds to alter with time, are extremely important, sincethe time scale for molecular formation is not too short (oforder 106 years) compared with the estimated lifetimes ofthe clouds (≤108 years). For example, the cooling rate forCO depends on the abundance of both dust and of H2 andCO by

�CO = 1.1 × 10−30n(�v/vth)T 1/2

1 + 1.4 × 10−4nT 1/2(1 + N/Nc)erg cm−3s−1,

(26)

where Nc = 2 × 1018T cm−2 and N is the column density,related to the extinction. Molecular species are thereforequite efficient in radiatively removing energy from theclouds and, literally, refrigerating the medium.

4. Shock Chemistry

Hydrodynamic and magnetohydrodynamic (MHD)shocks are important in the time-dependent chemistry ofthe diffuse interstellar medium. The time scales are very



674 Astrochemistry

short for shock passage through a region, typically lessthan 105 years per parsec, but they can cause considerableabundance variations and produce long-lived products.CH+ is primarily produced this way, and CH and CN alsoseem to have input from shocks.

The role of shocks in the chemistry of clouds is bestseen in the effect it can have on molecular hydrogen. Whilemany reaction products remain unchanged in abundance,CH4, H2O, and HCO can be greatly enhanced due to theincreased production of these molecules in the hotter, anddenser, shock environments. The chemistry is also depen-dent on the role of magnetic fields. Magnetic shocks canhave sizable compression without significant increases inthe temperature, due to the pressure provided by the mag-netic field. As a result, the relative abundance of shock-produced molecules serves as a probe of the nature of theshock producing the enhancement in the reaction rates.

Chemistry in the post-MHD shock environment is dom-inated by the separation between neutral and ionic species,the former being less affected than the latter by the mag-netic field. In consequence, the reaction sites are calculatedto show abundance stratification depending on the reac-tion channels. Since the fronts may be broad enough to bespatially resolved, it is possible to study the diffuse-phaseISM shock chemistry observationally in some detail.

5. Specific Molecular Reactions

a. Hydrogen. The most important ion for all molec-ular reactions is H+

3 . It is formed by several channels, theprimary one being capture of low-energy cosmic-ray pro-tons by molecular hydrogen, which is itself formed ongrains. It is stable at the densities and temperatures whichare typical of molecular clouds. The capture of a carbonatom to form CH+

3 is a critical step in the chemistry of theinterstellar medium, especially in the generation of theions of the cyanopolyyne series, such as HC11N. H+

3 hasbeen observed directly in several dense clouds along withits deuterated phase, H2D+. One can therefore assert withconfidence the role of this ion in molecular chemistry. Sub-sequent to carbon capture, interactions with H2 can formall of the hydrocarbons observed in molecular clouds. Anexample of this chemistry is given by the network

H+3 + C → CH+ + H2, (27)

CH+ + H2 → CH+2 + H, (28)

CH+2 + H2 → CH+

3 + H, (29)

CH+3 + H2 → CH+

5 + γ, (30)

CH+5 + e → CH4 + H, (31)

→ CH3 + H2, (32)

→ CH2 + H2 + H, (33)

→ CH + 2H2, (34)

which also illustrates the reason for the complexity ofmany of the reaction calculations: there are many productstates for electron-capture reactions, due to the role ofdissociative recombination.

b. Carbon. Carbon chemistry is both interesting andimportant for the determination of the detailed structureof molecular clouds. Early observations of formaldehydewere an indication that some form of gas-phase chemistrymust occur in clouds, and the reaction mechanism for theproduction of H2CO is

CH3 + O → H2CO + H, (35)

H3CO+ + e → H2CO + H. (36)

For CO, there are several reaction channels. All are initi-ated by the formation of the HCO+ ion:

H+3 + CO → HCO+ + H2, (37)

C+ + H2O → HCO+ + H, (38)

CH+3 + O → HCO+ + H2, (39)

C+ + H2CO → HCO+ + CH, (40)

HCO+ + e → CO + H. (41)

The CO is subsequently excited by nonreacting collisionswith H2 which produces the observed line emission. An-other possible pathway involves

H+3 + O → OH+ + H2, (42)

OH+ + H2 → H2O+ + H, (43)

H2O+ + H2 → H3O+ + H, (44)

H3O+ + e → OH + H2, (45)

→ H2O, (46)

OH + C+ → CO+ + OH, (47)

H2O + C+ → HCO+ + H, (48)

HCO+ + e → CO + H, (49)

CO + H+3 → HCO+ + H2. (50)

This illustrates the mediating role of oxygen in the for-mation of CO, and also the fact that the pathway can beblocked by photodissociation of H2O to form OH in allbut the densest regions of the clouds.

A most important aspect of CO is that it is self-shielding.Should it be possible to build up a significant column den-sity of the molecule, it will form a photodissociative blockto incoming UV. In the interstellar medium, this means that



Astrochemistry 675

the formation of C+ is important in the outer layers of theclouds, which are irradiated by the diffuse interstellar UVphotons, but that within a short distance (a layer that isperhaps no more than 1 pc in thickness), all of the photonshave been absorbed. The presence of ions is therefore agood indication that low-energy cosmic rays can penetratethe deepest regions of the cloud without being lost due toeither grain interactions or energy loss by scattering off ofinternal MHD turbulent eddies in the cloud cores. Furtherinput of electrons from grain ionization may contribute inthe intermediate layers of the cloud as well, but these areunlikely to be important in the innermost regions.

Temperature and density profiles are derived from COobservations. This is true for both circumstellar envelopesand molecular clouds. The optical depth is measured usingthe 13CO/12CO (1 → 0) transition, while the excitationtemperature is given by the ratio of the 12CO (2 → 1) to(1 → 0) intensities. The excitation is presumed to be dueto H2 collisions, so the populations should reflect the localthermal properties.

c. Nitrogen. Nitrogen is another important speciesfor reaction kinetics. Here the primary initiating reactionis

H+3 + N2 → N2H+ + H2. (51)

The most important reaction network is initiated by theionization of nitrogen by charge exchange with He+ or bycosmic-ray ionization of N:

N+ + H2 → NH+ + H, (52)

NH+ + H2 → NH+2 + H, (53)

NH+2 + H2 → NH+

3 + H, (54)

NH+3 + H2 → NH+

4 + H, (55)

NH+3 + e → NH + H2, (56)

→ NH2 + H, (57)

→ NH3, (58)

NH+4 + e → NH3 + H, (59)

→ NH2 + H2. (60)

The formation of NH+ by H2 capture is only probable attemperatures exceeding about 20 K; its slight endoergicnature at lower temperature inhibits this reaction channel.The presence of metals can also be of importance for theproduction of ammonia, because charge-exchange reac-tions can occur which will neutralize the ammonium ion.

Many complex polycyanoacetylenes are observed inboth circumstellar envelopes and dense molecular clouds,the heaviest being HC11N, one of the cyanopolyynes.As mentioned in the section on carbon chemistry, these

molecules are likely built through the formation of HCN,HNC, and CN, all though interactions initiated by theformation of CH+

3 . Heavier molecules are likely formedthrough the incorporation of cyanogen and HCN into themolecule, but because of the large number of species in-volved in these calculations, the mechanisms are still notwell understood. Many of the rates have yet to be calcu-lated in detail.

The discovery of molecules containing heavier ele-ments such as PN and iron compounds opened the fieldof heavy-ion chemistry. It is well known that phosphorusis important in the evolution of biota on the earth, andits discovery in the interstellar medium is a major clue tothe development of chemical processes during the earlystages of life’s development on planets.

d. Sulfur. Sulfur chemistry is also of great interestbecause of the abundance of CS. An important initiatingstep is

SH+ + H2 → SH+3 + γ, (61)

SH+3 + e → H2S + H, (62)

→ SH + H2. (63)

For carbon compounds, CS for example, there are severalvery important reactions:

CH + S → CS + H, (64)

CS + O → CO + S, (65)

H+3 + CS → HCS+ + H2. (66)

The helium ion is also important because charge transfercan lead to disintegration of the CS molecule:

He+ + CS → C+ + S + He. (67)

Observations of CS are important because they probesdense portions of the molecular clouds, where collisionalexcitation produces strong emission lines. However, sincethese dense interior parts of the cloud cores are also sites ofvery complex chemistry, the detection of CS and of relatedmolecular species may be very dependent, in ways still notwell understood, on the chemistry of these sites. SO2, HS,and SO have also been detected in molecular clouds, andit is also possible to study isotopic fractionation amongvery heavy molecules such as 13CS and C33S. As withmost isotopic species, these are optically thin and permitstudy of the ionization structure of the cloud.

e. Water as a special case. The H2O molecule iscentral to much organic chemistry, even in the interstel-lar medium. It has been observed in maser sources, indeuterated form in molecular clouds, and in its ion, butthe neutral molecule has not been observed in the cores



676 Astrochemistry

of molecular complexes. This aspect of the current obser-vational picture is puzzling, because according to modelsthe abundance should be of order H2O/H2 ≥ 10−6. This isthe about 10% of the CO fraction, indicating that muchof the oxygen in the clouds may be tied up in water. Thedifficulty is that so far, this species has not been observeddirectly. On the basis of the chemical fractionation (seenext section) and the abundance of the deuterated form ofwater, this abundance may be a lower limit.

The importance of H2O to cloud chemistry is seen fromthe reaction sequence:

CH+3 + H2O → CH3OH+

2 , (68)

CH3OH+2 + e → CH3OH + H, (69)

which competes with the reaction CH+3 + HCN →

CH3CNH+ in the destruction of the methyl ion. Wateris also important in the formation of another species ofinterest,

C+ + H2O → HCO+ + H, (70)

→ HOC+ + H, (71)

HOC+ + CO → HCO+ + CO, (72)

the last being a rearrangement collision due to the en-vironmental CO. In both cases, these rates compete withthe formation due to H+

3 and will enhance the formation ofHCO+, an easily observed species. The reason for thinkingthis important is that the diagnosis of physical conditionsin the densest parts of molecular clouds is affected throughthe use of complex chemical species. We do not have di-rect access to the cores via CO because of the high opticaldepths and self-absorption by other abundant molecules.However, we know from maser observations that the wateris being produced in at least some environments.

What this means for the structures of clouds is notpresently clear. It is possible that the clouds are fluffy—that UV radiation penetrates deeper into the clouds thanpreviously thought. There is some indication that the ion-ization fractions for the clouds are higher than we wouldhave expected.

f. Isotopic fractionation. The fingerprint of stellarnucleosynthesis, and of the chemical history of the galaxy,is most clearly seen in the abundances of the isotopes. Forexample, deuterium, D, is easily destroyed in stellar in-teriors via low temperature (≈106 K) reactions, but wassynthesized in the Big Bang via nonequilibrium nucle-osynthesis in the expanding universe during the first fewminutes of its existence. Thus its abundance was fixed pri-mordially. The rates of change of temperature and densityduring this initial epoch were fixed by the rate of expan-sion, which depends on the amount of mass in the universe;

the slower the expansion rate in this early period, the closerto equilibrium will be the proton process products andthe lower the D abundance. Because of the overwhelmingabundance of H, it is very difficult to observe the D abun-dance directly, especially in stellar atmospheres but alsoin the wings of the Lyα line from the interstellar medium.With an anticipated abundance ratio D/H ≈ 10−5, currentobservations of interstellar absorption lines cannot placegood limits on this cosmologically important number.

It is possible, however, to determine the D/H ratiothrough a different avenue, the isotopic shift caused bythe mass ratio of D/H in the rotational and vibrationalspectrum of the H2 molecule compared with HD. Thismethod is not free from difficulties, though, because ofthe many possible routes available for depletion of HDthrough molecular formation. The reaction energies forthe isotopic species are slightly different, by several tensof degrees (hundredths of an electron volt), which at in-terstellar temperatures produces substantial differences inreaction rates. A detailed calculation of the isotope’s mo-bility and reaction among the different species is required.

Both H2 and HD are formed on grain surfaces. Thesubsequent reactions that involve these molecules can en-hance the D abundance in the more complex species whichare formed, and also open up new channels. For example,

H+3 + HD → H2D+ + H2, (73)

which then competes with H+3 in the formation of hydro-

carbons. This reaction is especially important because ofthe influence of cosmic-ray ionization and dissociative re-combination on the fractionation process. The ratio of H+

3to H2D+ is given by

H2 + H(CR) → H+3 , (74)

H+3 + e → H2 + H, (75)

H+3 + HD → H2D+, (76)

H2D+ + H2 → H+3 + H, (77)

H2D+ + e → HD + H, (78)

→ H2 + D, (79)

where H(CR) represents a cosmic-ray proton.One well observed species, HCO+, is observed to yield

a higher than expected D/H ratio. This appears to be dueto the protonation reaction chain

H+3 + CO → HCO+ + H, (80)

H2D+ + CO → HCO+ + D, (81)

→ DCO+ + H, (82)

where both DCO+ and HCO+ are destroyed via dissocia-tive recombination to yield CO.



Astrochemistry 677

Other means have been determined for solving for theelectron density, for instance, the ratio of H2O to HDOand of H2D+ to H+

3 . These are all uncertain because ofthe incompleteness of the abundance catalogs for variousclouds; that is, many of the intermediate reactants are notwell determined, and this hampers understanding of theconditions in the clouds.

Similar behavior is observed for the CNO isotopes. Thatis, their relative abundances in molecular combination de-part from that expected on the basis of either the terres-trial abundance ratios or from nucleosynthesis. The effectsare caused by fractionation reactions, usually through ion-transfer reactions with CO. In general, the enhancement ofisotopic abundances of the CNO group seems to be due tocharge-transfer reactions with isotopic ions. For example,

13C+ + 12CO → 13CO + 12C+ (83)

will produce a net enhancement of 13CO, since it will thenfree the carbon atom for other channels. At low density,where the molecules are exposed to UV as well as cosmic-ray ionization, this is an important mechanism. The abun-dances of the CNO isotopes will therefore not reflect theinitial conditions in the cloud, but will rather reflect theprocessing which goes on during the time it takes forthe molecules to come into equilibrium, about 106 years.

Because of the importance of the CNO isotopes for thestudy of stellar evolution and of the chemical history ofthe galaxy, this is one of the most important areas forastrochemistry. In addition, because of the dependence ofthese reactions on the ion fraction, which in turn dependson the electron fraction in the dense parts of the clouds, theisotopes become useful tools for studying the ionization ofthe environment, probing the electron density in portionsof the cloud otherwise hidden from view.

g. Polycyclic aromatic hydrocarbons. We have re-peatedly stressed that the smallest grains behave like verylarge molecules, never coming into strict equilibrium withthe radiation field and radiating in diffuse bands in thenear-IR. There are several likely candidates as identifica-tions, all so-called PAHs. These are either linear or ringmolecules, which are very stable in the presence of UV ra-diation. For instance, coronene (C20H20) is especially wellstudied in the laboratory, although it is not specificallyimplicated in any of the emission lines. These moleculesproduce broad optical absorption bands, like the diffuseinterstellar features which have been known since Mer-rill’s discovery of the λ4430 A band in the 1930s, but areimportant mainly for their vibrational transitions in the 3-to 20-µm region, which in aggregate match virtually ev-ery unidentified feature. They can be built in the processof forming dust grains, in the atmospheres of carbon-richgiants and supergiants, and also from the process of grain

photodestruction. At interstellar conditions, their partialpressures allow them to remain stable against evaporation.They should, however, also be strong absorbers in the UV;this contradicts many available observations, which placestrong limits (less than a few percent) on the absorption-band strengths for these features. On the other hand, theIR cirrus, the ubiquitous diffuse emission detected by theIRAS and ISO missions throughout the galactic plane, can-not be explained any other way. The PAHs could incorpo-rate as much as 10% of the available carbon in the ISM,making them a major component of the dust.

Recent infrared observations with the ISO satellite havedetected fine structure in several of the bands, which indi-cates variable PAH composition throughout the medium.However, it is too early to begin identifying any of the par-ticular species. These species have been detected in the IRemission from the comma of comet Halley as well, and itappears that in at least some environments, the chemistryrequired to produce the PAHs is sufficiently efficient thatlarge abundances can be achieved. It has been suggestedthat fullerenes (such as C60) are responsible for some ofthe small grain population, but the spectral signatures—particularly in the visible and ultraviolet—have yet to beseen.

A remaining problem with the PAH explanation forthe diffuse bands is the lack of an UV signature of thesespecies. Complex organic molecules produce deep absorp-tion bands in the vacuum UV, between 2000 and 3000 A.To date, these have not been observed. An important re-sult is the discovery of deep λ4430 A absorption againstSN 1987a in the Large Magellanic Cloud. This argues thatat least this galaxy may have the same small grain com-ponent as our galaxy, despite its lower than solar metalabundances.

VI. COSMOLOGICAL CHEMISTRY

On area that will certainly develop in the early years of thetwenty-first century is the study of chemistry in the earlyuniverse. The need for this is obvious. Galaxies formedat a very early epoch within the much larger cluster andsupercluster scale masses that grew from primordial seeddensity fluctuations. This requires energy dissipation topromote the collapse toward progressively lower masses,precisely as we expect in star formation. However, sincestars did not form before this time, there were no heavyelements (in particular CNO) to form the major coolantmolecules such as CO. It is possible, however, to form H2

and H+3 in the expanding gas, provided sufficient ioniza-

tion remains after the recombination that forms the cosmicbackground radiation. The efficiency of formation is verylow and so is the abundance of the molecular species, but



678 Astrochemistry

TABLE I Some Molecules Detected in Cosmic Environ-mentsa

Molecule Wavelengths Transitions Environment

H2 UV, IR E, VR CSE, PS, ISM, MC

CO UV, IR, mm R, VR, R CSE, PS, ISM, MC

CH Opt, IR, cm E, R, �-doubling ISM, MC

OH UV, IR, cm E, R, �-doubling CSE, PS, MC; masers

SiO IR, mm VR, R; maser CSE, PS, MC

CS mm R CSE, MC

HCN IR, mm VR, R CSE, PS, MC

HNC mm R CSE, MC

H2O mm, cm R CSE, MC

HCO+ mm R CSE, MC

H2D+ sub-mm R MC

NH3 IR, mm, cm R, maser CSE, MC, PS

H2O IR, mm R, maser, ice CSE, PS, MC

H2CO mm, cm R MC

HC11N cm R CSE, MC

a Key: Transitions: E, electronic; R, rotational; VR, vibrotational.Environments: CSE, circumstellar envelopes; PS, protostars; ISM inter-stellar medium; MC, molecular clouds.

any cooling will lead to some structure formation. Othermolecules, particularly LiH, are expected to form from thechemical mix emerging from pregalactic nucleosynthesis.

VII. CONCLUSION

The field of observational astrochemistry is at an importantstage in its development. Several large-millimeter tele-scopes are currently operating. With increased spatial res-olution, the sites of complex molecular processing can beisolated from the overall structure of molecular clouds.More important is the fact that several interferometers areeither operating (such as BIMA in California and IRAMnear Grenoble), or under construction (ALMA in Chile).Many large-aperture millimeter and submillimeter tele-scopes are now available (such as the JCMT on MaunaKea). These provide detailed comparative maps of cloudsin the lines of specific molecules. Extragalactic astrochem-istry is coming of age, and many galaxies have now beenstudied in diatomic and even more complex species. Thecrucial step in determining abundances, and whether thesereflect local chemistry or excitation conditions, can onlybe accomplished through the comparison between specieswhich trace each. The coming years promise to realize thisgoal.

SEE ALSO THE FOLLOWING ARTICLES

COSMIC RADIATION • GALACTIC STRUCTURE AND EVO-LUTION • INFRARED ASTRONOMY • INTERSTELLAR

MATTER • PLANETARY ATMOSPHERES • QUANTUM

CHEMISTRY • GALACTIC STRUCTURE AND EVOLUTION

• SURFACE CHEMISTRY • ULTRAVIOLET SPACE ASTRO-NOMY

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Encyclopedia of Physical Science and Technology En002c-88 May 17, 2001 20:39

Celestial MechanicsSteven N. ShoreIndiana University, South Bend

I. Historical IntroductionII. Conic Sections and Orbital Elements

III. The Dynamical Problem in Gravitational PhysicsIV. Applications: A Few Interesting ExamplesV. Closing Remarks

GLOSSARY

Astronomical unit (AU) Distance of the earth from thesun.

Ecliptic Apparent orbit of the sun, the plane of the earth’sorbit.

Epicyclic frequency Rate at which an orbiting bodysees radial and angular oscillations in nearly comov-ing orbits due to variations in eccentricities of theorbits.

Mean anomaly Mean rate of motion of a body in an el-lipse, relative to the center of the osculating circle.

Osculating circular orbit Literally, the “kissing” orbit;the circular reference orbit that precisely matches aninscribed ellipse along the major axis

Perigee, perihelion Distance of closest approach to thecentral body, the earth or sun in this instance, respec-tively, in a conic section. The opposite of apogee oraphelion.

CELESTIAL MECHANICS is the study of dynamics ingravitational fields of cosmic bodies. In recent years, thishas come to include gravitational statistical mechanics,galactic dynamics, nonlinear stability theory and chaos,

and the practical field of satellite dynamics and attitudecontrol.

I. HISTORICAL INTRODUCTION

The history of celestial mechanics is essentially the historyof classical physics. The problem of predicting the motionof the planet is the central problem of most of the past twothousand years of physical investigation.

The first attempts to construct mathematical or physicalcosmologies were those of the Platonists during the fourthcentury B.C. These included the model of Eudoxus, whointroduced the homocentric spheres, and Aristotle, whoincluded physical arguments in the Eudoxian system. Theprimary assumption of the immobility of the earth leads tovery complex motions, which must be reproduced usingcompound circular motions in a series of nested inclinedspheres. In effect, this early approach is like a Fourieranalysis of the planetary motions into a set of periods andinclinations of the spheres.

The first alteration in the basic schema was introduced inApollonius, who added the eccentricity, thereby allowingthe motion to be regular about a point displaced from thecenter of the earth. In addition, he introduced the epicycleinto the system. This is a small secondary path on which

527

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528 Celestial Mechanics

a planet is transported and which has a period that maynot be the same as the period on the deferent circle. Thedeferent is the path along which the planet moves with themean period; the epicycle causes periodic accelerationsand decelerations relative to this mean value. Apolloniusalso proved a theorem for the determination of the relativeradius of the epicycle compared with the deferent usingthe stationary points in the orbit, those points at which themotion of the planet appears to halt before it reverses itsprojected direction of motion.

The equant was added by Ptolemy (second century A.D.)as a modification of the eccentric, a point on the oppositeside of the center of the deferent circle that carries theplanet. This added point was also permitted to move, asrequired for the motion of the moon and Mercury. All ofthese constructions were justified under the rubric of “pre-serving the appearances,” a dictum attributed to Plato. Inaddition, the physical basis for the model derived from theAristotelian doctrine of geocentricity and contact forces.These Hellenistic astronomers were doing celestial me-chanics, according to their lights.

The discovery of precession of the equinoxes by Hip-parchos (second century B.C.) provoked little theoreticalactivity until the eleventh century. Al Bitruji introducedthe trepidation, a mechanism that permitted the multipleperiodicity that appeared to be required to explain the vari-ation in the rate of precession. The mechanism, repeatedin Copernicus, derives from the erroneous determinationof the period of precession in which the rate of precessionof the poles varied with time from about 1◦ per century to0.75◦ per century. The mechanism demanded somethinglike an equant in the polar motion. As retained by Coper-nicus, this introduced a substantial complication into thetheory of rotation of the earth and also the calculationof celestial motions and the correction of star catalogs.It was not until the seventeenth century that the error wasrecognized and quietly suppressed, but the trepidation rep-resents one of the few innovations in the basic dynamicaltheory of the heavens in the period between the Alexan-drian school of astronomy and the early Renaissance.

To Copernicus (1472–1543) is ascribed the first con-certed effort to break with the geocentricity of the Greekconstructions. While Aristarchus had proposed a heliocen-tric system in the second century B.C., the system was nevercarried through to include the computation of planetaryorbits. Copernicus introduced the machinery for the de-termination of planetary phenomena but also argued phys-ically for the added effects attendant on the overthrow ofthe geocentric picture. This especially included the physi-cal explanation for the precession and the alteration of theascending node of the lunar orbit.

Celestial mechanics as we now think of it really startedwith Kepler (1571–1630), although in a rather oblique

form. It was Kepler who first pointed to a physical drivinginfluence of the sun and argued that its position at the cen-ter of the system was more than coincidence and of morethan kinematical significance. He attributed the planetaryorbits to magnetic influence by the sun. Kepler’s basicpoint, however, that some kind of action at a distance isnecessary for planetary motion, and not contiguous geo-centric spheres, provided the critical insight for the laterdevelopment of celestial mechanics.

Kepler’s principal contribution is summarized in hislaws of planetary motion. Originally derived semiempir-ically, by solving for the detailed motion of the planets(especially Mars) from Tycho’s observations, these lawsembody the basic properties of two-body orbits. The firstlaw is that the planetary orbits describe conic sections ofvarious eccentricities and semimajor axes. Closed, thatis to say periodic, orbits are circles or ellipses. Aperi-odic orbits are parabolas or hyperbolas. The second lawstates that a planet will sweep out equal areas of arc inequal times. This is also a statement, as was later demon-strated by Newton and his successors, of the conservationof angular momentum. The third law, which is the maindynamical result, is also called the “Harmonic Law.” Itstates that the orbital period of a planet, P , is related to itsdistance from the central body (in the specific case of thesolar system as a whole, the sun), a, by P2 ∼ a3. In moregeneral form, speaking ahistorically, this can be stated asG(M1 + M2) = a3�2, where G is the gravitational con-stant, � = 2π/P is the orbital frequency, and M1 and M2

are the masses of the two bodies. Kepler’s specific formof the law holds when the period is measured in years andthe distance is scaled to the semimajor axis of the earth’sorbit, the astronomical unit (AU).

The dynamical foundations of celestial mechanics de-rive from Newton’s (1642–1716) discovery of the Univer-sal Gravitational Law. This law states that, by action-at-a-distance, every mass, M , exerts a force proportional to theinverse square of its distance, r , from every other mass,m, in the proportion Fgrav = −GMm/r2. For a distendedmass, this amounts to the summation over the individ-ual mass elements to determine the gravitational acceler-ation, ggrav = −G

∫[dm(r )/r2] , and Newton produced a

proof that only the interior mass attracts a body in a ho-mogeneous spheroid. He also added the formalism thatthe gravitational force derives from a potential, � (a termintroduced nearly 150 years later by George Green, al-though employed in all earlier extensions of Newtonianformalism) F = −∇�. It was through the application ofthis general principle, and the assertion that G is a univer-sal constant independent of the composition of the body,that permitted the generalization of dynamics and enabledthe computation of planetary orbits. Newtonian methodol-ogy was quickly extended even to cosmological problems



Celestial Mechanics 529

of large-scale distribution of mass in space. The principleof inertia, originally discussed by Galileo and Descartes,was elevated to a basic axiom in the laws of motion and,combined with the gravitational law, served as the basisof modern dynamical theory. Newtonian gravitation thusprovided a basis for celestial mechanics by yielding themeans for deriving Kepler’s third law from first principlesand for identifying the proportionality constant with themass of the bodies.

The two centuries following Newton’s statement of hisdynamical laws in the Principia saw an explosive devel-opment of the mathematical formalism required to extendthe theory to many celestial mechanics problems. Laplace(1749–1827), in the Mechanique Celeste, the first compre-hensive treatment of gravitational mechanics, succeededin developing the concept of “field” into a complex struc-ture capable of calculating such diverse phenomena as or-bital resonances and tidal acceleration. He also introducedthe general equation for the gravitational field externalto a massive body, which solves the equation ∇2� = 0,the Laplace equation. Lagrange (1746–1813) stated thegeneral method for incorporating energy (vis viva) intothe system of dynamical equations, was the first to finda solution to the restricted three-body problem, and de-veloped a method for treatment of generalized coordinatesystems by variational principles. Clairaut (1713–1765)calculated the first example of the inverse problem, thefigure and density distribution of the interior of the earth.Bessel (1784–1846) extended the calculation of planetarymotions. Gauss (1777–1855), among his numerous con-tributions to mathematical physics, developed the methodof least squares for the calculation of orbits in the presenceof observational uncertainty and introduced spherical har-monics (also explored by Legendre) into the descriptionof the gravitational field of finite bodies. Poisson (1781–1840) and Green (1793–1841) created general methods forthe calculation of gravitational potentials. Maclauren, Rie-mann (1826–1866), and Jacobi (1804–1851) succeeded infinding general solutions for the gravitational equilibriumof rotating incompressible fluid masses, work that was ex-tended by George Darwin (1845–1912) and James Jeans(1877–1946) to the problem of the formation of the moonand the description of the tides.

But perhaps the pivotal event of nineteenth-century ce-lestial mechanics was the successful prediction of the orbitof Neptune through the analysis of orbital perturbationson Uranus. Accomplished by Adams and Le Verrier, thediscovery in 1846 of this hitherto unknown planet servedto inspire much of the revived interest in orbital dynamicsand the detailed exploration of perturbation theory. Signif-icant contributions were made by Delaunay, Hill, Hansen,Brown, and Airy in this regard, especially concerning themotion of the moon (a problem that had even perplexed

Ptolemy and still one of the most challenging dynami-cal calculations). Almost immediately on their invention,Hamilton applied quaternions and Gibbs applied vectorsto orbital computations with considerable success. Theenergy principle became more prominent after the devel-opment of potential theory, spurred by a renewed interestin tides and the configurations of strongly perturbed ro-tating bodies. In fact, virtually every physicist of the pastcentury was involved in the exploration of the properties ofgravitational fields for bodies of different shape and mass.

Modern theoretical celestial mechanics was founded inthe last quarter of the nineteenth century by Liapounovand Poincare, who were the first to detail the conditionsrequired for general orbital stability. Newcomb, Plummer,Moulton, and Brouwer were among those who made sub-stantial contributions to this problem. Much of the the-oretical development was driven by thoroughly appliedresults—the need to predict planetary positions for timekeeping and navigation, the need for a consistent geodeticreference frame, calculation of tides—although occasion-ally it came from the simple desire to push the calcula-tion to yet another decimal point (a spirit best describedby the American poet Walt Whitman in The Learned As-tronomer).

A major advance in the twentieth century has been thegeneralization of celestial mechanics to the problem oforbits of stars in galaxies. Statistical mechanics was firstapplied by Schwarzschild and Kapteyn to the velocity dis-tribution of stars in the vicinity of the sun. The differen-tial rotation of the galaxy was demonstrated by Oort. Thediscovery of internal orbital motion in spiral nebulae bySlipher and Hubble, generalized by many later investiga-tions, permitted the determination of the masses of theseenormous stellar aggregates. Tidal interaction betweengalaxies was discovered observationally by Vorontsov-Veliaminov and Arp, inspiring considerable theoreticaleffort in the past two decades. Chandrasekhar and vonNeumann in the 1940s began the study of dynamical in-teraction between stars and their neighbors, a field that hasblossomed in recent years. Jeans and Contopoulos, amongothers, have explored the role of resonances and integralsof motion in the dynamics of stars in galaxies. Densitywave theory, originally developed to explain spiral struc-ture of galaxies by Lin and Shu, has been generalized to thestudy of wave phenomena in planetary rings. And the listof applications of gravitational dynamics to astronomicalproblems expands each year.

The spur in this century to developing methods for thecomputation of orbits has been the advent of spaceflight.For the first time, gravitational mechanics has played acentral role in engineering, and many of the theoreticaldevelopments concerning control theory, nonlinear me-chanics, and orbit prediction have resulted from this need.




We here conclude this broadbrush overview of the his-tory of developmental work in celestial mechanics. Keepin mind that we have merely cataloged a few of the enor-mous advances achieved in this field. More detailed histo-ries can offer the full extent of this spectacular, and ongo-ing, intellectual effort. More details will be found in thesubsequent sections of this article.

II. CONIC SECTIONS ANDORBITAL ELEMENTS

In the classical two-body problem, the orbit is described bya finite number of elements. The eccentricity, the measureof the flatness of the conic, is given by:

e =(

1 − b2

a2

)1/2

(1)

where a is the semimajor axis, or half the length of the ma-jor axis, and b is the half-width of the minor axis. For a cir-cle, e = 0, for a parabola e = 1, and for a hyperbola e > 1.The quantity a(1 − e2) occurs frequently and is called thesemilatus rectum. The inclination, i , is defined relative tosome reference plane, usually taken to be the solar orbitfor solar system celestial mechanical calculations, whichis also called the ecliptic. The mean anomaly, M = n�tdepends on the mean angular rate n = 2π/P , where P isthe period, of the orbit about the center of the conic. Theosculating circle is the one that just touches the major axisat its extrema and represents the circle that can be trans-formed into the ellipse of the observed eccentricity byinclining the plane of reference. The eccentric anomaly,E , measures the difference between the mean motion, re-ferred to the osculating circle, and the motion about thecenter of the conic. The mean motion is related to the ec-centric anomaly by the Kepler equation, one of the earliesttranscendental equations of mathematical astronomy:

M = n�t = E − e sin E (2)

where �t is the elapsed time from some initial epoch t0.The true anomaly, f , is the angular motion relative to thefocus. We will return to this momentarily. The longitude ofperihelion, ω, is measured in the plane of the orbit relativeto the ascending node. For the solar system, this point isthe vernal equinox, the point where the sun’s orbit crossesthe earth’s equator. This point is, however, an arbitraryelement that depends on the definition of the referenceplane. The same is true of the argument of perihelion,�, which is measured in the reference plane (in the solarsystem, along with ecliptic).

For a conic section, the radial position is given by:

r = a(1 − e cos E) (3)

and therefore the true anomaly, f , is given by:

cos f = cos E − e

1 − e cos E(4)

This angular motion is referred to as the longitude of clos-est approach and is given by φ − ω where φ is the angularmotion about the focus and the coordinate appropriate tothe description of the angular momentum of the orbitingbody. Another form for this equation is:

tanf

2=

(1 + e

1 − e

)1/2

tanE

2(5)

These are purely geometric relations, having only akinematic basis. It is one of the results of classical ce-lestial mechanics to provide a firm dynamical foundationfor these relations, especially the Keplerian equal areaslaw and the harmonic law. For more complex orbits, thoseoften found in multiple systems, it is usually best to calcu-late the motion of the body exactly. However, the relativeephemeris of an object can be expressed in terms of theseorbital elements, which may change in time dependingon the orbital stability. For instance, earth satellite orbits(e.g., the space shuttle or the Hubble Space Telescope) arereferred to the earth’s equatorial plane, while deep spacesatellites (like Voyager) are referred back to the ecliptic.

III. THE DYNAMICAL PROBLEMIN GRAVITATIONAL PHYSICS

A. The Two-Body or Central Field Problem

The central field problem distinguishes celestial mechan-ics from other areas of classical dynamics. This deals withthe motion of a test particle, whose mass is negligible withrespect to the central body, in the gravitational field of apoint mass. The extended version of this problem is toallow the central mass to have a finite spatial extent, to de-part from spherical symmetry, and perhaps to rotate. Thebasic Newtonian problem is the following.

The equation of motion for a single particle under theaction of an arbitrary force, F, is mr = F, where m is themass of the particle and r is its position vector. In mostof what follows, we will assume a cylindrical or spheri-cal coordinate system (which will be specified), the mostappropriate one for use with planar motion. The radialcomponent of the momentum equation is

d2r

dt2− v2

φ

r= ar (6)

and for the angular motion

d

dt

(r2 dφ

dt

)= aφ (7)




and we will ignore the z component for the time being. Inthe absence of any angular torques, that is, for centrallysymmetric problems, the angular motion can be collapsedinto a conserved quality, the specific angular momentum,which is

j = rvφ = r2φ, (8)

and therefore the equation of motion is strictly radial forthe central force problem

r = −∂�

∂r+ j2

r3(9)

Here the solution to the central field problem makes spe-cific use of the gravitational force. The substitution of

ar = −G M

r2(10)

completes the specification of the central field problem.Since there is a conserved quantity for the angular coor-dinate, we can substitute d/dt = ( j/(d/r2)/dφ), so thatdefining u = 1/r , the equation for radial motion reducesto

d2u

dφ2+ u = −G M

j2. (11)

This is the equation for a harmonic oscillator in the radialdirection. Physically, this is an important result, indicatingthat the motion remains bounded within a finite range ofradius only for a limited range of j and binding energy,and repeats periodically for the cyclically varying angleφ. In other words, for small enough values of j , the orbitcloses on itself precisely; if j is large enough, the orbitis unbounded. The radial distance from a point mass istherefore

r = a(1 − e2)/[1 + e cos(φ − φ0)] (12)

where we can now identify

e =(

1 − j2

G Ma

)1/2

(13)

as the relation between the angular momentum and theeccentricity (note that for a = ∞, as in a parabola, e = 1).The term φ − φ0 is the true anomaly, f as earlier. The tworetrograde for a period until the viewpoint from the earthreaches a tangent point, at which time the planet’s motionreverses. Dynamically, a moving reference point in a dif-ferentially revolving system of masses, like the solar sys-tem viewed from the earth, knows of a natural frequency atwhich bodies commit epicyclic or retrograde motion. Theonly force that “drives” this motion is the Coriolis effect.The frequency, called the epicyclic frequency, is given byk = 2� . The importance for understanding the kinematicswithin the solar system, or in any rotating system, is thatany moving observer will see epicyclic motion as long as

the frame of observation is assumed to be stationary. Weshall generalize this result below.

B. Gravitational Potential Theory

The primary problem in central field dynamics is the cal-culation of the gravitational potential �(r). It is definedby Poisson’s equation

∇2� = −4πGρ (14)

where ρ is the density. For a vacuum, this reduces to theLaplace equation. The solution for this equation is

�(r) = −G∫

ρ(r′) dr′

|r − r′| (15)

where the kernel of this equation is called the Green func-tion. For nearly spherically symmetric bodies, this reducesto a series in Legendre polynomials, Pnm , whose coeffi-cients depend on the density (mass) distribution.

When the central gravitating body is not spherical, ad-ditional terms are required for this power series, and theequations of motion reflect the presence of a torque. Forthe external gravitational field, this potential is generallyexpressed by the series in the radius, R, latitude, θ , andlongitude φ:

�(r, θ, φ) = −G M

r+ G M

r

{ ∞∑n=2

[(R

r

)n

Jn Pn0(cos θ )

+n∑

m=1

(R

r

)n

(Cnm cos mφ + Snm sin mφ)

× Pnm(cos θ )

]}(16)

Here R and M are the radius and mass of the planet, re-spectively. The coefficients Cnm and Snm are called tesseral(m = n) or sectoral harmonic coefficients (m = n), and theJn are the zonal harmonic coefficients. These coefficientsare determined through fits to satellite orbits, and the samedescription can be applied to any planetary gravitationalfield for which in situ measurements have been accom-plished. For instance, the coefficient J2 measures the gravi-tational quadrupole moment of the body and is responsiblefor the largest contribution to the precession of the orbit ofa planet about a nonspherical central body. The applica-tion of this formalism to planetary gravitational fields canalso be accomplished by the solution of satellite orbits,but this is likely only to provide the lowest order terms.The specification of the potential for a planet provides im-portant information about the internal mass distribution,and in this sense the study of the interior structure of aplanet through its external gravitational potential is a clas-sic inverse problem, attempting to solve uniquely for the




distribution in the density that gives rise to the observedgravitational field.

The definition of the potential for various classes ofdistended bodies began in the eighteenth century with thework of Clairault, Maclauren, Laplace, and Roche. Clas-sic work on potentials involved some of the most illustri-ous mathematicians of the past century, including Gauss,Riemann, Jacobi, and Poincare. These were mainly ap-plications of gravitation theory to the figure of the earth.Recent discussions of the problem of calculating thesepotentials are due to Kellogg and Chandrasekhar. For as-trophysical systems the problem is harder because the po-tentials are often composite, consisting of spheroids anddisks in combination and often requiring bars or triaxialellipsoids.

One extreme example of a nonspherical gravitationalfield is that of the three-body problem (see Section III.F).Here one assumes that a point mass orbits in the corotat-ing frame of two (possibly unequal) masses. The motionof the large masses has a period P and is assumed to becircular about the center of mass. The third body, whosemass is negligible, orbits with any arbitrary inclination ito the (m1, m2) plane and with some initial energy, alsocalled the Jacobi constant. The particle is constrained byminimum energy to move along zero velocity or equipo-tential surfaces if the body is initially at rest in the coro-tating frame. The precise form of the potential was firstdiscussed by Roche, who also derived the limiting radiusof a self-gravitating body being acted upon tidally by a per-turber that now bears his name. The centrifugal term is atthe rate of rotation of the massive components and is takenrelative to the center of mass. The individual gravitationalterms are referred to the locations of the massive bodies:

�Roche(x, y, z) = −1

2(x2 + y2)�2

− G M1[(x − x1)2 + y2 + z2

]1/2

− G M2[(x − x2)2 + y2 + z2

]1/2 (17)

where x j is the position of the j th body relative to thecenter of mass. Although this potential involves pointmasses, it can be generalized to finite bodies.

C. Perturbation Theory

Gravity is a force of infinite range, and it is impossiblefor any pair of objects to be truly isolated and subject to apoint mass central field. The closed form solution of thetwo-body problem thus represents an idealized orbit. Thedepartures from this trajectory are treated by perturbationtheory. The action of any additional mass in a system can

be thought of as a perturbation on the central field problem.The basic assumption of perturbation theory is that themagnitude of the disturbance is small, so that the dynam-ical equations remain linear. In the presence of massive,nearby objects, or in the vicinity of resonances, nonlineartechniques must be applied.

Perturbations introduced by the action of external bod-ies fall into several categories. For examle, the effect offinite size of the central object in a two-body problem in-troduces precession in an orbit that can be treated as aperturbation above the point central field. These orbitalperturbations represent simple time-independent and pe-riodic departures from the closed ellipse. They will causethe orbiting body to evolve toward a stable trajectory ifthe central body is not rotating. Rotation of the centralbody introduces an additional time scale into the problemand can produce secular instabilities in the orbit. The ba-sic starting point of a perturbation calculation is that onealready knows what the orbit is for a particle. One is in-terested in finding out whether it is stable against smallperturbations, due to other bodies, and what the evolutionwill be for the orbit.

One of the best examples of the effects of perturbationsin the solar system is provided by the gravitational inter-action between comets and the Jovian planets, especiallyJupiter itself. New comets, that is, those coming into theinner solar system for the first time, begin their decent to-ward the sun in nearly parabolic orbits. As they come closeto Jupiter, the acceleration provided by the planet changesthe orbital angular momentum through a torque that, de-pending on the phase of the kick from the interaction, caneither increase or decrease the eccentricity of the orbit. Forcapture, the eccentricity is decreased below unity. CometEncke is one of the best examples of this, being trappedin an orbit that is nearly resonant with the Jovian period.Comet Halley is in a near resonance with Neptune. On theother hand, the eccentricity can be increased and the cometsent out of the solar system with an increased total energyand angular momentum in any hyperbolic orbit. The keyfactor is whether the perturbation is leading or trailing inthe orbit. Several asteroid families are trapped in resonantorbits with Jupiter, notably the Apollo asteroidal group.The Trojans are trapped in orbits near the triangular La-grangian points (L4 and L5) of Jupiter. These changes inthe orbital properties occur in real time, that is to say inthe course of a single orbit.

Tidal perturbations are important for the orbits of manysatellites. In the course of time, a satellite gains angularmomentum through interaction with the sun and moon, aswell as because of the nonspherical gravitational field ofthe earth. Orbital ephemerides must be frequently updatedto take these changes into account, especially for geosyn-chronous satellites.




The interaction of the sun and moon with the earthis responsible for several important physical effects, no-tably the precession of the rotation axis with time (thephenomenon first described by Hipparchos) and for thechange in the length of the day due to tidal friction anddissipation of rotational energy. The tidal term results fromthe finite size of the earth relative to its orbital radius andto that of the moon. The differential gravitational accel-eration across the body produces a torque that acceleratesthe moon outward and slows the earth’s rotation.

As we have discussed previously, an orbit is charac-terized by a finite number of orbital elements. Under theinfluence of an external force �, called the disturbing func-tion, all of these may vary. In particular, torques changea and e but also cause the orbit to precess so that � andω vary in time. The presence of additional mass in thesystem changes the orbital frequency, n, through changesin M . If the angular momentum changes, it is possible forthe total energy of the particle to change as well. The dis-turbing function has components in the cylindrically sym-metric coordinate system we have been using: R = ∂�/∂rfor the radial component, S = ∂�/r∂φ for the azimuthaltorque, and W = ∂�/∂z for the force perpendicular to theorbital plane. The full system of evolution equations forthe orbital constants under the action of these forces isgiven by

da

dt= 2

a(1 − e2)1/2

(Re sin f + S

a(1 − e2)

r

)

(18)

de

dt= (1 − e2)1/2

na

{eR sin f +

[a(1 − e2)

r− r

a

]S

}

(19)

di

dt= [na(1 − e2)1/2]−1 r

acos(ω + f )W (20)

sin id�

dt= i tan(ω + f ) (21)

dω

dt= (1 − e2)1/2

nae

[−R cos f

+ S

[r

a(1 − e2)+ 1

]sin f

]

− er sin( f + ω) cos i

a(1 − e2)W

](22)

d M

dt= n + 1

na

[((1 − e2) cos f

e− 2r

a

)R

− (1 − e2) sin f

nae

(1 + r

a(1 − e2)

)S

](23)

Notice that the variation of the semimajor axis depends onboth the radial and the torque, but because the orbit canbe taken in the two-body problem as planar, there is nodependence on W . Changes in ω and � are equivalent toorbital precession. All of these may be periodic or secu-lar, depending on the details of �. For a given disturbingfunction, this system of equations can be well exploredusing numerical methods.

D. Lunar Theory

Because of its centrality in the development of perturba-tion theory, the motion of the moon has its own terminol-ogy and also a special set of treatments. More is knownabout the motion of this body than of any other objectin the solar system. After the placement of laser retrore-flectors on the surface during the Apollo mission, regularranging from the earth has determined the lunar distanceas a function of time to an accuracy of tens of meters.

Historically, the departures of the moon’s motion fromcircularity have been among the driving anomalies thatcelestial mechanics was designed to address and explain.The inequalities were expressed as variations in the longi-tude of the moon relative to that expected in the simplesttheory in which its rate about the center of the deferentcircle, or later around the eccentric. The development oftheory by Newton, and workers in the past two centuries,has derived the precise forms of all of the classical in-equalities. All motion is referred to both the position ofthe moon along the ecliptic. λ and that of the sun λ′. Themost important terms are

1. the evection, discovered by Ptolemy, due to the motionof the longitude of perigee n′2a2e2 cos(2ω − 2λ′) as adeparture from the eccentric deferent;

2. the variation, which depends on n′2a2 cos(2λ − 2λ′),where n′ is the mean solar motion;

3. the annual equation, which depends only on thelongitude of the perigee: n′2a2e′ cos(λ′ − ω′), where e′

is the eccentricity of the solar orbit;4. the parallactic inequality, n2a3e cos(λ′ − ω)/a′,

where a′ is the semimajor axis of the solar orbit;5. the principal perturbation in longitude, which

depends on the inclination of the lunar orbit relative tothe ecliptic n2 cos2 ia2 cos(2λ′ − 2�).

The chief problem is that the rotation of the earth and thedisturbing tidal accelerations from the sun change the lu-nar orbit with time. Each of these motions must be treatedseparately in the system of equations that describe the lu-nar orbit.

The detailed study of the lunar motion has implicationsfor geophysics as well. The length of the day is affected




by the tidal interactions between the moon, sun, and earth.In the course of the millennia, the day has steadily length-ened; the change in the lunar orbital parameters reflect thisbecause of the variation in the tidal torque on the moon.These variations yield important information about thetidal coupling mechanism and the rate of dissipation ofthe angular momentum of the earth–moon system.

E. General Relativity and Celestial Mechanics

One of the first tests of the General Theory of Relativity(GRT) was the calculation of the precession of the or-bit of Mercury. A longstanding problem at the end of thenineteenth century was that it observed orbital precessionrate exceeded the value of 5557 arcsec per century, pro-duced by the combined effect of all of the planets, by about43.11 ± 0.45 arcsec per century. The planetary precessionvalue was based on the known masses of the planets andon the solar potential and assumed a spherical shape forthe sun. It is a tribute to the efforts of theorists in the pastcentury that a discrepancy of this tiny amount, less than0.1%, was considered not only significant but compelling.Several solutions were suggested, including as light mod-ification to the gravitational force law by making the lawvery slightly weaker at large distance giving the sun aquadrupole moment due to rotational distortion of about40 milliarcsec, or the presence of a planet within the or-bit of Mercury. The last of these suggestions, perhaps themost widely accepted solution at the close of the century,was made by Leverrier, whose successes in the predic-tion of the place of Neptune on the basis of perturbationtheory led to the eventual universal acceptance of Newto-nian methodology and represented the triumph of the pastcentury in classical dynamics. This hypothetical planet.Vulcan, was actually reported during several eclipses to-ward the end of the century, but subsequent investigationshave since eliminated it as a possible member of the solarsystem.

Einstein discovered the celestial mechanical conse-quences of GRT in 1914, just before his completion ofGRT. General relativity produces a change in the gravita-tional field in the vicinity of a massive body. The distortionis equivalent to introducing an additional term in the har-monic oscillator equation

d2u

dφ2+ u = G M

j2+ 3G Mu2 (24)

so that the magnitude of the advance of the peri-helion is predicted to be 3G M/(a(1 − e2)) = 12π2a2/

(c2 P2(1 − e2)), where c is the speed of light. AlthoughMercury is about 0.4 AU from the sun, this is only about100 solar radii, and the precession predicted by relativ-ity is 43 arcsec per century. For the earth, in contrast, the

rate is predicted to be only about 4 arcsec per century.Along with the deflection of starlight observed during the1919 eclipse expedition, this prediction stands as one ofthe great triumphs of the GRT.

Two types of GRT corrections are required for orbits.One is due to the precession of the orbit, the other is theradiation of gravitational waves. While not important inthe vast majority of dynamical systems, it plays a role inbinary star systems in which the components are massive,compact, and revolving with very short periods. The rateof gravitational wave radiation varies as �6, where � is theorbital frequency, so that for binaries like PSR 1913 + 21(the best studied of the binary pulsars) it produces a secularchange in the semimajor axis that can be measured fromseveral years of observation. These effects can be incor-porated into the standard perturbation evolution equationsthrough modifications to the distubing function.

F. The Three-Body Problem

The most celebrated problem in celestial mechanics isthe so-called three-body problem. First elucidated byLagrange, this problem focuses on the determination ofthe allowed class of periodic motions for a massless parti-cle orbiting a binary system. In this case, the motion is de-termined by the gravitational and centrifugal accelerationsand also the Coriolis force. A closed form analytic solutionis possible in only one case, that of equal masses in a cir-cular orbit. This so-called restricted three-body problemcan be specified by the curves of constant potential, alsocalled the zero velocity surfaces. Consider a binary with acoplanar orbit for the third mass. In this case, a local co-ordinate system (ζ, η) is defined as centered at (a, 1 − a)so that the equations of motion are

ζ + 2�η = −∂�

∂ζ

∣∣∣∣η

(25)

η − 2�ζ = −∂�

∂η

∣∣∣∣ζ

(26)

Here the gravitational potential, �, is the Roche potentialalready discussed. The assumption required for this po-tential is that the two massive bodies are in a circular orbitabout the center of mass. In the absence of eccentricity,stable orbits are possible in several regions of the orbitalplane. These are defined by the condition that ∇� = 0and are critical points in the solution of the equations ofmotion. These are stationary in the rotating frame. In thepresence of eccentricity, they oscillate and produce a lossof stability, as we shall explain in Section IV.C.

Several critical points in the three-body potential dom-inate the motion of particles. They are specified as thepoints at which the gravitational acceleration vanishes.




Called the Lagrangian points, two lie perpendicular to theline of centers (the L4 and L5 points) and are due to thebalance between centrifugal and gravitational forces mod-ified by the Coriolis acceleration that governs the angularmomentum of the particles. These points are actually po-tential maxima, and therefore the particle orbits are onlyquasi-stable. These points lose their stability for large massratio or in the presence of an eccentricity in the massivebinary. Two Lagrangian points, the L2 and L3 points, liealong the line of centers but beyond the two massive bod-ies. These are minima in � and form a barrier to mass loss.Finally, the most important is L1, the point of balance be-tween gravitational accelerations of the two bodies, whichlies along the line of centers between the massive mem-bers of the system. This point corresponds to the Rocheradius, the separation at which the gravitational perturba-tion of the companion dominates over the self-gravitationof a deformable, compressible, self-gravitating body. Or-bits are unconditionally unstable at L1, L2, and L3. Theyare asymptotic at L4 and L5. If the central orbit is eccen-tric, the tidal component of the gravitational field at theLagrangian points oscillates in the course of a single pe-riod. Depending on the local orbital frequency of a bodyabout the L4 or L5 point, this oscillation may render theorbit unstable on a short time scale, transferring angularmomentum to a trapped particle and sending it out of thesystem.

G. The Few-Body Problem

Few-body problems can be handled by conventional inte-grators, such as Runge–Kutta or Adams–Moulton meth-ods. Here one calculates the position and velocity for eachparticle and then the precise two-body interaction for thatbody with every other particle in the system. Both methodsare predictor-corrector procedures in which the next stepis computed and corrected iteratively. Leapfrog methods,which use the velocity from one step and the positionsfrom the previous step to compute the new positions, arealso computationally efficient and stable. The basic prob-lem is to solve the equations of motion for a particle atposition ri ,

mi ri = −∑j =i

Gmi m j

|ri − r j |3 (ri − r j ), (27)

supplemented by initial positions and velocities of the par-ticles. Thus, the angular momentum is initially specifiedby the set of velocities and coordinates (ri (0), ri (0)). Ef-ficient algorithms for the solution of this problem havebeen presented by Aarseth and have become standard inastrophysical calculations. For only a few bodies, Runge–Kutta procedure can be used. For more than about adozen particles, this becomes computationally expen-

sive, and leapfrog and predictor-corrector integrators areemployed.

H. N-Body Problems

When the number of objects becomes large, more than afew dozen, then conventional integration techniques fororbit calculation become inadequate, and new procedureshave to be introduced. The primary reason is not anychange in the physics. Rather, it is the enormous numberof individual quantities that must be tracked for the con-stituent particles (three coordinates, three velocities). Con-ventional few-body integrators require 1

2 N (N − 1) calcu-lations per step to determine the motion of the particles.So the rate of calculation scales like N 2. For complexsystems, like galaxies, this is prohibitively expensive andslow.

Instead, assume that the field is given by a statisticalgravitational field, �0, derived from the instantaneousdensity distribution. This is given, symbolically, by a con-volution of the density distribution with the Green function�0 = ρ ��. Therefore, the Fourier transform of the poten-tial is the product of the transforms of the density and theGreen function, both of which are known at each step. TheGreen function depends on the coordinate system, but oncecomputed can be tabulated to be reused without modifica-tion at every step. The potential calculation thus requiresonly a set of fast Fourier transforms (FFTs) for each step.The density is determined by some initial guess, the poten-tial is computed, and the particles are then pushed withinthis potential. In the next step, the density is recalculatedfor the particle distribution, and the process is repeated.Because the FFT is used for the potential, the complexityof the computation grows slowly with particle number, NIn N , and therefore handily wins over the more conven-tional N -body methods for large systems. While there aresome problems with this method due to the aliasing andgridding effect of the particles (for instance, the particlesmust be resampled at each step to a uniform grid for theFFTs), experiments with systems up to 106 bodies showthat the method is stable and reproducible.

A technique, called smoothed particle hydrodynamics(SPH) has been introduced to the N -body problem. Thisinvolves the combination of the two methods of conven-tional few-body integrators for each body with its im-mediate nearest neighbors and the overall computationof the distant gravitational potential via FFTs. SPH andFFT methods have also been merged with hierarchicaltree searching techniques to improve their speed. Com-putation of many-body effects, while not important forsatellite dynamics, which depend primarily on the centralfield approximation, may be important in the study of as-teroid and comet orbital evolution and also applies to the




computation of evolution of self-gravitating planetary ringsystems. Refinements of these methods have been rapidlymaking inroads into astrophysical calculations and alsoplasma and solid state physics.

IV. APPLICATIONS: A FEWINTERESTING EXAMPLES

A. Satellite Dynamics: Transfer Orbits

The simplest practical application of celestial mechanicsis in the computation of satellite dynamics, in particu-lar, the transfer orbit between two planets. This orbit isthe one that has the minimum energy and therefore hasan aphelion at the inner planet at ri and perihelion atthe outer planet, ro, so a = (ri + ro)/2. The eccentricityis e = ri/a, and thus the period of the orbit is given by(a3/4π2G M)− 1/2 and the binding energy can be calcu-lated using E = −G M/2a as before. The total change inthe energy is (ro − ri )(v2

o + v2i )/(ro + ri ), where v is the or-

bital velocity at each of the radii. The increase in the angu-lar momentum required for a parking orbit is smaller thanthat required from the surface of the body. As a side pieceof trivia, since 1925 this transfer orbit has been known asa Hohmann ellipse.

B. Solar System

Long before spacecraft encounters, celestial mechanicshad been employed to determine the masses of those plan-ets that possess moons. With the exceptions of Mercuryand Venus, for which the arguments were more indirect,the masses of all the planets are now known from satelliteobservations. Detailed examination of the periodicities oftheir moons also reveals that they interact through resonantorbits, which causes the structuring of the radial distribu-tion of the planetary satellite systems. Detailed observa-tions of satellite motion also permit the determination ofinternal mass distribution and oblateness for most of theplanets. These determinations have been augmented forthe outer planets by direct flybys with the Voyager 1 and2 spacecraft. Finally, mutual phenomena of the moons ofseveral of the major planets provide the determination ofsatellite masses through the solution of the motion undermutual perturbations for the satellite systems.

The evolution of cometary orbits—especially CometHalley for which there is a significant historical record—shows evidence for nongravitational forces. These are pre-sumed to arise from the mass loss from the comet producedby interaction with the solar wind and radiation-inducedoutgassing. The change in the mass of the comet carries an-gular momentum because of the finite escape velocity for

the lost gas. The effects of these “rocketlike” forces com-plicate the interpretation of cometary orbits. This problemis not merely of theoretical interest—accurate orbits areessential for predicting trajectories for artificial satelliteencounters with comets like Halley.

C. Orbital Resonances

One of the oldest problems in celestial mechanics is thatof resonances, the near coincidence of two frequencies ortheir rational multiples. Also called the problem of smalldivisor, it first appeared in the theory of the solar system.Two bodies are said to have commensurate periods whenthe ratio of their periods is the ratio of integers, m : n. Theproblem produced by such orbits is that their mutual inter-action will enhance phase-realted torques and lock bodiesinto specific periods. The best example of this resonancephenomenon is a child in a swing. The period of the systemis given by the length of the supports for the swing. Butthe child controls the amplitude of the swing by kickingin phase, or in antiphase, with respect to the maximumvelocity along the arc. Thus, with the proper phasing, aperiodic kick delivered at the minimum in the potential en-ergy (maximum velocity) will produce an increasing am-plitude. The same is true for bodies in gravitational orbits.These resonances grow without limit in the linear theorybecause the forces are always in phase, thereby producinga secular acceleration. In the case of two bodies in near res-onance, the tendency will be for the bodies to attract to theresonance and lock. To see this analytically, consider a sin-gle particle one-dimensional harmonic oscillator subjectto a periodic force: mx + mω2

0x = F(t) = a sin ωt whereω is the frequency. The amplitude as a function of timeis the Fourier transform of this frequency-dependent am-plitude, so that if there is a near commensurability, therewill be amplitudes which will grow linearly with time.The natural frequency of the oscillator is ω0 so that theamplitude is given by

x(ω) ∼ a

ω20 − ω2

(28)

Notice that as ω → ω0 the energy if the mode |xω|2 growswithout limit. In celestial mechanics as elsewhere, the pe-riods are generally in integer ratios if they resonate.

In the case of two orbiting bodies, the largest torques aredelivered at the point of closest approach. If the two bodiesare not in circular orbits, then the phasing of the kick isimportant, and should the body be going at its maximumspeed at the time the acceleration is delivered, its angularmomentum will be increased and the eccentricity of theorbit should increase secularly.

Such resonances were first realized in the problem ofthe so-called “Great Inequality” of the orbits of the outer




planets. Jupiter and Saturn have a period ratio of 5:2 forthe ratio of their frequencies. Other resonances were notedin the gaps in the Saturn ring system (the Cassini andEncke divisions being the most famous) and in the ra-tio of rotation and revolution periods for Mercury (2:3).But perhaps the most spectacular examples are noted inthe asteroid belt, manifested as the so-called KirkwoodGaps. These are low population zones in the asteroidaldistribution at points in resonance with the outer planets,especially Jupiter. The distribution of these gaps is com-plex because all possible commensurabilities should bepresent, and in fact there is denumerable infinity of them.The asteroid distribution, like the ring system of Saturn,represents a good example of a chaotic system because ofthe resonance and near resonance conditions.

The primary cause of resonant trapping is the beatingbetween the orbital frequency of the body being acted uponand that of the perturber. The phasing of the perturbationproduces an acceleration for a portion of the orbit and acompensating deceleration elsewhere in the orbit.

For a rotating coordinate system, we can introduce anew frequency, the epicyclic frequency, which is the rateat which bodies appear to revolve around the point of ob-servation. This frequency results from the gradient in thecentral gravitational field and is important for resonantorbits. To see where it comes from, consider a movingobserver in a coordinate system (r, φ) where φ is the az-imuth. Assume that this observer revolves about a centralbody in a gravitational field �(r ) at a distance r0 and withan angular frequency �. The radial velocity is thereforeassumed to vanish for this observer, and the angular speedof the frame is also constant. Now assume that we can cre-ate a comoving locally Cartesian coordinate system (ζ, η)around this orbit. A body with higher angular momentumthan required for the circular orbit will therefore have aradial speed ζ and a variable angular speed r0φ = η. Fora corotating frame of reference, the equations of motionare

ζ = 2�η − ∂2�

∂r2ζ (29)

for the radial equation and

η + 2�ζ = 0 (30)

for the angular equation. Therefore, there is a characteris-tic frequency

κ2 = 3�2 + ∂2�

∂r2(31)

which is the epicyclic frequency we were seeking. Thisfrequency depends on the steepness of the gravitationalfield gradient. For instance, for a Keplerian orbit, � ∼ r−1

and �′′ > 0, so that the epicyclic frequency is greater than

the orbital frequency. It should be remarked that κ = 0is also allowed for any central body comoving with theframe. In terms of the orbital frequency of the referencecircular orbit:

κ2 = 4�2

(1 + r

2�

d�

dr

)(32)

The importance of this frequency for the resonanceproblem is that any force that is periodic on this time scalewill produce a resonant interaction. For the more generalproblem of galactic structure, the points at which the per-turbation frequency is the same as the epicyclic frequencyare called the Lindblad resonances. These play a centralrole in density wave theory, which has been applied to awide variety of astrophysical problems, including plane-tary ring systems, accretion disks, and the structure andevolution of spiral disk galaxies.

Resonances of special interest in the solar system in-clude the lock between Neptune and Pluto (λP − 2λN −ωP = 180◦), the Trojan asteroids, which are trapped at thetriangular Lagrangian point of the Jovian orbit, and themoons of Jupiter. These last are perhaps the most acces-sible examples, because they can be readily observed byanyone with the patience to watch the moons for a fewdays with binoculars. The best is the coupling of Europaand Ganymede, λE − 2λG + ωE = 0, but the three moons,including Io, display λI − 3λE + 2λG = 180◦.

D. Planetary Ring Dynamics

Planetary ring systems represent the best available celes-tial mechanics laboratories. Here we can observe all of thephenomena of resonance, trapping, collisions, and bothperiodic and nearly periodic motion. The number of parti-cles in a typical planetary ring system like Saturn or Jupiteris great enough, and their masses low enough, that theyserve as tracers of the gravitational dynamics. Thus, theyconstitute the best observable examples of the conditionsrequired for the solution of many mechanical problems.

The first detailed examination of ring dynamics was ac-complished by James Clerk Maxwell in his 1857 SmithPrize essay, a study that still repays reading. He dealt withthe question of the composition and stability of Saturn’srings, demonstrating that they must consist of a swarm ofsmall particles trapped in planar orbits. The demonstrationof differential rotation in the Saturn rings by the observa-tion of Doppler shifts in a reflected solar spectrum wasfirst performed by Keeler about 30 years later.

In the best studied case, Saturn and Uranus, predic-tions of the placement and evolution of rings and gapsdue to resonances predicted the great number of sepa-rate rings observed by satellite flybys. However, observa-tions of Uranus during occultations of stars by the planet




produced a remarkable result. The thickness of the ringsystem was such that several separated rings could be ob-served from the immersion and emersion of stars behindthe planet. Five distinct rings were discerned from ground-based observations, each with remarkable optical depthbut extremely geometrically thin. The theoretical develop-ment of the “shepherding moon” model has successfullyaccounted for nearly all of the properties of these systems.

The basic idea is that moons with near commensura-bilities radially flank the orbit of a particle ring. As theparticle encounters the inner one, it is sped up and its or-bit starts slightly to increase. It then encounters the innerone, and it is torqued down back into a stable orbit, aroundwhich it executes a radial oscillation. In other words, thefact that there are several larger bodies which are nearlyco-orbiting with the test particle serve to keep it confinedwithin a narrow radial distance. The basic theory, first de-veloped by P. Goldreich and S. Tremaine to explain theε-ring of Uranus, works especially well for a number ofring systems. A notable and recently observed exceptionis the Neptune ring system. This planet displays what canbest be described as ring-arc structures, since the particleconcentrations display resonances that enhance the den-sity of particles in confined banana-shaped regions andalso form continuous rings around the planet. There issome evidence that these are also resonant, but the modelshave not been fully developed for this system.

Another possibility is that waves may be producedthrough resonant excitation of self-gravitating modes inthe rings. The Saturn rings show complex, wavelike pat-terns that move with a fixed pattern speed around theplanet. These may be density waves, collisionless modesthat produce a periodic variation in the gravitational poten-tial and thereby produce self-consistent density variationsthat support the waves. While there are serious problemsremaining in the theory of spiral galaxies, and no unam-biguous evidence has been represented for the existence ofsuch waves in galaxies, the possible application of densitywave theory to some planetary ring systems has been anencouraging indication that the basic physical mechanismis possibly realized in nature.

E. Binary Stars

The first test of Newtonian mechanics outside the solarsystem was the discovery of dynamically bound multiplestar systems, first by Herschel and later by Bessel andhis school in the nineteenth century. The observation anddetermination of orbits for visual binaries have been es-pecially important for understanding the masses of manystar systems. In addition, after the discovery of spectro-scopic binaries, the measurement of stellar masses becameroutine through the observation of eclipsing binary stars.

However, binaries provide many challenging problems fordynamical theory.

Close binaries interact via tides, and the stars are de-formable. Therefore, they are able to show changes onrelatively short time scales in the structure of the stellarenvelope and to provide important clues to the origin oftidal coupling.

Most stellar masses have been calibrated through theuse of double line eclipsing binary stars. Knowing theorbital parameters, such as the inclination, eccentricity,and period of an orbit, one can determine the masses ofthe two stars from their velocity amplitudes, the ratio ofwhich is the inverse ratio of the stellar masses, and theperiod through

f (m) = m31 sin3 i

(m1 + m2)2

= 1.04 × 10−7(1 − e2)3/2 K 31 P M� (33)

where K is the velocity amplitude of star m1, and M�is the solar mass. Therefore, since m1/m2 = K2/K1, foreclipsing systems for which i = 90◦, the individual massescan be determined.

These measurements constitute the corner stone of theedifice of stellar evolution. The simple applicability ofKepler’s third law to the motion of bodies highlights theimportance and astonishing success of classical mechanicsin yielding modern and diverse results.

F. Stellar and Galactic Dynamics

Large stellar systems behave much like a collisionless gasin which the interactions are all at large distances betweenthe particles but the forces are always attractive. Workduring the past half century has made considerable stridesin the elucidation of the detailed structure of stellar clustersand galaxies. The basic premise is that, much like a gas, theparticles prossess a velocity distribution function f (v) thatdepends only on a stable distribution in velocity. Unlike agas, however, there is a characteristic maximum velocityfor the system, the escape velocity v∞. In the case of acluster, two conditions govern the evolution. One is thatthe individual stars do not actually collide, but that they canexchange momentum at large distance via gravitationalinteractions. The other is that the cluster obeys the virialtheorem, which states that 2T + � = 0 for a stable clusterof stars. Here T is the kinetic energy of the cluster as awhole, and � is the potential energy. Since E = T + � isthe total energy, E = 1

2� and � < 0 implies that E < 0.The consequences of the virial theorem are important

and differentiate the behavior of a gravitating cluster froma normal gas. Because the total energy is negative, a lossof mass causes the cluster to contract. This is familiar




already from the argument earlier that a loss of energycauses the orbit of a particle in a central field to contract.Thus, the orbital frequency is increased, which is equiva-lent to the statement that the velocity dispersion in a clus-ter increases. This phenomenon, known as the “negativespecific heat problem” or the gravitothermal catasrophe,is essential for understanding the evolution of gravitation-ally dominated systems. If mass or energy is lost, the clus-ter must contract, leading to an increase in the collisionfrequency and enhanced loss of bodies. Eventually, thecluster becomes so low mass that the process stops, butone could think of the body as cooling so rapidly that itheats catastrophically (a seemingly paradoxical situationencountered as a result of the binding energy).

In celestial mechanics, or in this case the newer field of“gravitational statistical mechanics.” the lessons learnedfrom more traditional areas of celestial mechanics are ap-plicable. For instance, in the case of the collision betweentwo bodies, there is a gravitational deflection, and mo-mentum is exchanged between the bodies. If a single starmoves with respect to a background of more distant andperhaps more slowly moving stars, momentum is trans-ferred from the moving star to the background. This resultsin slowing the star down, much like a viscosity. Hence, theprocess is called dynamical friction. The basic theory wasdeveloped by S. Chandrasekhar. More recent work hasincluded the incorporation of low velocity interactions,tides, and more realistic specifications of the orbital dy-namics during the encounter. Put differently, there will bea finite time in any stellar system over which the bodiesmaking up the system will collisionally relax through dis-tant encounters with the background stars of the system.

Single particle stellar orbital mechanics is not unlikeplanetary ring theory. Bodies move under the influence ofa gravitational field created by the mutual interactions ofall of the stellar masses in the system, a spatially extendedand complicated potential.

Galactic differential rotation was discovered by J. Oortin 1927, and the introduction of rotation into the interpre-tation of stellar kinematics and dynamically fundamen-tally changed discussions of galactic structure. What Oortnoted was the epicyclic frequency in the radial and trans-verse velocities for stars in the solar neighborhood (thatis, stars within about 100 parsecs of the sun). For nearbystars, the transverse velocities can be determined throughproper motion and parallax measurements. The compo-nents of the velocity parallel to the galactic plane, andnormal to the direction toward the galactic center, and theradial velocities alone. Since stars have different angularmomentums, their orbits will have slightly different eccen-tricities, even for the same total energy. These deviate fromprecise corotation with the sun and show a periodic depen-dence on twice the galactic longitude. From the amplitude

of this effect, one can deduce the mass of the galaxy. TheOort constants are determined from the transverse and ra-dial velocities of stars in the solar neighborhood. Theyare defined from the relation: vT = d(A cos 2lll + B) andvR = d A sin 2lll , where lll is the galactic longitude and theconstants A and B are given by

A = 1

2

(�0

r0− d�

dr

)r0

(34)

and

B = −1

2

(�0

r0− d�

dr

)r0

(35)

where �0 is the orbital velocity of the sun about the galac-tic center. It should be noted that these coefficients are thesame as those found for epicyclic motion. The gradient inthe galactic gravitational potential is represented by thechange in � with radius.

G. Chaos Theory and Celestial Mechanics

The first manifestation of chaos theory was in celestialmechanics. In his fourteenth-century arguments againstastrology, Oresme pointed out that the planetary peri-ods were incommensurate, and therefore every planetaryconfiguration throughout all time was unique. The ideathat a particle could be trapped within a broad region ofphase space—where in the course of time a particle couldhave virtually any momentum at a given position withina bound energy—was first demonstrated by Poncare. Heshowed that single particle orbits could have propertiesmuch like the ensemble of particles in a gas at very highentropy. This state is called ergodic. This result was ex-tended by the ergodic theorem of Birkhoff, von Neumann,and Wiener and by the recurrence theorem of Poincare.Chaos is the stochastic behavior of deterministic physicalsystems, resulting from extreme sensitivity of the dynam-ical evolution of such a system to small changes in theinitial conditions. Strongly perturbed orbits, like those ofplanetary ring systems or stellar orbits in a galaxy, willdisplay chaotic behavior. Two different orbits in a Rochepotential, for instance, started out near the L4 or L5 point,will evolve along totally different trajectories for infinites-imal changes in the initial conditions. Perhaps stellar or-bits in a strongly barred potential, such as those observedin the centers of some spiral galaxies, or the orbits ofcomets in the outer solar system, constitute among the bestexamples of such behavior. During galaxy collapse, afterstar formation has occurred, the rapidly changing collec-tive gravitational field causes strong perturbations in eachof the stellar orbits and thoroughly mixes them in veloc-ity and position, or phase space, and produces a randominitial velocity distribution. This process, called violentrelaxation, is one of the most important areas of study in




stellar dynamics and may have analogs in the formationof orbits in planetary ring systems and the asteroid belt.

V. CLOSING REMARKS

Celestial mechanics, begun as an applied area of physics,has broadened into one of the most fruitful and excitingfields of theoretical mathematics and physics. The intro-duction of new computing techniques has made it practi-cal to calculate the dynamical evolution of quite complexsystems. For the first time it is possible to study questionsrelated to the long-term stability of the solar system, thestructure of planetary rings, and the evolution of spiraland elliptical galaxies. Problems related to the stabilityof orbits of stars in complicated galactic potentials haverevived entire areas of classical theory with dramatic re-sults. Renewed interest in triaxial bodies has been spurredby the observations of tidal interactions between galax-ies. Even the large-scale structure of the universe, a hugeN -body problem involving the expansion of the universeas a whole in addition to the gravitational interactions be-tween individual galaxies, has almost become a routinemechanical calculation. Now with the discovery of extra-solar planetary systems we can learn from new examplesabout the complex interactions of small bodies by naturalexperiments. The riches of celestial mechanics, the most“classical” area of all physical theory, are far from beingmined out.


BINARY STARS • CHAOS • COSMOLOGY • GRAVITA-TIONAL WAVE ASTRONOMY • MECHANICS, CLASSICAL •MOON (ASTRONOMY) • PERTURBATION THEORY • PLAN-ETARY SATELLITES (NATURAL) • RELATIVITY, GENERAL

• SOLAR PHYSICS • SOLAR SYSTEM, GENERAL • STELLAR

STRUCTURE AND EVOLUTION

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Astron. Astrophys. 14, 215.Plummer, H. C. (1918). “An Introductory Treatise on Dynamical Astron-

omy,” Dover, New York.Roy, A. E. (1982). “Orbital Motion,” Adams Hilger, Bristol.Saslaw, W. C. (1985). “Gravitational Physics of Stellar and Galactic

Systems,” Cambridge University Press, Cambridge.Spitzer, L., Jr. (1987). “Dynamical Evolution of Globular Clusters,”

Princeton University Press, Princeton.Sternberg, S. (1969). “Celestial Mechanics” (2 vols.), W. A. Benjamin,

Reading, Massachusetts.Szebehely, V. G., and Mark, H. (1998). “Adventures in Celestial Me-

chanics,” J. Wiley, New York.Wertz, J. R. (ed.) (1980). “Spacecraft Attitude Determination and Con-

trol,” D. Reidel, Dordrecht.Wilson, C. (1985). “The great inequality of Jupiter and Saturn: from

Kepler to Laplace,” Arch. Hist. Exact Sci. 33, 15.Winter, A. (1949). “Analytic Foundations of Celestial Mechanics,”

Princeton University Press, Princeton.

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Encyclopedia of Physical Science and Technology EN003K-150 June 13, 2001 23:1

Cosmic RadiationPeter L. BiermannMax-Planck Institute for Radioastronomyand University of Bonn

Eun-Suk SeoUniversity of Maryland

I. Introduction and HistoryII. Physical ConceptsIII. Energies, Spectra, and CompositionIV. Origin of Galactic Cosmic RaysV. The Cosmic Rays Between 3 and 50 EeV,

the Expected GZK CutoffVI. Particles beyond the GZK Cutoff

VII. Outlook

GLOSSARY

Active galactic nuclei When massive black holes accrete,their immediate environment, usually thought to con-sist of an accretion disk and a relativistic jet, emits aluminosity often far in excess of the emission of allstars in the host galaxy put together; this phenomenonis called an active galactic nucleus.

Antimatter All particles known to us have antiparti-cles, with opposite properties in all measures, such ascharge.

Big Bang Our universe is continuously expanding, andits earliest stage reachable by our current physical un-derstanding is referred to as the Big Bang.

Black holes Compressing a star to a miniscule size, inthe case of our sun to a radius of 3 × 105 cm, makes itimpossible for any radiation to come out; all particlesand radiation hitting such an object disappear from thisworld. This is called a black hole.

Chemical elements In atoms the number of protons Z

in the nucleus, equal to the number of electrons in thesurrounding shell, determines the chemical element.

Cosmic ray airshower When a primary particle at highenergy, either a photon or a nucleus, comes in to theupper atmosphere, the sequence of interactions and cas-cades forms an air shower.

Cosmic ray ankle At an energy of 3 × 1018 eV, or 3 EeV,there is an upturn in the spectrum, to an approximatespectral index of 2.7 again.

Cosmic ray GZK cutoff The interaction with the cosmicmicrowave background is predicted to produce a strongcutoff in the observed spectrum at 5 × 1019 eV calledthe GZK cutoff. This cutoff is not seen.

Cosmic ray knee At about 5 × 1015 eV, or 5 PeV, thereis a small bend downward in the cosmic ray spectrumby about 0.4 in spectral index, from 2.7 to 3.1.

Cosmic ray spectrum The number of particles at a cer-tain energy E within a certain small energy interval dEis called the spectrum. Flux is usually expresssed asthe number of particles coming in per area, per second,

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824 Cosmic Radiation

per steradian in solid angle (all-sky is 4π ), and perenergy interval.

Elementary particles The natural constituents of normalmatter are the proton, neutron, and electron.

Gamma ray bursts Bursts of gamma ray emission com-ing from the far reaches of the universe, and almostcertainly the result of the creation of a stellar massblack hole.

Interstellar matter The medium between the stars inour Galaxy, which is composed of very hot gas (or-der 4 × 106 K), various stages of cooler gas, down toabout 20 K, dust, cosmic rays, and magnetic fields.

Magnetic monopoles The physics of electric and mag-netic fields contains electric charges but no magneticcharges. In the context of particle physics it is likelythat monopoles, basic magnetically charged particles,also exist.

Microwave background The very high temperature ofthe Big Bang is still visible in the microwave back-ground, a universal radiation field of 2.73 K tem-perature.

Our Galaxy Our Galaxy is a flat, circular, disklike dis-tribution of stars and gas enmeshed with interstellardust and embedded in a spheroidal distribution of oldstars.

Nuclear collisions When elementary particles collidewith each other or with a photon, other particles canbe created that are often unstable.

Radio galaxies In the case that an active galactic nucleusproduces a very powerful and visible jet, often withlobes and hot spots, most readily observable at radiowavelengths, it is called a radio galaxy.

Spallation The destruction of atomic nuclei in a collisionwith another energetic particle such as another nucleusor, commonly, a proton.

Supernovae All stars above an original mass of morethan 8 solar masses are expected to explode at the endof their lifetime after they have exhausted nuclear burn-ing; the observable effect of such an explosion is calleda supernova.

Topological defects It is generally believed that in thevery early times of the universe, when the typical en-ergies were far in excess of what we can produce inaccelerators, there was a phase when the typical en-ergies of what might be called particles was around1024 eV, usually referred to as topological defects, orrelics.

Units: Energy Electron volts (eV); 1 eV is of the orderof what is found in chemical reactions; 1 eV = 1.6 ×10−12 erg.

Units: length Centimeters; the radius of the earth is6.4 × 108 cm and the radius of the Sun is 7 × 1010 cm.

Units: mass Grams; the sun has a mass of 2 × 1033 g; theearth has a mass of 6 × 1027 g.

Units: time Seconds; the travel time of light from the sunto the earth is about 8 min = 480 sec; the number ofseconds in a year is 3.15 × 107.

ENERGETIC PARTICLES, traditionally called cosmicrays, were discovered nearly a 100 years ago and their ori-gin is still uncertain. Their main constituents are the nor-mal nuclei as in the standard cosmic abundances of matter,with some enhancements for the heavier elements; thereare also electrons. Information on isotopic abundancesshows some anomalies as compared with the interstellarmedium. There is also antimatter, such as positrons andantiprotons. The known spectrum extends over energiesfrom a few hundred MeV to 300 EeV (=3 × 1020 eV),and shows a few clear spectral signatures: There is asmall spectral break near 5 PeV (=5 × 1015 eV), com-monly referred to as the knee, where the spectrum turnsdown; and there is another spectral break near 3 EeV(=3 × 1018eV), usually called the ankle, where the spec-trum turns up again. Due to interaction with the mi-crowave background arising from the Big Bang, there isa strong cutoff expected near 50 EeV (=5 × 1019 eV),which is, however, not seen; this expected cutoff is calledthe GZK cutoff after its discoverers, Greisen, Zatsepin,and Kuzmin. The spectral index α is near 2.7 belowthe knee, near 3.1 above the knee, and again near 2.7above the ankle, where this refers to a differential spec-trum of the form E−α . We will describe the various ap-proaches to understanding the origin and physics of cos-mic rays.

I. INTRODUCTION AND HISTORY

Cosmic rays were discovered by Hess and Kohlhorster inthe beginning of the 20th century through their ionizingeffect on airtight vessels of glass enclosing two electrodeswith a high voltage between them. This ionizing effect in-creased with altitude during balloon flights, and thereforethe effect must come from outside the earth, so the termcosmic rays was coined. The earth’s magnetic field actson energetic particles according to their charge, and hencethey are differently affected coming from east and west,and so their charge was detected, proving that they arecharged particles; at high energies near 1018 eV or 1 EeV,there is observational evidence that a small fraction of theparticles are neutral and in fact neutrons. From around1960 onward there has been evidence of particles at orabove 1020 eV, with today about two dozen such eventsknown. After the cosmic microwave background was dis-covered in the early 1960s, it was noted only a little later byGreisen, Zatsepin, and Kuzmin that near and above an en-ergy of 5 × 1019 eV (called the GZK cutoff) the interaction



Cosmic Radiation 825

with the microwave background would lead to stronglosses if these particles were protons, as is now believedon the basis of detailed air shower data. In such an interac-tion, protons see the photon as having an energy of abovethe pion mass, and so pions can be produced in the refer-ence frame of the collision, leading to about a 20% energyloss of the proton in the observer frame. Therefore foran assumed cosmologically homogeneous distribution ofsources for protons at extreme energies, a spectrum at earthis predicted which shows a strong cutoff at 5 × 1019 eV,the GZK cutoff. This cutoff is not seen, leading to manyspeculations as to the nature of these particles and theirorigin.

Cosmic rays are measured with instruments on bal-loon flights, satellites, the Space Shuttle, the InternationalSpace Station, and with ground arrays. The instrumentchosen depends strongly on what is being looked for andthe energy of the primary particle. One of the most success-ful campaigns has been with balloon flights in Antarctica,where a balloon can float at about 40 km altitude and cir-cumnavigate the South Pole once and possibly even sev-eral times during one Antarctic summer. For very high pre-cision measurements very large instruments on the SpaceShuttle or the International Space Station are used, suchas for the search for antimatter.

Critical measurements are the exact spectra of the mostcommon elements, hydrogen and helium, the fraction ofantiparticles (antiprotons and positrons), isotopic ratiosof elements such as neon and iron, the ratio of spallationproducts such as boron to primary nuclei such as carbonas a function of energy, the chemical composition near theknee, at about 5 × 1015 eV, and beyond, and the spectrumand nature of the particles beyond the ankle, at 3 × 1018 eV,with special emphasis on the particles beyond the GZKcutoff, at 5 × 1019 eV.

II. PHYSICAL CONCEPTS

Here we expand upon the terms explained briefly in theGlossary.

• Big Bang. Our universe is continuously expanding,and its earliest stage reachable by our current physical un-derstanding is referred to as the Big Bang, when energydensities were extremely high. Within the first 3 min thechemical elements such as hydrogen and helium were pro-duced, and minute amounts of deuterium (an isotope ofhydrogen), 3He, an isotope of helium, and 7Li, an isotopeof the third element, lithium.

• Microwave background. The very high temperatureof the Big Bang is still visible in the microwave back-ground, a universal radiation field of 2.73 K. There is acorresponding cosmic bath of low-energy neutrinos. Both

photons and neutrinos have a density of a few hundred percubic centimeter.

• Units: length Centimeters; the radius of the earth is6.4 × 108 cm and the radius of the sun is 7 × 1010 cm. Thedistance from earth to sun is 1.5 × 1013 cm. One pc =parsec = 3.086 × 1018 cm, 1 kpc = 103 pc, 1 Mpc =106 pc; 1 pc is about 3 light-years, the distance traveledby light in 3 years; the speed of light c is 3×1010 cm/sec,and is the same in any inertial reference frame. The basiclength scale of the universe is about 4000 Mpc.

• Units: mass. Grams; the sun has a mass of 2 × 1033 g.The earth has a mass of 6 × 1027 g. A typical galaxy likeour own has a mass of order 1011 solar masses. A protonhas a mass of 1.67 × 1027 g.

• Units: time Seconds; the travel time of light from thesun to the earth is about 8 min = 480 sec; the number ofseconds in a year is 3.15 × 107. The age of the solar systemis about 4.5 × 109 years, and the age of our Galaxy andalso of our universe is about 1.5 × 1010 years; our galaxyis younger than the universe, but we do not know the twoages well enough to determine the difference with anyreliability.

• Units: energy. Electron volts (eV); 1 eV is of theorder of what is found in chemical reactions, 1 eV = 1.6 ×10−12 erg; 1 MeV = 106 eV, 1 GeV = 109 eV, 1 TeV =1012 eV, 1 PeV = 1015 eV, 1 EeV = 1015 eV.

• Elementary particles. The natural constituents ofmatter are the proton, neutron, and electron. Protons havea mass of about 938 MeV, neutrons of about 940 MeV, andelectrons of about 0.511 MeV. This is in energy units usingEinstein’s equivalence E = mc2, where E is the energy, mthe rest mass, and c the speed of light. The proton is pos-itively charged, the electron negatively charged, with thesame charge as the proton, and the neutron is neutral. Allatomic nuclei are built from protons and neutrons, wherethe number of protons determines the chemical element,and the number of neutrons determines the various iso-topes of each chemical element. The surrounding shell ofelectrons has for the neutral atom exactly the same num-ber of electrons as the nucleus has protons. Photons areanother primary stable constituent, have no rest mass, nocharge, and always travel at the speed of light, in anyframe of reference. Neutrinos come in three varieties, andappear to continuously change among themselves; theyhave a very low mass.

• Antimatter. All known particles have antiparticles,with opposite properties in all measures, such as charge.The collision of a particle and its antiparticle always leadsto a burst of radiation, when both particles are annihilated.In cosmic rays we observe antiprotons, and positrons,the antiparticles to electrons. The search for antinucleihas not been successful; any detection of even a singleantinucleus, such as antihelium, would provide extremelystrong constraints on the physics of matter in the universe.




The instrument AMS, first on the Space Shuttle, and thenthe International Space Station, will search for antimatterparticles.

• Nuclear collisions. When elementary particles col-lide with each other or with a photon, other particles canbe created that are often unstable, i.e., they decay intoother particles and continue to do so until they reach astate where only stable particles result. Such a process iscalled a cascade. Common intermediate and final parti-cles are the pion, the muon, the photon, and the neutrino.The pion comes in various forms, charged and uncharged,the muon is always charged, and the neutrino is alwaysneutral. The neutrino is characterized by a very small in-teraction cross section with matter. The pions have a mass,again in energy equivalents, of about 140 MeV, the muonsof about 106 MeV, and the neutrinos of about 0.03 eV, astill rather uncertain number.

• Chemical elements. In atoms the number of protonsZ in the nucleus, equal to the number of electrons in thesurrounding shell, determines the chemical element. Thenumber of neutrons in the nucleus is approximately equalto the number of protons. Chemical elements are nowknown to beyond Z of 110. The first and most commonelements are hydrogen (Z = 1), helium (2), carbon (6),oxygen (8), neon (10), magnesium (12), silicon (14), sul-fur (16), calcium (20), and iron (26). The intermediateelements lithium (Z = 3), beryllium (4), and boron (5) arevery rare. The odd-Z elements are commonly rarer thanthe even-Z elements. The overall abundance by mass isabout 73% for hydrogen, 25% for helium, and the rest allother elements combined, with the most abundant amongthese being carbon and oxygen.

• Cosmic ray airshower. When a primary particle athigh energy, either a photon or a nucleus, comes into theupper atmosphere, the sequence of interactions and cas-cades forms an airshower. These airshowers are domi-nated by electrons and photons generated in electromag-netic subshowers. Cerenkov light, a bluish light, is emittedin a narrow cone around the shower direction, producedwhen particles travel at a speed (always less than or equalto c; particles have exactly the speed of light at zero restmass, such as photons) higher than the speed of light cdivided by the local index of refraction (which is 4/3 inwater, for instance, and about 1.0003 in air). Observingthis bluish light allows observations of high-GeV-to-TeVphoton sources in the sky because Cerenkov light allowsgood pointing. For particles such as protons or atomicnuclei at high energy, air fluorescence can be used as ameans of observation, advantageous because it is omni-directional in its emission and gives enough light at highenergy: Such fluorescence occurs when normal emissionlines of air molecules are excited. The airshower includesa pancake of secondary electrons and positrons as well

as muons. The ratio between Cerenkov light and fluores-cence light is almost constant and independent of particleenergy. Most modern observations of very high energycosmic rays are done either by observing the air fluores-cence (arrays such as Fly’s Eye, HIRES, or AUGER) or byobserving the secondary electrons and positrons (in arrayssuch as Haverah Park, AGASA, Yakutsk, or also AUGER).In the future such observations may be possible fromspace by observing the air fluorescence or the reflectedCerenkov light from either the International Space Stationor from dedicated satellites. Fly’s Eye was and HIRES isin Utah, AUGER is in Argentina, AGASA is in Japan,Yakutsk is in Russia, and Haverah Park was in the UnitedKingdom.

• Spallation. Spallation is the destruction of atomic nu-clei in a collision with another energetic particle, such asanother nucleus, or commonly a proton. In this destructionmany pieces of debris can be formed, with one commonresult being the stripping of just one proton or neutron,and another common result a distribution of smaller unitnuclei. Since the proton number determines the chemi-cal element, such debris is usually other nuclei, such asboron.

• Cosmic ray spectrum. The number of particles at acertain energy E within a certain small energy interval dEis called the spectrum. As a function of energy E this isusually described by power laws, such as E−2.7 dE ; theexponent is called the spectral index, here 2.7. Heat radi-ation from a normal object has a very curved spectrum inphotons. Cosmic rays usually have a power-law spectrum,which is called a nonthermal behavior. Flux is usually ex-presssed as the number of particles coming in per area,per second, per solid angle in steradians (all-sky is 4π ),and per energy interval.

• Cosmic ray knee. At about 5 × 1015 eV, or 5 PeV,there is a small bend downward in the cosmic ray spec-trum, by about 0.4 in spectral index, from 2.7 to 3.1. Thisfeature is called the knee. There is some evidence thatit occurs at a constant energy-to-charge ratio for differentnuclei. There is also considerable evidence that toward andat the knee the chemical composition slowly increases infavor of heavier nuclei such as iron. A similar somewhatweaker feature is suggested by new AGASA and HIRESdata near 3 × 1017 eV, where again the spectrum turnsdown a bit more.

• Cosmic ray ankle. At an energy of 3 × 1018 eV, or3 EeV, there is an upturn in the spectrum, to an approxi-mate spectral index of 2.7 again. At the same energy thereis evidence that the chemical composition changes frommoderately heavy to light, i.e., back to mostly hydrogenand helium.

• Cosmic ray GZK cutoff. The interaction with the cos-mic microwave background should produce a strong cutoff




in the observed spectrum at 5 × 1019 eV called the GZKcutoff; this is provided that (a) these particles are protons(or neutrons) and (b) the source distribution is homoge-neous in the universe. This cutoff is not seen; in fact, nocutoff is seen at any energy, up to the limit of data, at3 × 1020 eV, or 300 EeV. This is one of the most seriousproblems facing cosmic ray physics today.

• Black holes. Compressing a star to a miniscule size,in the case of our sun, to a radius of 3 × 105 cm, makes itimpossible for any radiation to come out; all particles andradiation hitting such an object disappear from this world.This is called a black hole. It is now believed that almostall galaxies have a massive black hole at their center, withmasses sometimes ranging up 1010 solar masses, but usu-ally much less. There are also stellar mass black holes, buttheir number is not well known, probably many thousandsin each galaxy.

• Our Galaxy. Our Galaxy is a flat, circular, disklikedistribution of stars and gas enmeshed with interstellardust and embedded in a spheroidal distribution of old stars.The age of this system is about 15 billion (=15 × 109)years; its size is about 30 kpc across, and its inner regionis about 6 kpc across. At its very center there is a blackhole with 2.6 × 106 solar masses. The gravitational fieldis dominated in the outer parts of the Galaxy by an un-known component, called dark matter, which we deduceonly through its gravitational force. In the innermost partof the Galaxy normal matter dominates. The mass ratio ofdark matter to stars to interstellar matter in our Galaxy isabout 100:10:1. Averaged over the nearby universe theseratios are shifted in favor of gas, with gas dominating overstars probably, but with dark matter still dominating overstars and gas by a large factor.

• Interstellar matter. The medium between the stars inour Galaxy is composed of very hot gas (order 4 × 106 K),various stages of cooler gas, down to about 20 K, dust,cosmic rays, and magnetic fields. All three components,gas, cosmic rays, and magnetic fields, have approximatelythe same energy density, which happens to be also closeto the energy density of the microwave background, about1 eV/cm3. The average density of the neutral hydrogengas, of temperature a few 1010 K to a few 103 K, is about1 partcile/cm3, but highly clumped, in a disk of thicknessabout 100 pc (=3 × 1020 cm). The very hot gas extendsmuch farther from the symmetry plane, about 2 kpc oneither side.

• Supernovae. All stars above an original mass of morethan 8 solar masses are expected to explode at the end oftheir lifetime after they have exhausted nuclear burning;the observable effect of such an explosion is called a super-nova. When they explode, they emit about 3 × 1053 ergs inneutrinos and also about 1051 erg in visible energy, suchas in shock waves in ordinary matter, the former stellar

envelope, and interstellar gas. These neutrinos have anenergy in the range of a few MeV to about 20 MeV. Whenstars are in stellar binary systems, they can also explodeat low mass, but this process is believed to give only 10%or less of all stellar explosions. The connection to gammaray bursts is not clear. It is noteworthy that above an orig-inal stellar mass of about 15 solar masses, stars also havea strong stellar wind, which for original masses above 25solar masses becomes so strong that it can blow out a largefraction of the original stellar mass even before the star ex-plodes as a supernova. The energy in this wind, integratedover the lifetime of the star, can attain the visible energyof the subsequent supernova, as seen in the shock wave ofthe explosion.

• Gamma ray bursts. Bursts of gamma ray emissioncome from the far reaches of the universe, almost certainlythe result of the creation of a stellar-mass black hole. Theduration of these bursts ranges from a fraction of a sec-ond to usually a few seconds, and sometimes hundredsof seconds. Some gamma ray bursts have afterglows inother wavelengths like radio, optical, and X rays, with anoptical brightness which very rarely comes close to beingdetectable with standard binoculars. The emission peaksnear 100 keV in observable photon energy, and appears tohave an underlying power-law character, suggesting non-thermal emission processes.

• Active galactic nuclei. When massive black holesaccrete, their immediate environment, usually thought toconsist of an accretion disk and a relativistic jet (i.e., wherethe material flies with a speed very close to the speed oflight), emits a luminosity often far in excess of the emis-sion of all stars in the host galaxy put together. There aresuch black holes of a mass near 108 solar masses, with asize of order the diameter of the earth orbit around the sunand a total emission of 1000 times that of all stars in theirhost galaxy.

• Radio galaxies. In the case that an active galacticnucleus produces a very powerful and visible jet, oftentogether with lobes and hot spots, most readily observableat radio wavelengths, it is called a radio galaxy. The radioimage of such a galaxy can extend to 300 kpc or more,dissipating the jet in radio hot spots embedded in giantradio lobes. The frequency of such radio galaxies withpowerful jets, hot spots, and lobes is rare, less than 1/1000of all galaxies, but in the radio sky they dominate due totheir extreme emission.

• Topological defects. It is generally believed that in thevery early times of the universe, when the typical energieswere far in excess of what we can produce in accelerators,there was a phase when the typical energies of what mightbe called particles was around 1024 eV, usually referredto as topological defects, or relics. It is conveivable thatsuch particles have survived to today, and some of them




decay, emitting a copious number of neutrinos, photons,and also protons. These particles then themselves wouldhave near 1024 eV initially, but interact strongly with thecosmic radiation field.

• Magnetic monopoles. The physics of electric andmagnetic fields contains electric charges but no magneticcharges. In the context of particle physics it is likely thatmonopoles, basic magnetically charged particles, also ex-ist. Such monopoles are a special kind of topological de-fect. The basic property of magnetic monopoles can bedescribed as follows: (a) Just as electrically charged par-ticles short-circuit electric fields, monopoles short-circuitmagnetic fields. The observation of very large scale andpermeating magnetic fields in the cosmos shows that theuniversal flux of monopoles is very low. (b) Monopoles areaccelerated in magnetic fields, just as electrically chargedparticles are accelerated in electric fields. In cosmic mag-netic fields, the energies which can be attained are of order1021 eV or more. Any relation to the observed high-energycosmic rays is uncertain at present.

III. ENERGIES, SPECTRA,AND COMPOSITION

The solar wind prevents low-energy charged articles fromentering the inner solar system due to interaction with themagnetic field in the solar wind, a steady stream of gasgoing out from the sun into all directions, originally dis-covered in 1950 from the effect on cometary tails: theyall point outward, at all latitudes of the sun, and inde-pendent of whether the comet actually comes into theinner solar system or goes outward, in which case thetail actually precedes the head of the comet. This pre-vents us from knowing anything about interstellar ener-getic particles with energies lower than about 300 MeV.Above about 10 GeV per charge unit Z of the particle, theeffect of the solar wind becomes negligible. Since cos-mic ray particles are mostly fully ionized nuclei (withthe exception of electrons and positrons), this is a strongeffect.

Our Galaxy has a magnetic field of about 6 × 10−6 Gin the solar neighborhood; the energy density of such afield corresponds approximately to 1 eV/cm3, just like theother components of the interstellar medium. In such amagnetic field charged energetic particles gyrate with aradius of gyration called the Larmor radius, which is pro-portional to the momentum of the particle perpendicularto the magnetic field direction. For highly relativistic par-ticles this entails that around 3 × 1018-eV protons, or othernuclei of the same energy-to-charge ratio, no longer gy-rate in the disk of the Galaxy, i.e., their radius of gyrationis larger than the thickness of the disk. Thus, they cannotpossibly originate in the Galaxy, and must come from out-

side; indeed, at that energy there is evidence for a changeboth in chemical composition and in the slope of thespectrum.

The energies of these cosmic ray particles that we ob-serve range from a few hundred MeV to 300 EeV. Theintegral flux ranges from about 10−5 per cm2, per sec, persterad at 1 TeV per nucleus for hydrogen or protons, to 1particle per sterad per km2 and per century around 1020 eV,a decrease by a factor of 3 × 1015 in integral flux, and acorresponding decrease by a factor of 3 × 1023 in the spec-trum, i.e., per energy interval, which means in differentialflux. Electrons have only been measured to a few TeV.

The total particle spectrum spectrum is about E−2.7 be-low the knee and about E−3.1 above the knee, at 5 PeV, andflattens again to about E−2.7 beyond the ankle, at about3 EeV. Electrons have a spectrum which is similar to thatof protons below about 10 GeV, and steeper near E−3.3

above this energy. The lower energy spectrum of elec-trons is inferred from radio emission, while the steeperspectrum at the higher energies is measured directly(Fig. 1).

The chemical composition is rather close to that of theinterstellar medium, with a few strong peculiarities rela-tive to that of the interstellar medium: (a) hydrogen andhelium are less common relative to silicon. Also, the ratioof hydrogen to helium is smaller. (b) lithium, beryllium,and boron, the odd-Z elements, as well as the sub-ironelements (i.e., those with Z somewhat less than iron) areall enhanced relative to the interstellar medium (Fig. 3).(c) Many isotope ratios are quite different, while some areidentical. (d) Among the cosmic ray particles there are ra-dioactive isotopes, which give an age of the particles sinceacceleration and injection of about 3 × 107 years. (e) To-ward the knee and beyond the fraction of heavy elementsappears to continuously increase, with moderately heavyto heavy elements almost certainly dominating beyondthe knee, all the way to the ankle, where the compositionbecomes light again. This means that at that energy we ob-serve a transition to what appears to be mostly hydrogenand helium nuclei. At much higher energies we can onlyshow consistency with a continuation of these properties;we cannot prove unambiguously what the nature of theseparticles is.

The fraction of antiparticles, ie., positrons and antipro-tons, is a few percent for the positron fraction and a few104 for antiprotons. No other antinuclei have been found(Figs. 3–5).

There is no significant anisotropy of cosmic rays at anyenergy, not even at the highest energies, beyond the GZKcutoff. Only at those highest energies is there a persistenthint that events at quite different energies occasionallycluster into pairs and triplets in the sky in the arrival direc-tion, and this is hard to understand in almost any model.




FIGURE 1 The Galaxy with some sample orbits of low energy and high energy cosmic ray particles. The Galaxy isshown with the disk and the spherodial component of older stars.

IV. ORIGIN OF GALACTIC COSMIC RAYS

It has been long surmised that supernova explosions pro-vide the bulk of the acceleration of cosmic rays in theGalaxy. The acceleration is thought to be a kind of ping-pong effect between the two sides of the strong shock wavesent out by the explosion of a star. This ping-pong effectis a repeated reflection via the magnetic resonant inter-action between the gyromotion of the energetic chargedparticles and waves of the same wavelength as the Larmormotion in the magnetic thermal gas. Since the reflectionis usually thought to be a gradual diffusion in direction,the process is called diffusive shock acceleration, or, afterits discoverer, Fermi acceleration.

For a shock wave sent out directly into the interstellargas this kind of acceleration easily provides particle en-ergies up to about 100 TeV. While the detailed injectionmechanism is not quite clear, the very fact that we observethe emission of particles at these energies in X rays pro-vides a good case and a rather direct argument for highlyenergetic electrons. Even though protons are by a factor ofabout 100 more abundant than electrons at energies near

1 GeV, we cannot yet prove directly that supernova shocksprovide the acceleration; only the analogy with electronscan be demonstrated.

However, we observe what ought to be galactic cosmicrays up to energies near the knee, and beyond to the ankle,i.e., 3 EeV.

The energies, especially for particles beyond 100 TeV,can be provided by several possibilities, with the only the-ory worked out to a quantitative level suggesting that thoseparticles also get accelerated in supernova shock waves,in those which run through the powerful stellar wind ofthe predecessor star. Then it can be shown that energiesup to 3 EeV per particle are possible (mostly iron). Analternate possibility is that a ping-pong effect betweenvarious supernova shock waves occurs, but in this caseseen from outside. In either (or any other) such theoryit is a problem that we observe a knee, i.e., a downwardbend of the spectrum at an energy-to-charge ratio whichappears to be fairly sharply defined. The concept that stel-lar explosions are at the origin entails that all such starsare closely similar in their properties, including their mag-netic field, at the time of explosion; this implies a specific




FIGURE 2 The proton and helium spectra at low energy. [FromSuzuki, T., et al. (2000). “Precise measurements of cosmic-rayproton and helium spectra with BESS spectrometer,” Astrophys. J.545, 1135–1142; The AMS Collaboration. (2000). “Protons in nearearth orbit,” Phys. Lett. B 472, 215–226; The AMS Collaboration.(2000). “Helium in near earth orbit,” Phys. Lett. B 494, 193–202.]

length scale in the explosion, connected to the thicknessof the matter of the wind snowplowed together by thesupernova shock wave. While this is certainly possible,we have too little information on the magnetic field ofpre-supernova stars to verify or falsify this. In the case ofthe other concept it means that the transport through theinterstellar gas has change in properties also at a fairlysharply defined energy-to-charge ratio, indicating a spe-cial scale in the interstellar gas, for which there is no otherevidence.

Galactic cosmic rays get injected from their sourceswith a certain spectrum. While they travel through theGalaxy from the site of injection to escape or to the ob-server, they have a certain chance to leak out from thehot magnetic disk of several kpc full-width thickness ofthe Galaxy; occasionally this thick disk is referred to asthe halo. The escape of cosmic rays becomes easier withhigher energy. As a consequence their spectrum steepens,as shown by comparing source and observed spectrum.The radio observations of other galaxies show consistencywith the understanding that the average spectrum of cos-

mic rays at least in the GeV to many GeV energy range isalways the same in various locations in a galaxy and alsoin different galaxies. During this travel inside a galaxythe cosmic rays interact with the interstellar gas, and inthis interaction produce gamma ray emission from piondecay, positrons, and also neutrons, antiprotons, and neu-trinos. The future gamma ray emission observations ofthe galactic disk will certainly provide very strong con-straints on this aspect of cosmic rays. In these interac-tions secondary nuclei and isotopes are also produced byspallation. This spallation also gives secondary isotopessuch as 10Be, which is radioactive and decays with a half-life of 1.6 × 106 years, allowing models of cosmic raypropagation to be tested.

One kind of evidence about where cosmic rays comefrom and what kind of stars and stellar explosions reallydominate among their sources is the isotopic ratios of vari-ous isotopes of neon, iron, and other heavy elements; theseisotope ratios suggest that at least one population is indeedthe very massive stars with strong stellar winds; however,whether these stars provide most of the heavier elements,as one theory proposes, is still quite an open question.

Antimatter as observed today can all be produced innormal cosmic ray interactions. However, even the de-tection of a single antinucleus of an element such ashelium would constitute proof that the universe con-tains antimatter regions and would radically change ourperception of the matter–antimatter symmetries in ourworld.

There is some evidence that just near EeV energies thereis one component of galactic cosmic rays which is spa-tially associated in arrival direction with the two regionsof highest activity in our Galaxy, at least as seen fromearth: the Galactic Center region as well as the Cygnusregion show some weak enhancement. Such a directionalassociation is only possible for neutral particles, and sinceneutrons at that energy can just about travel from those re-gions to here before they decay (only free neutrons decay,neutrons bound into a nucleus do not decay), a productionof neutrons in cosmic ray interactions is conceivable asone explanation of these data.

V. THE COSMIC RAYS BETWEEN 3 AND50 EeV, THE EXPECTED GZK CUTOFF

The cosmic rays between the ankle and the expected GZKcutoff are readily explained by many possible sources,almost all outside our Galaxy.

Some, but not all of these proposals can also explainparticles beyond the GZK cutoff, discussed in a separatesection.




FIGURE 3 The surviving fraction of 10Be in data and a comparison with models of cosmic ray propagation. [FromPtuskin, V. S. (2000). “Cosmic ray transport in the galaxy,” In “ACE-2000 Symposium” (R. A. Mewaldt et al., eds.), pp.390–395, AIP, Melville, NY.]

Pulsars, especially those with very high magnetic fields,called magnetars, can almost certainly accelerate chargedparticles to energies of 1021 eV. There are several prob-lems with such a notion, one being the adiabatic losses onthe way from close to the pulsar out to the interstellar gas,and another one the sky distribution, which should be veryanisotropic given the distribution and strength of galacticmagnetic fields. On the other hand, if this concept couldbe proven, it would certainly provide a very easy expla-

nation for why there are particles beyond the GZK cutoff:for galactic particles the interaction with the microwavebackground is totally irrelevant, and so no GZK cutoff isexpected.

Another proposal is gamma ray bursts. However, sincewe know that the bulk of gamma ray bursts arise from stel-lar explosions at cosmological distances this notion is hardto maintain. The frequency of nearby gamma ray bursts istoo small to provide any appreciable flux. However, since




FIGURE 4 The positron fraction compared with various models of cosmic ray interaction. [From Coutu, St., et al.(1999). “Cosmic-ray positrons: Are there primary sources?” Astrophys. J. 11, 429–435; The AMS Collaboration.(2000). “Leptons in near earth orbit,” Phys. Lett. B 484, 1022; Wiebel-Sooth, B., and Biermann, P. L. (1999). “Cosmicrays,” In “Landolt-Bornstein,” Vol. VI/3c, pp. 37–90, Springer-Verlag, Berlin.

ultimately we do not yet know what constitutes a gammaray burst, their contribution cannot be settled with fullcertainty.

Shock waves running through a magnetic and ionizedgas accelerate charged particles, as we know from in situobservations in the solar wind, and this forms the basisof almost all theories to account for galactic cosmic rays.The largest shock waves in the universe have scales ofmany tens of Mpc, and have shock velocities of around

FIGURE 5 The antiproton spectrum. [From Yoshimura, K., et al.(2000). “Cosmic-ray antiproton and antinuclei,” Advan. SpaceRes., in press.]

1000 km/sec. These shock waves arise in cosmologicallarge-scale structure formation, seen as a soap-bubble-likedistribution of galaxies in the universe. The accretion flowto enhance the matter density in the resulting sheets andfilaments is continuing, and causes shock waves to ex-ist all around us. In such shock waves, which also havebeen shown to form around growing clusters of galaxies,particles can be accelerated and can attain fairly high en-ergies. However, the maximum energies can barely reachthe energy of the GZK cutoff.

The most conventional and easiest explanation is ra-dio galaxies, of which provide the hot spots an obviousacceleration site: These hot spots are giant shock waves,often of a size exceeding that of our entire Galaxy. Theshock speeds may approach several percent, maybe evenseveral tens of percent, of the speed of light. Therefore, inthis interpretation, these radio galaxy hot spots provide avery straightforward acceleration site. Integrating over allknown radio galaxies readily explains the flux and spec-trum as well as chemical composition of the cosmic raysin this energy range, and quite possibly also beyond.

VI. PARTICLES BEYONDTHE GZK CUTOFF

Since we do not observe the expected GZK cutoff, weneed to look for particles which defy the interaction withthe microwave background or for a source distributionwhich reduces the time for interaction with the microwavebackground substantially.

Here we emphasize those concepts which can explainthe events beyond the GZK cutoff; these proposals do notnecessarily also explain those particles below the expectedcutoff.




FIGURE 6 The antihelium limits at present. [From Yoshimura, K., et al. (2000). “Cosmic-ray antiproton and antinuclei,”Advan. Space Res., in press.]

A source distribution which is closely patterned after theactual galaxy distribution in the nearby universe greatlyenhances the expected flux of events near the GZK cutoffand may allow an interpretation of the observed eventsgiven a properly biased version of the galaxy distributionand a source population like a special class of galaxies.

However, the data are also compatible with a spectrumwhich suggests a rise beyond the expected GZK cutoff,and this strongly hints at a totally different and new eventclass. This supports an interpretation as the result of the

decay of primordial relics, with an energy of 1024 eV.Such a decay produces a large number of highly ener-getic neutrinos, photons, and only 3% of ultimately pro-tons. Since these protons start with a much flatter spectrumthan normal cosmic rays, and also have such extreme ini-tial energies, the lack of a GZK cuotff can be understood.There is, however, a strong prediction: The large num-ber of photons produced yields a cascade that gives riseto a strong contribution to the gamma ray background.This gamma ray background adds to all the gamma rays




produced by active galactic nuclei. It is not finally re-solved whether observations exclude this option becauseof an excessive gamma ray background or whether theactual spectrum of the gamma ray background in factsupports it.

There is an interesting variant of this idea, and that isto consider neutrinos which come from large distances inthe universe and interact with the local relic neutrinos (thepopulation of Big Bang neutrinos predicted by standardBig Bang theory, akin to the microwave background). Insuch a theory, the low density of relic neutrinos may be aserious problem.

Obviously, if we could understand the sky distributionof events at these extreme energies, then the option of usingpulsars would become very attractive. For particles with asingle charge as protons, the anisotropies in arrival direc-tions would be severe, but for iron nuclei this constraintwould be much alleviated. Therefore, the option of con-sidering pulsars entails an interpretation as iron particles,inconsistent at the transition from galactic to extragalacticcosmic rays at about 3 EeV, but conceivable at a possibletransition from one source population to another at theexpected GZK cutoff.

On the other hand, these particles could be somethingvery different, as occasionally speculated, particles sug-gested by some versions of an extension of particle physicsthat may not interact with the microwave background andyet interact in the atmosphere very similarly to protons.In this case, we may ask what sources produce so extremeparticles. The class of compact radio galaxies has a power-ful jet, and hot spots that live currently inside a very largeamount of local interstellar gas, and so provide both ac-celerator and beam dump, i.e., make a particle physics ex-periment in the sky. However, whether anything detectablecomes down to us is open to question.

Finally, it has been shown that radio galaxy hot spotscan in fact accelerate protons to the required energies.Here the difficulty is to identify the single most importantsource for the events at the highest energies. One idea,originally suggested around 1960, has been to considerthe nearby radio galaxy M87. It has several advantages,and also disadvantages: First, the main problem with thisnotion is that the events do not show any clustering in di-rection with the direction to M87, which is in the nearbyVirgo cluster, and so magnetic scattering or bending isrequired. On the other hand, M87 clearly can accelerateprotons to the required energies, and in fact one needssuch protons to explain its nonthermal spectrum. Inter-galactic magnetic fields and also the fields in our galactichalo can bend and maybe even scatter the orbits of veryenergetic charged particles. These intergalactic magneticfields clearly play the key role here, and have not been fullyunderstood.

In conclusion, the origin of the events beyond the ex-pected GZK cutoff remains a unsolved problem in modernhigh-energy physics.

VII. OUTLOOK

The origin of cosmic rays with observed particle energiesto 300 EeV remains an unsolved problem.

A number of efforts related to cosmic rays will surelyhelp our understanding:

� The determination of gamma ray spectra and maps ofthe Galaxy at high energy.

� More information on stellar evolution includingrotation and magnetic fields. Are massive stars allconverging to a small set of final states, whichincludes the magnetic field?

� The search to determine the strength and structure ofcosmic magnetic fields, both in the halo of galaxiesand in the web of the cosmological galaxydistribution. Clearly this is the key to understand thepropagation of high-energy cosmic rays.

� The search for possible correlations in arrivaldirections of high-energy cosmic rays withastronomical sources. If there were such a subset ofevents, it would provide very strong constraints on thenature of the particles, as already is the case withsome events near EeV energies. At higher energies itmight provide new constraints on models for thefundamental properties of particles.

Progress in our understanding of cosmic rays will bemainly determined by much better data:

� Very accurate spectra, at low energies, such as nowavailable from the first AMS data.

� Very accurate data on antimatter, positrons,antiprotons, and antinuclei, also from AMS andextended campaigns of balloon flights.

� Very accurate data on isotopic ratios, from a newgeneration of balloon flights.

� Accurate chemical composition near the knee andbeyond.

� Accurate spectra, sky distribution, and information onthe nature of particles in the three energy ranges fromthe knee to the ankle, through the energy range from3 EeV to 50 EeV, the expected GZK cutoff, andbeyond.

The search for the origin of cosmic rays promises toremain at the focus of research in physics in the 21stcentury.




ACKNOWLEDGMENTS

The authors would like to thank Ray Protheroe and Todor Stanev forvery helpful comments. We thank Sera Markoff and Ramin Sina for helpwith the graphs.


COSMIC INFLATION • COSMOLOGY • GAMMA-RAY AS-TRONOMY • INFRARED ASTRONOMY • NEUTRINO AS-TRONOMY • PARTICLE PHYSICS, ELEMENTARY • RADI-ATION PHYSICS • SOLAR PHYSICS • SUPERNOVAE

BIBLIOGRAPHY

Bhattacharjee, P., and Sigl, G. (2000). “Origin and propagation of ex-tremely high-energy cosmic rays,” Phys. Rep. 327, 109–247.

Biermann, P. L. (1997a). “The origin of the highest energy cosmic rays,”J. Phys. G 23, 1–27.

Biermann, P. L. (1997b). “Supernova blast waves and pre-supernovawinds: Their cosmic ray contribution,” In “Cosmic Winds and theHeliosphere,” (J. R. Jokipii et al., eds.), pp. 887–957, University ofArizona Press, Tucson, AZ.

Clay, R., and Dawson, B. (1998). “Cosmic Bullets,” Addison-Wesley,Reading, MA.

Diehl, R., Kallenbach, R., Parizot, E., and von Steiger, R. (eds.) (2001).“The Astrophysics of Galactic Cosmic Rays,” Kluwer, Dordrecht.

Kronberg, P. P. (2000). “Magnetic fields in the extragalactic universe,and scenarios since recombination for their origin—A review,” In“Proceedings the Origins of Galactic Magnetic Fields,” Manchester,England.

Longair, M. S. (1992/1994). “High Energy Astrophysics,” Vols. 1 and 2;2nd ed., Cambridge Univesity Press, Cambridge.

Nagano, M., and Watson, A. A. (2000). “Observations and implicationsof the ultra-high energy cosmic rays,” Rev. Mod. Phys. 72, 689–732.

Piran, T. (1999). “Gamma-ray bursts and the fireball model,” Phys. Rep.314, 575.

Wiebel-Sooth, B., and Biermann, P. L. (1999). “Cosmic rays,” In“Landolt-Bornstein,” Vol. VI/3c, pp. 37–90, Springer-Verlag, Berlin.

P1: GGY/LOW P2: FLW Final Pages

Encyclopedia of Physical Science and Technology EN003C-151 June 13, 2001 23:2

CosmologyJohn J. DyklaLoyola University Chicago and Theoretical Astrophysics Group, Fermilab

I. Issues from Prescientific InquiriesII. Origins of Modern Cosmology in ScienceIII. Revolutions of the Twentieth CenturyIV. Unsolved Classical ProblemsV. Interaction of Quantum Physics and Cosmology

VI. Thoughts on Sources of Future Progress

GLOSSARY

Background radiation Field quanta, either photonsor neutrinos, presumably created in an early high-temperature phase of the universe. The photons lastinteracted strongly with matter before the temperaturefell below 3000 K and electrons combined with nu-clei to form neutral, transparent hydrogen and heliumatoms. Although shifted to the radio spectrum by theexpansion of the universe, this “light” has been mov-ing independently since this decoupling (in the standardmodel, ∼700,000 years after the “big bang”), provid-ing direct evidence of how different the universe was atthis early time from its appearance now. The measuredhomogeneity and isotropy of the photon backgroundare very difficult to account for in models, such as the“steady-state” theories, which avoid a “big bang.”

Black hole Region of space-time with so large a curva-ture (gravitational field) that, classically, it prevents anymatter or radiation from leaving. The “one-way” sur-face, which allows passage into the black hole but notout, is called an event horizon. Black holes are com-pletely characterized by their mass, charge, and angularmomentum.

Cosmological principle The assumption that at each mo-ment of proper time an observer at any place in the uni-verse would find the large-scale structure of surround-ing matter and space the same as any other observer(homogeneity) and appearing the same in all directions(isotropy). Combined with the general theory of rela-tivity, this forms the basis of the standard model incosmology. Observational evidence for the expansionof the universe, combined with the principle of con-servation of mass–energy, indicates that the large-scaleaverage density, though everywhere the same at a giventime, is decreasing as the universe evolves. The perfectcosmological principle seeks to avoid a “big bang” byasserting that the homogeneous and isotropic densityof matter at all points in space is also unchanging intime. Such an assumption could be reconciled with anexpanding universe only by postulating the continuouscreation of matter and appears untenable in light of themicrowave background radiation.

Dark matter problem The discrepancy by approxi-mately an order of magnitude between the ordinarymatter that is directly visible through astronomical ob-servations and the mass inferred from dynamic the-ory applied to the observed motions of galaxies and

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clusters of galaxies. The calculated average density isroughly the critical value for a flat universe, which isalso strongly favored by “inflationary” particle physicsscenarios. Thus, various exotic forms of astronomicalobjects and elementary particles have been proposed toaccount for the dark matter assumed present.

Doppler shift Change in frequency (or, inversely becauseof invariant speed of propagation, wavelength) of radi-ation due to the relative motion of source and observer.For motion purely along the line of sight, recession im-plies increased wavelength (redshift) and approach im-plies decreased wavelength (blueshift), complicated bynonlinear relativistic effects when the relative velocityof source and observer is an appreciable fraction of thevelocity of light. Purely transverse motion is associatedwith a relativistic and intrinsically nonlinear redshift.

Event Point in space at a moment of time. The general-ization, in the four-dimensional space–time continuumof relativity theory, of the concept of a point in a spaceas a geometric object of zero “size.”

General theory of relativity Understanding of gravi-tation invented by Albert Einstein as the curvatureof space-time, described mathematically as a four-dimensional geometric manifold. His field equationspostulate the way in which the distribution of mass–energy tells space–time how to curve and imply theequations by which curved space–time tells mass–energy how to move. With the cosmological principle,it forms the basis of the standard model in cosmology.

Nebula Latin for “cloud,” this old term in observationalastronomy refers to a confusing variety of extendedobjects easily distinguished from the pointlike stars.Some are now known to be dust or gas clouds associatedwith the births or deaths of stars in the Milky Way, butothers are galaxies far outside the Milky Way.

Perfect fluid Idealization of matter as continuous andcompletely characterized by three functions of space–time: mass–energy density, pressure, and temperature.At each event, these functions are related through athermodynamic equation of state.

Proper time Measure of time by a standard clock in thereference frame of a hypothetical observer. In describ-ing periods in the evolution of the entire universe, thereference frame is chosen as one that at each event iscomoving with the local expansion. The proper timesince the “big bang” singularity is called the age of theuniverse.

Singularity Event or set of events at which some phys-ical quantities that are generally measurable, such asdensity and curvature (gravitational field), are calcu-lated to have infinite values. It represents a limit to thevalidity of a field theory.

COSMOLOGY as a scientific endeavor is the attempt toconstruct a comprehensive model of the principal featuresof material composition, geometric structure, and tem-poral evolution of the entire physically observable uni-verse. The primary tools of the modern cosmologist arethose of observational astronomy and theoretical physics.Signals are gathered over a very broad range of wave-lengths of the electromagnetic spectrum, from radio wavescollected by the 300-m-diameter dish at Arecibo, PuertoRico, through visible quanta recorded by charge-coupleddevices attached to the twin 10-m Keck telescopes atopMauna Kea, Hawaii, to γ rays detected by instrumentsorbiting above the earth’s atmosphere. In recent years, ex-periments in particle physics have become increasinglyrelevant to cosmological questions. Examples includemeasurements of the solar neutrino flux which challengeour understanding of energy generation in the stars andattempts to detect the superpartners, axions, strings, andother exotic objects predicted by various models in high-energy physics and possible solutions to the missing-massproblem.

The standard theoretical model in cosmology for thepast several decades has been based on Einstein’s generaltheory of relativity, supplemented by assumptions aboutthe homogeneity and isotropy of space–time, and datafrom spectroscopy, consistent with understanding gainedfrom nuclear physics, about the distribution of ordinarymatter among various species. Recently, progress in un-derstanding the early universe has been made by fusingthis theory with the standard SU (3)C × SU (2)L × U (1)Y

model in particle physics, which seems to describe veryaccurately the interactions of quarks and leptons at ener-gies up to ∼2 × 103 GeV, the current limit of terrestrial ac-celerators. Traditional analytical techniques of the theoristare now often supplemented by the raw-number-crunchingpower of increasingly rapid and sophisticated computers,especially in applications to otherwise intractable calcula-tions involving real or speculative space–times or quantumfields. Further synthesis is clearly dependent on continuedadvances in observational astronomy, high-energy exper-imentation, and theoretical physics.

Research in cosmology is subject to one obvious butfundamental limitation that no other field of scientific in-quiry shares. By definition, there is only one entire physi-cal reality that we can observe and attempt to understand.Since we cannot acquire data from outside all this, it is im-possible in principle to perform a controlled experiment totest a truly comprehensive theory of the cosmos. The bestwe can hope for are ever more refined models, constrainedby data from increasingly diverse observational sources,which become more broadly successful as we continue tomeasure and to think.



Cosmology 839

I. ISSUES FROM PRESCIENTIFICINQUIRIES

A. Philosophical Speculations and Myths

Cosmological thought recorded in diverse cultures dur-ing past millennia displays a continued fascination witha relatively small number of fundamental questions aboutthe physical universe and our place within it. Many at-tempts to provide satisfying answers have been made,It is not appropriate to present here a comparative sur-vey of the myriad world views that have been proposed,but there is value in understanding those issues raised byearly thought that are still at the core of modern scientificcosmology.

Logically, the first issue is that of order versus chaos.Indeed, the word cosmology implies an affirmative an-swer to the question of whether the totality of physicalexperience can be comprehended in a meaningful pattern.We should be aware, however, that adherents of the viewthat nature is fundamentally inscrutable or capricious havepresented their arguments in many cultures throughoutrecorded history.

Is matter everywhere in the universe of the same typeas that which is familiar to us on earth, or are there somedistinctively “celestial” substances? Speculations favoringone view or the other have been stated with assurance aslong as humans have engaged in intellectual debate.

Is the space of the universe finite or infinite, boundedor unbounded? To this, also, pure thought unfettered byempirical evidence has, in many places and times, offereddogmatic pronouncements on either side. The logical in-dependence between the issues of finiteness and bound-edness was not fully clarified until the invention of non-Euclidean geometrics in the nineteenth century. Thus, wenow see that the opening question of this paragraph actu-ally comprises two distinct but related questions. Of theissues discussed in this section, this is perhaps the onlyone in which progress in pure thought has raised ques-tions not addressed by ancient philosophers and mythmakers.

Is the universe immutable in its total structure, or doesit evolve with the passage of cosmic time? If the latter,did it have a creation in time, or has it always existed?Similarly, will a changing cosmos continue forever, or willthere be an end to time that we can experience? Such ques-tions have sometimes been distinguished from the struc-tural questions of cosmology and said to be of a differentorder called cosmogony. We shall see that in scientificcosmology such a separation is artificial and unproduc-tive. Indeed, all the questions posed in this section are, inall current scientific models, inextricably interrelated.

B. Value of Some Early Questions

All modern science is predicated on the philosophicalassumption that its subject is comprehensible. Althougheven Albert Einstein remarked that this is the most in-comprehensible thing about the universe, it is difficult tosee how this can be a question for scientific debate. Thepresumption of discoverable regularities, not meaninglesschaos, is a necessary underpinning of any scientific en-deavor. Although twentieth-century quantum mechanicshas compelled reappraisal of earlier determinism, the workof physicists is founded upon belief in objective laws cor-relating observations of natural phenomena and confirmedby successful predictions.

Philosophical speculations in earlier ages about the sub-stance of the cosmos often assumed an insurmountablequalitative distinction between the “stuff” of terrestrialexperience and the matter of the celestial spheres. Theheginnings of modern science included an explicit rejec-tion of this view in favor of one in which all the matter ofthe universe is of fundamentally the same type, subject tolaws that hold in all places and at all times. It is interestingthat some recently proposed solutions to the dark matterproblem in astrophysics suggest that the vast majority ofthe matter of the universe may be in one or more exoticforms that are predicted by elementary particle theory butfor which we do not yet have experimental evidence. Thisis not a return to prescientific notions. It is still assumedthat, no matter what the substance of the universe, all phys-ical reality is subject to one set of laws. Most important,it is assumed that such laws can be discovered with theaid of data obtained from terrestrial experiments as wellas astronomical observations.

Although most early cosmologists imagined a finite andbounded universe, some thinkers (e.g., the Greek philoso-pher Democritus in the fifth century B.C.) argued elo-quently for an infinite and unbounded expanse of space.Until the latter part of the nineteenth century, however, afinite space was presumed synonymous with a boundedone. The non-Euclidean geometries of Riemann, Gauss,and Lobachevsky first presented the separation of the ques-tions of extension and boundedness in the form of logi-cally possible examples amenable to mathematical study.Originally, generalizations of the theorem of Pythagoras tocurved spaces assumed that the square of the distance be-tween two distinct points is greater than zero, described bya positive definite metric tensor. In relativity theory, timeis treated as an additional “geometric” dimension, distin-guished by the fact that the square of the interval betweentwo events may be a quantity of either sign (depending onwhether there is a frame of reference in which they are atthe same place at different times or a frame of reference in



840 Cosmology

which they are at different places at the same time) or zero(if they can be related only by the passage of a signal at thespeed of light). Gravitation is understood to be the relationbetween the curvature of space–time and the mass–energycontained and moving within it. Modern research on theasymptotic structure of space–times is based on the anal-ysis of four-dimensional geometries of indefinite metricwithin the framework of relativistic gravitational theory.All viable models consistent with minimal assumptionsabout our lack of privileged position describe spaces thatare without a boundary surface at each moment of time,although some are finite in volume.

Myths of creation, whether based on purely philosophi-cal speculations or carrying the authority or religious con-viction, are commonplace in almost all cultures of whichwe have any knowledge. Some suppose the birth of a staticuniverse in a past instant, but most describe a process offormation or evolution of the cosmos into its present ap-pearance. In many eras, some individuals or groups havechampioned an eternal universe. Most of these modelsof the universe are static or cyclic, but occasionally theyrepresent nature with infinite change, never repeating butwith no beginning. In earlier times, a beginning in timewas almost always taken to imply finiteness in a boundedspace. The new geometries mentioned earlier have madepossible serious consideration of a universe that began ata definite moment in the past, is not bounded in space, andmay be finite or infinite in extent. The question of whetherthere will be an end to time or whether there will be eter-nal evolution is intimately related to the question of finiteor infinite spatial extent in these models. At present, theempirical evidence about whether time will end is incon-clusive. The “inflationary scenarios” that are currently invogue favor a universe remarkably close to the marginallyinfinite and thus eternally unwinding “asymptotically flat”model, but allow the possibility of a miniscule differencefrom flatness of either sign, resulting in ultimate closureor eternal expansion. Although the observed density ofvisible matter appears much too small to halt the presentexpansion, there are numerous hypothetical candidates forthe dark matter.

II. ORIGINS OF MODERN COSMOLOGYIN SCIENCE

A. Copernican Solar System

Centuries before the Christian era, several Greek philoso-phers had proposed heliocentric models to coordinate theobserved motions of the sun, moon, and planets in relationto the “fixed” stars. However, the computational methodof Alexandrian astronomer Claudius Ptolemy which he

developed during the second century A.D. using a struc-ture of equants and epicycles based on the earth as the onlyimmovable point also made successful predictions of ap-parent motions. Although additional epicycles had to beadded from time to time to accommodate the increasinglyprecise observations of later generations, this system be-came dominant in the Western world. Its assumption of adichotomy between terrestrial experience and the laws ofthe “celestial spheres” stifled fundamental progress untilthe middle of the sixteenth century. In 1543, the Polishcleric Mikolaj Kopernik, better known by the Latin formof his name, Nicholas Copernicus, cleared the way formodern astronomy with the publication of De Revolution-ibus Orbium Coelestium (Concerning the Revolutions ofthe Celestial Worlds). Appearing in his last year, this worksummarized the observations of a lifetime and presentedlogical arguments for the simplicity to be gained by ananalysis based on the sun as a fixed point.

More important, this successful return to the heliocen-tric view encouraged the attitude that a universal set oflaws governs the earth and the sky. In the generationsfollowing Copernicus, the formulation of physical lawsand their empirical testing were undertaken in a mannerunprecedented in history: Modern science had begun. TheDane Tycho Brahe observed planetary orbits to an angularprecision of 1 arc min. The German Johannes Kepler usedBrahe’s voluminous and accurate data to formulate threesimple but fundamental laws of planetary motion. The Ital-ian Galileo Galilei performed pioneering experiments inmechanics and introduced the use of optical telescopes inastronomy. From these beginnings, a scientific approach tothe cosmological questions that humanity had been askingthroughout its history developed.

B. Newtonian Dynamics and Gravitation

The first great conceptual synthesis in modern science wasthe creation of a system of mechanics and a law of grav-itation by the English physicist Isaac Newton, publishedin his Principia (Mathematical Principles of Natural Phi-losophy) of 1687. His “system of the world” was basedon a universal attraction between any two point objectsdescribed by a force on each, along the line joining them,directly proportional to the product of their masses and in-versely proportional to the square of the distance betweenthem. He also presented the differential and integral cal-culus, mathematical tools that became indispensable totheoretical science.

On this foundation, Newton derived and generalized thelaws of Kepler, showing that orbits could be conic sectionsother than ellipses. Nonperiodic comets are well-knownexamples of objects with parabolic or hyperbolic orbits.The constant in Kepler’s third law, relating the squares



Cosmology 841

of orbital periods to the cubes of semimajor axes, wasfound to depend on the sum of the masses of the bodiesattracting one another. This was basic to determining themasses of numerous stars, in units of the mass of the sun,through observations of binaries. As Cavendish balanceexperiments provided an independent numerical value forthe constant in the law of gravitation, stellar masses inkilograms could be calculated. Later, analysis of observedperturbations in planetary motions led to the predictionof previously unseen planets in our solar system. Studiesof the stability of three bodies moving under their mutualgravitational influence led to the discovery of two clustersof asteroids sharing the orbit of Jupiter around the sun.These successes fostered confidence in the view of oneboundless Euclidean space, the preferred inertial frameof reference, as the best arena for the description of allphysical activity. Lacking direct evidence to the contrary,theoretical cosmologists at first assumed that the space ofthe universe was filled, on the largest scales, with matterdistributed uniformly and of unchanging density. Analysissoon disclosed that Newtonian mechanics implied insta-bility to gravitational collapse into clumps for an initiallyhomogeneous and static universe. This stimulated the ob-servational quest for knowledge of the present structureof the cosmos outside the solar system.

C. Technology of Observational Astronomy

Galileo’s first telescopes had revealed many previously un-seen stars, particularly in the Milky Way, where they couldresolve numerous individual images. Based on elementaryobservations and careful reasoning, the ancient concept ofa sphere of fixed stars centered on the earth had been sup-planted by a potentially infinite universe with the earthat a position of no particular distinction. Further progressin understanding the distribution of matter in space wasdependent on actual measurements of the distances to thestars. The concept of stellar parallax, variation in the ap-parent angular positions of nearby stars in relation to moredistant stars as seen from earth at various points in its or-bit around the sun, became useful when the observationalprecision of stellar location surpassed the level of 1 arcsec. An important contribution was the development ofthe micrometer, first used by William Gascoigne, later in-dependently by Christiaan Huygens, and systematicallyappearing in the telescope sights of Jean Picard and othersafter the latter part of the seventeenth century. The firstparallax measurements were reported by Bessel in Ger-many, Henderson in South Africa, and Struve in Russia,in rapid succession in 1838 and 1839. By 1890, distanceswere known for nearly 100 stars in the immediate neigh-borhood of the sun, and the limits of the trigonometricparallax approach (∼100 parsec, based on limits to the

useful size of an optical telescope looking through theearth’s atmosphere) were being approached.

As long as sufficient light can be gathered from a starto be dispersed for the study of its spectrum, much can belearned about it even if one is not certain how far away it is.Spectroscopic studies of stars other than the sun were firstundertaken by William Huggins and Angelo Secchi in theearly 1860s. In 1868, Huggins announced the measure-ment of a Doppler redshift in the lines of Sirius indicatinga recession velocity of 47 km/sec, and Secchi published acatalog of 4000 stars divided into four classes accordingto the appearance of their spectra. The introduction of theobjective prism by E. C. Pickering in 1885 tremendouslyincreased the rate at which spectra could be obtained. Thepublication of the Draper catalogs in the 1890s, basedon the spectral classification developed by Pickering andAntonia Maury, provided the data that led to the rise ofstellar astrophysics in the twentieth century.

D. Viewing the Island Universe

Some hazy patches among the fixed stars, such as theAndromeda nebula or the Magellanic Clouds, are clearlyvisible to the unaided human eye. When Galileo observedthe band called the Milky Way through his telescopeand was surprised to find it resolved into a huge numberof faint stars, he concluded that most nebulosities werecomposed of stars. Early in the eighteenth century, theSwedish philosopher Emanuel Swedenborg described theMilky Way as a rotating spherical assembly of stars andsuggested that the universe was filled with such spheres.The English mathematician and instrument maker ThomasWright also considered the Milky Way to be one amongmany but supposed its shape to be a vast disk contain-ing concentric rings of stars. By 1855, Immanuel Kanthad further developed the disk model of the Milky Wayby applying Newtonian mechanics, explaining its shapethrough rotation. He assumed that the nebulae are similar“island universes.”

Early in the nineteenth century, however, WilliamHerschel discovered the planetary nebulae, stars in as-sociation with true nebulosities. This reinforced a possi-ble interpretation of nebulae as planetary systems in themaking, in agreement with the theory of the origin ofthe solar system developed by Pierre Simon de Laplace.John Herschel’s observations of 2500 additional nebu-lae, published in 1847, emphasized that they were mostlydistributed away from the galactic plane. The “zone ofavoidance” was used by some to argue for the physicalassociation of the nebulae with the Milky Way. (It is nowknown that dust and gas in the plane of the galaxy dimin-ish the intensity of light passing through it, whether fromsources inside it or beyond.) In 1864, Huggins studied



842 Cosmology

the Orion nebula and found it to display a bright linespectrum similar to that of a hot gas. Also, photographsof Orion and the Crab nebula did not show resolutioninto individual stars. As the twentieth century began, thequestion of the nebulae was intricately linked with thatof the structure of the Milky Way. The size of nebu-lae was still quite uncertain in the absence of any reli-able distance indicators, but most astronomers believedthe evidence favored considering the nebulae part of theMilky Way, thus reducing the universe to this one island ofstars.

III. REVOLUTIONS OF THETWENTIETH CENTURY

A. New Theoretical Models

The two great conceptual advances of theoretical physicsin the twentieth century, relativity and quantum mechan-ics, have had profound implications for cosmology. Thegeneral theory of relativity provides the basis for the evolv-ing space–time of the now standard model, and fundamen-tal particle identities and interactions are keys to under-standing the composition of matter in the universe.

In 1905, Albert Einstein established the foundations ofthe special theory of relativity, which connects measure-ments of space and time for observers in all possible in-ertial frames of reference. He devoted the next decade todeveloping a natural way of including observers in acceler-ated frames of reference, using as a fundamental principlethe fact that all test masses undergo the same accelerationin a given gravitational field. The result was Einstein’s the-ory of space–time and gravitation, the general theory ofrelativity (GTR), completed in 1916. It was immediatelyapparent that the GTR would have a substantial impacton cosmological questions. Although many model space–times have been studied in the GTR, in 1922 AlexanderFriedmann showed that the assumptions of spatial ho-mogeneity and isotropy can be embodied in only three.They are presented here in the modern notation of theRobertson–Walker metric with the choice of units com-monly used in theoretical research. The intimate relation-ship of space and time in relativistic theories is recog-nized through units of measure in which the speed of lightis numerically 1, eliminating the letter c representing itsvalue in units such as those of SI. We may think of theunits as geometrized (e.g., time measured in meters) orchronometrized (e.g., length measured in seconds), where1 sec = 299, 792, 458 m (exactly, by definition).

The invariant element of separation ds between twoneighboring events in a homogeneous and isotropicuniverse can be expressed by:

ds2 = −dt2 + R2[dr2/(1−kr2) + r2(dθ2 + sin2 θ dφ2)]

(1)

where R(t) is the scale factor that evolves with cosmictime and k is the curvature constant, which may be pos-itive, negative, or zero. The invariant separation dependson k only through the pure number kr2, where r is a co-moving space coordinate, for which matter is locally atrest. Without loss in generality, we may choose k (andhence also r ) dimensionless and set the scale of r so thatk is +1, −1, or 0. Although R carries the units of spatiallength, it is not possible to interpret it as a “radius of theuniverse” if k is not positive, since the volume of a modelwith k = 0 or k = −1 is infinite.

To ensure that the physics is described in a manner in-dependent of arbitrary choices, it is useful to introducethe scale change rate, also known as the Hubble parame-ter, defined as H = (dR/dt)/R. Since H has dimensionsof velocity divided by length, 1/H is a characteristic timefor evolution of the model. For an expanding empty uni-verse, 1/H would be the time since the beginning of theexpansion. Assuming that the distribution of matter on alarge scale can be described in terms of a perfect fluid oftotal density ρ and pressure p, the coupled evolution ofspace-time and matter in the GTR are determined by theFriedmann equations,

H 2 = 8πGρ/3 − k/R2 and d(ρR3) = −p d(R3)(2)

where G is the Newtonian gravitational constant. (Notethat the term density can be taken as either mass per volumeor energy per volume in units where c = 1.)

Although the GTR implies that a homogeneous andisotropic space generally expands or contracts, at the timethe theory was formulated the common presumption heldthat the real universe was static. This led Einstein to mod-ify his original simple theory by introducing a “cosmo-logical term” into the field equations. The “cosmologicalconstant” in this term was chosen to ensure a stable staticsolution. When the evidence for an expanding universebecame apparent in the next decade, Einstein droppedconsideration of this additional term, calling its introduc-tion the biggest blunder of his career. We shall leave itout of the presentation in this section but later remarkon recent motivations for a possible reinstatement of thecosmological constant with a value other than that whichmakes the universe static. Thus, there are only three possi-ble homogeneous and isotropic universes in the GTR, theFriedmann models. In view of Eq. (2), which determinesthe evolution of the Hubble parameter, the curvature con-stant can be positive only if the density exceeds the valueρcrit = 3H 2/8πG. Thus, an expanding universe in whichk = +1 must halt its growth and begin to collapse before



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its mean density drops below this critical value. Such aspace-time is finite in volume at each moment but has noboundary. While this model is expanding, the Robertson–Walker coordinate time since the expansion began is lessthan 2/3H , depending on how much the density exceedsthe critical value. The classical GTR implies that a finiteproper time passes between its beginning in a singular-ity of zero volume and its return to such a singularity.(However, Charles Misner has argued that a logarithmictime scale based on the volume of the universe is moreappropriate as a measure of possible change that mayoccur, giving even this closed cosmology a potentially“infinite” future and past.) If the density is less than thecritical value, space–time has negative curvature and willhave a positive velocity of expansion into the infinite fu-ture of proper time, when H approaches zero. The timesince expansion began is greater than 2/3H , dependingon how much the density is less than the critical value,but never exceeds 1/H . Although such an open universestill had a beginning in proper time at a singularity, itsvolume is always infinite and it contains an infinite mass–energy. If the density precisely equals the critical value,then the curvature vanishes. Such a flat universe has beenexpanding for a time 2/3H , it has infinite mass–energyin an infinite volume described by Euclidean geometry ateach moment, and its expansion velocity as well as Hub-ble parameter will approach zero asymptotically as propertime in comoving coordinates continues toward the infi-nite future. Which of these three models best describesthe universe we inhabit is an empirical as well as theo-retical question that remains central to current research incosmology.

B. New Observational Evidence

Beginning in the late 1920s, Vesto Slipher, Edwin Hubble,and Milton Humason used the Hooker telescope at Mt.Wilson, California, then the largest optical instrument inthe world, to measure Doppler shifts in the spectra of neb-ulae that they realized were outside the Milky Way. Con-vincing reports of a relationship between recession veloci-ties v deduced from Doppler redshifts and estimates of thedistances d to these galaxies were published in 1929 and1931. Hubble pointed out that the velocities, in kilome-ters per second, were directly proportional to the distances,in megaparsecs (1 Mpc = 3.08 × 1019 km). The observa-tional relation is “smooth” only when the distances consid-ered are at least of the order of a few megaparsecs, allowingthe averaging of the distribution of galaxies to produce anapproximately homogeneous and isotropic density. Sincethe ratio v/d is clearly the current value of the scale changerate H in a Friedmann universe, this was the first obser-vational evidence in support of GTR cosmology.

The parameter H was at first called the Hubble con-stant but is now recognized as a misnomer, because theearly data did not extend far enough into space to cor-respond to looking back over a sustantial fraction of thetime since the expansion began. Hubble’s initial value ofH was so large that the time scale for expansion derivedfrom it was substantially less than geological estimatesof the age of the earth, ∼4.7 × 109 years. Subsequently,the numerical value of the Hubble parameter has under-gone several revisions due to reevaluations of the cosmicdistance scale, yielding a universe older than originallysupposed and thus a much larger volume from which sig-nals at the speed of light can be observed at our position.Allowing for present uncertainties, H is now believed tobe between 50 and 80 (km/sec)/Mpc. Thus, the time scaleof the cosmic expansion, 1/H , is between approximately1.2 and 2 × 1010 years.

When early large values of the Hubble parameter werein conflict with geological and astrophysical estimates ofthe age of the solar system, it was suggested that the simpleGTR cosmologies might not be viable. One solution was toreinstate the cosmological constant, not to halt the univer-sal expansion but merely to slow it down in a “coasting”phase. Recently, some observations of supernovae sug-gest an extragalactic distance scale with H greater than70 (km/sec)/Mpc. If we accept this and also believe thatstellar evolutionary theory is sufficiently established toyield precise ages of globular cluster stars in excess of1.3 × 1010 years, then invoking a nonzero cosmologicalconstant would be a way of avoiding the unacceptableconclusion that the universe contains stars older than itsexpansion time. Models studied by George Lemaitre andothers after 1927 often had unusual features, such as aclosed space of positive curvature that could continue ex-panding for an infinite proper time. A more radical idea,which had other motivations as well, was to abandon con-servation of energy in favor of a “steady-state” cosmologybased on the continuous creation of matter throughout aninfinite past. In such a theory, introduced by HermannBondi, Thomas Gold, and Fred Hoyle in 1948, there is noinitial singularity, or “big bang,” to mark the beginningof the expansion. In 1956, George Gamow predicted thata residual electromagnetic radiation at a temperature ofonly a few kelvins should fill “empty” space as a relic ofthe high temperatures at which primordial nucleosynthesisoccurred soon after the initial singularity in a GTR cosmol-ogy. In 1965, engineers Arno Penzias and Robert Wilsondetected a microwave background coming from all direc-tions in space into a communications antenna they haddesigned and built for Bell Laboratories in Holmdel, NewJersey. Cosmologists Robert Dicke and P. J. E. Peeblesat nearby Princeton quickly explained the significance ofthis 2.7 K blackbody spectrum to them and thus dealt a



844 Cosmology

severe blow to the viability of any cosmological modelthat avoids a “hot big bang.”

A direct determination of whether the universe is spa-tially closed or open would necessitate precisely measur-ing density over volumes of many cubic megaparsecs,detecting the sign of departures from Euclidean geom-etry in an accurate galactic census over distances exceed-ing several tens of megaparsecs, or finding the change inthe Hubble parameter associated with looking back to-ward the beginning over distances exceeding several hun-dred megaparsecs. Unfortunately, these conceptually sim-ple observations appear to be somewhat beyond the scopeof our present technology. However, there are various in-direct ways to estimate, or at least place bounds on, thepresent mean density of the cosmos. To eliminate the in-fluence of uncertainties in the Hubble parameter on theprecise value of the critical density, it is now common todescribe the resulting estimates or bounds in terms of thedimensionless quantity � = ρ/ρcrit. Clearly, � > 1 corre-sponds to a closed, finite universe and � ≤ 1 correspondsto an infinite universe. On the basis of the amount of ordi-nary visible matter observed as stars and clouds in galax-ies, we conclude that � > 0.01. Requiring the present den-sity to be low enough so that the age of the universe (whichdepends inversely on H and, through a monotonically de-creasing function, on �) is at least as great as that of theoldest stars observed, estimated to be 1010 years, yieldsan upper bound � < 3.2. Of the infinite range of conceiv-able values, it is quite remarkable that the universe can soeasily be shown to be nearly “flat.” Further evidence andtheoretical insight suggest that near coincidence (withinone or two powers of 10) of the density and the criticaldensity is not an accident.

The most severe constraints on the contribution of or-dinary matter to � presently come from demanding thatprimordial synthesis of nuclei during the “hot big bang”of a standard Friedmann model produces abundance ra-tios in agreement with those deduced from observation.In nuclear astrophysics, it is customary to specify tem-peratures in energy units which corresponds to setting theBoltzmann constant equal to 1. Thus, the relation betweenthe megaelectronvolt of energy and the kelvin of absolutetemperature is

1 MeV = 1.1605 × 1010 K

Primordial nucleosynthesis models are based on the as-sumption that the temperature of the universe was oncehigher than 10 MeV, so that complex nuclei initially couldnot exist as stable structures but were formed in, and sur-vived from, a brief interval as the universe expanded andcooled to temperatures of less than 0.1 MeV, below whichnucleosynthesis does not occur. Computing all relevantnuclear reactions throughout this temperature range to

determine the final products is a formidable undertaking.Of the various programs written since Gamow suggestedthe idea of primordial nucleosynthesis in 1946, the onepublished by Robert Wagoner in 1973 has become the ac-cepted standard. With updates of reaction rates by severalgroups since then, the numerical accuracy of the predictedabundances is now believed to be ∼1%. Since the weaklybound deuteron is difficult to produce in stars and eas-ily destroyed there, its abundance, 1 × 10−5 relative toprotons as determined in solar system studies and fromultraviolet absorption measurements in the local interstel-lar medium, is generally accepted as providing a lowerbound to its primordial abundance and hence an upperbound of 0.19 to the contribution of baryons to �. Anal-ogous arguments may be applied to establishing a con-cordance between predicted and observed abundances of3He, 4He, and 7Li, the only other isotopes calculated tobe produced in significant amounts during this primor-dial epoch. The resulting constraint on the contribution ofbaryons to the critical density, 0.010 ≤ �B ≤ 0.080, showsclearly that baryons alone cannot close the universe. Ofcourse, this does not eliminate the possibility that the uni-verse may have positive curvature due to the presence ofless conventional forms of as yet unseen matter.

IV. UNSOLVED CLASSICAL PROBLEMS

A. Finite or Infinite Space

Although concordance between the standard model andobserved nuclear abundances limits baryon density to wellbelow the critical value needed for closure of a Friedmannuniverse, the question of finite or infinite space remainsobservationally undecided owing to other complications.In principle, it should be possible to determine the cur-vature constant k by direct measurement of the deviationfrom Hubble’s simple linear relationship between veloc-ity and distance. Unfortunately, substantial deviation isnot expected, until sources at distances of the order of1/H are studied, and galaxies are too faint to have theirspectra measured adequately at such distances by presenttechnology. Furthermore, observing galaxies at such dis-tances implies seeing them at earlier times, and estimatesof their distance could be subject to systematic errors dueto unknown evolution of galactic luminosity.

Since the discovery of quasars by Maarten Schmidtat the Palomar Observatory in 1963, cosmologists havehoped that these most distant observed objects could beused to extend the Hubble relationship to the nonlinearregime and decide the sign of the curvature. Quasars arenow known with spectral features up to 6.0 times their ter-restrial wavelengths, corresponding to Doppler recession



Cosmology 845

velocities up to 96% of the speed of light, placing themat substantial fractions of the distance from us to the hori-zon of the observable universe. However, uncertainties inestimating very large distances in the universe due to in-sufficient understanding of the evolution of galaxies, notto mention the structure of quasars, have prevented un-ambiguous determination of the sign of the curvature. Infact, Hubble’s law is still used to estimate distances tothe quasars, rather than they being used to determine bothdistance and redshift and thus test their relationship. Thequestion of whether space is finite or infinite remains un-resolved by observation at this time.

B. Eternal Expansion or an End to Time

In the Friedmann cosmologies of the GTR, a finite spaceimplies an end to proper time in the future, but this isnot required in some nonstandard models. Assuming theRobertson–Walker form of the metric for a homogeneousand isotropic space–time, it is convenient to discuss thefuture evolution of any such expanding universe in termsof a dimensionless deceleration parameter, defined as:

q = −R(d2 R/dt2)/(dR/dt)2

Throughout most of its history, the dynamics of the uni-verse have been dominated by matter in which the averageenergy density is very much greater than the pressure. Ne-glecting the pressure of nongravitational fields, space willreverse its expansion and collapse in finite proper time ifand only if q > 1

2 . From the Friedmann equation for theHubble parameter, it is easy to show that q = �/2 in aspace–time described by the GTR with zero cosmologicalconstant. In nonstandard models, the deceleration param-eter depends on the density, the cosmological constant,and the Hubble parameter in more complicated ways. Forsome choices of cosmological constant, it is even possibleto have an accelerating universe (q < 0) with a positivedensity. However, a cosmological constant whose mag-nitude substantially exceeded the critical energy densitywould produce detectable local effects that are not ob-served. Thus, we can conclude that a sufficiently largedensity must imply an end to time.

Applications of the virial theorem of Newtonian me-chanics to galactic rotation and the dynamics of clustersindicate that masses often exceed those inferred from vis-ible light by about an order of magnitude. Such resultspush at the upper bound of the baryon density inferredfrom nucleosynthesis but are still far short of supportingq > 1

2 . However, if only one-tenth of the ordinary matterin galaxies and clusters may be visible to us, is it not pos-sible that there exists mass–energy, in as yet undetectedforms or places, of sufficient quantity to produce deceler-ation exceeding the critical value? Primordial black holes,

formed before the temperature of the universe had droppedto 10 MeV, would not interfere with nucleosynthesis inthe standard model but could substantially increase thevalue of �. (Notice that black holes due to the collapse ofstars are made of matter that contributed to �B during thetime of primordial nucleosynthesis and thus are limited bythe nuclear abundance data.) Calculations of the primor-dial black hole mass spectrum, such as those by BernardCarr, have demonstrated that present observational dataare insufficient to decide whether the contribution of blackholes to the density will reverse expansion. More conven-tional astronomical candidates for the dark matter includ-ing brown dwarfs (examples have been detected in thehalo of the Milky Way through gravitational lensing) anddead (radio-quiet) pulsars (almost certain to exist but notas yet detected) are unfortunately constrained by the nu-cleosynthesis limits on baryon density. Some speculativeideas in high-energy particle physics present other exoticcandidates for dark matter that may dominate the gravita-tional dynamics of the universe as a whole. These includemassive neutrinos (although observations of electron neu-trinos from SN1987A [Supernova Shelton] constrain theelectron neutrino mass to probably less than 10 eV, tauand mu neutrinos could be heavier), the axions requiredto banish divergences in grand unified theories (GUTs)(as yet undetected), and the supersymmetric partners ofall known fermions and bosons (none yet found experi-mentally). Empirically, whether there will be an end totime remains an unresolved question.

C. Observations and Significanceof Large-Scale Structure

The measured homogeneity and isotropy of the cosmicmicrowave background radiation temperature (�T/T ∼10−5) is strong evidence that the observable universe israther precisely homogeneous and isotropic on the largestscale (1/H is ∼3000 Mpc). However, it is well known thaton only slightly smaller scales, up to 120 Mpc, the universetoday is very inhomogeneous, consisting of stars, galax-ies, and clusters of galaxies. For example, the variationin density divided by the average density of the universe,δρ/ρ, is of the order of 105 for galaxies. The density ofvisible matter in large “voids” recently discovered is typ-ically less than average by about one order of magnitude.Since gravitational instability tends to enhance any inho-mogeneity as time goes on, the difficulty is not in cre-ating inhomogeneity but rather in deviating from perfecthomogeneity at early times in just the way that can ac-count for the structural length scales, mass spectra, andinferred presence of dark matter that are so obvious in theuniverse today. Opinions about the structure of the uni-verse at early times have run the gamut from Misner’s



846 Cosmology

chaotic “mixmaster” to Peebles’s quite precisely homo-geneous and isotropic space-times. The issue of the originof structure in the universe on the largest scales remainsunresolved, because conflicting scenarios that adequatelyaccount for galaxies and clusters can involve so many tun-able parameters that it is difficult to distinguish amongcompeting models observationally.

The three-dimensional map of more than 1.1 × 104

galaxies within a sphere of diameter 400 Mpc centeredon the Milky Way, created by Huchra and Geller on thebasis of more than 5 years’ data gathered with an earth-bound telescope comparable in aperture to the HubbleSpace Telescope (HST returned its first images May 1990),shows voids and filamentary structures on scales up toabout 120 Mpc. They strain “top down” scenarios of theevolution of cosmic structure, since it is difficult to havegravitationally bound structures so large which “later”fragmented to form quasars when the universe was lessthan 7% of its present age. Advocates of such pictures havequestioned the statistical significance of a sample only onthe order of 10−7 of the galaxies within our horizon. TheHST, despite initial difficulties in forming optimally sharpimages (corrected in 1993), has gathered spectra of a sam-ple from roughly an order of magnitude deeper into space(implying roughly 103 times as many galaxies). Combinedwith evidence of galaxy formation at early times visiblein the Hubble deep fields, this enlarged sample supportsa two-component model of structure formation. Hot darkmatter provides a gravitational field which fragments onthe large scale of galaxy clusters, while cold dark matterpockets act as seeds for the concurrent formation of sub-units of galaxies. HST will spend part of its remaining lifein orbit further improving statistics to refine the interpre-tation of an enlarged sample. It might finally gather datathat might unravel the contributions of galactic evolutionfrom that of the cosmological deceleration to the redshift-distance relation of the most distant active galaxies andquasars.

D. Viability of Nonstandard Models

The assumption that the universe is homogeneous andisotropic on a sufficiently large scale has been calledthe cosmological principle. This principle, applied to theRiemannian geometry of space-time using the methods ofgroup theory, leads to the Robertson–Walker form of theinvariant separation between events. This mathematicallyelegant foundation for theoretical cosmology is indepen-dent of a particular choice of gravitational field equations.However, the evolution of the scale factor and the rela-tion of the curvature constant to the matter distributionare, of course, intimately related to the structure of thegravitational theory that is assumed.

Previous mention was made of the logical possibility ofcomplicating the equations of the GTR by introducing acosmological constant. Though hints of a possible conflictbetween ages of galactic halo stars and the Hubble timemight be resolved by a nonzero cosmological constant,there is abundant evidence that it cannot be significantlylarger than the critical density. Attempts to derive a valuefrom quantum theories of fundamental interactions yieldestimates too large by many orders of magnitude. Thisembarrassing failure leaves advocates of a cosmologicalconstant only the unpleasant option of arbitrarily adjustingit to a suitable small value. Critics then ask why it shouldnot be chosen to vanish exactly.

Numerous alternatives to the GTR consistent with thespecial theory of relativity have been proposed. Some maybe eliminated from further consideration by noncosmo-logical tests of gravitational theory. For example, theoriesbased on a space–time metric that is conformally flat, suchas that published by Gunnar Nordstrom in 1912, are un-tenable because they fail to predict the deflection of lightrays in the gravitational field of the sun, first measured byDyson, Eddington, and Davidson during a solar eclipsein 1919. Others, such as the scalar–tensor theory pub-lished by Carl Brans and Robert Dicke in 1961, may bemade consistent with current observational data by suit-able adjustment of a parameter. Their cosmological conse-quences present distinct challenges to the standard modelfor some times during the evolution of the universe. How-ever, sufficiently close to singularities, the predictions ofmost such theories become indistinguishable from thoseof the GTR. For example, in 1971 Dykla, Thorne, andHawking showed that gravitational collapse in the Brans–Dicke theory inevitably leads to the “black hole” solutionsof the GTR. Hence, cosmological models based on thesetheories make predictions very much like those of the GTRfor the strong fields near the “big bang” and the nearly flatspace-time of today. If they are very different in some in-termediate regime, perhaps one important to the formationof structures such as galaxies, there currently appear to beno crucial tests that could cleanly decide in their favor.Thus, by an application of Occam’s razor, most contem-porary models are constructed assuming the validity of theGTR.

An influential exception to the dominance of GTR mod-els was the “steady-state” cosmology of Bondi, Gold, andHoyle. The philosophical foundation of this work wasthe extension of the cosmological principle to the “per-fect cosmological principle,” which asserted that thereshould be uniformity in time as well as spatial homo-geneity and isotropy. As remarked earlier, observationsof the microwave background presently render this modeluntenable. It is also unable to account for the abundancesof various light nuclei synthesized when the universe was



Cosmology 847

much hotter and denser than it is now. The apparent over-throw of the perfect cosmological principle encouragedquestioning of the assumption of spatial homogeneity andisotropy. Since the empirical evidence in favor of spatialuniformity on very large scales is quite strong, most cos-mologists today would like to deduce the cosmologicalprinciple rather than assume it. That is, we would liketo demonstrate that, starting with arbitrary initial condi-tions, inhomogeneities and anisotropies are smoothed outby physical processes in a small time compared with theage of the universe. A serious difficulty in attempts toderive the cosmological principle was first emphasized byMisner in 1969. Relativistic space–times of finite age haveparticle horizons, so that at any moment signals can reacha given point only from limited regions, and parts of theuniverse beyond a certain distance from one another havenot yet had any possibility of communicating. The corre-lation in conditions at distant regions that is asserted by thecosmological principle can be derived only if chaotic ini-tial conditions smooth themselves out through an infinitenumber of processes, such as the expansions and contrac-tions along different axes in “mixmaster” universes. In thestandard model, the cosmological principle is regarded asan unexplained initial condition.

V. INTERACTION OF QUANTUM PHYSICSAND COSMOLOGY

A. Answers from Particle Physics

The interaction between elementary particle physics andcosmology has increased greatly since 1980, to the benefitof both disciplines. Several initial conditions of classicalcosmology are given a tentative explanation in “inflation-ary universe” scenarios, proposed by Alan Guth in 1981and modified by Linde, Albrecht, and Steinhardt in 1982.These models assume a time when the energy density of a“false vacuum” in a grand unified theory (GUT) dominatedthe dynamics of the universe. Since the density was es-sentially constant throughout this period, the Robertson–Walker scale factor grew exponentially in time, allowingan initially tiny causally connected region (even smallerthan the small value of 1/H at the start of inflation) to growuntil it included all of the space that was to become thecurrently observable universe. The original version (1981)assumed that this occurred while the universe remainedtrapped in the false vacuum.

Unfortunately, such a universe that inflated sufficientlynever made a smooth transition to a radiation-dominated,early Friedmann cosmology. In the “new inflationary”models (1982), the vacuum energy density dominateswhile the relevant region of the universe inflates and

evolves toward the true vacuum through the spontaneousbreaking of the GUT symmetry by nonzero vacuum ex-pectation values of the Higgs scalar. The true vacuum isreached in a rapid and chaotic “phase transition” when theuniverse is of the order of 10−35 sec old, resulting in theproduction of a large number and variety of particles (andantiparticles) at a temperature of the order of 1014 GeV.It is supposed that the universe evolves according to thestandard model after this early time.

Since the entire observable universe evolves from a sin-gle causally connected region of the quantum vacuum, in-flationary models obviously avoid horizon problems. Thehomogeneity and isotropy of the present observable uni-verse are a consequence of the dynamic equilibrium in thetiny region. Since the density term in the Friedmann equa-tion for the evolution of the Hubble parameter remainsessentially constant throughout the inflationary era, whilethe curvature term is exponentially suppressed, these sce-narios also offer a natural explanation for the present ap-proximate flatness of the universe. In fact, plausible sup-pression of the curvature greatly exceeds that required byany astrophysical observations. Only by artificially con-trived choices of parameters in an inflationary universecould we avoid the conclusion that any difference betweenthe current value of � and unity is many orders of mag-nitude less than 1. If this result and the bounds on �B

from primordial nucleosynthesis are both true, we mustconclude that dark matter of as yet undetermined formdominates the dynamics of the universe. Since GUTs pre-dict the nonconservation of B (baryon number), C (chargeconjugation), and CP (product of charge conjugation andparity), the decay of very heavy bosons far from thermo-dynamic equilibrium offers a way of dynamically gener-ating the predominance of matter over antimatter ratherthan merely asserting it as an initial condition. In the ab-sence of observation of the decay of the proton or ac-celerators capable of attaining energies at which GUTspredict convergence of coupling “constants,” the apparentbaryon asymmetry of the universe is perhaps the best em-pirical support for some sort of unified theory of quarksand leptons.

B. Constraints from Cosmology

Even as elementary particle theory solves some prob-lems of cosmology, it is subject to limitations derivedfrom cosmological data involving energies far beyondthe 2 × 103 GeV limit of existing terrestrial accelerators.An important example involves the production of mag-netic monopoles in the early universe. In 1931, P. A. M.Dirac showed that assuming the existence of magneticmonopoles led to a derivation of the quantization ofmagnetic and electric charge and a relation between



848 Cosmology

them implying that magnetic charges would have to bevery large. However, other properties of the hypotheticalmonopoles, such as mass and spin, were undeterminedin his theory. In 1974, Gerhard t’Hooft and AlexanderPolyakov showed that monopoles must be produced ingauge theory as topological defects whenever a semisim-ple group breaks down to a product that contains a U (1)factor, for example,

SU (5) → SU (3) × SU (2) × U (1)

All proposed GUTs, which attempt to unify the strong andthe electroweak interactions, are examples of gauge theo-ries in which monopoles are required and have masses ofthe order of the vacuum expectation value of the Higgsfield responsible for the spontaneous symmetry break-ing. The present experimental lower limit, of the orderof 1033 years, for the mean life of the proton implies alower limit for this mass of the order of 1018 GeV. Onlywithin a time of at most 10−35 sec after the “big bang” wasany place in the universe hot enough to produce particlesof so great a mass, either as topological “knots” or as pairsof monopoles and antimonopoles formed in the energeticcollisions of ordinary particles.

In addition to their enormous masses and relatively largemagnetic charges, monopoles are predicted by GUTs toserve as effective catalysts for nucleon decay. Thus, ifpresent in any appreciable abundance in the universe to-day, monopoles should make their presence obvious by do-ing some conspicuously interesting things. If monopoleswere made in about the same abundance as baryons, theirdensity alone would exceed the critical value for a closeduniverse by a factor of ∼1011. Monopoles would use upthe potential energy of stationary magnetic fields, suchas that of the Milky Way, by converting it to increases intheir own kinetic energy. Collecting in a star throughout itshistory, they would render its collapsed “final state” short-lived by catalyzing nucleon decay. The observational up-per bound on�, lower limits on the galactic magnetic field,and the life spans of neutron stars place severe constraintson the flux of monopoles at present and hence on their rateof production during the spontaneous symmetry-breakingera. In fact, unacceptably large magnetic monopole pro-duction in the simplest GUTs was one of the primarymotivations for the development of the new inflationaryuniverse models, which solve the problem through an ex-ponential dilution of monopole density that leaves veryroughly one monopole in the entire observable universeat present. While such a scenario appears to make theexperimental search for monopoles essentially futile, itis important not to ascribe too much quantitative signifi-cance to this result, because the predicted number is ex-ponentially sensitive to the ratio of the monopole massto the highest temperature reached in the phase transi-

tion at the end of spontaneous symmetry breaking. Thus,an uncertainty of a mere factor of 10 (theoretical uncer-tainties are at least this large) in this ratio changes thepredicted number of monopoles by a factor of the orderof 108.

On the experimental front, Blas Cabrera claimed thedetection of a magnetic monopole on February 14, 1982,after 150 days of searching with a superconducting quan-tum interferometer device (SQUID). If this observationwere correct and even approximately corresponded to thetypical distribution of monopoles in space, then neither theexcessive production of a naive GUT model nor the ex-treme scarcity of a new inflationary model could be credi-ble. Confirmation of this monopole detection would leavecurrent theory totally at a loss to explain the monopoleabundance, but neither Cabrera nor other observers haveyet claimed another detection. After more than 3000 dayshad passed, most workers were of the opinion that thesingle “event” was due to something less exotic than amagnetic monopole.

The apparent smallness of the cosmological constant isa fact that has not yet been explained in any viable the-ory of particle physics or gravitation. Below some criticaltemperature in electroweak theory or GUTs, the effec-tive potential function of the Higgs fields behaves likea cosmological constant in contributing a term equal tothis potential function times the space–time metric to thestress–energy–momentum tensor of the universe. Empir-ical bounds on the vacuum energy density today implythat this potential at the spontaneous symmetry-breakingminimum was already less than 10−102 times the effec-tive potential of the false vacuum. There is no derivationof this extremely small dimensionless number within theframework of GUTs. In fact, the assumption that the cos-mological constant is negligible today is an unexplainedempirical constraint on the otherwise undetermined scaleof the effective potential in a gauge theory.

Another possible success of inflationary models is thenatural development of nearly scale-independent densityinhomogeneities from the quantum fluctuations in theHiggs field of GUTs during inflation. Inhomogeneitiesshould later evolve by gravitational clumping into galax-ies and clusters of galaxies. This opens the possibility ofcalculation from first principles of the spectrum of laterstructural hierarchies. Comparison of the results of suchcalculations with the observed large-scale structure of theuniverse may provide the most stringent constraints onnew inflationary models.

C. Singularities and Quantum Gravity

This survey has looked back nearly 1018 sec from thepresent to the “big bang” with which the standard



Cosmology 849

cosmological model claims the universe began. The at-tempt to understand its evolution reveals a number of sig-nificant eras. Let us review them from the present to theinitial singularity in reverse chronological order, which isgenerally the order of decreasing direct experimental ev-idence and thus increasing tentativeness of conclusions.At a time of the order of 1013 sec after the universe began,when the temperature was ∼0.3 eV, the photons that nowcompose the cosmic microwave radiation background lastappreciably interacted with matter, which then “recom-bined” into transparent neutral atoms of hydrogen, helium,and lithium and began to form the large-scale structuresfamiliar to us: stars, galaxies, and clusters of galaxies.At a time of the order of 10−2 sec after the beginning,when the temperature was ∼10 MeV, the free neutronsand some of the free protons underwent the primordialsynthesis that formed the nuclei of these atoms, and thecosmic background neutrinos ceased having significantinteractions with matter. At a time of the order of 10−5 secafter the beginning and a temperature ∼300 MeV, quarksbecame “confined” to form the hadrons as we now knowthem. At a time of the order of 10−12 sec after the begin-ning, the temperature was ∼103 GeV, the present limit ofterrestrial accelerators. The distinction between electro-magnetic and weak interactions was not significant beforethen. The reconstruction of earlier history is of necessitymuch more tentative. The spontaneous symmetry breakingof the grand unification of electroweak and strong inter-actions is thought to have occurred at a time of roughly10−34 sec and a temperature of the order of 1014 GeV.During the “inflation” preceding this epoch the baryonasymmetry of the universe may have been generated byfluctuations from thermal equilibrium in GUTs, and mag-netic monopoles may have been produced by symmetrybreaking. Any attempt to analyze events at substantiallyearlier times must address the unfinished program of con-structing a quantum theory that unifies gravitation withthe strong and electroweak interactions.

In the absence of complete understanding, the time andtemperature scales of quantum gravitational effects canbe estimated by dimensional analysis applied to the fun-damental constants that must appear in any such theory.These are the quantum of action, the Newtonian grav-itational constant, the speed of light, and the Boltzmannconstant. The results, a time of the order of 10−44 sec and atemperature of the order of 1019 GeV, delineate conditionsso near the classically predicted singularity of infinite den-sity and curvature at the “big bang” that the very concept ofa deterministic geometry of space–time breaks down. Vi-olent fluctuations of space–time should generate particlesin a manner analogous to that which occurs in the vicin-ity of a collapsing black hole, as first studied by StephenHawking in 1974. Such processes could conceivably be

the source of all existing matter, and the possible removalof an infinite-density singularity at time zero would makeit scientifically meaningful to ask what the universe wasdoing before the “big bang.”

Not only the existence and structure of matter but eventhe topology and dimensionality of space–time becomeproperties to be derived rather than postulated in the quan-tum gravity era. In 1957, John Wheeler suggested thatspace–time need not necessarily be simply connected atthe Planck scale (of the order of 10−35 m) but could havea violently fluctuating topology. If so, its description interms of a smooth continuum would not be appropriateand would have to be replaced by some other mathe-matical model. The first viable unification of electromag-netism and gravitation, proposed by Theodor Kaluza in1921 and independently by Oskar Klein in 1926, useda five-dimensional space–time with an additional “com-pact” spatial dimension subject to constraints that re-duced their model to a sterile fusion of Maxwell’s andEinstein’s field equations. Removing these constraints al-lows Kaluza–Klein spaces to be used for alternate for-mulations of gauge field theories. Models with a total of11 dimensions are currently being actively explored in re-lation to supersymmetry theories, which seek to providea unification of bosons and fermions and all interactionsamong them. Another approach, string field theory, in-volves replacing the pointlike particles of conventionalquantum field theory with fundamental objects with ex-tent in one spatial dimension. It has been demonstratedthat topology-changing processes can be explicitly re-alized in a Kaluza–Klein superstring theory, encourag-ing the hope that this could be the long-sought basisfor a theory of everything. The full implications of suchstudies for particle physics and for cosmology are notyet clear.

VI. THOUGHTS ON SOURCESOF FUTURE PROGRESS

A. Emerging Observational Technologies

Since the pioneering research of Galileo, advances in tele-scope capabilities have been the source of more and richerdata to constrain cosmological speculation. The currentgeneration of astronomers has seen photographic tech-niques increasingly augmented by electronic image inten-sifiers. Improvements in photon detectors, such as charge-coupled devices, are beginning to approach their limits,so that achieving substantial gains will involve increas-ing the aperture in the next generation of optical and in-frared instruments. The twin Keck telescopes, which canbe used as an optical interferometer of 85-m baseline, are



850 Cosmology

the largest general-purpose telescopes on earth. A con-sortium of nations have built Gemini, a matched pair of8-m telescopes, one in Hawaii and one in Chile. Ari-zona astronomers have built the Large Binocular Tele-scope, which will carry two 8.4-m mirrors in a singlemounting. The European Southern Observatory has com-pleted the first of four 8.2-m telescopes that will even-tually observe as a single Very Large Telescope fromthe Andes in Chile. Even larger telescopes are planned,and the use of adaptive optics will endow modern tele-scopes with “seeing” much better than that possible inthe past.

As more powerful telescopes looking farther into outerspace observe signals from earlier in the history of theuniverse, higher energy accelerators probing farther intoinner space measure particle behavior under conditionssimulating earlier times during the “big bang.” The in-stallation of superconducting magnets in the tevatron atthe Fermi National Accelerator Laboratory at Batavia,Illinois, enabled it to produce protons with an energy of103 GeV in 1984. In 1986, it made available a total en-ergy of 2 × 103 GeV by accommodating countercirculat-ing beams of protons and antiprotons that are made to col-lide. Since the pioneering effort toward the detection ofgravitational waves by Joseph Weber in the late 1960s, as-trophysicists have eagerly anticipated the maturing of thistechnology to open a new window on the universe. Longexperience with the Hulse–Taylor binary pulsar is strongevidence that gravitational waves do indeed exist and havethe properties predicted by Einstein’s general theory of rel-ativity. The development of large dedicated facilities suchas the laser interferometer gravitational-wave observatory(LIGO) at last promises to soon move gravitational waveastronomy from a curiosity with isolated applications toa tool for the exploration of any cosmic environment in-volving strong gravitational fields. As usual in the open-ing of a new area of science, the unexpected discoverieswill surely be the most exciting. Continued experimentsat energies of several thousand GeV will lead to importantnew insights into the structure of matter on a scale of lessthan 10−19 m.

B. Concepts and Mathematical Tools

The search for a viable extension of GUTs to a theory ofeverything (TOE), which would include quantum grav-ity as well as the strong and electroweak interactions, isan active area of particle theory research. The energies atwhich such unification was achieved in nature are presum-ably even higher than those for GUTs. Thus, no data fromaccelerators, even in the most optimistic projections offoreseeable future technology, can serve to constrain spec-ulation as well as does information from cosmology. Thecurrently fashionable attempts to derive a TOE are based

on “supersymmetry,” which is the idea that the fundamen-tal Lagrangian contains equal numbers of Bose and Fermifields and that they can be transformed into each other bya supersymmetry. This immediately doubles the particlespectrum, associating with each particle thus far observed(or predicted by GUTs) a “superpartner” of opposite quan-tum statistics. There is at present no experimental evidencefor the existence of any of these superpartners, invitingdoubt as to the necessity of the supersymmetry assump-tion. However, supersymmetric theories have the potentialto address one otherwise unanswered issue of cosmology:Why is the cosmological constant so small, perhaps pre-cisely zero? Supersymmetric theories are the only knownquantum field theories that are sensitive to the vacuumenergy level. This appears to imply that a derivation ofthe cosmological constant from first principles should bepossible within a supersymmetric theory, but the problemremains unsolved.

As the number of degrees of freedom being consideredin field theories increases, increased computing speed andpower become more important on working out the conse-quences of various proposed models. Some new hardwarearchitectures such as concurrent processing appear to be ameans of achieving performance beyond the limits of anyexisting machines but require the further development ofsoftware exploiting their distinctive features to achievetheir full potential. Progress in discrete mathematics is ofbenefit to both computer science and pure mathematics.In the past, fundamental insights have often been derivedfrom mathematical analysis without the benefit of “num-ber crunching,” and there is no reason to expect that thisprocess has come to an end. It is, of course, impossibleto predict what new closed-form solution of a recalcitrantproblem may be discovered tomorrow, or what impactsuch a discovery may have.

In the last analysis, any attempt to predict the directionof progress in cosmology further than the very near futureseems futile. By the nature of the questions that cosmologyseeks to answer, the scope of potentially relevant conceptsand information is limitless. It is entirely possible thatwithin a decade carefully reasoned thought, outrageousunexpected data, or some combination of the two mayoverthrow some of today’s cherished “knowledge.” Awareof the questions still unanswered and of the possibilitythat some of the right questions have not yet been asked,we can only hope that future discoveries, anticipated orunforeseen, will result in ever greater insights into thestructure, history, and destiny of the universe.


CELESTIAL MECHANICS • CHAOS • COSMIC INFLATION •DARK MATTER IN THE UNIVERSE •GALACTIC STRUCTURE



Cosmology 851

AND EVOLUTION • PARTICLE PHYSICS, ELEMENTARY •QUASARS • RELATIVITY, GENERAL • RELATIVITY, SPE-CIAL • STELLAR STRUCTURE AND EVOLUTION • UNIFIED

FIELD THEORIES

BIBLIOGRAPHY

Auborg, E., Montmerle, T., Paul, J., and Paul, P., eds. (2000). TexasSymp. on Relativistic Astrophys. and Cosmology, Nuclear Physics B(Proc. Suppl.) 80.

Bothun, G. (1998). “Modern Cosmological Observations and Problems,”

Taylor & Francis, London.Gribbon, J., and Rees, M. (1989). “Cosmic Coincidences,” Bantam

Books, New York.Kolb, E., Turner, M., Lindley, D., Olive, K., and Seckel, D., eds. (1986).

“Inner Space/Outer Space,” Univ. of Chicago Press, Chicago.Misner, C., Thorne, K., and Wheeler, J. (1973). “Gravitation,” Freeman,

New York.Peebles, P. J. E. (1980). “The Large-Scale Structure of the Universe,”

Princeton Univ. Press, Princeton, NJ.Isham, C., Penrose, R., and Sciama, D., eds. (1981). “Quantum Gravity

II,” Oxford Univ. Press, London.Rowan-Robinson, M. (1985). “The Cosmological Distance Ladder,”

Freeman, New York.

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Gamma-Ray AstronomyJ. Gregory StacyLouisiana State University and Southern University

W. Thomas VestrandLos Alamos National Laboratory

I. Introduction and Historical OverviewII. Sources of Cosmic Gamma Rays

III. The Challenge of Observation and Techniquesof Detection

IV. Future Missions and ProspectsV. Concluding Remarks

GLOSSARY

Accretion disk A flattened, circulating disk of materialdrawn in and heated to high temperatures under theinfluence of the intense gravitational field associatedwith a black hole or other compact object (such as aneutron star or white dwarf).

Active galactic nuclei (AGN) A collective term for activegalaxies whose emission is observed to come predom-inantly from the central nuclear region of the galaxy.Of these, blazars form a subclass that is observed toemit gamma radiation. It is likely that the viewing an-gle toward these latter objects is directed along jetsof relativistic material ejected from the nucleus of thegalaxy by supermassive black holes.

Bremsstrahlung The “braking” radiation given off byfree electrons that are deflected (i.e., accelerated) inthe electric fields of charged particles and the nuclei ofatoms.

Cherenkov light Radiation produced by a charged parti-cle whose velocity is greater than the velocity of light inthe medium through which it travels. Cherenkov light isstrongly directed along the line of travel of the particle.

Compton scattering The dominant process by which amedium-energy gamma ray interacts with matter byscattering and transferring a part of its energy to an elec-tron. “Inverse” Compton scattering refers to the sameprocess, but where a lower-energy photon is scatteredto higher energy after interaction with a relativisticelectron.

Cosmic rays High-energy charged particles, such as elec-trons, protons, alpha-particles (helium nuclei), andheavier nuclei that propagate through interstellar space.

Diffuse emission Radiation that is extended in angularsize on the sky, such as the gamma-ray emission aris-ing from the decay of radioactive nuclei dispersedthroughout the interstellar medium. A diffuse sourceis distinguished from a pointlike or point source ofemission that is not resolvable into further individualcomponents given the limited angular resolution of atelescope.

Electromagnetic cascades A phenomenon that occurs inthe upper atmosphere of the Earth when a very high-energy gamma ray interacts by the pair-production pro-cess, followed by further interactions resulting in exten-sive air showers (or EAS) of particles and photons. The

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398 Gamma-Ray Astronomy

relativistic cascade particles emit optical Cherenkovlight that is observable from the ground. Electromag-netic cascades are distinguished from the nucleonic (orhadronic) cascades produced by high-energy cosmic-ray particles in the upper atmosphere.

Electron volt (eV, and keV, MeV, GeV, TeV, PeV) Theelectron volt (eV) is a fundamental unit of energy com-monly used in high-energy astrophysics. It is defined tobe the energy acquired by an electron when acceleratedthrough a potential difference of one volt. One eV isequal to 1.602 × 10−19 J or 1.602 × 10−12 ergs.

Gamma rays The highest-energy form of electromag-netic radiation, above the X-ray portion of the spec-trum. Gamma rays have energies measured in millionsof electron volts and higher.

Pair production and annihilation The process by whichthe most energetic gamma rays (of MeV energies andabove) interact with matter, producing an electron–positron pair (the positron, with positive charge, isthe antiparticle to the electron). The inverse processis pair annihilation, in which an electron and positronmutually annihilate and produce a pair of high-energygamma rays.

Parsec (pc, and kpc, Mpc, Gpc) A unit of dis-tance commonly used in astronomy (an abbrevia-tion for “parallax-arcsecond”). One parsec is equal to3.086 × 1016 m, or 3.26 light-years.

Point source A source of emission that is not further re-solvable into individual components given the limitedangular resolution of a telescope. In gamma-ray astron-omy angular resolution is relatively poor compared toother branches of astronomy. Thus, in some instances agamma-ray point source may in fact consist of a num-ber of individual sources whose summed emission ismeasured by the gamma-ray telescope.

Supernova An endpoint of stellar evolution for the mostmassive stars, an explosion triggered by the gravita-tional collapse of the stellar core following the exhaus-tion of fuel for nuclear burning. The collapsed stellarcore, depending on its final mass, can become either ablack hole or a neutron star (and some of the latter maybe observable as pulsars).

Synchrotron radiation The emission produced bycharged particles as they spiral (i.e., accelerate) aroundmagnetic fields.

THE GAMMA-RAY regime constitutes one of the lastregions of the electromagnetic spectrum to be openedto detailed astrophysical investigation. Only within thepast decade has the field of gamma-ray astronomy be-come firmly established as a productive and dynamic disci-pline of modern observational astrophysics. This has been

largely due to the successful operation during the 1990s ofthe Compton Gamma Ray Observatory, whose telescopescarried out the first comprehensive surveys of the sky atgamma-ray energies (as shown in Fig. 1). Gamma raysform the highest-energy portion of the electromagnetic(E-M) spectrum with individual photon energies extend-ing from millions of electron volts (MeV) to values inexcess of 1016 eV (optical photons in contrast carry ener-gies of only a few electron volts). Observations of thesehighest-energy photons provide the means of investigat-ing the largest transfers of energy occurring in the Uni-verse and offer the key to understanding a host of chal-lenging cosmic phenomena occurring in a wide varietyof astrophysical settings. The environments in and aroundgamma-ray sources are among the most extreme to befound in the Universe, permitting the testing of modelsand hypotheses regarding high-energy phenomena underconditions impossible to achieve on the Earth. Further, theUniverse is essentially transparent to the propagation ofgamma radiation, and since, like all electromagnetic radia-tion, gamma rays are electrically neutral they are not devi-ated from their trajectories under the influence of magneticfields. Gamma rays arriving at the Earth therefore serveas direct messengers from high-energy celestial sourceswithin our own Milky Way galaxy and beyond, extend-ing to the most distant reaches and earliest epochs of thecosmos. Gamma-ray astronomy quite literally provides anew window into space that extends our view out to theedge of the observable Universe.

I. INTRODUCTION ANDHISTORICAL OVERVIEW

A. Fundamental Concepts and Terminology

To place the discipline of gamma-ray astronomy in con-text, we review some basic concepts and nomenclature.The electromagnetic spectrum encompasses the entirerange of radiation from the radio through gamma rays,and includes the subregions of radio, infrared (IR), op-tical (or visible), ultraviolet (UV), X-rays, and gammarays, in order of increasing energy or frequency of radi-ation. The fundamental relation between photon energy,frequency, and wavelength is the well-known expressiondue to Planck,

E = hν = hc/λ,

where E is the photon energy, ν the frequency, λ thewavelength of the radiation, c the speed of light (=3 ×108 m/s), and h is Planck’s constant (=6.626 × 10−34 J s= 4.135 × 10−15 eV s ). The speed of an electromagneticwave in vacuum is the speed of light, thus the product of



Gamma-Ray Astronomy 399

FIGURE 1 A map of the gamma-ray sky obtained with the high-energy EGRET telescope aboard the ComptonGamma Ray Observatory. The map is an all-sky Aitoff equal-area projection in Galactic coordinates with the directionof the Galactic Center at the middle of the map. The bright horizontal band is predominantly diffuse gamma-rayemission from the disk of the Milky Way. Prominent gamma-ray sources are indicated and labeled around the peripheryof the figure. (Courtesy NASA, the Max Planck Institute, and the CGRO EGRET Instrument Team.)

frequency and wavelength equals c (or, νλ = c). At en-ergies below or near the optical, sub-bands of the E-Mspectrum are traditionally referred to either in terms oftheir wave properties (in the radio, for example, there arethe meter, centimeter, millimeter, submillimeter, and mi-crowave bands), or in terms of their relation to the cen-tral optical band (the near versus far infrared bands, forexample, of shorter and longer wavelength, respectively,and the extreme ultraviolet beyond the optical and UV).Once in the X-ray band, however, one enters the realm ofhigh-energy astrophysics and tends to abandon the wave-length/frequency nomenclature in favor of particle andenergy terminology that is better suited to the descrip-tion of photon interactions at these energies. Thus X-raysare generally referred to in broad terms as either soft orhard in energy content (with a loosely defined boundary inthe keV energy range). Similarly, gamma rays themselveshave been subdivided into soft and hard regimes, or other-wise characterized as of low, medium, or high gamma-rayenergy. Given the very broad range of gamma-ray energies

that are now observable (spanning more than 10 orders ofmagnitude in energy) one now usually refers to gammarays by their energy designation alone, as either MeV, GeV,TeV, or even PeV, gamma rays, where standard order-of-magnitude prefixes apply (for the above, 106, 109, 1012,and 1015 eV, respectively).

Much of the radiation with which we are familiar ineveryday life is of thermal origin, arising by definitionfrom matter in thermal equilibrium. In an ideal atomicgas in thermal equilibrium, for example, the upward ver-sus downward transitions of bound electrons between en-ergy levels in individual atoms are in close balance dueto the exchange of energy between particles via colli-sions and the absorption and emission of radiation. Thevelocities of particles in an ideal thermal gas followthe well-known Maxwellian distribution, and the collec-tive continuous spectrum of the radiating particles is de-scribed by the familiar Planck black-body radiation curvewith its characteristic temperature-dependent profile andmaximum.




Gamma rays, in contrast to other forms of electromag-netic radiation, are most often of nonthermal origin, aris-ing usually from interactions involving high-energy, rela-tivistic particles in an ionized plasma whose constituentsare not in thermal equilibrium with their surroundings. Arelativistic particle is one whose kinetic energy is compa-rable to or exceeds its rest-mass energy given by Einstein’sfamous relation, E = mc2. Thus,

total particle energy = (rest-mass + kinetic)energy

= γ mc2,

where γ = (1−v2/c2)−1/2 is the relativistic Lorentz factorfor a particle traveling at velocity v. Interactions involvingrelativistic particles are properly treated within the frame-work of relativity. For sufficiently low velocities the famil-iar nonrelativistic case (v/c � 1, γ → 1) is re-obtained inwhich the relations of classical Newtonian physics ap-ply. In the standard relativistic regime the particle ve-locity approaches c, v/c → 1 and γ ≥ 1 (for example, aparticle traveling at 90% of the speed of light will havev/c = 0.9 and γ ∼= 2.3), whereas in the most extreme ultra-relativistic case (v/c ∼ 1, γ � 1) the total energy of theparticle is dominated by its kinetic energy. Photons of suf-ficiently high energy in cosmic sources can be diminishedin intensity via the photon–photon pair-production process(γ γ → e+e−) which is most likely to occur just above thereaction threshold when the product of the two photon en-ergies is equal to the product of the electron–positron rest–mass energies, Eγ 1 Eγ 2 ∼ 2(mec2)2 ∼ 0.52 (MeV)2. In as-trophysical sources, then, the energy density of gammarays may be sufficiently high to prevent their escape dueto their greater likelihood of producing pairs. Such mediaare said to have a high pair-production opacity.

Given the relativistic nature of the major gamma-rayproduction mechanisms we adopt in this review the energycorresponding to the rest–mass energy of the electron,mec2 ∼ 511 keV ∼ 0.511 MeV, as a natural referenceenergy defining the lower boundary of the gamma-rayregime. (We note that, historically, among physicists ofa certain age, gamma rays were defined simply as the ra-diation resulting from nuclear transitions, independent ofthe energies involved, in recognition of the predominantnuclear origins of gamma radiation. We adopt here themore current view of a specific energy regime.)

Gamma-ray astronomy is closely linked to several otherbranches of modern observational astrophysics. A numberof these subdisciplines of astronomy are described else-where in these volumes. Gamma-rays, by virtue of theirhigh energy, also play a particularly key role in broadbandmultiwavelength astronomy, by which is meant the studyof a celestial object or phenomenon over as broad a portionof the electromagnetic spectrum as possible.

B. The Production of Cosmic Gamma Rays

A wide variety of production mechanisms give rise togamma radiation, resulting in either continuum orspectral-line emission. Gamma rays most often result fromhigh-energy collisions between nuclei, particles, and otherphotons, or from the interactions of charged particleswith magnetic fields. Line emission can arise from thedeexcitation of nuclear states, from radioactive decay, orfrom matter–antimatter annihilation. The primary produc-tion mechanisms of interest to gamma-ray astronomy aresummarized in the following.

1. Particle–Nucleon Interactions

High-energy nuclear collisions frequently yield chargedand neutral mesons as unstable reaction products. Chargedpions (π+ and π−) decay into positive and negativemuons that decay in turn into relativistic electrons andpositrons. Neutral pions (π0) decay almost immediately(t1/2 ∼ 10−16 s) into two gamma rays of total energy equalto approximately 68 MeV in the rest frame of the decay-ing meson. The resulting gamma-ray spectrum depends onthe distribution of particle energies of the original emit-ted pions, and is generally a broad continuum centeredand peaked at Eγ ∼ mπc2/2 ∼ 68 MeV. Nucleon–nucleoninteractions play an important role in the production ofdiffuse high-energy gamma rays in the disk of the Galaxyfollowing the collision of high-energy cosmic rays (pri-marily protons) with the nuclei of the atoms and moleculesof the interstellar gas.

Collisions between high-energy particles and ambientmatter can also result in the copious production of numer-ous other secondary particles, including neutrons. High-energy neutrons are capable of exciting nuclei in sec-ondary collisions, leading to gamma ray line emission (seefollowing). Further, neutrons can be slowed in the inter-acting medium to thermal energies whereupon they can bequickly captured by nuclei, again giving rise to gamma-ray lines. Neutron processes play an important role in solarflares, and in the production of gamma rays on planetarysurfaces after cosmic-ray bombardment.

2. Nuclear Gamma-Ray Lines

Nuclear deexcitation following energetic collisions or ra-dioactive decay gives rise to spectral line radiation whosespecific energies are characteristic of the emitting nu-clides. Nuclear gamma-ray line radiation extends up to∼9 MeV in energy for the most commonly abundant el-ements and likely interaction processes. The intensitiesand ratios of observed gamma-ray lines can provide de-tailed information on elemental composition and relativeabundances (for example, in solar flares).




3. Relativistic Electron Interactions

Relativistic electrons can interact with charged particlesvia the bremsstrahlung process, with photons throughCompton scattering, and with magnetic fields by emittingsynchrotron radiation. These processes dominate manyof the energy regimes in the field of high-energy astro-physics. They give rise to continuum gamma radiation,whose spectral characteristics can be used to deduce thephysical conditions at the astrophysical source.

(a) Bremsstrahlung. Bremsstrahlung (or “brakingradiation”) is the radiation given off by free electronsthat are deflected (i.e., accelerated) in the electric fieldsof charged particles and the nuclei of atoms. Thermalbremsstrahlung is the emission given off by an ionizedgas of plasma in thermal equilibrium at a particular tem-perature, where the distribution of electron velocities fol-lows the well-known Maxwellian distribution. Relativis-tic electrons, whose distribution of energies often followsa power-law shape in astrophysical settings, give rise torelativistic bremsstrahlung radiation that is also of power-law shape with the same spectral index as the emittingelectrons.

(b) Compton scattering. Another major source ofcosmic gamma radiation is the Compton scattering oflower-energy photons to gamma-ray energies by relativis-tic electrons. This process is often referred to as “inverse”Compton scattering since it is the low-energy photon thatgains energy from the high-energy electron, in contrast tothe more standard view of the Compton mechanism. In theultrarelativistic case, it can be shown that the energy of thephotons scattered by high-energy electrons is E ∼ γ 2Ee

(in the Thomson limit when the energy of the photon inthe center-of-momentum frame of reference is much lessthan mec2), where γ is the relativistic Lorentz factor of theelectrons. For relativistic electrons with γ ∼100–1000, asobserved in many astrophysical sources, this implies thatlow-energy photons can be up-scattered to very high en-ergies indeed, well into the gamma-ray regime.

(c) Synchrotron radiation. Synchrotron emissionresults when an electron gyrates around a magnetic field.For electrons of sufficiently high energy, or for magneticfields of sufficiently high strength, high-energy photonemission readily results. Again, for a power-law distribu-tion of electron energies, a power-law synchrotron emis-sion spectrum follows. The relation between the observedintensity (I ) of the synchrotron radiation as a function offrequency (ν), the magnetic field strength (B), and thepower-law index (p) of the electron particle distributionis given by I (ν) ∝ B(p+1)/2ν−(p−1)/2.

Collectively, these emission processes represent theprimary energy-loss (or “cooling”) mechanisms for rel-ativistic electrons in astrophysical sources, the othermajor process being “ionization” losses via particle col-lisions. Observations of high-energy emission from ce-lestial sources that can be decomposed into synchrotron,bremsstrahlung, and Compton components from charac-teristic spectral signatures therefore provides a wealth ofinformation on the physical conditions within the emit-ting regions (such as particle densities, and the strengthsof radiation and magnetic fields).

4. Electron–Positron Annihilation

A free electron and its antiparticle, the positron, may inter-act to produce annihilation radiation yielding two gammarays (e+e− → γ γ ). The total energy of the two photons inthe center-of-momentum frame of reference is equal to thecombined rest–mass energy of the electron–positron pair,2mec2 ∼ 1.022 MeV. (Three-photon annihilation can alsooccur for free electrons and positrons, but is much lesslikely.) If an electron and positron are essentially at restupon annihilation then two gamma rays of equal energy(0.511 MeV) are produced. In the more general astrophys-ical case, however, one or both particles are at relativisticvelocities, and a more complicated emergent gamma-rayspectrum usually results.

An electron and positron of sufficiently low energy (typ-ically thermal, ≤5 eV) may combine to briefly form ahydrogen-like state of matter referred to as positronium.Positronium almost immediately self-annihilates yield-ing either a two- or three-photon decay into gamma rays(τ2γ ∼ 10−10 s, τ3γ ∼ 10−7 s).

C. A Brief History of Gamma-Ray Astronomy

It was quickly recognized at the dawn of the nuclear agethat the potential existed for the detection of celestialgamma rays from high-energy sources in the cosmos. Inthe early 1950s discussions were already underway on thelikelihood of gamma-ray production via cosmic-ray inter-actions in interstellar space (cosmic rays are high-energy,relativistic particles and nuclei of celestial origin). In now-classic papers Burbridge, Burbridge, Fowler, and Hoyle,in 1957, laid out the principles governing the synthesisof heavy elements in stellar nuclear burning and duringexplosive nucleosynthesis in supernovae, and Morrison in1958 similarly described many of the fundamental mech-anisms and sources for the production of cosmic gammarays.

Through the 1960s a number of balloon and early space-craft observations (e.g., the Ranger spacecraft missions tothe Moon) provided intriguing but inconclusive evidence




for the existence of cosmic gamma-rays. The first positivedetection of celestial gamma radiation was made with aninstrument aboard the third Orbiting Solar Observatory(OSO-3), whose investigators reported in 1972 the detec-tion of gamma rays from the Galactic disk, with a peakintensity observed toward the Galactic Center. In the early1970s several high-altitude balloon experiments were alsobeginning to report positive results, including detection ofthe Crab pulsar and of diffuse gamma radiation from thedisk and central region of the Galaxy. Nuclear gamma-raylines from the Sun were detected from large solar flares onAugust 4 and 7, 1972, with a spectrometer aboard OSO-7.The first reported detection of likely positron annihilationradiation (at 0.511 MeV) from the direction of the Galac-tic Center was based on balloon measurements from 1971,and later confirmed by other investigators with a detectorof higher spectral resolution in 1977. As described else-where in this review, gamma-ray spectrometers carriedto the Moon by both U.S. and Russian spacecraft in thelate 1960s and 1970s provided extensive orbital and insitu measurements of the elemental composition of thelunar surface. Similar experiments in the 1970s were car-ried to Mars aboard the U.S. Viking landers, and to Venuson the Russian Venera landers. Most intriguing was theannouncement in 1973 of the discovery of the mysteri-ous cosmic gamma-ray bursts with instruments aboardthe Vela series of nuclear surveillance satellites (launchedoriginally to verify compliance with the 1963 Nuclear TestBan Treaty).

A major advance in the field of gamma-ray astron-omy came with the launch in 1972 of the second SmallAstronomy Satellite (SAS-2). Over its 7-month lifetimeSAS-2 carried out a survey of high-energy gamma-rayemission (>50 MeV) from the Galactic plane, and pro-vided a first measure of the extragalactic diffuse gamma-ray background. This pioneering mission was followedwith the launch of the COS-B gamma-ray satellite by theEuropean Space Agency in 1975. Over its 7-year lifetimeCOS-B greatly extended our knowledge of the gamma-raysky, providing detailed maps of the diffuse gamma radia-tion arising from the Galactic plane, as well as cataloginga number of point sources of high-energy gamma rays, in-cluding the first detected extragalactic source, the quasar3C 273.

Two gamma-ray instruments were carried into spacein the late 1970s as part of NASA’s High Energy Astro-nomical Observatory (HEAO) series of satellites. HEAO-1conducted a survey of the sky from 10 keV to 10 MeV inenergy, and identified a number of active galaxies and char-acterized their spectra in the 10- to 100-keV range. TheHEAO-3 experiment discovered the first nonsolar nucleargamma-ray line of celestial origin, the 1.809-MeV spec-tral line emitted by radioactive 26Al that is produced in

massive stars and is a tracer of recent star formation inthe Galaxy. In 1980, NASA launched the Solar MaximumMission (SMM) satellite which carried a gamma-ray spec-trometer among its suite of instruments. Over its extended10-year lifetime SMM provided a wealth of new infor-mation on gamma-ray processes occurring during flareson the Sun, and also made fundamental contributions tononsolar gamma-ray astronomy. These included the dis-covery of greater-than-MeV emission from gamma-raybursts, confirmation of the diffuse 26Al emission detectedby HEAO-3, and further observation of the positron an-nihilation radiation coming from the central region of theGalaxy. Particularly notable was the SMM detection ofradioactive 56Co line emission from the Type II super-nova SN 1987A in the Small Magellanic Cloud, provid-ing a long-awaited first direct measure of explosive nu-cleosynthesis in supernovae. The French coded-apertureSIGMA telescope was carried into space aboard the SovietGRANAT satellite in 1989. Among other observations,this lower-energy (up to ∼1.3 MeV) instrument identifieda number of black-hole candidate sources in the centralregion of the Galaxy based on the observed spectral andtemporal behavior.

The realm of ground-based gamma-ray astronomy,where different observational challenges present them-selves, begins at photon energies of ∼50 GeV (some-times termed the very-high-energy, or VHE, gamma-rayregime). Gamma-rays approaching TeV energies becomeincreasingly rare in number, and cannot be well sampledby existing spacecraft-borne instrumentation. Further, theabsorbing medium of the Earth’s atmosphere precludestheir direct observation from the ground. Their presence,however, can be inferred indirectly from the electromag-netic cascades of electrons and positrons that they pro-duce upon interaction in the upper atmosphere. (Thesecascades are also referred to as extensive air showers, orEAS.) The relativistic cascade particles emit Cherenkovlight over a wide area that can be detected with opticaltelescopes on the ground. A particular difficulty, however,is distinguishing such photon-induced events from the nu-cleonic (or hadronic) cascades produced by high-energycosmic-ray particles in the atmosphere, which exhibit verysimilar observable effects. Atmospheric Cherenkov imag-ing telescopes were originally proposed in the 1970s, butonly in the 1990s did the techniques and instrumentationbecome sufficiently developed to achieve breakthroughdetections of several high-energy gamma-ray sources. Inthe late 1980s the Whipple Observatory first detected TeVemission from the Crab pulsar and nebula, and this hasbeen followed in recent years with detections by sev-eral groups of TeV emission from a small number ofboth Galactic and extragalactic sources (outlined in latersections).




FIGURE 2 Schematic of the four gamma-ray telescopes aboard the Compton Gamma Ray Observatory and theircorresponding overlapping energy ranges. Also indicated are classes of prominent gamma-ray sources by energyband. (Courtesy NASA.)

D. The Compton Gamma-Ray Observatory

The great potential of gamma-ray astronomy as a vi-able, productive branch of observational astrophysicswas not fully realized until the launch of the Comp-ton Gamma Ray Observatory (or CGRO) in April 1991.The Compton Observatory was the second of NASA’sfour planned Great Observatory missions that were de-signed to study the sky from space in different key re-gions of the electromagnetic spectrum. The first of thesewas the Hubble Space Telescope (launched in 1990), thesecond the CGRO (launched in 1991), and the third theChandra X-ray Observatory (launched in 1999). At thetime of writing, the Space Infrared Telescope Facility(SIRTF) is awaiting an anticipated launch in 2002. TheCGRO was named in honor of the American physicistArthur Holly Compton (1892–1962), whose pioneeringinvestigations into the scattering of X-rays and gammarays by charged particles earned him the Nobel prizefor physics in 1927. After more than 9 years of suc-cessful operation, the CGRO mission was terminated inJune 2000, when the spacecraft was deorbited for safetyreasons.

The CGRO carried four separate, complementarygamma-ray telescopes with overlapping energy ranges,

each designed for specific scientific objectives and de-veloped by an international collaboration of scientists.The combined energy coverage of the CGRO detectorsextended over 6 orders of magnitude from ∼30 keV to30 GeV (see Fig. 2). The key characteristics of eachof the four CGRO instruments are summarized in thefollowing.

The Burst and Transient Source Experiment (BATSE)was an all-sky monitor consisting of eight separate de-tectors mounted on the corners of the main platform ofthe CGRO spacecraft. Its primary objective was to de-tect and measure rapid brightness variations in gamma-raybursts and solar flares down to microsecond time scalesover the energy range from 30 keV to 1.9 MeV. BATSEcontinually monitored the sky for transient phenomena,searching for variable emission from both known and newsources.

The Oriented Scintillation Spectroscopy Experiment(OSSE) was designed to carry out pointed spectral obser-vations of gamma-ray sources in the range from 0.05 to10 MeV, with capability above 10 MeV for solar gamma-ray and neutron observations. The four OSSE detectorswere collimated scintillators (with a 4◦ × 11◦ field of view)that were movable over a single axis, allowing a rapidresponse to targets of opportunity such as solar flares,




FIGURE 3 An all-sky map of gamma-ray sources detected with the COMPTEL and EGRET telescopes aboardthe Compton Gamma Ray Observatory. Classes of sources are indicated by symbol, with increasing symbol sizerepresenting higher source intensity. The map is an Aitoff equal-area projection in Galactic coordinates (as in Fig. 1).(Courtesy NASA, the Max Planck Institute, and the CGRO COMPTEL and EGRET Instrument Teams).

transient X-ray sources, and other explosive astrophysi-cal phenomena.

The Imaging Compton Telescope (COMPTEL) de-tected gamma-rays by means of a double-scatter techniquewhereby an incident gamma photon Compton scatteredonce in an upper detector module, and then was totallyabsorbed in a lower detector module. The COMPTEL in-strument was sensitive over the energy range from approx-imately 0.75 to 30 MeV, and was also capable of detectingneutrons from solar flares. With its large field of view(∼1 steradian) COMPTEL carried out the first survey ofthe gamma-ray sky at MeV energies.

The Energetic Gamma Ray Experiment Telescope(EGRET ) covered the broadest energy range of the CGROinstruments, from∼20 MeV to 30 GeV. These high-energyphotons interact primarily via the pair-production pro-cess, and the EGRET spark chamber was designed to de-

tect the electron–positron pairs produced by high-energygamma rays. EGRET also had a relatively wide field ofview (∼0.6 sr), good angular resolution, and very lowbackground.

The coaligned COMPTEL and EGRET instruments op-erated as wide-field imaging telescopes and together car-ried out a comprehensive survey of the gamma-ray skyfrom MeV to GeV energies (see Figs. 1 and 3). Takentogether the four CGRO telescopes represented a majorimprovement in sensitivity, energy coverage, and spectraland angular resolution, compared to previous generationsof gamma-ray instruments. It can be said without exagger-ation that observations carried out with the CGRO havecompletely revolutionized our view of the high-energyUniverse. The bulk of the scientific results discussed inthe sections to follow are based on observations obtainedwith the four CGRO telescopes.




II. SOURCES OF COSMIC GAMMA RAYS

Our view of the gamma-ray sky has changed dramaticallyin recent years, and has been particularly influenced by theresults obtained with the instruments aboard the ComptonGamma Ray Observatory. The energetic and variable cos-mos revealed by gamma-ray telescopes stands in markedcontrast to the quiescent night sky viewed in visible lighton a placid summer evening. The Universe in the light ofgamma rays is a dynamic, diverse, and constantly chang-ing place.

A. The Sun

The Sun is a powerful site for the acceleration of energeticparticles. The source of energy for particle acceleration isbelieved to be the tangled magnetic field in the solar atmo-sphere. However, our understanding of both the propertiesof the accelerated particles and the nature of their acceler-ation during the explosive release of energy in a solar flareis still emerging. Gamma-ray measurements have provedto be an essential tool for studying particle accelerationduring flares.

The rich energy spectrum of gamma-ray emission fromsolar flares is quite complex and shows the signatures ofmany radiation processes. Below ∼1 MeV the observedemission is dominated by a strong line at 0.511 MeVfrom positron annihilation and a smooth continuum ofbremsstrahlung radiation from mildly relativistic elec-trons. In the energy band from 1 MeV to 10 MeV theemission results predominantly from the deexcitation ofnuclear levels following the bombardment of nuclei inthe solar atmosphere by energetic particles. This nucleardeexcitation emission is composed of four components:(1) promptly emitted narrow lines from the excitation of aheavy atmospheric nucleus by an energetic proton or alphaparticle, (2) broad lines from the excitation of an acceler-ated heavy ion by collision with an atmospheric hydrogenor helium nucleus, (3) delayed line emission such as thestrong line at 2.22 MeV from the capture of secondaryneutrons by atmospheric hydrogen to form deuterium,and (4) a quasi-continuum produced by the blending oflines from high-level transitions excited in both the accel-erated and target nuclei. Above 10 MeV the emission isdominated by two mechanisms: bremsstrahlung from bothultra-relativistic primary electrons and secondary elec-trons/positrons from meson decay, and gamma rays fromthe direct decay of neutral pions. The complexity of thegamma-ray spectra of flares provides many diagnostics forprobing the properties of flare-accelerated electrons andions (see Fig. 4).

Measurements of the bremsstrahlung continuum dur-ing solar flares indicate that relativistic electrons are a

common product of energy release in flares. The gamma-ray bremsstrahlung generated by relativistic electrons in-dicates that the yield in relativistic electrons scales roughlywith the total energy released in thermal X-rays by theflare. Further, increasingly sensitive searches for gamma-ray bremsstrahlung over the last 2 decades have foundno evidence of a flare-size threshold for relativistic elec-tron acceleration. The gamma-ray evidence therefore sug-gests that relativistic electron acceleration is a propertyof all flares. The gamma-ray observations also show thatthe relative amount of high-energy bremsstrahlung in-creases as the position of the flare approaches the so-lar limb. Since high-energy bremsstrahlung is directedmore strongly along the electron’s velocity vector thanbremsstrahlung at lower energies, the limb brighteningcan be explained by a distribution of emitting electronsthat increases in directions away from the surface normalat the flare site. The nature of this electron distribution isregulated by the complex magnetic field structure in flar-ing regions. Future techniques that can measure the angu-lar distribution of gamma-ray bremsstrahlung will allowus to explore the nature of relativistic electron transport inflaring regions.

Nuclear deexcitation emission during flares indicatesthat energetic ion acceleration is also a common propertyof solar flares. Gamma rays from nuclear deexcitationswere first detected from two giant flares that occurred inAugust 1972. The enormous size of those flares and thefact that they were the only ones detected during that so-lar cycle led to an initial suspicion that ion accelerationmight only occur when the flare energy surpasses a rela-tively high threshold. Sensitive detectors aboard the SolarMaximum Mission (SMM) satellite and the Compton Ob-servatory, however, showed that nuclear line emission ispresent even in relatively small flares. While the relativeimportance of accelerated ions and electrons is observedto vary by approximately an order of magnitude, existingmeasurements are consistent with the hypothesis that bothcomponents are accelerated in all solar flares.

The temporal structure of variations in gamma-ray fluxduring flares can be quite rich. Gamma-ray flares can rangefrom a single spiked pulse of 10-s duration to a complexseries of pulses with total duration of more than 1000 s.Typically flares are composed of two or more pulses. Aninteresting property of the pulse structure is that the timeof peak intensity is often energy dependent. When thisenergy dependence is present, the peak at higher energiestends to lag the peak intensity at lower energies by asmuch as 45 s. At one time, these delays were interpretedas reflecting the timescale needed for particle accelerationduring flares. However, we now know that there are manyflares where the peaks at X-ray through gamma-ray en-ergies show time coincidence to better than 2 s and that,




FIGURE 4 The gamma-ray spectrum of the June 4, 1991, solar flare obtained with the OSSE instrument aboardthe Compton Gamma Ray Observatory. Prominent gamma-ray emission lines are identified, along with the primaryprocesses responsible for both the observed line and continuum emission. (Courtesy NASA and the CGRO OSSEInstrument Team (G. H. Share and R. J. Murphy.))

even when significant peak delays are present, the pulsestarting times are simultaneous to within 2 s. Those obser-vations show that both electrons and nuclei can be rapidlyaccelerated to relativistic energies within seconds duringsolar flares. We now believe that the delays are largely gen-erated by propagation and interaction effects as particlesmove from a low-density acceleration region high in thesolar atmosphere to a higher-density interaction regiondeeper in the atmosphere where the high-energy emissionis generated.

B. The Solar System

The question of the origin and evolution of the solar sys-tem is one of the most fundamental in astronomy. It bearsdirectly on such related issues as stellar evolution, the for-mation of planetary systems, and on the existence of lifeitself. Gamma-ray observations from spacecraft, either viaremote sensing from orbit or through in situ measurements

from landers, contribute directly to the testing of evolu-tionary models of solar-system formation. Specifically,they provide a means of directly determining the elemen-tal chemical composition of planetary surfaces, thus pro-viding clues important to reconstructing the geochemicalhistory of the solar system. Related complementary obser-vational techniques include X-ray fluorescence measure-ments, and the detection of albedo neutrons and chargedparticles from planetary surfaces.

The gamma-ray observations relevant to planetary stud-ies are spectroscopic in nature, aimed at identifyingspecific key elements present in planetary surfaces viatheir characteristic emission energies. The abundances ofelements with different condensation temperatures andgeochemical behavior relate directly to the origin and evo-lution of planetary bodies. For example, the K/U ratioprovides a measure of the remelting of primordial conden-sates, while the K/Th ratio indicates the relative abundanceof volatile to refractory elements.




Gamma-ray spectral lines originate in nuclear pro-cesses, either from radioactive decay or from nuclear de-excitation following particle collisions. Natural radioac-tivity results from the decay of the primordial radioactiveelements 40K, 138La, 176Lu, and those in the uranium andthorium decay sequences. Collisions of primary Galacticcosmic rays (of which ∼90% are protons) with planetarymaterial can give rise to numerous interactions and sec-ondary particles, leading to gamma rays. Extensive modelcalculations of cosmic ray-induced gamma-ray emissionfrom planetary bodies have been carried out and can bereadily compared to the available observations.

Since the 1960s measurements of X-rays, gamma rays,alpha particles, and neutrons from the Moon, Mars, andVenus have been undertaken successfully with a variety ofinstruments aboard both U.S. and Russian spacecraft. Thetwo U.S. Viking landers on Mars, for example, carried outX-ray fluorescence measurements of the Martian surface,while the Russian Venera 8, 9, and 10 spacecraft mea-sured the natural radioactivities of potassium, uranium,and thorium at three landing sites on Venus.

Until very recently the most detailed and extensiveremote-sensing observations of a planetary body were car-ried out during the Apollo 15 and 16 flights to the Moon(1971, 1972) when instruments aboard the orbiting com-mand modules mapped approximately 20% of the lunarsurface in X-rays, gamma rays, and alpha particles. TheApollo missions were also unique in that a detailed com-parison could be made between the results of the remotemapping and follow-up compositional analysis of actualreturned samples of lunar material.

The Apollo measurements clearly demonstrated thatthe Moon’s crust is chemically differentiated, with a pro-nounced distinction between maria and highland regions,with the maria primarily basaltic in nature. On a more lo-calized scale, material around craters tends to exhibit a sig-nificant chemical contrast relative to surrounding regions,suggesting an excavation of material from the subsurfacedue to impacts from asteroids and comets. Distributionpatterns seem to favor an impact rather than a volcanicdispersal. The observed K/Th ratio has provided a mea-sure of the volatile-to-refractory material variation overthe lunar surface, which is found to be consistently lowerthan the terrestrial value, reflecting a global depletion ofvolatiles on the Moon compared to the Earth.

More recently the U.S. Lunar Prospector mission suc-cessfully obtained (1998–1999) global maps of the lu-nar surface using gamma-ray and neutron spectrometers.The results have generally confirmed the earlier Apollofindings. As a follow-up to the Apollo measurements,there is a particular interest in determining the distribu-tion of “KREEP”-rich material on the Moon. KREEPrefers to an unusual mixture of elements containing potas-

sium (K), rare-earth elements (REE), and phosphorous (P)that is believed to have formed at the lunar crust-mantleboundary as the final product of the initial differentia-tion of the Moon. Understanding the composition anddistribution of KREEP-rich material is thus consideredkey to reconstructing the evolution of the lunar crust. TheLunar Prospector data have demonstrated that KREEP-rich rocks tend to be found on the rims and boundariesof major lunar impact basins where there are surmised tohave been exposed, dredged up, and dispersed as a resultof these cataclysmic impact events. The most intriguing ofthe recent lunar neutron observations point to the possiblepresence of subsurface water ice at the lunar poles (whoseexistence was first indicated by radar measurements car-ried out with the Clementine spacecraft in orbit around theMoon in 1994).

In 2001, in an engineering tour de force, the Shoemaker-NEAR (Near Earth Asteroid Rendezvous) spacecraft com-pleted its successful year-long orbital study of the aster-oid 433 Eros with a spectacular unplanned landing on theasteroid’s surface, transforming its on-board X-ray andgamma-ray spectrometers from remote-sensing to in situinstruments. Initial analysis of the NEAR spectrometerdata suggests that Eros may remain in an undifferentiatedstate, unaltered by melting, constituting some of the mostprimitive material in the solar system yet studied. Also in2001, the NASA’s Mars Odyssey spacecraft is scheduledfor launch, carrying a gamma-ray spectrometer among itssuite of instruments. If the goals of these missions are fullyrealized complete global maps of elemental distributionfor the Moon, Eros, and Mars, representing three bodieswith distinct evolutionary histories, will be available fordetailed comparative studies.

C. Galactic Sources

As anyone who has gazed at the night sky from a darklocation knows, the distribution of visible stars is not ran-dom. Rather, stars tend to cluster in a bright band called theMilky Way that delineates the plane of the flat spiral galaxyin which we live. Like the stars, there is also a population ofgamma-ray sources that cluster in the plane of the Galaxyand that are believed to reside within the Milky Way. How-ever, our ability to associate them with visible counterpartsin the crowded Galactic plane is hampered by the fact thatthe angular resolution of the best gamma-ray telescopes isstill a hundred times coarser than even small backyard op-tical telescopes. As a consequence, many Galactic “point”gamma-ray sources have multiple counterpart candidatesand, even worse, in many directions in the Galactic planewe know that the gamma emission from several “point”sources is actually blended together and gamma-ray tele-scopes are “source confused.” Nevertheless, by studying




the temporal variations of the gamma-ray emission andcorrelating it with intensity variations measured by higher-resolution X-ray, optical, or radio telescopes, we have beenable to identify with certainty several classes of Galacticgamma-ray sources.

1. Isolated Pulsars

Among the best clocks known, natural or man-made, arethe spinning, magnetized neutron stars called pulsars. Pul-sars emit short bursts of electromagnetic radiation at in-tervals from one every few seconds to thousands of timesa second with a regularity that exceeds that of watchesof the highest precision. In some cases this electromag-netic pulse extends across the entire spectrum from radioto gamma-ray wavelengths, thereby allowing us to unam-biguously identify these Galactic gamma-ray sources.

The best-known gamma-ray emitting pulsar is the so-called Crab pulsar. It is embedded in and is the sourceof power for the famous Crab nebula in the constellationTaurus, the first object (M1) listed in the renowned cata-log of diffuse, nebular objects compiled by the French as-tronomer Charles Messier in the late 18th century. Frommedieval Chinese records describing the temporary ap-pearance of a “guest star” near the star we now call ZetaTauri, we know that the Crab pulsar was the product of asupernova explosion that occurred in the year 1054 AD.Every 33 ms, the Crab pulsar emits a pair of radiationpulses that are detectable from the radio band all the wayup to TeV gamma-ray energies. While pulsar physics stillhas many open questions, it is generally agreed that theemission from isolated pulsars is generated by energeticparticles that are accelerated by electric fields induced bythe spinning magnetic field of a rapidly rotating, mag-netized, neutron star. The energy reservoir that ultimatelypowers all the observed emission is therefore the rotationalenergy of the rapidly spinning pulsar.

At least six other isolated gamma-ray pulsars are cur-rently known to exist and from that small sample a fewgeneral patterns are apparent. First, for all known isolatedgamma-ray pulsars the gamma emission represents thelargest observable fraction of the total power emitted bythe pulsar. As a consequence, observational study of thegamma rays provides important diagnostics on the over-all efficiency for particle acceleration and interactions inthe extreme pulsar environment. Second, the gamma-rayvisibility increases with the spin-down luminosity (or, theratio of the magnetic field strength to the square of the spinperiod). Finally, all of the isolated gamma-ray pulsars ap-pear to be unvarying point sources when their emission isaveraged over the spin period.

Perhaps the most remarkable object in the sampleof known gamma-ray-emitting pulsars is Geminga. For

nearly 20 years this source, which is the second bright-est source in the gamma-ray sky, was a puzzle because itdid not appear to emit radiation in any other energy band.The unusual name, Geminga, was coined by Italian as-tronomers and is derived both from the source’s locationin the constellation Gemini and from a play on words,geminga meaning “is not there” in the Milanese dialect.The breakthrough in our understanding of Geminga oc-curred in 1991 when pulsating soft X-ray emission with aperiod of 0.237 s (=237 ms) was detected from the direc-tion of Geminga by the ROSAT X-ray satellite. Identifica-tion of Geminga as pulsar was therefore clinched when aphase analysis revealed that the gamma-ray emission wasalso modulated at the same 0.237-s period (see Fig. 5). Aparticularly interesting property of Geminga is that, unlikeother rotation-powered pulsars, it is not detectable as a ra-dio pulsar even though it is thought to be only 100 parsecsfrom the Sun. Since our census of the population of pulsarsis based on radio observations, it is possible that Gemingais just the nearest member of a large population of pre-viously unknown pulsars that are only visible at X-rayand gamma-ray energies. Many of the steady, unidenti-fied gamma-ray sources could therefore be Geminga-typepulsars with still unknown spin periods.

2. Accreting Pulsars

Not all pulsars are isolated. Some reside in binary stellarsystems and some of these pulsars are X-ray sources thatare powered by the gravitational energy released when gasfrom the companion star is accreted onto the neutron star.Those accreting pulsars are also likely sources of gamma-ray emission. Indeed, several groups using ground-basedCherenkov telescopes have reported the detections of TeVgamma-ray emission from systems containing an accret-ing pulsar. Unfortunately, most of the reported detectionshave been of low statistical significance and/or not con-firmed with subsequent more sensitive observations. Ifreal, they indicate that the gamma-ray emission from ac-creting pulsars is sporadic. On theoretical grounds, suchbehavior is plausible because accretion flows are often un-stable and shocks in the flow could efficiently accelerategamma-ray emitting particles.

Support for the idea that accreting pulsars sporadicallyemit gamma-ray emission was also found with the EGRETtelescope aboard the Compton Gamma Ray Observatory.In October 1994 a week-long outburst of GeV gamma-rayemission was detected from the direction of the massiveX-ray binary system Centaurus X-3. During the outburst,the accreting pulsar in Cen X-3 underwent an interval ofrapid spin-down. Phase analysis of the gamma-ray emis-sion showed evidence for spin modulation in step with therapidly drifting X-ray period.




FIGURE 5 Pulsed gamma-ray emission from the Geminga pulsar. Above: The light curve of the gamma-ray emissionfrom Geminga, with the gamma rays binned according to the pulsar period of 237 milliseconds. Below : Gamma-rayimages of the region of the sky containing the Geminga pulsar, showing the brightening of the source (in the upperleft of the image plots) in phase with the pulsed emission. The fainter object at the lower right is the Crab pulsar (witha different pulse period of 33 ms) which appears as a steady source in this representation. (Courtesy NASA and theCGRO EGRET Instrument Team (P. Sreekumar)).

3. Black-Hole Binary Systems

Some X-ray binary systems are believed to contain stellar-mass black holes that are embedded in disks of inwardlyspiraling accreted gas. These accretion disks are knownsources of both soft and hard X-ray emission and, in somecases, are also sources of soft gamma-ray emission. Per-haps the best-known example is Cygnus X-1, the brightestX-ray source in the constellation Cygnus. The X-ray lu-minosity of this high-mass X-ray binary (in which thenormal companion is an O or B star many times the massof the Sun) is variable and is correlated with differenthigh-energy spectral “states.” These states of activity arecomposed of different admixtures of two principal com-ponents: a soft thermal blackbody-like component and ahard nonthermal power-law component. It is this power-law component that can, at times, extend up to gamma-rayenergies of at least an MeV.

The origin of the MeV gamma ray emission fromCygnus X-1 is not well understood. Most models as-sume that the gamma rays are X-rays that were Comp-

ton scattered by mildly relativistic electrons. The pre-cise origin of those energetic electrons is still unclear.Some modelers have speculated that reconnecting mag-netic fields or shocks in disk outflows accelerate the elec-trons. However, a particularly attractive idea is that thescattering electrons arise naturally in the convergent ac-cretion flow from the innermost stable orbit of the accre-tion disk. If the accretion rate is high, Compton emissionfrom the bulk flow could generate the observed gamma rayemission.

Finally, Galactic sources that generate intense outburstsof X-ray emission that can persist for months before fad-ing are termed X-ray novae. They are known to occur inlow-mass binary systems in which the normal companionstar is of approximately solar mass in close orbit around acompact object. Such binary systems can undergo recur-rent outbursts that for a brief period can make them thebrightest high-energy sources in the sky. Optical observa-tions of these low-mass X-ray binary systems during theirquiescent states indicate that the compact object is typi-cally more massive than 3.0 solar masses and is therefore




most likely a black hole. Some outbursts of X-ray novaeare also accompanied by low-energy gamma-ray emis-sion. At least one such nova outburst, that of Nova Muscaein 1991 observed with the SIGMA instrument, displayeda variable positron annihilation line. Later observationswith telescopes aboard the Compton Observatory of NovaPersei 1992 confirmed that X-ray novae can give rise togamma-ray emission extending up to photon energies ofat least 2 MeV.

D. Gamma-Ray Lines of Galacticand Extragalactic Origin

One of the great triumphs of modern astrophysics has beenan increasingly detailed understanding of the nuclear re-action processes that govern the production of energy instars and that determine the course of stellar evolution.It is now clear that nucleosynthesis, or the production ofelements from the primordial building blocks of hydro-gen and helium, occurs almost exclusively in the coresof stars, or in the cataclysmic explosive events, super-novae and novae, that mark the end of a star’s lifetime.The study of gamma-ray spectral lines provides one of thefew direct means of verifying the predictions of the vari-ous models of stellar nucleosynthesis, and of the explosiveevents that disperse this material back into the interstel-lar medium, out of which new generations of stars areformed.

Gamma-ray lines result predominantly from nuclearprocesses, either from the decay of radioactive nuclidesand the deexcitation of excited nuclei (see Table I), or fromthe collisions of high-energy particles. The advantages ofgamma-ray line spectroscopy are manifest. Spectral linetransitions occur at specific characteristic energies thatprovide immediate identification of the isotopic speciesthat produced them. The comparison of line strengths orintensities between different elements and isotopes can betranslated into isotopic abundances, densities, and temper-atures in the emitting region. Similarly, the presence ofbroad, narrow, or Doppler-shifted lines provides a mea-

TABLE I Primary Radioactive Nuclear Decay Lines fromNucleosynthesis

Line energiesDecay process Mean halflife (MeV)

56Ni → 56Co → 56Fe 111 d 0.511, 0.847, 1.23857Co → 57Fe 272 d 0.014, 0.12222Na → 22Ne 2.6 y 0.511, 1.27544Ti → 44Sc → 44Ca ∼60 y 0.068, 0.078, 0.511, 1.15726Al → 26Mg 7 × 105 y 0.511, 1.80960Fe → 60Co → 60Ni 2 × 106 y 0.059, 1.173, 1.332

sure of gas motions and velocities, all of which can beinterpreted in terms of specific models of production.

1. Nucleosynthesis in Stars and Supernovae

Gamma-ray line radiation in the Galaxy results primarilyfrom two broad categories of production: either steady-state thermal or explosive nucleosynthesis. In the formercase, stars in hydrostatic equilibrium throughout the bulkof their lives generate energy via thermonuclear fusion re-actions in their high-temperature cores. Depending on thestellar mass (which determines core temperature), thesefusion reactions may progress over time through succes-sive stages of nuclear burning, leading to a buildup ofdifferent layers of nuclear reaction products at the centerof the star. For low- and intermediate-mass stars such asthe Sun, nuclear burning ceases with the fusion of heliuminto carbon. For the most massive stars (10–100 times themass of the Sun), however, with much higher core tem-peratures, nuclear burning leads ultimately to an iron coresurrounded by layers of silicon, magnesium, neon, oxy-gen, and carbon, along with remnant amounts of heliumand hydrogen in the outer envelope of the star. Towardthe end of its life, as it runs out of nuclear fuel, a star be-comes increasingly unstable, and the heavier elements atthe center of the star are brought to the surface via mix-ing and convective processes, and are ultimately dispersedback into the interstellar medium through high-speed stel-lar winds, flares, outbursts, and variable pulsations ofthe outer envelope and atmosphere of the star. Mixed inwith all of the reaction products are long-lived radioiso-topes that act as tracers of the various stages of nuclearburning.

Elements beyond iron in the periodic table are formedin the course of supernovae explosions that result eitherfrom the cataclysmic collapse of a white dwarf into aneutron star due to the accretion of matter from a bi-nary companion (a Type I supernova), or from the catas-trophic core-collapse of the most massive stars at the endof their lives when nuclear fuel is exhausted (a Type IIsupernovae). Subcategories of each type also exist. In theformer case, the entire star is disrupted, liberating approx-imately 1051 ergs in the explosion and about 0.5 to 1.0solar masses in synthesized radioactive material, while inthe latter class of event slighter higher energies may be lib-erated (up to ∼1053 ergs) but thick layers of ejecta partiallymask for a time the 0.1 solar masses of radioactive mate-rial synthesized in the explosion. Supernovae are amongthe most violent and luminous events known in the Uni-verse, with ejected material attaining speeds of thousandsof kilometers per second. A supernova at peak light maycompletely outshine its host galaxy (containing billions ofstars), and its light curve decays at the exponential rates




characteristic of the primary radioactive species producedin the explosion.

The gamma-ray lines of primary observational inter-est associated with nucleosynthesis are of MeV energies,and are listed in Table I. The radioisotopes 56Ni, 57Ni,44Ti, and 26Al are particularly important since they spana range of half-lives, from days to millions of years, thustogether providing a measure of both the “prompt” emis-sion from individual events, as well as of the “delayed” orintegrated cumulative emission dispersed throughout theinterstellar medium of the Galaxy arising from generationsof star formation. The lines originally predicted to be themost luminous from individual events are the 56Ni and56Co lines from Type Ia supernovae. The long-anticipatedbreakthrough in gamma-ray line detection, however, oc-curred for the now-famous SN 1987A, a type II super-nova which occurred at a distance of 55 kpc in our neigh-bor galaxy, the Large Magellanic Cloud (the LMC). Thegamma-ray spectrometer aboard the Solar Maximum Mis-sion (SMM) satellite detected and studied the 56Co linesfrom this event. The gamma-ray lines were detected ear-lier after the event than predicted, implying that the innerlayers of material containing the radioactive 56Co weremore thoroughly mixed than expected, or indicating per-haps that the ejecta were clumpier, allowing clearer linesof sight to the inner regions of the exploding star throughwhich the gamma rays could escape. After the launch ofthe Compton Observatory in 1991, several years after theevent, the OSSE instrument detected the longer-lived 57Coline (t1/2 ∼ 272 days) at 122 keV in energy. Its intensityimplied a ratio of synthesized 57Ni to 56Ni (from 56Feand 57Fe, respectively) of about 1.5 times the solar value,providing constraints on models of the progenitor star’sevolution. In other supernova observations, there were tan-talizing hints of gamma-ray detections with COMPTELof the 0.847- and 1.239-MeV lines of 56Co from the TypeIa supernova SN 1991T in the galaxy NGC 4527 at a dis-tance of about 13–17 Mpc, at the limit of this telescope’srange of detectability.

Of particular interest in gamma-ray line astronomy isthe detection of 44Ti (t1/2 ∼ 60 years) at 1.157 MeV fromyoung, distant obscured supernovae in the Galaxy. Abouttwo to three supernovae per century are predicted to oc-cur in the Milky Way, but most have remained undetectedbecause they are believed to remain hidden behind in-tervening clouds of interstellar gas and dust in the spi-ral arms. Gamma rays, in contrast to optical light, easilypenetrate the interstellar material and provide a means ofdetecting directly these interesting objects and confirmingpredictions regarding star formation rates in the Galaxy.Further, 44Ti is formed in the deepest layers of the super-nova ejecta, and its predicted line strength is sensitive tothe details of the explosion models and to the likelihood

of fall-back onto the collapsed, compact stellar core. TheCOMPTEL instrument aboard the CGRO has reported thedetection of 44Ti from the Cas A supernova remnant (a rel-atively close remnant about 3 kpc distant, believed to haveexploded about 250 years ago) and from the Vela region ofthe Galaxy. The next generation of gamma-ray spectrom-eter and imager aboard the INTEGRAL spacecraft willprovide critical confirmation of these first detections andshould also be able to map out in detail the spatial distri-bution of the emitting radioisotope, and, from a determi-nation of the exact shape of the gamma-ray line profiles,provide a measure of the symmetry of the initial explosionand subsequent expansion of the ejected material.

The longer-lived radioisotope 26Al with a decay line at1.809 MeV (t1/2 ∼ 710,000 years) traces the sites of mas-sive star formation and nucleosynthesis in the Galaxy overthe past million years. This interstellar line was originallydetected by the HEAO-3 and SMM spacecraft, followedby a number of balloon instruments. In a long-awaited re-sult, the first all-sky map in the light of this radioisotopewas produced by the COMPTEL instrument team follow-ing extensive observations and analysis. Clearly evident isthe disk of the inner Galaxy, with enhancements of emis-sion in particular regions (see Fig. 6). These tend to coin-cide in direction to spiral arms in the Galaxy, where recentstar formation and supernova activity are most likely tooccur (e.g., the Cygnus, Vela, and Carina regions). Fur-ther measurements of the spectral line of 26Al with high-resolution spectrometers and imagers are expected to yielddetailed identification of specific sources for this emission.

2. Electron–Positron Annihilation Radiation

A gamma-ray line at 0.511 MeV results from the mu-tual annihilation of an electron and a positron, a particle-antiparticle pair. A number of radioactive decay chains(see Table I) result in the emission of a positron as a decayproduct, which will annihilate upon first encounter withan electron. Also of astrophysical importance is the pro-duction of electrons and positrons via the photon–photonpair-creation process. Such pair plasmas are found in thevicinity of compact objects, such as neutron stars and blackholes, that are associated with heated accretion disks andrelativistic flows and jets, within which particle acceler-ation is known to occur. Thus, relatively narrow lines of0.511-MeV annihilation radiation are expected to arisein the interstellar medium through the decay of dispersed,nucleosynthetic radionuclides, while broadened, Doppler-shifted, and possibly time-variable lines may occur in thehigh-energy and dense environments associated with com-pact objects.

Direct annihilation of an electron–positron pair leadsto the emission of two photons. If the particles are at




FIGURE 6 An all-sky map of the gamma-ray line emission at 1.809 MeV due to the decay of radioactive 26Al inthe Galaxy, obtained with the COMPTEL instrument aboard the Compton Gamma Ray Observatory. The map is anAitoff equal-area projection in Galactic coordinates (as in Fig. 1). The gamma-ray line from 26Al traces the sites ofmassive star formation and nucleosynthesis in the Milky Way. Regions with enhanced emission are identified. Inset :A gamma-ray spectrum showing the emission line from 26Al at 1.809 MeV observed in the inner Galaxy. (CourtesyNASA, the Max Planck Institute, and the CGRO COMPTEL Instrument Team.)

rest two gamma rays of equal energy, 0.511 MeV, areproduced, while in-flight collisions will result in a rangeof possible photon energies (whose sum must equal thekinetic plus the rest–mass energies of the two particles,2mec2). If the velocities of the two particles are small,a bound state consisting of a positron and an electron ispossible, the positronium atom. Positronium decays aftera very short lifetime (<10−7 s) via one of two channels.Two-photon decay results again in the emission of twogamma photons of energy 0.511 MeV, while three-photondecay leads to a continuum of emission below the main0.511-MeV spectral peak. The observed positronium frac-tion, or continuum-to-line ratio, provides a unique diag-nostic measure of the physical conditions of the emittingregion.

Prior to the launch of the CGRO, from the 1970s on,a number of balloon and early satellite instruments de-tected the presence of apparently variable annihilation ra-diation from the direction of the Galactic Center. This led

to the widespread supposition that the observed emissionarose from two types of sources: a steady, dispersed dif-fuse component of nucleosynthetic origin in the disk ofthe Galaxy, and a time-variable point source (or sources)near the Galactic Center. Extensive observations of the0.511-MeV line from the inner Galaxy with the CGROOSSE instrument (see Fig. 7), however, have revealed asomewhat different picture: a central bulge, along withdiffuse emission in the Galactic plane, and an apparentextension of emission above the Galactic disk in the di-rection of the Galactic Center. No temporal variability ofthe annihilation radiation is evident in the OSSE observa-tions. The annihilation emission observed by OSSE canbe explained entirely in terms of radioactive isotopes fromsupernovae and similar sources. The apparent enhance-ment of 0.511-MeV radiation above the Galactic plane hasbeen variously interpreted as a “positron fountain” arisingfrom an asymmetric outflow of positrons from the regionof the Galactic Center following a period of enhanced star




FIGURE 7 The gamma-ray spectrum of the positron annihila-tion line at 0.511 MeV and associated positronium continuum to-ward the region of the Galactic Center, obtained with the OSSEinstrument aboard the Compton Gamma Ray Observatory. Thedata were fit with a model consisting of a narrow annihilation line,a positronium component, and an underlying power-law contin-uum, indicated by the dashed lines. (Adapted from W. R. Purcellet al., “OSSE mapping of galactic 511 keV positron annihilationline emission,” Astrophys. J. 491, 725–748, Copyright 1997, re-produced with permission of the AAS.)

formation and supernovae activity, or the result of jet ac-tivity from one or more black-hole sources in or near thecenter of the Galaxy, or even the result of a single cat-aclysmic gamma-ray burst-like event occurring near theGalactic Center about a million years ago.

E. Diffuse Galactic Gamma-Ray Emission

The most conspicuous feature in the gamma-ray sky isthe diffuse continuum radiation arising from the Galaxyitself, originating in the interstellar clouds of gas and dustthat reside within the spiral arms, disk, and bulge of theMilky Way. A narrow band of diffuse gamma-ray emissionis observed along the Galactic plane, with enhancementstoward the inner Galaxy and in directions that are tangent

to the spiral arms (where the column density of interstellarmaterial is greatest along the line of sight) and with hotspots of intensity in particular directions that may be dueto unresolved point sources of emission (see Fig. 1). Firstdetected by the OSO 3 satellite, this diffuse radiation wasalso observed and mapped at medium resolution by theSAS 2 and COS B satellites. The two wide-field gamma-ray telescopes aboard the CGRO, COMPTEL and EGRET,were specifically designed to carry out as one of theirprimary scientific objectives a complete mapping of theentire sky in gamma rays. A key result of this all-skysurvey was the first complete map of the Galactic diffuseradiation from approximately 1 MeV to 30 GeV in energy.The OSSE instrument aboard the CGRO also derived ameasure of the Galactic diffuse radiation toward the centerof the Galaxy up to an energy of approximately 10 MeV.

The Galactic diffuse emission arises from the interac-tion of energetic cosmic-ray particles, predominantly elec-trons and protons, with ambient material and low-energyphotons in the interstellar medium. The primary interac-tion mechanisms are (1) nucleon–nucleon collisions ofcosmic-ray protons that result in the creation of neutral pi-ons that decay into gamma-rays, (2) bremsstrahlung fromhigh-energy electrons, and (3) Compton up-scattering bycosmic-ray electrons of the low-energy photons (IR, opti-cal, and UV) that comprise the interstellar radiation field(or ISRF). Each of these gamma-ray production mecha-nisms is dominant over a particular energy range. Belowabout 100 MeV the bremsstrahlung component is impor-tant, while above that energy the decay of neutral pionsfrom nucleon–nucleon collisions is key. The relative im-portance of the Compton component is dependent on thespectral index (or “hardness”) of the cosmic-ray electronpopulation, and on the details of the ISRF, neither of whichis well determined, hence the added interest in studies ofthe diffuse gamma-ray emission to help fix these contribut-ing physical quantities. Finally, there is also an isotropiccomponent of the diffuse gamma radiation that is believedto be extragalactic in origin (described in the next section).

Since the interstellar medium is essentially transparentto the propagation of gamma rays, the observed gamma-ray intensity in a particular direction represents the to-tal, cumulative emission from all particle interactions andsources along that line of sight. Thus, the diffuse gammaradiation provides a simultaneous measure of both thecosmic-ray and matter distribution throughout the Galaxy.The challenge is to disentangle the cosmic rays (the “pro-jectile” particles) from the interstellar matter (the “target”particles) in the observed gamma-ray signal. The studyof the Galactic diffuse gamma radiation is therefore inti-mately related to Galactic radio astronomy. The distribu-tion of matter in the Galaxy is derived primarily from radiosurveys, in particular, those at 21-cm wavelength that map




the distribution of atomic hydrogen, and the millimeterCO surveys that serve as tracers of molecular hydrogen.A major advantage of the spectral-line radio observationsis that Doppler shifts in the observed line emission can beinterpreted in terms of a kinematic model of differentialGalactic rotation, which allows a determination of the dis-tance to the emitting gas based on its measured radial ve-locity. Continuum radio surveys of the synchrotron emis-sion from electrons interacting with Galactic magneticfields also provide important observational constraints onthe distribution and properties of the cosmic-ray elec-tron population. In turn, studies of the diffuse gamma-rayemission complement the radio observations in that theyserve to constrain a critical parameter in the molecular ra-dio surveys, namely, the CO-to-H2 conversion factor (theso-called “X-value,” for which the EGRET-determinedaverage over the whole Galaxy is (1.56 ± 0.05) × 1020

H-molecules cm−2 (K km s−1)−1).The diffuse gamma-ray studies, when combined with

the radio data, provide the best measure to date of the dis-tribution of high-energy cosmic rays within the Galaxy.Cosmic rays presumably arise following particle accel-eration via shocks in supernovae and their remnants inthe interstellar medium. As charged particles, however,their trajectories are influenced by magnetic fields and thustheir exact sites of origin and acceleration, as well as theircomposition, modes of propagation, and overall lifetimein the Galaxy are still not well understood. This situationis most severe for cosmic-ray electrons, since these less-massive particles “cool” rapidly due to energy losses viasynchrotron, bremsstrahlung, and Compton emission, andconsequently have relatively little time to diffuse far fromtheir place of origin in the Galaxy to be detected.

A number of approaches have been followed to modelthe diffuse gamma-ray observations. They can be char-acterized as either parametric models that are fit to thedata to study intensity and spectral variations as a func-tion of Galactic radius, dynamic balance models that seekto balance the gravitational attraction of interstellar mat-ter against the expansive pressures due to cosmic rays,matter and magnetic fields, and cosmic-ray propagationmodels that mimic the propagation of cosmic rays throughthe Galaxy by including such processes as diffusion, con-vection, reacceleration, fragmentation, the production ofsecondary particles, and the generation of gamma-rayand synchrotron radiation, as constrained by all availableobservations.

Analysis of the results obtained with the COMPTELand EGRET instruments aboard the Compton Observatorysuggest that the inverse Compton process may be a moreimportant contributor to the Galactic diffuse emission thanpreviously thought. The bremsstrahlung component of themedium-energy (1- to 50-MeV) diffuse emission, thoughcomparatively small, remains of interest in that it can be

combined with surveys of the Galactic radio synchrotronemission (which traces electrons with energies in the range100 MeV to 10 GeV) to derive the shape of the cosmic-ray electron spectrum. Historically, the electron spectrumbelow ∼10 GeV has been difficult to determine sincethese particles are excluded from direct detection near theEarth due to the periodic modulation of the solar wind. Athigher energies in the EGRET sensitive range (30 MeVto 30 GeV) the observed gamma-ray spectrum is softerin the direction of the outer Galaxy compared to the in-ner Galaxy, suggestive of a corresponding change in thespectrum of cosmic-ray nuclei with Galactic radius. Thiscould be explained if cosmic rays are accelerated pref-erentially in the inner Galaxy and then propagate to theouter Galaxy, or if the high-energy cosmic rays are lesswell-confined in the outer Galaxy. While overall agree-ment between model predictions and the gamma-ray datais quite good, one surprising finding is an excess in thediffuse emission observed above ∼1 GeV (see Fig. 8).

FIGURE 8 Spectrum of the diffuse gamma-ray emission fromthe inner Galaxy compared with calculations based on cosmic-ray propagation models. The data were obtained with theOSSE, COMPTEL, and EGRET instruments aboard the Comp-ton Gamma Ray Observatory. Curves show the calculated con-tributions to the observed gamma-ray emission due to inverseCompton, bremsstrahlung, and π0-decay processes, and thesummed total. (Adapted from Strong, A. W., Moskalenko, I. V.,and Reimer, O. (2000). “Diffuse continuum gamma rays from theGalaxy,” Astrophys. J. 537, 763–784, Copyright 2000, reproducedwith permission of the AAS.)




This has been the subject of some debate and may reflectuncertainties in the neutral pion production function usedin the model calculations, or perhaps is due to variationsin the cosmic-ray spectrum with Galactic radius. Anotherpossible explanation is enhanced Compton emission froma harder interstellar electron spectrum that may also giverise to an electron/inverse-Compton gamma-ray halo sur-rounding the disk of the Galaxy. Finally, at the very lowend of the gamma-ray regime, it has been suggested that apopulation of unresolved Galactic sources may be respon-sible for the upturn in emission observed at low gamma-ray energies.

Future space missions (such as GLAST) will be able toconfirm any spectral variations in the diffuse emission onsufficiently small angular scales (a few degrees) to permita serious test of the various production models. Furtherobservations with the next generation of ground-basedair-Cherenkov GeV and TeV telescopes (where to dateonly tantalizing upper limits have been obtained) shouldalso provide important confirmation of the GeV excessobserved by EGRET.

F. Active Galaxies

Active galaxies, though they comprise only a small per-centage of all known galaxies, rank among the most ener-getic and exotic objects in the Universe. They are excep-tionally luminous (up to 10,000 times brighter than normalgalaxies), and their emission is typically broadband andnonthermal in nature, spanning the entire electromagneticspectrum. Their luminosity is concentrated in the centralnucleus, which completely outshines the rest of the galaxyby factors of 100 or more, hence the alternate designationof “active galactic nuclei” (or AGNs). The emission fromAGNs is highly variable and fluctuates rapidly enough(≤day) to indicate that the source, or central engine, thatdrives the active behavior must occupy an extremely smallregion at the very unresolved core of the galaxy. AGNsare also associated with collimated bipolar jets and lobesof relativistic material emanating from the nucleus of thegalaxy, within which ejected blobs of plasma can appear totravel at superluminal velocities, in apparent violation ofthe laws of physics (though this latter effect is now knownto be a consequence of highly relativistic motion viewedalong the direction of travel). For decades, as discoveriesmounted, sub-categories of AGN proliferated, usually de-rived from some observational characteristic by which aparticular class was originally identified. Thus, AGNs arecategorized as radio-loud or radio-quiet, flat-spectrum orsteep-spectrum sources, core-dominant or lobe-dominantin their emission, with broad spectral lines (indicative ofhigh-velocity gas motions), narrow lines, highly polarizedlines, or no lines, Seyfert galaxies of type I or II, Fanaroff-Riley galaxies of type I or II, and, at the most energetic

extreme, the quasars, optically violent variables, and BLLacertae objects (or BL Lacs) which collectively make upthe class known as blazars (with luminosities in excess of1048 ergs s−1).

With the successful launch and operation of the Comp-ton Gamma Ray Observatory (CGRO), a remarkable newclass of active galaxy was discovered, the gamma-rayblazars. The high-energy EGRET experiment aboard theCGRO detected over 90 definite or probable gamma-rayAGNs (see Figs. 1 and 3), all but a few associated withactive galaxies of the blazar class. These discoveries com-prise the single largest category of gamma-ray source de-tected with EGRET and are all the more noteworthy in thatprior to the launch of the CGRO only one such gamma-rayAGN was known, the quasar 3C 273 (discovered with theCOS-B satellite). Gamma-ray blazars exhibit strong flar-ing behavior, and during active periods their gamma-rayluminosity can exceed that in other wavebands by factorsof 100 or more. The gamma-ray blazars also span a largerange in redshift (z ∼ 0.03 to 2.3) and thus serve as cos-mological probes of the intervening intergalactic medium.The discovery and study of the gamma-ray blazars hasgreatly enhanced our understanding of the blazar phe-nomenon in general, and has also provided strong con-firmation of the relativistic jet model for active galax-ies, since energy considerations require that the observedgamma-rays must be beamed in our direction via relativis-tic Doppler boosting.

In recent years, it has become clear that the vast major-ity of AGNs can be explained in terms of a single “unifiedmodel” for active galaxies. According to this concept thevarious subclasses of AGN can be explained as arisingfrom geometric effects due to different viewing anglesof the observer with respect to the central source. In thenow-standard picture, the central engine of an AGN isa supermassive black hole (of ∼106–1010 solar masses)that is powered by the accretion of surrounding infallingmaterial. It is the partial conversion via accretion of thehuge reservoir of gravitational potential energy into ther-mal energy due to the presence of the black hole that drivesthe energetic behavior of AGNs. In the standard scenariothe central supermassive black hole is surrounded by anaccretion disk and a thicker outer obscuring torus of ma-terial in the equatorial plane of the rotating black hole(see Fig. 9). Highly collimated bipolar jets of relativisticplasma are formed and ejected along the rotational axis,and intervening clouds of material of varying velocity,subject to bombardment from accelerated particles andradiation from the accretion disk and jets, give rise to thebroad and narrow spectral lines observed. Predominantlythermal emission, extending up to X-rays, arises from theheated accretion disk and surrounding torus, while broad-band nonthermal synchrotron and Compton emission,including gamma radiation, is given off by the relativistic




FIGURE 9 Schematic diagram of the central region of an ac-tive galaxy illustrating the main components of the “unified model”for active galactic nuclei (AGN). According to this model the var-ious subclasses of AGN can be interpreted as arising from theobserver’s viewing angle with respect to the central source (a su-permassive black hole) and the surrounding accretion disk, torus,intervening clouds, and relativistic jets. Gamma-ray blazars arepresumed to arise when the observer’s viewing angle is veryclosely aligned with the relativistic jets. (Adapted from Urry, C. M.,and Padovani, P. (1995). “Unified schemes for radio-loud activegalactic nuclei,” Publication of the Astronomical Society of the Pa-cific 107, 803–845, Copyright PASP 1995, reproduced with per-mission of the authors.)

particles in the jets. The appearance of an active galaxythus depends critically on one’s observing angle with re-spect to the central source and the surrounding accretiondisk, torus, and relativistic jets. The most extreme variablebehavior will be noted when the observer’s viewing angleis very closely aligned to one of the jets, when relativisticeffects reach their maximum.

The rapid variability observed in gamma-rays (≤ days)indicates that the high-energy emission arises from re-gions very near the central engine of the galaxy, wherejet formation and the acceleration of relativistic plasmaoccurs, phenomena that are not yet well understood. Thegamma rays therefore constitute a new direct probe ofthe inner-jet region, heretofore unobservable, even by thetechniques of very long baseline radio interferometry. Rel-ativistic beaming plays a critical role in the explanationof the luminous time-variable gamma-ray emission fromblazars, allowing rapid variations in the observed high-

energy emission, without the penalty of severe attenua-tion of the radiation due to the pair-production opacity.Shocks and instabilities in the bulk flow of relativisticparticles can lead to variable nonthermal emission over awide range of energies. Given the broadband nature of theemission from blazars it has become increasingly clearthat coordinated multiwavelength observations of flaresfrom blazars offers the prospect of determining the phys-ical structure and properties of the inner-jet region. A keyingredient of such multiwavelength campaigns is the abil-ity to measure time delays, between wavebands, of thebrightness variations occurring during a flare. The rela-tive order and delay of these frequency-dependent vari-ations differ according to the predictions of the variousmodels.

The emission mechanism most often employed tomodel gamma-ray production in AGNs is the Comp-ton scattering of lower-energy photons by high-energyelectrons. The scattered “seed” photons are typically ei-ther synchrotron photons generated within the jet bythe electrons themselves (the so-called Synchrotron Self-Compton, or SSC, model) or photons propagated directlyor scattered into the jet from the accretion disk sur-rounding the central engine (labeled “external” Comp-ton scattering). The broadband spectra predicted by thesemodels present a characteristic double-peaked appearance(see Fig. 10). The low-energy peak, broadly centered inthe millimeter radio to UV bands, is representative ofthe low-energy photons (usually of synchrotron origin)that are then Compton-scattered to higher gamma-ray en-ergies via the relativistic electrons. Of particular inter-est in this regard are the recent measurements of TeVgamma rays from relatively nearby BL Lac objects (mostnotably MRK 421 and MRK 501, both at z ∼ 0.03) withground-based Cherenkov detectors. These detections haverevealed high-energy emission extending up to 30 TeV,combined with the most rapid variability (flux-doublingtimes of less than 15 min!) observed to date at gamma-ray energies. Further confirming TeV measurements ofgamma-ray AGN are eagerly anticipated to place moreprecise observational constraints on the models describedabove.

Finally, it is important to note the utility of gamma-rayblazars as cosmological probes of the extragalactic dif-fuse background radiation, sometimes referred to as theextragalactic background light (or EBL). The propagationof high-energy gamma rays through intergalactic spaceis fundamentally limited by the pair-production opacityof the intervening medium. That is, the likelihood of in-teraction of the gamma radiation with the lower-energyphotons that make up the universal background radiation.Though the cosmic microwave background radiation, relicof the Big Bang, has been well measured, background




FIGURE 10 Broadband multiwavelength spectrum of the gamma-ray blazar MRK 501 from radio to TeV gamma-rayenergies. The broadband spectrum shows the double-peaked structure characteristic of gamma-ray blazars in whichlower energy photons are Compton scattered to gamma-ray energies by relativistic electrons. (Adapted from Kataoka,J. et al. (1999). “High-energy emission from the TeV blazar Markarian 501 during multiwavelength observations in1996,” Astrophys. J. 514, 138–147, Copyright 1999, reproduced with permission of the AAS.)

radiation fields at other wavelengths are not nearly as wellknown, and yet are of considerable interest since they pro-vide information about earlier epochs in the history of theUniverse. TeV gamma rays, for example, are most likely tointeract with infrared and optical photons. The optical/IRbackground radiation fields therefore limit the distance towhich TeV gamma-ray sources can be detected. Observa-tions of gamma-ray blazars as a function of redshift, then,provide a means of estimating the intensity of the EBL atthe lower optical and IR wavelengths that provide infor-mation on star and galaxy formation in the early Universe.

G. Gamma-Ray Bursts

As their name implies, cosmic gamma-ray bursts(GRBs) are intense bursts of gamma radiation, lastingfrom fractions of a second to minutes, which emit thebulk of their energy in the gamma-ray regime (above∼0.1 MeV). Unpredictable in occurrence, these transientevents form one of the most long-standing and challenging

puzzles in modern astrophysics, dating back to their acci-dental discovery over thirty years ago with the Vela seriesof nuclear-testing surveillance satellites. The Burst andTransient Source Experiment (BATSE) aboard the CGROwas specifically designed to serve as an all-sky monitor todetect these mysterious events. Over its nine-year lifetimeBATSE detected a total of 2704 GRBs, many times thenumber recorded previously, and amassed a formidablecollection of data on their properties. During their briefappearance GRBs are the brightest objects in the sky, out-shining all other gamma-ray sources combined. Indeed,gamma-ray bursts may be the most distant and explosiveevents (with energies greater than 1053 ergs) ever observedin Nature. GRBs occur at random intervals (∼1/day); theydo not seem to repeat (implying likely destruction of thesource); and they are isotropic in their distribution, comingfrom every direction in the sky. Each burst is different in itstemporal structure, which can vary dramatically in dura-tion and complexity from burst to burst (see Fig. 11). Fur-ther, the rapid variability of the emission (on the order of




FIGURE 11 Time profiles for a sample of gamma-ray bursts (GRBs), obtained with the BATSE instrument aboardthe Compton Gamma Ray Observatory. These profiles illustrate the rich diversity in temporal structure, intensities,and durations for gamma-ray bursts, no two of which are exactly alike in all respects. (Courtesy NASA and the CGROBATSE Instrument Team.)

milliseconds) measured during a given burst implies thatthe observed radiation arises from an extremely compactsource, requiring the relativistic expansion of the emittingparticles to avoid the photon–photon pair-creation opacitythat would otherwise quench the observed gamma radia-tion. This rapid expansion of emitting material could take

the form of a relativistic fireball resulting from an ini-tial explosion or from collimated beams of relativistic jetsemanating from a central source.

For many years the mystery of the origin of gamma-ray bursts was compounded due to their lack of detec-tion in any frequency band below the hard X-rays, a fact




difficult to reconcile with such an apparently catastrophicrelease of energy. Further complicating the situation wasthat few, if any, observational constraints could be placedon the distances to the sources of bursts, nor could GRBsbe associated with any known class of object. Conse-quently, the distance scale to bursts was studied indirectlythrough the angular distribution on the sky and the inten-sity distribution of the overall burst ensemble. The ob-served deficit in the number of weak bursts detected withBATSE (compared to the number expected for a uniform,homogeneous distribution of burst sources in flat three-dimensional Euclidean space) implied, for example, thatwe were seeing the far “edge” of the burst source pop-ulation. Still, this allowed for burst sources to be either“local” to our own Galaxy, or “cosmological” at the edgeof the observable Universe, leading to endless variety inproposed burst models and widespread debate and contro-versy within the field of burst studies.

It had long been recognized that the key to unravelingthe GRB mystery was the identification of burst counter-parts at other wavelengths. The short duration of gamma-ray bursts, however, combined with the unpredictabilityof their occurrence anywhere in the sky, and the rela-tively poor location-determination capabilities of gamma-ray instruments (compared to detectors operating in otherwavebands) severely limited the effectiveness of coordi-nated follow-up searches for GRB counterparts. Despiterepeated and valiant attempts at many wavelengths to de-tect either the remnant afterglow of a burst event, or of aquiescent counterpart within a gamma-ray burst error box,none was detected for many frustrating years. An obser-vational breakthrough occurred in early 1997, however,shortly after the launch of the Italian-Dutch BeppoSAXX-ray satellite. On a number of occasions BeppoSAX ob-served with one of its Wide-Field Cameras (WFCs) the un-mistakable X-ray afterglow associated with a gamma-rayburst. The occurrence of a burst was simultaneously reg-istered with the cesium–iodide (CsI) detectors that servedprimarily as shields for the satellite’s main X-ray tele-scope, but were also configured to operate as a separategamma-ray burst monitor. Following a suspected burstevent the spacecraft was reoriented to allow its high-resolution X-ray instruments to observe the same field,confirm the fading X-ray emission, and to exactly fix itspoint of origin (see Fig. 12). After rapid communicationof precise coordinates, followup observations were imme-diately initiated by observatories around the world, result-ing in the first detections of fading afterglow emission,lasting from hours to weeks, from a gamma-ray burst. Ina few instances, further observations of the fading opticalsource revealed the presence of faint, extended underlyingemission, suggestive of very distant host galaxies. Mea-surement of a host galaxy’s redshift has provided the first

incontrovertible evidence that GRBs occur at cosmologi-cal distances. In the 3 years following the initial detectionof a burst counterpart, over thirty GRBs have been rapidlylocalized by BeppoSAX, with over a dozen events yield-ing counterpart detections in other wavebands, includingX-ray, optical, infrared, millimeter, and radio, as well asredshift measurements to likely host galaxies (of charac-teristic redshift z ∼ 1). These results electrified investiga-tors in the field of gamma-ray burst research, and havecompletely revolutionized the study of GRBs.

The detection of both prompt and afterglow counter-part emission has permitted a serious revaluation of themany theories put forward to explain the origin of GRBs.In particular favor is the “relativistic fireball” model thatposits an enormous, instantaneous energy release withina small volume. In this scenario a relativistic fireball con-sisting of an electron-positron pair plasma with a Lorentzfactor of 100–1000 propagates outward following the ini-tial energetic event. The temporal structure observed inthe gamma-ray burst itself results from the collision ofshocks with somewhat different Lorentz factors within therelativistic outflow (so-called “internal” shocks). Promptburst emission (e.g., the dramatic optical flare seen bythe robotic ROTSE telescope during GRB 990123) is at-tributed to “reverse” shocks traveling backward throughthe dense ejecta. The longer-term afterglow emissionarises from forward-moving “external” shocks plowingthrough the surrounding medium. The relativistic parti-cles accelerated in these shocks radiate both synchrotronand Compton emission. The afterglow spectrum observedhours to weeks following a burst typically consists of aseries of synchrotron power laws whose breaks are de-pendent on the energy distribution in the population ofradiating nonthermal electrons. With time, the observedsynchrotron spectrum shifts to lower energies as a result ofthe cooling expansion and the decreasing Lorentz factor ofthe bulk flow. The delayed onset and characteristic smoothdecay observed for the counterpart emission at X-ray, op-tical, and radio wavelengths can be naturally explainedas arising from the expanding pair plasma that becomesprogressively more optically thin to lower-frequency ra-diation during the later stages of the cooling fireball. Thefireball model agrees remarkably well with the observa-tions, though the exact details of the broadband emissiondepend critically on the physical properties of the inter-stellar or intergalactic environment into which the fireballexpands.

A fundamental question is the nature of the energeticevent that sparks the detonation of the fireball itself. Theenormous energies (>1053 ergs) implied by the cosmolog-ical distances inferred from the most recent observationsof GRBs greatly restricts the number of possibilities. Onlythe mergers of the components of evolved binary systems




FIGURE 12 The discovery images of the first X-ray afterglow detected from a gamma-ray burst (GRB 970228),observed with the BeppoSAX satellite. The left panel shows bright X-ray emission from the location of the GRB shortlyafter burst occurrence on February 28, 1997, while the right panel shows the fading X-ray afterglow seen several dayslater on March 3, 1997. (Adapted from Costa, E. et al. (1997). “Discovery of an X-ray afterglow associated with thegamma-ray burst of 28 February 1997,” Nature 387, 783–785, Copyright 1997, by permission.)

containing pairs of compact objects (neutron stars or blackholes), or the collapse of the most massive stars at the endsof their lifetimes (as described in the “hypernova” and“collapsar” models), appear to meet the gigantic energyrequirements. The recent detection of iron-line emissionat X-ray wavelengths in GRB afterglows with instrumentsaboard BeppoSAX and the Chandra Observatory favorsthe latter class of models, since the quantity of iron es-timated from the observations seems most likely to haveoriginated in an evolved massive star that exploded in asupernova-like event.

Virtually all models for the ultimate energy source ofGRBs involve an endpoint of stellar evolution, particu-larly of the most massive stars. Thus it has been proposedthat the burst rate must be proportional to the overall cos-mic star formation rate. This view is supported by the factthat the typical redshifts (z ∼ 1) associated with GRB hostgalaxies correspond to an epoch of early active star for-mation in the Universe. Burst counterparts also tend to be

found in the outer regions of blue galaxies undergoing re-cent star formation, or in irregular galaxies that may haveundergone recent collisions or mergers, promoting a burstof star-forming activity at an early epoch.

H. The Extragalactic DiffuseGamma-Ray Emission

Studies of the Galactic diffuse gamma-ray emission re-vealed the presence of an isotropic component of diffuseemission that is now considered to be extragalactic in ori-gin. The existence of extragalactic diffuse gamma rayswas first demonstrated with the SAS-2 satellite and con-firmed on a large scale with the all-sky mapping carriedout with the COMPTEL and EGRET instruments aboardthe CGRO. Sometimes referred to as the cosmic diffusegamma-ray (CDG) background, this radiation has beenmeasured from ∼1 MeV to ∼100 GeV in energy. Sinceit is by definition the constant, isotropic “background”




radiation against which all other sources are measured, itis not characterized by any spatial or temporal signature.

The determination of the extragalactic diffuse gamma-ray background presents a particular observational chal-lenge. This stems from the fact that the basic procedurefor determining it involves the subtraction from the accu-mulated gamma-ray signal of all other known sources ofemission, including the contribution of point sources, theGalactic diffuse emission, and the effects of the instrumen-tal background. In other words, the extragalactic diffuseemission is assumed to be what is “left over” after all othersources of emission are accounted for and removed fromthe observations. Thus, by necessity it requires a profoundunderstanding of the instrumental response, and a detailedknowledge of the sources and structure of the gamma-raysky. Consequently, it is usually the last major result ob-tained with a gamma-ray telescope, often requiring yearsof observation, analysis, and study.

In this regard, the COMPTEL measurements of theextragalactic diffuse emission represent a major achieve-ment. The MeV energy band over which COMPTEL wassensitive has long been recognized as a notoriously dif-ficult one in which to operate, due to the high levels ofinstrumental background to which experiments are sus-ceptible. As the first MeV telescope launched into spacefor extended observations, COMPTEL was in a uniqueposition to provide a definitive measurement of the CDGat medium gamma-ray energies. The COMPTEL resultswere particularly anticipated in light of a series of earlier,shorter measurements that had indicated the existence ofa puzzling excess, or “MeV bump,” in the diffuse spec-trum between ∼2 and 9 MeV that could not be readilyexplained and which had provoked widespread discus-sion as to its possible origin. Initial COMPTEL resultswere derived from observations of the Virgo region, wellremoved from the Galactic plane. In contrast with the ear-lier observations, the COMPTEL measurements providedno hint of the MeV bump previously reported. Later con-firming observations were obtained in the direction of theSouth Galactic Pole, and these also did not indicate anyexcess emission, or any temporal variation or anisotropyin the diffuse gamma radiation. Most significantly, then,COMPTEL disproved the earlier reports of an MeV ex-cess, and provided a first definitive measurement of thecosmic diffuse radiation between ∼1 and 30 MeV. At30 MeV the COMPTEL results join smoothly with anextrapolation of the EGRET measurements at higher en-ergies (see Fig. 13).

The EGRET results were obtained following the analy-sis of data from 36 distinct regions of the sky well removedfrom the contaminating influence of the Galactic disk andbulge. From 30 MeV to 100 GeV the extragalactic diffuseemission is well described by a strikingly smooth power-

law photon spectrum of index-2.1, in remarkable agree-ment with the average spectrum derived from the largepool (>90) of gamma-ray blazars detected with EGRETover its lifetime. This immediately suggests that the ex-tragalactic emission at EGRET energies most likely arisesfrom numerous unresolved sources of the blazar class.

The origin of the extragalactic diffuse emission hasbeen the subject of much theoretical speculation for manyyears. Theories of truly diffuse processes include matter–antimatter annihilation in a baryon-symmetric cosmology,the evaporation of primordial black holes, supermassiveblack holes (∼106 solar masses) that collapsed at high red-shifts (z ∼ 100) at very early epochs, and the annihilationof exotic supersymmetric particles. Unfortunately, manyof these hypotheses cannot be tested realistically at thesensitivity of the current observations. The general con-sensus at present is that the extragalactic diffuse radiationmost likely results from the superposition of a number ofclasses of unresolved point sources. The CDG, since itrepresents the integrated emission from sources extend-ing back to the earliest cosmological epochs, provides animportant observational constraint for theoretical modelsdescribing source evolution with time.

In the COMPTEL energy range around ∼1 MeV it hasbeen proposed that a significant fraction of the diffuseemission could arise from gamma-ray lines due to thedecay of radionuclides produced in the course of super-novae of types Ia and II in distant, unresolved galaxies.Other possible sources at low MeV energies include ac-tive galaxies such as those of the Seyfert I and II class. Atthe higher gamma-ray energies observed with COMPTELand EGRET, blazars provide the most likely explanationof the observed diffuse emission. Of note in the EGRETband is the fact that the diffuse spectrum clearly extendsup to 100 GeV without significant deviation, implying thatthe quiescent emission from gamma-ray blazars, assumingthat they are responsible for the observed emission, mustnecessarily extend up to this energy as well. Consequently,the relativistic particles that give rise to gamma-ray emis-sion in blazars must extend to even higher energies. It isanticipated that the next generation of gamma-ray tele-scopes with higher resolution and sensitivity will begin todetect and map out the individual sources responsible forthe extragalactic diffuse gamma-ray emission.

I. Unidentified Gamma-Ray Sources

When any region of the electromagnetic spectrum isopened to new investigation, or detectors suddenly achievea marked improvement in sensitivity, an exciting era of dis-covery inevitably ensues. This is particularly true in thegamma-ray regime, where the launch of each new satel-lite mission has resulted in the discovery of previously




FIGURE 13 Broadband multiwavelength spectrum of the extragalactic diffuse emission from X-ray to gamma-rayenergies combining the observations of several high-energy satellite missions, most recently those of the COMPTELand EGRET telescopes aboard the Compton Gamma Ray Observatory. The dashed and dotted lines indicate theestimated contribution of several classes of unresolved point sources to the observed emission. (Adapted fromSreekumar, P. et al. (1998). “EGRET observations of the extragalactic gamma-ray emission,” Astrophys. J. 494,523–534, Copyright 1998, reproduced with permission of the AAS.)

unknown sources of gamma radiation. A large fractionof the gamma-ray sources discovered to date, however,remain unidentified. Indeed, one of the great continuingmysteries of gamma-ray astronomy is the nature of theunidentified sources, which in the Third EGRET Catalogoutnumber all other known gamma-ray sources combined(∼170 of the 271 cataloged 3EG sources are unidentified,see Fig. 3). These unidentified sources have no obviouscounterpart at other wavelengths, and cannot be clearlyassociated with any other known class of object based ontheir high-energy emission properties.

The unidentified gamma-ray sources can be broadlycategorized by their location in relation to the plane ofthe Galaxy, and by their spectral and temporal proper-ties. The sources at high Galactic latitudes, well removedfrom the disk of the Galaxy, are most likely to be extra-galactic objects, presumably galaxies. This supposition is

supported by the variable emission often observed fromthese objects, characteristic of flaring active galaxies. Thepositional error boxes of these high-latitude unidentifiedsources, however, do not contain the bright, radio-loudgalaxies of the blazar type that are typically associatedwith extragalactic gamma-ray sources. This suggests thatsome previously unrecognized class of radio-quiet or ac-tive galaxy can give rise to gamma radiation. The detectionof gamma rays from the nearby radio galaxy Centaurus Alends support to this hypothesis.

The vast majority of the unidentified gamma-raysources (>120) appear to belong to a Galactic population.Many of these are likely to be obscured objects whose ex-act properties are masked by the Galactic diffuse radiation,or cannot be accurately distinguished from those of othernearby sources in the crowded disk of the Milky Way.Gamma rays from the unidentified sources are presumed




to arise from the same objects and processes that gener-ate gamma radiation elsewhere in the Galaxy. The objectsand phenomena most closely linked to the production ofhigh-energy gamma rays in the Milky Way include (1)molecular clouds within the spiral arms and disk (wherehigh-energy cosmic rays interact to produce gamma-rays);(2) supernova remnants (whose shock waves are a pre-sumed site of particle acceleration and cosmic-ray pro-duction, leading to gamma-ray emission in their vicinity);(3) flares, winds, and outflows (within which gamma-rayscan be produced) from massive and evolved stars; (4) rel-ativistic jets and accretion disks associated with compactbinary systems containing neutron stars or black holes; and(5) radio-quiet pulsars (such as Geminga) in whose intensemagnetic fields particles are likely to be accelerated, lead-ing to gamma-ray production. Efforts have been made tostudy the statistical properties of the unidentified sourcesand to correlate them with the possible source classes out-lined above, though with limited success to date.

It has been noted that the unidentified Galactic sourcescan be separated into two apparently distinct popula-tions: brighter sources appear confined more closely tothe Galactic disk, while fainter sources are found to lieat medium Galactic latitudes (greater than about 5◦). Thebright sources in the disk are interpreted as more distantluminous objects, while the fainter sources may be muchcloser and more local to the Sun. Several investigators haveproposed that these weaker, medium-latitude sources maybe associated with Gould’s Belt in the Galaxy. Known forwell over a century from optical observations, Gould’sBelt is a ring of bright massive O and B stars that de-fine a great circle on the sky inclined by about 20◦ to theGalactic plane, tilted toward negative Galactic latitudesin the direction of Orion, and toward positive latitudes inOphiucus. Observations over the years at optical, radioand other wavelengths have established that a slowly ex-panding ring of material (with an expansion age of about30 million years) is interacting with and compressing theambient interstellar gas along the periphery of Gould’sBelt. This expansion has likely contributed to periods ofenhanced star formation along the boundary of the Belt.The ring of expanding material is presumed to have re-sulted from a supernova explosion, thus explaining theorigin of the local “superbubble” or evacuated region inthe interstellar medium within which the Sun currentlyresides. In the context of this scenario, the most promi-nent grouping of weak, unidentified gamma-ray sourcesat medium latitudes lie on the boundary of Gould’s Beltthat is closest to the Sun, at a distance of about 100–400 pcin the direction of Ophiucus. The exact physical natureof individual sources remains to be determined, but isexpected to be found among the list of candidates citedabove.

A definitive determination and classification of theunidentified gamma-ray sources discovered to date mustawait the launch of the next generation of gamma-ray tele-scopes whose development is currently underway. Whileinvestigators are confident that the mystery of the uniden-tified sources will ultimately be resolved, there still re-mains the exciting prospect that some of the unidentifiedgamma-ray sources may in fact represent truly new typesof high-energy cosmic sources previously unknown to sci-ence. The possibility that such fundamental discoveriesremain to be made provides heightened motivation for thecontinued study of these mysterious objects.

III. THE CHALLENGE OF OBSERVATIONAND TECHNIQUES OF DETECTION

As an observational discipline gamma-ray astronomy hasalways been extremely challenging. The very low fluxesof cosmic gamma-rays, combined with their high energy,necessitate the construction of large complex detectors.Since cosmic gamma rays are severely attenuated by theEarth’s atmosphere, the experimental apparatus must belifted above as much of this absorbing medium as possibleby high-altitude scientific balloon or placed in low-Earthorbit via satellite. Either of these possibilities places se-vere constraints on the size and weight of a gamma-rayexperiment. Further, since the detector must be designedto conduct observations quasi-autonomously, and sincesophisticated analytical techniques must be employed toaccurately identify true cosmic gamma-ray events fromthe multitude of background interactions that can mas-querade as such, the successful operation of a gamma-raytelescope presents unique challenges to the experimentalastrophysicist.

A. The Interaction of Gamma Rays with Matter

To observe a cosmic gamma ray, one must first devise ameans to stop it (or at least “to slow it down” in some mea-surable way) within a detecting medium. In the gamma-rayregime, the primary interaction mechanisms of photonswith matter are the photoelectric effect, the Compton ef-fect, and pair production. Extensive analyses are availableof these fundamental interaction processes. Here, we onlybriefly review their basic physical characteristics.

1. The Photoelectric Effect

Photoelectric absorption occurs when an incident pho-ton is completely absorbed in an atomic collision withpractically all of its energy transferred to an atomic elec-tron, which is ejected. For photoionization to occur, the




photon must necessarily have enough energy to overcomethe binding energy of the liberated electron. A small, usu-ally minimal, fraction of the initial photon energy is con-verted into the recoil of the atomic nucleus, required forthe conservation of momentum. As a consequence of thisconservation requirement, it is the most tightly bound in-nermost (K-shell) electrons that have the greatest proba-bility of interacting with photons of energies approachingthose of gamma rays. The cross section for photoelectricabsorption has a strong dependence on atomic number(proportional to Z5) and an inverse dependence on pho-ton frequency (proportional to ν−7/2). This is valid forphoton energies somewhat removed from the so-called“absorption edges,” those energies at which strong risesin the absorption cross section occur as photon ener-gies approach the binding energies of individual electronshells.

2. The Compton Effect

As mentioned previously, the Compton scattering processconsists of interactions between photons and free elec-trons. In “standard” Compton scattering, an incident high-energy photon loses a fraction of its energy to an electron,while in the “inverse” Compton process it is the photonthat gains energy at the expense of the electron. By ap-plying the standard criteria of conservation of momentumand energy, it is a straightforward exercise to derive theCompton wavelength shift for the scattered photon,

λ = λ′ − λ = h/mec(1 − cos θ ) = λc(1 − cos θ ),

where λc = h/mec = 2.426 × 10−10 cm is referred to asthe Compton wavelength. Related expressions are easilyobtained for the resultant electron and photon energies.The cross section for Compton scattering by an electron isgiven by the Klein–Nishina formula, and declines with in-creasing photon energy. There is a geometric dependenceto the scattering probability, and at very high energies thecross section rapidly becomes strongly peaked in the for-ward direction.

3. Pair Production

In the pair production process, an incident gamma ray ofsufficiently high energy is annihilated in the Coulomb fieldof a nearby charged particle, resulting in the creation ofan electron–positron pair. As with the photoelectric effect,conservation of momentum requires the presence of a thirdbody which takes up the balance of the momentum in theform of a recoil. For a recoil nucleus of mass much greaterthan the mass of the electron, the threshold energy forpair production is simply, Eth ∼ 2mec2 = 1.022 MeV. Thetotal cross section for pair production rises rapidly above

threshold and approaches at strongly relativistic energiesa limit that is roughly independent of energy.

4. Attenuation and Absorptionof Gamma Radiation

The relative importance of the interaction mechanisms de-scribed above as a function of photon energy is representedgraphically in Fig. 14. The cumulative effect of these pri-mary interaction processes is usually expressed in terms ofattenuation coefficients. The probability that an individualphoton will traverse a given amount of absorbing materialwithout interaction is simply the product of the probabili-ties of survival for each type of possible interaction. Givena collimated beam of monoenergetic gamma rays of initialintensity I0, the intensity observed after passage througha thickness x of absorber is given by

I (x) = I0e−µx ,

where µ = κPE + κC + κPP is the total linear attenuationcoefficient (units: cm−1), and κPE, κC, and κPP are the at-tenuation coefficients for the photoelectric, Compton andpair-production processes, respectively. The linear attenu-ation coefficient is related to the cross section σ by an ex-pression of the form κ = σN cm−1, where N is the numberdensity of atoms in the target medium. Of more fundamen-tal usefulness in terms of detector design is the mass at-tenuation coefficient, which is simply the linear coefficientdivided by the density of the given material (units: cm2/g),permitting straightforward comparison of the attenuationproperties of various types of materials. Numerous tablesand graphs of mass attenuation coefficients as a functionof energy for the most commonly used detector materialsare readily available.

FIGURE 14 The relative importance of the major processes bywhich gamma rays interact with matter as a function of pho-ton energy for elements of varying atomic number Z. (Adaptedfrom Evans, R. D. (1995). “The Atomic Nucleus,” Copyright 1955,McGraw-Hill, by permission.)




Some common detector materials include plastic or-ganic scintillators (i.e., hydrocarbon compounds) typ-ically used in charged-particle anticoincidence shield-ing, inorganic crystal scintillators such as sodium iodide(NaI), cesium iodide (CsI), and bismuth germanate oxide(BGO), and solid-state semiconductors such as germa-nium (Ge), and cadmium zinc telluride (CdZnTe) oftenused in high-resolution spectroscopic applications. Astheir name implies, scintillators are transparent materialsthat scintillate in visible light when high-energy photons orparticles interact within them. The scintillation light, pro-portional to the amount of energy deposited, is collected byattached photomultiplier tubes and converted to an elec-tronic pulse for further signal processing and recording.In semiconductor detectors interacting gamma rays de-posit energy in the detector material, creating electron-hole pairs that are collected following application of anelectric field to the material. Semiconductors are far su-perior spectroscopically to scintillators, due to their rela-tively low threshold for electron-hole creation (∼3 eV forGe). CdZnTe has the advantage that is a room-temperaturesemiconductor, while germanium, due to its narrow bandgap, must be operated at cryogenic temperatures for opti-mal performance. The technology associated with the de-tection of cosmic gamma rays is very often derived fromexperimental techniques developed originally for applica-tion in the fields of high-energy and nuclear physics.

B. Sources of Instrumental Background

Gamma-ray telescopes, due to their physical size andmass, are particularly susceptible to background radia-tion and particle interactions. Below a few MeV in energy,there is a high background due to continuum emission andnuclear decay lines, arising primarily from cosmic rays in-teractions in and around the detector. Above a few MeVthe background is somewhat less severe, but the photonfluxes are much weaker, still presenting a sizable signal-to-noise problem. Gamma-ray telescopes of necessitymust combine high sensitivity with superior background-suppression capability. The major sources of experimen-tal background in gamma-ray detectors are summarizedbelow.

1. Atmospheric Gamma Rays

Gamma rays are produced in copious quantities in the up-per atmosphere of the Earth as a consequence of cosmic-ray interactions. Balloon experiments rely typically on the“growth curve” technique to estimate the contribution ofatmospheric gamma rays to the observed event count rate.In this method, the total count rate of the detector is deter-mined as a function of the residual atmosphere remaining

above the balloon-borne instrument as it rises to float al-titude. Since the downward vertical atmospheric gamma-ray flux is assumed to be zero at the top of the atmosphere,all remaining event counts are assumed to be truly cosmicin nature (or locally produced within the experiment it-self, see following). Both Monte Carlo calculations andsemiempirical models are employed to test the reliabilityof such measurements.

2. Intrinsic Radioactivity

An ubiquitous source of background gamma radiationwithin a detector is the decay of naturally occurring ra-dioisotopes contained within the structure of the instru-ment itself. The two most common naturally occurringbackground lines result from the presence of the long-lived isotopes 40K and 232Th in many detectors and struc-tural materials. 40K, with a half-life of 1.26 × 109 years,undergoes decay to 40Ar giving rise to a gamma-ray line at1.46 MeV, while a 2.62 MeV gamma ray results from anexcited state of 208Pb, a daughter product of 232Th (t1/2 =1.4 × 1010 years).

3. Cosmic-Ray and SecondaryCharged-Particle Interactions

Background counts can arise in a gamma-ray telescopedue to high-energy cosmic-ray collisions (of protons pre-dominantly) with material in or around the detector, of-ten accompanied by secondary particle production. Fortu-nately, active anticoincidence shielding has proven to bean effective means of screening out direct charged particleinteractions within a detector. Of particular concern, how-ever, are high energy (E ∼ 100 MeV) proton collisions thatresult in radioactive spallation products which decay withlonger characteristic lifetimes, yielding secondary “activa-tion” gamma rays that can interact within the detector longafter the original charged-particle event has been vetoed.The gradual build-up of activation species within detectorsin low-Earth orbit, for example, must be monitored withcare given the long-term exposure of such instruments tohigh-energy particles from space or trapped in the Earth’sradiation belts. Extensive tables have been compiled de-tailing the dominant induced radioactive states with cor-responding lifetimes and energies for common detectormaterials.

4. Neutron-Induced Background

Atmospheric and albedo neutrons can interact within de-tectors at balloon altitudes and in low-Earth orbit. Tar-get nuclei can emit secondary particles or gamma raysthat contribute to the background counting rate of the




instrument. Three basic types of neutron interactions mustbe taken into account.

(a) Elastic scattering. Neutrons with energies be-low the first excited level of target nuclei are elasticallyscattered without excitation of the recoil nucleus. Theamount of energy transferred to the recoil nucleus for theintermediate and heavy elements typical of gamma-ray de-tectors is relatively small, implying that elastic scatteringis unlikely to generate a significant background in mostcases. Over a series of such collisions, however, a neutronmay lose sufficient energy to permit thermal neutron cap-ture, giving rise to secondary gamma rays as outlined in(c) below.

(b) Inelastic scattering. The inelastic scattering ofenergetic “fast” neutrons (in interactions of the type(n, n′γ ) or (n, xγ ), where the “x” particle is a proton oralpha particle) can lead to significant background countsin a gamma-ray detector. The secondary gamma radiationresults from the deexcitation of residual product nuclei.Such gamma-ray emission is usually prompt due to the rel-atively short lifetimes of low-lying nuclear excited states,though delayed activation gamma rays may result if theproduct nuclide is also radioactive. An important exampleof activation gamma rays resulting from fast neutron in-teractions is one involving aluminum, a commonly usedstructural material. The reaction 27Al(n, α)24Na yields twogamma rays of energies 1.37 and 2.75 MeV following theradioactive decay via cascade of 24Na (t1/2 = 14.96 h).

(c) Thermal neutron capture. Secondary gammaradiation can also result from the capture of thermal neu-trons by nuclei within a detector. In this type of inter-action, the secondary gamma emission is prompt and ofenergy comparable to the binding energy of the nucleus. Aprominent example of a neutron-capture background lineoccurs for organic scintillator detectors, where the cap-ture of thermal neutrons by the proton nuclei of hydrogenatoms leads to the production of 2.22 MeV photons fromthe deuterium recoil product.

C. Background Rejection Techniques

In order to optimize the cosmic gamma-ray signal meas-ured with a detector, a number of background-suppressiontechniques are usually employed. The most common areoutlined in the following.

1. Passive Shielding

One of the most fundamental techniques for backgroundrejection is the use of passive high-Z materials (usu-ally lead) to shield the central detector elements from

unwanted photons and particles. Typically, several radia-tion lengths of the chosen material are employed to sharplyattenuate the background flux. While the concept is sim-ple in principle, weight constraints tend to limit the totalamount of material that can be utilized. Additionally, sinceit is a passive technique, quantitative information as to theeffectiveness of the shield during the course of actual mea-surements is often difficult to obtain.

2. Active Shielding

Active shielding, as the name implies, provides additionalinformation over the passive approach. The active shield,commonly a plastic organic scintillator, has the advantageof being able to trigger a signal upon passage of a chargedparticle. Thus, active shielding is most commonly used inan anticoincidence mode. In other words, for a detectorplaced within charged-particle anticoincidence shielding,only those events which trigger the main detector elementand not the surrounding active shield will be registered asvalid events.

3. Pulse-Shape Discrimination (PSD)

One limitation of most active shields is that they are notefficiently triggered by the passage of neutral particles.Since neutron-induced reactions contribute a significantbackground to gamma-ray telescopes, it is imperative todevise a scheme for eliminating the neutron componentof the detector signal. This neutron rejection is most effi-ciently achieved by means of pulse-shape discrimination(or PSD). With this technique, one exploits the fact thatneutrons which interact in a scintillator crystal give riseto optical pulses that have a fundamentally different timeprofile compared to signals resulting from photon interac-tions. Electronic means can then be employed to separateone from the other.

4. Time-of-Flight (TOF) Discrimination

Finally, in telescopes containing multiple detectors onemay take advantage of the physical separation betweenthe detector elements to veto certain background events.By precisely timing interactions as they occur in two detec-tors, one may discriminate between upward-moving (i.e.,atmospheric) and downward-moving (celestial) events. Bydefining a time-of-flight window for allowable events, onemay also eliminate “slowly moving” downward particletransitions which could not have resulted from speed-of-light photon interactions. The rejection capability of a TOFsystem is, of course, limited by the detector-separationdistance and the temporal resolution attainable with theavailable electronics.




TABLE II Gamma-Ray Telescopes by Energy Band

Name Energy band Energy (eV) Telescope type Instruments

Low energy keV to MeV 105–106 Collimated scintillator, HEAO, SMM, GRANAT/SIGMA,Coded-aperture telescopes CGRO/BATSE, HETE-2, Swift,

CGRO/OSSE, INTEGRAL, HESSI

Medium energy MeV 106 Compton telescopes CGRO/COMPTEL

High energy MeV to GeV 106–109 Pair-production telescopes SAS-2, COS-B, CGRO/EGRET, GLAST

Very high energy (VHE) GeV to TeV 109–1012 Ground-based optical Cherenkov Whipple, CAT, CANGAROO, HEGRA,Durham, MILAGRO, STACEE, CELESTE,MAGIC, VERITAS

Ultra high energy (UHE) TeV to PeV 1012–1015 Ground-based optical Cherenkov and CASA-MIA, CYGNUS, MILAGRO, HEGRAparticle detection

D. Types of Gamma-Ray Telescopes

In the descriptions given in the following, refer toTable II for a listing of types of gamma-ray telescopesby energy band.

1. Low-Energy (keV to MeV)

In the low-energy portion of the gamma-ray spectrum pho-tons interact primarily via the photoelectric and Comptonprocesses. Historically, gamma-ray detectors sensitive tothis energy range have been collimated, well-type instru-ments in which the primary detector (often an inorganicscintillator such as NaI or CsI) is surrounded by an activeor passive shielding structure. The field of view of the tele-scope is determined typically by the opening angle of theshields or by passive collimators of some high-Z material,such as lead. The OSSE instrument aboard the CGRO isan example of such a configuration.

Another experimental approach used in the hardX-ray/low gamma-ray regime is that of coded-apertureimaging. The coded-aperture telescope operates essen-tially as a “multi-pinhole” camera. The telescope employsan absorbing mask to cast a shadow pattern of incident ra-diation on a position-sensitive detector plane below. Skyimages and the positions of sources within the field ofview are determined after applying standard deconvolu-tion techniques to the data. To minimize artifacts in the re-construction process the pattern of the coded mask is usu-ally of a type referred to as a “uniformly redundant array”(or URA) of elements. The angular resolution and source-location accuracy of a coded-aperture telescope (∼10′)is superior to that of more traditional gamma-ray instru-ments, and is determined by three factors: the size of theindividual mask elements, the mask-detector separationdistance, and the spatial resolution attainable in the de-termination of photon-interaction locations in the centraldetector. While coded-aperture telescopes have excellentangular resolution, there is a practical upper limit to their

sensitive energy range, determined by the thickness of themask required to fully attenuate the gamma rays of inter-est. The French SIGMA experiment aboard the RussianGRANAT spacecraft was a coded-aperture telescope, asare both the imaging and spectroscopic instruments aboardthe INTEGRAL spacecraft (see Fig. 15).

2. Medium-Energy (MeV)

The medium-energy gamma-ray regime extends from ap-proximately 1 to 30 MeV and is one of the most difficultin which to observe. The background over this energyrange is particularly severe, due to nuclear excitation anddecay lines and continuum radiation resulting from parti-cle interactions in and around the detector. The Comptonprocess is the most likely interaction mechanism for in-cident gamma photons in this energy range, and double-scatter Compton telescopes were developed to exploit thisfact.

A Compton telescope consists of two separate detec-tor assemblies which register in coincidence the Comptonscattering of an incident cosmic gamma ray in an upper de-tector array followed by the subsequent total absorptionof the scattered photon in a lower detector. Hence, twosimultaneous interactions (for which interaction positionsand energies are recorded) are required for the registrationof a valid event. The energy and direction of an incidentcosmic photon are determined after event reconstruction.Assuming total absorption of the scattered gamma ray, astraightforward application of the Compton scattering for-mula can be used to determine the Compton scattering an-gle from the upper to lower detectors of the telescope. Thescattering angle and recorded interaction positions withinthe detectors define an event circle on the sky on which thesource of the incident gamma ray must lie. The position ofthe gamma-ray source therefore is not unambiguously de-termined from a single event. Rather, numerous eventsmust be recorded, and event circles computed, whose




FIGURE 15 Schematic of the INTEGRAL SPI spectrometer showing the main components of this coded-apertureinstrument. (Courtesy INTEGRAL SPI Instrument Team.)

common point of intersection reveals the true source loca-tion. The partial, rather than total, absorption of incidentgamma rays, combined with other measurement errors, in-troduces uncertainties in source identification. In practice,detailed modeling of the instrumental response to incidentradiation is required to accurately identify and character-ize cosmic sources.

The COMPTEL instrument aboard the CGRO was aCompton telescope (see Fig. 16). The next generationof Compton telescopes currently under development willseek to remove the scattering angle ambiguity inherent inthe traditional design by also recording the energy and di-rection of the recoil electron in the upper detector fromthe initial Compton scatter. This will greatly enhance

instrument performance and aid in reducing the instru-mental background.

3. High Energy (MeV to GeV)

Above approximately 30 MeV in energy, gamma rays in-teract predominantly via the pair-production process. Thetraditional method of detecting such photons is through theuse of high-voltage spark-chamber grids, interleaved withsheets of a high-density converter material (such as tung-sten). In this technique an incident cosmic gamma ray isfirst converted into an electron–positron pair. As the pairtraverses the layers of the gas-filled spark chamber thetrajectories of the charged particles are detected via the




FIGURE 16 Schematic of the Imaging Compton Telescope(COMPTEL) on board the Compton Gamma Ray Observatory il-lustrating the double-scatter technique employed in Compton tele-scopes. (Courtesy NASA, the Max Planck Institute, and the CGROCOMPTEL Instrument Team.)

sparks they produce, the positions of which are recorded.A large scintillator below the spark chamber is typicallyused as a calorimeter to absorb any remaining particle en-ergy. The diverging tracks recorded for the electron andpositron are used to determine the incident direction of theoriginal gamma ray. Spark chambers are normally filledwith a gas (usually some mixture of neon) that acts as aspark-quenching agent, and which slowly degrades withuse. The gas is thus a consumable that must be periodi-cally flushed from the spark chamber and replenished forbest performance.

The SAS-2, COS-B, and EGRET experiments all em-ployed the same basic spark-chamber design, albeit ondifferent scales of size and complexity (see Fig. 17).The next generation of pair-production gamma-ray tele-scope will be the Gamma-Ray Large-Area Space Tele-scope (GLAST) in which the spark-chamber grids will bereplaced by semiconductor silicon strip detectors. GLASTis designed to be sensitive to gamma photons up to∼300 GeV in energy.

4. Very High Energy (GeV to TeV, and above)

Gamma rays in the energy range above ∼30 GeV havenot been well sampled from space to date, given their lowfluxes, and ground-based techniques have only recentlymatured to the point where efficient observations are fea-sible. As outlined previously, cosmic gamma rays are ab-sorbed in the Earth’s atmosphere and are not directly ob-servable from the ground. Photons of energy greater than∼30 GeV are detectable in principle, however, from theextensive air showers they produce upon interaction inthe upper atmosphere. A particular signature of such in-teractions is the visible pulse of Cherenkov light emittedcollectively by the relativistic electrons and positrons pro-duced in these electromagnetic cascades. Ground-basedoptical telescopes are used to detect this Cherenkov light(see Fig. 18), from which energies and directions of inci-dent cosmic gamma rays can be inferred.

To date the atmospheric Cherenkov technique hasbeen employed with greatest success for photon ener-gies above ∼300 GeV by several groups. The U.S.-basedWhipple collaboration (USA–UK–Ireland) has pioneeredmany of the techniques now commonly applied to TeV

FIGURE 17 Schematic of the EGRET instrument on board theCompton Gamma Ray Observatory illustrating the spark-chamberdesign characteristic of pair-production telescopes. For compari-son, schematics of the earlier SAS-2 and COS-B instruments areshown to scale. (Courtesy NASA and the CGRO EGRET Instru-ment Team.)




FIGURE 18 Photograph of the Whipple Observatory 10-m imag-ing atmospheric Cherenkov telescope. (Courtesy of the WhippleCollaboration.)

measurements. Other collaborations actively operatingair-Cherenkov telescopes include CAT (in France), theCANGAROO (Japan–Australia) and Durham, UK groups(with telescopes in Australia), and HEGRA (Germany–Armenia–Spain, in the Canary Islands). Among the sev-eral TeV sources detected in recent years are the Crab andVela pulsars, and AGNs such as MRK 421 and MRK 501.

The slightly lower energy domain from approximately30 to 300 GeV still remains largely unexplored. A lowerdetection threshold requires a much larger collectingarea for the atmospheric Cherenkov light. Two groups,STACEE and CELESTE, are in the process of convertinglarge-area heliostats from experimental solar-power sta-tions to this purpose. A German-Spanish project (MAGIC)is also underway to build a 17-m air-Cherenkov telescope.

At even higher gamma-ray energies, in the PeV range(1015 eV, the “ultra-high energy,” or UHE, regime), parti-cles associated with the photon-induced electromagneticcascades have sufficient energy to reach the ground, where

arrays of particle detectors can be used to detect them.Very large collecting areas are required, however, giventhe extremely low gamma fluxes expected. Early attemptsto detect photons of PeV energy with particle-detectorarrays included the CASA-MIA and CYGNUS efforts,among others. Ongoing attempts are being carried out bythe HEGRA and MILAGRO collaborations. Early reportsof positive PeV detections in the 1980s proved to be opti-mistic and have been unconfirmed by later more sensitivemeasurements.

IV. FUTURE MISSIONS AND PROSPECTS

The development of any new telescope has as its primarygoal an increase in sensitivity, combined with improvedangular and spectral resolution. In the gamma-ray regimethis translates invariably into improved determinationof photon-interaction positions and energy-depositionswithin the detecting medium. More accurate determina-tion of the properties of interacting gamma-rays leadsdirectly to a reduced background rate, since true celes-tial events are less likely to be confused with backgroundinteractions. Virtually every gamma-ray telescope undercurrent development seeks to improve these interactionmeasurements by exploiting new detector technologies.Spatial and energy resolution within detector materialsare greatly enhanced, for example, with the use of newlydeveloped semiconductor strip and pixel detectors (suchas silicon, germanium, and CdZnTe). The continuing chal-lenge is to fabricate such sensitive small-scale devices insufficiently large and reliable quantities to be incorporatedinto new large-area instrumentation, at costs that can bereasonably afforded. Another common characteristic ofhigh-energy telescopes is the large number of data sig-nals that must be processed and recorded in multi-channeldetector systems. Increased use of custom Application-Specific Integrated Circuit (ASICs) designs employingVery Large Scale Integration (VLSI) techniques is im-perative for the efficient operation of high-energy instru-ments. Fortunately, computational speed and data-storagecapacities continue to rise at a steady pace, and experi-mentalists are quick to exploit these new capabilities intheir instrument designs.

At the time of writing (2001), a number of gamma-raymissions are scheduled for launch in the near future (seeTable II). Key among these is the International Gamma-Ray Astrophysics Laboratory (INTEGRAL), a missionof the European Space Agency (ESA) with participationfrom Russia and NASA. INTEGRAL is to be launchedin 2002 and will be dedicated to high-resolution spec-troscopy (E/ E ∼ 500) and imaging (∼12′ FWHM) overthe energy range from 15 keV to 10 MeV. INTEGRAL




carries two gamma-ray instruments, the SPI spectrome-ter and the IBIS imager, both operated as coded-aperturetelescopes for accurate source identification. The SPI em-ploys high-purity germanium detectors, while the IBISuses two detector planes, a front layer of CdTe elementsand a second layer composed of CsI pixels. In recognitionof the need for broadband coverage INTEGRAL also car-ries two coded-aperture X-ray monitors (JEM-X), as wellas an optical monitoring camera (the OMC). The primaryscientific objective of the INTEGRAL instruments is tocarry out high-resolution spectroscopic studies of sourcesover the nuclear-line region of the spectrum.

The Gamma-Ray Large Area Space Telescope(GLAST), scheduled for launch by NASA in 2005, willbe the follow-on mission to the highly successful CGROEGRET experiment. The sensitivity of GLAST, from20 MeV to 300 GeV, will extend well beyond the EGRETrange, providing much-need coverage in the poorly ob-served GeV region of the spectrum. A more modernparticle-tracking technology (silicon strip detectors) willbe employed in GLAST in place of the spark-chambersgrids used in earlier pair-production telescopes. GLASTwill have a large field of view (∼2 sr) and achieve a fac-tor of 30 improvement in flux sensitivity and a factor of10 improvement in point-source-location capability com-pared to EGRET. GLAST will also carry a gamma-rayburst monitor.

Missions designed specifically for gamma-ray burststudies include HETE-2 and Swift. The High-EnergyTransient Experiment-2 (HETE-2) was launched in 2000,and became operational in early 2001. This satellite carriesthree science instruments: a near-omnidirectional gamma-ray spectrometer, a wide-field X-ray monitor, and a set ofsoft X-ray cameras. A major goal of the HETE-2 mis-sion is the rapid identification and accurate localizationof gamma-ray bursts, whose coordinates will be relayedwithin seconds to ground-based observatories for deepcounterpart searches. The recently selected Swift mission(scheduled for launch in 2003) will also carry out multi-wavelength studies of gamma-ray bursts, in the manner ofBeppoSAX and HETE-2. Like its avian namesake Swiftwill “feed on the fly” by rapidly localizing gamma-raybursts to ∼1–4′ precision, and transmitting coordinatesto the ground within ∼15 s for follow-up counterpartsearches. Swift can also be rapidly reoriented to carry outobservations with its X-ray and ultraviolet/optical tele-scopes that will be used to study afterglow properties, fixpositions to arcsecond levels, and determine distances viaredshift spectral measurements.

The High-Energy Solar Spectroscopic Imager (HESSI)is a NASA-funded mission to study the characteristicsof particle acceleration in solar flares via the X-ray andgamma-ray emission produced in these energetic events.

HESSI, scheduled for launch in 2001 at the peak ofthe solar cycle, will carry out high-resolution spectro-scopic measurements of nuclear lines and underlyingbremsstrahlung continuum over the energy range from3 keV to 20 MeV with a set of cooled high-purity germa-nium detectors. HESSI will carry out Fourier-transformimaging of the full Sun at ∼2′′–36′′ resolution over itssensitive range by using rotating modulating collimators.Since HESSI is unshielded it can also carry out other non-solar observations, including measurement of the Galacticdiffuse lines due to radioactive 26Al (at 1.809 MeV) andpositron annihilation (at 0.511 MeV).

In the area of planetary studies, NASA’s Mars Odysseymission is also scheduled for launch in 2001. Among itssuite of instruments are a gamma-ray spectrometer andtwo neutron detectors. These will be used to fully map theMartian surface and determine its elemental composition.The neutron and gamma-ray measurements in combina-tion will also be used to obtain an estimate of the watercontent of the Martian near-surface.

Other gamma-ray experiments and missions have beenidentified as a high-priority by the Gamma-Ray Astron-omy Program Working Group, an advisory panel to NASAcomposed of scientists from the high-energy community.Among their recommendations for future development isan advanced Compton telescope employing the latest de-tector technologies for application in the MeV region ofthe spectrum.

High-altitude scientific ballooning has long served as atest-bed for new instrumentation. Gamma-ray telescopesrequire long exposures, due to comparatively low sourcefluxes and high instrumental backgrounds, while the dura-tion of a typical balloon flight, unfortunately, can often berather limited (a few days at most). To counter this draw-back NASA has recently initiated the Ultra-Long DurationBalloon (ULDB) project whose planned 100-day around-the-world balloon flights will greatly extend the time aloftfor scientific instruments. The ULDB program will pro-vide much-needed opportunities for longer-exposure bal-loon flights, as well as an attractive low-cost alternative tofull-scale space missions.

Among the collaborations actively engaged in ground-based air-Cherenkov studies of TeV gamma rays thereare also a number of efforts underway to upgrade exist-ing facilities, primarily through an increase in optical col-lecting area. Perhaps the most ambitious are those of theVERITAS collaboration, with a planned array of seven10-m telescopes in the USA, the German-French-ItalianHESS group with 4 to 16 12-m class telescopes to be builtin Namibia, the German-Spanish MAGIC project with atelescope of 17-m aperture, and the Japanese SuperCAN-GAROO array of four 10-m telescopes in Australia. In arelated effort, the MILAGRO collaboration is constructing




a water-Cherenkov detector with a wide field of view inNew Mexico in the USA for TeV measurements. As acovered light-tight detector MILAGRO has the added ad-vantage that it can remain operational for 24 h a day.

V. CONCLUDING REMARKS

The future of gamma-ray astronomy looks very brightindeed, as the next generation of gamma-ray telescopesand missions stands poised to extend our knowledge ofthe high-energy sky. Over the past decade gamma-ray as-tronomy has become firmly established as a productiveand dynamic discipline of modern observational astro-physics. With the completion of comprehensive surveyswith the telescopes aboard the Compton Gamma Ray Ob-servatory the pioneering phase of gamma-ray explorationhas now been achieved and the promise of gamma-rayastronomy confirmed and realized. New questions havebeen raised and remain to be addressed, and ongoingtechnological advances will certainly continue to spur thedevelopment of future successor missions to build uponthe present findings. The results obtained with the Comp-ton Observatory and other spacecraft have revolutionizedour view of the high-energy Universe, and have under-lined the fundamental importance of the gamma-ray re-gion of the spectrum to a fuller and more complete under-standing of the high-energy processes that dominate thecosmos.

ACKNOWLEDGMENT

This review is dedicated to the memory of Frank J. Kerr, one of thefounding fathers of the field of Galactic radio astronomy, and an earlyadvisor to both of the authors. His gentlemanly manner and professionalexample will be long remembered by those who knew him. He wouldbe delighted and amazed at the many recent discoveries in gamma-ray

astronomy, and fully appreciative of their relevance to much of his ownwork.


COSMIC RADIATION • GRAVITATIONAL WAVE ASTRON-OMY • INFRARED ASTRONOMY • NEUTRINO ASTRONOMY

• PULSARS • SOLAR PHYSICS • SUPERNOVAE • ULTRAVI-OLET SPACE ASTRONOMY • X-RAY ASTRONOMY

BIBLIOGRAPHY

Catanese, M., and Weekes, T. C. (1999). Very high gamma-ray astron-omy. Publications of the Astronomical Society of the Pacific 111,1193–1222.

Diehl, R., and Timmes, F. X. (1998). Gamma-ray line emission fromradioactive isotopes in stars and galaxies. Publications of the Astro-nomical Society of the Pacific 110, 637–659.

Fichtel, C. E., and Trombka, J. I. (1997). “Gamma-Ray Astrophysics:New Insights into the Universe, Second Edition,” NASA ReferencePublication 1386. NASA, Greenbelt, MD.

Fishman, G. J., and Meegan, C. A. (1995). Gamma-ray bursts. Annu.Rev. Astr. Astrophys. 33, 415–458.

Gehrels, N., and Paul, J. (1998). The new gamma-ray astronomy. PhysicsToday 51, 26–32.

Hoffman, C. M., Sinnis, C., Fleury, P., and Punch, M. (1999). Gamma-rayastronomy at high energies. Rev. Mod. Phys. 71, 897–936.

Longair, M. S. (1997). “High Energy Astrophysics, Volume 1: Particles,Photons and their Detection,” Second Edition, Cambridge UniversityPress, Cambridge.

Longair, M. S. (1994). “High Energy Astrophysics, Volume 2: Stars,the Galaxy and the Interstellar Medium,” Second Edition. CambridgeUniversity Press, Cambridge.

van Paradijs, J., Kouveliotou, C., and Wijers, R. A. M. J. (2000). Gammaray burst afterglows. Annu. Rev. Astr. Astrophys. 38, 379–425.

Strong, K. T., Saba, J. L. R., Haisch, B. M., and Schmelz, J. T. (eds.).(1998). “The Many Faces of the Sun: A Summary of the Results fromNASA’s Solar Maximum Mission,” Springer-Verlag, Berlin.

Urry, C. M., and Padovani, P. (1995). Unified schemes for radio-loudactive galactic nuclei. Publications of the Astronomical Society of thePacific 107, 803–845.

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Encyclopedia of Physical Science and Technology EN007L-299 July 10, 2001 19:2

Gravitational Wave AstronomyPatrick R. BradyJolien D. E. CreightonUniversity of Wisconsin–M:Lwauxee

I. Introduction to Gravitational RadiationII. Observation Techniques

III. Data Analysis MethodsIV. Astrophysical SourcesV. Outlook

GLOSSARY

Characteristic strain The gravitational wave strain of asignal at some characteristic frequency times the squareroot of the number of cycles over which the signal isobserved near that frequency.

Detector sensitivity Characteristic strain due to gravi-tational waves that would exceed instrumental strainnoise in a detector.

Gravitational wave strain The fractional change in thedistance between two free-falling bodies produced bya gravitational wave as it passes the bodies.

Laser interferometric detector A laser interferometerwhich measures the relative lengths of two orthogonal(or nearly orthogonal) cavities. When a gravitationalwave impinges on the system, the relative change incavity length causes a change in the interference patternregistered by the interferometer.

Resonant-mass detector A massive cylinder of alu-minium, or nobium crystal, suspended in vacuum andmechanically isolated from its surroundings. When agravitational wave impinges on the cylinder, the rela-tive accelerations excite the cylinder’s natural modesof oscillation.

Tidal distortion The deformation of a massive body bythe gravitational field produced by other bodies.

GRAVITATIONAL WAVE ASTRONOMY is the studyof our universe using gravitational radiation emitted byastrophysical sources. Experimental efforts to directly ob-serve gravitational waves have a history spanning at least40 years. The construction and commissioning of long-baseline interferometric detectors is a landmark for thefield. Scientists believe that these instruments will makethe first (unambiguous) detection of gravitational waves,and will become tools for routine astronomical observa-tions.

I. INTRODUCTION TO GRAVITATIONALRADIATION

Gravitational radiation, like electromagnetic radiation(radio, infrared, light, and X-rays), transports energyvia propagating field fluctuations, or waves. Whereelectromagnetic radiation involves fluctuations of theelectromagnetic field, gravitational radiation involves

33

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34 Gravitational Wave Astronomy

fluctuations of the gravitational field. Gravitation andelectromagnetism are both long-range forces which ex-hibit radiative behavior. Two significant differences are(i) the electromagnetic force is stronger than the gravita-tional force, and (ii) the electric charge can be positive ornegative, while the gravitational charge—the mass of anobject—has only one sign.

Electromagnetic radiation originates from individualcharged particles which undergo rapid acceleration. Astro-nomical bodies tend to be electrically neutral due to thestrength of the electromagnetic force and the repulsionbetween like charges. Consequently, the brightest sourcesemit an incoherent superposition of high-frequency ra-diation from ionized material. Because electromagneticradiation is readily absorbed and scattered, observed radi-ation comes only from the outermost layers of the source.By observing electromagnetic radiation, astronomers gaininformation about the thermodynamic state of the radiatorand its constituent materials.

In contrast, strong gravitational waves originate fromthe bulk motion of large masses. Large accumulations ofmass are possible because the gravitational charge (mass)has only one sign and the force between charges is attrac-tive. Gravitational radiation tends to be strongest at lowfrequencies since significant coherent changes in motionoccur on macroscopic scales. The information carried bythe waves describes the dynamics of the source rather thanits thermodynamic state. Moreover, gravitational wavescouple weakly to matter, so there is almost no absorptionor scattering of the gravitational radiation—the universeis almost entirely transparent to gravitational waves. Thisweak coupling also makes it difficult to directly observegravitational waves.

General relativity is the simplest of modern theories ofgravitation; it attributes the gravitational field generatedby massive bodies to the curvature of spacetime. Moreprecisely, the curvature of spacetime is generated by themass, energy, and stress contained in matter. The familiarnotion of gravitational acceleration arises from the asser-tion that a free-falling test particle (i.e., a particle that doesnot contribute to the gravitational field) follows a shortestpath in spacetime. Tidal effects—the distortion of mas-sive bodies by the gravitational field produced by otherbodies—are manifestations of curvature; a pair of free-falling test particles which start out moving parallel maymove closer together or further apart due to a tidal field.Tidal fields and gravitational acceleration are also wellknown in Newtonian gravity theory. In general relativity,however, the gravitational field propagates at finite speed.

Gravitational waves are propagating fluctuations in thespacetime curvature. These fluctuations produce an os-cillating tidal field which changes the distance betweennearby free-falling bodies. The fractional change in the

FIGURE 1 The two polarizations of gravitational waves.

distance between two free-falling bodies initially sepa-rated by a distance � is the strain

h = ��/�

produced by the gravitational wave as it passes the twobodies. In general relativity, there are two polarizationsof gravitational waves, h+ and h×, which cause displace-ments in independent directions (see Fig. 1). The strain hon a particular pair of objects is a linear superposition ofthese two polarizations.

According to Einstein’s equations, accelerating massesgenerate gravitational radiation. The strongest sourcesconsist of large accumulations of dense matter. By analogywith electromagnetic radiation, it is both illuminating anduseful to describe radiating matter distributions in termsof their changing multipole moments. The monopole mo-ment is the total mass of the accumulation. It is conservedand thus cannot change. Similarly, the gravito-electric andgravito-magnetic dipole moments are the momentum andangular momentum of the distribution. They are also con-served, so there is no dipole radiation. (This contrasts withelectromagnetism, in which the charge of an object is in-dependent of its inertia. The absence of dipole radiationin general relativity is related to the equivalence of grav-itational and inertial mass.) Consequently, gravitationalwaves are radiated if the source has a changing quadrupole(or higher) moment.

For weakly gravitating sources composed of mattermoving slowly compared to the speed of light, the am-plitude of the gravitational wave strain h is proportionalto the second time derivative (retarded, to account for thefinite speed of propagation of the gravitational wave) ofthe quadrupole moment of the system. The strain, due toa passing gravitational wave, on two free-falling bodieslocated a distance D from the source is

h ≈ 2G

c4 D

d2 Q

dt2

∣∣∣∣retarded



Gravitational Wave Astronomy 35

where Q is the projection of the quadrupole moment ten-sor first transverse to the direction of propagation of thewave and then along the direction separating the two free-falling bodies. Because Q ∼ mx2 (see below), the secondtime derivative of Q is essentially the kinetic energy of thesource attributable to nonsymmetric motion of the parti-cles in the source, ENS. To produce significant amountsof gravitational radiation, the nonsymmetric mass–energyof the source M must be compressed into a small region.In general relativity, this region must be bigger than ablack hole of the same mass, i.e., R = 2G M/c2 where Gis Newton’s gravitational constant and c is the speed oflight. For a stellar mass source (M ∼ M�) at astrophysicaldistances, the strain at gravitational wave observatoriescan be estimated as

h ∼ G(ENS/c2)

c2 D

∼ 10−20

(ENS/c2

M�

) (Mpc

D

).

That is, to observe waves from a system with a solar-mass worth of energy in nonsymmetric motion at themegaparsec scale (the distance to the nearest galaxy), as-tronomers need to measure strains on the order of 10−20.This sensitivity is just now becoming possible for broad-band detectors.

Until the 1960s there was considerable debate whethergravitational waves were observable at all. Complicationsof general relativity made it difficult to separate physi-cal effects from artifacts associated with the mathematicaltreatment of the theory. The most convincing theoreticalarguments in favor of gravitational waves as observablephysical quantities are based on energy content of thewaves. It is well known that work is done on bodies sub-jected to time-varying tidal fields. For example, work isdone to raise ocean tides by the changing tidal field of themoon and sun as the Earth rotates. Gravitational wavesare produced by accelerating masses that produce time-varying tidal fields. Since the propagating tidal field cando work, gravitational waves must carry the energy re-quired to do the work. Consequently, bodies that producedynamic tidal fields lose energy in the gravitational wavesthey produce. The amount of energy carried by gravita-tional waves through an element of area d A in an elementof time dt scales as the rate of change of the two polariza-tions of the gravitational wave strain squared:

d E = c3

16πG

[(∂h+∂t

)2

+(

∂h×∂t

)2]

d A dt.

Within the quadrupole approximation, the rate of energyloss from a source is therefore given by

d E

dt= G

5c5

3∑i, j=1

(d3 Qi j

dt3

)2

where Qi j is the quadrupole moment tensor given by

Qi j = qi j −3∑

k=1

qkk

where

qi j =∑

particles

mxi x j .

Here m is the mass of a given particle in the source and {xi }is the set of components describing its position relative tothe (irrelevant) origin of the coordinates.

II. OBSERVATION TECHNIQUES

The methods used to observe gravitational radiation sug-gest that four frequency bands be identified. The bandsare:

� Extremely Low Frequency (ELF) band:10−18–10−15 Hz. The canonical source in this band isgravitational waves from the big bang. These wavesform a cosmological stochastic background much likethe famous cosmic microwave background discoveredby Penzias and Wilson. Limits on the cosmologicalstochastic background gravitational waves are providedby observations of the cosmic microwave background.

� Very Low Frequency (VLF) band: 10−9–10−4 Hz.Pulsar timing provides a method to detect thesegravitational waves. For example, timingmeasurements of the Hulse–Taylor binary pulsarprovide indirect evidence for gravitational wavesemitted by binary neutron star systems. Promisingsources for direct detection by radar ranging includewaves from a variety of cosmological defectsoriginating in the early universe.

� Low Frequency (LF) band: 10−4–100 Hz. Gravitationalwave detectors in space, e.g., the Laser InterferometerSpace Antenna (LISA), and radar ranging of spacecraftcan observe in this band. Close white dwarf binariesare so common in our Galaxy that they are expected toproduce a stochastic background of gravitationalwaves below ∼10−3 Hz, while gravitational wavesfrom super-massive black holes (105–109 M�) will bethe strongest point sources.

� High Frequency (HF) band: 100–104 Hz.Ground-based interferometers and resonant-massdetectors operate in this band. The most promisingsources of gravitational waves are inspiral andcoalescence of compact stellar-mass black holes and




neutron stars (1–103 M�). Other sources includedistorted pulsars and supernovae.

The experimental techniques used (or planned) to observegravitational waves are described below in order from highfrequency to low frequency.

A. Resonant Mass Detectors

Massive cylinders of aluminum, or niobium crystal, aresuspended in vacuum and mechanically isolated from theirsurroundings. When a gravitational wave impinges on thecylinder, the relative accelerations excite the cylinder’snatural modes of oscillation. These excitations are mea-sured using transducers attached to the cylindrical bar.Detectors of this type are typically most sensitive to grav-itational waves in the HF band traveling orthogonal to thecylinder’s axis. The first instruments constructed with theexpress purpose of observing gravitational waves wereresonant bar detectors. Future resonant mass detectorsmay be spheres or truncated icosahedra which would haveomnidirectional sensitivity.

Gravitational waves deposit energy into resonant massdetectors when they excite their normal modes. The ab-

TABLE I Gravitational Wave Astronomy Frequency Bands

Frequency band Sources and methods of observation

Extremely Low Frequency (ELF) Stochastic gravitational waves from the early universe. Can be detected as anisotropies of the Cosmic Microwave10−18–10−15 Hz Background Radiation (CMBR). Waves from the big bang may be parametrically amplified by inflation.

They may be produced by cosmic strings or domain walls during phase transitions as the universe cooled.

Very Low Frequency (VLF) (a) Gravitational waves from widely separated binary systems. Can be detected using radio timing observations10−9–10−4 Hz of binaries containing millisecond pulsars, e.g., PSR 1913+16.

(b) Stochastic background of gravitational waves. Has been constrained using pulsar timing data.

Low Frequency (LF) Space-based laser interferometers provide the best method to observe in this frequency band. It is anticipated that10−4–100 Hz the Laser Interferometric Space Antenna (LISA) should launch circa 2010.

(a) Inspiral waves from binary systems comprised of white dwarfs, neutron stars, or stellar-mass black holes inour Galaxy. At the lower frequencies in this band, There are so many white dwarf binary systems that thesignals will be confused; these systems will produce a stochastic background of gravitationalwaves at lower frequencies in this band.

(b) Gravitational waves from supermassive (M ∼ 105–109 M�) black holes disturbed by infalling stars andother debris.

(c) Cosmological stochastic background of gravitational waves; has been constrained by radar ranging ofinterplanetary spacecraft.

High Frequency (HF) Ground-based interferometers and resonant-mass detectors provide the best method to observe in this frequency100–104 Hz band. Resonant mass detectors have been operating since the early 1960s; prototype interferometric detectors

have been operating since the 1970s. The new generation of kilometer-scale interferometric detectors will bein continuous operation from 2002 onward.

(a) Waves from the inspiral and merger of binary systems comprised of neutron stars or black holes (with massM < 1000M�).

(b) The birth of neutron stars and supernova explosions. Rotation-induced asymmetries, convection, orunstable modes in the nascent neutron star (e.g., bar mode instabilities and r-modes) will generategravitational waves in this band.

(c) Wobbling or distorted pulsars will produce nearly monochromatic continuous waves.

(d) Cosmological stochastic background of gravitational waves.

sorption cross section of the bar increases with the massof the bar and with the square of the speed of sound in thebar’s material. Thus, it is desirable to construct high-massresonant bars with a high speed of sound. Accurate mea-surement of the normal mode excitations is hampered bynoise, due to Brownian motion, in the bar and the trans-ducer. Modern bar detectors are cryogenically cooled toliquid helium temperatures, or lower, to reduce this noisesource. Bar detectors are also limited by the electronicnoise in the amplifier. The strain-noise power spectral den-sity (see below) of a bar detector is

S( f0) = π

2

kT

Mv2s Q f0

where f0 is the frequency of the excited mode, Q is thequality factor (the number of radians of oscillation in themode it takes to damp by a factor of e) of the mode, vs isthe speed of sound in the bar, T is its temperature, and kis Boltzmann’s constant. This sensitivity is achieved in anarrow frequency band, � f ∼ 1 Hz for modern detectors,around the mode frequency.

Modern resonant bar detectors have mode frequenciesof f0 ∼ 900 Hz with bandwidths of � f ∼ 1 Hz, quality




factors of Q ∼ 106, masses of M ∼ 2000 kg, and tempera-tures T ∼ 1 K. The rms strain sensitivity of these detectorsis hrms = [ f0S( f0)]1/2 ∼ 10−20. There are five currentlyoperating cryogenic resonant bar detectors: EXPLORER(located at CERN), ALLEGRO (located in Baton Rouge,USA), NIOBE (located in Perth, Australia), NAUTILUS(located in Frascati, Italy), and AURIGA (located in Leg-naro, Italy).

B. Ground-Based Interferometers

Interferometric gravitational wave detectors measure therelative lengths of two orthogonal (or nearly orthogonal)cavities. The simplest interferometric detector is basedon the Michelson interferometer. In this configuration, abeam of light is split at a beam splitter and enters the twocavities (see Fig. 2). The light traverses the cavities andreflects off the mirrors at the ends of the cavities. The lightbeams from the two cavities interfere at the beam splitter(after traversing the cavities). A photodiode is used todetect changes in the interference pattern when the cavitieschange length. The interferometer is normally configuredso that no light hits the photodiode if the two cavities haveidentical length; the photodiode is trained on the dark portof the beam splitter. When a gravitational wave passes thedetector, the relative lengths of the two cavities change asthe end mirrors are affected by the tidal field. This causeslight to fall on the photodiode, and thus provides a read-outof the gravitational wave signal.

Modern interferometric detectors often use modifiedoptical topologies which provide greater sensitivity togravitational waves. Instead of a simple Michelson in-terferometer, a Fabry–Perot cavity is created within eachof the arms to store the laser light. The quality of thecavity determines the storage time for the light and thecorresponding effective increase in the length of the cavi-ties. Since readout is sensitive to the relative difference inlength of the two arms, this provides additional sensitivity

FIGURE 2 Schematic of an interferometric gravitational wavedetector.

if the light is stored for less than one gravitational wavecycle.

There are three dominant sources of noise in ground-based interferometric detectors. At low frequencies, seis-mic noise creates a “wall” at ∼10 Hz below which theground motion is no longer isolated by the suspension.At intermediate frequencies, the thermal noise of the testmasses and their suspensions is dominant. At high fre-quencies, the combination of shot (photon counting) noise,and, for cavities with a high light-power, radiation pressurenoise are dominant. The sensitivity at high frequencies canbe improved using a power-recycling mirror to reflect lightcoming from the beam splitter back into the cavities. Thisincreases the light power stored in each arm, thus reducingphoton shot noise. Further improvement may be achievedusing signal-recycling—a mirror is added to the dark portof the beam splitter and the signal is fed back into theinterferometer.

Currently operating kilometer-scale interferometersinclude the Laser Interferometer Gravitational-waveObservatories (LIGO) with sites located in Hanford,Washington, and Livingston, Louisiana; the GEO-600 in-terferometer in Hannover, Germany; and the TAMA-300interferometer in Tokyo, Japan. In addition, the VIRGOobservatory is under construction near Pisa, Italy.

C. Space-Based Interferometers

Seismic and gravitational field gradients limit the sensitiv-ity of terrestrial detectors in the LF band. Very long base-line (∼106 km) interferometers in space would be sensitiveto gravitational waves in this band. A joint ESA/NASAmission for a space-based gravitational wave detectorcalled Laser Interferometer Space Antenna (LISA) is pro-posed and under consideration for launch around 2010.The mission would place three identical spacecraft in aheliocentric orbit about 20◦ behind the Earth. The space-crafts would each house a laser and two proof masses.These masses would be allowed to orbit freely insidethe spacecraft—they would not be attached in any way,rather they would be protected from buffeting by the solarwind and radiation pressure. The spacecraft would use ionpropulsion drives to follow the proof masses in drag-freeorbits. The positions of the proof masses with respect toeach other would be monitored using heterodyne interfer-ometry; this provides the readout sensitive to the gravita-tional wave signal.

D. Pulsar Timing

Millisecond pulsars are excellent clocks, comparable inaccuracy to the best atomic clocks on earth. When a gravi-tational wave is present, either at the pulsar or at the earth,




TABLE II Physical Data for Modern Cryogenic Resonant Bar Detectors

Detector ALLEGRO AURIGA EXPLORER NAUTILUS NIOBE

Material Aluminum Aluminum Aluminum Aluminum Niobium

Length (m) 3.0 2.9 3.0 3.0 2.75

Mass M (kg) 2296 2230 2270 2260 1500

Mode frequencies f0 (Hz) 895, 902 912, 930 905, 921 908, 924 694, 713

Quality factor Q 2 × 106 3 × 106 1.5 × 106 5 × 105 2 × 107

Temperature T (K) 4.2 0.2 2.6 0.1 5

Sensitivity hrms 3 × 10−20 6 × 10−21 2 × 10−20 6 × 10−21 2 × 10−20

Latitude N 30◦27′45′′ 45◦21′12′′ 46◦27′ 41◦49′26′′ −31◦56′

Longitude E −91◦10′44′′ 11◦56′54′′ 6◦12′ 12◦40′21′′ 115◦49′

there will be a dilation of time due to the gravitationalwave; this time dilation can be measured as the clocksbecome unsynchronized. Pulsar timing data puts the bestcurrent observational limits on the stochastic backgroundof gravitational waves with periods on the order of thetotal observation time (several years), i.e., in the very lowfrequency band.

E. Radar Ranging

Tracking of interplanetary spacecraft affords the oppor-tunity to use radar ranging over very long baselines forgravitational wave detection. A highly stable radio signalis sent to the spacecraft which transponds it back to anearth-based receiver. The presence of a gravitational wavewould create a Doppler signature δ f/ f proportional to thewave-strain in the radio signal. Gravitational waves withperiods on the order of the round-trip time (∼10−3 Hzfor solar system distance scales) can be detected if theiramplitudes exceed h ∼ 10−15. This detection method islimited by dispersion of the radio waves in the interplane-tary plasma and by water vapor in the earth’s atmosphere.

III. DATA ANALYSIS METHODS

Despite the many observational methods available tosearch for gravitational wave signals, a direct observa-tion remains elusive to this day. With the advent of long-baseline, ground-based interferometers, a new era in grav-itational physics has arrived. These sensitive instrumentswill likely transform the field of gravitational wave detec-tion into the new field of gravitational wave astronomy.With the improved sensitivity and the planned duty cycle,i.e., continuous operation of multiple detectors around theworld, comes a new challenge: data analysis. The antici-pated sources of gravitational waves will be close to thelimit of detectability, so it is necessary to use optimal dataanalysis tools. Since routine astronomical observationsare likely to be made with the interferometric or resonant

bar detectors, attention is restricted to these instrumentsbelow.

The output from gravitational wave detectors is gener-ally time series data that provide a direct measure of thestrain on the detector. Extraction of the gravitational wavesignal is frustrated by noise which limits the sensitivity ofthe instrument. If the calibrated strain signal from a givendetector is h(t), the detector sensitivity can be expressedin terms of the mean square instrumental noise per unitfrequency. Specifically, the noise power spectral densityof the instrumental strain noise is

S( f ) = 2

T〈|hnoise( f )|2〉

where 〈·〉 represents an average over an ensemble of noiserealizations and

hnoise( f ) =∫ T

0hnoise(t)e2π i f t dt

is the Fourier transform of the strain noise hnoise(t) overa time interval T . The power spectral density provides ameasure of instrumental noise as a function of frequency.As indicated above, each detector has a frequency band ofoptimal sensitivity which determines the type of source itmay observe.

Optimal detection of signals in noise relies on accumu-lation of all the signal power into a single number. Forperiodic signals, this is achieved by taking the Fouriertransform of h(t) and examining the power at the signal’sfrequency. In general, the strength of a signal is describedby its characteristic amplitude hchar, which represents theintrinsic amplitude of the signal at some characteristic fre-quency times the square-root of the number of cycles overwhich the signal is observed near that frequency (see be-low for precise definitions). For comparison with signalstrength, detector sensitivity is better expressed in terms ofthe root mean square dimensionless strain per logarithmicfrequency interval

hrms =√

f S( f ).




TABLE III Physical Data for Modern Ground-Based Interferometric Detectors

LIGO

Detector LHO 2 km LHO 4 km LLO 4 km GEO-600 TAMA-300 VIRGO

Arm length(s) (m) 2000 4000 600 300 3000

Frequency fmin (Hz) 125 125 200 300 100

Bandwidth � f (Hz) 200 200 300 300 800

Strain sensitivity hrms( fmin) 6.5 × 10−22 3.5 × 10−22 8 × 10−22 3 × 10−21 6 × 10−22

Elevation (m) 142.554 −6.574 114.425 90 51.884

Latitude N 46◦27′18′′.528 30◦33′46′′.4196 52◦14′42′′.528 35◦40′35′′.6 43◦37′53′′.0921

Longitude E 240◦35′32′′.4343 269◦13′32′′.7346 9◦48′25′′.894 139◦32′9′′.8 10◦30′16′′.1878

X arm orientation N of E 125◦.9994 197◦.7165 115◦.9431 180◦ 70◦.5674

Y arm orientation N of E 215◦.9994 287◦.7165 21◦.6117 270◦ 160◦.5674

A. Detection of Burst Sources

1. Interferometers

Since interferometers have broadband sensitivity, one canmonitor the phase evolution of a gravitational wave overmany cycles. This provides a method of discriminatingthe signal from noise, and increases the detectability of agravitational wave signal.

a. Known waveform. When the waveform of thesource is known, the method of matched filtering is op-timal in the sense that the deduced probability of a sig-nal being present depends upon the collected data onlythrough the matched filter. The matched filter is computedby correlating the observed interferometer output h(t) withthe known gravitational wave signal hgw(t), weighted in-versely by the noise power spectrum:

x(t) = 4Re∫ ∞

0

h∗( f )hgw( f )

S( f )e−2π i f t d f.

If the detector noise originates from stationary, Gaussianrandom processes and the instrument is calibrated withzero-offset, this matched filter output is a zero-mean Gaus-sian random variable with variance equal to the powersignal-to-noise ratio of the known signal:

σ 2 = 4∫ ∞

0

|hgw( f )|2S( f )

d f = 4∫ ∞

0

[hchar( f )

hrms( f )

]2

d ln f

where the characteristic amplitude of a signal is

hchar( f ) = | f hgw( f )| ≈ h√

n

if it spends roughly n cycles with amplitude h in a fre-quency band � f ∼ f about the frequency f . In order fora signal to be detectable by matched filtering, it must havean amplitude signal-to-noise ratio, σ , somewhat greaterthan unity. In this way, comparison between hchar for aparticular source and hrms for a particular detector pro-vides an estimate of detectability of the source.

b. Unknown waveform. The class of sources forwhich the gravitational wave signal can be accurately de-termined in advance is very small. Other techniques areneeded when the precise phase evolution of the expectedgravitational wave burst is not known. For signals withknown frequency support � f and known time duration�t , the signal can be effectively detected by examiningthe amount of power for durations �t in the detector out-put that has been band-limited to the band of interest, againweighted by the noise power spectral density in the band:

ε(t) =∫ t+�t

t

∣∣∣∣∫ f +� f

f

h( f )

S( f )e−2π i f t d f

∣∣∣∣2

dt.

(This method is optimal when only the band and durationof the signal are known.) Because this method lacks thediscriminating power of known phase evolution that thematched filter provides, it is somewhat less powerful atdistinguishing a signal from noise; consequently, a signalneeds to have a greater amplitude to be detected. Typically,the signal has to be stronger (in amplitude) by a factorof (�t × � f )1/4 in order to have the same probability ofdetection.

There are other methods of detecting “unknown” sig-nals when different information about them is known. Forexample, if it is known that the signal is nearly monochro-matic at any instant but sweeps from low to high frequen-cies with time, it can readily be detected by searching fortracks in a time-frequency plot.

2. Bars

In contrast to interferometric detectors, resonant bar de-tectors have optimal sensitivity only in a narrow frequencyband � f about a resonant frequency f0. Gravitationalwave bursts with time duration τ < 1/� f act like im-pulsive hammer blows at the resonant frequency withamplitude hchar = | f0hgw( f0)|. Consequently, significantlyless information about the waveform is needed to achieve




optimal sensitivity to gravitational wave bursts in bar de-tectors. A burst is detected by searching for excess powerdeposited in the bar by the impulsive burst within the sen-sitive band of the bar.

B. Detection of Continuous Wave Sources

Sources in this category emit gravitational waves for timeslong compared to the expected observation time. Two cir-cumstances must be distinguished: (i) sources whose grav-itational waveform can be inferred by electromagnetic ob-servations and (ii) sources which can only be detected bytheir gravitational wave signals.

Rapidly spinning neutron stars are the main source ofcontinuous waves in the HF band accessible to earth-basedinterferometers and resonant bar detectors. When the neu-tron star can be observed using radio (or other) telescopes,the expected gravitational waveform can be inferred (upto small uncertainties) from observations of the spin pe-riod. In this case, the optimal data analysis strategy ismatched filtering. The implementation may be slightlydifferent than for burst sources, but the idea is the same.Successful detection of waves from these sources will relyon direct interaction between the radio astronomers andgravitational astronomers.

Generally, continuous-wave signals are expected to benearly periodic and very weak. When a target source can-not be identified using electromagnetic observations, theoptimal strategy involves coherent accumulation of signal-to-noise using Fourier transforms of long stretches of data(months to years). The power signal-to-noise ratio at fre-quency f0 is given by

σ 2 = 2|h( f0)|2T S( f0)

where h( f ) is the Fourier transform of T seconds of cali-brated data. By analogy with burst sources, the character-istic amplitude of a continuous wave signal is defined ashchar = h0

√( f0T ) where h0 is the rms strain amplitude of

the signal, f0 is the frequency of the signal. Here the obser-vation time T is the total integration time for truly continu-ous wave signals, or the duration of quasi-monochromaticbursts.

Earth-motion-induced Doppler shifts, and intrinsic fre-quency evolution of the sources, will reduce the narrow-band signal-to-noise by spreading power across many fre-quency bins; therefore, it is necessary to correct for theseeffects before performing the Fourier transform. The cor-rections can be implemented by a parametrized model inwhich one searches over a discrete set of points in theparameter space of corrections. The signal-to-noise ratiorequired for a confident detection depends on the numberof points which must be considered in the search.

C. Detection of a Stochastic Background

A stochastic background of gravitational waves cre-ates correlations between (otherwise) independent grav-itational wave detector outputs. The correlation of thestochastic background of gravitational waves between twosites is

〈h∗gw 1( f )hgw 2( f )〉 = 3H 2

0

20π2

T

f 3�gw( f )γ ( f )

where H0 ≈ 65 km s−1 Mpc−1 is Hubble’s constant, T isthe length of the observation, and �gw( f ) is the measureof the stochastic background of gravitational waves that isconvenient for describing cosmological sources (see be-low). The overlap reduction function γ ( f ) describes howsensitive the two sites are at detecting the stochastic back-ground. Several factors are important in determining theoverlap reduction function: (i) the relative alignment of thetwo detectors (if the two detectors are aligned, they are sen-sitive to the same polarization of gravitational waves) and(ii) the relative separation of the two detectors (widelyseparated detectors are most sensitive to low-frequencystochastic background waves that have wavelength greaterthan the separation). The overlap reduction function ap-proaches a constant at low frequencies. This constant isunity for aligned detectors but less than unity if the de-tectors are misaligned. The overlap reduction function de-creases and becomes an oscillatory function at higher fre-quencies.

To detect the stochastic background, one simply crosscorrelates the detector output at the two sites, with anappropriate weighting factor to suppress those frequenciesat which the detector combination is not sensitive:

2Re∫ ∞

0

3H 20

20π2

γ ( f )�gw( f )

f 3S1( f )S2( f )h∗

1( f )h2( f ) d f.

This method is tuned to detect a stochastic background ofgravitational waves with an anticipated spectrum �gw( f ).

If the stochastic background is significantly above theknown instrumental noise, it is possible to measure it us-ing the autocorrelation of the noise in a single detectorrather than the cross correlation between detectors. Therelevant detection method is the same as above but whereh1( f ) is the same as h2( f ), S1( f ) is the same as S2( f ),and γ ( f ) = 1. In this case, it makes sense to define thecharacteristic strain

hchar( f ) = ( fH/ f )[�gw( f )]1/2

with fH = H0√

(3/20π2) ≈ 3 × 10−19 Hz; then the auto-correlation statistic is the same as the statistic used todetect an unknown burst (above). Even if the cross corre-lation statistic is used, this quantity is a reasonable charac-terization of the strength of the background for detectionpurposes if the detectors used are sufficiently similar.




IV. ASTROPHYSICAL SOURCES

Since the direct observation of gravitational waves re-mains elusive (but see Outlook below), candidate sourcescan only be identified by a combination of theoretical cal-culations and observations of electromagnetic phenomenawhich might reasonably be powered by gravitational po-tential energy. In this section, the likely sources are listedalong with estimates of their detectability using currenttechnology.

A. Supernovae and Neutron Star Formation

Supernova explosions are among the most violent andspectacular events in the electromagnetic universe and arebelieved to be the birthplace of neutron stars and blackholes. They occur a few times per century in our Galaxy,and once every few weeks in the Virgo cluster of galaxies.The physics of supernovae is under active investigation.Research suggests several viable scenarios which end ina supernova.

Type-II supernovae, distinguished by strong hydrogenlines, occur when the core of a massive super-giant star(M > 10M�) collapses at the end of silicon burning. Thecore, which is composed of iron nuclei, cannot undergoexothermic nuclear reactions; it is supported against grav-itational collapse by the degeneracy pressure of its elec-trons. The onset of the collapse occurs when the star runsout of silicon to burn. The outer layers collapse and crushthe core. The iron nuclei fragment in endothermic reac-tions, and the electrons are captured by protons to formneutrons; both of these processes reduce the ability of thecore to support the star, and the collapse is accelerated.Eventually, the core collapses to the point at which neu-tron degeneracy pressure is sufficient to support the core.At this stage, the outer layers of the in-falling core bounceoff the neutron-degenerate inner core and form a shockwave. A second shock wave is generated by an expandingbubble of neutrinos, which are being convected from thecenter of the star outward. These shocks expand throughthe outer layers, heating them as they go, and eventuallyproduce the supernova explosion.

Type-I supernovae have weak or no hydrogen lines.Evidence suggests that these events occur when a whitedwarf, or other small dense star, accretes material from acompanion in a binary system. Eventually, the star cannotsupport the additional material, and collapse is initiated.Type-Ia supernovae are thought to be explosions of heliumwhite dwarf stars that accrete enough matter to detonatetheir thermonuclear fuel. Other type-I supernovae may becaused by the accretion-induced collapse of white dwarfscontaining heavier metals, by the collapse of Wolf–Rayetstars, which are the cores of very large stars (M > 50M�)

whose strong stellar winds have blown off all of their man-tle, or by core collapse in helium stars with M ∼ 5M�whose outer hydrogen envelope has been stripped by acompanion star.

The star which seeds a supernova explosion is knownas a progenitor. For gravitational astronomers, bulk prop-erties of the progenitor distinguish possible scenarios forgravitational wave emission. If the supernova progenitoris slowly rotating, the collapse will be nearly spherical,and only weak gravitational waves are expected. (Even inthis case, a few cycles of strong gravitational waves maybe produced by convective turnover in the hot core.) Thelarger the rotation rate of the progenitor, the less symmet-ric will be the collapse. High rotation rates can triggersecular instabilities in the core.

1. Axisymmetric Supernovae

If the core of the supernova progenitor is slowly rotating,the core collapse will be nearly spherical. The gravitationalcollapse, though violent, produces only a modest change inthe quadrupole moment of the star; such supernovae emitweak bursts of gravitational waves. Numerical simulationssuggest characteristic strains of hchar ∼ 10−21 at distancesof 10 kpc in frequency bands of ∼100 Hz between 100 Hzand 1 kHz.

2. Nonaxisymmetric Supernovae

When the collapsing stellar core has significant rotation,it will flatten to form a rapidly rotating disk (a few hun-dred kilometers in radius) around a nascent neutron star. Atlarge rotation rates, this disk may become unstable. Mattercan clump together into an elongated bar which tumblesend-over-end; this bar-mode grows secularly under dissi-pation, which can originate with fluid viscosity or grav-itational wave emission. If a sizable rotating bar forms,it can generate significant amounts of gravitational radia-tion. Numerical estimates suggest hchar ∼ 10−20 at 10 kpcin the frequency band 500–1000 Hz. The gravitational ra-diation may provide the mechanism by which the diskloses angular momentum during the collapse.

Bar formation may also occur in the proto-neutron starwhen it is ∼20 km in radius. In this case, the growth ofthe bar is caused by a hydrodynamic instability. Typicalcharacteristic strain amplitudes of hchar ∼ 10−19 can occurat frequencies of ∼100 Hz for sources within our Galaxy(D ∼ 10 kpc).

3. Nascent Neutron Star Boilingand Neutrino Emission

The newborn neutron star will start its life at a very hightemperature and central density. The dominant coolingmechanism in the mantle of the neutron star will be the




emission of neutrinos generated during weak nuclear pro-cesses within the star. The outer layers of the neutronstar will be transparent to neutrino emission, but the neu-tron star core will initially be opaque. Within the opaquecore, fluid will boil up from the center to the point wherethe neutron star becomes transparent to neutrino emis-sion (the “neutrinosphere”), it will cool, and then set-tle back to the center. This “boiling” of the neutron starcore will generate gravitational radiation. In addition, aneutrino bubble is created around the proto-neutron star,which is responsible for generating the shock that powersthe supernova explosion. The characteristic amplitude ofgravitational waves due to these convective instabilities ishchar ∼ 10−22 for events within our Galaxy (within a fewtens of kpc).

4. Unstable Modes of Nascent Neutron Stars

Hot, rapidly rotating, newborn neutron stars may be sub-ject to unstable modes of fluid oscillation that will grow,driven by gravitational radiation, on a time scale muchshorter than the viscous time scales that would damp thesemodes in colder neutron stars. The mechanism by whichgravitational radiation can cause a mode of fluid oscilla-tion to grow is known as the Chandrasekhar–Friedman–Schutz (CFS) instability. This instability arises when afluid mode, rotating in a retrograde motion with respectto the neutron star, is dragged forward (prograde) with re-spect to the inertial frame due to the rotation of the neutronstar. In the inertial frame, the gravitational field sees thefluid oscillation as having positive angular momentum;consequently, the gravitational radiation produced by theoscillation carries away positive angular momentum. Withrespect to the neutron star, however, the oscillation pos-sesses negative angular momentum, so the gravitationalradiation reaction causes the oscillation to lose even moreangular momentum, which results in the growth of theamplitude of the oscillation.

There are several types of neutron star modes that mayexhibit the CFS instability, but the most significant amongthem are the r-modes. R-modes are described by circu-lar flow patterns with (almost) no radial component; therestoring force for these cycles of fluid motion is the Core-olis force. The r-modes are very similar (and derive theirname from) Rossby waves, which are observed in theearth’s oceans. The r-modes have the property of alwaysrotating retrograde with respect to the neutron star, butare dragged prograde in the inertial frame due to the neu-tron star’s rotation, and are thus always subject to the CFSinstability. The r-modes also radiate copious amounts ofgravitational radiation (they possess a significant gravito-magnetic quadrupole moment), and the growth time scale

is significantly shorter than viscous time scales in young,hot, and rapidly rotating neutron stars.

It is believed that gravitational radiation from ther-modes in nascent neutron stars is the mechanism bywhich newborn neutron stars, which could be rotating atnear their breakup speed (∼1 kHz), lose most of their angu-lar momentum. The result is the slowly spinning neutronstars that are observed. R-modes could produce nearlymonochromatic gravitational radiation with a characteris-tic strain as large as hchar ∼ 10−22 at frequencies of ∼1 kHzand distances of ∼10 Mpc, lasting for several tens ofseconds.

B. Continuous Waves from Neutron Stars

The most likely sources of quasi-periodic gravitationalwaves in the frequency bands of terrestrial detectors arerapidly rotating neutron stars. A rotating neutron star willradiate gravitational waves if its mass distribution (ormass-current distribution) is not symmetric about its rota-tion axis. A neutron star with nonzero quadrupole momentwhich rotates about a principle axis produces gravitationalwaves at a frequency equal to twice its rotation frequency.Equally strong gravitational waves can be emitted at otherfrequencies when the rotation axis is not aligned with aprincipal axis of the source. If the star precesses, the grav-itational waves will be produced at three frequencies: therotation frequency, and the rotation frequency plus andminus the precession frequency.

1. Isolated Pulsars

Rapidly rotating neutron stars (pulsars) tend to be axisym-metric; however, they must break this symmetry in orderto radiate gravitationally. Several mechanisms may leadto deformations of the star, or to precession of its rotationaxis, and hence to gravitational wave emission. The char-acteristic amplitude of gravitational waves from neutronstars at 10 kpc distance scales as

hchar ∼ 10−19 I

1045 g cm2

ε

10−5

(f

1 kHz

)5/2 (T

107 s

)1/2

where I is the moment of inertia of the star, f is the grav-itational wave frequency, ε is a measure of the deviationfrom axisymmetry, and T is the observation time.

Neutron stars are thought to form in supernova explo-sions. The outer layers of the star crystallize as the new-born neutron star cools by neutrino emission. Estimates,based on the expected breaking strain of the crystal lat-tice, suggest that anisotropic stresses, which build up as thepulsar loses rotational energy, could lead to ε � 10−5; theexact value depends on the breaking strain of the neutron




FIGURE 3 Sources of gravitational radiation and detector sensitivities.

star crust as well as the neutron star’s “geological his-tory,” and could be several orders of magnitude smaller.Nonetheless, this upper limit makes neutron stars a poten-tially interesting source for kilometer-scale interferome-ters (see Fig. 3).

Large magnetic fields trapped inside the superfluid inte-rior of a neutron star may also induce deformations of thestar. Numerical simulations suggest that this effect is ex-tremely small for standard neutron star models (ε � 10−9).

Another plausible mechanism for the emission ofgravitational radiation in very rapidly spinning stars isaccretion-driven asymmetries. The principal axes of themoment of inertia can be driven away from the rotationalaxes by accretion from a companion star. Accretion canproduce relatively strong radiation, since the amplitude isrelated to the accretion rate rather than to structural effectsin the star.

2. Low-Mass X-Ray Binaries

A low-mass X-ray binary (LMXB) is a neutron star or-biting around a stellar companion from which it accretesmatter. The accretion process deposits both energy andangular momentum onto the neutron star. The energy isradiated away as X-rays, while the angular momentumspins the star up. It has been suggested that the accre-tion could create nonaxisymmetric temperature gradientsin the star, resulting in a substantial mass quadrupole andgravitational wave emission. The star spins up until thegravitational waves are strong enough to radiate away theangular momentum at the same rate as it is accreting; esti-

mates suggest that the equilibrium occurs at a gravitationalwave frequency ∼500 Hz. The characteristic gravitationalwave amplitudes from these sources would be

hchar � 2 × 10−23

(R

10 km

)3/4 (M

1.4M�

)−1/4

×(

F

10−8 erg cm−2 s−1

)1/2 (T

1 day

)1/2

,

where R and M are the radius and mass of the neutronstar, and F is the observed X-ray flux at the earth.

The amplitude of the gravitational waves from thesesources make them excellent candidates for targetedsearches using interferometric detectors. If the source isan X-ray binary pulsar—an accreting neutron star whoserotation is observable in radio waves—then one can applythe exact phase correction deduced from the radio tim-ing data to optimally detect the gravitational waves. (Inthis process, one must assume a relationship between thegravitational wave and radio pulsation frequencies.) Un-fortunately, radio pulsations have not been detected fromthe rapidly rotating neutron stars in all LMXBs (i.e., neu-tron stars which rotate hundreds of times a second). In theabsence of direct radio observations, estimates of the neu-tron star rotation rates are obtained from high-frequencyperiodic, or quasi-periodic, oscillations in the X-ray out-put during Type I X-ray bursts. But this does not provideprecise timing data for a coherent phase correction. Todetect gravitational waves from these sources, one mustsearch over the parameter space of Doppler modulationsdue to the neutron star orbit around its companion, and




fluctuations in the gravitational wave frequency due tovariable accretion rates. The Doppler effects of the gravi-tational wave detector’s motion can be computed exactly,because the sky position of the source is known.

C. Massive Compact Binaries

The end-over-end tumble of binary star systems is anexcellent source of gravitational waves in both the LFand HF bands. The gravitational wave frequency increaseswith the total mass of the system, and is inversely pro-portional to the separation of the binary elements. Thus,compact binaries composed of neutron stars and/or stellar-mass black holes radiate at the highest frequencies sincethe elements can get very close together without merging.

As a binary system emits gravitational waves, it loosesenergy. The loss of energy is compensated by decay ofthe orbit so that the binary elements orbit with a smallerseparation and at a higher frequency. As energy is drainedfrom the system, the binary elements spiral together andeventually collide. The orbital evolution can be calcu-lated to high accuracy using post-Newtonian formalismwhich is valid until the very late stages of inspiral forcompact objects. (Post-Newtonian formalism is a math-ematical scheme which captures Newtonian gravitationaleffects and slow-motion corrections introduced by generalrelativity.) The gravitational wave luminosity depends onthe masses of the two bodies, m1 and m2, their separation(semi-major axis), a, and the eccentricity of the ellipticalorbit, e:

d E

dt= −32

5

G4µ2 M3

c5a5(1 − e2)7/2

(1 + 73

24e2 + 37

96e4

)

where M = m1 + m2 is the total mass of the system andµ = m1m2/M is the reduced mass. The time it takes the bi-nary elements to coalesce due to gravitational wave emis-sion is the decay time of the orbit. For a nearly circularorbit, with initial separation given by a0, the decay time is

τ = 5

256

c5a40

G3µM2.

A pair of neutron stars, with initial separation 500 km,would spiral together in a matter of minutes, whereas aneutron star would take more than a decade to spiral into asuper-massive black hole (106 M�) from 5 times the radiusof the black hole. The decay time is shorter for eccentricorbits.

In the LF band, the typical decay time for a binarywill be longer than any reasonable observation time, andthe gravitational wave signal can be considered to be acontinuous wave signal. The characteristic amplitude (fornearly circular orbits) is

hchar( f ) ≈ 1 × 10−17 (4η)

(M

106 M�

)5/3 (D

3 Gpc

)−1

×(

f

10−4 Hz

)7/6 (T

4 months

)1/2

,

where T is the observation time, D is the distance tothe neutron stars, M is the total mass of the binary, andη = µ/M is the mass fraction (η = 1/4 for equal masscompanions, or less if one companion is less massive).Neutron star and stellar-mass black holes are sufficientlycompact that they will enter the HF band before merging.In the HF band, the inspiral waveform will “chirp” up infrequency in a relatively short period of time, and the sig-nal will be detectable as a burst rather than a continuouswave. In this case, the characteristic strain is given by

hchar( f ) ≈ 5 × 10−20√

4η

(M

M�

)5/6

×(

D

1 Mpc

)−1 (f

1 Hz

)−1/6

.

1. Binary Neutron Stars

Compact binary systems with pairs of neutron stars havebeen observed using radio telescopes. The famous mil-lisecond pulsar PSR 1913+16 discovered in radio databy Hulse and Taylor orbits with a (radio quiet) neutronstar companion. Emission of gravitational waves from thissystem has been confirmed by measuring the decay of theorbit, and the loss of energy agrees with the predictions ofgeneral relativity to high precision.

There are a total of three known binary neutron star sys-tems in our Galaxy whose orbits are decaying fast enoughthat they will collide within the age of the Universe. Thissuggests that there are many extra-galactic binary neutronstar systems that are coalescing even now. Current esti-mates indicate that the rate of binary neutron star coales-cences is in the range between 10−8 and 5 × 10−5 eventsper year per Mpc3. The expected sensitivity of the fu-ture ground-based gravitational wave observatories shouldmake several events per year accessible to gravitationalwave astronomers.

During the final few minutes before coalescence, thegravitational wave from a neutron star binary sweeps up inamplitude and frequency (“chirps”) through the HF band.When the binary system reaches a frequency of ∼1 kHz,the orbit will become unstable either due to the tidal in-teraction between the two stars or because of a dynamicalinstability of orbital motion in general relativity. At thisstage, the details of the merger may depend on the internalproperties and spins of the two neutron stars.




2. Binaries With Black Holes

Black holes in binary systems spiral together, as they emitgravitational waves, just as binary neutron stars do. Thegravitational waves from, and the dynamics of, the coa-lescence will be quite different, however.

Neutron stars in orbit around stellar-mass black holeswill emit strong gravitational wave signals in the HF band.Moreover, if the black hole is rapidly rotating, the gravito-magnetic spin-orbit coupling may cause measurable pre-cession of the binary orbit. Also, if a neutron star orbitsclose to a rapidly spinning but relatively small black hole,tidal disruption of the neutron star may imprint its signa-ture on the gravitational waves emitted from the system.

Unlike a neutron star, the mass of a black hole has noupper bound. Indeed, black holes are known to exist withmasses of ∼10 M� (e.g., in Cyg X-1), ∼106 M� (e.g., atthe center of our Galaxy), ∼109 M� (e.g., in M87 at thecenter of the Virgo cluster of galaxies), and there is re-cent evidence that black holes with masses of ∼1000 M�also exist. Since the frequency at coalescence of the bi-nary system decreases with increasing total mass, moremassive binary systems (M > 105 M�) will emit gravi-tational waves primarily in the LF band. The merger oftwo supermassive black holes will be the strongest emit-ters of gravitational radiation in the LF band, and couldeasily be detected to cosmological distances (Gpc) with aspace-based interferometer such as LISA.

Binary black hole systems with masses of tens of so-lar masses should be among the most interesting sourcesin the HF band. For these systems, the late stages of in-spiral and merger will be observable to earth-based inter-ferometric detectors; a direct observation of these waveswould provide great insight into strong-field interactionsof general relativity. At present, theorists can accuratelypredict only the early phase of the evolution during whichthe binary elements have speeds significantly less than thespeed of light. The late inspiral and merger phases of thesebinary systems require the full nonlinearity of Einstein’sequations to be addressed; the black holes rapidly spiral to-gether in a whirl of spacetime curvature, and finally mergeinto a single distorted black hole. Numerical relativity re-mains the best tool to make theoretical predictions aboutthe dynamics of this phase. Finally, the distortions of theevent horizon are rapidly dissipated as the black hole emitsgravitational waves; this is known as black-hole ringdownsince the waves are predominantly emitted at a single fre-quency with a decaying amplitude determined by the massand angular momentum of the black hole.

The merger and ringdown of the black hole will pro-duce a burst of gravitational radiation that is in the HFband for stellar-mass black holes, or in the LF band forsupermassive black holes. Typically, the black holes will

be rotating close to their maximum angular momentum, inwhich case the frequency of the ringdown radiation thenscales inversely with the mass of the black hole

fringdown ≈ 32 kHz

(M

M�

)−1

and the characteristic strain produced by the ringdownburst can be related to the fraction ε of the total mass-energy of the black hole that is radiated (a canonical valueis 1%):

hchar ≈ 2 × 10−21

(ε

1%

)1/2 (M

M�

) (D

Mpc

)−1

.

The inspiral of compact stellar-mass objects into super-massive (105–109 M�) black holes can be readily calcu-lated by treating the small stellar-mass object as a per-turbation to the black hole geometry. If the supermassiveblack hole is rapidly rotating, the motion of the inspirallingobject can be quite complex, with epochs of whirling nearthe black hole followed by zooms in which it is thrownfar away from the black hole. The resulting gravitationalwaves will be in the LF band and should be easily detectedby space-based gravitational wave observatories.

On the speculative side, there may be a population ofsubstellar mass black holes (M ∼ 0.5M�) in the Galac-tic halo. If they exist, these black holes could comprisea substantial portion of the MACroscopic Halo Objects(MACHOs) that have been observed; the population ofblack hole MACHOs could be as high as 1012 if all MA-CHOs are black holes. If this is the case, then event ratesof coalescence of black hole MACHO binaries could be aslarge as 10−5 events per year in our Galaxy, or several peryear in the Virgo cluster of galaxies. Once again, detec-tion of the gravitational waves from such a binary wouldbe a dramatic discovery with substantial implications forGalactic dynamics.

3. Binaries with White Dwarfs and Dwarf Stars

Gravitational waves from binary systems with whitedwarfs, or other dwarf stars, are generally in the LF bandaccessible to space-based detectors. Since dwarf stars areconsiderably larger than neutron stars and stellar-massblack holes, the orbital separation is greater and the wavefrequency lower. For example, close white dwarf binarysystems and cataclysmic variables (binary systems involv-ing a low-mass red star and a white dwarf) will be de-tectable at mHz frequencies. In fact, since such systemsare so common in our Galaxy, the superposition of thenumerous unresolved (for some finite observation time)signals will become hopelessly confused and will producean effective stochastic background of gravitational waves.Only the strongest emitters will be detectable above this




stochastic background, though the background itself willprovide valuable information about the distribution anddensity of the binary systems in our Galaxy. The grav-itational waves from sources like WZ Saggitae (a cata-clysmic variable) and 44ι Bootes BC (a contact binary ofdwarf stars) may be directly detectable because of theirknown location and orbital periods.

D. Cosmological Sources

A variety of phenomena can produce a stochastic back-ground of gravitational waves arising from the early uni-verse. The conventional measure of the spectrum as a func-tion of frequency f of this stochastic background is givenby the function

�gw( f ) = 1

ρc

dρgw

d ln f

where ρc = 3c2 H 20 /(8πG) is the critical energy density

(energy per unit volume) required to make the universespatially flat (H0 ≈ 65 kms−1 Mpc−1 = 2 × 10−18 s−1 isHubble’s constant), and ρgw is the energy density con-tained in gravitational waves.

Current knowledge of the physics of the early universeis highly speculative, as are the sources of the stochas-tic background described below. However, gravitationalwave astronomy may provide the only method of di-rectly observing the conditions in the universe as earlyas ∼10−22 sec after the big bang (in the HF band) sincethe universe was opaque to electromagnetic radiation until∼105 years after the big bang. The signature of processeswhich occurred between these times may be imprinted onthe spectrum of the stochastic background of gravitationalradiation.

1. Microwave Background RadiationMeasurements

The measured anisotropy of the Cosmic Microwave Back-ground Radiation (CMBR) places strong constraints onthe gravitational wave background from the early universein the extremely-low-frequency band.

The CMBR was produced in the early universe whenthe temperature of the universe dropped below ∼3000 Kand the plasma of protons and electrons combined to formatomic hydrogen. At that time, known as the time of lastscattering, the universe became (essentially) transparentto electromagnetic radiation. Observations of the CMBRshow that it is highly uniform, with only very smalltemperature fluctuations. Inflationary models of the veryearly universe explain this uniformity. However, evenif the universe had a perfectly uniform temperature atthe time of last scattering, gravitational waves produce

observed temperature fluctuations via the Sachs–Wolfeeffect. The presence of an extremely-low-frequency grav-itational wave causes a difference, from point to point inthe sky, in the gravitational potential through which theCMBR must travel to reach the earth. This difference inthe gravitational potential induces a change in theapparent temperature of the CMBR. The observed degreeof homogeneity of the temperature of the CMBR thusprovides an upper limit on the gravitational wave spec-trum �gw( f ) < 10−10(H0/ f )2(hchar( f ) < 10−4( fH/ f )2)for H0 < f < 30H0.

Future measurements of the polarization of the CMBRwith the Microwave Anisotropy Probe (MAP) and thePlanck Surveyor satellites will be able to distinguish be-tween scalar perturbations, which are caused by densityperturbations, and tensor perturbations, which are causedby gravitational waves, and thus provide a method of di-rectly observing cosmological gravitational waves.

2. Pulsar Timing Limits

The regularity of the electromagnetic pulses from pulsarsrivals the best atomic clocks. By measuring the timingresidual, which is the amount of time drift between thepulsar “clock” and earth-based atomic clocks, after cor-recting for Doppler effects due to the relative motion of theearth and the pulsar, a limit on the stochastic backgroundof gravitational waves between the earth and the pulsarcan be set: Gravitational waves, with periods compara-ble to the observation time, cause a slight time dilationwhich would be in the very-low-frequency band. Mea-surements of several stable millisecond pulsars for abouta decade have given a bound �gw < 10−8(hchar < 10−15) atf = 10−8 Hz. (This bound is on any stochastic backgroundof gravitational waves, not just those of cosmological ori-gin.)

3. Limits Based on Nucleosynthesis

Comparison of measured primordial element abundancesto those predicted by proposed cosmological modelsprovides a sensitive test of the model. A similar testcan be used to constrain the stochastic backgroundof gravitational waves. The total amount of energy ingravitational waves will affect the expansion rate of theuniverse during the period of nucleosynthesis, and is thustightly constrained by the observed abundances. Onlythose frequencies of the stochastic background radiationwith frequencies greater than the Hubble expansion rateat the time of nucleosynthesis are so constrained. Theresulting bound is

∫�gwd ln f < 10−5




where the integral includes frequencies greater than 10−9

Hz.

4. Inflation Models

Inflationary cosmological models invoke an epoch of rapidexpansion (power-law or exponential) of the universe atearly times to solve various problems in cosmology suchas the flatness problem (why the universe is so close tobeing spatially flat) and the horizon problem (why theCMBR is so homogeneous). Inflation is often predicted tohave taken place when the universe had cooled to energydensities associated with physics at the Grand UnificationTheory (GUT) scale, approximately 10−35sec after the bigbang, when the strong (color) force becomes distinct andquarks form.

If such an inflationary period did exist in the early uni-verse, it would have created a stochastic background ofgravitational waves by parametric amplification of theprimordial gravitational wave spectrum produced in thebig bang. The initial spectrum of gravitational waves pro-duced by the big bang, which is usually taken to be theground-state quantum vacuum fluctuations of the gravi-tational field, is dramatically red-shifted during a rapidinflation, but the amplitude of the waves grows so as tomaintain nearly the same amount of energy in the grav-itational wave background. Typical models of inflationinvolve expansions of the universe by a factor of 1027, andthus will produce a dramatic increase in the amplitudeof the primordial stochastic background of gravitationalwaves. Predictions based on an exponentially growing in-flationary period triggered at GUT-scale energy densitiesyield a flat spectrum of stochastic gravitational waves:

�gw = (1 + zeq)−1 16

9

ρgut

ρpl≈ 10−16

where ρgut/ρpl ≈ 10−12 is the ratio of the GUT-scale en-ergy density of the universe during inflation to the Planck-scale energy-density ρpl = h--−1G−2c7 at the big bang, andzeq ≈ 6000 is the red-shift of the universe when it changedfrom being radiation dominated to matter dominated. Thecharacteristic amplitude of this stochastic background ishchar ≈ 10−8( fH/ f ) for f � fH.

The stochastic background spectrum in this scenario isflat over many decades of frequency including the rangefrom the ELF band to the HF band. The last two decades ofthe ELF band, 10−16–10−18 Hz, however, contain wavesthat have “emerged” (have frequencies greater than Hub-ble’s constant) since the universe became matter domi-nated; for these waves, the stochastic background spec-trum �gw( f ) ∼ f −2.

The spectrum of the stochastic background of gravita-tional waves depends on the details of the inflation modelas well as on the assumptions about the initial state ofgravitational waves produced by the big bang.

5. Gravitational Waves from Cosmic Strings

Cosmic strings may have formed during a phase transitionas the strong force separated from the electroweak forcewhen the universe was at the GUT-scale. They are one-dimensional defects, or strings, which oscillate rapidly andproduce gravitational waves. Depending on how many (ifany) cosmic strings are present in the universe, these oscil-lations may produce a sizable component of the stochasticbackground of gravitational waves. Most models of thespectrum produced by cosmic strings show that �gw( f ) isrelatively flat in the LF and HF bands. The spectrum typ-ically increases in the very-low-frequency band, wherepulsar timing data provides an upper limit on the cosmicstring contribution to the stochastic background.

6. Bubbles from a Phase Transition

As the universe cools after the big bang, matter may un-dergo a phase transition and produce bubbles of materialwith a lower energy-density than the surrounding material.These bubbles expand relativistically as the latent heat oftransition from the newly incorporated matter is convertedinto the kinetic energy of the bubble wall. The collisionsof the expanding bubbles produce large amounts of grav-itational radiation.

Unlike the other examples of cosmological sourcesof gravitational radiation, the spectrum of gravitationalwaves from colliding bubbles will be peaked at a charac-teristic frequency set by the time the phase transition tookplace. For example, for the standard-model electroweakphase transition, the peak frequency is fpeak ∼ 10−3 Hz, inthe LF band, and the spectrum of gravitational waves isexpected to be �gw( fpeak) ∼ 10−22(hchar ∼ 10−27) at thispeak frequency. Though this level of stochastic back-ground could not be observed, it is possible that there areother first-order phase transitions in the earlier universe,which could produce significantly larger contributions tothe stochastic background of gravitational waves.

V. OUTLOOK

Efforts to directly observe gravitational waves have a his-tory spanning at least 40 years; Joseph Weber constructedthe first resonant mass detectors in the early 1960s. At thestart of the 21st century, a new generation of interfero-metric detectors will have sufficient sensitivity to detectmany anticipated astrophysical sources. The commission-ing and scientific operation of these instruments marks thebirth of gravitational wave astronomy.

In the short term, observations will bring informa-tion about source populations beyond that available us-ing current astronomical techniques. Direct detections will




provide information that is complementary to, but qual-itatively different from, that provided by electromag-netic radiation. It also seems likely that novel and un-expected astrophysical sources of gravitational radiationwill be discovered soon after the detectors begin operation.Efforts are already under way to improve the sensitivi-ties of these instruments to the point where detection willbe routine. As gravitational wave astronomy matures, itwill provide unique tests of general relativity and strong-field gravity; these tests will become more powerful whenthe LF band is opened to observation using space-basedantennas.

In the long term, gravitational wave observations willrevolutionize both astronomy and gravitational physics.These observations will support some predictions dis-cussed in this article, they will confute others, and theywill bring surprises about the Universe in which we live.

ACKNOWLEDGMENTS

The authors are grateful to the National Science Foundation for continuedsupport of their research into gravitational waves through Grants PHY-9970821 and PHY-0071028.


ELECTROMAGNETICS • GAMMA-RAY ASTRONOMY •GLOBAL GRAVITY MODELING • GRAVITATIONAL WAVE

DETECTORS • GRAVITATIONAL WAVE PHYSICS • INFRA-RED ASTRONOMY • NEUTRINO ASTRONOMY • PULSARS

• RADIO ASTRONOMY, INTERFEROMETRY SUPERNOVAE •ULTRAVIOLET SPACE ASTRONOMY •X-RAY ASTRONOMY

BIBLIOGRAPHY

Brown, J. D. (2000). Gravitational waves from the dynamical bar insta-bility in a rapidly rotating star. Physical Rev. D 62, 084024.

Hulse, R. A. (1994). Nobel lecture: The discovery of the binary pulsar.Rev. Modern Physics 66, 699–710.

Lindblom, L., Tohline, J. E., and Vallisneri, M. (2001). Non-linear evolu-tion of the r-modes in neutron stars. Physical Rev. Lett. 86, 1152–1155.

Muller, E. (1997). Gravitational radiation from core-collapse super-novae. Classical Quantum Gravity 14, 1455–1460.

Nakamura, T., Sasaki, M., Tanaka, T., and Thorne, K. S. (1997). Gravi-tational waves from coalescing black hole macho binaries. Astrophy.J. 487, L139–L142.

Peters, P. C. (1964). Gravitational radiation and the motion of two pointmasses. Physical Rev. B 136, 1224–1232.

Peters, P. C., and Mathews, J. (1963). Gravitational radiation from pointmasses in a Keplerian orbit. Physical Rev. 131, 435–440.

Saulson, P. S. (1994). “Fundamentals of Interferometric GravitationalWave Detectors.” World Scientific, Singapore.

Schutz, B. F. (1999). Gravitational wave astronomy. Classical QuantumGravity 16, A131–A156.

Taylor, J. H. (1994). Nobel lecture: Binary pulsars and relativistic gravity.Rev. Modern Physics 66, 711–719.

Thorne, K. S. (1994). “Black Holes and Time Warps: Einstein’s Outra-geous Legacy,” W. W. Norton & Company, New York.

Thorne, K. S. (1997). Gravitational radiation: A new window onto theuniverse. http://arXiv.org/abs/gr-qc/9704042.

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Encyclopedia of Physical Science and Technology En007I-962 July 2, 2001 20:42

Gravitational Wave DetectorsRosa PoggianiUniversita di Pisa and Istituto Nazionale di FisicaNucleare

I. IntroductionII. Gravitational Wave SourcesIII. Interferometric DetectorsIV. Resonant DetectorsV. Gravitational Wave Astrophysics

VI. Future DevelopmentsVII. Conclusions

GLOSSARY

Black hole Celestial body with such a high density thateven light cannot escape from it.

Equation of state Description of the state of a system interms of its thermodynamics variables pressure, vol-ume, and temperature.

Event horizon Black hole boundary.Fabry–Perot cavity Instrument in which a light beam is

reflected several times between two transparent platesbefore transmission.

Interferometer Optical instrument that splits a lightbeam into two beams recombined to produceinterference.

Michelson interferometer Interferometer that usesa beam splitter and a pair of mirrors to split andrecombine the beams.

Neutron star High-density star consisting mainly of neu-trons as a result of gravitational collapse.

Pulsar Rotating neutron star that emits periodic bursts atradio frequencies.

Space–time The four-dimension space which includesthe three spatial coordinates and time as the fourthdimension.

Supernova Explosion of a massive star whose core col-lapses gravitationally.

Transducer Device converting one form of energy to an-other one, generally electromagnetic.

GRAVITATIONAL WAVES are ripples in space–timecaused by the coherent accelerated motion of massive bod-ies. The potential gravitational wave sources span a widerange of cosmic environments: neutron stars, black holes,supernovae, and binary systems. This review focuses onthe instruments currently under construction that are ex-pected to perform the first direct detection of gravitationalwaves.

49

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50 Gravitational Wave Detectors

I. INTRODUCTION

A. Gravitational Waves in General Relativity

The existence of gravitational waves has been predicted byEinstein since 1916, but to date it remains the last predic-tion of general relativity that has not been experimentallyverified. When large masses are accelerated, the result-ing perturbation of the metric of space–time propagates atthe speed of light as a ripple. A gravitational wave exertsa tide-like force between pairs of free masses or acrosssolid bodies. The force causes a variation of the relativedistances of free masses or of the solid faces. The waveamplitude is expressed by the dimensionless amplitude,or strain, h. The strain h = �L

L measures the fractionalvariation of the distance between two free masses initiallyat distance L . The gravitational waves have two polariza-tion states rotated by 45◦, labeled + (plus) and × (cross).The effects of gravitational waves with the plus and crosspolarizations on a ring of test masses are shown in Fig. 1.

Any gravitational wave detector uses masses that canmove freely with respect to each other. Two main detectiontechniques are used:

� Interferometric detection: An interferometer is used tomeasure the change of the relative position betweentest masses equipped with mirrors; the gravitationalwave produces a variation in the length of theinterferometer arms and in the interference pattern.

� Resonant detection: This technique uses a mechanicalresonator, such as an elastic solid body, whoseresonance is excited by the gravitational wave.

FIGURE 1 Effects of the plus (top row) and cross (bottom row) polarizations on a ring of masses during one cycleof the gravitational wave.

The prominent characteristic of the gravitational wavesis the extreme weakness of their interaction with matter.Gravitational waves are only marginally absorbed or scat-tered by matter between the source and the detector, op-posite to what happens to electromagnetic waves. More-over, the gravitational waves are preferably emitted bythe bulk motion of their sources, typically objects withstrong gravity, while astronomical electromagnetic wavesare the incoherent superposition of the emission of individ-ual electrons or atoms. Common electromagnetic sources(interstellar gas, stellar atmospheres) are not relevant grav-itational wave emitters. On the other hand, gravitationalsources are often not electromagnetically visible becausethey do not emit or because their radiation is absorbed.Thus, the gravitational wave information is complemen-tary to the electromagnetic information. The weaknessof the wave coupling to matter preserves the original in-formation of the gravitational event, allowing researchersto investigate the interior of strong gravity sources (neu-tron stars, supernovae) or to gain information about thevery beginning of the universe (down to ∼10−24 s age).The direct detection of gravitational waves holds the po-tential of a rich physics and astronomy wealth: It couldopen the field of gravitational wave astronomy to givea new picture of the universe that could be as surpris-ing as the opening of the radio window after the opticalone.

B. Indirect Evidence for Gravitational Waves

Indirect evidence for the existence of gravitational waveswas provided by the Hulse and Taylor discovery of the

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Gravitational Wave Detectors 51

neutron star binary system PSR 1913+16 and successiveobservations over many years. The two bodies have masses∼1.4 M (where M is the solar mass, ∼2 × 1030 kg) andhave an orbital period of 7.8 hr. The system is radiatingenergy that causes the two bodies to spiral toward eachother speeding up the orbit by 3 mm/orbit. The observedincrease in speed agrees with the general relativity predic-tion of gravitational wave emission to an accuracy betterthan 0.4%. Hulse and Taylor were awarded the Nobel Prizein 1993.

II. GRAVITATIONAL WAVE SOURCES

The emission of gravitational waves is caused by thequadrupole moment Q of the source, according to thisrelation:

h ∼ G

c4

Q

r, (1)

where Q is the second derivative of Q, r the distanceof the source, G the Newton gravitational constant(6.67 × 10−11 m3 kg−1 sec−2), and c the speed of light.

The radiated power is the gravitational wave luminosity:

L = G

c5

...Q2. (2)

The quadrupole moment can be approximated byQ ∼ Ml2, where M is the source mass and l the scale ofdeviation from symmetry. An axisymmetric body doesnot radiate gravitational waves. The strongest gravita-tional radiators are nonspherical, with Q ∼ 2Mv2 ∼ 4Ens

K ,where v is the velocity, Ens

K is the nonspherical componentof kinetic energy:

h ∼ 4G

c4rEns

K ∼ 2G

c4rMv2. (3)

A binary system of two masses M at distance r0 rotatingwith frequency f about their common center of mass ex-hibits the maximum variation of quadrupole moment sincethe whole kinetic energy is nonspherical. The emission oc-curs at twice the rotation frequency with this intensity:

h ∼ 4G

c4rMr2

0 ω2. (4)

Due to the tiny value of the factor Gc4 ∼ 8 × 10−45 sec2

kg m ,man-made gravitational waves are by far too weak to bedetected. A hypothetical dumbbell made of two masses of104 kg at the ends of a 10-m rod rotating at 10 Hz about thecenter of mass produces waves with an amplitude belowh ∼ 10−40 in the wave zone. The candidate gravitationalwave sources are very compact and heavy celestial bod-ies, like neutron stars and black holes. Bodies with strong

gravity in binary systems radiate gravitational waves. Forsuch bodies the radius is of the order of the Schwarzschildradius rs = 2G M

c2 . The emitted wave has an amplitude of

h ∼ 1

rr0rs1rs2 (5)

where rs1, rs2 are the Schwarzschild radii of the bodies.For a binary system of two neutron stars in the Virgo clus-ter of galaxies (at the distance of 15 Mpc, where 1 pc =1 parsec = 3.1 × 1016 m), with M ∼ 1.4 M, r0 ∼ 20 km,and orbital rotation frequency of some hundreds of hertz,the resulting strain is h ∼ 10−21. This value is the initialgoal of ground-based detectors.

Since a gravitational source of mass M cannot besmaller than its Schwarzschild radius, the emission fre-quency cannot exceed the reciprocal of the travel time oflight along rs:

f ≤ c3

4πG M. (6)

Having in mind compact celestial bodies with massesabove the Chandrasekar limit of ∼1.4 M, the highestexpected frequency is ∼104 Hz.

The gravitational wave physics span a wide range of fre-quencies, which is traditionally divided into four regions:

1. Extremely low frequency region, 10−18–10−15 Hz:The gravitational waves produce quadrupole anisotropiesin the cosmic microwave background (CMB) radiation.The wave spectrum is described by the fraction of energydensity �g( f ) (in a bandwidth f ) needed to close the uni-verse. From observations of the COBE satellite �g ≤ 10−9

at 10−18 Hz.2. Very low frequency region, 10−9–10−7 Hz: The grav-

itational waves produce fluctuations in the arrival times ofpulsar radio signals. From the timing of millisecond pul-sars, �g < 6×10−8

H 2 at 4 × 10−9 Hz, where H is the Hubbleconstant in units of 100 km/sec.

3. Low-frequency region, 10−4–1 Hz: The experimen-tal approaches actually under investigation are Dopplertracking of spacecrafts from earth and laser interferom-etry in space (which is discussed in Section III.F). Thelower frequency cutoff is determined by the fluctuationsof solar radiation pressure. The potential sources in thelow-frequency region are galactic binary stars, supermas-sive coalescing black hole binaries (masses from 102 Mto 108 M), neutron stars, and small black holes fallinginto massive black holes (M ∼ 106 M).

4. High-frequency region, 1–104 Hz: This region in-cludes ground-based interferometers and resonant detec-tors, which are discussed in detail in Sections III and IV.The lower frequency cutoff is given by the earth vibra-tions and by fluctuations of the gravity gradient. Several

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sources are expected to emit at high frequency: rotatingneutron stars, collapsing supernovae, neutron stars, andsmall coalescing black holes.

The gravitational wave observational window of the de-tectors described in this review covers the low- and high-frequency regions (10−4–104 Hz).

From the point of view of the signal they produce,the sources can be classified into three main types: burstsources, with very short duration, i.e., broadband in fre-quency; narrowband sources, which are periodic or quasi-periodic; and stochastic backgrounds. Catastrophic events,such as supernova explosions or coalescence of binarysystems, produce burst signals. Rotating asymmetricneutron stars or binary systems far from coalescenceare narrowband sources. The addition of several weaksources produces a stochastic background.

The characteristics of the most relevant sources are de-scribed in the next paragraphs. The last years have seenvigorous theoretical efforts directed at source modeling,mainly with the advance of the techniques of numericalrelativity.

A. Supernovae

Supernovae have been the first historical target of gravita-tional wave detectors. The gravitational collapse of a starinto a supernova leads to the birth of a neutron star. If thecollapse of a type II supernova is not symmetrical, emis-sion of gravitational waves is expected as a burst signalwith a timescale on the order of milliseconds. The detailedfeatures of the bursts are not yet very well known. Thegravitational emission is related to the fraction of massthat is converted into gravitational waves. Assuming anefficiency of 0.1%, the current estimates predict one eventevery 30 years with h ∼ 10−18 within our galaxy (10 kpc)and a few events per year detecting events up to the Virgocluster (15 Mpc), where several interesting sources areexpected.

B. Pulsars

Pulsars are rotating neutron stars with typical radii of∼10 km and masses of 1.4 M, with rotation periods rang-ing from fractions of hertz to hundreds hertz. Pulsars canemit gravitational waves if deviating from axial symmetry.The emission is continuous at twice the rotation frequency,with an amplitude of

h ∼ 8π2G

c4

I f 2

rε, (7)

where f is the rotation frequency, I the average momentof inertia (∼1038 kg m2), and ε the deviation parameter

(ellipticity, estimated to be below 10−6). The expectedsignal for known pulsar is below 10−26 but the signal canbe integrated over long time intervals. To date, more than1000 pulsars are known, out of the 109 predicted in thegalaxy. The rotation frequency peaks at a few hertz, whichdemands a low-frequency sensitivity of detectors. Neutronstars could also be gravitational wave radiators for the firstfew years of life if born with a high rotation frequency.

C. Black Holes

Black holes should be quite common in the universe.There is indirect evidence that stellar mass black holes(M ∼ 10 M) are in X-ray binary systems and many galax-ies host massive or supermassive (from M ∼ 106 M toM ∼ 1010 M) black holes at their centers. Despite thegreat variety of phenomena that can lead to their forma-tion and history, unperturbed black holes are describedby mass, charge, and angular momentum only. However,when objects are captured by a black hole, its event hori-zon vibrates emitting gravitational waves before comingback to equilibrium. The gravitational waves are a strongsignature of the black hole physics. The natural emissionfrequency of a body of mass M and radius R is

fn = 1

4π R

√3G M

Rs(8)

where Rs is the Schwarzschild radius of black hole. Thusstellar mass black holes oscillate in the kilohertz region,while more massive ones oscillate in the millihertz regionor below.

D. Coalescing Binaries

Binary systems such as PSR 1913+16 emit gravitationalwaves. We have seen above the strain intensity [by Eq. (5)];for a neutron star binary system in the Virgo cluster, thestrain is h ∼ 10−21. Since the gravitational wave emissionproduces a gradual shrinking of orbit radius, the wave fre-quency increases as a chirp, until final coalescence. Thelower the cutoff frequency of the detector, the longer themonitoring time of the waveform. The amplitude andthe chirp rate depend on the chirp mass Mc = µ3/5 M2/5

t ,where µ is the reduced mass and Mt is the total mass ofthe system. Measuring the chirp time allows for deduc-ing the chirp mass, and the distance to the source can bedetermined from the amplitude.

The simplicity of the system makes this event thepotentially clearest signature for gravitational waves.The coalescence of compact binary systems—neutronstar/neutron star (NS/NS), neutron star/black hole(NS/BH), black hole/black hole (BH/BH)—can provide

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FIGURE 2 The intensity of some astrophysical sources. CB, compact binaries; WDB, white dwarf binaries; CBC,compact binary coalescence; SN, supernovae; a, coalescence of binary black holes with 106 M; b, black holeformations with 106 M; c, black hole binary with 106 M ; d, black hole–black hole with 103 M .

information about several physics topics. The NS/NScoalescence can provide a probe of the nuclear equationof state and hopefully an explanation of the γ -ray burstphenomenon; BH/BH coalescence can provide a superbtest of the general relativity theory in the strong gravityregime. The predicted event rate per galaxy is ∼10−5 yr−1

for NS/NS and ∼10−7 yr−1 for BH/BH coalescence.To have a few events per year, it is necessary to havedetectors sensitive up to 200 Mpc (including 6 × 105

galaxies).

E. Stochastic Background

The stochastic background includes all unresolved sourcesand cosmological gravitational waves. Primordial gravita-tional waves are of special interest since they should havebeen generated ∼10−24 sec after the Big Bang. The grav-itational waves could probe the universe at a much earlierlife than any other measurement, such as the one of CMB.

The detectors under construction have a noise level ofthe same order of the signals mentioned above. The noiseis usually described by the power spectrum SN( f ) or thespectral density N ( f ) = √

SN( f ), measured in units of

noise amplitude√Hz

. As an example, if a signal with h ∼ 10−21

is detected in a bandwidth of 1 kHz, then the spectraldensity is h = 3 × 10−23 1√

Hz . All sources of noise in the

detectors are assumed to be uncorrelated and thus addin quadrature.

The ability to detect signals is given by the character-istic amplitude hc = h

√Ncycl, where Ncycl is the number

of cycles spent by the waveform close to the maximumamplitude, i.e., Ncycl ∼ f ∗to with f ∗ typical frequency ofthe signal and to the observation time.

The intensity of the main astrophysical sources is shownin Fig. 2.

III. INTERFEROMETRIC DETECTORS

A. Basic Principles

The first suggestions to use electromagnetic radiation,namely, interferometers, to monitor the variation of rel-ative distance between test masses were made in 1956 byPirani and in 1962 by Gertsenshtein. The first tabletopprototype Michelson interferometer with an He–Ne laserand optical elements in vacuum was realized in 1970 by

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Forward; it achieved a sensitivity of h ∼ 10−16 Hz−1/2 at1 kHz, comparable with the Weber bar interferometer (seebelow). In the early 1970s Weiss made the first detailedstudy of noise sources and the first design of a large-scaleinterferometer, with potentially a better sensitivity thanbars. The study triggered the construction of several pro-totypes, at MIT (USA), at the University of Glasgow (UK),at the Max Planck Institut for Astrophysics in Garching(Germany), and at Caltech; the arm length ranged from 1to 40 m. The prototypes allowed a deep understanding ofthe noise sources and the development of suitable tech-niques to improve the sensitivity, quickly achieving a sen-sitivity of h ∼ 10−18 Hz−1/2 at 1 kHz. The success of theprototypes was a determinant for the submission of vari-ous proposals for full-scale interferometers to the fundingagencies in Europe and in the United States. Several in-terferometers are now under construction or beginning tooperate (see Section III.E).

Interferometric detectors monitor the relative positionchange between free masses using a laser beam. The basicconfiguration is the Michelson interferometer (Fig. 3). Thelaser beam is split into two beams traveling along distinctarms; the beams are reflected by mirrors at the end of eacharm, then recombined. The interference signal, measuredby a photodiode, is related to the relative change in the armlength due to the gravitational wave. The beam splitterand the mirrors are suspended as pendulums; with thisarrangement they behave as free masses above the pendu-lum resonance frequency. Assuming that the gravitationalwave is polarized along the arm directions, the arm lengthswill change in antiphase, with a total change in the opticalpath:

�L = hL , (9)

FIGURE 3 Scheme of an interferometric detector.

where L is the physical arm length. For an arm lengthof 3 km and a strain h ∼ 10−21, the change in the opticalpath is the very tiny value �L ∼ 3 × 10−18 m, whichis 1/1000 the diameter of a nucleus. We see that thesensitivity of the interferometer is proportional to thearm length. Practical considerations limit the physicalarm lengths to a few kilometers. The optical path can beincreased by folding the light up to the optimum value ofone-half of the wavelength of the gravitational wave. Thiscorresponds to 150 km for a 1-kHz wave, which gives anoptical path variation of �L ∼ 1.5 × 10−16 m. Even withsuch a large optical path, the induced displacement ismuch smaller than the thermal vibrations of single atomsof test masses. However, the precision in the position ofthe test mass is defined by the averaged position of allatoms over the laser beam width, which is below the levelof the displacement due to gravitational waves.

The first solution for folding the optical path is theHerriot delay line, with two concave mirrors having a ra-dius of curvature such that the injected light exits fromthe entrance hole after N round-trips, which means afteran optical path 2NL. The number of reflections is limitedby the reflection losses, thus the mirrors should have highoptical quality over the whole surface. During the N tripsthe laser spots move over a circle with radius Nω0, whereω0 is the minimum laser beam width; in typical workingconditions, the mirrors should be 1 m in diameter, a num-ber with a great impact on the scale and the cost of thevacuum system.

The second solution is the use of Fabry–Perot cavi-ties, where the laser spots from all reflections coincide. AFabry–Perot cavity consists of two plane mirrors at dis-tance L . The power transmitted by the cavity is maximumat the resonance, when kL = nπ , where k = 2π

λis the

wave vector. In this case, the power trapping in the cavityreplaces the many round-trips of the laser beam. The phaseof the light leaving from the cavity depends on the cavitylength. If the cavity is working at resonance, the passageof a gravitational wave produces a phase shift near the res-onance. The resonance characteristics of the Fabry–Perotcavity are described by the finesse F , which is related tothe reflectivities r1, r2 of the mirrors:

F = π√

r1r2

1 − r1r2. (10)

A Fabry–Perot cavity with finesse F produces a phase shift2Fπ

times the shift of a single trip. The Fabry–Perot mirrorsmust be large enough to allow the reflection of a singlebeam, thus with a diameter of a few tens of centimeters.In addition to the high reflectivity, the mirror substratesmust be of very optical quality, since light enters the cavitythrough one of them. Since a single Fabry–Perot cavity isvery sensitive to changes in cavity length and to changes

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FIGURE 4 Sensitivity curve (thick solid line) for a 3-km baseline interferometer with 30-kg test masses. The sourcesof noise are outlined: standard quantum limit (thin solid line); seismic noise (long dashed line); gravity gradient noise(dotted line); thermal noise (short dashed line); shot noise (dash–dot line).

in laser frequency, there is a Fabry–Perot cavity in eacharm. The laser is locked in frequency to the first cavity andthe second cavity is locked to the wavelength of the laser.The locking signal of the second cavity gives the relativevariation of the cavity length with respect to the first cavity.

The variation of the optical path corresponds to a phaseshift:

�� = 4π�L

λ, (11)

where λ is the laser wavelength. The phase shift is mea-sured operating the interferometer at a dark fringe, i.e.,at a minimum of interference, to reduce the effect of thelaser power fluctuations. The wave intensity is deducedfrom the error signal that must be applied to maintain thedark fringe when the test masses move because of thegravitational wave.

We see that the response of interferometers is inherentlybroadband. The beam pattern of the antenna is almostnondirectional. An interferometer is very different from atelescope, which can be pointed to a specific location inthe sky. The position of the source in the sky is determinedmeasuring the difference in the arrival time of signals indetectors at distant locations. The broad angular responseof the interferometer, however, is an advantage for a surveyof the sky.

B. Noise Sources

Noise in an interferometer arises from fundamentalphysics processes, such as shot noise and thermal noise,

or from technical factors, such as seismic noise and laserfluctuation noise. The first category sets the intrinsic lim-its to the interferometer sensitivity. The various sourcesof noise and their contribution to the interferometersensitivity are summarized in Fig. 4.

1. Photon Shot Noise and RadiationPressure Noise

The shot noise is caused by the fluctuations in the numberof photons detected at the photodiode. The shot noise hasa spectral density of

hsn ≈ 1

N L

√hcλ

2πηP, (12)

where P is the laser power and η the quantum efficiencyof the photodiode (η ∼ 1). The contribution of this noise isminimized by having a large laser power. All long baselineinterferometers have chosen neodymium:YAG (Nd:Yag)lasers, with a wavelength of 1.064 µm and typical powersof 10–20 W. With an effective arm length of NL ∼ 150 km,the power laser required to achieve h = 3 × 10−23 1√

Hzis

well above the current laser performance. The effectivelaser power is increased by using the power recycling tech-nique. The optimal operation point of the interferometer isin dark fringe, with most of the laser light bounced backto the entrance. A mirror in front of the laser in a suit-able position can reflect the light into the interferometeragain, allowing a gain factor in the available power of upto 1000. The technique of power recycling and the high

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reflectivity needed demand mirrors with scattering and ab-sorption losses below a few parts per million. The substratematerial should have a very low expansion coefficient be-cause of heating from the high-power laser.

The laser power cannot be arbitrarily high because thelaser light induces mirror motion because of radiationpressure. The linear spectral density of the radiation pres-sure noise is

hrp ≈ N

L M f 2

√2hP

π3cλ, (13)

where f is the frequency and M is the mass of the op-tical element. Shot noise and radiation pressure noisecontribute in quadrature as optical readout noise. Thereis an optimum power that minimizes this contribution(P = πcλM f 2

2N 2 ), giving the standard quantum limit (SQL):

hSQL ≈ 1

π f L

√2h

M. (14)

The quantum limit is below the sensitivity of the inter-ferometers under construction but at the level of second-generation detectors. Thus the shot noise is the limitingnoise at high frequencies for terrestrial detectors.

Despite the fact that the significant term for shot noise isthe effective optical length NL, it is still important to havea large physical arm length L . In fact, the other sourcesof noise at low frequency are thermal noise and seismicnoise, which are displacement noises causing the motionof the optical elements according to

h = 2x

L, (15)

where x is the displacement and L is the physical armlength. Thus the physical scale of the interferometer ismainly determined by displacement noises.

2. Seismic Noise

For ground-based interferometers, the ground motion(seismic noise) is several orders of magnitude above theexpected path difference induced by the gravitationalwave. The optical elements must be isolated with specialisolation systems. The main goal of isolation systemsis the reduction of horizontal motions along the laserdirection. The seismic noise is described by the linearspectral density:

x = A

f 2

m√Hz

(16)

where the coefficient A ranges from 10−7 to 10−6 for dif-ferent sites. An attenuation factor of 1010 at least is re-quired at 10 Hz. The isolators use multistage pendulums.

A pendulum suspension with resonant frequency fr pro-vides an isolation factor of f 2

rf 2 above fr, i.e., a factor of 100

at 10 Hz for a 1-Hz pendulum. A cascade of N pendulumsprovides an attenuation of ( f 2

rf 2 )N above fr. The presence of

unavoidable cross-couplings between different degrees offreedom, mainly the vertical one, demands additional iso-lation. The vertical cross-coupling is due to asymmetriesof the suspension. However, hanging pendulums point to-ward the earth’s center: there is an intrinsic lower limitgiven by the ratio of interferometer arm length to the earthradius (∼10−3 for long baseline interferometers).

The isolation systems are designed in such a way thattheir mechanical resonances do not inject additional noise.Mechanical isolators are generally passive systems con-sisting of mass–spring systems. Historically, the first de-veloped detectors were stacks of alternating layers of steeland rubbers. The stacks provide horizontal and verticalisolation at the same time. They generally have a largetemperature coefficient and how to make them vacuumcompatible is not obvious. Another solution is the use ofcascaded multistage pendulums equipped with cantileversprings to achieve vertical isolation. The suspension ma-terials should have low creep since the sudden release ofenergy could introduce additional noise. In active isola-tion techniques the relative motion of test masses and thesuspension point are sensed and the signal is used to movethe last one. The isolation system can include a preisolatorstage with very low resonant frequency since the residualmotion of test mass is on the order of a few microns: Thelocking of the laser becomes difficult since one needs largeforces.

There is a lower limit to the achievable seismic atten-uation because of direct coupling of seismic motion totest masses (gravity gradient noise) due to motion of theground close to the interferometers, motion of close ob-jects, etc. This noise is well below the sensitivity of theforthcoming interferometers, but could maybe precludethe achievement of SQL.

The isolation systems of most interferometers currentlyunder construction are passive systems (with a small de-gree of active parts) designed to provide good attenuationdown to tens of hartz or a few hertz at best. Thus seismicnoise is the dominant noise source at low frequencies interrestrial interferometers.

Whatever the choice of suspension systems, the opticalelements of first-generation interferometers are suspendedwith one or two loops of wires as pendulums to behave asfree masses.

3. Thermal Noise

As soon as seismic noise has been reduced, the domi-nant noise source at low frequency is thermal noise. This

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noise arises from the modes of the test masses and the laststage of their suspensions: pendulum mode, violin modesof the wires, and internal modes of the test masses. Eachvibration mode can be described as a damped oscillator attemperature T that is excited by thermal noise to a meanenergy kBT , where kB is the Boltzmann constant. Thecontribution from the residual gas damping is made neg-ligible by operating the interferometer in high vacuum.The main contribution to damping is coming from inter-nal dissipation in the suspension material, or anelasticity.To describe oscillator damping, the usual elastic constantk is replaced by a complex elastic constant k(1 + iφ(ω)),where φ(ω) is the loss factor, which is a function of fre-quency. At the resonance frequency ωr the loss factor isthe reciprocal of the quality factor of the oscillator, i.e.,φ = 1

Q . The power spectral density of the thermal noise ofan oscillator of mass M and loss factor φ can be deducedfrom the fluctuation–dissipation theorem:

x2(ω) = 4kBT ω2r φ

ωM[(

ω2r − ω2

)2 + ω4r φ

2] . (17)

At the resonant frequency the noise spectral density hasa maximum; thus resonant frequencies should lie outsidethe bandwidth of the detector or be narrow enough to befiltered in the data analysis. Far from resonance, the spec-tral density of thermal noise is lower for low loss factorsφ: The test masses and the last stage of isolation systemsare made of low loss materials. There is experimental ev-idence that for most materials the loss factor is almost in-dependent of frequency; thus below resonance x2(ω) ∝ 1

ω

and above resonance x2(ω) ∝ 1ω5 .

The isolation systems contribute with several modes,mainly the pendulum mode of the test mass and the vio-lin modes of the suspension wires. Since test masses aresuspended as pendulums, the effective loss factor is

φpendulum = φn

2Mgl

√ITY , (18)

where φ is the loss factor of wire material, n the numberof wires, M the pendulum mass, l the pendulum length, Ithe moment of cross section of wire, T the wire tension,and Y Young’s modulus. Typical values of φ are 10−3–10−4 for metals and ∼10−8 for monolithic fused silicasuspensions. Most long baseline interferometers will startwith conventional wire suspensions.

The violin modes are the vibrations of the suspensionwires, an harmonic series starting at about a few hundredsof hertz. The violin modes have a quality factor on theorder of the pendulum quality factor and look like narrowpeaks in the sensitivity band.

The normal modes of the test mass have a typical fre-quency on the order of fint = vs

2d (where vs is the soundvelocity): The frequencies are above the bandwidth of the

detector. Due to the 1ω

tail below resonance, materials withvery low losses are used to reduce this contribution. Thematerial should also be low absorption and low expansionbecause of shot noise requirements. The material currentlyused is fused silica, with a quality factor of ∼107. The waytest masses are suspended has an impact on the losses andmust be carefully studied.

The choice of the quality factors of the suspension com-ponents is not trivial. From the point of view of thermalnoise, the quality factor of the suspension modes shouldbe high to reduce dissipation, but from the point of viewof seismic noise it should be low to reduce noise am-plification

√Q fr at the resonance. The strategy is to use

relatively low quality factors for the suspensions stagesand a high value for the last stage.

In typical working conditions, the thermal noise domi-nates the radiation pressure noise at low frequency.

4. Other Noise Sources

The sensitivity of forthcoming laser interferometers is lim-ited by seismic noise at low frequencies (from a few hertzto tens of hertz according to the isolation strategy), by ther-mal noise up to some hundreds of hertz, and by shot noiseabove. Other sources of noise, however, can contribute tothe total noise budget:

� The fluctuations of the refraction index of residual gasalong the laser beam can induce noise. For this reason, allinterferometers operate in a high vacuum (≤10−8 mbar).High-vacuum operation also prevents test mass dampingby friction. The vacuum should also be contamination freeto preserve the optical properties of the optics. The longbaseline laser interferometers will be the largest evacuatedvolumes on earth, which accounts for a large part of theconstruction costs.

� The light scattered by the optical elements can be re-flected by the vacuum vessel, which is not isolated fromseismic vibrations, and can recombine with the unscat-tered beam. The vacuum tubes are thus equipped withbaffles to eliminate the reflected beam rays.

� The fluctuations in the laser frequency contribute tonoise if the interferometer arm lengths are not equal. Fora mismatch x in the arm length, the required frequencystability is

� f

f� h

L

x. (19)

The lasers are stabilized using high finesse reference cav-ities, typically a Fabry–Perot cavity in one arm.

� The laser power fluctuations contribute to noise if theinterferometer is slightly offset from the dark fringe by anamount δL . The required power stability is

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FIGURE 5 Schematics of an advanced interferometer using power recycling and signal recycling.

�P

P� h

L

δL . (20)

Active stabilization techniques are used.� The laser beam geometry fluctuations (lateral and an-

gular movements, wavefront or size variation) producenoise if the recombining beams are not perfectly aligned.The forthcoming interferometers will include long modecleaning cavities (high finesse optical resonators) in frontof the laser.

C. Technical Requirements

An interferometer needs both local and global controls.Local controls provide the damping of the normal modesof the suspension systems at low frequency. Global con-trols provide control of the interferometer arm length toa relative motion of ∼10−12 m. Since residual motion oftest masses induced by seismic noise is still present, theinterferometer output moves over many fringes, unless itis operated at a fixed point (dark fringe). Feedback tech-niques keep the interferometer fixed at the working point;a sensor reads how far the device is from the working pointand an actuator brings it back there. The useful signal ofthe interferometer is no longer the output power, but theintensity of the feedback needed to keep the interferom-eter at the working point (locking). The position of testmasses is corrected using coils acting on magnets on theirsurface. To reduce the effect of laser power fluctuationsand 1/ f noise in general, the measurement is performed in

the megahertz region using modulation and demodulationtechniques.

The basic interferometer comes in different variants toimprove sensitivity. In a standard interferometer only avery small part of the light gets to the detection region;most goes back to the input. In the power recycling tech-nique mentioned above, the light is reused using a partiallytransmitting mirror to add it coherently in phase with thelaser light. The sensitivity of the interferometer can be in-creased in a narrow bandwidth using the signal recyclingscheme. A partially reflecting mirror at the output of theinterferometer makes the whole interferometer a resonat-ing cavity. In the resonant recycling scheme, a mirror setis used in such a way that after a gravitational wave pe-riod the light in each arm is exchanged, building at theend a large phase shit. The scheme is useful for realizingenhanced sensitivity in a narrowband and useful to de-tect periodic signals. In the dual recycling scheme, botha power recycling mirror and a signal recycling mirrorare used. A scheme of an advanced design interferometerusing dual recycling is shown in Fig. 5.

D. Interferometric Detectors in Operation

The sensitivity of the prototypes with tens of meters ofarm length are on the order of a few units of 10−19 m√

Hzabove some hundreds of hertz. In addition to the invalu-able contribution to the development of the techniquesof interferometric detection, the prototype interferometershave been used to perform gravitational wave searches.

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Among these first runs, the 100-hr coincident run betweenthe 10-m Glasgow and the 30-m Garching prototypes hasdemonstrated the possibility of reliably and simultane-ously operating such complex instruments for long times.The coincident run has set an upper limit of 4.9 × 10−16

on gravitational wave bursts. More recently, the 40-m pro-totype at Caltech has posed the upper limit of 0.5 hr−1

on the rate of coalescence of binary neutron stars in thegalaxy.

E. Long Baseline Interferometersunder Construction

The major planned ground-based interferometers areLIGO, VIRGO, GEO600, TAMA, and AIGO. The sensi-tivity is shown in the top part of Fig. 6.

The LIGO project is a Caltech/MIT collaboration con-sisting of two detectors, each with a 4-km arm length, atHanford (Washington state) and Livingston (Louisiana),plus a 2-km detector sharing the vacuum system of the4-km apparatus at Hanford. All detectors are Michelsoninterferometers equipped with Fabry–Perot cavities anduse power recycling. The seismic attenuation system is afour-stage stack cascade. The detectors are expected beoperative in 2002.

FIGURE 6 Strain noise sensitivity of the interferometric detectors. Top figure: ground-based interferometers VIRGO(solid line), LIGO (dashed line), GEO600 (dotted line), and TAMA (dot–dash line). Bottom figure: the space interfer-ometer LISA.

The VIRGO project is a French/Italian collaborationusing a 3-km arm length detector close to Pisa, Italy. TheMichelson interferometer is equipped with Fabry–Perotcavities. The seismic attenuation system is the combina-tion of an inverted pendulum for preisolation and a five-stage pendulum cascade (superattenuator). The arrange-ment allows for an extension of the sensitivity band downto 4 Hz. The interferometer is actually under constructionand is expected to be operative in 2002.

The GEO600 project is a British/German collabora-tion using a 600-m arm length detector, which is a pureMichelson interferometer. The seismic suspension systemuses stacks in the first stages and multiple pendulums inthe last stages. The detector is designed to use from thebeginning several second-generation techniques for theoptical configurations (signal recycling) and the suspen-sions (monolithic fused silica) to approach the sensitivityof the longer baseline detectors in some regions. The in-terferometer will be operational in 2001.

The TAMA300 project is a Japanese interferometerwith 300-m arm length and Fabry–Perot cavities. Thedetector began operating in 1999 with a sensitivity of∼3 × 10−20 1√

Hzand has recently set an upper limit of

0.59 hr−1 on the rate of coalescence of close binaryneutron stars.

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The first stage of the AIGO detector in Australia wascompleted in 2000.

F. Very Long Baseline Interferometersin Space

Laser interferometry in space is immune form seismicnoise and allows for investigation of the frequency rangefrom 0.1 mHz to 1 Hz. The LISA interferometer is aMichelson made of three spacecraft 5 × 106 km distantfrom each other at the vertexes of an equilateral triangle.The third arm is used for polarization studies (and givesredundant information). The three spacecraft are in a he-liocentric orbit lagging of 20◦ behind the earth. The rele-vant noises are a result of solar radiation pressure and solarwind, which demand accurate shielding of the test masses.The sensitivity is shown in the bottom part of Fig. 6.

IV. RESONANT DETECTORS

A. Basic Principles

Historically, resonant detectors were the first gravitationaldetectors, since the work by Weber during the 1960s.Weber searched gravitational waves from star collapseusing room-temperature aluminum bars resonating at1600 Hz. Tentative evidence for gravitational events wasfound using two detectors at a 1000-km distance in coin-cidence, but not confirmed by other detectors. In searchof a higher sensitivity, in the 1970s the development ofthe first cryogenic detectors started all over the world:Stanford, Louisiana State University, University of Romein Italy, and University of Western Australia. Severalcryogenic antennas are now in operation.

A pair of masses attached to a spring is the simplest typeof resonant gravitational wave detector. A gravitationalwave with a frequency spectrum including the resonancefrequency of the detector fr induces an oscillation of themasses about their center of mass. The lowest resonantfrequency of an elastic solid body such as a metal cylindercan be modeled as a pair of masses connected by a spring.The typical resonant detectors are cylindrical metallic barsof some meters length and some tons mass, oscillating inthe fundamental longitudinal mode (resonant detectors arealso named bars). The fundamental oscillation occurs atfrequency ωr = 2π fr = πvs

L , where vs is the sound velocityin the bar material and L the bar length. A bar is most sen-sitive to signals with a frequency very close to its resonantfrequency. The actual bars are resonant at about 1 kHz, afrequency relevant for detection of supernova events. Theefficiency of a bar is given by its cross section, the ratioof absorbed energy to the incoming energy:

� ∼ 8GM

πc

v2s

c2 . (21)

The bar should be as massive as possible and made of amaterial with a high sound velocity. Similar to interfer-ometers, resonant detectors are almost omnidirectional. Aresonant detector needs some further stages to producea signal (see Fig. 7). A transducer transforms the me-chanical oscillation into an electric signal, which is thenamplified. The transducer is a sensor that can also be mod-eled as a mass connected to a spring. The transducer fre-quency ft is tuned to resonate at the same frequency fr

of the bar. The resonant detector and the transducer be-have as two coupled oscillators in series. This system hastwo normal modes at the frequencies f± = f0(1 ±

√µ

2 ),where f0 = fr = ft, µ = √

mM , where M , m are the masses

of the bar and of the transducer, respectively. The ratioµ is low to achieve a large transducer motion. When thegravitational wave arrives, the bar initially experiences themaximum displacement; the transducer is almost quiet.Bar and transducer exchange energy through beatings ofthe normal modes, until the relative displacement is max-imum. Finally the transducer vibrates with an amplitude√

Mm times larger than the original vibration of the bar.

The bandwidth of a resonant detector is of the order of thedistance between the normal modes � f = fr

√mM , of the

order of a few hertz for current detectors. A much largerbandwidth would require close mass values for trans-ducer and antenna, at the cost of a smaller transducermotion.

The efficiency of the transducer is characterized by theratio β of the electrical energy stored in the transducer tothe total mechanical energy stored in the detector. A trans-ducer with high β value allows a larger bandwidth sinceit reaches equilibrium with the bar faster. Since ωrtm ∼ 1

β,

if β ∼ 1 the bandwidth could be as large as the resonantfrequency. Achieving such performance is difficult sinceit has been experimentally observed that a high β causes a

FIGURE 7 Schematics of a resonant detector. The bar, at tem-perature T and with damping time t d, is coupled (with couplingβ) to a transducer that converts the mechanical energy to elec-trical energy. The signal is then amplified and acquired with anintegration time t m.

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FIGURE 8 (A) Inductively coupled transducer; (B) parametrictransducer using capacitive modulation.

degradation of the antenna damping time. The transducercan be either passive or parametric (Fig. 8). Passive trans-ducers use capacitive or inductive sensing; the variationof the capacitance or inductance is proportional to the barmotion relative to the capacitor or inductor. Since there isno intrinsic gain, an amplifier is needed, usually a SQUID(superconducting quantum interference device). The lim-its of this technique are electrical losses in the circuitsand the SQUID noise. Parametric transducers use a high-frequency resonator, whose frequency is modulated by thechanging capacity or inductance. There is an intrinsic gainsince they have an intrinsic pump oscillator. The couplingfactor β is enhanced by the electrical quality factor of theresonator. Most detectors uses passive transducers withβ ≤ 10−2.

B. Noise Sources

1. Thermal Noise

In interferometric detectors thermal noise mainly con-tributes far from resonances, since care is taken to shiftmost of them outside the detection band. In bars the reso-nance provides the detection mechanism. The resonancecan also be excited from noise, including thermal noise.Thermal noise has a power spectral density Stn = kBT Mω

Q ,

thus the expected rms amplitude is xtn =√

kBTMω2

r. The recipe

to reduce the thermal noise contribution is the choice ofmaterial with a high quality factor and low-temperature

operation. The material of the bar should have a high qual-ity factor to reduce thermal noise, but it should have den-sity and high sound velocity to maximize the absorbedenergy. The best choices are Nb, Al5056, and sapphire.Sapphire exhibits the highest quality factor (3 × 109), butit is not available on the scale of a few tons. The currentoperating bars are made of Nb or Al5056 and operate atcryogenic temperatures. For a typical bar with a mass of1 ton and a length of 3 m, resonant at 1 kHz, the expectedminimum detectable h = xtn

L is ∼10−16 for operation atroom temperature and ∼10−17 for operation at liquid he-lium (4.2 K). In both cases, the noise is too high to al-low the detection of the astrophysical sources discussedabove. However, if the quality factor Q of the resonance ishigh, the oscillation induced by a burst event will be veryslowly damped with a typical time td = 1

ωr Q . If the mea-surement is performed with an integration time tm shorterthan td, the effective rms noise budget is diluted by thefactor ∼

√tmtd

. The damping time is maximized by havinga resonant detector with a high quality factor Q. The de-pendence of the dissipation factor on the frequency is notrelevant, since the bandwidth of the detector is very nar-row. In this way, the effective noise temperature Te = T tm

tdcan be much lower than the physical temperature T . Thespectral density of thermal noise is

Stn(ω) = 2kBTtmtd

. (22)

2. Electronic Noise

Any transducer modulates a source of electrical energy,acting in some way on an electrical circuit and producingeither a voltage, current, or frequency output. A trans-ducer can be modeled as a two-port device described bya 2 × 2 impedance matrix Zi j . It has two inputs, forceand velocity, and two outputs, current and voltage. Theparameters Z12 (forward transconductance) and Z21 (re-verse transconductance) are the transducer sensitivity andthe back-action effect on the bar. In fact, any transducercan operate in reverse mode and a current noise at its out-put can apply a fluctuating force on the bar. Moreover, anamplifier is in series to the transducer to amplify the signal.The noise sources due to the transducer and amplifier aredescribed using the voltage and current noise V (ω) andI (ω) at the entrance of the amplifier. The spectral densityof the back-action noise is

Sba(ω) = |Z12|22M

I (ω)tm. (23)

The spectral density of the series noise is

Ssn(ω) = 2M

|Z12|2V (ω)

tm. (24)

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While the thermal noise and the back-action noise areproportional to tm, the series noise is proportional to t −1

m ;there is an optimal measurement time.

The total noise budget must be compared to the stan-dard quantum limit. Using the spread σp ∼ M ωr σx in theuncertainty principle, it is possible to deduce the minimumdetectable strain:

hmin ∼ 1

L

√h

M ωr. (25)

For a typical bar with a mass of 1 ton and a length of3 m, resonant at 1 kHz, hmin ∼ 10−21, on the order of therelevant astrophysical signals. Having fixed the frequencyof interest, there is not too much room to improve the limitsince the sound velocity is not varying very much frommaterial to material; thus the size of the bar is fixed as well.

3. Seismic Noise

For resonant detectors it is also necessary to reducethe seismic noise at the resonant frequency below thegravitational signal level. The vibration isolation systemsare multistage suspensions that have normal modefrequencies below the bar frequency and internal modesfrequencies above it. The isolation band extends froma few hundreds of hertz to a few kilohertz. A typicalattenuation system provides a 1010 reduction at 1 kHz.The actual bars operate at cryogenic temperatures, usinga room-temperature isolator to which the cryogenicsystem is suspended. The cryogenic section uses cablesuspensions to hang the bar as a pendulum or cantilevers.Although parametric transducers are noncontacting, pas-sive transducers require additional cabling, which must bedamped to avoid direct injection of noise. Cryogenic an-tennas operating at tens of millikelvins temperature haveadditional problems since they need cooling by conduc-tion, which can inject noise from the cryostat vibrations.

4. Disturbances from Cosmic Rays

High-energy cosmic rays incident on the bar produce heat-ing and expansion of the bar. The main sources are high-energy hadrons and muons. There are a few significantevents per day for bars operating at a few millikelvinsand hundreds for bars at a few microkelvins. The resonantdetector should be underground to minimize cosmic raynoise.

C. Resonant Detectors in Operation

A world array of five resonant detectors is in actual op-eration as the International Gravitational Event Collab-oration, The detectors are Explorer at CERN, Auriga in

TABLE I Main Parameters of the Resonant DetectorsCurrently in Operation

Allegro Auriga Explorer Nautilus Niobe

T (K) 4.2 0.25 2.6 0.1 5

Material Al5056 Al5056 Al5056 Al5056 Nb

Length (m) 3.0 2.9 3.0 3.0 2.8

Mass (kg) 2296 2230 2270 2260 1500

Q (106) 2 3 1.5 0.6 20

Frequency (Hz) 900 900 900 900 700

h (×10−19) 6 4 6 4 6

Legnaro (Italy), Nautilus in Frascati (Italy), Allegro inBaton Rouge (Louisiana, USA), and Niobe in Perth (Aus-tralia). The characteristics of the currently operating de-tectors are shown in Table I. The bandwidth is on the orderof 1 Hz for all detectors. The bars are aligned within a fewdegrees of each other to maximize the chance of coinci-dent detection.

The resonant detector network has recently set upperlimits on burst events using coincidence analysis fromthree and four event detectors (complete with numbers).The limit on monochromatic pulsar signals is ∼10−23.

V. GRAVITATIONAL WAVE ASTROPHYSICS

Gravitational signal detection involves the use of suit-able data processing techniques for burst, continuous, andstochastic signals.

The observations with resonant detectors are narrow-band. The optimum filter watches for changes in the am-plitude or in the phase of the bar oscillation during themeasurement interval tm; thus the filter is not sensitive toslow drifts. The bandwidth of this filter is ∼t−1

m , muchlarger than the intrinsic resonance width fr

Q . Such a fil-ter is sensitive to the magnitude and phase of the Fouriertransform of the signal, but not to the details of the signalshape.

The output of interferometer is a time series where thegenuine signal is hidden in the noise. Burst signals fromsupernova events can be identified by choosing a suitablethreshold: in fact, assuming that the noise is Gaussian,the probability of a large deviation due to noise is verysmall (for example, 0.046 and 0.0027 for 2σ and 3σ ).Very careful environmental monitoring is necessary; thereis no way to measure noise distribution alone since grav-itational waves cannot be shielded. The solution is to useseveral detectors at different locations and use a coinci-dence method; while the genuine gravitational signal canproduce coincident signals, the noises should be uncor-related. The rate of chance coincidence is the product

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of threshold crossing probability in each detector. Thetime delay between events for detectors at distance D∗

(measured through the earth) is �t = ± D∗c . The delay be-

tween European detectors and LIGO is ∼20 msec, whilefor the two LIGO detectors it is ∼6 msec. The coincidencewindow should be large enough to allow detection of realevents (but at the cost of a larger rate of chance coinci-dences). Coincidences can also occur between detectorsin the same location, like the two Hanford interferome-ters: The second detector can provide a veto signal, sincea genuine gravitational event must be detected in both ofthem with a signal ratio scaling as their sensitivities.

For the burst signal of binary coalescences, it is pos-sible to use a matched filter since the signal waveformis known. The output of the detector is multiplied by thetemplate of the waveform and integrated: the presence ofthe signal will give a higher output than the presence ofnoise alone. The matched filter is very demanding fromthe point of view of computation; in fact, the expectedsignals depend on several parameters and the burst arrivaltime is not known. The evolution of the signal frequencyduring coalescence provides information about the massesof the components, while the intensity is related to the sys-tem distance from earth. The final part of coalescence isparticularly interesting since it has not been computed yet.

For continuous signals, there is no need for templatessince the waveform is a sinuosoid. The Fourier transformof monochromatic signals exhibits peaks at the signal fre-quencies, which are a clear signature of the signal sincethe probability of having a spectral peak with noise aloneis very low. The coincidence of detection in different de-tectors is of great help. There is another strong signature:the relative motion of the earth and the source causes bothamplitude and frequency modulations of the signal, whichdepend on the source position. However, the number ofoperations needed to reconstruct the source direction iscomputationally demanding.

Stochastic background can be detected by cross-correlating the signal of different detectors. The relativedistance of the planned detectors is of the same order orsmaller than the gravitational wave wavelength.

A. Gravitational Detectors Network

In the near future, a global network of interferometric andresonant detectors will be performing observations in co-incidence. The coincident observations improve the sig-nificance of the observations and allow correlation withthe measured intensity at each detector with the delay dueto the finite propagation speed. The network operation willallow a precise determination of the source direction andof the wave polarization. It is estimated that with a timeresolution of 0.1 msec and a network of detectors at a few

thousands of kilometers from each other, the source posi-tion can be reconstructed at about (5 mrad)2. The deter-mination of position is important to check the consistencyof data measured by different detectors.

B. Coincidence with NongravitationalDetectors

Gravitational wave astronomy will benefit from coinci-dence with observations in other astronomical bands. Ifthe source position has been determined with good pre-cision, there could be an optical or radio or γ - or X-raycounterpart. As an example, coincidence with the intenseoptical emission of a supernova should be observed incoincidence with a gravitational wave burst. The coin-cidence with neutrinos from a supernova collapse offersanother opportunity. The observation of optical and neu-trino emission together with gravitational emission allowsresearchers to check the equality of gravitational wave ve-locity propagation with the speed of light. On the otherhand, assuming that gravitational waves propagate withvelocity c, the measurement can be used to put limits onthe neutrino mass.

The coalescence of a binary neutron star system in co-incidence with a γ -ray burst should allow researchers totest the origin of this process. A coalescing binary systemcan also be used as a standard candle, up to hundreds ofMpc. In fact, the measurement of the chirp time allows fordeduction of the chirp mass and prediction of the signalintensity, thus determining the distance of the binary sys-tem. If an optical counterpart of the source is found, itsredshift can be determined by classical methods. In thisway, the Hubble constant can be determined.

VI. FUTURE DEVELOPMENTS

Hopefully the first generation of gravitational detectorswill allow the first direct detection of gravitational waves.To build the field of gravitational astronomy, further im-provements in sensitivity are needed. A vigorous researchand development program is being carried out for bothinterferometers and bars in attempts to approach the fun-damental SQL.

A. Interferometric Detectors

The LIGO collaboration is planning to upgrade the ini-tial detector in 2006 (LIGO II), improving the sensitiv-ity by one order of magnitude at least. The research isbeing performed by the LIGO Scientific Collaboration,which includes groups from the United States, Europe,and Australia. On the European side, Virgo and GEO600

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FIGURE 9 Sensitivity of the initial (dashed line) and advanced LIGO (solid line) detectors.

collaborations have considered the realization of the de-tector EURO around 2010. In Japan there is a project fora 3-km scale interferometer.

The research in sensitivity improvements covers allsources of noise. All collaborations are planning to haveeffective seismic isolation down to a few hertz. The ther-mal noise can be reduced, in principle, by working at cryo-genic temperatures, which is foreseen in future Japanesedetectors. However, the loss factor of various materialsdoes not always improve at low temperature, and thetest mass becomes more sensitive to heating from thelaser beam. For this reason, other techniques are nowbeing studied. The first improvement comes from usingmonolithic suspensions (fused silica fibers or ribbons) tohang test masses. Losses on the order of 10−8 have beenachieved for several suspension modes. Another plannedimprovement is the replacement of fused silica test masseswith sapphire test masses, where losses are one order ofmagnitude smaller. The improvements of sensitivity in theregion where shot noise dominates are performed withseveral techniques. First of all, plans call for increase-ing the input laser power from 10 to 100 W. Moreover,signal recycling will be used to improve sensitivity in anarrowband.

The possible improvements in sensitivity of the LIGOdetector are shown in Fig. 9.

B. Resonant Detectors

The cross section of a bar is proportional to its mass, thusthere are efforts to build a 100-ton spherical resonant de-tector, with high sensitivity and omnidirectional response.The sphere must be equipped with several transducers todetect the fundamental modes: the quadrupole modes andthe monopole mode (not sensitive to gravitational waves).Efforts are also being devoted to developing more efficientelectronics systems (transducers and amplifiers) to achievebetter sensitivity. Another major improvement foreseen isthe increase of the bandwidth from the current few hertzto several tens of hertz. In this way, coincident runs couldallow the determination of source position.

VII. CONCLUSIONS

The forthcoming gravitational wave detectors have aninitial sensitivity close to the expected level of the sig-nals from astrophysical sources and should perform thefirst direct detection of waves. The research in gravi-tational physics involves several aspects of physics andtechnology, ranging from theoretical and numerical cal-culations to applied research in lasers and optics. Fur-ther developments in detector sensitivity should allow

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the birth of gravitational wave astronomy, to give a newview in the physics of neutron stars, black holes, andthe primordial universe. The connection of the gravita-tional measurements with other astronomical observa-tions should contribute to a more complete view of theuniverse.


BINARY STARS • COSMOLOGY • GRAVITATIONAL WAVE

ASTRONOMY • GRAVITATIONAL WAVE PHYSICS • NEU-

TRON STARS • PULSARS • RADIO ASTRONOMY, INTER-FEROMETRY • RELATIVITY, GENERAL • SUPERNOVAE

BIBLIOGRAPHY

Blair, D. G., ed. (1991). “The Detection of Gravitational Waves,” Cam-bridge University Press, Cambridge.

Ju, L., Blair, D. G., and Zhao, C. (2000). “Detection of gravitationalwaves.” Rep. Prog. Phys. 63, 1317.

Saulson, P. R. (1994). “Fundamentals of Interferometric GravitationalWave Detectors,” World Scientific, Singapore.

Thorne, K. S. (1987). In “300 Years of Gravitation” (S. W. Hawking andW. Israel, eds.), Cambridge University Press, Cambridge.

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Encyclopedia of Physical Science and Technology EN0071-327 June 29, 2001 20:16

Image Restoration, MaximumEntropy Method

R. J. SaultAustralia Telescope National Facility

I. Image RestorationII. Bayesian InferenceIII. Maximum Entropy Image Restoration in PracticeIV. Some ApplicationsV. Closing Remarks

GLOSSARY

Bayesian probability theory The approach to probabil-ity theory which views a probability as a measure ofour uncertainty of knowledge rather than as relativefrequency of occurrence.

Convolution A position-independent blurring operationon an image.

Deconvolution The process of inverting a convolutionoperation.

Lagrange multiplier A variable introduced into an opti-mization problem. It ensures the solution of the opti-mization obeys a particular equality constraint.

Modulation transfer function The Fourier transform ofthe point-spread function for a position-independentsystem.

Mosaicing The practice in radio astronomy of makingan image of a large region of the sky from many obser-vations of smaller regions.

Pixel “Picture element.” The smallest element of a picture

or image, when represented as an array of elements, asin a computer.

Point-spread function The response of an imagingsystem to a hypothetical point source. Point-spreadfunctions can be position-dependent or position-independent.

Sidelobe The nonzero response of the point-spread func-tion well away from the main response peak.

IMAGE RESTORATION is the process of estimatinga “true” image, given a degraded (generally noisy andblurred) version of that image. Maximum entropy imagerestoration is a class of approaches to this problem. Thistakes as the solution the image that has a maximum entropymeasure while still remaining consistent with the mea-sured data. Unlike classical linear techniques, maximumentropy methods provide a framework where it is simpleto include a wide variety of forms of data in the restorationprocess. Being a nonlinear technique, maximum entropy

631

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632 Image Restoration, Maximum Entropy Method

methods allow extrapolation and interpolation of unmea-sured Fourier information. These properties can result insubstantially better results than those possible with clas-sical linear techniques. One of the main disadvantages ofmaximum entropy techniques is that the results tend tohave significant biases.

I. IMAGE RESTORATION

A. Introduction to Imaging

Image restoration can be simply defined as the process offorming a high-quality estimate of an image from availabledata. The term restoration is generally used where the dataare in the form of a degraded (blurred) image, whereas theterm reconstruction tends to be used where the data aresome more general measure of the image. Restoration andreconstruction are quite similar (indeed restoration is asubset of reconstruction), and although image restorationwill solely be considered here, many of the general prin-ciples apply equally well to the reconstruction problem.

The need for image restoration arises because image ac-quisition systems are never perfect, regardless of whetherthe image is formed from a simple camera or from a multi-billion dollar space telescope. Many imaging systems area good deal more complex than simple lens systems, andso are the degradations that are present in their measuredimage. Whereas some imaging techniques involve nonlin-ear processes (e.g., the response of photographic film isrelated to the light intensity through a very nonlinear re-lationship), many are linear to good approximation. Thatis, the output of the imaging system is proportional tosome intensity of the input. The response of such linearimaging systems is conveniently described in terms ofthe point-spread function. This is the response to a pointsource (this is the two-dimensional analog of the impulseresponse function in traditional time-series analysis). Thepoint-spread function can generally be thought of as a blur-ring function. At the very least, any real imaging systemhas a finite resolution, and the point-spread function is thatfunction which describes how an infinitely narrow sourceis blurred by that system. In general, the point-spread func-tion will be affected by many other characteristics of theimaging system. In addition to this blurring, the outputimage will be corrupted by noise. Representing the im-age as a function of two variables x and y, the true imagei(x , y), is related to the measured image, iM (x , y), by anintegral

iM (x, y) =∫ ∫

i(x ′, y′)b(x, y; x ′, y′) dx ′ dy′ + n(x, y).

Here b(x, y; x ′, y′) is the point-spread function of theimaging system and n(x, y) is additive noise. This gives

the general case where the point-spread function varieswith position in the image. That is, the response of thesystem to a point source at (x ′, y′) is b(x, y; x ′, y′). Thisintegral recognizes that the true image can be thought of asa sum of infinitesimal point sources, and so the measuredimage will be the sum of the responses to these infinitesi-mal point sources.

Many imaging systems are position-independent. Thismeans that the point-spread function is independent of theposition of the point source in the image. The point-spreadfunction at (x ′, y′) is then of the form b(x − x ′, y − y′), andthe integral relating true image to the measured image isa two-dimensional convolution relationship:

iM (x, y) =∫ ∫

i(x ′, y′)b(x−x ′, y−y′) dx ′ dy′ + n(x, y).

This convolution is often written as

iM (x, y) = i(x, y) ∗ b(x, y) + n(x, y).

Whereas image processing and image manipulation wereonce the domain of optical engineers, digital representa-tion of images is now pervasive. Digitally, images are rep-resented as a discrete array of picture elements or pixels,with each pixel taking on a value (or perhaps three valuesfor color images). In this digital representation, the inte-grals above are replaced with sums, and the point-spreadfunction is represented as an array of numbers. We willuse i(m, n) and b(m, n) to represent these discrete-valuedimages.

Real systems often are approximately position-independent, at least over small regions or near the centerof the region being imaged. One of the attractions of mod-eling an imaging system as being position-independent isthat they are amenable to analysis using Fourier theory.The Fourier transform of the image i(x, y) is defined

I (u, v) =∫ ∫

i(x, y) exp(i2π (xu + yv) dx dy.

Similarly the inverse Fourier transform is

i(x, y) =∫ ∫

I (u, v) exp(−i2π (xu + yv) du dv.

Note that there is no generally agreed convention on thesign in exponentials in the forward and inverse Fouriertransform, other than the forward and inverse transforma-tions have opposite signs. By analogy with time-domainsignals, the (u, v) coordinates in the Fourier domain arecalled spatial frequencies. Fourier transforms of real func-tions will generally be complex-valued. A discrete versionof the Fourier transform (for sampled data) also exists.



Image Restoration, Maximum Entropy Method 633

One of the more important properties of Fourier trans-forms (both continuous and discrete) is the convolutiontheorem: a convolution in the image domain transformsto a multiplication operation in the Fourier domain. IfIM (u , v), N (u , v), and B(u , v) are the Fourier transformsof iM (x , y), n(x , y), and b(x , y), then

IM (u , v) = I (u , v) · B(u , v) + N (u , v).

B(u , v), the Fourier transform of the point-spread func-tion, is known as the modulation transfer function. Aswell as being amenable to Fourier analysis, position-independent systems are attractive from a computationalpoint of view: for an image of size N × M , the com-putational cost of simulating a position-dependent sys-tem is of order (NM)2, whereas that for a position-independent system is of order NM log(NM). For imagesof realistic size, this difference in computational com-plexity often separates the computational feasibility andtotal infeasibility. The difference is purely because ofthe existence of the “Fast Fourier Transform” algorithm(devised by J. W. Cooley and J. W. Tukey in 1965).As the name implies, this algorithm allows a fast com-putation of the discrete Fourier transform, which in turnallows fast convolution algorithms to be developed.Because of this computational advantage, instances con-taining position-dependent point-spread functions areusually decomposed and approximated as multipleposition-independent systems. For these reasons, we

(a) (b)

FIGURE 1 The point-spread function of an aberration-free lens system. The left grayscale uses a linear transferfunction, whereas the right uses a logarithmic transfer function to bring out low-level details.

will largely restrict our attention to position-independentsystems.

For an aberration-free lens system, the point-spreadfunction will be the diffraction limit, which gives a re-sponse of the form

b(x , y) =(

2J1(ar )

ar

)2

.

Here J1(r ) is the first-order Bessel function, r =√

x2 + y2,and a is a constant related to the lens size and wavelengthof the light. This point-spread function is known as theAiry disk, after Sir George Airy who was the first toderive its form. The Airy disk is a comparatively cleanpoint-spread function: most of the power in the responseis confined to the main peak.

Many point-spread functions, however, are far less well-behaved. For example, Fig. 1 shows an Airy disk and thepoint-spread functions of particular observations of theHubble Space Telescope and the Very Large Array (a radiotelescope) are shown in Figs. 3 and 4.

B. Image Restoration

The technique of image restoration (or “deconvolution”)can now be simply put: given the measured, noisy, imageiM (x, y) and the point-spread function b(x, y), estimatethe true image i(x, y).




The basic problem of image restoration is that it is fun-damentally ill-posed: the blurring resulting from the point-spread function means that some information is lost. Asa consequence, the restoration step is nonunique—manyimages, if not an infinite number, are typically consis-tent with the measured data. Using Fourier analysis, itis clear that image information is fundamentally lost atthose spatial frequencies where the modulation transferfunction falls to zero. Although it is clear that no spa-tial frequencies are measured beyond the diffraction limit,many imaging instruments fail to measure spatial frequen-cies within this limit. That is, the Fourier information isincomplete.

The ill-posed nature is even more apparent when noise isconsidered. If the modulation transfer function is such thatthe signal-to-noise ratio drops below unity, then the signalhas, again, effectively been lost. Any image restorationtechnique must be robust to noise or errors in the data andthe assumed point-spread function.

The challenge of image restoration is to make a goodestimate of the true image despite noise and nonuniquesolutions.

C. “Classical” Image Restoration Algorithms

The “obvious” image restoration algorithm is the so-calledinverse filter. Given that

IM (u, v) = I (u, v) · B(u, v) + N (u, v),

then an estimate of the true image is

I (u, v) = IM (u, v)/B(u, v).

There is a major flaw with the inverse filter which rendersit useless: when B(u, v) falls to near zero, the correctionbecomes large, and any noise present is substantially am-plified. Even computer rounding error can be substantial.An alternative approach, which avoids this problem, isbased on the approach of Wiener. This approach modelsthe image and noise as stochastic processes, and asks thequestion: What re-weighting in the Fourier domain willproduce the minimum mean squared error between thetrue image and our estimate of it? The Wiener solutionhas the form

I (u, v) = IM (u, v) · B∗(u, v)

|B(u, v)|2 + RN (u, v)/RI (u, v).

Here the spectral density functions of the true imageand noise are RI (u, v) and RN (u, v), respectively. Notethat at spatial frequencies where the signal-to-noise isvery high, the ratio RN (u, v)/RI (u, v) approaches zero,and the Wiener filter reduces to the inverse filter. However,when the signal-to-noise ratio is very poor (i.e., RN (u, v)/RI (u, v) is large), the estimated spatial frequencies ap-

proach zero. This is a moderately interesting property—whereas the inverse filter gives an unbiased estimate ofthe true image, the Wiener filter output is biased toward 0when the signal-to-noise ratio is poor.

The Wiener filter is seldom used in real-image restora-tion applications for a simple but critical reason: it is alinear technique. With a linear technique, the spatial fre-quencies present in the true image estimate are those inthe measured image multiplied by some factor. This is ad-equate if all spatial frequencies are reasonably sampled.However, in those cases where the spatial frequencies areunmeasured, the Wiener filter will simply estimate themas 0. Linear techniques, in general, cannot extrapolate orinterpolate to estimate unmeasured spatial frequencies.Techniques that do not estimate these missing spatial fre-quencies will produce images with plainly visible defects.To produce a good restoration technique, some plausiblevalues need to be estimated for these missing spatial fre-quencies. Consequently nonlinear restoration techniquesare required.

II. BAYESIAN INFERENCE

A. Bayes Theorem

To provide a grounding in some of the theory around max-imum entropy methods, we digress here to describe someof the important aspects of Bayesian probability theory.Although this is arguably the original form of probabilitytheory, Bayesian theory fell into disrepute, however, in-terest in it has been re-awakened and re-invigorated in thelast half century. Although the differences between con-ventional and Bayesian theory can appear subtle at times,they are based on quite different approaches. Conventionaltheory defines probability functions as normalized fre-quency distributions ultimately derived from a nominallyinfinite number of trials (or perhaps a physical principlethat allows us to predict the outcome of an infinite numberof trials). Bayesian probability, on the other hand, viewsprobabilities as degrees of belief that are modified by in-formation. A Bayesian probability is refined as more in-formation becomes available. In the limit of an infinitenumber of trials, Bayesian and conventional probabilityconverge. In the presence of limited information, Bayesianprobabilities are often easily assigned when conventionalprobabilities cannot.

In Bayesian probability, Bayes theorem is an importanttool used to incorporate information to refine the probabil-ity assigned to a hypothesis. Bayes theorem can be statedas a relationship between conditional probabilities:

P(H | D) = P(H ) · P(D | H )

P(D).




Here H is a hypothesis and D is some data, and soP(H | D) is the probability of the hypothesis given thedata. Bayes theorem relates this to the probability ofthe hypothesis before the data became available, P(H ), theprobability of the data given the hypothesis, P(D | H ), andfinally the probability of the data P(D). The term P(H ) isusually called the prior probability, or simply the prior, asit is obviously the probability that is assigned before thedata is available. As the probability P(D) is independentof the hypothesis, knowledge of this is not needed whencomparing the relative probability of different hypotheses.In this sense, it is a normalization term that is often notimportant to an argument.

B. The Principle of Maximum Entropy

A major problem in Bayesian probability had been as-signing the prior probability. Pioneering work by E. T.Jaynes has shown that there is a unique consistent wayto assign prior probabilities, with this approach becomingknown as the principle of maximum entropy. This prin-ciple states that the prior probabilities, p1, p2, . . . , pN ,that we associate with the mutually exclusive hypothesesH1, H2, . . . , HN , should be those which maximize

S = −N∑i

pi log(pi ),

subject to this being consistent with whatever informationis already available.

The concept of entropy is present in many disciplines.In statistical mechanics, Boltzmann introduced entropyas a measure of the number of microscopic ways that agiven macroscopic state can be realized. A principle of na-ture is that it prefers systems that have maximum entropy.Shannon has also introduced entropy into communicationstheory, where entropy serves as a measure of information.The role of entropy in these fields is not disputed in the sci-entific community. The validity, however, of the Bayesianapproach to probability theory and the principle of maxi-mum entropy in this, remains controversial.

To illustrate Bayesian probability and the principle ofmaximum entropy, consider the roll of a die (or perhaps acomputer program that generates a number between 1 and6). What is the probability of the roll showing a 6? Theprobabilities of the hypotheses for rolling a 1, 2, throughto 6 will sum to 1 (no other events are possible). Lack-ing any information, the Bayesian prior probability is thatwhich maximizes the entropy. This leads to the intuitiveresult that all faces of the die have equal probability ofbeing thrown (all have the probability of 1

6 ). This is thecrux of the difference between Bayesian and conventionalprobability—a Bayesian is comfortable in saying that the

faces of the die have equal probability in coming up. Thisis despite lack of information supporting this conjecture,but, importantly, despite lack of information to refute it.Strict conventional probability would not be able to an-swer such a seemingly simple question as its probabilityfunction is derived from either a notional infinite num-ber of throws of the die to derive a frequency distributionor some physical argument to assure us that the die wasfair.

Note that whereas the equal probability agrees witheveryday intuition, it does not necessarily represent the“truth.” If it were a computer program, rather than a die,then it is far less obvious that the numbers would haveequal probability. Furthermore, if the die was in a gam-bling den of dubious repute, then you might be quite rightto doubt the fairness of the die—further tests of the diemight be called for before you are willing to bet. In such aden, if a person with Bayesian beliefs was presented withthe extra data that the mean value from the throw of the diewas 5, then this extra information could be included in de-termining the prior probabilities. Maximizing the entropysubject to this information, the chances of throwing a 1through 6 are given by probabilities 0.02, 0.04, 0.07, 0.13,0.25, and 0.48, respectively. Again, Bayesian probabilityis able to give such an answer, whereas a conventionalprobability would still not be willing to conjecture. In thiscase, however, intuition is no guide as to whether this is areasonable choice, and the reader might be more comfort-able with the conventional choice of not making a choice.

It is fair to say that there is no universal agreementbetween those who champion either Bayesian or conven-tional probability theory. Indeed, as a bystander, one canfind it interesting to watch the tussle. Conventional prob-ability theory is very successful at modeling situationswith large numbers of random events (e.g., the pressurein a vessel resulting from gas molecules colliding withthe vessel walls). Indeed, statistical mechanics is basedon conventional probability theory. On the other hand,Bayesian approaches seem to be more successful whenthe number of random events is smaller, and where thereis insufficient information available.

C. Maximum Entropy Applied to Images

Bayesian probability theory shares some similarities withthe problem of image restoration; they both are requiredto make some choice in the presence of insufficient dataor information. It is not surprising, then, that Bayesiantechniques have been applied in image restoration. Ap-plying Bayesian principles, of the possible solutions toan image restoration problem (i.e., of all the images thatare consistent with the data), we choose that image whichmaximizes the entropy.




Historically, however, there have been two differentschools of thought as to how the entropy of an imageshould be measured, and there has been no resolution asto whether one, both, or neither of these schools are correctin the arguments that they champion.

The original school (resulting from the work of J. P.Burg) applied the Bayesian logic and the principle of max-imum entropy rigorously to the problem of estimating apower spectrum of a signal, given discrete and limitedmeasurements of the autocorrelation function of that sig-nal. This work showed that the power spectrum, R(υ),which maximized the measure

S =∫

log(R(υ)) dυ

was the preferred spectrum. The argument behind this con-siders the signal as a Gaussian random process, and so theFourier components of the signal will also be Gaussianvariables. The entropy associated with these componentsis proportional to the logarithm of the variance, and thevariance is simply R(υ). Hence we should be maximizingthe above entropy measure. Extending this argument toimaging, the electric field pattern of an electromagneticwave can also be treated as a Gaussian random process,and a similar argument leads to the entropy measure of animage as

S =N∑n

M∑m

log(i(m, n)).

An alternative school, introduced by B. R. Frieden, andwhich will be called the Gull and Daniell form (after twoearly champions of this measure), takes a different ap-proach. It models an image as being composed of a largenumber of luminance elements. If there are K luminanceelements that are to be laid down on an image with N × Mpixels, what are the most likely images to be formed? Ifp(m, n) is the probability of a luminance element landingon pixel (m, n), then the image expected from K lumi-nance elements will be i(m, n) = Kp (m, n). The entropymeasure of the image is then

S = −N∑n

M∑m

p(m, n) log(p(m, n))

= − 1

K

N∑n

M∑m

i(m, n) log(i(m, n)/K )

Using this argument, the preferred image is the one whichis consistent with any data, but which maximized this en-tropy. An amusing analogy sometimes used to illustratethis is to imagine an infinite troop of monkeys at work,with each monkey having K building blocks or luminanceelements to make an image. The image most often made,

which is consistent with the data, will be that which max-imizes entropy.

As will be discussed below, the scaling by K in thismeasure of entropy is important. A more common andintuitive way to represent this scaling is

S = −N∑n

M∑m

i(m, n) log

(1

e

i(m, n)

d(m, n)

),

where d(m, n) is called the default image and e is thebase of natural logarithms. Differentiating S with respectto the pixel values will show that, in the absence ofother information, the image that maximizes the entropyis simply d(m, n). While a uniform (flat) default imagewould be used where there is no prior information onthe true image, a nonuniform default can also be used.In this case, solution image will be biased toward thisdefault.

The argument with luminance elements suggests ana-lyzing the situation in terms of photons. The Bose formulafor the entropy of n photons in a mode is

(1 + n) log(1 + n) − n log n.

In the limit of n � 1, which is the case at radio wave-lengths, this reduces to log n, whereas when n � 1, asat optical wavelenghts, this reduces to −n log n. Unfortu-nately, the statistics of photons does not resolve the disputein entropy measures.

Although the entropy measure used can appreciably af-fect the solutions when there is limited information, inpractice there is usually a good quantity of data to con-strain possible solutions. The data ultimately should (andgenerally do) drive the solutions.

III. MAXIMUM ENTROPY IMAGERESTORATION IN PRACTICE

A. Data Constraints

Maximum entropy image restoration problems are usu-ally formulated as optimization problems, with the pixelvalues being the variables of the optimization. The dataare generally included in these optimizations by way ofequality constraints. Equality constraints are attractive, asthey can be easily included in an optimization problemby augmenting the problem with extra variables calledLagrange multipliers. For example, if we wish to maxi-mize S subject to a data constraint, D = 0, then by intro-ducing the Lagrange multiplier α, the augmented problemof maximizing

J = S − αD




will produce the desired result. That this is so requires alittle thought. However, note that at the maximum, D willbe 0 and so does not affect the value of S achieved, and thederivative of J with respect to α is simply the data con-straint, and so will be 0. The Lagrange multiplier, α, doeshave a well-defined value at the maximum, and can bethought of as a mediator between the competing require-ments to maximize S and to enforce the data constraint D.

One possible set of data constraints in image restora-tion is

b(m, n) ∗ i(m, n) = iM (m, n).

This uses a data constraint for each pixel in the measuredimage, and requires the introduction of one Lagrange mul-tiplier per pixel. The main problem with this is that it failsto recognize that the data are noisy. Consequently, exactagreement with the data should not be enforced. An alter-native, the so-called χ2 constraint, requires only statisticalagreement. In particular,

χ2 =N∑n

M∑m

(b(m, n) ∗ i(m, n) − iM (m, n))2/σ 2

is constrained to equal its statistically expected value. Hereσ 2 is the expected noise variance of each pixel. For M × Npixels, the expected value of χ2 will be MN. Thus, to findthe maximum entropy solution, for entropy measure S, wemaximize

J = S − α(χ2 − MN ).

Many other data constraints are possible. For example, theintegrated flux constraint is common, where the sum of allthe pixels is constrained to equal some fixed value,

F =N∑n

M∑m

i(m, n).

Again, this constraint can be included in the maximizationprocess using a Lagrange multiplier.

In addition to the data, there is often other physicalinformation to constrain possible solutions. These include:

1. Image data are often positive-valued by definition.Indeed, the maximum entropy measures discussedabove only make sense for positive-valued images,and so positivity is a natural consequence. Whereasthis enforcement of positivity is often seen as astrength, for images that can be negative-valued, it iscertainly a hindrance.

2. Often an image is known to be nonzero in only asmall subregion.

Including as many constraints in the entropy maximiza-tion process is important—the more information present,

the better conditioned the problem will become, and theresultant image will be more reliable.

B. Entropy Measures

Even though there is no general agreement on the “correct”measure of entropy for an image, this does not preventthe use of these measures. Indeed, many maximum en-tropy practitioners take a more pragmatic approach, andare unmoved by the philosophical debates between thedifferent camps as to whether the Gull and Daniell or theBurg form is the appropriate entropy measure. In manyinstances, practitioners use maximum entropy because itworks—information-theoretic arguments are not required.It is possible to take the argument a step further and chooseany entropy function that is effective.

Maximum entropy, as applied to image restoration,can be thought of as a particular case of a more generaltechnique known as regularization. One approach to ill-posed problems, such as image restoration, is to find solu-tions that are consistent with the data, but which possessother desirable features. Maximum entropy is but one ofmany possible desirable features. Another possibility is ameasure such as

S =N∑n

M∑m

(i(m, n) − 1

4(i(m + 1, n) + i(m − 1, n)

+ i(m, n + 1) + i(m, n − 1))

)2

.

This measures the roughness of an image (it is the sumof the square of second derivatives). By choosing a solu-tion image which minimizes this roughness measure, butwhich remains consistent with the data, a “good” recon-struction can be expected. This regularizing function istypical of many that convolves the image estimate withsome filter kernel, k(m, n), and then sums the squares ofthe result. In the example above, the kernel was a simplederivative filter. When using the sum of squares of a filteras the regularizing function, and when the data constraintis the χ2 approach, the solution has a form similar to theWiener filter discussed previously. In particular,

I (u, v) = IM (u, v) · B∗(u, v)

|B(u, v)|2 + K (u, v)/α,

where K (u, v) is the Fourier transform of the filter ker-nel and α is the Lagrange multiplier in the χ2 constraint.As with the Wiener filter, a regularization function likethis will result in a linear algorithm, and this will not ex-trapolate/interpolate any missing Fourier data. To estimatemissing Fourier data, the regularization/entropy functionmust have first derivatives that are neither constant norlinear functions of the data.




Apart from the two information-theoretic entropy mea-sures, other forms that have been suggested include

S =N∑n

M∑m

√i(m , n)

and

S = −N∑n

M∑m

log(cosh(λi(m , n))

∼= −λ

N∑n

M∑m

|i(m , n)| + constant where λi(m , n) � 1.

The latter measure is called the maximum emptiness crite-rion. When λ is chosen to be comparable to the reciprocalof the noise level, this will be approximately equivalent tooptimizing the L1 norm of the image.

C. Combining Data

One of the advantages of a nonlinear approach, such asmaximum entropy, is that it can extrapolate and interpo-late missing information in the Fourier domain. Almosta corollary of this is that all available data must be usedin the restoration process simultaneously. To see the dif-ference here from a linear approach, assume we have twosets of data: D1 and D2. If we use a linear approach, wewill achieve identical results if we restore D1 and D2 sep-arately and then combine the result, as compared againstcombining the two sets of data and then restoring. That is,it does not matter with a linear approach when the com-bining is done; it can be done before or after the linearrestoration. With a nonlinear approach, this is not the caseas quite different results will generally follow. From aBayesian’s viewpoint, this should be no surprise. A betterresult should be possible when more information is avail-able. Nonlinear processing encourages so-called “joint”approaches, where all data is processed jointly. In thisway, full advantage can be made of the relationships be-tween the different data. We will see examples of thisbelow.

D. Maximum Entropy Algorithms

In general, a maximum entropy problem can be expressedas the maximizing of an expression such as

J = S − α1 D1 − α2 D2 + · · ·.Here S is the entropy measure, D1, D2, etc., are data equal-ity constraints and α1 , α2, etc., are Lagrange multipliers.One of the important differences in formulating a restora-tion problem in this way is that it does not focus on trans-forming the data into the solution. Rather, this approach

aims at a more general formalism, which readily accom-modates adding more data and constraints. As no directinversion between the data and true image is called for,it is easy to include data that is related to the true imagein quite an indirect fashion. The approach, which couldbe called data-oriented rather than procedural, is far moregeneral than just image restoration. The maximum entropyapproach has been used in a broad variety of ill-posed in-verse problems.

A maximum entropy image restoration can be solvedin a fashion similar to many traditional optimizationproblems—the derivatives of J can be used to drive al-gorithms such as steepest descent, Newton-Raphson, orconjugate gradients. The algorithms, like solutions to mostnonlinear problems, are invariably iterative. The compu-tationally expensive part of such algorithms is usuallythe implementing of convolutions (or similar operations).In practice, these are generally done using Fourier trans-forms. Because the number of variables in the maximiza-tion is typically large (it equals the number of pixels plusthe number of Lagrange multipliers), there are often someapproximations and simplifications required when com-pared with more traditional optimization problems.

E. General Properties

Somewhat paradoxically, general characteristics of max-imum entropy solutions are more easily analyzed thansolutions to a number of other image restoration algo-rithms. This is despite maximum entropy methods beingmore difficult to implement. This ability to characterizethe solutions results from them all obeying a general setof properties—they maximize the entropy. On the otherhand, image restoration techniques that are described pro-cedurally (particularly those described by an iterative pro-cedure) are difficult to analyze as their solution is definedby nothing more than the end point of a procedure. Herewe consider a number of general properties of maximumentropy solutions.

Positivity and compression of pixel range—With theexception of the maximum emptiness criteria, all theentropy measures described above are only defined forpositive-valued pixels. Clearly then, these measures (orrather their optimization algorithms) enforce positivity.

Figure 2 plots the various entropy measures and theirderivatives, with the entropy for a pixel S equalling log p,−p log p,

√p and −log(cosh p). Although the entropy

measures at first glance look quite dissimilar, their similar-ity becomes more apparent when their derivatives are com-pared. Ignoring the data constraints, for a small change,�p, the change in the entropy will be

�S = dS

dp�p.




(a) (b)

FIGURE 2 Plots of different maximum entropy functions and their derivatives. Shown are the Burg (logp), Gull andDaniell (−p log p), maximum emptiness (−log(cosh p)), and square root (

√p) measures.

The derivatives all have the property that, for a givenchange in �p, there is a greater change in entropy forsmaller rather than larger values of p (i.e., the secondderivative of S is negative). For parts of an image that ismostly blank, this property tends to compress the pix-els to small nonzero values, and to suppress ripples.This compressing effect becomes less effective for pixelswith large values. It is this property that leads to maxi-mum entropy’s stabilizing influence on image restorationproblems.

Flux-scale dependence—An interesting property ofthe Gull and Daniell measure is that, without the defaultimage, it is flux-scale dependent. That is, the answer poten-tially depends on the units of the measurements. As a triv-ial example, consider an experiment where two lengths,x and y, are measured to be 1 and 2 inches, respectively,and there is a known uncertainty in each measurement ofσ 2 = 1

4 . Formulating this as a maximum entropy problemwith χ2 constraint, we must maximize

J = −x log x − y log y + α

((x − 1)2 + (y − 2)2 − 1

2

).

This gives a result (x, y) = (0.62, 1.40). On the other hand,using the same data and variance, apart from forming the

problem in centimeters and centimeters squared, the resultwould be, after converting back to inches, (x, y) = (0.69,1.36).

None of the other forms of entropy described abovesuffers from this undesirable property∗—it is a propertyof the Gull and Daniell measure only. The key to the dif-ference here is that the other entropy measures describedabove have derivatives that are a power of |p|.

This flux-scale dependence of the Gull and Daniell mea-sure underlines the effect the default image has on the finalsolution. Even when using a flat default, the final result willdepend on the value of that flat default level. Indeed, thisreveals a flaw in the luminance elements argument pre-viously used to justify this entropy measure. It assumesthat the number of luminance elements is known a priori,which is often not the case. Without knowing this a priori,the luminance element argument cannot be used.

Interestingly, if an integrated flux constraint is com-bined with the Gull and Daniell measure, the solution be-comes scale-independent.

Bias—Maximum entropy solutions are invariably bi-ased solutions. This means that the expected value of the

∗Strictly, the maximum emptiness measure is also scale-dependent,but the dependence becomes negligible if λi(m, n) � 1.




maximum entropy solutions, given an infinite number ofdifferent realizations of the possible noise, does not con-verge to the truth. Biased estimators in statistical tech-niques are by no means uncommon, there is always atrade-off between bias and stability, with the more sta-ble estimators tending to be biased. Indeed, the Wienerfilter, and those regularization techniques that share theWiener form, are all biased estimators.

The Gull and Daniell measure will tend to bias the so-lution toward the default image. This generally means thatpeaks are underestimated, and regions of low value tendto be overestimated. For example, when using a χ2 dataconstraint, some analysis shows that the solution image isapproximately

i(m, n) ∼= d(m, n) · exp(β · r (m, n)),

where β is a positive-valued constant, d(m, n) is the de-fault image as before, and r (m, n) is the discrepancy be-tween the measured and solution images:

r (m, n) = iM (m, n) − b(m, n) ∗ i(m, n).

This shows that when the solution image deviates signif-icantly from the default image, then the residuals mustbe large. This bias can become quite problematic when agood default image is not known. For example, a flat de-fault will bias the solution to have flux across the image,even if the true image might be quite clumpy. This canlead to an artificial plateau in the image, where there is noreal emission.

Super-resolution and variable resolution—One ofthe prime motivations in using a nonlinear restoration al-gorithm is its ability to interpolate and extrapolate un-measured information in the Fourier plane. Thus, virtuallyby definition, nonlinear algorithms can generate solutionswith a greater resolution than are present in the data. Thisis usually called super-resolution. Clearly, when there isa characteristic in an image that relies on extrapolation ofunmeasured information, caution is needed in analyzingthe results (extrapolating data is never as good as measur-ing the data in the first place).

Maximum entropy restorations also generally havevariable resolution; the resolution can differ between sev-eral features in a single image. Features that are measuredwith good sensitivity will generally have better resolutionthan features with poor sensitivity. Because of variableresolution, and the dangers of interpreting super-resolvedimages, it is usual in some fields to convolve maximumentropy restorations back to the fundamental resolutionof the data. In doing so, a convolving function that lackssome of the artifacts of the point-spread function is used.

IV. SOME APPLICATIONS

Maximum entropy image restoration is used in a num-ber of fields, including photographic, medical, and as-tronomical imaging. As concrete examples of maximumentropy restoration, we will consider two specific applica-tions from astronomy: the restoration of images from theHubble Space Telescope and from radio interferometricimaging. In both these subfields, maximum entropy im-age restoration, using the Gull and Daniell measure, hasfound considerable favor.

A. Hubble Space Telescope

Image restoration is used much less in optical astronomythan one might first expect. This is because the carefuldesign of optical instruments ensures that the point-spreadfunction achieved is relatively artifact-free. Additionally,the earth’s atmosphere is usually the main aberration inthe observing system, and the point-spread function in-troduced by the atmosphere is often known only in astatistical sense as the atmosphere is constantly fluctu-ating. Unless the image can be sampled at a high rate(≈100 Hz), the high spatial frequencies in the image arecompletely lost. Regardless of the telescope size, the res-olution achieved with a conventional system is approxi-mately that of an ideal 20-cm aperture. Although opticalobservatories are specifically built on high mountains to beabove much of the earth’s atmosphere and its aberratingeffect, diffraction-limited imaging can only be achievedby placing a telescope in space.∗ Such was the intentionof the Hubble Space Telescope.

The Hubble is a 2.3-m aperture telescope in earth or-bit that operates at infrared, optical, and ultraviolet wave-lengths. Rather than producing diffraction-limited images,soon after its launch in 1990 it was discovered to have asignificant spherical aberration in the main reflector of thetelescope. This was traced back to an error in the manu-facture and testing. Fortunately, the Hubble was designedto be serviced by the Space Shuttle, and in 1993 correc-tor optics were installed to eliminate the aberration. Inthe intervening years, however, much effort was placedin understanding the aberration and in deconvolving theresultant images.

The spherical aberration caused the point-spread func-tion to cover a region of 5 arc seconds in diameter (an arcsecond is 1/3600th of a degree), with only 15% of the lightfalling in the central 0.1 arc second core. The telescope

∗Increasingly, the techniques of adaptive optics are making this state-ment false. Adaptive optics works by measuring the aberrating effect ofthe atmosphere in real-time, and deforming the imaging system in sucha way as to compensate for these aberrations.




FIGURE 3 An image from the Hubble Space Telescope, showingthe effects of spherical aberration. The point-spread function of thetelescope is quite apparent around the two bright stars. The spotspeppering the image result from cosmic ray hits or bad pixels inthe detector.

design had intended that approximately 80% of the lightshould have fallen in this core. A significant extra com-plication was that the point-spread function varied withtime, source position on an image, and observing wave-length. Time restrictions often prevented high-quality ob-servations to determine the point-spred function. Attemptsto model (and so predict) the point-spread function werenever entirely satisfactory, and so direct measurement ofthis function (where possible) gave best results in imagerestoration processes. To compound the problems, imageswere often badly undersampled, and detector nonlinear-ities could be problematic (the Hubble had not been de-signed with image restoration in mind). Figure 3 shows animage from the Hubble. The halos and tentacle-like side-lobes around the two brightest stars are quite apparent.

The maximum entropy method was one of several tech-niques that were used to restore the Hubble images. How-ever, all techniques were hampered by lack of completeknowledge of the point-spread function. Using a point-spread function that included errors (either because ofnoise in a measured point-spread function, or model-ing imperfections in predicted point-spread function) fur-ther adds to the ill-posed nature of the restoration prob-lem. Although the modulation transfer function tendednot to be zero-valued (at least not as severely as in theradio interferometry case described below), this was ofonly small comfort when imaging weak objects, as the

loss in senstivity over the design specification was quitesubstantial.

To restore large fields, the problem of the position-dependent point-spread function had to be addressed.Because of time constraints, the point-spread functioncould generally not be measured as a function of position.Instead, the restorations had to rely upon point-spreadfunctions predicted by models. By segmenting the Hubbleimages into a large number of subimages, each subimagecould then be deconvolved using a point-spread functionthat was assumed to be position-independent in thisregion.

An important issue in the restoration process is photo-metric linearity—the ability of the restoration techniqueto maintain a linear relationship between the brightnessof a star and the response. Unfortunately, the biases inmaximum entropy methods make photometric linearity adifficult proposition.

B. Radio Interferometric Image Restoration

There are two main forms of imaging used in radio as-tronomy: single dish telescopes, which form images byscanning a single antenna across the sky, and radio inter-ferometric arrays. An interferometric array consists of anumber of antennas, with the outputs of all antennas beingbrought back to a central site. The signal from each an-tenna is then cross correlated with all the other antennas.This cross correlation of each pair (which is a complex-valued quantity) is a sample of the Fourier transform ofthe sky intensity distribution. The Fourier coordinate of thesample is the projection onto the plane of the sky, at thesource, of the position vector from one antenna to the other.As the earth rotates, this geometry changes, and so differ-ent Fourier samples are measured. For N antennas, thereare potentially N (N − 1)/2 different antenna pairs, andso this many different simultaneous measurements of theFourier plane. By using many antennas, allowing for earthrotation and possibly using physical reconfiguration of theantenna array, many different measurements of the Fouriertransform of the image can be collected. When complete,these data can be Fourier transformed to produce an image.If the sampling of the Fourier plane is complete, then theresultant image would be perfect. However, getting com-plete Fourier coverage is infeasible: the number of anten-nas clearly will be finite, and available observing time willbe limited. In practice, no interferometric observation evercompletely samples the Fourier plane, and the samplingcan vary from quite good to very sparse. Two examples ofFourier plane sampling patterns and their correspondingpoint-spread functions are given in Fig. 4.

Given that an interferometer measures the data in theFourier domain, the modulation transfer function will




(a)

(b)

(c)

(d)

FIGURE 4 The Fourier plane sampling pattern (top) and the resulant point-spread functions (bottom) for an obser-vation with the Very large Array (near Socorro, New Mexico). The first sampling pattern corresponds to a very briefobservation (a so-called snapshot). The second corresponds to a 6-hr observation, where the earth’s rotation hasbeen used to improve the sampling pattern in the Fourier plane.

simply have a value of 1 where a sample is measured,and a value of 0 otherwise.∗ Consequently, the modulation

∗Strictly, an extra weight is often applied to the Fourier samples beforetransforming them, and so the value of the modulation transfer functionwill not be 1, but the value of this weight. The weights are chosen in a waythat is a compromise between good sensitivity and a clean point-spreadfunction.

transfer function and the point-spread function for an inter-ferometric observation are well defined. Radio interferom-etry produces a classical image restoration problem, wherelarge parts of the modulation transfer function are zero-valued. Consequently, it is a very nonunique problem.

The point-spread functions in radio interferometry dif-fer from those in many imaging applications. First, the




point-spread function is both positive- and negative-valued, and, secondly, there is typically a significant non-zero response to a point source across the entire image.The responses away from the main peak of the point-spread function are known as sidelobes (i.e., as distinctfrom the main lobe of the response). The sidelobes from astrong source, or the combined sidelobes from an extendedsource, make it impossible to analyze subtle features inthe raw image (the raw image being that formed by sim-ply transforming the Fourier data). Image restoration hasbecome an integral part of radio interferometry. Ratherdescriptively, radio astronomers talk of the raw image asbeing “dirty,” and the process of restoring (or deconvolv-ing) this image as “cleaning.”∗

As with optical astronomy, bias of the maximum en-tropy solution can be problematic in blank regions of thesky. The bias tends to create an artificial plateau of emis-

∗In interferometry, the term clean is used both as a generic termmeaning to restore an image, and as a particular algorithm (introducedby Hogbom) which implements such as restoration.

(a) (b)

FIGURE 5 Images of the so-called Vela-X region formed by a radio interferometric observation at 20-cm wavelength.This image uses 35 pointings to form an image much bigger than the field-of-view of the telescope. The left and rightpanels are before and after restoration (using a Gull and Daniel maximum entropy algorithm). Single-dish data wereincluded in the restoration process.

sion. Although this is most noticeable in low-sensitivityimages, the bias exists (but in a more subtle form) evenwhen the sensitivity is very good. Deconvolving pointsources is also problematic with maximum entropy al-gorithms, particularly when the point source lies on top ofa plateau of emission.

A significant problem in interferometry is that it is notpossible to measure the smallest spatial frequencies—these are inaccessible because the antennas physically can-not get closer than one diameter apart. Thus, the integratedflux of a source cannot be measured (it corresponds to ameasurement at the origin of the Fourier plane), nor canlarge-scale structure. An alternative way of thinking ofthe same problem is to recognize that the field-of-view ofan observation (or pointing of the telescope) is fixed bythe antenna size. It is not possible to accurately measurestructure with a scale size comparable or larger than thisfield-of-view.

Radio astronomers have solved this problem by using atechnique known as mosaicing. Mosaicing is the practiceof combining the data from many pointings of adjacent




parts of the sky to form a single image. In principle, mo-saicing allows spatial frequencies down to just above 0 tobe recovered. Maximum entropy image restoration is eas-ily generalized to handle a joint restoration of the mosaicdata. The data from the different pointings simply consti-tute added constraints to be included in the entropy maxi-mization process. Modeling of the differing fields-of-viewand point-spread functions of the various pointings arereadily handled.

Even with mosaicing, it is still not possible to mea-sure the sample at the origin of the Fourier plane withan interferometer. The interferometer data must be aug-mented with single-dish observations (single-dish datameasures all spatial frequencies up to the dish diame-ter). Again, using a maximum entropy approach, combin-ing single-dish and interferometer data together is quitenatural and straightforward—the single-dish data is yetmore data constraints. Figure 5 gives an example of a mo-saiced observation that includes single-dish data. Whereasthe restoration shown in Fig. 5 is plainly far superior tothe dirty image, one of the weaknesses is apparent inthe strong point source to the south: maximum entropyhas failed to completely remove the sidelobes from thissource. The data does not rule out this source havingrings around it, although physically such a structure isimplausible.

V. CLOSING REMARKS

Nonlinear approaches to image restoration have proven tobe far superior to classical linear approaches. The max-imum entropy approach, in particular, has proven to bevery flexible in allowing a wide and complex variety ofdata and constraints to be used in the restoration process.The maximum entropy method, however, is not without

shortcomings. The biased nature of the solution, in partic-ular, is problematic in a number of applications.

Ideally an image restoration technique will deliver animage that is consistent with available data and constraints(e.g., positivity), and which is free of obvious artifacts.Any technique that achieves this should be taken seriously,regardless of whether it is based on an ad hoc procedure orjustified by a formalism such as maximum entropy. It is thedata, ultimately, that must drive a restoration process. Inanalyzing the solution to any ill-posed problem, it is impor-tant to differentiate between those characteristics dicatatedby the data, and those that are dependent on the solutiontechnique. Any physically implausible feature that is notrequired by the data should be ignored.


IMAGE PROCESSING • IMAGING OPTICS • IMAGING

THROUGH THE ATMOSPHERE • OPTICAL INFORMATION

PROCESSING • SMART PIXELS • SOLID-STATE IMAG-ING DEVICES • STATISTICS, BAYESIAN • TELESCOPES,OPTICAL

BIBLIOGRAPHY

Taylor, G. B., Carilli, C. L., Perley, R. A., eds. (1999). “Synthesis Imagingin Radio Astronomy II,” Astronomy Society of the Pacific ConferenceSeries, Vol. 180.

Jansson, P. A., ed. (1996). “Deconvolution of Images and Spectra,”Academic Press, San Diego.

Hanisch, R. J., and White, R. L., ed. (1994). The Restoration of HSTImages and Spectra—II, Proceedings of a workshop held at the SpaceTelescope Science Institute (http://www.stsci.edu/stsci/meetings/irw).

Sivia, D. S. (1996). “Data Analysis: A Bayesian Tutorial,” Oxford Sci-ence Publications, Oxford.

Wu, N. (1997). “The Maximum Entropy Method,” Springer Series inInformation Sciences, 32, Springer-Verlag, New York.

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Encyclopedia of Physical Science and Technology En007C-338 June 30, 2001 15:49

Infrared AstronomyRodger I. ThompsonUniversity of Arizona

I. Infrared BandsII. Infrared ObservationsIII. Techniques for Observing Infrared RadiationIV. Infrared Astronomical InstrumentsV. Ground-Based Infrared Astronomy

VI. Space Infrared AstronomyVII. High-Altitude Infrared Astronomy

VIII. SurveysIX. Future

GLOSSARY

Blackbody An object that is a perfect absorber and emit-ter of electromagnetic radiation at all wavelengths.

Diffraction limit The smallest image possible for a tele-scope observing a point-like object such as a star.The larger the telescope the smaller the angular sizeof the image. Without adaptive optics, ground-basedtelescopes larger than about 12 inches cannot achievediffraction-limited imaging due to distortions causedby the earth’s atmosphere.

Dewar A container for very cold material or cryo-gens such as liquid nitrogen or helium. The dewarusually contains both the cryogen and the detectorsystem.

Infrared bands Spectral regions, usually defined by at-mospheric transmission, where the brightness of theinfrared flux of an astronomical object is measured.

Jansky A unit of flux measurement equal to 10−26 wattsm−2 Hz−1.

Kelvin (K) A unit of temperature with increments equalto centigrade units but with 0◦ at absolute 0; 0◦C is273.15◦K.

Luminosity The total amount of power emitted by anastronomical object. The luminosity of the sun is ap-proximately 4 × 1033 ergs s−1.

Magnitude A logarithmic system expressing the bright-ness of an astronomical object. The larger the magni-tude, the fainter the object.

Spectral classification A system of classifying stars bytheir temperature. The range of spectral classificationsgoes as O, B, A, F, G, K, M, and recently added L.The hottest stars are O stars and the coolest L. Eachtemperature is also generally divided into subclasses,which depend on the luminosity of the star.

INFRARED ASTRONOMY encompasses astronomicalobservations in the spectral region from 1 µm to 1 mm, afactor of 1000 in wavelength. Optical astronomers often

771

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772 Infrared Astronomy

declare the region from 7000 A to 1 µm as the near in-frared; however, most infrared astronomers define the nearinfrared as the spectral region between 1 and 5 µm. Themidinfrared includes the region between 5 and approxi-mately 100 µm, and the region from 100 µm to 1 mm isdeclared the far infrared region. The region between about400 µm to 1 mm is also often referred to as the submil-limeter region by radio astronomers. The divisions histori-cally derived from both atmospheric windows and detectortypes. In the modern world of space infrared astronomy,the boundaries between the definitions are quite blurred,with many detector types covering more than one infraredregion. As we will see as this chapter progresses, observa-tions in the near infrared region are predominantly of theintrinsic radiation of an astronomical object, whereas ob-servations in the mid- and far infrared region are predomi-nantly of reradiated emission, where the intrinsic radiationof an object has been absorbed by dust and re-emitted atinfrared wavelengths.

The decade of the 1990s witnessed a phenomenalgrowth in the capabilities of infrared astronomy with theintroduction of large-format detector arrays covering alarge spectral band of the infrared region. At this timeonly the far infrared utilizes single detectors or smallhand-crafted arrays. At the same time the sensitivity ofthe array detectors has increased, with each pixel of thecurrent detector arrays being far more sensitive than anyof the previous single detectors.

I. INFRARED BANDS

Ground-based infrared observations must be conductedin the wavelength regions where the earth’s atmosphereis transparent to infrared radiation. These transmissionbands generally define the common photometric bandsused by infrared astronomers. Harold Johnson who alsodefined the ultraviolet, blue, visible (UBV) photometricsystem for visible wavelengths first defined the near in-frared bands of J, K, and L. Table I gives the commoninfrared photometric bands in use today. Note that thereare subtle differences in the exact definition of the bands.

TABLE I Common Infrared Photometric Bands

Band designation Wavelength range

J 1.1–1.4

H 1.5–1.8

K 2.0–2.4

L 3.5–4.5

M 4.4–5.0

N 8.0–12.6

Q 16.5–23.0

Commonly used systems are the Johnson system, theArizona system, and the Caltech system. For extremelyaccurate work it is important to know what system is be-ing utilized. Some of these bands have alternative filtersdesignated by a prime such as K′ that are designed to re-duce the thermal emission inside the band by narrowingthe spectral range to only the highest transmission regions.The longer wavelength filters that define the M, N, and Qregion are often tuned to the expected spectral transmis-sion for a particular observatory. Observatories at veryhigh and dry locations may be able to use broader filterranges than observatories at less favorable locations.

The intensity of the detected radiation is often expressedin magnitudes, units that are peculiar to astronomy. Mag-nitudes are a logarithmic unit. The flux of an object in aunit such as ergs cm−2 sec−1 is given by

F = C × 10−mag/2 , (1.1)

where C is a constant defined for each band and mag isthe astronomical magnitude. The value of C varies withthe magnitude system even for a given band, so all re-ported values should be checked to see which systemis being used. As is evidenced by Eq. (1), the largerthe magnitude the fainter the object. In one system ofmagnitudes the observed flux from the star Vega de-fines zero magnitude in each band. Another system ofmagnitudes called the Ab magnitude defines a flux of3.6 × 10−20 ergs cm−2 sec−1Hz−1 as zero magnitude. It isalso common in infrared astronomy to express the flux inthe more physical units of Janskys borrowed from radioastronomy. One Jansky is 10−26 watts m−2 hz−1.

All astronomical objects emit infrared radiation. In fact,the peak of the integrated light from all of the stars in anormal galaxy is near a wavelength of 1 µm. The amountof infrared radiation emitted by a star, planet, or other as-tronomical object is determined by its temperature, theblackbody or Planck curve, and its emissivity at eachwavelength, as given in Eq. (1.2).

F(λ) = ε(λ)B(λ), (1.2)

In Eq. 1.2, F(λ) is the flux as a function of wavelengthλ, ε(λ) is the emissivity and B(λ, T ) is the Planck func-tion. Figure 1 shows the Planck function for two tempera-tures, 3000 K and 2500 K. 3000 K is a typical temperatureof a late K star, the stellar type that generally dominatesthe spectrum of galaxies. Note that as the temperature de-creases the peak wavelength shifts to longer wavelengthsand the amount of emission decreases. It is important tonote that the lower temperature Planck curve falls be-low the higher temperature curve at all wavelengths. ThePlanck curves of various temperatures are nested curvesthat do not cross each other.

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Infrared Astronomy 773

FIGURE 1 The blackbody spectrum at two different temperatures.

II. INFRARED OBSERVATIONS

There are some objects that radiate predominantly by in-frared light and in fact are not detectable at the shorteroptical wavelengths. Historically, infrared astronomy hasconcentrated on these types of objects, but recently nearand midinfrared observations are increasingly studyingobjects that traditionally have been the study of opticalastronomy.

A. Predominantly Infrared Objects

An object may radiate predominantly in the infrared forseveral reasons. It is in fact these reasons that make in-frared astronomy essential for a complete understandingof an object’s physics.

1. Objects Affected by Interstellar Dust

Interstellar dust is a ubiquitous component of our galaxyand most other galaxies. Extinction by interstellar dust isoften called “reddening” since the dust is far more effi-cient at absorbing and scattering blue light than red orinfrared light. We see this same phenomenon in terres-

trial sunsets. The dust in our atmosphere removes the bluelight much more efficiently, turning the sun into a redorb. In some cases the reddening can be so great as tomake objects undetectable at optical wavelengths whileremaining quite bright at infrared wavelengths. Primaryexamples of this are regions of star formation, which aregenerally obscured by large amounts of dust, and the cen-ter of our own and other galaxies. The central region ofour galaxy suffers about 100 magnitudes of extinction atoptical wavelengths but less than 10 magnitudes at thenear infrared wavelength of 2.2 µm. We will discuss thefate of the absorbed radiation in section II.A.3.

2. Objects That Radiate Infrared Light

Objects that radiate mainly at infrared wavelengths maydo so because of their low temperature by astronomicalstandards. Objects that fall in this category start with starsof spectral classifications of K or cooler extending downthe newly designated spectral classification of L. The sub-stellar classification of Brown Dwarf links stars generatingenergy by nucleosynthesis to planets such as the giant andterrestrial planets in our own solar system. The planetssuch as the earth radiate like blackbodies at their surface

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temperature modified by their emissivity, as described inEq. (1.1). At an average temperature of approximately300 K, the peak of the earth’s radiation lies at the mid-infrared wavelength of 10 µm. The peak wavelength inmicrometers of radiation is given simply by Wien’s Law,where the temperature T is in Kelvins.

λmax = 2898 µm (1.3)

3. Reradiated Light

Some objects are either surrounded by dust or are embed-ded in dense dust clouds. The dust may be directly asso-ciated with objects, such as the dust disks around youngstellar objects or the ejected dust clouds in late-type gi-ant or supergiant stars. Examples of embedded objects areclusters of newly formed stars in star formation regions,more evolved giant and supergiant stars such as infrared(OH/IR) stars or the central stars and perhaps central blackhole of a galaxy. In either case the nearby dust is heatedby the central object and reradiates the absorbed energyat mid- and far infrared wavelengths. In general, the tem-perature of the dust runs from a few 100s to a few 10s ofdegrees. The approximate maximum temperature of dustbefore it is destroyed is 1500 K. Equation (1.2) shows that

FIGURE 2 The infrared spectrum of M82 by D. Lutz et al. PAH, polycyclic aromatic hydrocarbons; ISO, InfraredSpace Observatory.Source: Lutz, D., et al., “Probing starbursts with ISO mid-IR spectroscopy,” in Extragalactic Astronomy in the Infrared,MPI fur extraterrestrische Physik.

even at this temperature the maximum emission wave-length is in the infrared range. The amount of reradiatedemission is equal to the amount of light absorbed by thedust, as described in section II.A.1.

The InfraRed Astronomical Satellite (IRAS) descri-bed in section VI.B found that many galaxies have mostof their starlight absorbed by dust and reradiated at mid-and far infrared wavelengths. Follow-up observations bythe Infrared Space Observation (ISO) (section VI.D) mea-sured the midinfrared spectra of many of these galaxies.Figure 2 shows the spectrum of a galaxy, M82, known tobe producing stars at a greatly accelerated rate. Galaxiesof this type are often designated as starburst galaxies.

The continuum emission in this spectrum is due to ther-mal emission from hot dust that has been heated by absorb-ing starlight. The sharp emission lines are due to radiationfrom various atoms and atomic ions. Atomic designationswith square brackets such as [NeII] indicate the emissionis due to a forbidden transition. A forbidden transition is atransition via the atom’s electronic quadrapole moment ormagnetic dipole moment rather than the electronic dipolemoment. The broader emission features designated byPAH (polycylic aromatic hydrocarbons) are emission bydust components. One of the major discoveries with ISOspectroscopy has been that these PAH emission features

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appear to be ubiquitous in the spectra of galaxies withsignificant starburst activity. Also note the broad absorp-tion feature near 10-µm designated silicates. This is avery commonly observed feature in the spectrum of dust-emitting objects. It indicates there is a solid-state siliconoxygen bond in the dust material. This is similar to themineral olivine found on earth.

4. Objects That Are Red Shifted

Objects such as galaxies can have their observed radia-tion be predominantly at infrared wavelengths due to theredshift caused by the expansion of the universe. Beforethe advent of modern infrared array detectors, this wasnot a normally observed class of objects due to the lackof sensitivity in previous detectors. The redshift of lightfrom distant objects is often described as a Doppler shiftof light due to the high recession speed of distant objects.This is actually not a correct interpretation. The redshiftis due to the expansion of the universe. When we observevery distant objects we see them as they were a long timeago. This time is simply the time it takes for the emittedlight to travel from the object to us. In some cases thetime is so long that we are seeing the universe when it wasmuch smaller that it is now. If the galaxy or object emittedradiation with a wavelength λ at that early time, then thewavelength of the emitted radiation has expanded alongwith the universe to a longer or redder wavelength by thetime we receive it. We call this expansion of wavelengththe redshift and give it a quantitative name z defined by

λobser ved = (1 + z)λemitted . (1.4)

This simply states that the universe at the time of obser-vation is 1 + z times bigger than the universe was at thetime the light was emitted. Since most galaxies are intrin-sically red to begin with, very distant galaxies have mostof their radiation in the infrared region due to the redshift.This makes the infrared spectral region very critical in thestudy of the early universe.

A second aspect of the universe makes the infrared spec-tral region important for high redshift observations. Hy-drogen gas in a galaxy and in the intergalactic mediumabsorbs all of the starlight at wavelengths shorter than912 A. In fact, for high redshift objects the intergalacticgas absorbs almost all of the light shorter than the Lymanα line at 1215 A. The absorption due to the intergalacticgas clouds is called the Lyman α forest. The absorptiondue to the Lyman α forest is so strong that for objectsat a redshift of 4 or more no light with rest wavelengthsshorter than 1215 A reaches the earth. At a redshift of7, the 1215 A light is shifted to a wavelength of almost1 µm. This means that for objects with redshifts greater

FIGURE 3 The near infrared view of part of the Northern HubbleDeep Field.Source: R. Thompson, NASA.

than about 7, all of the light that reaches earth is in theinfrared or longer spectral region and thus can only beobserved at infrared and radio wavelengths.

At this time the majority of near infrared observationsof very distant galaxies have been carried out either withlarge ground-based telescopes or with the NICMOS in-strument on the Hubble Space Telescope (HST) (describedin section IV.A). Figure 3 shows a region of sky observedvery deeply with the near infrared camera and muliobjectspectrometer (NICMOS) that contains the most distant ob-jects observed to date. This is in a part of the sky called theNorthern Hubble Deep Field that has been observed verydeeply at optical wavelengths with HST as well. Sincethe NICMOS images were only in two bands centered on1.1 and 1.6 µm, a third band was added, which is a bandfrom previous Wide Field and Planetary Camera 2 obser-vations at 0.606 µm. The 1.6-, 1.1-, and 0.606-µm imagesare combined as red, green, and blue to form a full-colorpicture. It is evident by looking at Fig. 2 that most galax-ies are red, indicating more infrared than optical emission.Note that the only object in this image that is not a galaxyis the central bluish dot, which is an individual star in ourown galaxy. The expected launch of the Space InfraRedTelescope Facility (SIRTF) (section IV.C) in 2001 shouldprovide midinfrared observations of very distant objects.

Observations of distant objects at infrared wavelengthshas been deemed so important that NASA’s largest futureproject is dedicated to that mission. It is called the NextGeneration Space Telescope (NGST) and is scheduled tobe launched before 2010. A description of the current sta-tus of NGST is given in section IX.B.

5. Cosmic Background Radiation

Our universe started with an event called the Big Bang. Atthe moment of its creation the universe was an infinitesi-mally small point, called a singularity, that contained allof the matter and radiation. The radiation in the singularity

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was extremely hot and dense. Since that time the universehas expanded to its present size and the original radiationhas cooled to a temperature of approximately 2.7◦K. Ac-tually, the radiation has redshifted to much longer wave-lengths as explained in section (II.A.3). Radiation at thistemperature peaks in the radio region, but it also has asignificant far infrared component. The remnant big bangradiation is present throughout the universe and can beseen in all directions in the sky. It is called the cosmicbackground radiation and has been the subject of intensestudy recently. Much of this study has been stirred by thephenomenal success of the Cosmic Background Explorer(COBE) satellite (described in section IV.E). COBE oper-ated over a large wavelength region spanning the submil-limeter through the near infrared region. It first found thevery subtle differences in temperature at various points inthe sky that are the precursors of the density fluctuationsthat eventually grew into galaxies such as the one we livein. Current studies are attempting to detail these fluctu-ations to learn about the fundamental parameters of ouruniverse. Figure 4 shows a map of the sky with fluctu-ations found by COBE. The higher temperature regionsappear lighter in the map. This map contains about 1 yearof data from the differential microwave radiometer (DMR)instrument on COBE.

Very recently there have been two balloon-borne in-struments, Maxima and Boomerang, that have measuredsmaller pieces of the sky but at higher spatial resolution.These experiments have concentrated on how the spatialvariations of the background match to predictions madefrom various models of the universe. They are consistentwith a universe that is flat rather than curved and implythat most of the matter in the universe must be in a cur-rently unobservable form, which has the designation darkmatter.

The bottom of Fig. 4 shows another profound measure-ment by COBE. The far infrared absolute spectrophotome-ter (FIRAS) instrument on COBE measured the spectrumof the cosmic background radiation and found it to bean essentially perfect fit to a blackbody spectrum. Thesolid line in the figure is a theoretical perfect blackbodyspectrum and the squares are the measurements. Any cos-mological theory must be able to predict this remarkablyperfect fit. These two measurements are among the mostimportant observations ever made in infrared astronomy.

B. Normal Objects Studied in the Infrared

Infrared astronomy is no longer limited to those objectswhose main emission is in the infrared spectral region. In-frared studies are now carried out on objects to determinecharacteristics that are not visible at other wavelengths,are easier to determine at infrared wavelengths, or are cou-

pled with observations at other wavelengths to tell a morecomplete story about the object. This is particularly true inthe near infrared spectral region, where many studies pre-viously carried out predominantly in the optical spectralregion are now performed in the near infrared. Below arejust a very few examples of these types of observations.

1. Stellar Atmospheres

The infrared region offers some unique spectral featuresthat yield significant information about the compositionand conditions in stellar atmospheres. In particular, manymolecules such as carbon monoxide (CO) have strong ab-sorption features in the infrared due to vibration-rotationtransitions. The higher energy electronic transitions willoften lie at ultraviolet energies so that infrared observa-tion is the only practical way to study these molecules withground-based facilities. In cool stars there is also very littleradiation at ultraviolet wavelengths.

2. Molecular Hydrogen

Near infrared spectra and images have been particularlyfruitful in the observation of interstellar molecular hy-drogen. The strongest line is a quadrapole transition at2.12 µm first observed in a region of intense star forma-tion. Although it is possible to excite the line through ul-traviolet fluorescence, in most cases the excitation comesfrom shocks due to outflowing gas around young stars.Regions of high star formation, such as the Orion neb-ula where molecular hydrogen emission was first discov-ered, have extensive areas of intense emission. Molecu-lar hydrogen emission has also been observed in othergalaxies, particularly in galaxies with high star formationrates, which are often called starburst galaxies. Hydrogenmolecules lack a dipole moment, so there are no spectralfeatures in the visible wavelength region.

3. Stellar Radiation in Galaxies

Our optical view of galaxies, particularly of spiral galax-ies, is often biased by the youngest, most luminous, andmost massive stars. These stars so outshine their col-leagues at optical wavelengths that the actual distributionof stellar masses is difficult to observe. It is also the casethat the central regions or nuclei of spiral galaxies andvery active galaxies called AGNs are obscured by dust, asare many of the very active star forming regions. Exten-sion of our observations into the infrared gives us a muchbetter view of the actual distribution of stars in the galaxy.Mid- and far infrared studies also measure the amount ofoptical and ultraviolet light that is absorbed by dust inthe galaxy by observing the reradiated light described in

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FIGURE 4 The top figure shows the distribution of temperature fluctuations in the cosmic background radiation. Thebottom figure shows the exact match between the spectrum of the cosmic background radiation and a blackbodyspectrum. COBE, Cosmic Background Explorer; DMR, differential microwave radiometer.Source: Mather, J. C., and Boslough, J., “The Very First Light.” Basic Books, New York, 1996.

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section (II.A.2). In some cases most of the optical and ul-traviolet light is absorbed and the total power of the galaxycan only be measured by observations in the infrared.

4. Galaxy Morphology

A very detailed and extensive classification process hasbeen developed to characterize the shapes or morpholo-gies of galaxies. This has become increasingly complexto describe the very large range of the optical appear-ance of galaxies. It is now being realized that this opticalclassification scheme may be very influenced by the dis-tribution of dust and extremely luminous stars in a galaxyrather than by the actual distribution of stars. Near in-frared images of galaxies generally show a much simplerand smoother structure which has led some morpholo-gists to suggest that our classification process be revisedand based on near infrared rather than optical images ofgalaxies. This was impractical in the past due to the limi-tations of infrared imaging mentioned at the beginning ofthis chapter. The presence of large format infrared cam-eras now makes such a change fairly easy in practice ifnot in preference.

III. TECHNIQUES FOR OBSERVINGINFRARED RADIATION

Since the infrared region spans a factor of 1000 in wave-length, it is not surprising that there are several detectortechnologies needed to cover the entire infrared spectrum.Detector technology is changing fast, and a thorough dis-cussion is impossible in this limited space. The followingis a brief summary of some of the major technologies. Al-though in the last decade single-detector elements wereemployed for astronomical observations, that is rarelythe case today. Most detectors are now arrays except forsubmillimeter receivers and bolometers, although thereare now arrays containing a small number of individualbolometers.

A. Detector Arrays

Optical astronomy has long used large-format detector ar-rays with most of the arrays employing the charge-coupleddevice (CCD) technology. Unfortunately, the almost uni-versal material for CCDs, silicon, is not a good infrareddetector. There have been some devices that employed in-frared detectors on top of CCDs, but these have generallybeen abandoned in favor of multiplexed direct readout de-vices. These arrays employ a large-format detector arraythat is indium bump bonded to a multiplexer (or mux)using silicon technology, as shown in Fig. 5.

Each detector pixel transfers charge to a multiplexercell that contains a complete readout circuit. The signalfrom this circuit is sent to the output amplifiers via shiftregisters. An early version of the circuit for the detectionand transfer of charge deposited by the radiation is shownFig. 6.

The detector is represented by the diode symbol at thelower right of the circuit diagram just above the wordsDET SUB. The transistor circuit with the labels M1through M4 are a set of switches that isolate the detectorwhen observing, allow the voltage to be sensed when beingread out, and reset the voltage to zero after the observationis finished. The voltage is due to the charge collected onthe capacitance of the detector, which is the signal charge.The rest of the circuit contains the shift registers for ad-dressing a particular pixel and the output amplifier thatamplifies the detected voltage for measurement, but sub-sequent readout electronics are not shown.

Unlike CCDs the signal charge is not transferred fromcell to cell. This has the general advantage of nondestruc-tive readouts, which allows the signal to be monitored asit is built up. Unwanted events such as cosmic ray hits canthen be detected and removed from the final signal. Wewill now take a quick look at some detector technologiesin the various wavelength regime.

1. Near Infrared (1–5 µm)

There are two major detector materials in the near infrared,mercury cadmium telluride (Hg:Cd:Te), and indium anti-mony (In:Sb), although some lower efficiency detectorarrays have been made with platinum silicide (PtSi). Thiswavelength region was the first to utilize arrays and isthe most developed to date. Part of this has been due tothe development in the early 1990s of Hg:Cd:Te arraysfor the NICMOS on the HST. The NICMOS arrays con-tained 256 × 256 elements. Currently, 2048 × 2048 arraysof both Hg:Cd:Te and In:Sb are under development.

The advantage of Hg:Cd:Te good operation at liquidnitrogen temperatures (77 K), whereas In:Sb generallyrequires operation at liquid helium temperatures (4 K).In general, however, In:Sb has a lower dark current thanHg:Cd:Te arrays that can operate out to 5 µm. Hg:Cd:Tearrays can tune their long wavelength cut-offs by varyingthe amount of mercury in the detector. The shorter thecut-off wavelength, the lower the dark current.

2. Midinfrared (8–30 µm)

The wavelength region between 5 and 8 µm is blockedfrom ground-based observation due to atmospheric ab-sorption. Therefore not much attention has been paid tothat particular region, although it is available via space

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FIGURE 5 The structure of a hybrid detector array and multiplexer.

observation, and some space observatories (ISO andCOBE) have made observations there. The major detec-tor technologies in this region are the blocked impurityband (BIB) and impurity band conductor (IBC) detectors.These detectors have an additional layer of pure undopedmaterial between the detection impurity or doped materialand the electrical contacts. This layer increases the resis-tance and also the sensitivity of the detector. Examples ofcurrent detector types are silicon arsenic (Si:As) in boththe BIB and IBC format and silicon antimony (Si:Sb) BIBdetectors. All of these detectors now exist in array config-urations. In addition, silicon gallium (Si:Ga) operating ina photoconductive mode is operating in a ground-basedinfrared camera. The multi band imaging photometer(MIPS) instrument on SIRTF will employ germanium gal-lium (Ge:Ga) array detectors out to a wavelength of 70µm.

3. Far Infrared

The same detector material (Ge:Ga) used in midinfraredarrays can also be utilized for small arrays in the far in-frared region. It was discovered that if a mechanical stressis placed on the detector material, it increased its wave-

length response to significantly longer wavelengths. Ingeneral the requirement of applying mechanical stress haslimited these units to small arrays only two pixels wide inone direction.

B. Bolometers

As its name implies, a bolometer is a detector designed forbolometric measurements or measurements that are sensi-tive to all wavelengths. In practice, however, the incomingradiation is limited to a given spectral region by a filter inthe optical system. The thermometer used by Herschel tofirst detect near infrared radiation from the sun was a typeof bolometer. The modern version is an individual Ge:Gaor doped Si detector suspended in a small enclosure. Thedetector is coated with material that is highly absorbingat the wavelengths of interest. The incident radiation ab-sorbed by the detector raises its temperature. Since theelectrical resistance of a bolometer is temperature sensi-tive, there is a change in the current carried by the thinsuspending wires, which in turn produces a signal. Thetime duration of the signal is determined by the rate atwhich heat leaks from the bolometer. This is generally

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FIGURE 6 An electrical schematic of the unit cell for each pixel along with the shift registers and output amplifier.

controlled by the mounting system and is tuned to the ex-pected observing conditions. Most far infrared detectionsystems are differential systems that compare the radia-tion from a source with the signal from a nearby pieceof sky by moving the telescope between the two areas.The frequency of this movement or nodding will set thefrequency requirements of the bolometer.

Bolometers have been produced in small arrays by sim-ply mechanically placing them at the foci of an array offeed horns designed to channel far infrared radiation tothem. Since bolometers are not as sensitive as other de-tectors and they are difficult to produce in large arrays,they are generally only used for far infrared astronomywhere other detectors are not sensitive. They are operatedat temperatures of 1 to 2 K or below in dewars containingliquid helium.

C. Submillimeter Astronomy

Submillimeter astronomy occupies the boundary betweenradio and infrared astronomy. As its name implies, thesubmillimeter wavelength region is at wavelengths lessthan 1 mm to about 0.3 mm or 300 µm. Most current sub-millimeter observations are carried out with special high-precision radio antennas that have smoother and more ac-curate shapes than antennas used at longer wavelengths.

Detector systems for submillimeter observations can beeither very high-frequency radio detection systems orbolometer-based systems such as described in the previoussection. Observations in this wavelength region, particu-larly at 850 µm, have been very important for detectingstar formation in galaxies that has been hidden by largeamounts of dust. This work has been pioneered by the sub-millimeter common user bolometer array (SCUBA) on theJames Clerk Maxwell Telescope. This telescope is on thesummit of Mauna Kea, Hawaii, one of the highest anddriest sites in the world. Even in the windows of transmis-sion for submillimeter radiation the attenuation of signalby water vapor in the earth’s atmosphere is quite high. Forthis reason there are only a few sites around the world thatattempt ground-based submillimeter astronomy.

IV. INFRARED ASTRONOMICALINSTRUMENTS

The existence of excellent infrared detectors solves onlypart of the problem of producing excellent infrared as-tronomical observations. The other part is producinghigh-quality infrared instruments to place the image orspectrum on the array. Although there are many types ofinstruments for measuring aspects of the radiation, such

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as polarization, we will concentrate in this chapter on twotypes of instruments, cameras and spectrometers.

A. Cameras

Infrared astronomical cameras relay the image formed bythe telescope onto the detector array with the proper mag-nification for the desired observation. In this way theyare no different from the cameras used in optical obser-vations. The main difference in infrared cameras comesin the baffling and pupil stop requirements. Baffling isused to prevent stray light from contaminating the image,and pupil stops ensure that only light coming from thedirection of the primary mirror falls on the detector. Theproblem with infrared cameras is that at the temperaturesencountered in ground-based telescopes the baffles andpupil stops themselves become sources of contaminatinginfrared radiation. This problem is solved by placing thebaffles and pupil stops inside the cold dewar along withthe detector. Infrared cameras then have the requirementthat a new pupil and image must be created inside the coldenvironment. A very simple schematic of this arrangementis shown in Fig. 7.

This arrangement refocuses the telescope focal planeonto the detector array to produce the image at the desiredmagnification. It also places an image of the telescope’sprimary mirror at the location of the cold pupil, where acold stop masks out the warm areas around the primarymirror such as the mirror cell. The cold stop should alsomask out the primary hole and perhaps the spiders thathold the secondary as they are also sources of stray in-frared radiation. The transparent window is required totransmit the light into the dewar while maintaining the

FIGURE 7 A simplified optical arrangement for an infrared camera.

vacuum inside the dewar. The window itself is sometimesoptically figured to be part of the reimaging system. Thereimager is shown as a simple lens, but in practice infraredoptics are generally mirrors rather lenses. This avoidsany chromatic effects and utilizes the high reflectivitiesthat can be achieved at infrared wavelengths. Since thebackground radiation is often far more intense than theobserved source, careful baffling and placement of pupilstops is essential for good performance. Most cameras uti-lize a set of filters to take images in different wavelengthbands. These filters must also be cold so that they do notradiate energy in the wavelengths they were designed toblock. If mechanically possible, the best location for thefilters is at the cold pupil spot. When located at the pupil,any spatial variations in the filters due to optical flaws orother reasons get spread out over the whole detector arrayrather than being imaged onto the detector, where they canbe misinterpreted as spatial features in the image.

B. Spectrometers

Modern infrared spectrometers are almost universally dis-persive spectrometers utilizing a dispersive element, suchas a grating, grism, or prism. A grism is simply a gratingand prism combined. Before the advent of good qualitydetector arrays, multiplexing instruments such as Fouriertransform spectrometers (FTSs) were often used since theycould observe spectra more efficiently with single detec-tors than scanning dispersive spectrometers that had tomeasure spectra one element at a time. Once arrays be-came available, dispersive spectrometers became the in-strument of choice because the amount of light fallingon a single pixel is much less than in an FTS. Since the

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photon noise is proportional to the number of photonsdetected, the dispersive spectrometer has a significantlybetter signal-to-noise ratio than a multiplexer such as anFTS. There are some applications where FTS systems dohave some advantages. An example is very high-resolutionsolar astronomy where the signal levels are so high thatsignal-to-noise considerations are secondary. In this casethe high-wavelength precision of an FTS is an advan-tage. In some specialized cases, Fabry–Perot spectrom-eters have been used. These spectrometers are useful formapping out emission lines over a large area. A typicaluse might be finding the velocity structure of molecularhydrogen emission in a star-forming region.

As with infrared cameras, proper baffling and pupilstops are essential. Besides the dispersive element, themain difference in spectroscopic instruments is the re-quirement that the beam be well collimated when it en-counters the disperser. Spectroscopic systems thereforegenerally have two main optical components. First thereis a collimator that produces a collimated beam for the dis-perser and then a camera that focuses the dispersed lightonto the detector array.

V. GROUND-BASEDINFRARED ASTRONOMY

The vast majority of infrared astronomical observationshave been made with ground-based telescopes. In generalthese are telescopes that have been primarily designedfor observations at optical wavelength, although more re-cently there have been telescopes built that are optimizedfor infrared observations. Most of the achievements listedin section II came from ground-based observations. Inthis section we will discuss some of the unique aspects ofground-based infrared observations.

A. Limitations Due to the Earth’s Atmosphere

Infrared observations from the ground encounter severalobstacles that are either absent or far less of a problem atoptical wavelengths. One of the major problems is block-age of a large portion of the infrared spectrum by theearth’s atmosphere. As discussed in section I, the posi-tions of the infrared bands are set by the transparent orsemitransparent wavelength regions in the atmosphere.Figure 8 shows the transparency of the earth’s atmosphereat both the altitude of the ground-based observatory onMauna Kea mountain in Hawaii and from the altitude ofa high-flying aircraft.

The atmospheric constituent that contributes the mostabsorption is water vapor. For this reason good infrared ob-servatories are located in high dry sites. Other atmospheric

gases such as carbon dioxide and methane also blocksome wavelengths. There is no way around these block-ages except to move the telescope to much higher regionswith airplanes, high-altitude balloons, or space craft.

At near infrared wavelengths, out to 2 µm, there is asevere problem from emission from the OH radical in ouratmosphere. OH radicals in an excited state are producedby the chemical reaction O3 + H → O2 + OH in the highearth’s atmosphere. The majority of this emission comesfrom altitudes much higher than the highest mountains,so it cannot be overcome by site location. The emissionis spectral line emission from the transitions of the OHmolecule, but the lines are very closely spaced so onlymoderately high-resolution spectroscopy can see regionsbetween the emission lines. The emission is also time andspatially variable, which complicates accurate subtractionof the emission from the observation. The sky bright-ness from OH emissions overwhelms all but the brightestsources at this wavelength.

At longer wavelengths, thermal emission from the at-mosphere becomes a problem. Even in the infrared obser-vational bands, the atmosphere is not completely transpar-ent. This means that the atmosphere emits infrared radia-tion that adds noise to the observations. Most observationswhere this is a problem compare images or spectra of thedesired source with images or spectra of a nearby regionof sky off the source to remove the background sky con-tribution. This method, however, cannot remove the noisedue to the photon statistics of the background emission.This noise is generally the largest contributor to the totalnoise of the measurement.

Another major problem is thermal emission from thetelescope itself and the instrument used to measure theinfrared signal. Objects at room temperature emit radia-tion throughout the infrared region, with a peak at 10 µm.The infrared detectors themselves are of course cooled tovery low temperatures. The infrared instrument itself is of-ten also cooled with the optical system contained inside aevacuated chamber called a dewar. The dewar is kept coldby adding a cryogenic fluid such as liquid nitrogen or liq-uid helium or by mechanical refrigerators. The telescopeitself cannot be cooled. If it were cooled then atmosphericwater vapor would condense on the mirrors and eventu-ally ice over if the temperature was lowered far enough.Infrared instruments compensate for the thermal emissionfrom the telescope by using optics that limit the detectorsfield of view to only the low emissivity telescope mirrorsthat reflect the observed radiation into the instrument.

B. New Large Telescopes

Infrared astronomy has received a substantial boost withthe advent of several new 8-m diameter or larger ground-based telescopes at high dry sites. These telescopes have

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FIGURE 8 The transparency of the earth’s atmosphere from a ground-based observatory and from a high-altitudeaircraft by E. Erickson.Source: Ericksen, E. F., SOFIA: Stratospheric observatory for infrared astronomy in next generation infrared spaceobservatory, in “Next Generation Infrared Space Observatory” (B. Burnel, Ed.), pp. 62. Kluwer Academic Publishers,The Netherlands (1992) with kind permission from Kluwer Academic Publishers.

more than four times the light-gathering power than theprevious 4-m class telescopes. When coupled with mod-ern detector arrays they are advancing the sensitivityof infrared observations. One area of infrared astron-omy where the new telescopes will be particularly ef-fective is infrared spectroscopy. With the new low-noiseand low-dark-current detectors, spectroscopic observa-tions are generally limited by the statistical noise of thegathered photons even at moderate resolution. Due toPoisson statistics, photon noise is equal to the squareroot of the number of photons detected. In this case thesignal-to-noise of the observation only increases as thesquare root of the observing time. This means that infraredspectroscopic observations on an 8-m telescope proceed16 times faster than on a 4-m telescope. This is an ex-tremely important advantage in executing follow-up spec-troscopic observations on sources originally imaged by theNICMOS instrument and to be observed by the SIRTFinstrument described in the section on space infraredastronomy.

C. Adaptive Optics

Recently there have been significant advances in correct-ing for the distortions caused by atmospheric seeing inground-based telescopes. The basic technique is to mea-sure the motion of the image or wave front with one op-tical system and then to adjust the optics in the imagingsystem to counteract the distortion. This can be done invarious ways, but the technique in general is termed adap-tive optics. The great significance to infrared astronomyof this technique is that the correction becomes progres-sively easier as the wavelength increases. There has beengreat success with this technique for images in the K bandat 2.2 µm.

The adaptive optics correction depends on having abright point source near the field of view to provide theinformation on the atmospheric distortion to the system.This source can be a bright astronomical source or an ar-tificial point source created by a laser beam. The require-ment for proximity is such that the measurement of the

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distortion occurs in the same region of the earth’s atmo-sphere that the light from the field of view passes through.The characteristic distance in the atmosphere that has com-mon distortion is referred to as Fried’s parameter. It is thisparameter that increases with wavelength, making correc-tion easier at longer wavelengths and increases the fieldof view that can be corrected.

One drawback for infrared astronomy has been thatthe image motion or wave-front detection systems havegenerally operated on visible light. This has limited thetechnique’s usefulness in regions highly obscured by dust,where bright visible light sources are hard to find. It alsomeans that the image corrections are not done at the samewavelength as the image. This can cause loss of accuracydue to the differences in the indices of refraction betweenthe visible and optical wavelengths. Use of infrared arraysin the image-motion systems can eliminate this problem.

The big gain of adaptive optics systems is that theycan concentrate a significant amount of light into thediffraction-limited point-spread function (PSF) of a largetelescope. This is very important for resolving objects suchas close binaries or the nuclei of merging galaxies. It isalso very important for infrared spectroscopy, where thesize of the spectrometer is proportional to the size of theimage.

The distribution of light in an image of a point ob-ject, such as a star, is called the PSF. The diffraction-limited PSF is a sharply peaked image that exploits thefull diameter of the telescope. The seeing-limited PSFis the spread-out image caused by the distortions in theearth’s atmosphere. The ratio of the light that is in thediffraction-limited peak of the PSF to the theoretical max-imum peak is called the Strehl ratio. Excellent adaptiveoptics systems can achieve a Strehl ratio of about 60%,which leaves 40% of the light in the seeing-limited PSF.This spread-out light can cause problems in some types ofobservations that call for very high accuracy. That is onereason why space infrared telescope systems and adaptiveoptic systems complement each other.

D. South Pole Observatory

The South Pole is a unique location for astronomy and in-frared astronomy in particular. Both pole regions have longperiods of darkness and the opportunity to track celestialobjects continuously. Only the South Pole, however, is onsolid land, which allows a stable observatory to be estab-lished. Even more importantly the South Pole is quite high.The combination of the high altitude and extremely coldtemperatures reduces the water vapor to very low levels.This means that the South Pole has the lowest attenua-tion of infrared and particularly of submillimeter radia-tion of any earth-based observatory. There are, of course,

some environmental drawbacks for all but the heartiest ofobservers.

VI. SPACE INFRARED ASTRONOMY

There have been relatively few infrared space missions,partly because, for wavelengths longer than about 2 µm,the whole telescope must be cooled to very low temper-atures to reduce infrared emission from the telescope it-self. This is quite costly and requires the use of cryogensthat limit the lifetime of the instrument or high-powerconsumption to provide refrigeration through mechanicalor thermoelectric coolers. Techniques for passive radia-tive cooling are under development. They require largesunshades and orbits other than low-earth orbits, whereblocking both the solar and terrestrial infrared emission isvery difficult.

The advantages of doing infrared astronomy in spaceare quite large. The absence of the earth’s atmosphereeliminates the image distortions, termed seeing, thatplagues ground-based observations. It also eliminates theinfrared emission from the atmosphere, which limits thesensitivity of ground-based telescopes. The opportunityof cooling the entire telescope, although costly as men-tioned above, again greatly improves the sensitivity ofspace-based telescopes. Finally, since many regions ofthe infrared spectral range are blocked by absorption inthe earth’s atmosphere, space missions offer the only wayto observe the entire infrared spectral range with no con-tamination by telluric absorption features.

A. Limitations of Space-Based Observations

Although vastly superior to ground-based observations,infrared observations from space are not completely back-ground free. The primary source of infrared backgroundradiation in space is reflection and emission by zodiacaldust. This is dust in our solar system that is distributedmainly in plane of the planets or zodiac. As shown inFig. 9, there are two minima in the background radiation,one at 3 µm and another at 400 µm.

The minimum at 3 µm is at the crossover point betweenreflected and emitted zodiacal radiation. At shorter wave-lengths the emission is dominated by reflected sunlight.At wavelengths longer than 3 µm, the main emission isthermal emission from the dust. The minimum at 400 µmis due to the fall off of the warmer emission from the zodi-acal dust and extrasolar dust, termed cirrus, and the shortwavelength falloff of the cosmic microwave background,which has a much colder temperature. These backgroundminima are very useful regions for the observation of faintsources such as distant galaxies.

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FIGURE 9 The emission spectrum as seen from space by Leinert et al. The O2 and OH airglow are terrestrialemissions and are not seen from space.Source: From Leinert, Ch. et al. Astron. Astrophys. Suppl. 127, 1 (1998).

Although there have been few space infrared missions,the missions carried out to date have proved quite success-ful. Due to the advantages of space infrared observations,there are also several missions in the planning stage. Wewill review a few of the major missions here.

B. InfraRed Astronomical Satellite

The IRAS was the first orbital space mission devotedsolely to observations at infrared wavelengths. The advan-tage of space observation are clearly demonstrated by not-ing that IRAS, with a diameter of only 60 cm, vastly out-performed ground-based observations with even the 5-mMt. Palomar observatory, the largest major observatory atthe time. IRAS, launched January 1983, surveyed the skyfor a little less than a year. Observations of approximately96% of the sky were made in broad photometric bands at12, 25, 60 and 100 µm, with an array of discrete Ge detec-tors. Its nearly polar orbit meant that in the survey modeit covered the sky in strips that overlapped at the equator

but had a significantly greater time of coverage near thepoles. IRAS also operated part of the time in a pointed setof observations on objects or regions of particular interest.

The IRAS focal plane (Fig. 10) contained column de-tectors arranged so that the centers of the detectors wereoffset from each other by a little less than the length ofthe detectors. The detectors were rectangles with the longdimension parallel to the column line, which was perpen-dicular to the scan direction. Each column had two lines ofdetectors and a filter for one of the four wavelength bands.As the satellite scanned along the sky, sources would passover the detectors producing a transient signal that re-peated in each detector at a rate set by the rate of scanthrough the sky. Since the detector centers were offset, asource would pass through different parts of each detec-tor as it ran down the column. Keeping track of the sig-nal strengths and which detectors responded as differentstrips of sky were observed gave additional spatial infor-mation in the direction perpendicular to the scan. IRASalso contained a low spectral resolution spectrometer that

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FIGURE 10 Above is a schematic of the InfraRed Astronomical Satellite focal plane. The different-sized rectanglesrepresent the detectors.

operated in the 7.7- to 22.6-µm region. This spectrometermeasured over 5000 sources with signal strengths greaterthan 10 Janskys.

IRAS established a then unprecedented database that isstill being utilized at the present time. Catalogs of bothextended and point sources were published from the sur-vey. A very significant finding from these catalogs was therealization that many galaxies have the majority of theirluminosity at mid- and far infrared wavelengths. IRASalso established that some stars that had been consideredquite normal, such as Vega, were actually surrounded bylarge clouds of dust that might be the building blocks forplanetary systems.

C. Cosmic Background Explorer

COBE has produced some of the most dramatic scientificachievements in infrared astronomy. COBE measured thespectral shape of the cosmic background and found it to bea perfect blackbody spectrum at a temperature of 2.37 K.COBE also made the first observations of structure in thedistribution of cosmic background radiation that are theprobable first step in changes that produced the galax-ies, stars, and planets we know today from the primordialsmooth distribution of matter produced by the Big Bang.

(See the discussion in section II.A.5.) COBE had threeinstruments for observing the background radiation: theDMR, the FIRAS, and the diffuse infrared backgroundexperiment (DIRBE).

The DMR experiment utilized techniques more com-mon to radio astronomy than infrared. The main part ofthe instrument consisted of sets of opposed antennas look-ing at different parts of the sky. These antennas lookedfor differential signals indicating different temperaturesat different locations. FIRAS was a version of the FTSdiscussed earlier. It compared the spectral shape of thecosmic background radiation against the spectral shapeof internal blackbody calibrators. The DIRBE instrumentwas more similar to standard infrared instruments than theother two COBE experiments. DIRBE used a suite of fourdifferent detector types to map out the sky at several in-frared wavelengths. This instrument has contributed veryimportant information on the contribution of various typesof astronomical objects to the total background radiationin the universe.

D. Infrared Space Observatory

The ISO was launched in November 1995. Its various in-struments operated over the wavelength range between 2.5

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Cryo-Telescope AssemblySpacecraft

Solar Panel

Solar Panel Shield

Spacecraft Shield

Spacecraft Bus

Low Gain Antennae

Telescope Barrel Baffle

Outer Shell

Low ThrustHelium Vent

Star TrackerAperture Shield

Helium Servicing Lines

Star Trackers &IRUs (Gyros)

Cold Gas Nozzles

High Gain Antennae

Observatory external configuration

FIGURE 11 Configuration of the Space InfraRed Telescope Facility spacecraft.

and 240 µm. With a primary mirror diameter of 60 cm,it was similar in size to IRAS but carried improved de-tectors and a more versatile instrument complement. ISOdiffered in its mission from IRAS. Instead of surveys asits main mission, ISO was designed primarily for pointed

FIGURE 12 Artist’s Concept of the Stratospheric Observatory forInfrared Astronomy.

observations of objects of interest. Like COBE and IRAS,ISO was cooled by cryogens in order to operate in themid- and far infrared bands. The liquid helium cryogenslasted until April 1998, providing an observing period ofabout 2 1

2 years. ISO was put into a highly elliptical or-bit that provided significant observing time at large dis-tances from the earth with data transmission to two groundstations. ISO was the first infrared space mission to of-fer observing opportunities to the entire community. Thefour instruments on the ISO mission were a combinationof cameras and spectrometers described below. This mis-sion also provided important information about the perfor-mance of some classes of infrared detectors in high radia-tion environments. In spite of the problems with some ofthe detectors, ISO was a highly successful mission whosedatabase is an important tool in astrophysics. Its spec-trometers demonstrated the richness of the mid- and farinfrared spectral region. We will discuss below the ISOinstruments.

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1. ISOPHOT

This instrument provided photometric, polarimetric, andspectrophotometry over the entire wavelength range ofISO. Small arrays of Si:Ga, Si:B, and Ge:Ga detectors alsoprovided limited imaging capabilities. The main role ofISOPHOT was to provide accurate photometry of sources.It included an internal chopper and several calibrationsources.

2. ISOCAM

ISOCAM provided the main imaging capability for themission. It was split into two channels. The short wave-length channel was sensitive between 2.5 and 5.5 µm, andthe long wavelength channel between 4 and 18 µm. Thesecameras provided imaging capability in several spectralregions that are inaccessible from the ground. The detec-tor arrays were 32 × 32 pixels of In:Sb and Si:Ga. Theshort wavelength In:Sb array was operated in a charge-integrating mode, which has since been superseded bymultiplexed readouts for much larger arrays. The longwavelength Si:Ga array was operated as a photoconduc-tor. ISOCAM provided diffraction-limited optical perfor-mance with several filter options.

3. Short Wavelength Spectrometer

The short wavelength spectrometer (SWS) covered thespectral range between 2.38 and 42.5 µm, with a spectralresolution ranging from 1000 to 2000. It also carried aFabry-Perot etalon to enhance the spectral resolution inthe 11.4 to 44.5-µm region. Fabry-Perot etalons pass ra-diation in a narrow wavelength range that is altered bychanging the spacing between the optical components. Acombination of In:Sb, Si:Ga, Si:As, Si:Sb, and Ge:Be lin-ear arrays provided the detectors for the large wavelengthrange covered by the instrument. Most of the arrays were1 × 12 pixels, but the Si:Sb and Ge:Be arrays were 1 × 2.The SWS detector arrays were found to be very sensitive tothe radiation environment encountered in space missions.

4. Long Wavelength Spectrometer

The long wavelength spectrometer (LWS) operates be-tween 43.0 and 196.9 µm. Coupled with the SWS it pro-vides continuous spectral coverage from 2.4 to 196.9 µm.This has been a great advantage in studying the emis-sion of objects such as active galactic nuclei and starburstgalaxies. The detector array is linear and consists of oneGe:Be, five unstressed Ge:Ga, and four stressed Ge:Gaphotoconductive detectors. Like SWS, LWS also carrieda Fabry-Perot etalon to increase the spectroscopic resolu-tion of the instrument.

E. Near Infrared Camera MultiobjectSpectrometer on the HubbleSpace Telescope

The NICMOS is an instrument on board the HST. Al-though HST is the largest current telescope in space, witha 2.4-m primary mirror, it is not a cooled telescope. Itsmirrors are maintained at a temperature of 18◦C or aboutroom temperature. For this reason, NICMOS limits itsobservations to wavelengths shorter than 2.5 µm. Obser-vations at wavelengths longer than 2 µm are somewhat de-graded by thermal emission from the telescope’s mirrors.At wavelengths shorter than 2 µm, the NICMOS sensitiv-ity is greater than the largest ground-based telescopes dueto the absence of the bright OH background (discussed insection IV). The absence of the earth’s atmosphere alsomeans that NICMOS can achieve very high spatial reso-lution over its entire field of view. This advantage is alsoenjoyed by the optical instruments on HST. NICMOS hasthree separate cameras for observations at various spatialresolutions. It also has the capability of performing po-larimetric and coronagraphic imaging and low-resolutionspectroscopy.

The NICMOS detectors were cooled with a large blockof solid nitrogen at 65 K, which sublimated away at theend of 1998. Revitalization of NICMOS with a mechan-ical cooling system is scheduled for late 2001. If this issuccessful, NICMOS can be operational for the remaininglifetime of HST. Sensitivity curves for all HST instrumentsare maintained by the Space Telescope Science Instituteand are available on their web site: http://www.stsci.edu

F. Space InfraRed Telescope Facility

The SIRTF is a 85-cm diameter telescope (Fig. 11) thatwill be cooled to 5.5 K and specialize in mid- and far in-frared observations. Scheduled to be launched on a Deltarocket in December of 2001, SIRTF will provide an excel-lent follow-up on the ISO observations and offer uniqueareas of science of its own. At this time SIRTF is expectedto provide a significant increase in sensitivity and fieldof view over ISO, primarily due to an improved detectorcomplement. The SIRTF orbit is a unique earth-trailingheliocentric orbit that will place the spacecraft at a consid-erable distance from Earth. This will facilitate the coolingof the telescope, which will be launched warm and thencooled once the proper orbital position is achieved. SIRTFcontains three focal plane instruments described below.

1. Multiband Imaging Photometer

The MIPS for SIRTF will provide diffraction-limitedimaging over the wavelengths between 20 and 180 µm.This range is covered by three detector arrays optimized

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for photometric bands centered at 24, 70, and 160 µm.The respective detector arrays are a 128 × 128 pixel Si:AsBIB array, a 32 × 32 pixel gallium-doped Germanium(Ge:Ga) photoconductor, and a 2 × 20 pixel Ge:Ga ar-ray that has been mechanically stressed to extend its longwavelength coverage to 180 µm. MIPS also has low-resolution (R = 14–25) spectroscopic capabilities in thewavelength region between 52 and 99 µm. R is a measureof resolution and is given by λ/δλ, where λ is the wave-length and δλ is the spectral resolution of two pixels in theNyquist sampled case. A cryogenic scan mirror systemwill increase the efficiency of MIPS for mapping regionsof sky larger than its field of view.

2. InfraRed Array Camera

The InfraRed Array Camera (IRAC) provides imaging atshorter wavelengths with bands centered at 3.6, 4.5, 5.8and 8.0 µm. The 3.6 and 4.5 µm bands utilize two256 × 256 pixel In:Sb detector arrays while the two longerbands utilize 256 × 256 pixel Si:As impurity band conduc-tion detectors. Although there are four photometric bandsIRAC has only two entrance apertures. Dichroic beamsplitters allow the 3.6 and 5.8 band to share one aperturewhile the 4.5 and 8.0 bands share the other. This doublesthe efficiency for multiband observations.

3. InfraRed Spectrograph

The InfraRed Spectrograph (IRS) provides the primaryspectroscopic capability for SIRTF. It covers the wave-length range of 5.3 to 40.0 µm with low-resolution(R = 60–120) spectroscopy and the range between 10and 37 µm at higher resolution (R = 600). IRS utilizes128 × 128 Si:As and Si:Sb BIB arrays to cover its wave-length region.

VII. HIGH-ALTITUDE INFRAREDASTRONOMY

As we have seen above, infrared space missions are quiteelaborate and expensive, both in time and in money.Throughout the history of infrared astronomy there hasbeen a quest to gain some of the benefits of space missionsbut with less expense and with more frequent access thanprovided by space missions. As discussed earlier, the bestobservatory sites are on very high, very dry mountains,but this still leaves a large part of the infrared spectrumblocked from ground viewing. The obvious alternative hasbeen observations from aircraft and high-altitude balloons.We will discuss some of these observations below.

A. Aircraft

The first aircraft to be used routinely for infrared observa-tions was a Lear jet operated by NASA from the AmesResearch Center. It was equipped with a 12-inch tele-scope that looked out from the side of the aircraft. Theaircraft was modified to accommodate the telescope andfor high-altitude performance, with flights typically reach-ing 50,000 feet. It could accommodate two observers anda pilot. With this platform observations of roughly 1 hrcould be taken at high altitudes.

1. The Kuiper Airborne Observatory

The first large aircraft devoted solely to astronomical ob-servations was the Kuiper Airborne Observatory (KAO).This was a C141 jet transport with a 36-inch telescopeagain looking out the side of the aircraft. The obser-vatory could operate for roughly 8 hr at an altitude of45,000 ft. This high altitude was needed to be above thetropopause, which is the boundary in earth’s atmospherebetween water-rich and water-poor air. Before IRAS andISO, most of the available far infrared measurements weremade with this aircraft. Unlike satellites, the KAO offereda platform for a large number of different types of in-struments so that a wide range of studies could be made.The KAO was taken out of operation in 1995 to providefunding for the successor aircraft, the Stratospheric Ob-servatory for Infrared Astronomy (SOFIA).

2. SOFIA

The SOFIA is a 747 SP modified to accommodate a side-looking 2.5-m infrared telescope (Fig. 12). The larger tele-scope will increase both the sensitivity and spatial reso-lution of the observations. SOFIA offers a combinationof facility-maintained and observer-provided sets of in-struments for observations. The location of the telescopeopening section aft of the wing is unusual for aircraft ob-servatories but was necessitated by the structure of theaircraft.

B. High-Altitude Balloons

As a less expensive, but less reliable, platform for infraredobservations, high-altitude balloons have played an im-portant role. Balloons offer much higher altitudes than air-craft and can provide observing times as long as severaldays under favorable conditions. The observations mustbe either preprogrammed or remotely controlled. Attitudecontrol is somewhat harder with a balloon platform, andthe descent phase can be hard on the equipment. Modernballoon astronomy flights are unmanned. An early NASA

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guide on the various methods of high-altitude observationlisted one of the drawbacks of high-altitude manned bal-loon observations as “usually results in the death of theobserver.” Balloon flights are expected to play an impor-tant role in the mapping of the cosmic background radi-ation. The Maxima and Boomerang flights discussed insection II are just the beginning of these efforts.

VIII. SURVEYS

Up until the late 1990s, the only large-scale survey of thesky at near infrared wavelengths was at 2.2 µm and wascomplete over part of the sky to a limiting magnitude of+3. The IRAS survey went much deeper at longer wave-lengths but was limited to a spatial resolution of about 1min of arc. Recognizing the need for much deeper andmore complete surveys, several groups have planned andare carrying out extensive surveys of the sky.

A. NASA Catalog of Infrared Observations

Although technically not a survey, the NASA GoddardSpace Flight Center maintains a catalog of infrared obser-vations that are not part of a massive survey such as theones listed below. It contains a database of over 374,000published infrared observations of more than 62,000 in-dividual astronomical sources. It includes observationsmade between 1 and 1000 µm. Up until 1993, this heroiceffort was published in a paper version with the last edi-tion published as NASA Reference Publication RP-1294.Now the database is electronically available. The URLat the time of publication is http://ircatalog.gsfc.nasa.gov.This database is invaluable for anyone who would like tofind the infrared characteristics of an object. A completebibliography is part of the searchable database.

B. 2Mass

The 2Mass survey utilizes two 1.3-m telescopes in theNorthern and Southern Hemispheres to survey the sky inthe three near infrared bands of J, H, and Ks, a special Kband filter centered at 2.17 µm. It will survey the entire skywith a spatial resolution of 2.0 arc sec. The limiting fluxlevel in each band is about 1mJy, with a signal-to-noise ra-tio of 10. It uses the NICMOS detectors developed for theNICMOS instrument on HST (see section VI.E). The datafrom the 2-Mass Survey will be available electronically inthree separate catalogs. The first is a digital atlas of the skyat a resolution of 4 arc sec. The second is point-source cata-log of all unresolved sources, and the third is an extendedsource catalog of all resolved objects. The point-sourcecatalog is expected to have about 300 million objects andthe extended source catalog over 1 million objects. It has

already contributed to the identification of a new stellarclassification of stars fainter and redder than M dwarfs.The new classification has been designated L dwarfs.

C. Deep Near Infrared Southern Sky Survey

The Deep Near Infrared Southern Sky (DENIS) surveycovers the southern sky in the I, J, and K bands. The Iband is actually just shortward of 1 µm. The survey willcover the declinations between −88◦ and +2◦ with a 1-mtelescope. A NICMOS detector array is used to image theJ and K bands, and a Tektronix CCD detector is used forthe I band. The resolution is 1 arc sec, and the limitingmagnitudes at I, J and K are 18.0, 16.0, and 13.5.

D. Other Infrared Spaceand Ground-Based Surveys

Both the IRAS and COBE missions completed essentiallyall sky surveys at several wavelengths that were discussedin the sections devoted to the missions. That data com-bined with the near infrared ground-based surveys dis-cussed above will provide a very valuable database.

There also exist limited-area surveys from both theground and space. One of the best surveyed areas is thenorthern and southern Hubble Deep Fields discussed insection III.A.4. There are also surveys with ISOPHOTon ISO, termed FIRBACK, looking for light from highlyluminous obscured galaxies. With the common usage ofimproved infrared detector arrays we expect these surveysto greatly increase in number.

IX. FUTURE

A. Large Ground-Based Telescopesand Adaptive Optics

In the next decade there will be several 8-m diameter orlarger ground-based telescopes coming on-line. At thesame time the availability of large-format detector ar-rays at even midinfrared wavelengths will greatly increase.These two factors alone will significantly improve the sen-sitivity and power of infrared observations, where power isdefined as a product of sensitivity times field of view. Theincrease in sensitivity will be particularly large for spec-troscopy, where the sky brightness is greatly reduced dueto the dispersion of the light over many pixels. At the sametime the push to observe the universe at increasingly largerredshifts will make infrared imaging and spectroscopy es-sential for conducting cosmological studies.

Also in the next decade the number and quality of adap-tive optics systems will increase. Adaptive optic systemsare planned or in use at both Keck telescopes, the VLT

P1: GRB Final Pages



array of four telescopes, and the large binocular telescope(LBT). Infrared images at the diffraction limit of the largetelescopes will be possible over almost all of the infraredspectral range. The implementation of laser-created pointsources will also increase the area of sky available foradaptive optics imaging. In spectroscopic systems, adap-tive optic systems will allow spectrometers designed forpoint sources to be much smaller due to the smaller inputslit size provided by adaptive optics.

B. Next-Generation Space Telescope

The Next-Generation Space Telescope (NGST) will bean exceedingly powerful tool for infrared observation. Itsplanned mirror diameter is 8 m in contrast to HST’s 2.4-mdiameter. This alone will provide a large increase in sensi-tivity. Even more important than the increase in diameteris the expected very low temperature of the telescope.The telescope will be placed at the second Earth–SunLagrange point, which is quite distant from the earthcompared to the low-earth orbit of HST. At that distance alarge shade will block the radiation from both and the sunwhich allows the telescope to radiatively cool to a temper-ature of about 60 K. This immensely reduces the infraredemission from the telescope and thus greatly improves thesensitivity of the observations. At the same time the largerdiameter of the telescope will make the images almostfour times sharper than the already excellent HST images.

The main purpose of NGST will be the exploitation ofthe minimum of the sky background at a wavelength of3.0 µm to make observations of very distant and very faintgalaxies for cosmological purposes. The primary wave-length range of operation will be from 1.0 to 5.0 µm.Extensions to longer infrared wavelengths are under con-sideration, however. Instrumentation for the telescope isexpected to include both cameras for imaging and spec-trometers for spectral analysis.

Construction of NGST will be challenging. At presentwe do not have a launch vehicle that is capable of carrying

a payload with an 8-m diameter. Unless such a launchvehicle becomes available, the primary mirror will haveto be made in sections that are folded into place after thetelescope is launched. This requires exquisite positioningaccuracy to achieve the precision that maintains the qualityof an diffraction-limited 8-m telescope.

ACKNOWLEDGMENTS

Rodger I. Thompson is supported in part by NASA grant NAG 5-3042and the University of Arizona.


COSMIC RADIATION • GALACTIC STRUCTURE AND EVO-LUTION • INFRARED SPECTROSCOPY • INTERSTELLAR

MATTER • PLANETARY SATELLITES, NATURAL • SOLAR

SYSTEM, GENERAL • STELLAR SPECTROSCOPY • STEL-LAR STRUCTURE AND EVOLUTION • ULTRAVIOLET SPACE

ASTRONOMY

BIBLIOGRAPHY

Allen, D. A. (1975). “Infrared, the New Astronomy,” John Wiley & Sons,New York.

Bicay, M. D., Beichman, C. A., Cutri, R. M., and Madore, B. F. (eds.)(1999). “Astrophysics with Infrared Arrays: A Prelude to SIRTF,”Astronomical Society of the Pacific, San Francisco.

Glass, I. S. (1999).“Handbook of Infrared Astronomy,” Cambridge Uni-versity Press, Cambridge.

Mather, J. C, and Boslough, J. (1996). “The Very First Light,” BasicBooks, New York.

McLean, I. S. (ed.) (1994). “Infrared Astronomy with Arrays: The NextGeneration,” Kluwer Academic Publishers, Dordrecht.

Minnitti, D., and Rix, H.-W. (eds.) (1996).“Spiral Galaxies in the Near-IR,” Springer, Berlin.

Smoot, G., and Keay, D. (1993).“Wrinkles in Time,” William Morrowand Company, Inc., New York.

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Encyclopedia of Physical Science and Technology EN008L-392 June 30, 2001 10:15

Magnetic Fields in AstrophysicsSteven N. ShoreIndiana University South Bend

I. IntroductionII. Observational Techniques for Measuring

Cosmic Magnetic FieldsIII. Observational ResultsIV. Some Theoretical Developments on Magnetic

Field Generation and DecayV. Final Words

GLOSSARY

Ambipolar diffusion Generation of drift currents, dueto differences in mass between ions and electrons, bycharge separation.

Dynamo magnetic field generation The process where-by magnetic fields are amplified by fluid motions andrestructured to change the symmetry of the poloidalfield to toroidal.

Faraday effect The rotation of the plane of polarizationby a bifringent medium. Produced astrophysically bythe differential response of electrons in a magnetic fieldto right- and left-handed circular polarization.

Flux freezing High conductivity condition which trans-ports magnetic energy as if the material were frozen tofield lines.

Magnetic reconnection The process of magnetic to par-ticle kinetic energy conversion, assumed to be due toannihilation of magnetic flux in thin current sheets.

Synchrotron emission Nonthermal radiation producedby free relativistic electrons spiraling in magneticfields.

Units Solar masses (M�) (2 × 1033 g); solar radius (R�)(7 × 1010 cm); parsec (pc) (3.1 × 1018 cm = 3.26 lightyears).

Zeeman effect The splitting of atomic (or molecular) en-ergy levels by an externally imposed magnetic field.Transitions between magnetic sublevels show differ-ential displacement from the unperturbed wavelengthdepending on the field strength.

Zeeman polarimetry Photoelectric method for measur-ing the displacement in the hydrogen Balmer lines bymeasuring modulation in the line wing between twoopposite circularly polarized states.

THIS ARTICLE reviews some of the theoretical andobservational features of the role played by magneticfields in cosmic bodies. Time-dependent fields are gen-erated by dynamos driven by turbulence and differen-tial rotation. In stars, this produces flaring, coronae, andstarspots. Galactic-scale fields are important in regu-lating star formation and in structuring the interstellarmedium. Extragalactic magnetic fields dominate emission

903

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904 Magnetic Fields in Astrophysics

from active galaxies and may structure the gas in galaxyclusters.

I. INTRODUCTION

Magnetism, after gravity, is the most important force struc-turing cosmic environments. But astrophysically impor-tant magnetic fields are not forever. This truism domi-nates all research on their origin and evolution. The scalesof time and length involved in stellar and galactic environ-ments are so great that it is virtually impossible for anyphenomenon to remain static over the entire lifetime of anobject.

In this article, we will concentrate on extra-solar-system magnetic fields. The problem of remote sensingof such fields is highlighted in extraterrestrial environ-ments, where in situ measurements are generally not pos-sible. The sole exception to this is the sun, where we havesufficient spatial resolution in groundbased imaging andfor which the magnetic field of the solar wind has beendirectly determined using spacecraft.

II. OBSERVATIONAL TECHNIQUESFOR MEASURING COSMICMAGNETIC FIELDS

The measurement of magnetic fields in stars and in othercosmic sources has reached a high degree of refinement.Because of this ability to achieve high sensitivity in the de-termination of both magnetic-field strength and geometry,the importance of magnetic fields in astrophysics has be-come a central issue. New phenomena requiring magneticactivity are continually being discovered, and it appearsthat far from being a panacea invoked by astrophysicistsfor the explanation of otherwise mysterious effects, the-oretical models can be increasingly constrained by directobservations. Before discussing the results of these mea-surements, we will outline some of the methods used forthe study of cosmic magnetic fields.

A. Measurement of Magnetic Fields in Stars

The discovery of the Zeeman effect at the close of thenineteenth century proved to be the first essential stepin the study of extraterrestrial magnetism. The classicalderivation is based on Lorentz electron theory. An electronspirals about a magnetic-field line due to the Lorentz force,

F = e

cv × B, (1)

where B is the magnetic field strength, v is the velocity ofthe electron, e is the electronic charge, and c is the speedof light. The spiral produces a specific helicity, due to the

sign of the electron charge, so that circularly polarized ra-diation excites the orbits in one sense but not in the other.The effect is immediately applicable to the explanation ofthe Faraday effect (see the following) but also predicts thatclassical electrons orbiting the atomic nucleus should pro-duce two oppositely circularly polarized emissions whenseen longitudinally (that is, down the magnetic axis). Theseparation in wavelength of these two components is de-pendent on the force constraining the electron’s motionand is consequently directly proportional to the strengthof the local magnetic field, ωL = eB/mc. Thus, from themeasurement of the separation of the circularly polarized,or σ± components, it is possible to determine the locallongitudinal component of the magnetic field. In linearlypolarized light, the line splits into three components (inthe normal Zeeman effect), the central, undisplaced com-ponent being designated π .

The quantum mechanical derivation of the Zeeman ef-fect is a bit more complicated, since it involves elec-tron spin. The electron possesses an intrinsic magneticmoment, directly proportional to its spin. The magneticmoment of an atom in a specific state depends on the com-bined effect of all of the intrinsic moments of all of theconfiguration electrons and their coupling with the atomicnucleus. This combined moment gives rise to one compo-nent of the energy in the overall structuring of the atomicstate but depends only on the intrinsic symmetries in theatom. An externally imposed magnetic field breaks thesymmetry of the atomic potential, and the net magneticmoment either aligns or antialigns with this field. Thus,the interaction energy

EB = µ · B (2)

depends on the sign of the direction cosine between themoment and the field. Spin quantization produces multi-ple components along the field direction, each of whichhas a different projected magnetic moment. The net effectof the external field is therefore to lift the degeneracy ofthe energy level, or in other words to split the unperturbedatomic state into several components that depend on theangular momentum of the state j . There are 2 j + 1 com-ponents to each state (regardless of the coupling schemefor the interacting bound electrons).

1. Atomic Parameters

Atomic lines result from the transitions between energylevels, and lines can form between substates that differ inthe projected angular momentum m by m = 0, ±1. Themaximum separation of the components thus depends onthe combined separation of the individual states involvedwith the line formation:

λZ = δL gBλ2, (3)



Magnetic Fields in Astrophysics 905

where δL is the classical Lorentz factor for the electronand g is the Lande factor, which for L − S coupling is

g = 1 + J (J + 1) − L(L + 1) + S(S + 1)

2J (J + 1), (4)

which depends on the orbital (L), spin (S), and total angu-lar momentum of the state (J ). The quantum mechanicalresult is that the line separation in frequency depends onlyon the intrinsic properties of the atomic state and is lin-early dependent on the strength of the local magnetic field.For a strong enough field, the (possibly complex) patternof subcomponents becomes classical again, looking like aLorentz triplet. Neither of these effects changes the cen-tral wavelength of the transition. If the external field isso strong that the magnetic perturbation becomes compa-rable with the strength of the atomic potential, the meanenergy of the atomic level shifts and the spectrum will bedisplaced in wavelength, depending on the quantum num-bers for the states from which the lines arise. For hydrogen,the shift is proportional to n2.

All of these effects are observed in astrophysical ob-jects. For instance, G. E. Hale’s application of the Zeemaneffect to sunspot spectra soon after its original discoverydemonstrated that solar activity is an essentially magneticphenomenon. Since different atomic lines are differentlyaffected by the external field, one can determine a meanfield through the combination of measurements for a num-ber of atomic transitions of different g value. These linesmay also be formed in different regions of the stellar at-mosphere, and at different depths depending on their exci-tation and ionization state, and thus can be used to map outthe magnetic field as a function of position and height inthe atmosphere. For solar-type stars, this is a more compli-cated task since we lack the ability to separate out the spe-cific regions on the stellar photosphere. Experience withsolar spectra proves here to be a valuable guide to theinterpretation of the observations.

For the sun, and for other stars, both the splitting andthe polarization of the Zeeman pattern have been ex-tensively used to determine longitudinal field strengths.Since the σ -components are oppositely polarized, theywill also produce a net polarization in the absorbed orscattered light of the photosphere. Viewed through oppo-sitely circularly polarizing filters (quarter-wave plates),the centroid of the line shifts from λσ+ to λσ−. Thusthe difference in the intensity of the line in the twostates is a direct measure of the strength of the localfield along the line of sight, provided the lines can beresolved.

Increased resolution of spectrographs equipped withCCD detectors now permit resolution of λ/λ ∼ 105 to106, with attendant reductions in the limits on global fields.

2. Zeeman Polarimetry

A very elegant technique, called Zeeman polarimetry, isnow used to measure both solar and stellar magnetic fields.Consider a line that is only marginally resolved, either be-cause of rotational broadening of the profile due to lackof spatial resolution of the stellar disk or because of in-trinsic broadening mechanisms. The wings of the two σ -components may overlap, but because the fields are weakand the polarization states are orthogonal, there is no mix-ing of the light between the two profiles. Place a filter atone wavelength in the line wing and chop rapidly betweenthe two polarization states using a Pockels cell (an electro-optical device that passes either right- or left-circularlypolarized light along the extraordinary ray of the crystaldepending on the sense of the applied electric field). At afixed wavelength the two σ -components contribute differ-ent absorption to the profile, so the chopping produces aperiodic intensity variation that can be detected photomet-rically with very high accuracy. Knowing the slope of theunresolved line wing at some wavelength λ0, (d I/dλ)0

the polarization is related to the variation in the intensitydue to the switching between right- and left-circular po-larizations:

p ≡ I

I= 1

I0

(d Iλdλ

)0

λ ∼ λZ ∼ Beffλ2, (5)

where the effective magnetic field Beff is the value mea-sured for the longitudinal field. If the field reverses polar-ity, the sense of polarization switches sign, so it is possibleto determine both the magnitude and the relative polarityof the field.

The power of the Zeeman polarimetric technique lies inits extreme sensitivity to weak fields. The technique caneven be applied to stellar hydrogen lines despite their largeStark broadening. Instead of measuring the separation ofthe components by direct observation of the two profiles,as in the traditional Zeeman that passes either right- orleft-circularly polarized light analyzer, which yields typ-ical errors of hundreds of gauss even for sharp lines, thismethod achieves errors as low as 50 G for hydrogen lines inbright stars. The hydrogen line is also of singular value be-cause it is the only low-ionization, strong line that displaysthe classical Zeeman effect. Continuing development ofthe polarimetric method has been of tremendous impor-tance in the study of magnetic fields in a wide range ofstars, from main sequence to white dwarfs.

3. Differential Zeeman Broadening

A final way of measuring stellar fields is by looking at theoverall broadening of spectral lines of different Lande fac-tor and Zeeman structure to discover broadening in excess




of that expected from turbulence, rotation, and thermalbroadening in the stellar atmosphere. If the field is com-plex, and there is no strong, global field, the polarimetricmethod will fail. A field may be present, but if its geometryis such as to produce no strongly directed field in the lineof sight it will not produce a net polarimetric signal in theline wings. Instead, for such fields, one exploits the factthat, by chance, some atomic transitions produce Landefactors of zero. These lines do not split in the presence of amagnetic field even though their constituent energy levelsdo. The excess broadening of lines arising from the sameionization state over these null lines directly measures themean surface field.

B. Measurement of Magnetic Fieldsin the Interstellar Medium

1. Direct Measurement of Zeeman Splittingfor Radio Lines

For extremely weak fields, such as those observed in theinterstellar medium, it is impossible to directly measurethe Zeeman broadening using optical or infrared spec-tral lines. This is because of the λ2 factor in the splitting.By going to very low frequency and using the strongestline observable in diffuse interstellar clouds, the 21-cmgroundstate transition of neutral hydrogen, it is possibleto measure fields as weak as tens of microgauss. Put dif-ferently, as the field becomes progressively weaker, thewavelength of the line must be matched to the expectedfield strength. Once the field is weaker than a few milli-gauss it is necessary to observe at millimeter or centimeterwavelengths, where few atomic lines are available. The HIinterstellar Zeeman effect has been detected in a number ofclouds, and provides an important handle on the strengthof the field in the diffuse interstellar medium. However,the measurement suffers from the same limitations as thestellar polarimetric method—it is sensitive only to directedfields.

2. Faraday Effect

The free thermal of the phenomenon electrons in the in-terstellar medium behaves classically, and it is straight-forward to apply the Lorentz theory to the transfer ofpolarized radiation through this medium. The index ofrefraction depends on the sense of polarization becausethe resonant frequency of the electron is moved to greateror lesser values depending on the sense of helicity of theparticles around the local field direction. Thus, if the indexof refraction of an electron gas is

n = 1 −(ωp

ω

)2, (6)

where

ωp =(

4πe2ne

m

)1/2

(7)

is the plasma frequency, where ne is the local electronnumber density, then the difference in the index of refrac-tion between the two senses of circular polarization is

n = ω2pωL

ω3, (8)

where ωL is the Lorentz frequency eB/mc. As a signalpropagates through this bifringent medium, its sense ofpolarization will change due to the projection of the B fieldalong the line of sight, and the phase shift resulting fromthis field is the integrated action of the bifringence alongthe line of sight. The plane of polarization for linearlypolarized light thus rotates through an angle:

φ = ω

c

∫n ds ∼ λ2

∫ne B · ds. (9)

Unfortunately, this Faraday rotation depends on boththe projected field strength along the line of sight and onthe local electron density of the magnetoactive medium.Variations in the orientation or strength of the magneticfield, or in the electron density, can produce changes in therotation angle. Further, randomly oriented fields can pro-duce no net change in the polarization, no matter how largethe local field may be. Each polarization reversal reducesthe overall rotation measure, and φ is reduced by N 1/2

for N random changes in the direction of the magneticfield along the line of sight. Independent estimates, usingpulsar dispersion measurements, Hα diffuse line emissionfrom the interstellar medium, and scintillation measure-ments of galactic and extragalactic centimeter wavelengthpoint sources, help constrain the electron density along anyobserving direction, but only the Faraday effect can yieldinformation about the magnetic field directly.

3. Dust and Interstellar Polarization

The discovery of interstellar polarization was accidental,made while Hall and Hiltner in 1947 were attempting tomeasure the intrinsic polarization resulting in hot stellaratmospheres from electron scattering. The correlation be-tween extinction (also called color excess) and the degreeof polarization identified the source as intervening dust be-tween the observer and the star. Dust consists of materialthat may have either a permanent or induced magnetic mo-ment and that is forced through collisions with charged andneutral particles to spin about the magnetic field direction.In doing so, it preferentially aligns with its largest momentof inertia orthogonal to the field direction. Scattering by




nonspherical particles causes the direction of the polar-ization vector to lie parallel to the minimum cross sec-tion, hence the polarization is along the direction of theexternal field. The degree of alignment, produced by themagnetic torque µ × B, is proportional to the magneticfield strength, but because of the collisional dealignmentthe degree of polarization is not a good measure of thelocal field strength. The position angle, on the other hand,is a direct measure of the local direction of the magneticfield.

Unlike the Faraday effect, dust scattering provides ge-ometric information about the field structure. The ori-entation of the magnetic field in the diffuse interstellarmedium has been determined largely by large-scale op-tical polarimetric mapping surveys. Advances in infraredinstrumentation have allowed for the extension of thesemeasurements into wavelength regimes at which interstel-lar clouds are less opaque, and it is even possible now toobtain information about the structures of magnetic fieldswithin molecular clouds and in regions of active star for-mation, previously inaccessible to optical measurement.The technique of measuring dust polarization is insensi-tive to the spectral distribution of the background lightsource and is essentially a continuum measurement. Po-larizations as small as 0.05% can be measured in this wayusing electronic cameras like CCDs over extended struc-tures. Additional details are obtained through the obser-vation of circular polarization of starlight, resulting fromthe variation in the position angle of the magnetic fieldacross the line of sight and linear to circular conversion ofthe propagated photons.

4. Synchrotron Radiation

Synchrotron radiation is the only emission mechanismthat is uniquely dependent on the presence of magneticfields. A relativistic electron spiraling in an external mag-netic field radiates photons at a characteristic frequencyωc = γ 2(eB/mc) = γ 2ωL, where γ = E/mc2, which de-pends only on the local field strength. An ensemble ofelectrons with energy spectrum N (E) radiates with anintensity I (ω) ∼ B(p+1)/2ω−(p−1)/2 while even for an op-tically thick source at low frequencies, the spectrum isI (ω) ∼ B−1/2ω5/2. Here, ω is the frequency of the radi-ation. The extra factor of ω1/2 is, in effect, because theelectrons have an effective radiation temperature that de-pends on their energy.

In contrast, an optically thick thermal spectrum varies asω2 at low frequencies. The emission is polarized, since theelectron radiates orthogonally to the local field direction;circular polarization results from viewing the source lon-gitudinally. The synchrotron spectrum thus reflects the ex-ponent of N (E), so the identification of this radiation is

generally straightforward, using the shape of its emittedspectrum. Another measure of the nonthermal nature ofthe emission is that the brightness temperature, the tem-perature required for a blackbody source to produce thesame monochromatic flux, can be as high as 1011 K. Evenfor mildly relativistic electrons, it is possible to observe thesynchrotron emission, which is strong in the radio spec-trum at centimeter wavelengths at which most thermalemitters (except for hot optically thin plasmas) are notstrong sources. Still less energetic electrons emit gyro-cyclotron (or gyro-resonance) radiation when trapped inmagnetic fields. Observed in solar flares and coronal loopstructures where temperatures reach as high as 109 K, thisemission can be due to an input thermal spectrum of elec-trons (a Maxwellian velocity distribution for a hot gas in amagnetic field) although the form of the emitted spectrumwill not be thermal.

There are many strong cosmic sources of synchrotronradiation, both within the Galaxy and in extragalactic ob-jects. Often, they are distinguished from thermal emissionregions by their brightness temperatures and by their beinglinearly polarized. The degree of polarization depends onthe shape of the electron spectrum and on the optical depthof the emitting volume, Plinear = 3(p + 1)/(3p + 7) if thesource is optically thin, and Plinear = 3/(6p + 13) if it isoptically thick. Nonmagnetic, homogeneous, thermalizedplasmas do not radiate polarized light.

III. OBSERVATIONAL RESULTS

A. Stellar Magnetic Fields

After planets, the most detailed information and the mostextensive theoretical work are available for stellar mag-netic fields. In the case of the sun, we have an enormouswealth of information about the spatial distribution andtemporal evolution of magnetically related structures. Oneof the major discoveries of this past decade is the extentto which solar-type stars share many of the characteristicsobserved for solar active regions, and also the remark-able range of energy and length scale on which magneticfield activity can manifest itself in stellar envelopes. Itshould be borne in mind that stellar envelopes are probablythe best places for the study of dynamo processes. Theyare observationally accessible, they vary on a timescaleshort compared with a human lifetime, and there are manyplasma diagnostic spectral features with which to analyzethe physical state of the star. Most of the work on dynamofield generation is constrained by the study of stellar andplanetary fields, after which the models can be extrap-olated to larger-scale phenomena, such as galactic fieldstructures.




1. The Sun and Solar-Type Main Sequence Stars

The solar magnetic field is organized into complex struc-tures, without a large-scale geometry other than an approx-imate polarity for the individual hemispheres. Structureexists on scales ranging from several tens of kilometers,about the size of individual convective elements, to largeactive regions that can be more than 104-km across. Thestrongest and most obvious fields are detected in sunspots,in which fields of several kilogauss are common. Theseregions are dominated by their local fields, which typicallyreach values of 1 to 3 kG in the umbra and are directed nor-mally to the stellar surface. Peripheral, penumbral fieldsare weaker and are transverse to the surface. The internalfields of these spots are transient, decaying on timescalesranging from days to months depending on the area ofthe spot. Convective motion is suppressed within the spot,a primary cause of the relative darkness of the spot re-gion in contrast with the convectively active photospheres.The field structures extend into the chromosphere and thecorona above the active regions, often reaching heightsof order 105 km, about 0.1 R�. Such fields are entirelyresponsible for the thermal and dynamical structuring ofthe corona.

Sunspot activity, as is well known, behaves in a roughlycyclic manner with a mean timescale of about 11.5 yearsbetween successive maximum disk-covering fraction. Themagnetic field of the sun, however, reverses on abouttwice this timescale, although the cycle closely resemblesa strange attractor. The most prominent manifestation ofthis change is that the polarity of the leading spot in a givenhemisphere is systematically of one polarity throughoutone sunspot cycle and reverses during the next. The sameis true in the more disorganized photospheric magneticnetwork, the umbral pores and uncoalesced magnetic fluxthat emerge over the majority of the solar disk.

The solar wind, and the entire outer solar atmosphere,are completely dominated by the magnetic field. Ultravi-olet and X-ray images of the sun show that the corona iscomposed of numerous regions of heated, magneticallyconfined, plasma. The coronal geometry and rate of ex-pansion are controlled by the variations of surface fields.Indeed, coronal activity appears to be a primarily mag-netic phenomenon. For example, a solar flare involves therapid acceleration of coronal electrons and protons to rel-ativistic energies, along with radiative emission of a broadvariety of spectral signatures ranging from gamma rays toradio, on timescales of several minutes. Coronal transientsare also energetic and dramatic events in that they involvethe dissipation and restructuring of magnetic fields in thecorona. The most likely cause is magnetic field reconnec-tion and the fast conversion of magnetic into radiative andparticle kinetic energy.

Magnetic heating is also responsible for the high tem-perature of the corona, and, by extension, the heating ofthe outer atmospheres of solar-type stars to temperaturesgreater than 106 K. The dissipation of Alfven waves, mag-netic disturbances that propagate along field lines with avelocity of vA = B/(4πρ)1/2, where ρ is the mass density,and reconnection, taking place on many length scales inconfined magnetic loops (like prominances), play impor-tant roles in the heating of the outer atmosphere. Recon-nection and flaring activity also serve as an energy sourcefor coronal activity, although the detailed mechanism isstill a subject of considerable investigation. X-ray satelliteobservations, with Yokok and TRACE, reveal the complexstructure of coronal magnetic fields and highlight the roleof reconnection in the heating.

All stars with surface temperatures cooler than about7500 K appear to have convective envelopes, the primaryoptical signature of which is the emission observed inthe resonance lines of ionized calcium, Ca II, at λλ3927and 3933 A. The strength of this emission appears to de-cline with age, as does the rotational velocity of the star,thus supporting the contention that magnetic activity is theprimary agent for the production of chromospheres andcoronae in low-mass stars. We shall return to this pointlater.

Ultraviolet spectra also show the presence of chro-mospheric and coronal regions in late-type stellar atmo-spheres. All late-type main sequence and more evolvedstars for which ultraviolet spectra have been obtained be-low λ3300 A show the emission-line signatures of hot en-velopes. The Mg 11 λ2800 A doublet is especially goodas a chromospheric indicator, since it is an analog tothe Ca II doublet. Additional support for hot exospherescomes from the C IV λ1550 A doublet, C II λ1334 A, OI λ1304 A, and the Si III and C III intercombination linesnear 1900 A. These lines also vary in response to flareactivity. They are also far more sensitive than the opticallines to the local heated structure in the outer atmosphere,so are tied closely to the active regions. As these heatedregions are carried by rotation across the line of sight, theUV emission lines vary in intensity and also in velocitystructure. While this is better studied in binary systems(see Section III.A.2), the variation in the UV and opticallines in single stars form much of the basis for the inter-pretation of magnetic activity in normal stars.

Many of the late-type stars close enough to be detectedby X-ray satellites have been observed. The X-ray lumi-nosities LXR are typically 10−4 Lbol and the coronal tem-peratures are consistent with the solar coronal value. Sup-port for the link between magnetic activity and coronalemission comes from the correlation between XR lumi-nosity and stellar rotation frequency LXR ∼ �n , where nappears to be between unity and 2.




Very low-mass main sequence (hydrogen core-burning)stars, less than about 0.5 M�, have been observed to dis-play flaring activity on a scale about 105 or higher thanthat of the sun. These so-called flare stars, or dMe stars,show many of the same emission processes observed insolar flares, although the timescales and energies involvedare greater than seen on the sun. To date, however, nofields have been directly measured. Instead, activity cy-cles have been observed in the periodic variations of CaII emission intensity, and individual regions have beenmapped on many main sequence stars by observing themodulation of the line strength on a timescale of weeksto months, comparable to the rotation period of the stars.One indirect measure of the field strengths is provided bythe excess broadening of lines with large Lande factorsover that observed for small g-factor lines, and from theperiodic variation in the optical brightness of some of thedMe stars due to star-spot activity.

2. Magnetic Chemically PeculiarMain Sequence Stars

The magnetic chemically peculiar stars, also called the Apor Bp stars, are confined to the effective temperatures, onthe main sequence, between roughly 7500 and 25,000 Kand have masses ranging from about 1.5 to about 10 M�.These stars are notable for their strong absorption linesof anomalously abundant species, like the rare earths andsilicon, and also for abnormally weak lines of helium. TheAp/Bp stars typically rotate more slowly than field stars ofthe same mass. They show strong magnetic fields rangingfrom the limits of detectability of about 100 G to morethan 30 kG. The strongest field yet observed in a mainsequence star, HD 215441, measured by the transverseZeeman effect, is 32 kG. About 50 bright stars have beendirectly measured to possess these strong fields. Typicallythe field has a strong dipolar component that is oblique tothe rotational axis by a random angle between 0◦ and 90◦.The field of HD 37776 is especially notable in having apredominantly quadrupolar field that is also oblique. Thefield bears a remarkable resemblance to that observed byVoyager 2 at Neptune. The magnetic fields often must befit using decentered dipoles, probably indicating that mostof the magnetic stars have strong nondipolar components.

An important difference between these fields and thoseobserved in late-type stars is that the chemically pecu-liar star fields show no time dependence. The rotationalphase of the dipole remains constant, in some cases overmore than 3000 rotation periods (as in α2 CVn), and thereis no evidence for changes in the surface distribution ofoverabundance patches. Thus these fields seem to be a relicfrom an earlier stage of evolution and not to be continuallygenerated by any dynamo activity. While their frequency

in the main sequence stellar population is not well known,it appears that as large a fraction as 10% of all main se-quence stars in this mass range have some strong surfacemagnetism. One possibility is that the stars were initiallyrapid rotators in the pre-main-sequence stage of their evo-lution, and generated strong dynamo fields while in pos-session of deep convective envelopes. Subsequent to thiscontraction stage, when the envelopes turn radiative andthe stellar surface temperature increases on its way towardthe main sequence, these fields might be preserved and ad-ditionally amplified by stellar contraction. The field wouldalso torque the star down, constraining mass loss to largeradii and increasing the angular momentum loss of the starover that which would be seen for a nonmagnetic star.

3. Magnetic Activity in Close Binary Stars

Two classes of close binary stars display evidence for mag-netic activity, both connected with solar-type stars. Mainsequence contact binaries of the W UMa type are gen-erally low-mass systems of large mass ratio. The lowermass star in the system is generally ≤1.5 M� and there-fore has a convective envelope. These stars, of the W-typein the taxonomy of contact systems, show a light curveinstability and emission spectrum in the UV that has beeninterpreted as arising from dynamo activity in the lowermass star. Dark waves move systematically through thelight curve, indicative of regions of lower (about 300 K ormore) effective temperature that may occupy a few percentof the photosphere of the pair. Chromospheric emission isseen for these systems. The orbital periods are typicallyabout 0.5 day. These stars have rotational rates about a fac-tor of 20 to 100 slower than this, hence the expectation thatthese close binaries should show strong magnetic fields.Nonthermal radio emission and flaring activity have beenreported for several of these systems, but these reports arestill controversial. The best available evidence that thesestars maintain dynamo fields comes from the photometricsignature of dark waves.

Considerably more certain identification of large-scalemagnetic field generation is available for the RS CVnand Algol-type binaries. These are also short-period sys-tems, ranging from about 0.5 to 40 days, which consistof evolved primaries and main-sequence secondaries. Inthe classical Algol systems, the more evolved star is ac-tually the lower mass member of the binary, having lostconsiderable mass both to the unevolved star and fromthe system as a whole; these evolved stars are currentlyin contact with their Roche surface and losing mass ontothe main sequence member. Both radio and X-ray flaringhave been observed in these systems, the most notablebeing Algol(β Per). Ultraviolet observations taken duringeclipse show strong chromospheric emission spectra for




the cool star in the system. Because the evolved star isoptically the fainter member of the system, starspot activ-ity is not directly observable in the light curve.

Better evidence for dynamo activity comes from the RSCVn stars, which like Algols have evolved members. Inmost of the RS CVn systems, however, the more massivestar is the photometric primary and also the more evolvedmember. These stars display several characteristics of en-hanced magnetic activity when compared with normalstars: (1) Ca 11 emission (by as much as a factor of 10);(2) dark waves in their light curves that show cyclic vari-ations on timescales of years to decades; (3) strong UVchromospheric signatures (C II, O I, Si III], and C III] areespecially strong for their spectral class); (4) hot coronaswith temperatures up to 107 K; and (5) most important,strong flaring activity, reaching luminosities greater than1027 erg s−1 over timescales up to weeks (the most ex-tensively studied being the 1978 radio flare of HR 1099).Ultraviolet flares have been observed in a number of RSCVn binaries with energies higher than 1035 ergs overtimescales of nearly one day. In Algol systems, X-rayflare energies have detected up to 1035 erg, comparablewith the UV output. In contrast, the strongest flares ob-served for the sun emit about 1022 erg s−1 in the radio andhave a total bolometric energy of about 1025 erg. Moretypically, the total radio luminosities in RS CVn flaresare of order 1030 erg, comparable with those observed inthe sun. These radio flares may last for several hours, whilesolar radio flares are rapid, of order 103 seconds.

The RS CVn systems are especially important becausethe optical and UV spectra of the primary can be directlystudied, and individual active regions can be followed asthey rotate across the line of sight. The technique, calledDoppler imaging, has been applied to a number of systems,notably AR Lac, HR 1099, and λ And. The RS CVn starsare also rotating much faster than single stars of the samemass and effective temperature, by up to a factor of 10.For a few systems, FF Aql and V471 Tau, ultraviolet ob-servations have revealed the presence of prominencelikematerial located above the limb of the evolved star. Thetemperatures of this material (above 104 K) and densities(above 107 cm−3) support the contention that it is trappedin magnetic loops located above active regions in the pho-tosphere. The similarity of the Algol and RS CVn starsis taken as a strong argument for the ubiquity of mag-netic activity in any star with deep envelope convection,provided the rotational frequency is large, and connectsthe enhanced activity in these stars to their more normal,single, main sequence counterparts.

4. Pre–Main Sequence Stars

The photometric and high-energy signatures of magnetic-field generation have been observed in several T Tau stars,

which are pre-main-sequence stars still in the process ofcontraction toward the main sequence before the onset ofhydrogen core burning. The rotation periods obtained forthese stars on the basis of their light curves are shorterthan 7 days. For instance, V410 Tau has a period of about4 days. The starspot characteristics are quite similar tothose encountered in the W Uma and RS CVn systems,although they have not displayed the strong radio flaresseen in the latter; they do, however, show strong X-rayflaring activity (especially several of the sources observedin the ρ Oph molecular cloud).

A few stars belonging to the Herbig Ae/Be subclassof pre-main-sequence stars display time variable chromo-spheric features in both the optical and ultraviolet. Theseare fairly hot (>7000 K) clearly unevolved stars that arefound in regions of recent star formation but are usuallynot embedded in their parent cloud. The profiles of severalresonance lines, notably Ca II, Mg II, and C IV, are mod-ulated on timescales of about 40 h. This seems to indicatethe presence of active regions, or at least surface inhomo-geneities. This result is surprising since the Ae/Be starshave high effective temperatures, about 10,000 K, and sodo not have extensive convective envelopes, which nor-mally appears to preclude such magnetic activity. Thesestars do not show flares, unlike the cooler T Tau stars, andthey are not strong radio or IR sources. Nonetheless, theyshow classic symptoms of magnetic activity evidenced bytheir spectral features.

Indirect evidence of the role of magnetic fields in thepre-main-sequence stage of evolution comes from the dis-covery of bipolar mass outflows from these systems. ManyT Tau stars are associated with jetlike CO and Hα flows,which are collimated and supersonic relative to the cloudmedium (velocities as high as 50 km s−1, or upwards ofMach 50, have been observed). The theoretical explana-tion of these flows involves magnetic torquing of accretiondisks surrounding the nascient protostar, which generatesAlfven waves that accelerate disk material off the diskand preferentially out the poles. Such fields are assumedto originate within the molecular clouds, by amplificationof the field of the galaxy, and to be transported as frozen-influx onto the protostar by the accreting matter.

5. White Dwarf Magnetic Fields

White dwarfs are the remnant of the evolution of low andintermediate (≤5 M�) mass stars, formed by core contrac-tion during the last stages of nuclear burning. Since theyreach densities in excess of 108 g cm−3 and typically haveradii of order 0.01 R� they were expected, by simple the-ory, to be able to possess very strong surface fields. Anyweak field remnant in the core at the time of contraction,should the field be able to survive this stage of evolution,would be amplified by flux-freezing to very large values, of




order 106 G. Such fields have been discovered in a numberof isolated white dwarf systems, by measurement of polar-ization properties both of the continuum (due to scatteringby electrons in such strong fields) and by the Zeeman ef-fect they produce in photospheric lines (through the useof Zeeman polarimetry).

There is also an important class of white dwarf for whichthe magnetic field plays an important role in structuring theaccretion of matter onto the star. These are the AM Her-culis stars, extremely close binary systems with periodsof order hours in which the primary, a low-mass star, hasexpanded sufficiently to transfer mass onto the surface ofits companion white dwarf. If the accreter is magnetic, theinfalling mass funnels preferentially to the poles where itaccretes in a column of hot, shocked, plasma onto the whitedwarf. Like the Ap and Bp stars, these dwarfs have ob-liquely oriented fields and by the rotation of the star, theaccretion columns vary in their angle to the line of sight.There are two observable effects of this rotation. One isthat the strength and velocity of emission lines formedin the polar columns vary with phase of rotation. A sec-ond is that the lines thus formed are polarized by thestrong fields and can be studied using the same Zeeman po-larimetric techniques used for more ordinary and weakerfields. Observation shows that the field strengths in thesesystems are in the range of 1–10 MG, and that the rota-tion of the white dwarf is synchronous with the orbitalperiod.

The presence of magnetic fields in white dwarf starsis important as a physical process for many binary starsystems, notably cataclysmics like novas and dwarf novas.Accretion of matter from a circulating disk accumulatedin the environment of the white dwarf transfers angularmomentum to the star and spins it up. The tidal couplingbetween the dwarf and its companion produces spin-orbitcoupling, which then alters the angular velocity of thebinary, causing it to shrink to compensate for the loss oforbital angular momentum. Thus the presence of a strongfield on the accreter can drive the evolution of the starand maintain the mass transfer in excess of that whichwould be expected solely from nuclear evolution of thecompanion star. A number of classical novas, especiallyDQ Her (N 1936) and V1500 Cyg (N 1975), have magneticwhite dwarf components.

6. Neutron Stars and Pulsars

The strongest fields encountered in astrophysical environ-ments are found for neutron stars, the end product of stellarcore collapse at the start of the supernova event for mas-sive stars. These objects, having about 1 M� but radii oforder 10 km, have been observed to have fields upwardsof 1012 G. Two indirect means have been used to inferthe strengths of these fields, which defy direct detection

because of the lack of spectral diagnostics on the neutronstar surface. Pulsars were first observed as radio sourcesrotating with periods between tens of milliseconds andseconds, which display both pulsed radio emission andslow secular increase in the rotation rate. It is this spin-down that serves as a measure of the surface field strength.A rotating magnetic dipole loses energy at a rate:

dE

dt∼ �4 B2, (10)

since the rate of radiation depends on µ2, the square of thesecond derivative of the magnetic dipole moment. Sincethe rotational energy is 1

2/�2, where I is the stellar mo-ment of inertia, the rate of spindown � is proportionalto B2. This is measured by the spindown time �/� andprovides fields of such large magnitude. Such large (TG)fields are also required for the production of the emissionobserved at all wavelengths from pulsars. In addition, forneutron stars still embedded in supernova remnants, theemission of low-frequency (at a frequency �) electromag-netic radiation can power synchrotron emission from thesurrounding plasma (as in the Crab Nebula). Such super-nova remnants are called pleirons, after the Greek wordfor crab. The observed emission from these remnants isconsistent with the model.

The weakest fields observed to date for neutron starshave come from the discovery of the millisecond pul-sars, neutron stars with rotation periods of order 1.5 to10 ms. While such rapid rotation would have been ex-pected naively only for extremely young pulsars, all in-dications are that these stars are rather old. They showbreaking ages of more than 109 years; in fact, to date,spindown has not been observed for any of these systems.The theoretical explanation for their rapid rotation andslow spindown is that they have far weaker magnetic fieldsthan previously detected for neutron stars, of order 109 to1010 G. While such fields may be the product of decay ofa stronger initial field, considerable controversy currentlysurrounds the theory of neutron star magnetic field decay.Rather, these stars appear to have formed with initiallyweak fields. Their rapid rotation is presumed to have orig-inated from accreted matter from a one-time close binarycompanion. The lack of a strong field ensures that the highangular frequency is preserved for a long time, making thebinary look “forever rotationally young.”

B. Interstellar Magnetic Fields

The source for stellar magnetism, at least in the proto-stellar phase, must lie in the environment. Measurementsof dust-induced polarization in nearby molecular clouds,especially Taurus-Auriga and ρ Ophiuchus, show thatthe magnetic field is complex and pervasive throughoutthe parent cloud in which star formation is occurring.




Additional evidence for large-scale magnetism in the in-terstellar medium comes from the radio observation of su-pernova remnants, strong synchrotron sources that showthe effects of the expanding blast wave in the redirectionand shock-amplification of the ambient galactic field.

There are two methods for measuring the magnetic fieldof the interstellar medium. The most direct method is thedetection of the Zeeman splitting of the 21-cm line ofneutral hydrogen, or the splitting of the ground state tran-sitions of the OH molecule. Both of these are present inlow-density clouds that pervade the interstellar mediumand that have low enough internal temperatures that thelines are not too broad for the measurement.

Individual HI clouds having temperatures of order100 K display internal fields of order 10 µG, larger thanthat inferred for the low-density gas and consistent withflux-freezing in the clouds. OH transitions, which are col-lisionally excited and arise from masers that are pumpedin the presence of strong infrared sources, provide similarfield measurements.

The magnetic field in the diffuse interstellar medium issignificantly lower than that observed in the clouds. Oneindication of the presence of magnetic fields in molecu-lar clouds comes from the observation that line widths inthese clouds are far larger than would be expected from thecloud temperatures. The sound speed in a typical molec-ular cloud that has a temperature of 30 or 40 K (measuredusing infrared emission from the embedded dust) is about0.5 km s−1. Yet line widths are often observed in excessof 2 km s−1, and it is possible that this indicated the pres-ence of turbulent Alfven waves within the cloud. Suchturbulence is also apparently needed to support the cloudsagainst gravitational collapse. Fields of order milligaussappear to be required to supply this turbulence. Theoreticalmodels of collapse of magnetic clouds show that flux con-servation during cloud formation is capable of amplifyingthe microgauss fields observed in the diffuse medium tothese large values.

Observations of the galactic center show filamentarystructures extending from the core nonthermal source,Sgr A, that extend radially to about 50 pc and have fieldstrengths of order 1 mG. These structures, which showboth clustered arclike emission regions and isolated fila-ments extending up to 50 pc from the plane, may be similarto the structures observed in the active nuclei of externalgalaxies, and their connection with the nuclear molecularclouds argues for the ubiquity of magnetic activity in allportions of the interstellar medium and its central role inthe structuring of galactic scale activity.

The Orion Molecular Cloud (OMC-1) is perhaps thebest studied galactic region of recent star formation. Themagnetic field has been measured in the cloud by a varietyof methods. All of these methods show that the weakest

fields are of order of a few microgauss, while the strongestfields exceed about 100µG. The condition of flux-freezingprovides for such large amplifications, assuming that theygrow like ρ1/2.

The strongest interstellar fields are observed in OHmasers. These sources are especially difficult to measurewith Zeeman effect because beam smearing usually lim-its the accuracy of the polarization determination. Sincethe sources are very compact, it is necessary to use verylong baseline interferometry to separate out the various(circularly) polarized components. The fields observed ina number of maser knots range from 2 to 10 mG. Theconversion between magnetic field strength and velocitywidth for the normal Zeeman pattern for the OH lines,which have a wavelength of about 18 cm (1.6 GHz) is ap-proximately 0.3 km s−1 mG−1 so that for a 10 mG field, thelines are completely resolved even in the total intensity.This means that it is possible to measure the total field—much as in the case of Babcock’s star HD 215441—notjust the projected field along the line of sight. In fact, thefield is responsible for the desaturation of the maser. OHobservations are the most certain test to date of the scal-ing of the magnetic field of any interstellar region withambient density, and show that the field follows the ρ1/2

scaling law.The role played by magnetic fields in the support and

structuring of molecular clouds is highlighted by molec-ular observations. These indicate that the line widthsobserved in CO, CS, and other strong molecular trac-ers of the density and dynamics of the cloud coresare far in excess of the thermal widths. The primarymechanism for support of the clouds against gravita-tional collapse is turbulence supported by Alfven wavestrapped within the clouds, which provides the equiva-lent of an added pressure (δB2 >/4π ). It is also possi-ble that the fields help regulate star formation by servingas the primary mechanism for transferring angular mo-mentum away from the collapsing cores of the cloudsand assisting accretion of matter. As previously men-tioned, the observation of bipolar molecular outflows as-sociated with newly formed stars supports the contentionthat magnetic fields, amplified in the process of col-lapse, are responsible for the growth of the protostellarobject.

C. Galactic Scale Magnetic Fields

In the 1980s, with the advent of aperture synthesisradio telescopes, the study of the large-scale structure ofmagnetic fields in external galaxies has undergone explo-sive growth.

The synchrotron emission from the diffuse interstellarmedium is the most direct measure of the overall magnetic




energy of a galaxy. Perhaps the most significant result inthe 1980s is the study of the large-scale structure of mag-netic fields in galaxies and on scales of clusters of galaxies.This cannot be accomplished optically, and must be per-formed using aperture synthesis techniques. Cosmic rayelectrons are the primary agents for producing the dif-fuse synchrotron radiation in galaxies. Because of theirdistribution throughout the galactic interstellar medium,and the fact that their motion is tied to the magneticfield structure, they serve as excellent tracers of the fieldconfigurations.

There is little evidence for magnetic fields in the diffuseinterstellar medium of elliptical galaxies. Many of thesegalaxies, however, display large radio structures on scalesup to megaparsecs. These appear the result of mass andflux transport from active nuclei deep within the parentgalaxy, likely arising in the vicinity of a massive cen-tral black hole. Imaging reveals that many galaxies, espe-cially the central cD-type galaxies in large clusters, haverelativistic jets directed orthogonally to a central accre-tion disk. Evidence for transported magnetic fields comesfrom the synchrotron luminosity of the jets and their at-tendant terminating radio lobes, and the magnetic field ge-ometry is suggested by the polarization of the emission.The fields observed along the jets appear to be initiallyradial and directed along the jet axis, while at large dis-tances (kpc) from the core, the fields become more helical.Synchrotron losses appear to be concentrated toward theboundaries of the jets, especially in M87, the central cDin the Virgo cluster and one of the most extensively im-aged nearby (20 Mpc) galaxies. The mechanism for thegeneration and transport of these fields is an open ques-tion. It is possible, however, to estimate the magnetic fieldstrength using a minimum energy argument. This analy-sis assumes that the total energy of the relativistic fluid isminimized with respect to the local field. When applied tothe large-scale structures observed in radio galaxies, thederived fields are usually in the range of 100 µG to a fewmilligauss.

In spiral galaxies, there is abundant evidence for large-scale magnetic fields. Relativistic particles supplied bystellar activity, supernovas, and local acceleration withinthe interstellar medium, serve as synchrotron emittingmarkers of the local field intensity and direction. This dif-fuse emission has been mapped for the nearby spirals,and appears to be well aligned with the spiral structure.Several nearby spirals, especially M83, have been shownto have large-scale fields ordered by the galactic differ-ential rotation. In external galaxies, as in our own, thefield shows complex structure, consisting of holes, loopsreaching several kiloparsecs above the plane, and order-ing on scales ranging from a few parsecs to the size of thegalaxy.

The study of magnetic fields in external galaxies iscomplicated by the resolution of currently available radiotelescopes. We see structure on all scales in the interstel-lar medium of our galaxy from subparsec to kiloparseclengths, and the magnetic field is structured on similarscales. Across an external galaxy, the average synthesizedradio beam is between 0.1 and a few arcsec, dependingon the radio telescope and its configuration of antennas.This corresponds to scales ranging from a few parsecsto several hundred parsecs per beam even for relativelynearby galaxies within about 100 Mpc. At present, itis only possible to place limits on the extent of thesmall-scale structure, and the total measured field is un-certain at best. For the large-scale field, on the kiloparsecscale, the general statements appear more secure. Severalgalaxies have been mapped, and generally the geometryof magnetic fields determined from the synchrotron emis-sion corresponds well with that obtained from optical(dust) polarization. This is especially well represented byM 31 = NGC 224, M 51 = NGC 5195, and M 81. How-ever, recent results for M 83 = NGC 5236 do not showcorrespondence with the spiral arm tracers. It appears thatin actively star-forming galaxies. the presence of H 11regions and supernovas distorts the magnetic structuresfrom that ordered by the grand design spiral pattern. Aslarger radio telescopes become operational, especiallythe Very Long Baseline Array (VLBA) now underconstruction in the United States, the detailed mappingof the nonthermal emission in nearby galaxies should beable to reach the sensitivity and spatial/resolution to studythe complex small-scale structures in the ISM of externalgalaxies.

IV. SOME THEORETICAL DEVELOPMENTSON MAGNETIC FIELD GENERATIONAND DECAY

A. Dynamo Generation of Magnetic Fields

The discovery of the activity cycle of the sun, and of stars,supports the contention that magnetic fields in cosmic ob-jects must be continually regenerated. The decay of thefield, due to the finite electrical conductivity of matter, issufficiently rapid to require that if a field is observed atall, it must not be primordial.

The electric field in a moving medium is due to two con-tributing physical processes, one from the induced fielddue to the motion if there is already a magnetic fieldpresent, and the other due to the finite rate of dissipa-tion of the field from the potential difference and finiteelectrical conductivity. That is, if a current is set up, thestrength of the current is assumed due to an electric field.




Therefore

E′ = E − 1

cv × B, (11)

which by Ohm’s law relates the electric field to the current:

E = 1

σJ. (12)

The Maxwell equations govern the temporal evolution ofthe fields. For the electric field, the rate of change of thefield with time is

∂E∂t

= c∇ × B − 4πJ, (13)

while for the magnetic field we have:

∂B∂t

= −c∇ × E. (14)

In other words, the two effects that induce the forma-tion of a magnetic field are the displacement current andthe free charges that form J, while the decay of the mag-netic field is due to the generation of a spatially variableelectric field. If we assume that the material is in motion,then the form of the equations is invariant, but the motionof a charged medium through a magnetic field producesthe appearance of an electric field, thus adding to the de-cay term for the field because the generation of the electricfield is at the expense of the magnetic field already presentin the medium.

Assuming that the electric field in the moving mediumis vanishingly small—that the conductivity is very high(although not infinite)—we obtain

∂B∂t

= ∇ × v × B − c

σ∇ × J

= ∇ × (v × B) + η∇2 B + ∇ × �. (15)

Here the magnetic diffusion coefficient is η = 4πc2/σ , and� is the electromotive force. This last equation, the so-called dynamo equation, is of the most interest to us. Thefirst term is that of a generator, the fluid motions beingused to produce a magnetic field from the preexisting field.The latter is a diffusive term, resulting from the transportof magnetic field through the fluid by random motions.

B. Flux-Freezing

Any attempt to maintain an internal electric field in a per-fectly conducting medium will be thwarted by the mobil-ity of the charges, which immediately move to cancel anypotential difference. The timescale for this cancellation isvery short in comparison with the timescales for the fieldto begin building in the medium; that is, they take place ontimes short in comparison with the actual fluid motions,

so there will be no net electric field. The meaning of thediffusive term to the evolution of a magnetic field can thusbe explained more clearly by thinking about the effect ofmass motions in a magnetic field. For a net current to re-sult from the fluid motion in some medium, there must beuncanceled potential differences that manage to survivewithin the fluid. In a highly conducting medium, there isa simpler amplification mechanism for the field that actseven without recourse to a dynamo. The magnetic field ap-pears to move as if “frozen” into the medium, the spatialenergy density of the magnetic field precisely followingthe fluid density. So if the density increases locally, sodoes the magnetic field.

To see this, assume that σ is the value usually quotedfor the conductivity of stellar plasma, >1015 s−1. Thisconductivity is large enough to ensure that the magneticdiffusion term effectively vanishes. Then,

dBdt

= −B∇ · v. (16)

From the continuity equation, we have

dρ

dt= −ρ∇ · v. (17)

Here, we have used the convective, or co-moving, deriva-tive: d/dt = ∂/∂t + v · ∇. The magnetic flux is thereforesimply a scalar multiple f of the mass density, or B ≈ f p.Thus, if the density is locally increased, so is the magneticfield strength. The magnetic field seems to move with thefluid, hence the appellation “frozen.”

Now imagine that there is a small deviation from per-fect conductivity. As the fluid moves, there will be someslippage of the mass through the field. This appears tochange the magnetic field strength in the co-moving fluid.At the same time, the fact that the field is changing in-duces the formation of a potential difference which, in afinite conductivity environment, induces the generation ofa current. All of this is at the expense of the magneticfluid. The field consequently decreases in local strengthand will do so everywhere throughout the fluid in time.In fact, the form of the magnetic field decay is the sameas that of the heat equation, so the field can be said tobe diffusively lost. The energy simply goes over intoheat, since the field generates dissipative currents thatlose their energy through collisions throughout the fluid,and the result is the gradual fading away of the field withtime.

The characteristic timescale for the decay of the fielddepends on the scale length for the field generation andthe dissipation scale for the currents. To see this, look atthe dimensionless form of the dynamo equation, but nowignore the effects of the fluid motions. The equation islinear in the field strength, which means that we can scale




it by any arbitrary value of the field at any time. The changewith time is related to the second derivative in space, sothat we can relate the timescale for the change in the fieldstrength τ to the length scale L by

τ = 4π L2

η→ 4π L2 σ

c2. (18)

Again, notice that in the case of an infinitely conductingmedium the time for the decay is infinitely long. We haveused only one possible representation for the magneticdiffusion coefficient, however, and we shall shortly seethat this is one of the longer estimates.

The field throughout a magnetized body will thereforedecay with time, unless it is regenerated or the mediumundergoes steady collapse at a rate that is rapid comparedwith the decay rate. Eventually, regardless of the artifice,the body will be unable to prevent the dissipation of itsinternal field without constant mechanical, that is dynamo,input.

C. Building Dynamos: Differential Rotationand Turbulence

The simplest way to imagine that a cosmic body willgenerate a magnetic field is if it is rotating. Since mostplasmas have high conductivities, the amplification of anexternal field by collapse or compression (like shocks),coupled with rotation should generate a strong Lorentzforce. This field is not, however, supported for indefi-nite lengths of time. Instead, Cowling’s theorem—alsoknown as the antidynamo theorem—states that no station-ary (time-independent) axisymmetric dynamo is possible.But shear is essential to breaking the spherical symmetry.

The symmetry is further broken, and the effect of therotation translated into a poloidal field, through the com-bined action of circulation and turbulence. An initiallyaxisymmetric field is sheared by differential rotation, andif it is initially cylindrical (Bz) or poloidal (Br , Bθ ), thenan azimuthal field (Bφ) results. Here r and θ are the ra-dius and latitude, respectively. A poloidal field resultsfrom a toroidal potential field, Bp = × Aφ , so that thetoroidal magnetic field results from a distortion of thepoloidal field. Finally, to convert the toroidal field backinto a toroidal potential, some additional symmetry break-ing is required. Turbulence in a rotating medium has vor-ticity, or handedness, which is parallel to the local angular-velocity vector and neither radial nor even hemisphericallysymmetric.

In an electrically conducting fluid, buoyant turbulentcells produce a helical twist to the toroidal field and inducea poloidal conversion. This is the basis of the α−ω dynamomodel. The electromotive force is � = αB, where α is re-lated to the velocity correlation function and essentially

measures the amplitude of velocity fluctuations in thefluid. In a fluctuating medium, the velocity breaks intoa mean component V plus a fluctuating part u (which hasa vanishing mean value, but for which 〈u2〉 does not van-ish). Here the brackets 〈· · ·〉 represent ensemble averagesover the turbulent spectrum of the eddies in the fluid. Themagnetic-field evolution depends on both the mean fieldB and the fluctuating part b, and the dynamo equationbecomes

∂B∂t

= ∇ × (V × B) + ∇ × 〈u × b〉 + η∇2B, (19)

where � = 〈 u × b〉 = αB. Thus α represents the fluctu-ations in the fluid, and describes schematically the waythat this feeds back into the magnetic field strength. Theevolution of the fluctuating part of the field is given by

∂b∂t

= ∇ × (u × B × V × b) + ∇

× (u × b 〈u × b〉) + η∇2b. (20)

Then α ∼ l0 〈u2〉/η and therefore depends on the velocityfluctuation spectrum. The turbulence therefore controlsthe small-scale structure, and the differential rotation(shear) controls the large-scale, ordered field and pro-vides the symmetry breaking necessary to generating thedipole.

D. The Dynamo Number and Scaling Relations

A schematic estimate of the strength of the dynamo com-ponents, and an approximate scaling law, results from thequantitative side of this picture. Differential field stretch-ing causes poloidal to toroidal conversion, which takesplace at a rate δvφ/L . Vorticial motion of rising convec-tive eddies transforms toroidal to locally poloidal field ata rate �, which is a pseudo-scalar quantity whose sign de-pends on the hemisphere. The dynamo equations simplifyby dimensional analysis. For the poloidal field, which isgiven by a vector potential field,

Bp = ∇ × Aφ → Aφ

L. (21)

The rate at which the poloidal field dissipates by turbu-lence and diffusion is, in the steady state, balanced by theconversion of toroidal to poloidal flux:

−η∇2Aφ ≈ �Bφ → −ηAφ

L2∼ −�Bφ. (22)

Finally, the poloidal field is wrapped to form the azimuthalfield at a rate that depends on the shear δ�

−η∇2Bφ ≈ ∇ × (νφ × Bp) → −ηBp

L2∼ δνφ

LBφ ∼ �

Bp.

(23)




The dimensionless number

ND = ��L2

η2, (24)

called the Dynamo Number, serves as the scaling param-eter for the generation by the α—� process. Notice thatND is independent of the magnetic field, and that in thesteady-state case it is of order unity. For large values,the field will not be steady (what is usually meant by anactive dynamo).

Observationally, it appears that X-ray emission fromlate-type stars correlates with a slightly different mea-sure of the dynamo activity. This is the Rossby num-ber, which actually measures the convective (buoyant)timescale compared with the rotation rate: Ro = �τc,where τc is the convective turnover time for some largedepth in the stellar envelope. When Ro is large, eitherthe rotation is very rapid or the turnover line is large (thegravity is low and the stellar envelope is very distended).Empirically, UV emission line strengths and LXR corre-late with Ro, although the precise law is still debated.It seems reasonable that the Rossby number measures atleast something of the α–ω dynamo activity. The � factorin ND is a measure of the vorticity in the buoyant cells,so depends on both � and τc. The turbulent diffusion co-efficient η scales as L2τ−1

c for some characteristic lengthL . However, the determination of an empirical scaling re-lation, drawn as it is from very indirect measures of themagnetic field strength and its rate of generation and struc-ture, does not provide a serious constraint on the dynamotheories. In general, the most that can be said from themeasurement of activity in late-type stars is that a dynamomust be acting, that the field must be constantly emerginganew at the photosphere, and that the mechanism mustdepend on surface gravity, effective temperature, and ro-tational frequency.

E. Planetary Magnetic Fields as Testsfor Dynamo Mechanisms

Planetary magnetic fields are the only ones for which it ispossible to obtain direct in situ measurements of the de-tailed field configuration and time variability. The terres-trial field is probably the best studied. It displays complextime-variable structure; most important are the long-termglobal polarity reversals on timescales between 104 and106 years. These appear to be random and have been mod-eled as chaotic. The earth’s dipole field maintains its sameorientation, inclined to the rotational axis by about 11◦, butits higher order moments vary with different timescales,and the geometry of the field changes slowly as a result.For scaling purposes, the earth’s magnetic dipole momentis 7.9 × 1030 G cm3 and polar field strength is about 0.6 G.

With the exception of Mercury, Mars, and Venus, allof the planets studied by spacecraft have strong magneticfields. Neptune and Uranus have highly inclined fields,similar to those seen in the chemically peculiar stars, andalso have strong nondipole components. The Jovian fieldis about 4 G, it has a dipole moment about 500 times thatof Earth, it is inclined similarly (about 9.5◦). These plan-ets also display polar auroral rings that strikingly resemblethose on Earth, which can be imaged in the UV and opticalfrom Earth orbit with HST. These clinch the link betweentrapped magnetospheric high energy particles and ioniza-tion of the upper atmosphere and support other measure-ments of the magnetic field geometry and structure. Saturnis the anomaly. Although its field is about the same strengthas Earth’s (0.2 G), and its magnetic dipole moment is4.6 × 1028 G cm3, it is almost perfectly aligned (about aone-degree inclination to the rotation axis). It is also in-teresting to note that no changes in the field configurationor strength were detected for either Jupiter or Saturn be-tween the Pioneer and Voyager flybys of these two planets.The groundbased radio measurements of Jupiter, while notvery sensitive to the precise field strength, are also consis-tent with little change in the dominantly dipole geometrythrough the 1980s. It is now possible to compare the pre-vious in situ measurements of the Jovian field with thosefrom the Galileo probe, since these sample a timescale ofnearly 20 years. Cassini will provide similar informationfor Saturn beginning in 2004. Uranus and Neptune havesimilar magnetic fields, both being highly inclined (>40◦)and with polar field strengths of order 0.2 G. The extremeoffset required for the Neptune field, discovered by Voy-ager 2 in the 1989 flyby, makes this planet an especiallyinteresting test case for dynamo models and seems to in-dicate the presence of a complicated field geometry, morecomplex than observed for any of the other planets.

The absence of a strong field on Venus, despite itsotherwise terrestrial bulk properties, is probably consis-tent with the dynamo mechanism. The planet rotates abouta factor of 250 times more slowly than Earth. Mercury ro-tates slowly and is too small to support a strong convectivecore, but it does have a very detectable dipole moment of2.4 × 1022 G cm3. Its field is very small, about 0.002 G,and is nearly aligned and probably a relic from the earlierstages of planetary evolution. Mars rotates with nearlythe same period as Earth, but it is smaller and may onlysupport a very small convective core. Mars has displayedvulcanic activity in the past, evidence for core or mantleconvection, but the planet does not possess even a veryweak intrinsic magnetic field.

Polarity reversals were observed in the sun in the firstdecades of the twentieth century, long before they wererecognized in the earth. The explanation for the reversal ofthe terrestrial field, therefore, lends support to the dynamo




explanation for the magnetic fields in late-type stars andserves to link the study of dynamo processes across a largescale of mass and size of cosmic objects.

F. Galactic-Scale Dynamos

The formation of a large-scale field by dynamo actionrequires the conversion of toroidal magnetic fields topoloidal configurations. The presence of turbulence anddifferential rotation on the galactic scale, and the require-ment that these act in concert in stars to produce the ob-served fields, thus invite a comparison between the twoenvironments. While the length scales are much larger forgalactic-size field structures, the timescales over whichthey are generated are also longer. Thus the scaling of thedynamo process to the interstellar medium as a whole doesnot seem an outlandish idea and has been attempted by anumber of groups. (A good critical review of this was donein 1999 by R. Kulsrud.) Most of the details of the problemare still to be understood, but in broad outline the galacticdynamo is largely indistinguishable from a stellar one; thenotably differences are the planarity of the differentiallyrotating disk and the nonthermal nature of the turbulenceand buoyancy of the medium. These models have the ad-vantage that α can be determined from the turbulence ofthe diffuse interstellar medium and that � is specified bydifferential galactic rotation.

G. Ambipolar Diffusion

The relation between the strength of a magnetic field andthe density of the ambient medium strictly holds only ifthe medium is highly ionized. In stellar plasmas, this isalmost certainly a good assumption, as it also appears tobe for large-scale extragalactic radio jets and lobes. But ininterstellar clouds, where the densities may become largeenough and the opacity high enough, ultraviolet radiationis effectively screened out of the cloud cores. Thus, inthe densest part of a molecular cloud, the ionization is ex-pected to be due primarily to cosmic ray penetration of thecloud, leaving ionization fractions <10−5 in those regionswhere the density is >105 cm−3. When the temperature inthis region falls below about 100 K, it becomes locally un-stable to gravitational collapse. A trapped magnetic fieldwill be transported inward with the collapsing gas, butbecause of the low conductivity will not be amplified asrapidly as one would expect from flux freezing. Insteadof increasing in strength as ρ2/3 or ρ, the matter sepa-rates from the field, and models show that Bcollapse ∼ρ1/2.The separation of the field and the material is due to am-bipolar diffusion, the tendency of ions to separate in anexternal magnetic field, and also the field-line slippagerelative to the gravitationally contracting medium. Direct

measurements support this approximate scaling relation,although models constrain the exponent n in the relationBcollapse ∼ ρn to lie only between about 1

3 and 23 .

H. Magnetic Reconnection

Magnetic reconnection is presumed to occur when regionsof oppositely directed polarity are brought into contact byturbulent motions. This mixing results in the annihilationof the field within a small volume and the transformationof magnetic energy into kinetic energy through the gener-ation of extremely strong local electric fields within verysmall-scale (of order 100 to 1000 km) lengths.

The rate at which the field destruction takes place is amatter of debate, and significantly affects estimates of theheating of the confining plasma. The fastest timescale, theAlfven wave crossing time m appears to be too short (µs)to explain the acceleration observed in solar flares. Theserequire an extended period of electric-field amplificationduring the annihilation phase. Theoretical particle simu-lations suggest that strong MHD turbulence is probablypresent during the reconnection phase of magnetic fieldline merging, and that the electrons are energized throughbeing scattered off of these waves.

Reconnection processes have been implicated in the ac-celeration of particles in the terrestrial magnetotail and inthe generation of disconnection events in comets, whenthe plasma tail of a comet separates from the coma as itcrosses regions in the solar wind of oppositely directedmagnetic polarity (sector boundaries). There is strong ev-idence, from fast observations of stellar flares, that the fre-quency dependence and energetics of large stellar activeregions mimic those observed on the sun, where reconnec-tion is more secure. Finally, it may be possible to see fieldlines merging in radio lobes and jets of external galax-ies. Large-scale filamentation may be associated with thissame instability.

V. FINAL WORDS

The theoretician H. C. van de Hulst has remarked that“magnetic fields are to astrophysics as sex is to psy-chology,” suggesting that magnetic fields are seen as theuniversal explicans for all cosmic phenomena. As longas measurements remained inexact and theory was onlyqualitative, this could certainly have been true in factas well as in jest. The late twentieth century has seen avast improvement in the available techniques for the mea-surement of magnetic-field-related phenomena, especiallythe introduction of high-resolution imaging polarime-ters, improvements in spectrograph design and detectorsensitivity, and the availability of polarimetric instruments




over a broad wavelength regime going from the ultravioletinto the radio. Supercomputers have grown increasinglyimportant in magnetohydrodynamic modeling of stellarand galactic-scale objects, and predictions are well enoughrefined to be testable. Plasma codes for particle simula-tions of reconnection and small-scale processes are reach-ing a mature stage and can confront many of the radioobservations of solar and stellar flare processes. Radioimaging allows now for the study of structures in extra-galactic sources with a dynamic range of as much as 105.And in the past decade, high spatial and spectral resolutionspace observations have finally become routine with thelaunch of the Hubble Space Telescope, ASTRO, FUSE,and ISO. We finally see magnetic fields as the necessaryproduct of astrophysical processes.


BINARY STARS • GALACTIC STRUCTURE AND EVOLU-TION • GEOMAGNETISM • INTERSTELLAR MATTER •NEUTRON STARS • PULSARS • SOLAR SYSTEM, MAG-NETIC AND ELECTRIC FIELDS • STELLAR STRUCTURE AND

EVOLUTION

BIBLIOGRAPHY

Beck, R., Brandenburg, A., Moss, D., Shukurov, A., and Sokoloff, D.(1996). Galactic magnetism: Recent developments and perspectives.Annu. Rev. Astron. Astrophys. 34, 155.

Belton, M., West, R. A., and Rahe, J. (eds.) (1989). “Time-Variable

Phenomena in the Jovian System,” NASA SP494.Borra, E. F., Landstreet, J. D., and Mestel, L. (1982). Annu. Rev. Astron.

Astrophys. 20, 191.Chanmugam, G. (1992). Magnetic fields in degenerate stars. Annu. Rev.

Astron. Astrophys. 30, 143.Cravens, T. E. (1997). “Physics of Solar System Plasmas,” Cambridge

Univ. Press, Cambridge, UK.Crutcher, R. (1999). Magnetic fields in molecular clouds: Observations

confront theory. Astrophys. J. 520, 706.Hartmann, L., and Noyes, R. (1987). Rotation and magnetic activity in

main sequence stars. Annu. Rev. Astron. Astrophys. 25, 271.Krause, F., and Raedler, K. H. (1980). “Mean Field Magnetohydrody-

namics and Dynamo Theory,” Pergamon Press, Oxford.Kulsrud, R. (1999). A critical review of galactic dynamos. Annu. Rev.

Astron. Astrophys. 37, 37.La Rosa, T. N., Kussim, N. E., Lazio, T. J. W., and Hyman, S. D. (2000).

Wide-field 90 cm VLA images of the galactic center region. Astron.J. 119, 207.

Moffatt, H. K. (1978). “Magnetic Field Generation in Electrically Con-ducting Fluids,” Cambridge Univ. Press, Cambridge.

Morris, M., and Serabyn, E. (1996). The galactic center environment.Annu. Rev. Astron. Astrophys. 34, 645.

Myers, P. C., Goodman, A. A., Gusten, R., and Heiles, C. (1995). Ob-servations of magnetic fields in diffuse clouds. Astrophys. J. 442,177.

Parker, E. N. (1979). “Cosmical Magnetic Fields,” Oxford Univ. Press.London.

Priest, E. R. (1984). “Solar Magnetohydrodynamics,” Reidel, Dordrecht,The Netherlands.

Priest, E. R., and Forbes, T. (2000). “Magnetic Reconnection: MHDTheory and Applications,” Cambridge Univ. Press, Cambridge, UK.

Verschuur, G., and Kellerman, K., ed. (1988). “Galactic and ExtragalacticRadio Astronomy,” 2nd ed. Springer-Verlag, New York.

Zel’dovich, Y. B., Ruzmaikin, A. A., and Sokoloff, D. D. (1983). “Mag-netic Fields in Astrophysics,” Gordon & Breach, New York.

Zwaan, C. (1987). Elements and pattern in the solar magnetic field. Annu.Rev. Astron. Astrophys. 25, 83.

P1: GNB/GLT P2: FYD Final Pages

Encyclopedia of Physical Science and Technology EN009G-450 January 22, 2002 17:25

Millimeter AstronomyJeffrey G. MangumNational Radio Astronomy Observatory

I. Millimeter Astronomical ObservatoriesII. Millimeter Astronomical Observing Techniques

III. Science at Millimeter Wavelengths

GLOSSARY

Correlator An electronic device that performs the mul-tiplication and averaging of the astronomical signalsfrom a radio telescope. Correlators are used both to pro-cess spectral measurements from single antenna tele-scopes and to process the signals from a collection ofelectronically connected telescopes.

Interferometer A collection of electronically connectedtelescopes used to make high spatial resolution astro-nomical measurements.

Isomerism The existence of more than one substancehaving a given molecular composition and mass butdiffering in structure. For example, HNC is an isomerof HCN.

Jansky Unit of flux density used in radio astronomy. 1jansky (Jy) is equal to 10−26 W m−2 Hz−1.

MILLIMETER ASTRONOMY involves the study of as-trophysical phenomena through observations at wave-lengths from about 0.3 to 4.5 mm (frequencies from about65 to 900 GHz). Millimeter astronomical investigationsare conducted within a wide range of astronomical cate-gories, including planetary astrophysics, studies of the in-terstellar medium and its inhabitants, and investigations ofthe properties of external galaxies. Millimeter astronom-

ical observations use the measurements of the emissionfrom dust grains and the spectroscopic signature from in-terstellar molecules to study the physical, chemical, anddynamical state of the universe.

I. MILLIMETER ASTRONOMICALOBSERVATORIES

There are two basic types of millimeter astronomical ob-servatory: single antenna facilities and interferometers.Both can be operated either on the surface of the earthor as space-based observatories, although to date onlysingle antenna measurements have been conducted fromsatellites. Both types of observatory operate in funda-mentally the same way, by collecting millimeter wave-length radiation from a celestial object and processingthat signal into radiant flux information about the objectunder study. When a group of two or more single an-tennas are electronically linked and commanded to ob-serve the same celestial object, the group of antennas hasa spatial resolution equivalent to a single antenna witha diameter equal to the separation of the individual el-ements. This allows millimeter interferometers to makeastronomical measurements with very high spatial resolu-tion not easily obtainable with single antenna millimetertelescopes.

853



854 Millimeter Astronomy

TABLE I Millimeter Astronomical Observatories

Latitude Elevation DiameterName Location (degrees) (m) Telescopes (m) λ (mm)

CSO Mauna Kea, HI +19 4000 1 10.4 0.3–1.0

IRAM Pico Veleta, Spain +37 2920 1 30 0.8–3.5

JCMT Mauna Kea, HI +19 4000 1 15 0.3–0.8

NRAO Kitt Peak, AZ +32 1914 1 12 1.0–4.5

NRO Nobeyama, Japan +36 1350 1 45 1.3–15.0

OSO Onsala, Sweden +57 24 1 20 3.0, 13.0

SEST La Silla, Chile −29 2347 1 15 0.9–4.3

SMT Mt. Graham, AZ +33 3186 1 10 0.3–1.0

UMASS Amherst, MA +42 314 1 14 3.0

BIMA Hat Creek, CA +41 1043 10 6 1, 3

NMA Nobeyama, Japan +36 1350 6 10 1, 2, 3

OVRO Owens Valley, CA +37 1216 6 10.4 1, 3

PdBI Plateau de Bure, France +45 2560 5 15 1.2–3.7

SMA Mauna Kea, HI +19 4000 8 6 0.3–0.8

Table I lists the characteristics of the currently operatingmillimeter single antenna and interferometer facilities inthe world. Note that most of these facilities are located athigh altitude sites. This is owing to the fact that millimeterastronomical observations made from the surface of theearth must contend with the earth’s atmosphere. Many ofthe molecular constituents of the earth’s atmosphere arevery good absorbers of millimeter wavelength emission.Figure 1 shows the millimeter absorption spectrum of theearth’s atmosphere, displayed as signal transmission as afunction of frequency. The frequencies in Fig. 1 that showlow transmission coincide with energy transitions from O2

and H2O. The atmospheric scale heights of O2 and H2O areapproximately 8000 and 2000 m, respectively. Therefore,by locating millimeter astronomical observatories at highaltitude sites, measurements made with these facilities areless adversely affected by the absorptive properties of theearth’s atmosphere.

II. MILLIMETER ASTRONOMICALOBSERVING TECHNIQUES

A. Single Antenna Techniques

The basic millimeter single antenna receiving sys-tem contains the components shown in Fig. 2. Sincethe astronomical signals which millimeter telescopesare trying to detect are often thousands of timesweaker than the atmospheric and instrumental emissionthat accompanies the astronomical signal, all measure-ments made with single antennas involve some kind ofswitching.

1. Position Switching

In position switching, the telescope acquires total powermeasurements at the source position and at a nearby ref-erence position by pointing the telescope and integratingon each position in succession. Since the entire telescopestructure must be moved to each position, these measure-ments are usually made over 30–60 sec time scales. To pro-duce the final astronomical signal, the individual sourceand reference measurements are differenced. Figure 3shows a pictorial representation of a position switchedobservation. As long as the received signal from the in-strumentation or the atmosphere has not changed signifi-cantly during the time between a source and its respectivereference measurement, position switching will producereliable astronomical measurements.

2. Beam Switching

In beam switching, the telescope acquires total power dataat signal and reference positions by repositioning one ofthe optical components of the telescope system, usuallythe secondary mirror (see Fig. 3). Since the optical com-ponents are usually relatively small, they can be switchedand positioned accurately at a rapid rate, often several Hz.This allows for rapid switching between source and refer-ence positions, which often allows for better subtractionof the fluctuating emission from the earth’s atmosphere,but is limited by the relatively small reference positionoffsets attainable with most telescope optics.

3. Frequency Switching

In this observing mode, a reference spectrum is obtainedby shifting the center frequency of the source spectral



Millimeter Astronomy 855

FIGURE 1 Millimeter emission spectrum from the earth’s atmosphere from an elevation of 4000 m. The scaling fromprecipitable water vapor column to atmospheric opacity at a frequency of 225 GHz is shown in the upper right.

measurement. Since it is not necessary to move the tele-scope or any of the telescope optics, on-source integrationtime is increased through “in-band” switching. Frequencyswitching also alleviates the need to find an emission-freereference position when observing in a (spatially) complexemission region. Frequency switching also entails less sys-tem overhead than most other observing modes. In prin-ciple, frequency switching can be done by switching thefrequency of the local oscillator (LO) or an intermediatefrequency (IF) oscillator. A pictorial description of fre-quency switching is shown in Fig. 3. If the frequency shiftis small enough, usually less than 50 MHz, the spectralline will appear in both the source and reference spectra.When the resultant spectrum is formed, the line will ap-pear twice, once in emission and once in absorption. Thespectrum can be “folded” to obtain a

√2 improvement

in signal-to-noise. The primary drawback of frequencyswitching is that the spectral baselines are generally notas good (flat) as with position or beam switching. This isbecause the two frequency positions each have their ownspectral bandpass shapes that do not cancel in the com-

putation of the final spectrum, thereby leaving a residualstanding wave in the overlapped spectrum. A number oftechniques, including focus modulation and beam peakscattering, can be used to dampen this residual standingwave.

B. Interferometric Techniques

A basic (two antenna element) interferometer is shownin Fig. 4. Measurements with millimeter interferometersare usually done by having all telescopes in the interfer-ometer measure the millimeter signal from an object. Theindependent but phase-coherent signals from each antennaare then multiplied and integrated (together referred to ascorrelation), which results in interference fringes contain-ing the amplitude and phase information of the astronomi-cal signal. As the earth rotates, the interferometer receivesvarying responses to the structure in the source being mea-sured, and in the process builds up a two (spatial) or three(spatial and spectral) dimensional picture of the astronom-ical source.




FIGURE 2 Basic components of the single antenna millimeterobservatory. Following signal collection by the primary reflectorand nutating subreflector, the receiver amplifies the astronomi-cal signal. The intermediate frequency (IF ) then downconvertsthe received signal to a frequency that can be processed by thespectrometer. The output from the spectrometer, following dataprocessing, is astronomical data.

In principle, millimeter wavelength interferometersoperate in the same way as centimeter wavelength in-terferometers, but with the complication that millimeterinterferometers are sensitive to atmospheric effects. Thevarying atmosphere above a millimeter interferometer in-fluences the received signals through absorption and byintroducing fluctuations in the received phase of a mea-surement. Therefore, as with millimeter single antennaobservations, it is advantageous to locate millimeter in-terferometers at high mountain sites. Atmospheric phasefluctuations produce a blurring of the image producedby a millimeter interferometer. Since these atmosphericphase fluctuations seem to depend upon the distance be-tween the antennas, increasing the separation betweenthe antennas in a millimeter interferometer leads to in-creasingly blurry images for a given level of atmosphericstability.

To correct for the detrimental affects of atmosphericphase fluctuations, a number of correction techniqueshave been developed. One technique uses a bright pointsource in the image as a fringe reference point. Thistechnique is often referred to as self-calibration. Since

bright point sources are not always available within agiven image, techniques which simultaneously measurethe atmospheric emission at wavelengths which provideinformation regarding the amount of water in the Earth’satmosphere have been developed in recent years. Theseatmospheric phase correction schemes have proven to bequite successful, allowing for phase corrections which im-prove the phase noise in a measurement by factors of2–3. Future improvements in these phase correction sys-tems will likely yield higher levels of improvement to thereceived astronomical signals.

III. SCIENCE AT MILLIMETERWAVELENGTHS

A. Star Formation

1. Molecular Clouds

As early as the mid-1920s, optical astronomers identi-fied regions in our galaxy that possessed moderate to highlevels of visual extinction. Simple interstellar molecules,such as CH, CH+, and CN, were discovered in these re-gions by optical astronomers as early as 1937–1941, indi-cating the presence of an interstellar medium containingregions with densities large enough to support the forma-tion and existence of molecules. The discovery of com-plex molecules had to await the advent of radio astronomy.In 1968, water (H2O) and ammonia (NH3) were discov-ered toward the regions identified by optical astronomersas having high visual extinction. The existence of thesemolecules indicated the presence of dense, cool, opaqueregions that were eventually recognized as the sites of starformation.

Within the general evolution of spiral galaxies, the starformation process is catalyzed by the continued conden-sation of gas and dust from the interstellar medium. Inthis molecular cloud phase, vast regions of the interstellarmedium are characterized by high densities, low temper-atures, and kinematic motions indicating the existence ofinfall and outflow. Our galaxy contains about 109 M� ofmolecular gas. The majority of this gas is located in gi-ant molecular clouds containing approximately 104−6 M�of material. A cloud with support only through kinematicmotions of the gas will collapse upon itself if the massexceeds the Jeans mass,

MJ =(

πkTK

µmH G

)1.5

ρ−0.5,

while a molecular cloud without pressure support willfree-fall collapse on a timescale given by




FIGURE 3 Graphical description of the position, beam, and frequency switching observing techniques.

tff =(

3π

32Gρ

)0.5

,

where k is Boltzmann’s constant (1.380658 × 10−16 ergK−1), TK is the kinetic temperature of the gas (K), µ

is the mean mass per particle (which is equal to 2.29in a cloud which is 100% molecular composed of 25%He by mass), mH is the mass of a hydrogen atom (g),G is the gravitational constant (6.67259 × 10−8 cm3 g−1

sec−2), and ρ is the mass density (g cm−3). Since themoderate to high densities and low temperatures foundin these giant molecular clouds indicate that most of themshould be collapsing, indicating a star formation efficiencythat does not agree with the observed star formation rate,there must be some form of additional support in theseregions.

Two mechanisms have been considered as candidatesfor the additional structural support for molecular clouds:turbulence and magnetic fields. The theoretical and ob-servational investigations into the importance of each of

these mechanisms in the physical evolution of molecularclouds currently reach inconclusive results regarding theimportance of each.

2. Measurements of Physical Conditions

The study of molecular cloud stability and evolution leadsnaturally to studies of the physical and chemical evolutionof the star formation process. Fundamental to this studyof the star formation process is the characterization of thephysical conditions in the gas and dust comprising theseregions. For the gas, volume density n (cm−3), kinetictemperature TK (K), chemical composition X , turbulentmotion �v (km sec−1), and magnetic field strength B(Gauss) are fundamental physical quantities. For thedust, the dust temperature Td (K), dust volume densitynd (cm−3), and dust opacity κ describe the physical condi-tions representative of the dust component of a molecularcloud. Note that all of these quantities are dependent upontime and position.




FIGURE 4 A basic interferometer. After the signals from an astronomical object are received and amplified by thetwo antennas, they are combined in a correlator. The correlator multiplies and integrates the two signals, yieldinginterference fringes that contain the correlated amplitude and phase information from the astronomical source. Thisinformation is then processed in a computer to produce an astronomical image.

Most of the material in molecular clouds is in the formof H2, which owing to its lack of a permanent dipole mo-ment has no easily observable rotational transitions. It canbe observed through rovibrational and fluorescent transi-tions, but only within environments which are very spe-cific, such as shocks and regions containing high levelsof ultraviolet emission. Therefore, the principal compo-nent of molecular clouds is effectively unmeasurable. Thisfact forces astronomers to use trace constituents, othermolecules and dust, to measure the physical conditions inmolecular clouds.

a. Molecular emission as a tracer of physical con-ditions. The primary constituent of molecular clouds,H2, is also the main collision partner with other molec-ular inhabitants of these regions. These collisions leadto the excitation of rotational transitions in a variety of

molecules, many of which emit at observable millime-ter wavelengths. The most abundant molecule after H2 iscarbon monoxide (12C16O, usually simply written CO).It was the first molecule discovered at millimeter wave-lengths by Wilson, Penzias, and Jefferts in 1970 usingthe National Radio Astronomy Observatory 36 ft (now12 m) millimeter telescope located on Kitt Peak, Arizona.It has been used extensively as a probe of the volume den-sity and kinetic temperature in molecular clouds throughmeasurements of its lowest two rotational transitions at115.271 and 230.538 GHz. CO has proven to be a verygood tracer of the global physical conditions in molecularclouds, but for more compact regions with a larger num-ber of particles along the line of sight [referred to as thecolumn density (N ) of a particular molecule], it loses itssensitivity to the bulk of the gas as the opacity in the mea-sured transitions rises. Fortunately, there are other less




abundant molecular tracers, including isotopomers (iso-topic variants) of CO, such as 13CO, C18O, and 13C18O,which prove to be better probes of these high column den-sity environments.

There are a wide variety of molecules that can be usedas tracers of the volume density and kinetic temperaturein molecular clouds. The choice of molecular probe de-pends upon what environment one wishes to study. Forexample, to measure the physical conditions in the densecores of molecular clouds, it is best to choose a moleculartracer that is particularly sensitive to the prevalent condi-tions in this environment. A useful guide used to calculatethe sensitivity of a transition to volume density is the crit-ical density ncrit, which is the volume density requiredto collisionally excite a transition assuming optically thinconditions,

ncrit = Ai j

Ci j

= 64π4ν3i j

3hc3gi Ci j|⇀µ j i |2

= 64π4ν3i j

3hc3gi Ci jSµ2,

where Ai j is the spontaneous emission (Einstein A) co-efficient for level i, Ci j is the collisional deexcitation rateper molecule in level i, gi is the upper state degeneracy,|⇀µ j i | is the dipole moment matrix element for the transi-tion, S is the line strength for the transition, µ is the dipolemoment for the molecule, and the other terms have theirusual meanings. Critical densities for common moleculessuch as CS, HCN, and H2CO are in the range 104−8 cm−3

for a kinetic temperature of 10 K.Therefore, a simple detection of a transition from one

of these molecules implies the existence of dense gas. Asecond consideration is to choose molecules that allowone to derive accurate measures of the volume densityand kinetic temperature in a molecular cloud. Since thecollisional excitation of molecular transitions is depen-dent upon the coupled effects of volume density and ki-netic temperature, it is often necessary to use moleculesthat allow one to decouple these effects. The ability todecouple these physical effects depends upon the prop-erties of the molecular structure. There are three basictypes of molecules in this regard; linear, symmetric rotor,and asymmetric rotor. Figures 5–7 show the energy levelstructure for these three types of molecules. As can be seenfrom Fig. 5, linear molecules have one ladder of energylevels, the transitions between which are excited by thecoupled effects of volume density and kinetic temperature.In general, linear molecules are used to derive the volumedensity in a molecular cloud by assuming a kinetic temper-

FIGURE 5 Rotational energy level diagram for HC3N, a typicallinear molecule. The rotational quantum number “J” and associ-ated energy above the ground state are indicated for each level.

ature or by using a calculation of the kinetic temperaturebased on measurements of the transitions from anothermolecule. The energy level structures for the symmetricand asymmetric rotor molecules shown in Figs. 6 and 7indicate a more complex structure. Like linear molecules,the strengths of transitions within a given ladder (desig-nated by the “K” rotational quantum numbers) are de-pendent upon the coupled effects of volume density andkinetic temperature. A comparison of the strengths of tran-sitions from the same J levels but from different K lad-ders, though, is dependent only on the kinetic temperature,thus making it possible to derive a decoupled measure-ment of the kinetic temperature in a molecular cloud. Ingeneral, then, symmetric and asymmetric molecules havemolecular level properties that, when the appropriate tran-sitions are compared, allow decoupled measurements ofthe volume density and kinetic temperature in a molecularcloud. Linear molecules do not possess these decouplingproperties, thus requiring an independent measurement ofeither the volume density or kinetic temperature.

By comparing the measured intensities of a varietyof transitions from a given molecule with molecularline intensity predictions from a molecular cloud model,




FIGURE 6 Rotational energy level diagram for CH3CN, a typical symmetric rotor molecule. The rotational quantumnumbers J and K, along with the associated energy above the ground state, are indicated for each level.

FIGURE 7 Rotational energy level diagram for H2CO, a typical asymmetric rotor molecule. The rotational quan-tum numbers J, K−1, and K+1, along with the associated energy above the ground state, are indicated for eachlevel.




estimates of the volume density and kinetic tempera-ture within a molecular cloud can be made. In general,these estimates reveal that the volume densities in the re-gions where stars form within molecular clouds exceed104 cm−3, while the kinetic temperatures range from 10to 300 K. These models also indicate that many molecularcores possess density gradients, suggestive of a structurethat could evolve into a collapsing protostar.

b. Kinematics. The shape of a spectral line is deter-mined by the radial velocity structure along the line ofsight through a molecular cloud. The measured widths ofspectral lines are generally larger than the thermal width,indicating that the velocity fields within molecular cloudsare dominated by Doppler broadening owing to turbu-lence:

�v = vtherm + vturb

= 2

√2 ln 2kTK

m+ vturb

where �v is the full width at half maximum of the spec-tral line, TK is the kinetic temperature of the gas, and mis the mass of the particles which make up the molecularcloud (principally molecular hydrogen). Unfortunately, adetailed derivation of the spectral line shape has provenelusive, owing to the effects of kinetic temperature andvolume density gradients, spatial structure, and radiativetransfer effects within the molecular cloud. Measurementsof the line center velocity as a function of position over amolecular cloud do indicate that, in general and on largescales, they are neither collapsing nor rotating. This isnot the case on small scales. Evidence for rotation andcollapse of molecular cloud cores on 0.1 pc scales haveyielded interesting clues to the details of the star forma-tion process. Measurements of cloud core rotation indicatethat in magnitude it is only 2% of the gravitational po-tential energy before collapse, making it relatively unim-portant to the overall dynamics of a molecular cloudcore.

The physical nature of the turbulent component of aspectral line in a molecular cloud is currently a source ofconsiderable debate. Physical processes that have beensuggested as sources of the turbulence in molecularclouds are expanding HII regions, supernova remnants,cloud–cloud collisions, galactic differential rotation, andstellar winds. Unfortunately, for all of these processesthere are theoretical problems with coupling the energyproduced into turbulence.

c. Magnetic fields. An understanding of the mag-netic field properties of molecular clouds is an important

aspect of the overall physical understanding of molecularclouds given their apparent role in providing dynami-cal support in these environments. There are three meth-ods that have been used to measure the magnetic fieldstrength and direction within molecular clouds: atomicand molecular Zeeman effect splitting, which tell us aboutthe line-of-sight magnetic field component (BZ); polar-ization of the emission from dust grains, which gives usinformation about the component of the magnetic fieldsperpendicular to the line-of-sight (B⊥); and measure-ments of spectral line emission polarization, which alsotells us about B⊥. Measurements of the Zeeman split-ting in atoms and molecules have concentrated on studiesof HI, OH, and CN, yielding typical values for BZ of10–20 µG within regions with volume densities of ap-proximately 103 cm−3. At higher volume densities, mag-netic fields as large as 700 µG have been measured. Mil-limeter dust continuum emission polarization levels of atmost a few percent have shown that the magnetic fieldwithin the high volume density (n ≥ 106 cm−3) cores ofmolecular clouds is perpendicular to the major axis ofthe high density structures (such as disks) and parallelto the outflows associated with these objects. Althoughthe possibility of there being measurable levels of po-larization of thermal millimeter spectral line emissionhas been known for years, it has only recently been de-tected. The percentage of measured polarized emission isequivalent to that detected through millimeter continuumpolarimetry.

Turbulence and magnetic fields cannot simply be ap-plied as independent solutions to the problem of cloudsupport since turbulence should tangle magnetic fields,thus reducing their effectiveness as a source of support.The theory of magnetohydrodynamic turbulence withinmolecular clouds has shown that magnetic fields shouldslow the decay of turbulent motions if these motions areless than the propagation speed along the magnetic fieldlines, referred to as the Alfven velocity. However, the sta-bility of magnetic support in the presence of turbulencehas been called into question, and the interplay betweencloud stability and dynamics drives our understanding ofthe importance of magnetic fields as a means of molecu-lar cloud support. Future measurements of the magneticfield and direction in molecular clouds should clarify theirinfluence on the overall dynamics and evolution of theseregions.

3. Dust Emission as a Tracerof Physical Conditions

Dust is also a viable probe of physical conditions inmolecular clouds through attenuation measurements atultraviolet through near-infrared wavelengths and by using




measurements of its emission at far-infrared throughradio wavelengths. As noted earlier, extinction of back-ground starlight can be used as a probe of the dust col-umn density along the line of sight. Studies of the ex-tinction of optical starlight probe molecular clouds at lowextinctions (Av ≤ 5), thus giving information about theouter skins of molecular clouds. Recently, surveys of thenear-infrared extinction have probed much deeper intomolecular clouds, as much as Av ∼ 30 magnitudes. Thesenear-infrared surveys have revealed much regarding theinner structure of molecular clouds.

Dust also reveals its presence through emission at mil-limeter wavelengths. That the opacity of dust continuumemission possesses a power-law dependence on wave-length,

κν ∝ νβ,

where β ∼ 1−2, allows that dust emission at long wave-lengths can trace large column densities in molecularclouds. Millimeter emission from dust can therefore probelarger column densities in molecular clouds, as deeply asAv ∼ 104 magnitudes. Since the dust emission dependsupon the physics of the dust as follows:

Sν = 2hν3 s

c2

1 − exp

[−τ0

(ν

ν0

)β]

exp

(hν

kTD

)− 1

,

where Sν is the emission flux at frequency ν, s is thesource solid angle, τ0 is the optical depth at frequency ν0,β is the dust emissivity power law, and TD is the dust tem-perature, an independent estimate of the kinetic tempera-ture within a molecular cloud can be obtained assumingthat the gas and dust are coupled (TD � TK). The columndensity and mass of a molecular cloud can also be inferredfrom dust emission measurements as follows:

N = Nλ

(λ

λ0

)β

τλ,

M = Cν D2Sνc2

2hν3

[exp

(hν

kTD

)− 1

],

where Cν is a coefficient that describes the physical sizeand millimeter emission properties of the dust grains atfrequency ν, D is the distance to the molecular cloud,c is the speed of light, and the other terms have beenpreviously defined. Therefore, measurements of the dustcontinuum emission from molecular clouds adds comple-mentary physical information to that obtainable throughmolecular emission measurements.

4. Classification of Sources andEvolutionary Scenarios

In order to understand the evolutionary characteristics ofthe star formation process, it is convenient to have a sourceclassification system. A classification scheme that usedthe infrared spectral index for λ > 2 µm was developedin the 1980s to characterize infrared sources. This clas-sification scheme contained three categories, Class I–III,which are distinguished by a decreasing amount of emis-sion at longer wavelengths. Once detailed models of theevolution of the star formation process for an isolated low-mass core were developed, these categories became asso-ciated with stages in the star formation process. Later, afourth younger class had to be added to this system, Class0, when it became apparent that there were a significantnumber of sources with even larger amounts of emissionat longer wavelengths. Figure 8 shows a pictorial descrip-tion of these classes. Figure 9 shows an integrated CO 2–1emission image from a portion of the Ophiuchus star for-mation region, which contains a rich variety of protostellarand young stellar objects.

5. Isolated and Clustered StarFormation Properties

The star formation process is thought to proceed in two dif-ferent physical environments: isolated regions containinga single, usually lower mass (M < 10 M�), object evolv-ing toward the formation of a star, and a group or clus-ter of dense cores, usually of higher mass (M ≥ 10 M�),which appear to be forming stars. The detailed evolu-tionary sequence described in Section 4 has been de-veloped mainly to explain the isolated star formationprocess given its simplicity. Observations of the molec-ular spectral line and continuum emission from these iso-lated star formation regions are currently being used totest these detailed evolutionary sequences. Specifically,studies of the core collapse signature from spectral linemeasurements, multifrequency dust emission measure-ments of the emission signature from dense cores, andimaging studies of the molecular spectral line and con-tinuum emission from these regions are being used toprovide stringent tests of the theories of isolated starformation.

Our understanding of the clustered star formation pro-cess is quite a bit different than that for isolated star for-mation. High mass stars represent a much smaller fractionof the stellar population than low mass stars, so the nearestexamples of high mass star formation are far more distantthan their low mass cousins. Fortunately, though, stellarluminosity is a strong function of mass, which makes itrelatively easy to detect high mass stars at large distances.




FIGURE 8 Pictorial description of the star formation evolutionaryprocess. The column on the left of the figure depicts the radi-ant flux of each class as a function of frequency. The emissionfrom physically distinct components which compose each classare indicated. The column in the center of the figure presentsa pictorial description of each class. Arrows indicate mass in-flow and outflow. The column on the right of the figure lists theclass name, its primary physical component, its age, and themass of the central accreting protostar (for Class 0 and I) orthe mass of the stellar disk (for Class II and III). [From Andre, P.(1994). In “Proceedings of the XIIIth Moriond Astrophysics Meet-ing, The Cold Universe” (T. Montmerle, C. J. Lada, I. F. Mirabel,and J. Tran Thanh Van, eds.), Editions Frontieres, Gif-sur-Yvette,France.]

The quantity of observational information on clusteredhigh mass star formation is equivalent or greater than thatfrom isolated low mass star formation regions. This infor-mation is often difficult to interpret, though, owing to thefast evolution of massive stars in a clustered environment,the strong influence that high mass stars exert on their sur-roundings, and the poor spatial separation of multiple starformation events in these regions afforded by current mil-limeter astronomical instrumentation. The general pictureof low mass protostellar evolution described in Section 4 islikely to be generally valid for high mass star formation inclusters, but the higher densities and more kinematically

dynamic environments in which high mass star formationproceeds forces the process to evolve more quickly thanin a low mass environment. In general, our overall under-standing of clustered star formation is quite a bit moreincomplete than it is for isolated star formation, but it isbelieved that the two evolutionary sequences have manysimilarities.

B. Evolved Stars

During the evolution of many stars, mass loss duringthe giant branch phase modifies a star’s physical prop-erties. Studies of the stellar envelopes that result fromthis mass loss process indicate that evolved stars are asignificant contributor of processed material to the in-terstellar medium. Since this processed material is even-tually incorporated into the next generation of stars, anunderstanding of evolved stars and their mass loss mech-anisms is key to understanding the entire star formationprocess.

Toward the end of their lifetimes, low and intermediatemass stars (1M� M 10 M�) go through a high massloss phase. As a result, a circumstellar envelope is formedthat can often be detected with spectral line and continuumobservations at millimeter wavelengths. These objects in-clude (1) classical Mira and semiregular variable stars,(2) OH/infrared (OH/IR) and carbon stars, (3) early spec-tral type (warm) stars of type B–F, and (4) planetary nebu-lae (PN). Stellar evolution theory places variables, OH/IR,and carbon stars on the asymptotic giant branch (AGB).These stars lose mass at very high rates of up to 10−5 M�per year through continuous flows and episodic outbursts.The total galactic rate of mass loss from evolved starscould be as high as 0.35 M� per year, making them a sig-nificant contributor to the cycle of star formation and thereturn of processed material to the interstellar medium.The mass loss mechanism in these objects is not wellunderstood, but a prime suspect is radiation pressure ongrains that are condensing in the cool extended atmo-spheres of these objects. Planetary nebulae have evolvedbeyond the AGB stage, characterized by the ejection andionization of the star’s envelope.

The morphology and extent of circumstellar envelopesis determined by the dynamics of the mass loss processand by the stellar and interstellar radiation field. Since theenvelope’s density structure is approximately known, thetime exposure of the interstellar radiation field can be es-timated, and the distribution of molecular photoproductscan be measured. Stellar envelopes represent an unparal-leled astrochemistry and radiative transfer laboratory. Forthis reason, evolved stars have been prime targets for thedetection and study of rare molecules in the overall inves-tigation of interstellar chemistry.




FIGURE 9 Spectrally integrated CO 2–1 emission image of a portion of the Ophiuchus star formation region. Theintensity scale is in K ∗ km sec−1. Symbols identify the positions of the young stellar objects in the region, some ofwhich possess molecular outflows.

C. Chemistry and the Roleof Interstellar Molecules

There are currently 120 known interstellar molecules, 82of which were discovered at millimeter wavelengths, andthe majority of which are organic (see Table II). Cosmicatomic abundances are generally reflected in the relativeabundances of interstellar molecules, with H, C, O, andN being highly important in molecules. The atomic abun-dances of S, Si, P, Na, Al, Cl, F, K, and Mg are seenin fewer species, partly owing to reduced abundance andpartly owing to inefficient chemistry. Carbon chemistry isthe dominant form in the interstellar medium, with longcarbon chains playing a dominant role among the organiccompounds.

Because of the very low densities and temperaturesprevalent in the interstellar medium, molecules cannot beformed by the same processes that produce them on earth.Astrochemistry appears to be dominated by three chemicalreaction regimes: ion-molecule, grain surface, and shockchemistry.

1. Ion-Molecule Chemistry

Gas-phase reactions involving molecular ions are the bestunderstood and are thought to be the most important ofthe three chemical regimes in the interstellar medium.Ion-molecule chemistry appears to explain fairly well theformation of the simpler interstellar molecules (those con-taining less than 5 atoms), and recently the formation of afew of the more complex molecules have been explainedby ion-molecule reactions.

2. Grain Surface Chemistry

Catalytic reactions on the surfaces of interstellar dustgrains, followed by release into the gas phase, can ex-plain the formation of the most abundant molecule, H2,and appears to be successful at explaining the formation ofmany of the more complex interstellar molecules. Unfor-tunately, grain chemistry processes are poorly understoodand difficult to simulate. Grain surfaces are also recog-nized as repositories for many interstellar molecules that




TABLE II Known Interstellar Molecules (January 2001) (Courtesy Barry Turner)

Inorganic molecules (stable)

Diatomic Triatomic 4 Atom 5 Atom

H2 HCl H2O NH3 SiH4

CO PN H2S

CS NaCl SO2

NO AlCl OCS

NS KCl N2O

SiO AlF

SiS HF

Organic Molecules (stable)

AldehydesAlcohols and ketones Acids Hydrocarbons

CH3OH H2CO HCN C2H2

CH3CH2OH CH3CHO HCOOH C2H4

H2CCO HNCO CH4

(CH3)2CO

HCCCHO

HOCH2CHO

Amides Esters and ethers Organosulfur

NH2CHO CH3OCHO H2CS

NH2CN (CH3)2O HNCS

NH2CH3 CH3SH

Paraffin Acetylenederivatives derivatives Other

CH3CN HC3N CH2NH

CH3CH2CN CH3C2H CH2CHCN

C6H6

Unstable molecules

Radicals Ions Rings Carbon chains Isomers

CH C3H CH+ SiC2 HC5N HNC

CN C3N HCO+ C3H2 HC7N CH3NC

OH C3O N2H+ C3H HC9N HCCNC

SO C4H HOCO+ C2H4O HC11N HNCCC

HCO C5H HCS+ SiC3 CH3C3N MgNC

C2 C6H H3O+ CH3C4H MgCN

C2H C2S HCNH+ CH3C5N NaCN

C3 C3S H2D+ SiC4

HNO CH2CN HOC+ H2CCC

CP SiC SO+ H2CCCC

SiH2 CH2 CO+ C7H

NH2 C2O H3+ C8H

HCCN C5N H2COH+ H2C6

SH HC3NH+ SiC3

CH3 CH2D+

SiCN




may have been produced during a cooler and denser phaseof the parent molecular cloud. These grain repositories arethought to be composed of grain surface ices, which whenwarmed by a nearby star formation event release the storedmolecules into the interstellar medium.

3. Shock Chemistry

Strong shocks produced by the expanding ionized en-velopes of massive stars and supernova remnants heatand compress the interstellar medium, leading to con-ditions ripe for many high-temperature chemical reac-tions. Like grain surface chemistry, reactions within theshock chemistry environment are difficult to simulate, butare progressing toward a physical framework that can becompared to observations. While OH and H2O are promi-nent products of ion-molecule chemistry as well as shockchemistry, SiO, and SiS are predominently produced inshocks.

In nonquiescent regions, the chemistry is generally timedependent. This means that the chemical abundance ofmany molecules are a function of time and evolutionarystate of the parent molecular cloud. With a more thoroughunderstanding of the chemical processes at work in theinterstellar medium, studies of the abundances of inter-stellar molecules will in future be coupled to the physicalevolution of the interstellar medium to allow a better deter-mination of the ages of various types of processes whichoccur in the interstellar medium.

A fundamental role played by molecules in the inter-stellar medium is as one of the cooling catalysts for the starformation process. Molecular clouds that exceed the max-imum stable mass for a cloud with only thermal support,known as the Jeans mass (see Section A1), are predictedto gravitationally collapse. In order for this collapse toproceed, molecules and dust are required to radiate awayenergy released by the gravitational collapse. Many ofthe stars formed will eventually produce novae and super-novae, which further enrich the interstellar medium withmolecules that can be used as catalysts to future star for-mation events.

D. Solar System

1. The Sun

Studies of the millimeter emission from the sun have con-centrated on the identification and characterization of thenonthermal millimeter emission produced by solar flares.Only the most energetic electrons (energies >1 MeV) ac-celerated in solar flares produce millimeter emission. Mil-limeter interferometric observations made in recent yearshave shown that the electron population that produces the

millimeter emission is different than the electron popula-tion that produces the keV-energy bremsstrahlung at x-rayfrequencies. These observations suggest that two distinctelectron acceleration mechanisms may be at work in solarflares.

2. Comets

Molecular spectral line and millimeter continuum mea-surements of comets are used to study the physicalconditions within the comae and nuclei of these objectsusing the same basic techniques that are applied to thesekinds of measurements made toward molecular clouds.In general, millimeter observations of comets are muchmore difficult to make given the rather small apparentangular size (generally less than 10′′) of most comets.In any event, inspired by the recent visitation by cometHale–Bopp, which was the most massive comet ever ob-served, quite a few millimeter continuum and spectralline observations of comets have been made in the pastdecade.

For example, millimeter continuum observations ofcomets P/Halley and Hale–Bopp have been used to mea-sure the dust particle properties of cometary nuclear mat-ter. These measurements have shown that the dust par-ticle sizes in these comets are greater than 1 mm andthat the mass of dust contained in the radiating grainsis 1010−1012 kg. Molecular spectral line observationsof approximately 28 molecular species have been madetoward a number of comets, with the recent visitationby the extremely large comet Hale–Bopp accounting forover half of these. Many of the molecules observed incomets are thought to be “parent” species, or speciesdeposited onto icy grain mantles in the core during theformation of the comet. These species are released intothe coma of a comet when it receives enough heat-ing from the sun to sublimate them into the gas phase,thus allowing them to be observable through their rota-tional transitions. Thus, measurements of parent molec-ular species in comets are a direct measure of the chem-ical properties of the material from which comets weremade, which is thought to be the same material fromwhich the solar system formed. It is theorized that par-ent species chemically react with other parent speciesand atoms in the coma gas to produce other molecules,called “daughter” species. Since the intensity and distri-bution of a molecular species in a comet can be used toderive the physical conditions within the cometary nu-cleus and coma, studies of molecules in comets are a keyelement to an understanding of the physical structure ofcomets. An example of the variety in spatial distributionfound in the molecular emission from comets is shown inFig. 10.




FIGURE 10 Spectrally integrated intensity images of the CO2–1, HCN 3–2, H2CO 312−211, and HCO+ 3–2 emission fromcomet Hale–Bopp. Taken near perihelion in the spring of 1997,these four images reveal the chemical diversity of molecular emis-sion from comets.

3. Planets

The millimeter wavelength emission from planets is madeup of a combination of the black body continuum emissionfrom the surface of the planet and atmospheric molecularspectral line emission. Spectral line profiles owing to mil-limeter wavelength molecular transitions from planetaryatmospheres are used to derive its atmospheric tempera-ture and abundance structure. Examples include measure-ments of CO, HDO, HCN, HC3N, and CH3CN from the at-mospheres of Mars, Venus, Jupiter, Titan, Saturn, Uranus,and Neptune. These measurements are then used to derivethe atmospheric chemistry and transport mechanisms. Forexample, measurements of the deuterated water (HDO)distribution in the atmosphere of Mars have been used totrace variations in the abundance of water as a function ofmartian latitude and season. Recent measurements pointto the presence of significantly more water vapor near thenorth polar cap during northern summer on Mars, consis-tent with the sublimation of water deposits in the northpolar cap. Coupled with measurements of the martian at-mospheric temperature profile, the vertical atmosphericwater profile has been derived. Comparison with the wa-ter vapor measurements made by the Viking lander in the1970s indicates that the global mean water vapor contentabove 5 km is significantly lower today. Either the water

vapor resides at very low altitudes in the Martian atmo-sphere or the entire atmosphere is 10 times drier than itwas 20 years ago.

4. Asteroids

Observations of asteroids at millimeter wavelengths arelimited to measurements of their continuum emission.The dust emission properties from an asteroid can beused to derive the dielectric properties of its surface ma-terial, which is a direct indicator of the physical prop-erties of the asteroid surface. This information is com-plementary to that which one can obtain through opticaland infrared observations, but the accuracy of many ofthe physical measurements made using millimeter obser-vations is often better owing to the millimeter emissionprocess in these objects. For example, at millimeter wave-lengths the absorption and emission of radiation happenin the surface layers of the asteroid at a depth of just afew wavelengths. This causes the thermal inertia to bemuch larger at millimeter wavelengths than it is at op-tical and infrared wavelengths, making the time scalesfor changes in the millimeter emission properties muchlonger (tens of hours) than the measured rotation peri-ods of asteroids (a few hours). Another simplifying fac-tor that makes millimeter observations more sensitive tothe asteroid surface physical conditions is the fact thatthe emissivity at millimeter wavelengths is very close tounity. This implies that the observed brightness temper-ature of an asteroid is equal to its equilibrium physicaltemperature.

The rather simple millimeter emission properties of as-teroids have made them a very attractive option for ac-curate flux calibration at millimeter wavelengths. Cur-rent flux calibration at millimeter wavelengths is basedon models of the millimeter emission from Mars extrap-olated to measurements of other planets such as Jupiter,Saturn, Uranus, and Neptune. Unfortunately, the millime-ter emission from Mars is complicated by the poorly un-derstood effects of the polar ice caps, the longitudinal de-pendence of the disk temperature, and the atmosphericdust storms, making the uncertainty in the Mars-basedflux calibration scale 5–10%. Asteroids can provide a fluxcalibration standard that is accurate to better than 5%.Their small apparent angular size of less than 2′′ has lim-ited their utility in this capacity as this angular size gen-erally represents a small fraction of the spatial resolutionof a telescope that operates at millimeter wavelengths.Advances in millimeter observing instrumentation in thenext decade will overcome this limitation and further de-velop the use of asteroids as millimeter wavelength fluxcalibrators.




E. Extragalactic Astrophysics

Studies of the dust and molecular components of galax-ies parallel the analyses of the physical properties in starformation regions in our own galaxy. Most studies of themolecular and dust component of galaxies concentrate onthe morphological and evolutionary impact of these com-ponents. For example, stars form within the dense molec-ular clouds that inhabit galactic disks, and these stars con-tribute significantly to the total luminosity of their parentgalaxy. Measurements of the CO and dust continuumemission from a wide variety of galaxies have allowedscientists in recent years to study the global content ofH2 as a function of morphological type, luminosity, andenvironment in these objects. Following are some of theareas of research into extragalactic astrophysics done atmillimeter wavelengths.

1. Mass Determination in External Galaxies

For the reasons discussed in Section III.A, molecular emis-sion is a good tracer of H2. Since CO is the most abundantmolecule after H2, it has become the de facto standard forderiving the molecular mass in galaxies. The molecularmass is derived from measurements of the CO emissionby first measuring the CO luminosity from a molecularcloud in a galaxy:

LCO = D2∫

ICO d ,

where D is the distance to the galaxy, ICO is the CO bright-ness temperature integrated over the line profile

ICO =∫

TCO dv,

and is the angular size of the molecular cloud. Assum-ing for simplicity a spherical cloud that is in virial equi-librium, such that for a cloud of mass Mc the linewidth isgiven by

�v =√

G Mc

R,

the cloud mass Mc is derived from the CO luminosity withthe following:

Mc = LCO

TCO

√4ρ

3πG,

where ρ is the mass density of the gas. One obtains the totalCO luminosity, and therefore the total molecular mass, fora galaxy by integrating over all of the individual molecularclouds in the galaxy. A key assumption used when relatingthe total CO luminosity to the molecular mass is the con-stancy from galaxy to galaxy of the ratio

√ρ/TCO. Studies

of this ratio in molecular clouds in our own galaxy, in addi-tion to studies of the CO emission from external galaxies,indicate that this factor varies by about at least a factor of2, indicating a reasonable accuracy to the proportionalitybetween CO luminosity and molecular mass.

2. Morphological Studies

The spatial distribution of molecular gas in a variety ofgalaxies has been used to address a variety of morpho-logical issues. Studies of spiral structure have consideredthe relationships between the HI, H2, and HII gas in spi-ral arms, the nature of spiral arm streaming motions, andthe possible existence of higher order resonance patternswithin spiral structure. One result from these studies is thatin spiral galaxies the radial distributions of CO emissiongenerally peak in the center and decrease monotonicallywith radius, while the atomic distributions (as traced by HIemission) in these objects show a central depression fol-lowed by a relatively constant distribution with increasingradius. An excellent example of the information availablethrough millimeter spectral line studies of spiral arm struc-ture in external galaxies is the image of CO 1–0 in M51shown in Fig. 11. This image shows a clear definition ofthe molecular gas associated with the major spiral arms inM51. A comparison with an optical image obtained with

FIGURE 11 CO emission contours shown superimposed on aHubble Space Telescope image of M51. The CO image, which wasconstructed by combining 19 individual pointings of the OwensValley Radio Observatory millimeter array, has a resolution of 2.3′′.[From Aalto et al. (1999). Astrophysical Journal 522, 165.]




the Hubble Space Telescope shows the positional coinci-dence between the molecular gas and the visible dust lanesin this galaxy. The CO 1–0 imaging of M51 has revealedspiral arm molecular cloud associations with masses of107–108 M�, spatial extents of approximately 150 pc, andstreaming motions in the range 20–50 km sec−1. Imagingstudies of the millimeter dust continuum emission fromM51 show a good correlation with the distribution of COemission in this galaxy.

Barred spiral galaxies have been found to have an en-hancement of CO emission along the optical bar. Addition-ally, many galaxies that do not show barred morphology inthe optical have been found to exhibit bar-like structuresin their central regions. For example, the nearby spiralgalaxy IC342 contains a molecular bar, but no apparentoptical bar (see Fig. 12). Spiral arms that trace the loca-tions of young stars are also apparent in high resolutionimaging studies of the CO emission in these objects.

During the past five years morphological studies of spi-ral galaxies have been significantly advanced through twomajor millimeter interferometric surveys of the CO 1–0

FIGURE 12 Overlay of the CO 1–0 (green) integrated intensityobtained using the NRAO 12 Meter Telescope, a Very Large ArrayHI (red) emission image, and the Palomar Observatory Sky Sur-vey red optical image (blue) from the nearby Scd galaxy IC342.Note that the CO and optical emission coexist in the central partof the galaxy, where the HI emission is very weak. Note also that anumber of spiral arms apparent in the HI emission from the outerparts of the galaxy can be traced smoothly into spiral arms appar-ent in the CO emission in the central parts of the galaxy. Photocourtesy of Jean Turner.

emission in nearby galaxies. Using the OVRO and BIMAmillimeter arrays, complete images of the CO emissionfrom samples of 20 and 44 galaxies, respectively, weremade at resolutions of 2–4′′ (OVRO) and ∼7′′ (BIMA).Both of these surveys incorporated single antenna mea-surements (NRO 45 m measurements for OVRO, NRAO12 Meter Telescope measurements for BIMA) into theirinterferometer data to provide a complete sample of theCO emission in each galaxy. These surveys have made itpossible to compare the detailed morphologies within eachsample and derive physical models that describe the evolu-tion of these morphologies. For example, the OVRO/NROsurvey has found that barred spirals exhibit a higher degreeof central gas concentration, but a lower overall moleculargas surface density than normal spirals. This property ofbarred spiral galaxies confirms theoretical predictions ofrapid radial transport of gas toward the center of this typeof spiral galaxy. The lower overall molecular surface den-sity in barred spiral galaxies is thought to be caused by amore rapid expenditure of the material which feeds starformation in these galaxies.

3. Galactic Evolution

Studies of galactic evolution have focused on the com-parison between the atomic (HI) and molecular (H2) gasproperties and star formation rates as a function of envi-ronment, luminosity, and galaxy type. The general con-clusions from these studies are as follows:

1. The sum of the galactic atomic and molecular massesrange from 106 to 5 × 1010 M�.

2. The ratio of molecular to atomic gas mass MH2/MHI

decreases as a function of morphological type forspiral galaxy types Sa–Sd.

3. The ratio of total neutral gas mass to dynamical massMgas/Mdynamic increases from 4% for early type (Sa)spiral galaxies to 25% for late type (Sd) galaxies.

4. The global star formation rates and efficiencies forspiral galaxies do not show a strong dependence onmorphology.

Of special consideration are galaxies that are interactingwith other galaxies. Active galactic nuclei (AGN) andultraluminous infrared galaxies (ULIRGs) represent twocategories of galactic systems whose evolution has beenmodified by an interaction event. Galaxy–galaxy interac-tions are known to disrupt the stellar component of galacticdisks and enhance the star formation rate. The molecularcomponent of these systems appears also to be disrupted,leading in many cases to an order-of-magnitude increasein the star formation efficiency, with a more efficient pro-duction of massive stars.




4. Galactic Nuclei

The most dominant molecular component in galaxies istheir nuclei. In recent years the level of sensitivity avail-able for studies of galactic nuclei has allowed for not onlythe detection of CO in these nuclei, but also studies of thespatial distribution of CO and other molecules. Studiesutilizing measurements of the spatial distribution of HCNand CS from a number of nearby active galactic nuclei andstarburst galaxies have resulted in a better understandingof the physical properties, kinematics, and mass distribu-tion of the dense gas in these regions. The informationgathered from these studies has also been used to inves-tigate the relationships among various types of “active”galaxies, such as AGN, ULIRGs, and starburst galaxies.

Studies of nearby galaxies have provided informationon the physical properties of the dense gas in galacticnuclei, which in turn have provided a useful comparisonto studies of the dense gas properties in our own galaxy.For example, the nearby starburst galaxy NGC 253 hasbeen studied with high spatial resolution multitransitionmeasurements of CO and HCN. The spatial distributionof the molecular clouds imaged in NGC 253 is similar tothat found in the central regions of our own galaxy, butthe kinetic temperature and volume density is 100 K and104–105 cm−3, warmer and denser than average galacticmolecular clouds. Similar studies of the dense gas distribu-tion and properties in other nearby galaxies such as M82,NGC 1068, and M51 have yielded comparative informa-tion useful in defining the detailed physical characteristicsof these galaxies.

5. High Redshift Galaxies

Important constraints on the evolution of galaxies havebeen provided by the search for and characterization ofdistant galaxies. These searches, conducted using CO asa tracer of molecular gas, have pointed to the existenceof massive quantities of dust and molecular gas out toredshifts as high as 4.69. This high redshift correspondsto ages within a few billion years of the Big Bang, thusindicating enrichment of molecular gas through chemicalprocessing at a very early epoch. Currently 12 galaxieshave been measured with redshifts greater than 2. Imag-ing studies of these objects have provided information ontheir gas and dynamical mass, information that cannot begleaned from observations at other wavelengths. The gasmass fraction in these systems is used as a measure of theirevolutionary state, providing a constraint on the epoch ofinitial star and galaxy formation. A characterization of thephysical properties of the high redshift systems is alsobeing used to establish whether galaxies formed hierar-

chically or as systems that were given their present daymasses during formation.

F. Cosmology

In addition to the cosmological implications of studiesof the millimeter emission properties of galaxies, thestructure of the cosmic microwave background radia-tion (CMBR) and direct measurements of the Hubbleconstant H0 have been made using millimeter astronom-ical techniques. The recent measurements of the Sun-yaev Zel’dovich effect (SZE) toward a sample of 27clusters using 26–36 GHz receivers on the BIMA andOVRO millimeter arrays have provided some of the mostdirect measurements of several cosmological parameters.The SZE is the spectral distortion of the CMBR owingto inverse Compton scattering of photons by electrons inhot gas confined to the deep gravitational potential pro-duced by galaxy clusters. A fundamental property of SZEemission is that the observed brightness is a function ofthe cluster properties and is independent of its distance.Therefore, SZE measurements can yield a very accuratemeasure of the Hubble constant H0 and the matter den-sity of the universe M. Current results from these SZEmeasurements indicate that H0 = 67 km sec−1 Mpc−1 and Mh100 ∼ 0.25 ± 0.06 (h100 is the Hubble constant nor-malized to a value of 100 km sec−1 Mpc−1). Note that thedistance-independent nature of these SZE measurementsmakes them the most accurate way in which to measureH0 and M astronomically.


CLOUD PHYSICS • COMETARY PHYSICS • COSMOLOGY •GALACTIC STRUCTURE AND EVOLUTION • INTERSTELLAR

MATTER • MAGNETIC FIELDS IN ASTROPHYSICS • RADIO-ASTRONOMY INTERFEROMETRY • SOLAR SYSTEM, MAG-NETIC AND ELECTRIC FIELDS • STELLAR STRUCTURE AND

EVOLUTION

BIBLIOGRAPHY

Andre, P., Ward-Thompson, D., and Barsony, M. (2000). From Pre-Stellar Cores to Protostars: The Initial Conditions of Star Formation.In “Protostars and Planets IV” (V. Mannings, A. P. Boss, and S. S.Russell, eds.), in press. University of Arizona Press, Tucson, AZ.

Bachiller, R. (1996). “Bipolar molecular outflows from young stars andprotostars,” Ann. Rev. Astron. Astrophys. 34, 111–154.

Butler, B. J., and Gurwell, M. A. (2001). Solar System Science withALMA. In “Science with the Atacama Large Millimeter Array”(A. Wootten, ed.), in press, Astronomical Society of the Pacific, SanFrancisco, CA.




de Pater, I. (1990). “Radio images of the planets,” Ann. Rev. Astron.Astrophys. 28, 347–399.

Evans, N. J., II (1999). “Physical conditions in regions of star formation,”Ann. Rev. Astron. Astrophys. 37, 311–362.

Neininger, N. (1999). Interferometric Observations of Nearby Galax-ies. In “The Physics and Chemistry of the Interstellar Medium” (V.Ossenkopf, J. Stutzki, and G. Winnewisser, eds.), pp. 42–49. GCA–Verlag, Herdecke, Germany.

Sargent, A. I., and Welch, W. J. (1993). “Millimeter and submillimeterinterferometry of astronomical sources,” Annual Reviews of Astron-omy and Astrophysics. 31, 297–343.

Scoville, N. Z., and Sargent, A. I. (2000). Imaging Spectroscopy at mm-Wavelengths. In “Imaging the Universe in Three Dimensions: Astro-physics with Advanced Multi-Wavelength Imaging Devices” (W. vanBreugel and J. Bland-Hawthorn, eds.), pp. 236–247. ASP ConferenceSeries Vol. 195, Astronomical Society of the Pacific, San Francisco.

Turner, B. E. (1992). Interstellar Medium, Molecules. In “The Astron-omy & Astrophysics Encyclopedia” (S. Maran and C. Sagan, eds.),p. 378, The Astronomy and Astrophysics Encyclopedia. van Nostrand,New York.

van Dishoeck, E. F., and Blake, G. A. (1998). “Chemical evolution ofstar-forming regions,” Ann. Rev. Astron. Astrophys. 36, 317–368.

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Encyclopedia of Physical Science and Technology EN010K-476 July 18, 2001 18:53

Neutrino AstronomyRaymond J. Davis, Jr.Alfred K. MannUniversity of Pennsylvania (Emeritus)

I. Detecting NeutrinosII. Neutrinos from the Sun

III. Atmospheric (or Cosmic Ray) NeutrinosIV. Neutrino OscillationsV. Conclusions

GLOSSARY

Carbon–nitrogen cycle Sequentially ordered set of fu-sion reactions of hydrogen with carbon and nitrogenisotopes, serving to combine four hydrogen atoms intohelium.

Cerenkov light Light radiated by a charged particletraversing a medium. Cerenkov radiation occurs whenthe particle has a velocity greater than the velocity oflight in that medium.

Leptons General term for the light elementary particles—electrons, muons, tauons, and their associatedneutrinos—that interact with nuclei and with each otherby the weak force.

Main sequence Narrow region on a plot of the luminos-ity versus surface temperature of stars (Hertzsprung–Russell diagram) where the hydrogen-burning stars arelocated.

Muon Unstable, weak-interacting, charged particle (+ or−) with a mass 207 times that of an electron. It decaysto an electron and two neutrinos, µ− → e− + νe + νµ,with a mean lifetime of 2.2 × 10−6 sec.

Neutrino oscillation Hypothetical process that would

allow different neutrino types, or flavors, to changeinto one another.

Proton–proton chain Set of nuclear fusion reactions thatconverts four hydrogen atoms into helium. This chainis the dominant energy producer in the sun.

Solar model Theoretical calculation of the internal struc-ture of the sun that follows the changes in structure,temperature, and composition as the sun ages.

Weak interaction or weak force One of the fundamentalforces in nature that governs the interaction of leptons.

THE NEUTRINO is an electrically neutral elementaryparticle that has the unique capability of penetrating matteron the scale of stellar dimensions and densities. Neutrinosare produced abundantly in nuclear processes (includingbeta-decay) in the interior of stars and planets and by avariety of processes in the cosmos. The study of neutrinoradiation from stars is a direct means of observing the en-ergy production mechanism occurring in their interiors. Inaddition, intermediate mass stars at the end of their nuclearlife, i.e., after exhausting their nuclear fuel, suffer a catas-trophic collapse (supernovae) and emit an intense burst of

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382 Neutrino Astronomy

neutrinos. Furthermore, neutrinos are a component of cos-mic radiation and of cosmic black body radiation, and, ifthey have nonzero mass, they may conceivably contributesignificantly to the total mass of the universe.

For these reasons, the detection of neutrinos from suchsources is a subject of considerable interest in astronomyand cosmology. Because of their weak interaction withmatter, neutrinos are difficult to observe directly. Avail-able techniques require massive detectors on the order of100–10,000 tons to record a neutrino event rate between0.1 and 1.0 event per day arising from not-too-distantsources. Because of this constraint, studies have been lim-ited primarily to observations of neutrino radiation fromthe sun which were carried out to verify and understandthe hydrogen fusion reactions that are the source of thesun’s energy. Also, an intense pulse of antineutrinos wasobserved for the first time on February 23, 1987, emanat-ing from a supernova (SN1987A) in the Large MagellanicCloud (LMC), a nearby satellite galaxy 165,000 light yearsdistant. In this article, we discuss principally the observa-tions of solar neutrinos and the supernova event in 1987and briefly mention other neutrino sources in the cosmos.

I. DETECTING NEUTRINOS

A. Classification of Neutrinosas Elementary Particles

Neutrinos belong to the family of elementary particlescalled leptons (originally, “smaller mass” particles). Lep-tons, of which there are three known subfamilies, are dis-tinguished from other elementary particles by a uniqueproperty: They are coupled to all other particles by theweak force, which results in extremely feeble interactionsof leptons with the nuclei of atoms, with other elemen-tary particles, and with themselves. Charged leptons, ofcourse, may interact with other charged particles and fieldsthrough the much stronger electromagnetic force. As ele-mentary particles, leptons carry an angular momentumof 1

2 unit of spin and are therefore regarded as fermions(particles with 1

2 unit of spin). With zero or very smallmass, all neutrinos spin in a left-handed direction, and allantineutrinos spin in a right-handed direction. The threelepton families are designated by their charged members:the electron, e− (and e+); the muon, µ− (and µ+); andtauon, τ− (and τ+). Each charged set has a negative anda positive member, referred to as particle and antiparticle,respectively. Associated with each set of charged mem-bers is a corresponding set of neutral particles. These arethe neutrinos and antineutrinos: νe, νe, νµ, νµ, ντ , ντ . Thelepton families are listed in Table I. Recently, it has beendemonstrated experimentally that only these three rela-tively low mass, stable lepton families exist in nature.

TABLE I The Lepton Families

Electron family Muon family Tauon family

Particle e−, le = +1 µ−, lµ = +1 τ−, lτ = +1

Antiparticle e+, le = −1 µ+, lµ = −1 τ+, lτ = −1

Particle νe, le = +1 νµ, lµ = +1 ντ , lτ = +1

Antiparticle νe, le = −1 νµ, lµ = −1 ντ , lτ = −1

The masses of neutrinos may be zero and, in anyevent, are much smaller than the masses of their chargedpartners. The electron, muon, and tauon have massesof 0.511, 105.7, and 1784 MeV, respectively, and themuon and tauon have mean lives of 2.2 × 10−6 sec and3.0 × 10−13 sec, respectively. Many experiments havebeen performed in an effort to measure the masses ofthe three neutrinos. The most sensitive experimental mea-surement published to date reports an upper limit on theelectron neutrino mass of a few electron volts, or less than1/50,000th the mass of the electron. New experiments toimprove this limit continue to be performed. Only crudeupper limits have been set directly on the masses of themuon and tauon neutrinos from the kinematics of their de-cay modes: 0.2 and 35 MeV, respectively. It is generallypresumed that the masses of all neutrinos are very muchsmaller than those upper limits, probably too small to bemeasured directly. A cosmological argument suggests thatthe sum of the three known stable neutrino masses shouldbe less than a constant times the square of the Hubbleconstant, or roughly 100 eV. Later, we discuss means ofdetermining mass differences between neutrino types, orflavors, from observations of neutrinos from the sun. Thesestudies using the sun as a primary source of electron neutri-nos have led to tests of neutrino flavor conservation, neu-trino masses, and other fundamental neutrino properties.

Neutrinos are created in nuclear processes and in vari-ous elementary particle interactions. The most familiarprocess is nuclear beta-decay, in which an unstable nu-cleus simultaneously emits an electron (beta-ray) and aneutrino. This process may be visualized as an unstablenucleus radiating its energy by creating a pair of leptons: aneutrino and an electron. It is referred to as beta-minus de-cay when an electron (e−) is emitted with an antineutrino(ve) or beta-plus decay when a positron (e+) is emittedwith a neutrino (νe). In another beta-decay process, calledelectron capture, one of the orbital electrons in an atom isabsorbed by the nucleus and a neutrino is emitted. Exam-ples of these processes are

14C → 14N + e− + νe, beta-minus decay (1)

11C → 11B + e+ + νe, beta-plus decay (2)

e− + 37Ar → 37Cl + νe, electron capture (3)

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Neutrino Astronomy 383

In these examples, the guiding principle is the principleof lepton number conservation. In any process, the totalnumber of leptons and antileptons does not change; thenumber before and after is conserved. Table I lists the as-signed lepton numbers for each lepton family. The leptonnumber is positive for a lepton and negative for an anti-lepton. By applying the lepton numbers for the electronfamily, the principle of lepton conservation is exhibited inthe three examples given.

The principle of lepton conservation applies to each ofthe three families, and in addition, the leptons of each fam-ily appear to be separately conserved. It has been shown,for example, that when a neutrino of the muon type (νµ)is absorbed in a nucleus, a muon is emitted, never an elec-tron, for example,

νµ + Fe → Co + µ−.

It was by this process that the muon neutrino was discov-ered and shown to be a different particle from the electronneutrino. The principle of lepton conservation for eachlepton type (or flavor) has been tested experimentally inmany different ways and appears to be valid, but it is pos-sible that separate lepton conservation is not rigorouslytrue and additional tests are still needed. A superior wayof testing these lepton properties is by studying the neu-trino spectrum from the sun and cosmic rays. This topicwill be discussed further in Section II.

B. Detection of Neutrinos

The weak force has both a charged and a neutral compo-nent, arising from the exchange of massive intermediat-ing particles. The existence of these particles, the W ±

for charged currents, and the Z0 for neutral currents,was directly demonstrated in 1983. The theory of weak-interaction processes is now well understood and allowsone to calculate the interactions of neutrinos with nucleiand electrons. Using this theoretical foundation, it is pos-sible to determine the sensitivity of detectors to fluxes ofneutrinos as a function of neutrino energy. The interactionprobability is expressed as the equivalent target area of anucleus, or electron, or other particle that is presented toa neutrino. It is referred to as the cross section (σ ) and isusually given in units of square centimeters per atom orparticle.

C. Interactions with Nuclei

Neutrinos may be absorbed in nuclei with the emissionof an electron, a muon, or a tauon, depending on the in-cident neutrino type. These are called inverse-beta-decayprocesses because they are, in the case of the electron neu-trino, the inverse of normal radioactive beta-decay. Neu-

trino (νe) absorption by an inverse beta-decay reaction isillustrated by two examples, one for antineutrinos and onefor neutrinos:

νe + p → n + e+ (4)

νe + 37Cl → 37Ar + e− (5)

Reaction (4) was used by Reines and Cowan in the firstexperiment to detect antineutrinos. The antineutrinos orig-inated from the beta-minus decay of fission products in anuclear reactor. The same reaction was also used in detec-tors to observe antineutrinos from a collapsing star. Reac-tion (4) is the inverse of the beta-decay of the neutron,

n → p + e− + νe,

and requires that the antineutrino have sufficient energyto provide the mass difference between the neutron andthe proton and to create the positron, a minimum total en-ergy of 1.804 MeV. The minimum energy needed to carryout the reaction is called the threshold energy, E(thresh).Given the half-life of the neutron (∼15 min), the thresh-old energy, the spin change (none in this case), and theweak-interaction coupling constant, the theory of weakinteractions may be used to calculate the cross section forreaction (4) as a function of the antineutrino energy. Forexample, a 5-MeV antineutrino would have a cross sec-tion of 2.4 × 10−43 cm2/H atom. With this cross-sectionvalue, we can calculate the distance that an antineutrinoor neutron will penetrate through ordinary water. A beamof 5-MeV neutrinos would be reduced in intensity by 50%in traveling through 45 light years of water!

Reaction (5) is used for detecting neutrinos from thesun. It is the inverse of the electron capture of 37Ar [see re-action (3)], a decay process with a half-life of 35 days.Again, the νe capture cross section can be calculated,knowing the half-life, the threshold energy (0.814 MeV),the spins of the 37Cl and 37Ar nuclei, the weak inter-action coupling constant, and the overlap of the wavefunctions of orbital electrons in the nucleus. In complexnuclei such as 37Cl, the neutrino absorption also pro-duces 37Ar in various excited states. The excited statesdecay rapidly to the ground state by emitting gamma-rays. In the 37Cl–37Ar case, the transition probabilitiesto all relevant excited states can be evaluated, so thatthe cross section for capture can be calculated accuratelyover the range of neutrino energies expected from the sun.One excited state in 37Ar, the so-called analog state withan excitation energy of 4.98 MeV, is of particular im-portance. Neutrinos with energy greater than 5.79 MeVwill feed this state and have a higher νe capture crosssection.

These two examples of neutrino absorption reactionsillustrate the procedures used in calculating the neutrino

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capture cross sections. The neutrino capture cross sectionfor reaction (4) is the only one that has been measured ex-perimentally with good accuracy (±5%). An approximatemeasurement of the cross section of the reaction

νe + d → p + p + e− (6)

has also been performed (≈30%); the cross section ofthis reaction can also be calculated with confidence. Thisreaction is of potential importance in observing neutri-nos from the sun. For all other neutrino capture reactionsconsidered for radiochemical neutrino detectors, one mustrely on a theoretical calculation. There is a particular diffi-culty in calculating the capture cross section for complexnuclei to produce the product nucleus in an excited state.In these cases, one must resort to nuclear reaction stud-ies and theoretical nuclear models to estimate the crosssection.

D. Interactions with Electrons

Neutrinos of all types, νe, νµ, and ντ , can scatter elas-tically from an electron. This process is a result of theweak-interaction coupling between the neutrino and thecharged lepton, a coupling that may have a charged and aneutral current component. The cross section for scatter-ing from electrons depends on the neutrino type, νe, νµ, ντ ,and whether it is a neutrino or an antineutrino. Only theelectron neutrino is coupled to the electron by both thecharged and the neutral currents, whereas other neutrinotypes are coupled by neutral currents. These reactions maybe represented schematically as follows:

νe + e− → νe + e− (recoil), charged and neutral current

σ (νe) = 0.933 × 10−43 (Eν/10 MeV) cm2 (7)

νµ + e− → νµ + e− (recoil), neutral current

σ (νµ or ντ ) = 0.159 × 10−43 (Eν/10 MeV) cm2 (8)

νe + e− → νe + e−(recoil), charged and neutral current

σ (νe) = 0.388 × 10−43 (Eν/10 MeV) cm2 (9)

νµ + e− → νµ + e−(recoil), neutral current

σ (νµ or ντ ) = 0.130 × 10−43 (Eν/10 MeV) cm2 (10)

Monoenergetic electron neutrinos, when scattered fromelectrons, produce a flat recoil energy spectrum. On theother hand, monoenergetic electron antineutrinos producea spectrum of electron recoils that decreases inverselywith the energy. The maximum energy of the recoil elec-tron corresponds approximately to the energy of the neu-trino, disregarding the initial binding energy of the struckelectron. An important characteristic of the ν-electron

scattering process is that the recoil electron moves inapproximately the same direction as the incoming neu-trino. Therefore, the neutrino-electron scattering processcan be used to determine the direction as well as the en-ergy of the neutrino. However, measuring neutrino en-ergies and directions is difficult because of backgroundprocesses. One must reduce the flux of cosmic rays, exter-nal gamma-radiation, and energetic neutrons to low levels.This can be accomplished by going deep underground, byusing massive self-shielding, and by particle detectors toobserve and veto charged particles that enter the activeregion of the detector from outside. In addition, radioac-tive elements that produce energetic electrons by beta-decay must be removed from the target and constructionmaterials.

The method to distinguish the direction of the elec-tron is to observe the Cerenkov light emitted by the recoilelectron. When an electron (or any other charged parti-cle) passes through a medium traveling faster than lighttravels in that medium, a cone of light is emitted aroundthe direction of the electron. The cone of Cerenkov lightis observed by a large number of light-sensitive detectors(photomultiplier tubes) located on the walls of the detec-tor. This technique was employed in very large detectorsfilled with several thousand tons of water to search for thedecay of the proton. Such detectors have recently turnedprincipally to the detection of neutrinos.

II. NEUTRINOS FROM THE SUN

A. Theoretical Solar Models

Our sun is classified as a dwarf G-type main sequence starwhich is generating energy primarily by the fusion of hy-drogen into helium. The overall hydrogen fusion processcan be represented:

4H → 4He + 2e+ + 2νe + gamma-radiation

+ kinetic energy. (11)

The fusion of hydrogen into helium can be accom-plished by two separate reaction sequences. known re-spectively as the proton–proton chain of reactions and thecarbon–nitrogen cycle (Table II). It can be observed fromTable II that the proton–proton chain has three compet-ing branches, designated for reference as PP-I, PP-II, andPP-III. All stars generate energy by the proton–protonchain in the early stage of their evolution. The sun, withan age of 4.7 billion years, is still generating energychiefly by this mechanism and will continue to do sofor a few billion years more. As a star ages, its internaltemperature increases, and the carbon–nitrogen cycle be-gins to play a more prominent role in energy production.

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TABLE II The Proton–Proton Chain and Carbon–Nitrogen Cycle

Neutrino energy Neutrino fluxa

Reaction (MeV) (cm−−2 sec−−1)

The proton–proton chain

0–0.420 spectrum 6.0 × 1010

PP-I

H + H → d + e + + νe (99.75%)

or

H + H + e − → D + νe (0.75%)

D + H → 3He + γ

3He + 3He → 2H + 4He(87%)

1.44 line 1.4 × 108

PP-II

3He + 4He → 7Be + γ (13%)7Be + e − → 7Li + νe7Li + H → γ + 8Be|→ 2 4He

{0.861 (90%) line

0.383 (10%) line

}4.7 × 109

PP-III

7Be + H → 8B + γ (0.017%)8B → 8Be + e τ + νe|→ 2 4He

0–14.1 spectrum 5.8 × 106

The carbon–nitrogen cycle

H − 12C → 13N + γ

13N → 13C + e + + νe 0–1.20 spectrum 6.1 × 108

H + 13C → 14N + γ

H + 14N → 15O + γ

15O → 15N + e+ + νe

H + 15N → 12C + 4He 0–1.73 spectrum 5.2×108

a From Bahcall and Ulrich (1988). Rev. Mod. Phys. 60, 297.

All of the reactions shown in Table II are used in solarmodel calculations and are the only reactions considered.

The nuclear reactions in Table II have been studied ex-tensively in the laboratory. It has been established thatthese are the only reactions that are important in the hy-drogen fusion processes. However, the primary reactionthat initiates the proton–proton chain,

p + p → d + e+ + νe, (12)

has too low a cross section to be measured directly inthe laboratory, but it is possible to calculate accuratelythe cross section at thermal energies. All the reactionsare exothermic, producing the energies listed in Table II.Six of the reactions produce neutrinos; two emit mono-energetic neutrinos; and the other four emit a spectrum ofneutrinos from near-zero energy to the maximum energynoted.

To determine the rates of these reactions in the sun,detailed calculations must be made of the temperatures,particle densities, and chemical composition of the differ-ent regions of the solar interior. Knowing the rates of theneutrino-producing reactions, one can calculate the en-ergy spectrum and fluxes of the neutrinos emitted by thesun.

The internal conditions in the sun are derived from acomplex solar model calculation, which follows the evo-

lution of the sun from its initial formation to its ultimatestate as a cooling white dwarf star, devoid of fuel. The sunis the only star for which mass, radius, luminosity, surfacetemperature, and age are well known. These parametersare used in the model and provide boundary conditions.It is assumed, with good physical justification, that theprimitive sun was well mixed and heated by the releaseof gravitational energy. For this reason, it is thought thatthe initial elemental composition throughout its mass wasidentical with that now observed in the photosphere. Theelemental composition is introduced in the solar model asthe ratio of the abundance of each element heavier thanhelium to the abundance of hydrogen. This ratio is a di-rectly measured quantity for each element. The principalelements heavier than helium, in order of their weightpercent, are O, C, Fe, Ne, N, Si, Mg, and S. The totalpercentage of these elements is 1.8% by mass. The he-lium composition is not directly entered in the model butis calculated from the model. The initial helium composi-tion calculated for the standard model is around 25% bymass. As the sun evolves, the helium content in the coregradually increases as a result of the fusion reactions.

The chemical composition of the sun is an importantfactor in determining the internal temperatures, becausean increase in the composition of the heavier elementsaffects the rate of energy transport. The transmission of

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TABLE III Calculated Solar Neutrino Fluxes and Cross Sections for the Reactionνe ++ 37Cl →→ 37Ar ++ e

Flux on eartha Capture crossb Capture ratec

Neutrino source (cm−2 sec−1) section (cm2) (SNU)

H + H → d + e+ + νe 6.0 × 1010 0 0 (0)

H + H + e− → d + νe 1.4 × 108 1.56 × 10−45 0.2 (0.2)7Be decay 4.7 × 109 2.38 × 10−46 1.1 (1.0)8B decay 5.8 × 106 1.08 × 10−42 6.1 (4.1)13N decay 6.1 × 108 1.66 × 10−46 0.1 —15O decay 5.2 × 108 6.61 × 10−46 0.3 —

Total 7.9 ± 0.9 (5.8 ± 1.3)

a From Bahcall, J. N., and Ulrich, R. K. (1988). Rev. Mod. Phys. 60, 297.b From Bahcall, J. N. (1978). Rev. Mod. Phys. 50, 881.c From reference a above and (in parentheses) Turck-Chieze et al. (1988). Astrophys. J. 335, 415.

energy depends on a number of processes in which thethermal radiation interacts with unbound electrons andwith atoms in various states of ionization and excita-tion. These processes must be calculated from simplifiedatomic models and photon-electron scattering theory. Thecomplex calculations of opacity are provided by scientistsfrom Los Alamos and Livermore National Laboratories.Their results are extensively employed in astronomicalcalculations.

The structure of the sun is expressed by equations ofhydrodynamic equilibrium. That is, at every radius shell,the downward gravitational forces are balanced by theoutward kinetic and radiation pressures. The calculationsfollow the initial collapse of the gravitating mass of the sunto the main sequence. The only additional energy is thatintroduced by the nuclear fusion reactions. When a star,such as the sun, is on the main sequence, where it remainsfor more than 6 billion years, all of the energy is providedby the hydrogen fusion reactions. The nuclear reactionrates are derived from the kinetic energy of the reactants,assuming a Maxwellian velocity distribution and a nuclearbarrier penetration factor. Experimental nuclear reactioncross sections are used. They are usually measured in thelaboratory at energies above 100 keV and extrapolatedto the energies corresponding to the temperatures inthe sun’s interior (less than 1 keV). The theoreticallycalculated value of the primary p–p reaction is used.

The theoretical forecasts of the neutrino fluxes used tocompare with experimental observations are those fromthe so-called standard solar model (SSM). This model re-lies on the values of the solar mass, radius, luminosity, andage (4.7 billion years) and on the best-considered valuesof the nuclear reaction cross sections. In addition, thereare some special assumptions. It is presumed that the sunis not rotating, or differentially rotating, rapidly enough inits interior to affect its internal structure or dynamics. Pro-cesses that could mix the solar interior, such as diffusionor periodic hydrodynamic oscillation, are not taken into

account. Magnetic fields are not regarded as sufficientlyintense to affect the sun in any important way. A simplifiedconvective theory is used for determining the transport ofenergy in the convective zone, the outer dynamic regionof the sun.

Table III shows the neutrino flux at the earth for eachneutrino source in the proton–proton cycle and the carbon–nitrogen cycle, obtained by standard solar model calcula-tions. It may be noticed that the total neutrino flux at theearth is 6.6 × 1010 neutrinos/cm−2 sec−1, and 92% ofthe flux can be attributed to the low-energy neutrinos fromthe proton–proton reaction.

B. The Chlorine Solar Neutrino Experiment

In the early 1960s, it was clear that the neutrinos from thesun could be observed. This conclusion was reached afterit was realized that the PP-II and PP-III branches werean important part of the energy generation of the sun andsufficiently energetic to drive the neutrino capture reaction

νe + 37Cl →← 37Ar + e−. (13)

This reaction has too large a threshold energy (0.816 MeV)for observing the abundant neutrinos from the p–p reac-tion but is suitable for measuring the neutrino flux from thePP-II and PP-III branches and from the carbon–nitrogencycle. A radiochemical method is used which employs alarge volume of a suitable chemical compound of chlorine.The radioactive product is removed, purified, and placedin a small detector for measuring the decay of 37Ar backto 37Cl (half-life, 35 days). There are several reasons forchoosing the Cl–Ar method for solar neutrino detection:chlorine compounds are inexpensive; the 37Ar can be re-covered by a simple efficient chemical procedure; 37Ar hasa convenient half-life of 35 days; and the decay of 37Ar iseasily measured.

A radiochemical detector does not observe or char-acterize a neutrino capture event. It is only capable of

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measuring a radioactive product that has accumulated overa period of time. In designing a detector, it is thereforeimportant to consider all possible nuclear processes thatcould produce 37Ar in the detector and to be sure that theyare small compared to the production expected from so-lar neutrinos. In general, these background processes aresmall for radiochemical detectors. It is necessary, how-ever, to carry out the measurement deep underground toreduce the 37Ar production by cosmic ray muons to a levelthat is low compared to that expected from solar neutrinocapture.

During the period 1965–1967, Brookhaven NationalLaboratory built a chlorine solar neutrino detector inthe Homestake Gold Mine at Lead, South Dakota, tomake a quantitative test of the theory of solar energygeneration. The detector uses 380,000 liters (615 tons)of tetra-chloroethylene (C2Cl4) as the target material.This liquid is an inexpensive, commerical, dryclean-ing fluid, known as perchloroethylene. The experimentwas installed 1480 m (4850 ft) underground in a spe-cially designed chamber. Figure 1 shows the experimentalarrangement.

It was learned, in the first few years of operation, thatthe 37Ar production rate in the detector was lower than ex-pected from the SSM and, in fact, was comparable to the

FIGURE 1 The chlorine (37Cl) solar neutrino detector in the Homestake Gold Mine, Lead, South Dakota.

expected background rate in the detector. It was neces-sary to improve the sensitivity of detection, which wasaccomplished by improving the counting technique sothat 37Ar decay events could be distinguished clearly frombackground events. After these improvements, measure-ments from 1970 to 1990 produced a positive result. Aradiochemical detector observes the sum of the produc-tion rate from all solar neutrino sources having an en-ergy above the threshold energy. Table III lists the the-oretical neutrino flux and neutrino capture cross sectionof 37Cl for each neutrino reaction that occurs in the sun.The chlorine experiment would respond to the sum offlux × cross section for each of these sources. The ex-pected neutrino capture rate in the chlorine experiment,derived from the most recent theoretical calculations, isbetween 5.8 and 7.9 × 10−36 captures per second per 37Clatom. This rate is usually expressed in solar neutrino units(SNU); an SNU is defined as 10−36 captures per secondper atom. It is difficult to express quantitatively the un-certainties in the solar model prediction, since the modelmay not correctly represent in detail the structure and dy-namics of the sun. If however, one uses the combinederrors in the astronomical and nuclear reaction data em-ployed in the calculation, an uncertainty of about 1 SNU isobtained.

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FIGURE 2 Plots showing a five point running average of 37Ar production, solid circles; smoothed sunspot numbers,dotted curve; both against time in years.

The average rate observed by the chlorine detector from1970 to 1990 was 2.3 ± 0.3 SNU. The average rate is afactor of 3–4 below the theoretical predictions in Table III.

It is of interest to see if there are any systematic changesin the signal rate of the chlorine detector with time.Figure 2 shows the data smoothed by taking a five pointrunning average. In this figure, the solar activity cycle,as measured by the monthly average sunspot numbers, isplotted with inverted scale. The data suggest that from1977 to 1988 the neutrino capture rate might have beeninversely correlated with the quantity of sunspot numbers.The greatest change in rate occurs at about the time thesunspot cycle turns on. The statistical significance of thiscorrelation is reasonably good; the correlation coefficientis 0.8. This effect has not been observed in other, laterexperiments, however. Moreover, it is generally believedthat the solar energy processes do not change in short pe-riods of time (≈105 years) and the solar core is regardedas a constant (in time) source of neutrinos.

C. The Kamiokande-II Solar Neutrino Detector

The Kamiokande-II detector, shown schematically inFig. 3, was an imaging water Cerenkov detector of usefulmass 2140 metric tons, of which the central 680 tons makeup the fiducial mass for observation of the 8B solar neu-trinos. Kamiokande-II (K-II) was the successor to the nu-cleon decay experiment (nde) located in the Kamioka minein Gifu prefecture, Japan. K-II was a collaboration amongthe Japanese universities Tokyo, Niigata, Tokai, Osaka,and Kobe, together with the National Laboratory for HighEnergy Physics of Japan (KEK), and with the University

of Pennsylvania in the United States. Solar neutrinos weredetected through the reaction νe + e− → νe + e− and bymeasuring the initial position and vector momentum of therecoiling electron. It is difficult to detect electrons with en-ergy less than about 6 MeV in such large water Cerenkovdetectors, and consequently, the energy threshold for solarneutrino detection was approximately that value. On theother hand, the kinematics of the elastic scattering reactionimposes an angular constraint on the recoiling electron,θ2

e ≤ 2me/Eν, which implies that the recoiling electrondirection is closely aligned with the incident neutrino di-rection. This, combined with the imaging property of thedetector, made it possible to project the incident neutrinosback to the sun and to establish the sun as their origin.

The properties of the K-II detector relevant to thedetection of solar neutrinos are given in Table IV. Theresolutions in energy, position, and angle in Table IV

FIGURE 3 Schematic drawing of the Kamiokande-II detector inthe Kamioka Mine in Japan, showing the location of the waterpurification system, anticounter, and electronics hut.

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TABLE IV Properties of the Kamiokande-IIDetector at Low Energies

Trigger threshold (at present)a 6.1 MeV

Energy resolution (10 MeV) ±20%

Vertex position resolution (10 MeV) ±1.0 m

Angular resolution (10 MeV) ±28

Energy calibration uncertainty ≤3%

a Detection efficiency was 50% at 6.1 MeV and 90%at 7.9 MeV over the fiducial volume of 680 tons. Triggerrequired ≥20 photomultiplier tubes to give signal within100 nsec.

were limited by the low intensity of Cerenkov radiation,by scattering of the Cerenkov light in the detector water,and principally by multiple scattering of the low energyrecoiling electrons in the water. The energy calibrationwas achieved through measurement of photons froma radioactive source inserted in the detector, throughmeasurement of the energy spectra of electrons from thedecays of cosmic ray muon-induced spallation productsin the detector water, and through measurement of thespectrum of electrons from the decays of cosmic raymuons that stop in the detector.

For the low energy electrons produced by solar neu-trino interactions, there are backgrounds arising from nat-ural radioactivity, primarily radon dissolved in the detectorwater, from gamma-rays emitted by radioactive elementsin the rock of the cavity housing the detector, and fromthe beta-decays of the muon-induced spallation nuclei inthe water.

After major reductions in the backgrounds by means offiducial volume and event selection criteria, the ratio ofthe observed integrated (mostly remaining background)event rate to the corresponding event rate predicted by thestandard solar model was roughly 20:1. The final criterionto extract the 8B solar neutrino signal from the backgroundwas the angular correlation of the neutrino signal with thedirection of the sun.

Figure 4 shows the distribution in cos θsun forEe ≥ 9.3 MeV for a data sample of 1040 live detectordays, where θsun is the measured angle of the trajectoryof each observed electron with respect to the radius vec-tor from the sun (cos θsun = 1 corresponds to the directionfrom the sun to the earth). The solid histogram in the figuregives the shape of the solar neutrino signal expected froma Monte Carlo simulation based on the energy and angularresolution of the detector. For simplicity, the area underthe histogram is made equal to the numerical predictionof the solar model calculation of Bahcall and Ulrich. Onesees that the cos θsun distribution is enhanced in the direc-tion from the sun above the isotropic background, but themagnitude of the enhancement is less than that expectedfrom the solar model calculation.

FIGURE 4 Plot of the cosine of the angle between the electrondirection and a radius vector from the sun, showing the signal fromthe sun plus an isotropic background. This plot is for Ee ≥ 9.3 MeVand the time period is January 1987 through April 1990, a total of1040 live detector days.

The intensity of the observed signal relative to the stan-dard solar model value, denoted by Data/SSM, was ob-tained directly from the data in Fig. 4 and was Data/SSM =0.46 ± 0.05 (stat.) ±0.06 (syst.), where again the SSM re-ferred to the calculation of Bahcall and Ulrich. If the SSMcalculation of Turck Chieze et al. was used as the ba-sis of comparison, the result was Data/SSM = 0.70 ± 0.08(stat.) ±0.09 (syst).

The energy spectrum of the final state (recoiling) elec-trons induced by the solar νe after background subtractionwas also determined and is shown in Fig. 5 along with thebest fit of a calculated spectrum based on the cross sectionfor the reaction νee → νee, the known shape of the energydistribution of the νe from 8B decay, and on the measuredenergy resolution of the K-II detector. The shapes of thedata and the histogram in Fig. 5 are seen to be in good

FIGURE 5 Differential electron total energy distribution of theevents produced by 8B solar neutrinos. The dashed histogramis the best fit to the data of a Monte Carlo calculation based onσ (νee → νee), the known shape of the neutrino flux from 8B decay,and the energy resolution of the detector. The solid histogramhas the shape dictated by the considerations above but the areapredicted by the SSM in Bahcall and Ulrich (see Table III).

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FIGURE 6 Plot of sunspot numbers vs time in the period 1987–1990.

agreement and are independent of the magnitude of thetotal 8B neutrino flux prediction of the SSM.

The K-II data were also of interest in connection witha possible time variation of the 8B solar neutrino flux be-cause the data-taking time extended over a period in whichsunspot activity, reflecting the solar magnetic cycle, rosesteeply from a minimum value at the end of solar mag-netic cycle 21 to a maximum value approximately 15 timeslarger at the peak of solar cycle 22, as shown in Fig. 6.The time dependence of the K-II data is shown in Fig. 7,in which the data are separated into five time intervals,each approximately 200 live detector days. The reducedchi-squared value calculated under the assumption of aconstant flux with respect to time is 0.40, which corre-sponds to a confidence level of 81% in the validity of theassumption.

Other possible short-time variations of the neutrino flux,such as day/night, seasonal, and semiannual variations,are also of interest. Results of the searches for these vari-ations in the K-II data were, within statistical errors, alsonegative.

The totality of the 8B solar neutrino data from the K-IIdetector provided clear two-part evidence for a neutrinosignal from 8B production and decay in the sun; namely,the directional correlation of the neutrino signal with thesun, and the consistency of the differential electron en-ergy spectrum of the signal in shape and energy scale withthat expected from 8B decay. Accordingly, the mechanismof energy generation in the sun based on the fusion reac-

FIGURE 7 Plot from the K-II detector of the solar neutrino fluxin five time intervals, each approximately 200 live detector days,from January 1987 through April 1990. The earliest two points areEe ≥ 9.3 MeV, and the latest three points are with Ee ≥ 7.5 MeV.

tions that give rise to 8B as a by-product, and which weresuggested by the 20 years of data from the 37Cl detector,would appear to be unequivocally confirmed by the K-IIdetection of neutrinos that could only have originated inthe core of the sun.

D. Later Experiments

During the last decade of the 20th century, there were twoadditional radiochemical solar neutrino experiments, bothusing gallium, and two additional real-time, directional(electronic) experiments using massive water Cerenkovdetectors, all following the methods established by thepioneer experiments described in detail above.

E. The Gallium Experiments

The gallium experiments stemmed from the intense inter-est in the scientific community to devise an experiment tomeasure the low energy neutrinos from the reaction thatinitiates the fusion cycle, the p–p reaction. A gallium de-tector (Ethresh = 0.233 MeV) utilizes the neutrino capturereaction:

νe + 71Ga → 71Ge + e−.

The produced 71Ge is extracted from many tons of gallium;the isolated germanium is purified; chemically convertedto germane gas, Ge4; and placed in a miniature propor-tional counter to observe the radioactive decay of 71Ge(half-life of 11.4 days).

Two independent gallium experiments were performed,one by a collaboration of Soviet scientists from the Insti-tute of Nuclear Research of Moscow with the Americaninstitutions of the Brookhaven and Los Alamos NationalLaboratories and the University of Pennsylvania. The ex-periment known by the acronym SAGE was located in theinstitute’s underground laboratory in the Baksan Valleyin the north Caucasus mountains. In this Soviet-Americanexperiment, 60 tons of gallium metal (melting point 30◦C)were used. The germanium was extracted by an oxidizinghydrochloric acid solution.

A second gallium experiment was prepared by theGALLEX collaboration of several institutions in WesternEurope and the United States. It used 30 tons of galliumchloride-hydrochloric acid solution, from which germa-nium is easily removed as germanium tetrachloride bypurging with nitrogen gas, an extraction technique devel-oped earlier at Brookhaven National Laboratory. This ex-periment was in the Gran Sasso underground laboratoryin Italy.

A gallium experiment responds to the entire spectrumof solar neutrinos; it is important to determine the neutrinocapture cross section in 71Ga to produce 71Ge in variousexcited states. The ground state is easily calculated from

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the known half-life of 71Ge, but the contribution to excitedstates is more difficult to determine. The proton–proton re-action alone would contribute 70 SNU. The correspondingtotal neutrino capture rate in an experiment using 30 tonsof gallium is expected to be only 1.2 atoms of 71Ge perday, which, after correction for detection efficiency, wouldcorrespond to about four observed 71Ge decays per month.

F. The Electronic Detector Experiments

The electronic detector solar neutrino experiments thatfollowed the K-II experiment were larger, more elaborateversions of the K-II detector. There were two of them, oneof which has published its results and one on the vergeof doing so. In addition, two other experimental measure-ments utilizing nuclear reactor antineutrinos, with energyspectra overlapping the solar neutrino energy spectrum,have reported results that bear importantly on the inter-pretation of the solar neutrino data.

G. SuperKamiokande

A Japanese-American collaboration that succeeded theoriginal one responsible for K-II constructed the detec-tor known as Superkamiokande (SuperK) between 1990,when K-II had largely outlived its usefulness, and 1995.The properties of K-II and SuperK—which employed thesame detection method—differ in their size and in thefractional area covered by photomultiplier tubes (PMTs);SuperK is 50 kilotons in volume compared with 3 kilo-tons for K-II, and PMT cover 40% of the internal area ofSuperK compared with 20% for K-II. The solar neutrinoresults from both experiments, shown in Table V with allother solar neutrino results, are in good agreement withintheir reported errors, although the statistical errors quotedby SuperK are significantly lower than those from K-IIand the precision accordingly is significantly greater.

TABLE V Summary of Recent Measured and Calculated Solar Neutrino Fluxes

Experiment or calculation 37Cl →→ 37Ar (SNU)a 71Ga →→ 71Ge (SNU)a 8Bv flux (106 cm−−2 s−−1) Reference

Homestake (DAVIS) 2.33 ± 0.25 Annu. Rev. Nucl. Part. Sci. 39, 467 (1989)

GALLEX (HAMPEL) 69.7 ± 6.7+3.9−4.5 PL B388, 384 (1996)

SAGE (ABDURASHITOV) 73+18+5−16−7 PL B328, 234 (1994)

Kamiokande-II (FUKUDA) 2.80 ± 0.19 ± 0.33 PRL 77, 1683 (1996)

Superkamiokande (FUKUDA) 2.42 ± 0.05+0.09−0.07 PRL 81, 1158 (1998)

Bahcall et al. 7.7+1.2−1.0 129+8

−6 5.15+0.19−0.14 PL B433, 1 (1998)

Brun 7.18 127.2 4.82 Astrophys. J. 506, 913 (1998)

Dar 4.1 ± 1.2 115 ± 6 2.49 Astrophys. J. 468, 933 (1996)

Bahcall 9.3+1.2−1.4 137+8

−7 6.6(100+0.14−0.17) Rev. Mod. Phys. 67, 781 (1995)

Turck-Chiese 6.4 ± 1.4 123 ± 7 4.4 ± 1.1 Astrophys. J. 408, 347 (1993)

Bahcall 8.0 ± 3.0+ 132+21†−17 5.69(1.00 ± 0.43)b Rev. Mod. Phys. 64, 885 (1992)

a 1 SNU (solar neutrino unit) = 10−36 captures per atom per second.b 3σ error.

H. Results from Solar Neutrino Experiments

The available results from the solar neutrino experimentsdiscussed above are given in Table V, which summarizesboth the measured and the calculated values of the solarneutrino fluxes in several energy regions of the solar neu-trino spectrum. The discrepancies between the measuredand calculated solar neutrino fluxes in Table V are notlikely to be explained by an error in the current mathe-matical simulation of the sun. They are thought to be theresult of long-suspected properties of neutrinos which al-low them to oscillate spontaneously between energy statesafter traversing a given distance in free space or in mat-ter with appropriate electron density. The enhancement ofneutrino oscillations in the presence of matter, the MSWeffect (see suggested readings), is expected to be particu-larly important in the sun, where the variation of electrondensity with the solar radius is likely to satisfy the con-ditions for enhancement and to induce a level crossingbetween two neutrino states. The question of neutrino os-cillations is further addressed below.

III. ATMOSPHERIC (OR COSMIC RAY)NEUTRINOS

Atmospheric (cosmic ray) neutrinos are extraterrestrialneutrinos which originate in the collisions of the primaryproton component of cosmic rays with the earth’s atmo-sphere, giving rise to mesons that decay to a muon anda neutrino. The muons are the penetrating charged lep-tons of the cosmic ray spectrum that reach the earth; theneutral, even more penetrating neutrinos are their leptonicbirth partners and also the muons’ decay products. Theenergy spectrum of the atmospheric neutrinos is shown inFig. 8, which extends to a much higher region than thesolar neutrinos.

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FIGURE 8 Calculated atmospheric neutrino flux, φ(νµ + νµ), asa function of Eν .

The three-body decay of muons includes a charged elec-tron and a neutrino and antineutrino, each of the type orflavor to conserve a separate lepton number, i.e., one muontype and one electron type, while the meson (pion or kaon)decay produces almost exclusively muon type neutrinosor antineutrinos (see Table I). As a consequence, atmo-spheric neutrinos interacting in a detector such as K-II orSuperK would be expected to produce, on average, twiceas many muons as electrons. The double ratio: Rmeas (no.of muons/no. of electrons) divided by Rcalc (no. of muons/no. of electrons) was explored in K-II and subsequently inSuper K, and the results are shown in Table VI, where itis seen that apart from one experiment (Frejus; less thanthree standard deviations from the average of the otherexperiments), the double ratio Rmeas/Rcalc is significantlydifferent from the expected value of unity.

IV. NEUTRINO OSCILLATIONS

A. Interpretation of Data

The discrepancies in both Tables V and VI probably stemfrom neutrino oscillations. Briefly, the idea originated inthe speculation that the energy eigenstates of the threeknown neutrinos might differ from the weak eigenstatesof the neutrinos, νe, νµ, and ντ , that are found in the labora-tory, e.g., in nuclear beta-decay, and the decays of mesonsand the weak intermediate vector bosons. Assuming eachneutrino of a definite flavor (or weak eigenstate) is a co-herent superposition of mass (or energy) eigenstates, andtaking into account the time evolution of the energy eigen-states, one finds for the probability of a two-flavor oscil-lation, say, νe ↔ νµ,

TABLE VI Summary of the Ratio of Ratios R(µ/e) ≡≡Measured Ratio (µ/e)/Expected Ratio (µ/e) fromatmospheric neutrinos

Author R(µ/e) Reference

SuperK PRL 81, 1562 (1998)

Fukuda 0.63 ± 0.03 ± 0.05(sub-GeV)

0.65 ± 0.05 ± 0.08(multi-GeV)

Soudan PL B391, 491 (1997)

Allison 0.72 ± 0.19+0.05−0.07

Frejus Z Ph C66, 417 (1995)

Daum 1.00 ± 0.15 ± 0.08

K-II PL B335, 237 (1994)

Fukuda 0.06+0.06−0.05 ± 0.05

(sub-GeV)

0.57+0.08−0.07

(multi-GeV)

IMB PR D46, 3720 (1992)

Becker-Szendy Close to Kamiokande value for sameenergy limitsb

a Systematic effects, such as flux uncertainties, tend to cancel inR(µ/e), which should equal unity in the absence of new physics.

b See Beier (1992). PL B283, 446.

P(νe ↔ νµ; L) = sin2 2θeµ sin2

× [1.27 m2

12(eV2)L(meters)/E(MeV)]. (14)

Correspondingly, the probability that a beam initiallyof νe remains νe after traversing a distance L is

P(νe ↔ νe; L) = 1 − P(νe ↔ νµ; L) − P(νe ↔ ντ ; L).

(15)

In Eqs. (14) and (15), L is the neutrino source to detectordistance; E is the neutrino energy, m2

12 ≈ |m21 − m2

2|; andm1, m2 represent the mass eigenstates ν1 and ν2 whichmake up νe and νµ. The amplitude, sin 2θeµ, specifies thestrength of neutrino mixing. Most experiments searchingfor oscillations have been analyzed, assuming that onlytwo flavors mix appreciably, and the numerical result ispresented in terms of the regions allowed and forbidden inthe parameter space of m2 and sin2 2θ . Eq. (15) describesall of the experiments in which a fraction of the initial beamhas disappeared and which have therefore found allowedregions in that space.

The results from the astroneutrino experiments inTables V and VI are consistent with different numericaldescriptions of neutrino oscillations. One finds solutionsin which m2 is of the order of 10− 5 eV2 from two MSWsolutions and 10−10 eV2 from the so-called solar neu-trino vacuum oscillation solution, nominally representinga νe ↔ νµ oscillation. A fourth solution yields 10−3 eV2

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from the atmospheric neutrino oscillation data nominallyfrom νµ ↔ ντ . In three of the allowed solutions, sin2 2θ islarge (sin2 2θ ≥∼ 0.8), while in one of the MSW solutions,sin2 2θ lies between 10−3 and 10− 2.

There is reason to believe that the above propertiesreflect the major neutrino oscillation channels, althoughonly one of the three solar neutrino solutions will ulti-mately turn out to be valid. Neutrino searches for oscilla-tions at nuclear reactors in France, in southern Californiain the United States, and in Japan, all past or near thedata-taking stage, will ultimately help clarify the choiceof solutions. More importantly, at least one of those ex-periments or the experiments discussed below may pro-vide a conclusive demonstration that the astroneutrinodata is correctly interpreted by the neutrino oscillationexplanation.

B. Sudbury Solar Neutrino Experiment

During the 10-year period in which the data in Tables Vand VI were acquired, the electronic solar neutrino ex-periment in the Sudbury Neutrino Observatory (SNO) inCanada was completed and began data taking. The heartof SNO is a transparent acryclic sphere holding 1000 tonsof heavy (deuterated) water with which to observe the re-action initiated by νe from the 8B in the sun.

νe + d → e− + p + p, (16)

νe + d → νe + n + p, (17)

and

νx + e− → νx → e−. (18)

Note that reaction (3) will be induced by νe, νµ, and ντ ,although with different rates. Measurement of the rates ofreactions (1)–(3) should go far toward a definitive solutionof the neutrino oscillation problem and, ultimately, towardabsolute numerical values of neutrino masses.

Another solar neutrino electronic experiment directedprimarily at a measurement of the flux of 0.861-MeV neu-trinos from the reaction 7Be + e− → 7Li + νe is known asBorexino; it should help to unravel the integrated energyspectrum measurements from the radiochemical detectors.There are also less advanced plans for further detailedstudy of the solar neutrino spectrum in proposed elec-tronic experiments which seek to explore the neutrinosfrom the primary fusion reaction p + p → d + e+ = νe.

C. Long Baseline Terrestrial Experiments

The data in Table VI are currently taken as the strongestevidence for the existence of neutrino oscillations. De-spite having been observed in two independent atmo-spheric neutrino experiments—K-II and SuperK—a need

is felt to confirm them by a long baseline experimentusing terrestrial neutrinos from a particle accelerator.There are three very long baseline experiments, utiliz-ing accelerator-produced νµ beams, that are aimed at adefinitive test of neutrino oscillations. The neutrino sourcein one of them is from a newly built, external, 10-GeVproton beam at KEK, the detector is SuperK, 250 kmaway; the experiment is referred to as K2K. This experi-ment is already taking data. It will most likely duplicatethe disappearance of vµ that was observed in the atmo-spheric neutrino data and probably do so as a functionof muon energy. That information should be sufficientto demonstrate the validity of the neutrino oscillation in-terpretation of the disappearance experiments. Two otherexperiments—using high energy neutrinos, one (MINOS)from Fermilab and the other (ICARUS) from CERN—also plan for detectors very far away, about 730 km ineach case. The Fermilab beam will be directed at theSoudan Mine in northern Minnesota; and the CERN beamwill be directed at the Apennine Mountains joining eastand west Italy. Both seek to observe a νµ ↔ ντ oscilla-tion directly through the appearance of ντ interactions atthe end of the beam lines. Success depends on their abil-ity to devise and construct νtau detectors adequate for thepurpose.

A linear array of the original Kamiokande-style detec-tors, arranged on a long baseline (50–100 km), might alsotrack the sinusoidal dependence on distance of the fla-vor content of a νµ beam. This disappearance experimentwould bypass the difficult problem of devising a ντ de-tector for the Fermilab and CERN experiments and wouldstill serve the equivalent purpose of demonstrating neu-trino oscillations conclusively.

V. CONCLUSIONS

The observations of extraterrestrial neutrinos from the sunby different experimental methods have confirmed thedetails of the nuclear processes in the core of the sun andhave verified its internal structure and method of energygeneration. Moreover, the neutrinos from the earth’s atmo-sphere and from the sun appear to exhibit the phenomenonof neutrino oscillations which, if fully verified, will con-clusively demonstrate that at least one of the neutrinos inthe current model of elementary leptons has nonzero massand that at least two of them can spontaneously exchangeflavor.

Neutrinos observed from the supernova SN1987A, ap-proximately 55 kiloparsecs from earth, have quantitativelyconfirmed the current description of type II supernovaeand the particle physics and astrophysics principles onwhich the description is based.

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Together, these detailed observations have establishedexperimental neutrino astronomy, or, perhaps more ap-propriately, neutrino astrophysics, as a source of funda-mental information relating to the internal structure andbehavior of stars. As more powerful neutrino detectors be-come available and permit observation of other neutrinoradiation from the sky, we expect that neutrino astron-omy will be an increasingly valuable adjunct of the olderastronomy employing electromagnetic radiation as itsmeans of observation.


COSMIC RADIATION • DARK MATTER IN THE UNIVERSE

• GAMMA-RAY ASTRONOMY • GRAVITATIONAL WAVE

ASTRONOMY • NEUTRON STARS • NUCLEAR CHEMISTRY

• PARTICLE PHYSICS, ELEMENTARY • SOLAR PHYSICS •STELLAR STRUCTURE AND EVOLUTION • SUPERNOVAE

BIBLIOGRAPHY

Bahcall, J. N. (1994). “Solar Neutrinos: First Thirty Years,” Addison–Wesley, Reading, MA.

Faessler, A. (1998). “Progress in Particle and Nuclear Physics: Neutrinosin Astro, Particle and Nuclear Physics,” Vol. 40, Pergamon, Elmsford,NY.

Livio, M. (2000). “Unsolved Problems in Stellar Evolution,” CambridgeUniv. Press, Cambridge, UK.

Prialnik, D. (2000). “An Introduction to the Theory of Stellar Structureand Evolution,” Cambridge Univ. Press, Cambridge, UK.

Suzuki, Y., and Totsuka, Y., eds. (1999). “Neutrino Physics and Astro-physics,” North-Holland, Amsterdam.

Winter, K. (2000). “Neutrino Physics,” 2nd ed., Cambridge Univ. Press,Cambridge, UK.

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Planetary Radar AstronomySteven J. OstroCalifornia Institute of Technology

I. IntroductionII. Techniques and Instrumentation

III. Radar Measurements and Target PropertiesIV. Prospects for Planetary Radar

GLOSSARY

Aliasing Overlapping of echo at different frequencies orat different time delays.

Antenna gain Ratio of an antenna’s sensitivity in the di-rection toward which it is pointed to its average sensi-tivity in all directions.

Circular polarization ratio Ratio of echo power re-ceived in the same sense of circular polarization astransmitted (the SC sense) to that received in the oppo-site (OC) sense.

Doppler shift Difference between the frequencies of theradar echo and the transmission, caused by the relativevelocity of the target with respect to the radar.

Echo bandwidth Dispersion in Doppler frequency of anecho, that is, the width of the echo power spectrum.

Ephemeris Table of planetary positions as a function oftime (plural: ephemerides).

Klystron Vacuum-tube amplifier used in planetary radartransmitters.

Radar albedo Ratio of a target’s radar cross section ina specified polarization to its projected area; hence, ameasure of the target’s radar reflectivity.

Radar cross section Most common measure of a target’sscattering efficiency, equal to the projected area of that

perfect metal sphere that would give the same echopower as the target if observed at the target’s location.

Scattering law Function giving the dependence of a sur-face element’s radar cross section on viewing angle.

Synodic rotation period Apparent rotation period of atarget that is moving relative to the observer, to bedistinguished from the “sidereal” rotation period mea-sured with respect to the fixed stars.

Time delay Time between transmission of a radar signaland reception of the echo.

PLANETARY RADAR ASTRONOMY is the study ofsolar system entities (the Moon, asteroids, and cometsas well as the major planets and their satellites and ringsystems) by transmitting a radio signal toward the targetand then receiving and analyzing the echo. This field ofresearch has primarily involved observations with Earth-based radar telescopes, but also includes certain experi-ments with the transmitter and/or the receiver on boarda spacecraft orbiting or passing near a planetary object.However, radar studies of Earth’s surface, atmosphere,or ionosphere from spacecraft, aircraft, or the groundare not considered part of planetary radar astronomy.Radar studies of the Sun involve such distinctly individual

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296 Planetary Radar Astronomy

methodologies and physical considerations that solar radarastronomy is considered a field separate from planetaryradar astronomy.

I. INTRODUCTION

A. Scientific Context

Planetary radar astronomy is a field of science at the inter-section of planetology, radio astronomy, and radar engi-neering. A radar telescope is essentially a radio telescopeequipped with a high-power radio transmitter and spe-cialized electronic instrumentation designed to link trans-mitter, receiver, data acquisition, and telescope-pointingcomponents together in an integrated radar system. Theprinciples underlying operation of this system are not fun-damentally very different from those involved in radarsused, for example, in marine and aircraft navigation, mea-surement of automobile speeds, and satellite surveillance.However, planetary radars must detect echoes from tar-gets at interplanetary distances (∼105–109 km) and there-fore are the largest and most powerful radar systems inexistence.

The advantages of radar observations in astronomy stemfrom the high degree of control exercised by the observeron the transmitted signal used to illuminate the target.Whereas virtually every other astronomical technique re-lies on passive measurement of reflected sunlight or nat-urally emitted radiation, the radar astronomer controls allthe properties of the illumination, including its intensity,direction, polarization, and time/frequency structure. Theproperties of the transmitted waveform are selected toachieve particular scientific objectives. By comparing theproperties of the echo to the very well known propertiesof the transmission, some of the target’s properties canbe deduced. Hence, the observer is intimately involvedin an active astronomical observation and, in a very realsense, performs a controlled laboratory experiment on theplanetary target.

Radar delay-Doppler and interferometric techniquescan spatially resolve a target whose angular extent isdwarfed by the antenna beamwidth, thereby bestowinga considerable advantage on radar over optical techniquesin the study of asteroids, which appear like “point sources”through ground-based optical telescopes. Furthermore,by virtue of the centimeter-to-meter wavelengths em-ployed, radar is sensitive to scales of surface structuremany orders of magnitude larger than those probed invisible or infrared regions of the spectrum. Radar isalso unique in its ability to “see through” the denseclouds that enshroud Venus and the glowing gaseouscoma that conceals the nucleus of a comet. Because ofits unique capabilities, radar astronomy has made essen-

tial contributions to planetary exploration for a third of acentury.

B. History

Radar technology was developed rapidly to meet militaryneeds during World War II. In 1946, soon after the war’sconclusion, groups in the United States and Hungary ob-tained echoes from the Moon, giving birth to planetaryradar astronomy. These early postwar efforts were moti-vated primarily by interest in electromagnetic propagationthrough the ionosphere and the possibility for using theMoon as a “relay” for radio communication.

During the next two decades, the development of nu-clear weaponry and the need for ballistic missile warn-ing systems prompted enormous improvements in radarcapabilities. This period also saw rapid growth in radioastronomy and the construction of huge radio telescopes.In 1957, the Russia launched Sputnik and with it the spaceage, and in 1958, with the formation by the U.S. Congressof the National Aeronautics and Space Administration(NASA), a great deal of scientific attention turned to theMoon and to planetary exploration in general. During theensuing years, exhaustive radar investigations of the Moonwere conducted at wavelengths from 0.9 cm to 20 m, andthe results generated theories of radar scattering from nat-ural surfaces that still see wide application.

By 1963, improvements in the sensitivity of planetaryradars in both the United States and Russia had permittedthe initial detections of echoes from the terrestrial plan-ets (Venus, Mercury, and Mars). During this period, radarinvestigations provided the first accurate determinationsof the rotations of Venus and Mercury and the earliestindications for the extreme geologic diversity of Mars.Radar images of Venus have revealed small portions ofthat planet’s surface at increasingly fine resolution sincethe late 1960s, and in 1979 the Pioneer Venus Space-craft Radar Experiment gave us our first look at Venus’sglobal distributions of topography, radar reflectivity, andsurface slopes. During the 1980s, maps having sparse cov-erage but resolution down to ∼1 km were obtained fromthe Soviet Venera 15 and 16 orbiters and from ground-based observations with improved systems. Much morerecently, the Magellan spacecraft radar revealed most ofthe planet’s surface with unprecedented clarity, reveal-ing a rich assortment of volcanic, tectonic, and impactfeatures.

The first echoes from a near-Earth asteroid (1566Icarus) were detected in 1968; it would be nearly anotherdecade before the first radar detection of a main-belt aster-oid (1 Ceres in 1977), to be followed in 1980 by the firstdetection of echoes from a comet (Encke). During 1972and 1973, detection of 13-cm-wavelength radar echoes



Planetary Radar Astronomy 297

from Saturn’s rings shattered prevailing notions that typi-cal ring particles were 0.1 to 1.0 mm in size—the fact thatdecimeter-scale radio waves are backscattered efficientlyrequires that a large fraction of the particles be larger than acentimeter. Observations by the Voyager spacecraft con-firmed this fact and further suggested that particle sizesextend to at least 10 m.

In the mid-1970s, echoes from Jupiter’s Galilean satel-lites Europa, Ganymede, and Callisto revealed the mannerin which these icy moons backscatter circularly polarizedwaves to be extraordinarily strange and totally outside therealm of previous radar experience. We now understandthat those echoes were due to high-order multiple scatter-ing from within the top few decameters of the satellites’regoliths, but there remain important questions about thegeologic structures involved and the nature of electromag-netic interactions with those structures.

The late 1980s saw the initial detections of Phobosand Titan; the accurate measurement of Io’s radar proper-ties; the discovery of large-particle clouds accompanyingcomets; the dual-polarization mapping of Mars and theicy Galilean satellites; and radar imaging of asteroids thatrevealed an extraordinary assortment of radar signaturesand several highly irregular shapes, including a “contact-binary” near-Earth asteroid.

During the 1990s, the novel use of instrumentation andwaveforms yielded the first full-disk radar images of theterrestrial planets, revealing the global diversity of small-scale morphology on these objects and the surprising pres-ence of radar-bright polar anomalies on Mercury as wellas Mars. Similarities between the polarization and albedosignatures of these features and those of the icy Galileansatellites argue persuasively that Mercury’s polar anoma-lies are deposits of water ice in the floors of craters thatare perpetually shaded from sunlight by Mercury’s lowobliquity. The first time-delay-resolved (“ranging”) mea-surements to Ganymede and Callisto were carried out in1992. That same year, delay-Doppler images of the closelyapproaching asteroid 4179 Toutatis revealed this strangeobject to be in a very slow, non-principal-axis spin stateand provided the first geologically detailed pictures of anEarth-orbit-crossing asteroid. This decade also saw thefirst intercontinental radar observations and the beginningof planetary radar in Germany, Japan, and Spain. By 2000,the list of small planetary objects detected by radar in-cluded 7 comets, 37 main-belt asteroids, and 58 near-Earthasteroids (Table I).

Perhaps the most far-reaching recent development isthe upgrading of the Arecibo telescope’s sensitivity byover an order of magnitude. At this writing, Arecibo hasjust returned to operation, and radar astronomy is be-ginning a new era of major contributions to planetaryscience.

II. TECHNIQUES AND INSTRUMENTATION

A. Echo Detectability

How close must a planetary target be for its radar echo tobe detectable? For a given transmitted power PT and an-tenna gain G, the power flux a distance R from the radarwill be PTG/4π R2. We define the target’s radar cross sec-tion, σ , as 4π times the backscattered power per unit ofsolid angle per unit of flux incident at the target. Then, let-ting λ be the radar wavelength and defining the antenna’seffective aperture as A = Gλ2/4π , we have the receivedpower defined as follows:

PR = PTGAσ/

(4π )2 R4. (1)

This power might be much less than the receiver noisepower, PN = kTS � f , where k is Boltzmann’s constant,TS is the receiver system temperature, and � f is the fre-quency resolution of the data. However, the mean level ofPN constitutes a background that can be determined andremoved, so PR will be detectable as long as it is at leastseveral times larger than the standard deviation of the ran-dom fluctuations in PN. These fluctuations can be shownto have a distribution that, for usual values of � f and theintegration time �t , is nearly Gaussian with standard devi-ation �PN = PN/(� f �t)1/2. The highest signal-to-noiseratio, or SNR = PR/�PN, will be achieved for a frequencyresolution equal to the effective bandwidth of the echo. Asdiscussed in the following, that bandwidth is proportionalto D/λP , where D is the target’s diameter and P is the tar-get’s rotation period, so let us assume that � f ∼ D/λP .By writing σ = σπ D2/4, where the radar albedo σ is ameasure of the target’s radar reflectivity, we arrive at thefollowing expression for the echo’s signal-to-noise ratio:

SNR ∼ (system factor)(target factor(�t)1/2 (2)

where

system factor ∼ PT A2/λ3/2TS

∼ PTG2λ5/2/

TS (3)

and

target factor ∼ σ D3/2 P1/2/R4. (4)

The inverse-fourth-power dependence of SNR on targetdistance is a severe limitation in ground-based observa-tions, but it can be overcome by constructing very power-ful radar systems.

B. Radar Systems

The world has two active planetary radar facilities: theArecibo Observatory (part of the National Astronomyand Ionosphere Center) in Puerto Rico and the Goldstone




TABLE I Radar-Detected Planetary Targets

Year of first Planets, Main-beltdetection satellites, rings asteroids Near-Earth asteroids Comets

1946 Moon

1961 Venus

1962 Mercury

1963 Mars

1968 1566 Icarus

1972 1685 Toro

1973 Saturn’s rings

1974 Ganymede

1975 Callisto 433 ErosEuropa

1976 Io 1580 Betulia

1977 1 Ceres

1979 4 Vesta

1980 7 Iris Encke

16 Psyche 1862 Apollo

1981 97 Klotho 1915 Quetzalcoatl

8 Flora 2100 Ra-Shalom

1982 2 Pallas Grigg-Skjellerup

12 Victoria

19 Fortuna

46 Hestia

1983 5 Astraea 1620 Geographos IRAS-Araki-Alcock

139 Juewa 2201 Oljato Sugano-Saigusa-Fujikawa

356 Liguria

80 Sappho

694 Ekard

1984 9 Metis 2101 Adonis

554 Peraga

144 Vibilia

1985 6 Hebe 1627 Ivar Halley

41 Daphne 1036 Ganymed

21 Lutetia 1866 Sisyphus

33 Polyhymnia

84 Klio

192 Nausikaa

230 Athamantis

216 Kleopatra

18 Melpolmene

1986 393 Lampetia 6178 1986DA

27 Euterpe 1986JK

3103 Eger (1982BB)

3199 Nefertiti

1987 532 Herculina 1981 Midas

20 Massalia 3757 1982XB

1988 Phobos 654 Zelinda 3908 1980PA

105 Artemis

continues




TABLE I (Continued )

Year of first Planets, Main-beltdetection satellites, rings asteroids Near-Earth asteroids Comets

1989 Titan 4034 1986PA

1989JA

4769 Castalia (1989PB)

1917 Cuyo

1990 78 Diana 1990MF

194 Prokne 1990OS

4544 Xanthus (1989FB)

1991 324 Bamberga 1991AQ

796 Sarita 6489 Golevka (1991JX)

1991EE

1992 5189 1990UQ

4179 Toutatis

1994 4953 1990MU

1995 2062 Aten (1976AA)

1996 1992QN Hyakutake (C/1996 B2)

1993QA

2063 Bacchus

1996JG

1991CS

4197 1982TA

1997 7341 1991VK

7482 1994PC1

1997BR

1998 1998BY7

6037 1988EG

4183 Cuno

1998KY26

1998 1998 KY26 C/1998 K5

1998 8201 1994 AH2

1998 1998 ML14

1999 10115 1992 SK

1999 1999 FN19

1999 1999 GU3

1999 1999 FN53

1999 1999 JM8

1999 1999 NW2

1999 1999 RQ36

1999 1999 TY2

1999 1999 TN13

Solar System Radar in California. Radar wavelengths are13 and 70 cm for Arecibo and 3.5 and 13 cm for Gold-stone; with each instrument, enormously more sensitivityis achievable with the shorter wavelength. The upgradedArecibo telescope has twice the range and will see threetimes the volume of Goldstone, whereas Goldstone seestwice as much sky as Arecibo and can track targets atleast three times longer. Figure 1 shows the relative sen-

sitivities of planetary radar systems as a function of targetdeclination.

The Arecibo telescope (Fig. 2) consists of a 305-m-diameter, fixed reflector whose surface is a 51-m-deep sec-tion of a 265-m-radius sphere. Moveable feeds designedto correct for spherical aberration are suspended from atriangular platform 137 m above the reflector and can beaimed toward various positions on the reflector, enabling




FIGURE 1 Sensitivities of planetary radar systems. Curves plotthe single-date, signal-to-noise ratio of echoes from a typical 1-kmasteroid (σ = 0.1, P = 5 hr) at a distance of 0.1 AU for the upgradedArecibo telescope (A), Goldstone (G), and bistatic configurationsusing those instruments and the Very Large Array (VLA) or theGreenbank Telescope (GBT).

FIGURE 2 The Arecibo Observatory in Puerto Rico. (a) Aerial view prior to the recent upgrade. The diameter ofthe spherical reflector is 305 m. (b) A close-up view of the structure suspended above the reflector, showing the old430-MHz line feed and the radome that encloses the new Gregorian secondary and tertiary subreflectors.

the telescope to point within about 20◦ of the overheaddirection (declination 18.3◦N). Components of the recentupgrade included a megawatt transmitter, a ground screento reduce noise generated by radiation from the ground,and replacement of most of the old single-frequency linefeeds with a Gregorian reflector system (named after the17th-century mathematician James Gregory) that employs22-m secondary and 8-m tertiary subreflectors enclosedinside a 26-m dome.

The Goldstone main antenna, DSS-14 (DSS stands forDeep Space Station), is part of the NASA Deep SpaceNetwork, which is run by the Jet Propulsion. Labora-tory (JPL). It is a fully steerable, 70-m, parabolic reflec-tor (Fig. 3). Bistatic (two-station) experiments employ-ing transmission from DSS-14 and reception of echoesat the 27-antenna Very Large Array (VLA) in New Mex-ico have synthesized a beamwidth as small as 0.24 sec ofarc versus 2 min of arc for single-dish observations withArecibo or Goldstone. Bistatic experiments using DSS-14 transmissions and reception of echoes at DSS-13, a34-m antenna 22 km away, have been conducted on severalvery close targets. In coming years, bistatic observationsbetween Arecibo and Goldstone, or using transmissionfrom Arecibo or Goldstone and reception at the 100-m




FIGURE 2 (Continued )

Greenbank Telescope, now under construction in WestVirginia, should prove advantageous for outer planet satel-lites and nearby asteroids and comets.

Figure 4 is a simplified block diagram of a planetaryradar system. A waveguide switch, a moveable subreflec-tor, or a moveable mirror system is used to place the an-tenna in a transmitting or receiving configuration. Theheart of the transmitter is one or two klystron vacuum-tube amplifiers. In these tubes, electrons accelerated by apotential drop of some 60 kV are magnetically focusedas they enter the first of five or six cavities. In this firstcavity, an oscillating electric field at a certain radio fre-

quency (RF, e.g., 2380 MHz for Arecibo) modulates theelectrons’ velocities and hence their density and energyflux. Subsequent resonant cavities enhance this velocitybunching (they constitute what is called a “cascade ampli-fier”) and about half of the input DC power is converted toRF power and sent out through a waveguide to the antennafeed system and radiated toward the target. The other halfof the input power is waste heat and must be transportedaway from the klystron by cooling water. The impact ofthe electrons on the collector anode generates dangerousX-rays that must be contained by heavy metal shieldingsurrounding the tube, a requirement that further boosts




FIGURE 3 The 70-m Goldstone Solar System Radar antenna,DSS-14, in California.

the weight, complexity, and hence cost of a high-powertransmitter.

In most single-antenna observations, one transmits for aduration near the roundtrip propagation time to the target(i.e., until the echo from the beginning of the transmis-sion is about to arrive) and then receives for a similarduration. In the “front end” of the receiving system, theecho signal is amplified by a cooled, low-noise ampli-fier and converted from RF frequencies (e.g., 2380 MHzfor Arecibo at 13 cm) down to intermediate frequencies(IF, e.g., 30 MHz), for which transmission line losses aresmall, and passed from the proximity of the antenna feedto a remote control room containing additional stagesof signal-processing equipment, computers, and digitalrecorders. The signal is filtered, amplified, and convertedto frequencies low enough for analog voltage samples to bedigitized and recorded. The frequency down-conversioncan be done in several stages using analog devices calledsuperheterodyne mixers, but in recent years it has be-come possible to do this digitally, at increasingly higherfrequencies. The nature of the final processing prior torecording of data on a hard disk or magnetic tape dependson the nature of the radar experiment and particularly onthe time/frequency structure of the transmitted waveform.Each year, systems for reducing and displaying echoes in“real time” and techniques for processing recorded dataare becoming more ambitious as computers get faster.

FIGURE 4 Block diagram of a planetary radar system. RF LO andIFLO denote radio frequency and intermediate frequency localoscillators, and ADC denotes analog-to-digital converter.

C. Echo Time Delay and Doppler Frequency

The time between transmission of a radar signal and re-ception of the echo is called the echo’s roundtrip timedelay, τ , and is of order 2R/c, where c is the speed oflight, 299,792,458 m sec−1. Since planetary targets arenot points, even an infinitesimally short transmitted pulsewould be dispersed in time delay, and the total extent�τTARGET of the distribution σ (τ ) of echo power (in unitsof radar cross section) would be D/c for a sphere of diame-ter D and in general depends on the target’s size and shape.

The translational motion of the target with respect to theradar introduces a Doppler shift, ν, in the frequency of thetransmission. Both the time delay and the Doppler shiftof the echo can be predicted in advance from the target’sephemeris, which is calculated using the geodetic positionof the radar and the orbital elements of Earth and the tar-get. The predicted Doppler shift can be removed electron-ically by continuously tuning the local oscillator used forRF-to-IF frequency conversion (see Fig. 4). Sometimesit is convenient to “remove the Doppler on the uplink”by modulating the transmission so that echoes return at afixed frequency, the predicted Doppler must be accurateenough to avoid smearing out the echo in delay, and thisrequirement places stringent demands on the quality of the




observing ephemeris. Time and frequency measurementsare critical because the delay/Doppler distribution of echopower is the source of the finest spatial resolution and alsobecause delay and Doppler are fundamental dynamical ob-servables. Reliable, precise time/frequency measurementsare made possible by high-speed data acquisition systemsand stable, accurate clocks and frequency standards.

Because different parts of the rotating target will havedifferent velocities relative to the radar, the echo will bedispersed in Doppler frequency as well as in time delay.The basic strategy of any radar experiment always involvesmeasurement of some characteristic(s) of the functionσ (τ, ν), perhaps as a function of time and perhaps usingmore than one combination of transmitted and receivedpolarizations. Ideally, one would like to obtain σ (τ, ν)with very fine resolution, sampling that function withinintervals whose dimensions, �τ × �ν, are minute com-pared to the echo dispersions �τTARGET and �νTARGET.However, one’s ability to resolve σ (τ, ν) is necessarilylimited by the available echo strength. Furthermore, asdescribed in the next section, an intrinsic upper bound onthe product �τ �ν forces a trade-off between delay res-olution and Doppler resolution for the most commonlyused waveforms. Under these constraints, many planetaryradar experiments employ waveforms aimed at provid-ing estimates of one of the marginal distributions, σ (τ )or σ (ν). Figure 5 shows the geometry of delay-resolutioncells and Doppler-resolution cells for a spherical target

FIGURE 5 Time-delay and Doppler-frequency resolution of theradar echo from a rotating spherical target.

and sketches the relation between these cells and σ (τ ) andσ (ν). Delay-Doppler measurements are explored furtherin the following.

D. Radar Waveforms

In the simplest radar experiment, the transmitted sig-nal is a highly monochromatic, unmodulated continuous-wave (cw) signal. Analysis of the received signalcomprises Fourier transformation of a series of time sam-ples and yields an estimate of the echo power spectrumσ (ν), but contains no information about the distance tothe target or σ (τ ). To avoid aliasing, the sampling ratemust be at least as large as the bandwidth of the low-pass filter (see Fig. 4) and usually is comparable to orlarger than the echo’s intrinsic dispersion �νTARGET fromDoppler broadening. Fast-Fourier transform (FFT) algo-rithms, implemented via software or hardwired (e.g., inan array processor), greatly speed the calculation of dis-crete spectra from time series and are ubiquitous in radarastronomy. In a single FFT operation, a string of N timesamples taken at intervals of �t seconds is transformedinto a string of N spectral elements with frequency resolu-tion �ν = 1/N �t . Most planetary radar targets are suf-ficiently narrowband for power spectra to be computed,accumulated, and recorded directly on disk or magnetictape at convenient intervals. In some situations, it is desir-able to record time samples on tape and Fourier-analyzethe data later, perhaps using FFTs of different lengths toobtain spectra at a variety of frequency resolutions. Inothers, it is convenient to pass the signal through an au-tocorrelator to record autocorrelation functions, and thenapply FFTs to extract spectra.

To obtain delay resolution, one must apply some sortof time modulation to the transmitted waveform. For ex-ample, a short-duration pulse of cw signal lasting 1 µsecwould provide delay resolution of 150 m. However, theecho would have to compete with the noise power in abandwidth of order 1 MHz so the echo power from manyconsecutive pulses would probably have to be summedto yield a detection. One would not want these pulses tobe too close together, however, or there would be morethan one pulse incident on the target at once and interpre-tation of echoes would be insufferably ambiguous. Thus,one arranges the pulse repetition period tPRP to exceed thetarget’s intrinsic delay dispersion �τTARGET, ensuring thatthe echo will consist of successive, nonoverlapping “repli-cas” of σ (τ ) separated from each other by tPRP. To generatethis “pulsed cw” waveform, the transmitter is switched onand off while the frequency synthesizer (see Fig. 4) main-tains phase coherence from pulse to pulse. Then Fouriertransformation of time samples taken at the same positionwithin each of N successive replicas of σ (τ ) yields the




power spectrum of echo from a certain delay resolutioncell on the target. This spectrum has an unaliased band-width of 1/tPRP and a frequency resolution of 1/NtPRP.Repeating this process for a different position within eachreplica of σ (τ ) yields the power spectrum for echo froma different delay resolution cell, and in this manner oneobtains the delay-Doppler image σ (τ, ν).

In practice, instead of pulsing the transmitter, one usu-ally codes a cw signal with a sequence of 180◦ phasereversals and cross-correlates the echo with a representa-tion of the code (e.g., using the decoder in Fig. 4), therebysynthesizing a pulse train with the desired values of �tand tPRP. With this approach, one optimizes SNR becauseit is much cheaper to transmit the same average powercontinuously than by pulsing the transmitter. Most mod-ern ground-based radar astronomy observations employcw or repetitive, phase-coded cw waveforms.

A limitation of coherent-pulsed or repetitive, binary-phase-coded cw waveforms follows from combiningthe requirement that there never be more than oneecho received from the target at any instant (i.e., thattPRP > �τTARGET) with the antialiasing frequency require-ment that the rate (1/tPRP) at which echo from a givendelay resolution cell is sampled be no less than the tar-get bandwidth �νTARGET. Therefore, a target must satisfy�τTARGET �νTARGET ≤ 1 or it is “overspread” (Table II)and cannot be investigated completely and simultaneouslyin delay and Doppler without aliasing, at least with thewaveforms discussed so far. Various degrees of aliasingmay be “acceptable” for overspread factors less than about10, depending on the precise experimental objectives andthe exact properties of the echo.

How can the full delay-Doppler distribution be obtainedfor overspread targets? Frequency-swept and frequency-stepped waveforms have seen limited use in planetaryradar; the latter approach has been used to image Saturn’srings. A new technique uses a nonrepeating, binary-phase-coded cw waveform. The received signal for any givendelay cell is decoded by multiplying it by a suitablylagged replica of the code. Developed for observations ofthe highly overspread ionosphere, this “coded-long-pulse”or “random-code” waveform redistributes delay-aliasedecho power into an additive white-noise background. TheSNR is reduced accordingly, but this penalty is acceptablefor strong targets.

III. RADAR MEASUREMENTSAND TARGET PROPERTIES

A. Albedo and Polarization Ratio

A primary goal of the initial radar investigation of anyplanetary target is estimation of the target’s radar crosssection, σ , and its normalized radar cross section or “radar

albedo,” σ = σ/Ap, where Ap is the target’s geometricprojected area. Since the radar astronomer selects thetransmitted and received polarizations, any estimate ofσ or σ must be identified accordingly. The most com-mon approach is to transmit a circularly polarized waveand to use separate receiving systems for simultaneousreception of the same sense of circular polarization astransmitted (i.e., the SC sense) and the opposite (OC)sense. The handedness of a circularly polarized wave isreversed on normal reflection from a smooth dielectric in-terface, so the OC sense dominates echoes from targetsthat look smooth at the radar wavelength. In this context,a surface with minimum radius of curvature very muchlarger than λ would “look smooth.” SC echo power canarise from single scattering from rough surfaces, multi-ple scattering from smooth surfaces or subsurface het-erogeneities (e.g., particles or voids), or certain subsur-face refraction effects. The circular polarization ratio,µC = σSC /σOC, is thus a useful measure of near-surfacestructural complexity or “roughness.” When linear po-larizations are used, it is convenient to define the ratioµL = σOL/σSL, which would be close to zero for normalreflection from a smooth dielectric interface. For all radar-detected planetary targets, µL < 1 and µL < µC. Althoughthe OC radar albedo, σOC, is the most widely used gauge ofradar reflectivity, some radar measurements are reportedin terms of the total power (OC + SC = OL + SL) radaralbedo σT, which is four times the geometric albedo usedin optical planetary astronomy. A smooth metallic spherewould have σOC = σSL = 1, a geometric albedo of 0.25,and µC = µL = 0.

If µC is close to zero (see Table II), its physical interpre-tation is unique, as the surface must be smooth at all scaleswithin about an order of magnitude of λ and there can beno subsurface structure at those scales within several 1/epower absorption lengths, L , of the surface proper. In thisspecial situation, we may interpret the radar albedo as theproduct gρ, where ρ is the Fresnel power-reflection co-efficient at normal incidence and the backscatter gain gdepends on target shape, the distribution of surface slopeswith respect to that shape, and target orientation. For mostapplications to date, g is <10% larger than unity, so theradar albedo provides a reasonable first approximation toρ. Both ρ and L depend on very interesting characteristicsof the surface material, including bulk density, porosity,particle size distribution, and metal abundance.

If µC is ∼0.3 (e.g., Mars and some near-Earth aster-oids), then much of the echo arises from some backsca-tering mechanism other than single, coherent reflectionsfrom large, smooth surface elements. Possibilities includemultiple scattering from buried rocks or from the interiorsof concave surface features such as craters or reflectionsfrom very jagged surfaces with radii of curvature muchless than a wavelength. Most planetary targets have values




TABLE II Characteristics of Selected Planetary Radar Targetsa

Maximum dispersionsc

Minimum Radar cross Circularecho delayb section Radar polarization Delay Doppler

Target (min) (km2) albedo σ0 ratio, µC (msec) (Hz) Product

Moon 0.04 6.6 × 105 0.07 0.1 12 60 0.7

Mercury 9.1 1.1 × 106 0.06 0.1 16 110 2

Venus 4.5 1.3 × 107 0.11 0.1 40 110 4

Mars 6.2 2.9 × 106 0.08 0.3 23 7600 170

Phobos 6.2 22 0.06 0.1 0.1 100 10−2

1 Ceres 26 2.7 × 104 0.05 0.0 3 3100 9

2 Pallas 25 1.7 × 104 0.08 0.0 2 2000 4

12 Victoria 15 2.3 × 103 0.22 0.1 0.5 590 3

16 Psyche 28 1.4 × 104 0.31 0.1 0.8 2200 2

216 Kleopatra 20 7.1 × 103 0.44 0.0 ? 750 ?

324 Bamberga 13 2.9 × 103 0.06 0.1 0.8 230 0.2

1685 Toro 2.3 1.7 0.1 0.2 0.02 14 10−4

1862 Apollo 0.9 0.2 0.1 0.4 0.01 16 10−4

2100 Ra-Shalom 3.0 1.0 0.1 0.2 0.01 5 10−4

2101 Adonis 1.5 0.02 <0.3 1.0 ? 2 ?

4179 Toutatis 0.4 1.3 0.24 0.3 0.01 1 10−5

4769 Castalia 0.6 0.2 0.15 0.3 0.01 10 10−4

6178 1986DA 3.4 2.4 0.6 0.1 12 15 0.2

1998 KY26 0.09 2.5 × 10−5 0.01 to 0.1 0.5 0.0001 15 0.0015

IAAd nucleus 0.5 2.4 0.04? 0.1 ? 4 ?

IAA coma 0.5 0.8 ? 0.01 ? 600 ?

HYAe nucleus 1.7 0.11 ? 0.5 ? 12 ?

HYA coma 1.7 1.3 ? <1 ? 3000 ?

Io 66 2 × 106 0.2 0.5 12 2400 29

Europa 66 8 × 106 1.0 1.5 10 1000 11

Ganymede 66 1 × 107 0.6 1.4 18 850 15

Callisto 66 5 × 106 0.3 1.2 16 330 5

Saturn’s rings 134 108–109 0.7 0.5 1600 6 × 105 106

a Typical 3.5- to 13-cm values. Question marks denote absence of radar data or of prior information about target dimensions.b For asteroids and comets, this is the minimum echo time delay for radar observations to date.c Doppler dispersion for transmitter frequency of 2380 MHz (λ13 cm). The product of the dispersions in delay and Doppler is the overspread factor

at 2380 MHz.d IAA denotes comet IRAS-Araki-Alcock.e HYA denotes comet Hyakutake (C/1996 B2).

of µC < 0.3 at decimeter wavelengths, so their surfaces aredominated by a component that is smooth at centimeter tometer scales.

The observables σOC and µC are disk-integrated quanti-ties, derived from integrals of σ (ν) or σ (τ ) in specific po-larizations. How their physical interpretation profits fromknowledge of the functional forms of σ (ν) and σ (τ ) isshown below.

B. Dynamical Properties fromDelay/Doppler Measurements

Consider radar observation of a point target a distance Rfrom the radar. As noted above, the “roundtrip time delay”

between transmission of a pulse toward the target and re-ception of the echo would be τ = 2R/c. It is possible tomeasure time delays to within 10−7 sec. Actual delaysencountered range from 2 1

2 sec for the Moon to 2 12 hr

for Saturn’s rings. For a typical target distance ∼1 astro-nomical unit (AU), the time delay is ∼1000 sec and canbe measured with a fractional timing uncertainty of 10−9,that is, with the same fractional precision as the definitionof the speed of light.

If the target is in motion and has a line-of-sight com-ponent of velocity toward the radar of vLOS, the tar-get will “see” a frequency that, to first order in vLOS/c,equals fTX + (vLOS/c) fTX, where fTX is the transmit-ter frequency. The target reradiates the Doppler-shifted




signal, and the radar receives echo whose frequency is,again to first order, given by the following:

fTX + 2(vLOS/c) fTX.

That is, the total Doppler shift in the received echo is

2vLOS fTX/c = vLOS/(λ/2)

so a 1-Hz Doppler shift corresponds to a velocity of half awavelength per second (e.g., 6.3 cm sec−1 for λ12.6 cm).It is not difficult to measure echo frequencies to within0.01 Hz, so vLOS can be estimated with a precision finerthan 1 mm sec−1. Actual values of vLOS for planetary radartargets can be as large as several tens of kilometers per sec-ond, so radar velocity measurements have fractional errorsas low as 10−8. At this level, the second-order (special rela-tivistic) contribution to the Doppler shift becomes measur-able; in fact, planetary radar observations have providedthe initial experimental verification of the second-orderterm.

By virtue of their high precision, radar measurementsof time delay and Doppler frequency are very useful inrefining our knowledge of various dynamical quantities.The first delay-resolved radar observations of Venus, dur-ing 1961–1962, yielded an estimate of the light-secondequivalent of the astronomical unit that was accurate toone part in 106, constituting a thousandfold improvementin the best results achieved with optical observations alone.Subsequent radar observations provided additional refine-ments of nearly two more orders of magnitude. In additionto determining the scale of the solar system precisely, theseobservations greatly improved our knowledge of the or-bits of Earth, Venus, Mercury, and Mars and were essentialfor the success of the first interplanetary missions. Radarobservations still contribute to maintaining the accuracyof planetary ephemerides for objects in the inner solarsystem and have played an important role in dynamicalstudies of Jupiter’s Galilean satellites. For newly discov-ered near-Earth asteroids, whose orbits must be estimatedfrom optical astrometry that spans short arcs, a few radarobservations can mean the difference between success-fully recovering the object during its next close approachand losing it entirely. Even for near-Earth asteroids withsecure orbits, delay-Doppler measurements can shrink thepositional error ellipsoid significantly for decades or evencenturies.

Precise interplanetary time-delay measurements haveallowed increasingly decisive tests of physical theories forlight, gravitational fields, and their interactions with mat-ter and each other. For example, radar observations verifygeneral relativity theory’s prediction that for radar wavespassing nearby the Sun, echo time delays are increased be-cause of the distortion of space by the Sun’s gravity. Theextra delay would be ∼100 µsec if the angular separation

of the target from the Sun were several degrees. (The Sun’sangular diameter is about half a degree.) Since planets arenot point targets, their echoes are dispersed in delay andDoppler, and the refinement of dynamical quantities andthe testing of physical theories are tightly coupled to es-timation of the mean radii, the topographic relief, and theradar scattering behavior of the targets. The key to this en-tire process is resolution of the distributions of echo powerin delay and Doppler. In the next section, we consider in-ferences about a target’s dimensions and spin vector frommeasurements of the dispersions (�τTARGET, �νTARGET)of the echo in delay and Doppler. Then we examine thephysical information contained in the functional forms ofthe distributions σ (τ ), σ (ν), and σ (τ, ν).

C. Dispersion of Echo Powerin Delay and Doppler

Each backscattering element on a target’s surface returnsecho with a certain time delay and Doppler frequency(see Fig. 5). Since parallax effects and the curvature of theincident wave front are negligible for most ground-basedobservations (but not necessarily for observations withspacecraft), contours of constant delay are intersections ofthe surface with planes perpendicular to the line of sight.The point on the surface with the shortest echo time delayis called the subradar point; the longest delays generallycorrespond to echoes from the planetary limbs. As notedalready, the difference between these extreme delays iscalled the dispersion, �τTARGET, in σ (τ ), or simply the“delay depth” of the target.

If the target appears to be rotating, the echo will bedispersed in Doppler frequency. For example, if the radarhas an equatorial view of a spherical target with diameterD and rotation period P , then the difference between theline-of-sight velocities of points on the equator at the ap-proaching and receding limbs would be 2π D/P . Thus thedispersion of σ (ν) would be �νTARGET = 4π D/λP . Thisquantity is called the bandwidth, B, of the echo powerspectrum. If the view is not equatorial, the bandwidth issimply (4π D sin α)/λP , where the “aspect angle” α isthe acute angle between the instantaneous spin vector andthe line of sight. Thus, a radar bandwidth measurementfurnishes a joint constraint on the target’s size, rotationperiod, and pole direction.

In principle, echo bandwidth measurements obtainedfor a sufficiently wide variety of directions can yield allthree scalar coordinates of the target’s intrinsic (i.e., side-real) spin vector W. This capability follows from the factthat the apparent spin vector Wapp is the vector sum of Wand the contribution (Wsky = e × e, where the unit vector epoints from the target to the radar) from the target’s plane-of-sky motion. Variations in e, e, and hence Wsky, all of




which are known, lead to measurement of different valuesof Wapp = W + Wsky, permitting unique determination ofall three scalar components of W.

These principles were applied in the early 1960s toyield the first accurate determination of the rotations ofVenus and Mercury (Fig. 6). Venus’s rotation is retro-grade with a 243-day sidereal period that is close to thevalue (243.16 days) characterizing a resonance with therelative orbits of Earth and Venus, wherein Venus wouldappear from Earth to rotate exactly four times between suc-cessive inferior conjuctions with the Sun. However, twodecades of ground-based observations and ultimately im-ages obtained by the Magellan spacecraft while in orbitaround Venus have conclusively demonstrated nonreso-nance rotation: the period is 243.0185 ± 0.0001 days. Todate, a satisfactory explanation for Venus’s curious spinstate is lacking.

For Mercury, long imagined on the basis of optical ob-servations to rotate once per 88-day revolution around theSun, radar bandwidth measurements (see Fig. 6) demon-strated direct rotation with a period (59 days) equal totwo-thirds of the orbital period. This spin–orbit couplingis such that during 2 Mercury years, the planet rotatesthree times with respect to the stars but only once withrespect to the Sun, so a Mercury-bound observer wouldexperience alternating years of daylight and darkness.

What if the target is not a sphere but instead is irregularand nonconvex? In this situation, which is most applicableto small asteroids and cometary nuclei, the relationshipbetween the echo power spectrum and the target’s shapeis shown in Fig. 7. We must interpret D as the sum of thedistances r+ and r− from the plane ψ0 containing the lineof sight and the spin vector to the surface elements withthe greatest positive (approaching) and negative (receding)line-of-sight velocities. In different words, if the planesψ+and ψ− are defined as being parallel to ψ0 and tangent tothe target’s approaching and receding limbs, then ψ+ andψ− are at distances r+ and r− from ψ0. Letting f0, f+, andf− be the frequencies of echoes from portions of the targetintersecting ψ0, ψ+, and ψ−, we have B = f+ − f−. Notethat f0 is the Doppler frequency of hypothetical echoesfrom the target’s center of mass and that any constant-Doppler contour lies in a plane parallel to ψ0.

It is useful to imagine looking along the target’s pole atthe target’s projected shape, that is, its poleon silhouetteS. D is simply the width, or “breadth,” of this silhouette(or, equivalently, of the silhouette’s convex envelope or“hull,” H ) measured normal to the line of sight (see Fig. 7).In general, r+ and r− are periodic functions of rotationphase φ and depend on the shape of H as well as on theprojected location of the target’s center of mass, aboutwhich H rotates. If the radar data thoroughly sample atleast 180◦ of rotational phase, then in principle one can

FIGURE 6 Measurements of echo bandwidth (i.e., the dispersionof echo power in Doppler frequency) used to determine the rota-tions of (a) Venus and (b) Mercury. [From Dyce, R. B., Pettengill,G. H., and Shapiro, I. I. (1967). Astron. J. 72, 351–359.]




FIGURE 7 Geometric relations between an irregular, noncon-vex rotating asteroid and its echo power spectrum. The plane ψ0contains the asteroid’s spin vector and the asteroid–radar line.The cross-hatched strip of power in the spectrum corresponds toechoes from the cross-hatched strip on the asteroid.

determine f+(φ) and f −(φ) completely and can recoverH as well as the astrometrically useful quantity f0. Formany small, near-Earth asteroids, pronounced variationsin B(φ) reveal highly noncircular pole-on silhouettes (seeFig. 8 and Section III.J).

D. Topography on the Moon and Inner Planets

For the Moon, Mercury, Mars, and Venus, topographyalong the subradar track superimposes a modulation on theecho delay above or below that predicted by ephemerides,which generally are calculated for a sphere with the ob-ject’s a priori mean radius. Prior to spacecraft explorationof these objects, there were radar-detectable errors in theradii estimates as well as in the target’s predicted orbit.These circumstances required that an extended series ofmeasurements of the time delay of the echo’s leading edgebe folded into a computer program designed to estimatesimultaneously parameters describing the target’s orbit,mean radius, and topography. These programs also con-tain parameters from models of wave propagation throughthe interplanetary medium or the solar corona, as well

as parameters used to test general relativity, as notedabove.

Radar has been used to obtain topographic profilesacross the Moon and the inner planets. For example, Fig. 9shows a three-dimensional reconstruction of topographyderived from altimetric profiles obtained for Mars in thevicinity of the giant shield volcano Arsia Mons. The al-timetric resolution of the profiles is about 150 m (1 µsecin delay), but the surface resolution, or footprint, is verycoarse (∼75 km). Figure 10 shows altitude profiles acrossimpact basins on Mercury. The Magellan radar altimeter,with a footprint typically 20 km across and vertical resolu-tion on the order of tens of meters, has produced detailedtopographic maps of most of Venus.

E. Angular Scattering Law

The functional forms of the distributions σ (τ ) and σ (ν)contain information about the radar scattering process andabout the structural characteristics of the target’s surface.Suppose the target is a large, smooth, spherical planet.Then echoes from the subradar region (near the center ofthe visible disk; see Fig. 5), where the surface elements arenearly perpendicular to the line of sight, would be muchstronger than those from the limb regions (near the disk’speriphery). This effect is seen visually when one shines aflashlight on a smooth, shiny ball—a bright glint appearswhere the geometry is right for backscattering. If the ballis roughened, the glint is spread out over a wider area and,in the case of extreme roughness, the scattering would bedescribed as “diffuse” rather than “specular.”

For a specular target, σ (τ ) would have a steep leadingedge followed by a rapid drop. The power spectrum σ (ν)would be sharply peaked at central frequencies, falling offrapidly toward the spectral edges. If, instead, the spec-trum were very broad, severe roughness at some scale(s)comparable to or larger than λ would be indicated. Inthis case, knowledge of the echo’s polarization propertieswould help to ascertain the particular roughness scale(s)responsible for the absence of the sharply peaked spectralsignature of specular scattering.

By inverting the delay or Doppler distribution of echopower, one can estimate the target’s average angular scat-tering law, σ0(θ ) = dσ/d A, where d A is an element ofsurface area and θ is the “incidence angle” between theline of sight and the normal to d A. For the portion ofthe echo’s “polarized” (i.e., OC or SL) component thatis specularly scattered, σ0(θ ) can be related to statisticsdescribing the probability distribution for the slopes ofsurface elements. Examples of scattering laws applied inplanetary radar astronomy are the Hagfors law:

σ0(θ ) ∼ C(cos4 θ + C sin2 θ )−3/2, (5)




FIGURE 8 Constraints on the shape of near-Earth asteroid 1620 Geographos from Goldstone radar echoes.(a) Spectra obtained at phases of bandwidth extrema. OC (solid curve) and SC (dotted curve) echo power is plottedversus Doppler frequency. (b) Comparison of an estimate of the hull (H ) on the asteroid’s pole-on silhouette (S ) withan estimate of S itself. The white curve is the cw estimate of H and the X marks the projected position of the asteroid’scenter of mass (COM) with respect to H . That curve and the X are superposed on an estimate of S from delay-Dopplerimages; the bright pixel is the projection of the COM determined from analysis of those images. The absolute scalesand relative rotational orientations of the two figures are known: border ticks are 1 km apart. The offset between theX and the bright pixel is a measure of the uncertainty in our knowledge of the COM’s delay-Doppler trajectory duringthe experiment. In the diagram at right, the arrows point to the observer at phases of lightcurve maxima (M1 and M2)and minima (m1 and m2). [From Ostro, S. J., et al. (1996). Icarus 121, 46–66.]

the Gaussian law:

σ0(θ ) ∼ [C exp(−C tan2 θ )]/ cos4 θ, (6)

and the Cosine law:

σ0(θ ) ∼ (C + 1) cos2C θ, (7)

where c−1/2 = S0 = 〈tan2 θ〉1/2 is the adirectional rmsslope.

Echoes from the Moon, Mercury, Venus, and Marsare characterized by sharply peaked OC echo spectra(Fig. 11). Although these objects are collectively referredto as “quasispecular” radar targets, their echoes also con-tain a diffusely scattered component and have full-diskcircular polarization ratios averaging about 0.07 for theMoon, Mercury, and Venus, but ranging from 0.1 to 0.4for Mars, as discussed below.

Typical rms slopes obtained at decimeter wavelengthsfor these four quasispecular targets are around 7◦ and

consequently these objects’ surfaces have been describedas “gently undulating.” As might be expected, valuesestimated for S0 increase as the observing wavelengthdecreases. For instance, for the Moon, S0 increases from∼4◦ at 20 m to ∼8◦ at 10 cm to ∼33◦ at 1 cm. At opticalwavelengths, the Moon shows no trace of a central glint,that is, the scattering is entirely diffuse. Thisphenomenonarises because the lunar surface (Fig. 12) consists ofa regolith (an unconsolidated layer of fine-grainedparticles) with much intricate structure at the scale ofvisible wavelengths. At decimeter wavelengths, the ratioof diffusely scattered power to quasispecularly scatteredpower is about one-third for the Moon, Mercury, andVenus, but two to three times higher for Mars. This ratiocan be determined by assuming that all the SC echois diffuse and then calculating the diffusely scatteredfraction (x) of OC echo by fitting to the OC spectrum amodel based on a “composite” scattering law, for example,





S0(θ ) = xσDIF(θ ) + (1 − x)σQS(θ ). Here σQS(θ ) mightbe the Hagfors law and usually σDIF(θ ) ∼ cosm θ ; whenthis is done, estimated values of m usually fall be-tween unity (geometric scattering, which describes theoptical appearance of the full Moon) and 2 (Lambertscattering).

For the large, nearly spherical asteroids 1 Ceres and2 Pallas (see Section III.J), the closeness of µC to zeroindicates quasispecular scattering, but the OC spectra,rather than being sharply peaked, are fit quite well usinga Cosine law with C between 2 and 3 or a Gaussianlaw with C between 3 and 5. Here we can safely inter-pret the diffuse echo as due to the distribution of surfaceslopes, with S0 between 20◦ and 50◦. OC echo spectra ob-tained from asteriod 4 Vesta and Jupiter’s satellite Io havesimilar shapes, but these objects’ substantial polarizationratios (µC ∼ 0.3 and ∼0.5, respectively) suggest thatsmall-scale roughness is at least partially responsible forthe diffuse echoes. Circular polarization ratios between0.5 and 1.0 have been measured for several asteroids (seeTable II) and parts of Mars and Venus, implying extremedecimeter-scale roughness, perhaps analogous to terres-trial lava flows (Fig. 13). Physical interpretations of thediffusely scattered echo employ information about albedo,scattering law, and polarization to constrain the sizedistributions, spatial densities, and electrical propertiesof wavelength-scale rocks near the surface, occasiona-lly using the same theory of multiple light scattering

applied to radiative transfer problems in other astrophys-ical contexts.

F. Radar Mapping of Spherical Targets

The term “radar image” usually refers to a measured dis-tribution of echo power in delay, Doppler, and/or up to twoangular coordinates. The term “radar map” usually refersto a display in suitable target-centered coordinates of theresiduals with respect to a model that parameterizes thetarget’s size, shape, rotation, average scattering properties,and possibly its motion with respect to the delay-Dopplerephemerides. Knowledge of the dimensions of the Moonand inner planets has long permitted conversion of radarimages to maps of these targets. For small asteroids, theprimary use of images is to constrain the target’s shape(see Section III.J).

As illustrated in Fig. 5, intersections between constant-delay contours and constant-Doppler contours on a sphereconstitute a “two-to-one” transformation from the target’ssurface to delay-Doppler space. For any point in the north-ern hemisphere, there is a conjugate point in the southernhemisphere at the same delay and Doppler. Therefore, thesource of echo in any delay-Doppler resolution cell can belocated only to within a twofold ambiguity. This north–south ambiguity can be avoided completely if the radarbeamwidth (∼2 arcmin for Arecibo at 13 cm or Goldstoneat 3.5 cm) is comparable to or smaller than the target’sapparent angular radius, as in the case of observationsof the Moon (angular radius ∼15 arcmin). Similarly, nosuch ambiguity arises in the case of side-looking radar ob-servations from spacecraft (e.g., the Magellan radar), forwhich the geometry of delay-Doppler surface contoursdiffers somewhat from that in Fig. 5. For ground-basedobservations of Venus and Mercury, whose angular radiinever exceed a few tens of arcseconds, the separation ofconjugate points is achievable by either (1) offsetting thepointing to place a null of the illumination pattern on theundesired hemisphere or (2) interferometrically, using tworeceiving antennas, as follows.

The echo waveform received at either antenna from oneconjugate point will be highly correlated with the echowaveform received at the other antenna from the sameconjugate point. However, echo waveforms from the twoconjugate points will be largely uncorrelated with eachother, no matter where they are received. Thus, echoesfrom two conjugate points can, in principle, be distin-guished by cross-correlating echoes received at the twoantennas with themselves and with each other, and per-forming algebraic manipulations on long time averages ofthe cross product and the two self products.

The echo waveform from a single conjugate point willexperience slightly different delays in reaching the two




FIGURE 9 Topographic contours for the southern flank (large rectangle) of the Martian shield volcano Arsia Mons,obtained from radar altimetry. [From Roth, L., Downs, G. S., Saunders, R. S., and Schubert, G. (1980). Icarus 42,287–316.]

antennas, so there will be a phase difference between thetwo received signals, and this phase difference will dependonly on the geometrical positions of the antennas and thetarget. This geometry will change as the Earth rotates,but very slowly and in a predictable manner. The anten-nas are best positioned so contours of constant phase dif-ference on the target disk are as orthogonal as possibleto the constant-Doppler contours, which connect conju-gate points. Phase difference hence becomes a measure ofnorth–south position, and echoes from conjugate pointscan be distinguished on the basis of their phase relation.

The total number of “fringes,” or cycles of phase shift,spanned by the disk of a planet with diameter D and a dis-tance R from the radar is approximately (D/R)(bPROJ/λ),where bPROJ is the projection of the interferometer baselinenormal to the mean line of sight. For example, Arecibo in-terferometry linked the main antenna to a 30.5-m antennaabout 11 km farther north. It placed about seven fringeson Venus, quite adequate for separation of the north–southambiguity. The Goldstone main antenna (see Fig. 3) has

been linked to smaller antennas to perform three-elementas well as two-element interferometry. Tristatic observa-tions permit one to solve so precisely for the north–southlocation of a given conjugate region that one can obtainthe region’s elevation relative to the mean planetary radius.Goldstone tristatic interferometry of the Moon’s polar re-gions has produced topographic maps with 150-m spatialand 50-m height resolution as well as correspondingly de-tailed backscatter maps (Fig. 14). Altimetric informationcan be extracted also from bistatic observations using thetime history of the phase information, but only if the vari-ations in the projected baseline vector are large enough.

In constructing a radar map, the unambiguous delay-Doppler distribution of echo power is transformed to plan-etocentric coordinates, and a model is fit to the data, usinga maximum-likelihood or weighted-least-squares estima-tor. The model contains parameters for quasispecular anddiffuse scattering as well as prior information about thetarget’s dimensions and spin vector. For Venus, effects ofthe dense atmosphere on radar wave propagation must also




FIGURE 10 Mercury altitude profiles (bottom) showing topography across Homer Basin and a large, unnamed basinto the west, estimated from observations whose subradar tracks are shown on the USGS shaded-relief map (top).Broken lines indicate approximate locations of the basin rims as seen in Mariner 10 images. Arrows locate Homer’sinner/outer (I/O) basin rings. [From Harmon, J. K., Campbell, D. B., Bindschadler, D. L., Head, J. W., and Shaprio, I. I.(1986). J. Geophys. Res. 91, 385–401.]

be modeled. Residuals between the data and the best-fitmodel constitute a radar reflectivity map of the planet.Variations in radar reflectivities evident in radar maps canbe caused by many different physical phenomena, andtheir proper interpretation demands due attention to theradar wavelength, echo polarization, viewing geometry,prior knowledge about surface properties, and the natureof the target’s mean scattering behavior. Similar consider-ations apply to inferences based on disk-integrated radaralbedos.

Delay-Doppler interferometry is not currently feasi-ble for targets like the Galilean satellites and the largestasteroids, which are low-SNR and overspread (see Sec-

tion II.D). A different, “Doppler mapping” technique, de-veloped for these spherical targets, reconstructs the globalalbedo distribution from cw echo spectra acquired as afunction of rotation phase and at an arbitrary number ofsubradar latitudes. To visualize how Doppler mappingworks, note that a target’s reflectivity distribution can beexpanded as a truncated spherical harmonic series andthat the distribution of echo power in rotation phase andDoppler frequency can be obtained as a linear, analyticfunction of the series coefficients. Estimation of thosecoefficients from an observed phase-Doppler distributioncan be cast as a least-squares problem to form a linearimaging system. Doppler mapping works best when the




FIGURE 11 Mars 13-cm radar echo spectra for subradar pointsalong 22◦ north latitude at the indicated west longitudes obtainedin the OC (upper curves) and SC (lower curves) polarizations.In each box, spectra are normalized to the peak OC cross sec-tion. The echo bandwidth is 7.1 kHz. Very rough regions on theplanet are revealed as bumps in the SC spectra, which move frompositive to negative Doppler frequencies as Mars rotates. [FromHarmon, J. K., Campbell, D. B., and Ostro, S. J. (1982). Icarus 52,171–187.]

limbdarkening is minimal and is ideally suited to over-spread targets whose echoes are too weak for the random-code method. Removal of the north–south ambiguity inDoppler images (or in single-antenna delay-Doppler im-ages) is possible if the data sample nonequatorial subradarlatitudes because then the Doppler (or delay-Doppler)versus rotation-phase trajectories of conjugate points aredifferent.

A novel kind of radar observation using Goldstone as a3.5-cm cw transmitter and the Very Large Array in NewMexico as a synthetic aperture receiver has been used fordirect measurement of the angular distribution of echopower. The 27-antenna VLA constitutes a 351-baseline in-terferometer whose synthesized beamwidth is as narrow as0.24 arcsec at the Goldstone transmitter frequency, provid-ing resolutions of roughly 80, 40, and 70 km for Mercury,Venus, and Mars at closest approach. (The finest resolu-tions in published ground-based delay-Doppler maps ofthose planets are approximately 15, 1, and 40 km, butthe maps cover small fractions of the surface at such fineresolutions.) Radar aperture synthesis has produced full-disk images of those planets and Saturn’s rings that arefree from north–south ambiguities, avoid problems re-lated to overspreading, and permit direct measurement oflocal albedo, polarization ratio, and scattering law. TheGoldstone–VLA system has achieved marginal angularresolution of main-belt asteroid echoes and could readily

image any large-particle comet clouds as radar detectableas the one around comet IRAS-Araki-Alcock. Goldstone–VLA resolution of asteriods and comet nuclei is impairedby the VLA’s coarse spectral resolution (>380 Hz) and in-ability to accommodate time-modulated waveforms. Fig-ures 14–18 show examples of radar maps constructed us-ing various techniques.

G. Radar Evidence for Ice Depositsat Mercury’s Poles

The first full-disk (Goldstone–VLA) radar portraits ofMercury surprisingly revealed anomalously bright polarfeatures with µC > 1, and subsequent delay-Doppler im-agery from Arecibo established that the anomalous radarechoes originate from interiors of craters that are perpet-ually shaded from sunlight because of Mercury’s near-zero obliquity (see Fig. 15). The angle between the or-bital planes of Mercury and Earth is 7 ◦, so portions ofthe permanently shadowed regions are visible to Earth-based radars. Most of the south pole anomalies are con-fined to the floor of the 155-km crater Chao Meng-Fu.At each pole, bright radar features in regions imaged byMariner 10 correlate exactly with craters; numerous radarfeatures lie in the hemisphere not imaged by that space-craft. [No convincing radar evidence has been found forice in perpetually shadowed lunar craters (Fig. 14). If iceexists on the Moon, it is likely to have extremely low con-centration in the soil.]

Similarities between the radar-scattering properties ofthe Mars and Mercury polar anomalies and those of the icyGalilean satellites (see Section III.K) support the inferencethat the radar anomalies are deposits of water ice. Temper-atures below 120 K in the permanent shadows are expectedand are low enough for ice to be stable against sublimationfor billions of years. Temperatures several tens of kelvinslower may exist inside high-latitude craters and perhapsalso beneath at least 10 cm of optically bright regolith.Plausible sources of water on Mercury include comet im-pacts and out-gassing from the interior. It has been notedthat most water vapor near the surface is photodissociated,but that some molecules will random-walk to polar coldtraps. Ices of other volatiles, including CO2, NH3, HCN,and SO2, might also be present.

H. Venus Revealed by Magellan

The Magellan spacecraft entered Venus’s orbit in August1990 and during the next 2 years explored the planet witha single scientific instrument operating as a radar imager,an altimeter, and a thermal radiometer. Magellan’s imag-ing resolution (∼100 m) and altimetric resolution (5 to100 m) improves upon the best previous spacecraft and




FIGURE 12 Structure on the lunar surface near the Apollo 17 landing site. Most of the surface is smooth and gentlyundulating at scales much larger than a centimeter. This smooth component of the surface is responsible for thepredominantly quasispecular character of the Moon’s radar echo at λ 1 cm. Wavelength-scale structure producesa diffuse contribution to the echo. Wavelength-sized rocks are much more abundant at λ ∼ 4 cm than at λ ∼ 10 m(the scale of the boulder being inspected by astronaut H. Schmitt), and hence diffuse echo is more substantial atshorter wavelengths.

ground-based measurements by an order of magnitude,and does so with nearly global coverage. Analysis ofMagellan’s detailed, comprehensive radar reconnaissanceof Venus’s surface topography, morphology, and electrical

FIGURE 13 This lava flow near Sunset Crater in Arizona is anexample of an extremely rough surface at decimeter scales and issimilar to terrestrial flows yielding large circular polarization ratiosat decimeter wavelengths.

properties ultimately will revolutionize our understandingnot only of that planet, but of planetary geology itself.

Venus’s surface contains a plethora of diverse tectonicand impact features, but its formation and evolutionhave clearly been dominated by widespread volacnism,whose legacy includes pervasive volcanic planes, thou-sands of tiny shield volcanoes, monoumental edifices, sin-uous lava flow channels, pytoclastic deposits, and pan-cakelike domes. The superposition of volcanic signaturesand elaborate, complex tectonic forms records a historyof episodic crustal deformation. The paucity of impactcraters smaller than 25 km and the lack of any as smallas a few kilometers attests to the protective effect of thedense atmosphere. The multilobed, asymmetrical appear-ance of many large craters presumably results from at-mospheric breakup of projectiles before impact. Atmo-spheric entrainment and transport of ejecta are evidentin very elongated ejecta blankets. Numerous craters aresurrounded by radar-dark zones, perhaps the outcome ofatmospheric pressure-wave pulverization and elevation ofsurface material that upon resettling deposited a tenuousand hence unreflective “impact regolith.” Figure 17 showsexamples of Magellan radar images.


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FIGURE 14 Digital elevation model (a) and radar backscattermap (b) of the lunar south polar region from Goldstone tristatic in-terferometry. Absolute elevations with respect to a 1738-km-radiussphere are shown. The elevation map establishes that the interi-ors of many of the craters visible in (b) are in permanent shadowfrom solar illumination. (a) Reprinted with permission from J. M.Margot, D. B. Campbell, R. F. Jurgens, and M. A. Slade, Science284, 1658–1660, copyright 1999 American Association for the Ad-vancement of Science. (b) Courtesy J.-L. Margot.

FIGURE 15 Arecibo 13-cm delay-Doppler images of the (a) north and (b) south poles of Mercury, taken in the SCpolarization. The resolution is 15 km. The radar-brightness regions are shown here as dark. [From Harmon, J. K.,Slade, M. A., Velez, R. A., Crespo, A., Dryer, M. J., and Johnson, J. M. (1994). Nature 369, 213–215. Copyright 1994Macmillan Magazines Limited.]

I. The Radar Heterogeneity of Mars

Ground-based investigations of Mars have achieved moreglobal coverage than those of the other terrestrial targetsbecause the motion in longitude of the subradar point onMars (whose rotation period is only 24.6 hr) is rapid com-pared to that on the Moon, Venus, or Mercury and be-cause the geometry of Mars’s orbit and spin vector per-mits subradar tracks throughout the Martian tropics. Theexisting body of Mars radar data reveals extraordinarydiversity in the degree of small-scale roughness as wellas in the rms slope of smooth surface elements. For ex-ample, Fig. 19 shows the variation in OC echo spectralshape as a function of longitude for a subradar track along∼16◦S latitude. Slopes on Mars have rms values fromless than 0.5◦ to more than 10◦. Chryse Planitia, site ofthe first Viking Lander, has fairly shallow slopes (4◦–5◦) and, in fact, radar rms slope estimates were utilizedin selection of the Viking Lander (and Mars Pathfinder)sites, and their accuracy was confirmed by the spacecraftresults.

Diffuse scattering from Mars is much more substantialthan for the other quasispecular targets and often accountsfor most of the echo power, so the average near-surfaceabundance of centimeter-to-meter-scale rocks presumablyis much greater on Mars than on the Moon, Mercury, orVenus. Features in Mars SC spectra first revealed the exis-tence of regions of extremely small-scale roughness (see




FIGURE 16 Arecibo delay-Doppler OC radar map of Maxwell Montes on Venus. (Courtesy of D. B. Campbell.)

Fig. 11), and the trajectory of these features’ Doppler po-sitions versus rotation phase suggested that their primarysources are the Tharsis and Elysium volcanic regions.The best terrestrial analog for this extremely rough ter-rain might be young lava flows (see Fig. 13). Goldstone–VLA images of Mars at longitudes that cover the Tharsisvolcanic region (see Fig. 18) confirm that this area is thepredominant source of strong SC echoes and that local-ized features are associated with individual volcanoes. A2000-km-long band with an extremely low albedo cutsacross Tharsis; the radar darkness of this “Stealth” fea-ture probably arises from an underdense, unconsolidatedblanket of pyroclastic deposits ∼1 m deep. The strongestSC feature in the Goldstone–VLA images is the residualsouth polar ice cap, whose scattering behavior is similar tothat of the icy Galilean satellites (Section III.K). Areciboobservations of Mars, including Doppler-only and coded-long-pulse delay-Doppler mapping, have charted the de-

tailed locations and fine structure of Mars SC features (seeFig. 18b).

J. Asteroids

Echoes from 37 main-belt asteroids (MBAs) and 58 near-Earth asteroids (NEAs) have provided a wealth of new in-formation about these objects’ sizes, shapes, spin vectors,and surface characteristics such as decimeter-scale mor-phology, topographic relief, regolith porosity, and metalconcentration. During the past decade, radar has been es-tablished as the most powerful Earth-based technique fordetermining the physical properties of asteroids that comeclose enough to yield strong echoes.

The polarization signatures of some of the largestMBAs (e.g., 1 Ceres and 2 Pallas) reveal surfaces thatare smoother than that of the Moon at decimeter scales butmuch rougher at some much larger scale. For example, for




FIGURE 17 Magellan radar maps of Venus. (a) Northern-hemisphere projection of mosaics. The north pole is atthe center of the image, with 0◦ and 90◦E longitudes at the six and three o’clock positions. Gaps use Pioneer Venusdata or interpolations. The bright, porkchop-shaped feature is Maxwell Montes, a tectonically produced mountainrange first seen in ground-based images. (b) A 120-m-resolution map of the crater Cleopatra on the eastern slopes ofMaxwell Montes. Cleopatra is a double-ringed impact basin that resembles such features seen on the Moon, Mercury,and Mars. (Courtesy of JPL/NASA.) (continues)

Pallas, µc is only ∼0.05 and, as noted above, surface slopesexceed 20◦. For asteroids in the 200-km-diameter range,the echoes provide evidence for large-scale topographicirregularities. For example, brightness spikes within nar-row ranges of rotation phase suggest large, flat regions on 7Iris (Fig. 20), 9 Metis, and 654 Zelinda, and delay-Dopplerimages of 216 Kleopatra reveal a dumbbell shape.

There is a 10-fold variation in the radar albedos ofMBAs, implying substantial variations in these objects’surface porosities or metal concentrations or both. Thelowest MBA albedo estimate, 0.04 for Ceres, indicatesa lower surface bulk density than that on the Moon.The highest MBA albedo estimates, 0.31 for 16 Psycheand 0.44 for Kleopatra, are consistent with metal





concentrations near unity and lunar porosities. These ob-jects might be the collisionally stripped cores of differ-entiated asteroids and by far the largest pieces of refinedmetal in the solar system. Surprisingly, there is no reasonto believe that the two largest classes of radar-observed as-teroids (C and S) have different radar-albedo distributions.

The diversity of NEA radar signatures is extreme (seeTable II). Some small NEAs are much rougher at decime-ter scales than MBAs, comets, or the terrestrial planets.The radar albedo of the 2-km object 6178 (1986DA),0.58, strongly suggests that this Earth-approacher is aregolith-free metallic fragment, presumably derived fromthe interior of a much larger object that melted, differen-tiated, cooled, and subsequently was disrupted in a catas-trophic collision. This asteroid, which appears extremelyirregular at 10- to 100-m scales and shows hints of be-ing bifurcated, might be (or have been a part of) the par-ent body of some iron meteorites. At the other extreme,an interval estimate for 1986JK’s radar albedo (0.005 to0.07) suggests a surface bulk density within a factor of 2of 0.9 g cm−3. Similarly, the distribution of NEA circu-lar polarization ratios runs from near zero to near unity.

The highest values, for 2101 Adonis, 1992QN, 3103 Eger,and 3980 1980PA, indicate extreme near-surface struc-tural complexity, but we cannot distinguish between mul-tiple scattering from subsurface heterogeneities (see Sec-tion III.K) and single scattering from complex structureon the surface.

The MBAs 951 Gaspra and 243 Ida, imaged by theGalileo spacecraft, probably are marginally detectablewith the upgraded Arecibo. Both Goldstone and Arecibohave investigated the Gaspra-sized Martian moon Phobos,whose radar properties differ from those of most small,Earth-approaching objects but resemble those of large(∼100-km), C-class, main-belt asteroids. Phobos’s sur-face characteristics may be more representative of Ceresand Pallas than most NEAs. The upper limit on the radarcross section of Deimos, which has defied radar detection,argues for a surface bulk density no greater than about1 g cm−3.

During the past decade, delay-Doppler imaging of as-teroids has produced spatial resolutions as fine as a fewdecameters. The images generally can be “north–south”ambiguous; that is, they constitute a two-to-one (or even




FIGURE 18 Mars radar maps. (a) Goldstone–VLA 3.5-cm, SC radar images of Mars at six longitudes. In the northernhemisphere, the brightest features are in Tharsis, which is traversed by the low-albedo Stealth region. Note the verybright residual south polar ice cap. [From Muhleman, D. O., Butler, B. J., Grossman, A. W., and Slade, M. A. (1991).Science 253, 1508–1513. Copyright 1991 American Association for the Advancement of Science.] (b) Arecibo 13-cm,SC reflectivity map of the Elysium region of Mars, obtained from random-code observations made with the subradarlatitude 10◦S. The map is north–south ambiguous, but more northerly observations confirm that all of the strongfeatures come from the north. The radar-bright regions (shown here as dark) correspond to Elysium Mons (at ∼214◦Wlongitude, 25◦N latitude) and the Elysium flood basin and outflow channel. The SC brightness of these regions isprobably caused by extremely rough lava flows. [From Harmon, J. K., Sulzer, M. P., Perillat, P. J., and Chandler, J. F.(1992). Icarus 95, 153–156.]




FIGURE 19 Mars echo power spectra as a function of longitude obtained along a subradar track at 16◦ south latitude.The most sharply peaked spectra correspond to the smoothest regions (i.e., the smallest rms slopes). (Courtesy ofG. S. Downs, P. E. Reichley, and R. R. Green.)

many-to-one) mapping from the surface to the image.However, if the radar is not in the target’s equatorial plane,then the delay-Doppler trajectory of any surface point isunique. Hence images that provide adequate orientationalcoverage can be inverted, and in principle one can recon-struct the target’s three-dimensional shape as well as itsspin state, the radar-scattering properties of the surface,and the motion of the center of mass through the delay-Doppler ephemerides.

The first asteroid radar data set suitable for reconstruc-tion of the target’s shape was a 2.5-hr sequence of 64 delay-Doppler images of 4769 Castalia (1989PB) (Fig. 21a),obtained two weeks after its August 1989 discovery. Theimages, which were taken at a subradar latitude of about35◦, show a bimodal distribution of echo power over thefull range of sampled rotation phases, and least-squares es-timation of Castalia’s three-dimensional shape (Fig. 21b)reveals it to consist of two kilometer-sized lobes in contact.Castalia apparently is a contact-binary asteroid formedfrom a gentle collision of the two lobes.

If the radar view is equatorial, unique reconstructionof the asteroid’s three-dimensional shape is ruled out, buta sequence of images that thoroughly samples rotationphase can allow unambiguous reconstruction of the as-teroid’s pole-on silhouette. For example, observations of

1620 Geographos yield ∼400 images with ∼100-m res-olution. The pole-on silhouette’s extreme dimensions arein a ratio, 2.76 ± 0.21, that establishes Geographos as themost elongated solar system object imaged so far (seeFig. 8). The images show craters as well as indications ofother sorts of large-scale topographic relief, including aprominent central indentation. Protuberances at the aster-oid’s ends may be related to the pattern of ejecta removaland deposition caused by the asteroid’s gravity field.

Delay-Doppler imaging of 4179 Toutatis in 1992 and1996 achieved resolutions as fine as 125 nsec (19 m inrange) and 8.3 mHz (0.15 mm sec−1 in radial velocity),placing hundreds to thousands of pixels on the asteroid.This data set provides physical and dynamical informa-tion that is unprecedented for an Earth-crossing object.The images (Fig. 22) reveal this asteroid to be in a highlyunusual, non-principal-axis (NPA) spin state with several-day characteristic time scales. Extraction of the informa-tion in this imaging data set required inversion with a muchmore comprehensive physical model than in the analysisof Castalia images; free parameters included the aster-oid’s shape and inertia matrix, initial conditions for theasteroid’s spin and orientation, the radar-scattering prop-erties of the surface, and the delay-Doppler trajectory ofthe center of mass. The shape (Fig. 23) reconstructed from




FIGURE 20 Thirteen-centimeter echo spectra of the ∼200-km-diameter asteroid 7 Iris, obtained within three narrowrotation-phase intervals. OC echo power in standard deviations is plotted versus Doppler frequency. The shadedboxes show frequency intervals thought to contain the echo edges. A radar “spike” appears in (b) at −305 Hz, butnot in spectra at adjacent phases, so it is probably not due to a reflectivity feature but rather to a temporary surge inradar-facing surface area, perhaps a flat facet ∼20 km wide. [From Mitchell, D. L., et al. (1995). Icarus 118, 105–131.]

the low-resolution images of Toutatis has shallow craters,linear ridges, and a deep topographic “neck” whose geo-logic origin is not known. It may have been sculpted byimpacts into a single, coherent body, or Toutatis might ac-tually consist of two separate objects that came together ina gentle collision. Toutatis is rotating in a long-axis mode(see Fig. 23) characterized by periods of 5.4 days (rotationabout the long axis) and 7.4 days (average for long-axisprecession about the angular momentum vector). The as-teroid’s principal moments of inertia are in ratios within1% of 3.22 and 3.09, and the inertia matrix is indistinguish-able from that of a homogeneous body. Such informationhas yet to be determined for any other asteroid or comet,and probably is impossible to acquire in a fast spacecraftflyby. Higher resolution images (e.g., Fig. 22b) from the1992 and 1996 experiments are now being used to refinethe Toutatis model.

Accurate shape models of near-Earth asteroids openthe door to a wide variety of theoretical investigations thatpreviously have been impossible or have used simplisticmodels (spheres or ellipsoids). For example, the Castaliaand Toutatis models are being used to explore the stabil-ity and evolution of close orbits, with direct applicationto the design of robotic and piloted spacecraft missions,to studies of retention and redistribution of impact ejectaand to questions about plausible origins and lifetimes of

asteroidal satellites. Accurate models also allow realisticinvestigations of the effects of collisions in various energyregimes on the object’s rotation state, surface topography,regolith, and internal structure. Simulations of impactsinto Castalia using smooth-particle hydrodynamics codehave begun to suggest how surface and interior damage de-pends on impact energy, impact location, and the equationof state of the asteroidal material. These computer inves-tigations have clear ramifications for our understandingof asteroid collisional history, for exploitation of aster-oid resources, and eventually for deflection/destruction ofobjects found to be on a collision course with Earth.

K. Jupiter’s Icy Galilean Satellites

Among all the radar-detected planetary bodies in the solarsystem, Europa, Ganymede, and Callisto have the mostbizarre radar properties. Their reflectivities are enormouscompared with those of the Moon and inner planets (seeTable II). Europa is the extreme example (Fig. 24), withan OC radar albedo (1.0) as high as that of a metal sphere.Since the radar and optical albedos and estimates of frac-tional water frost coverage increase by satellite in the orderCallisto/Ganymede/Europa, the presence of water ice haslong been suspected of playing a critical role in deter-mining the unusually high reflectivities even though ice




FIGURE 21 Radar results for near-Earth asteroid 4769 Castalia (1989PB). (a) Arecibo radar images. This 64-frame“movie” is to be read like a book (left to right in the top row, etc.). The radar lies toward the top of the page, in theimage plane, which probably is about 35◦ from the asteroid’s equatorial plane. In each frame, OC echo power (i.e., thebrightness seen by the radar) is plotted versus time delay (increasing from top to bottom) and frequency (increasingfrom left to right). The object is seen rotating through about 220◦ during the 2.5-hr sequence. [From Ostro, S. J.,Chandler, J. F., Hine, A. A., Shapiro, I. I., Rosema, K. D., and Yeomans, D. K. (1990). Science 248, 1523–1528.Copyright 1990 AAAS.] (b) Three-dimensional computer model of Castalia from inversion of the images in (a). Thereconstruction uses 167 shape parameters and has a resolution of about 100 m. This contact-binary asteroid is about1.8 km long. [From Hudson, R. S., and Ostro, S. J. (1994). Science 263, 940–943. Copyright 1994 AAAS.]




FIGURE 22 Radar images of near-Earth asteroid 4179 Toutatis. (a) Goldstone low-resolution images (top three rows)and Arecibo images (bottom row) obtained on the indicated dates in December 1992, plotted with time delay increasingtoward the bottom and Doppler frequency increasing toward the left. On the vertical sides, ticks are 2 msec (300 m)apart. Two horizontal sides have ticks separated by 1 Hz for Goldstone and 0.28 Hz for Arecibo; those intervalscorrespond to a radial velocity difference of 18 mm sec−1. (b) A high-resolution (125 nsec × 33 mHz) Goldstoneimage obtained with Toutatis 3.6 million km (10 lunar distances) from Earth. The spatial resolution is 19 × 46 m. [FromOstro, S. J., et al. (1995). Science 270, 80–83. Copyright 1995 AAAS.] (continues)

is less radar reflective than silicates. Despite the satel-lites’ smooth appearances at the several-kilometer scalesof Voyager’s high-resolution images, a diffuse scatteringprocess and hence a high degree of near-surface structure

at centimeter to meter scales is indicated by broad spectralshapes and large linear polarization ratios (µL ∼ 0.5).

The most peculiar aspect of the satellites’ echoes is theircircular polarization ratios, which exceed unity. That is,





in contrast to the situation with other planetary targets,the scattering largely preserves the handedness, or helic-ity, of the transmission. Mean values of µC for Europa,Ganymede, and Callisto are about 1.5, 1.4, and 1.2, re-spectively. Wavelength dependence is negligible from 3.5to 13 cm, but dramatic from 13 to 70 cm (Fig. 25). Sig-nificant polarization and/or albedo features are present inthe echo spectra and in a few cases correspond to geologicfeatures in Voyager images.

The icy satellites’ echoes are due not to external sur-face reflections but to subsurface “volume” scattering.The high radar transparency of ice compared with thatof silicates permits deeper radar sounding, longer pho-ton path lengths, and higher order scattering from regolithheterogeneities—radar is seeing. Europa, Ganymede, andCallisto in a manner in which the Moon has never beenseen. The satellites’ radar behavior apparently involvesthe coherent backscatter effect, which accompanies anymultiple-scattering process; occurs for particles of anysize, shape, and refractive index; and was first discoveredin laboratory studies of the scattering of electrons andof light. Coherent backscatter yields strong echoes andµC > 1 because the incident, circularly polarized wave’sdirection is randomized before its helicity is randomizedand also before its power is absorbed. The vector-wave the-ory of coherent backscatter accounts for the unusual radarsignatures in terms of high-order, multiple anisotropicscattering from within the upper few decameters of theregoliths, which the radar sees as an extremely low-loss, disordered random medium. Inter- and intrasatellite

albedo variations show much more dynamic range thanµC variations and are probably due to variations in icepurity.

As sketched in Fig. 25, there are similarities betweenthe icy Galilean satellites’ radar properties and those of theradar-bright polar caps on Mars, features inside perpetu-ally shadowed craters at the poles of Mercury (see Fig. 15),and the percolation zone in the Greenland ice sheet. How-ever, the subsurface configuration in the Greenland zone,where the scattering heterogeneities are “ice pipes” pro-duced by seasonal melting and refreezing, are unlikely toresemble those on the satellites. Therefore, unique modelsof subsurface structure cannot be deduced from the radarsignatures of any of these terrains.

L. Comets

Since a cometary coma is nearly transparent at radio wave-lengths, radar is much more capable of unambiguous de-tection of a cometary nucleus than are optical and infraredmethods, and radar observations of several comets (seeTable I) have provided useful constraints on nuclear di-mensions. The radar signature of one particular comet(IRAS-Araki-Alcock, which came within 0.03 AU ofEarth in May 1983) revolutionized our concepts of thephysical nature of these intriguing objects. Echoes ob-tained at both Arecibo (Fig. 26) and Goldstone have a nar-rowband component from the nucleus as well as a muchweaker broadband component from large particles ejectedmostly from the sunlit side of the nucleus. Models of the




FIGURE 23 Toutatis’s shape and non-principal-axis spin state from inversion of the images in Fig. 21a. The axeswith no arrow tips are the asteroid’s principal axes of inertia and the vertical arrow is its angular momentum vector; thedirection of the spin vector (the arrow pointing toward 11 o’clock) relative to the principal axes is a (5.41-day) periodicfunction. A flashlamp attached to the short axis of inertia and flashed every 15 min for 20 days would trace out theintricate path indicated by the small spheres stacked end-to-end; the path never repeats. Toutatis’s spin state differsradically from those of the vast majority of solar system bodies that have been studied, which are in principal-axisspin states. For those objects, the spin vector and angular momentum vector point in the same direction and theflashlamp’s path would be a circle.

echoes suggest that the nucleus is very rough on scaleslarger than a meter, that its maximum overall dimensionis within a factor of 2 of 10 km, and that its spin period is2–3 days. The particles are probably several centimetersin size and account for a significant fraction of the partic-ulate mass loss from the nucleus. Most of them appear tobe distributed within ∼1000 km of the nucleus, that is, inthe volume filled by particles ejected at several meters persecond over a few days. The typical particle lifetime mayhave been this short, or the particle ejection rate may havebeen highly variable.

In late 1985, radar observations of comet Halley, whichwas much more active than IRAS-Araki-Alcock, yieldedechoes with a substantial broadband component presumedto be from a large-particle swarm, but no narrowband com-ponent, a negative result consistent with the hypothesisthat the surface of the nucleus has an extremely low bulkdensity. In 1996, Goldstone obtained 3.5-cm echoes fromthe nucleus and coma of comet Hyakutake (C/1996 B2).The coma-to-nucleus ratio of radar cross section is about12 for Hyakutake versus about 0.3 for IAA. The radarsignatures of these three comets strengthen impressions




FIGURE 24 Typical 13-cm echo spectra for the terrestrial planetsare compared to echo spectra for Jupiter’s icy moon Europa. Theabscissa has units of half the echo bandwidth.

about the diversity, and unpredictability, of comet physi-cal properties and have obvious implications for spacecraftoperations close to comets.

M. Saturn’s Rings and Titan

The only radar-detected ring system is quite unlikeother planetary targets in terms of both the experimen-tal techniques employed and the physical considerations

FIGURE 25 Radar properties of Europa, Ganymede, and Cal-listo compared to those of some other targets. The icy Galileansatellites’ total-power radar albedos do not depend on wavelengthbetween 3.5 and 13 cm, but plummet at 70 cm. There are largeuncertainties in those objects’ µC at 70 cm. The solid symbolsshaped like Greenland indicate properties of that island’s perco-lation zone at 5.6 and 68 cm. The domain of most of the brightpolar features on Mars and Mercury is sketched.

FIGURE 26 OC and SC echo spectra obtained at 13 cm for cometIRAS-Araki-Alcock, truncated at 2% of the maximum OC ampli-tude. The narrowband echo from the nucleus is flanked by a broad-band echo from large (1-cm) particles in a 1000-km-radius cloudsurrounding the nucleus. [From Harmon, J. K., Campbell, D. B.,Hine, A. A., Shapiro, I. I., and Marsden, B. G. (1989). Astrophys. J.338, 1071–1093.]

involved. For example, the relation between ringplanelocation and delay-Doppler coordinates for a systemof particles traveling in Keplerian orbits is differentfrom the geometry portrayed in Fig. 5. The rings aregrossly overspread (see Table II), requiring the use offrequency-stepped waveforms in delay-Doppler mappingexperiments.

Radar determinations of the rings’ backscattering prop-erties complement results of the Voyager spacecraft ra-dio occultation experiment (which measured the rings’forward scattering efficiency at identical wavelengths) inconstraining the size and spatial distributions of ring par-ticles. The rings’ circular polarization ratio is ∼1.0 at3.5 cm and ∼0.5 at 13 cm, more or less independent ofthe inclination angle δ between the ring plane and theline of sight. Whereas multiple scattering between par-ticles might cause some of the depolarization, the lackof strong dependence of µc on δ suggests that the parti-cles are intrinsically rougher at the scale of the smallerwavelength. The rings’ total-power radar albedo showsonly modest dependence on δ, a result that seems to favormany-particle-thick models of the rings over monolayermodels. Delay-Doppler resolution of ring echoes indicatesthat the portions of the ring system that are brightest op-tically (the A and B rings) also return most of the radarechoes. The C ring has a very low radar reflectivity, pre-sumably because of either a low particle density in thatregion or compositions or particle sizes that lead to inef-ficient scattering.

Apart from landing a spacecraft on Titan, radar providesthe most direct means to study the cloud-covered surfaceof Saturn’s largest moon. Voyager and ground-based dataindicate a surface temperature and pressure of 94 K and1.5 bar and show that the atmosphere is mostly N2 with




traces of hydrocarbons and nitriles. Thermodynamic con-siderations imply a nearsurface reservoir of liquid hydro-carbons, possibly consisting of a kilometer-deep globalocean. However, that configuration which would give aradar albedo of only several percentages, has been ruledout by Goldstone–VLA and Arecibo detections that yieldOC albedo estimates that are significatly higher, at leastfor part of the object. More work is needed to elucidateTitan’s radar properties.

IV. PROSPECTS FOR PLANETARY RADAR

The 1993–1999 upgrading of the Arecibo telescope in-creased the instrument’s average radar sensitivity bya factor of 20, more than doubling its range and re-ducing by nearly an order of magnitude the diame-ter of the smallest object detectable at any given dis-tance. The impact of the Arecibo upgrade on planetaryscience is expected to be fundamental and far-reaching, es-pecially for studies of small bodies and planetary satellites.The quality, in terms of signal-to-noise ratio and spatialresolution, of radar measurements has jumped by an orderof magnitude. Several short-period comets will becomeeasy targets. The preupgrade Arecibo could barely skimthe inner edge of the main asteroid belt, but the upgradedtelescope has access to asteroids throughout the belt. Theinstrument is expected to provide high-resolution imagesof dozens of asteroids per year.

Efforts are underway to increase the near-Earth asteroiddiscovery rate by one to two orders of magnitude. Most ofthe optically discoverable NEAs traverse the detectabil-ity windows of the upgraded Arecibo and/or Goldstonetelescopes at least once during any given several-decadeinterval. In view of the utility of radar observations for or-bit refinement and physical characterization, there is con-siderable motivation to do radar observations of newlydiscovered NEAs whenever possible. The initial radar re-connaissance of a new NEA might eventually become analmost-daily opportunity. Interferometric radar techniquesusing the 10-antenna Very Long Baseline Array (VLBA)to receive echoes from Arecibo or Goldstone transmis-sions should synthesize unambiguous, high-resolution im-ages of NEAs. Also, observations using transcontinentaland intercontinental baselines should permit direct mea-surement of the shapes of these objects.

Radar investigations of natural satellites will rap enor-mous benefits from ground-based and space-borne radarreconnaissance. The near-surface physical properties ofDeimos, Io, and Titan will be readily discernible withArecibo. Doppler images of Titan may furnish a coarse-resolution, nearly global albedo map, while the Cassinispacecraft, with its high-resolution, 13.8-GHz (2.2-cm)

radar instrument, is journeying toward its arrival at Sat-urn in 2004. That instrument, which will function as asynthetic-aperture radar imager, an altimeter, and a pas-sive radiometer, is designed to determine whether oceansexist on Titan and, if so, to determine their distribution.There is growing interest in the possibility of a subsurfaceocean on Europa and in the feasibility of using an orbit-ing, long-wavelength (∼6-m) radar sounder to probe manykilometers below that object’s fractured crust, perhaps by2010. In summary, planetary radar astronomy appears tobe on the verge of producing an enormously valuable bodyof new information about asteroids, comets, and the satel-lites of Mars, Jupiter, and Saturn.


GAMMA-RAY ASTRONOMY • GRAVITATIONAL WAVE

ASTRONOMY • MILLIMETER ASTRONOMY • PRIMITIVE

SOLAR SYSTEM OBJECTS: ASTEROIDS AND COMETS •RADAR • RADIO ASTRONOMY, PLANETARY • SOLAR

SYSTEM, GENERAL • ULTRAVIOLET SPACE ASTRONOMY

• X-RAY ASTRONOMY

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Margot, J. M., Campbell, D. B., Jurgens, R. F., and Slade, M. A. (1999).“Topography of the lunar poles from radar interferometry: A surveyof cold trap locations,” Science 284, 1658–1660.

Mitchell, D. L., Ostro, S. J., Hudson, R. S., Rosema, K. D.,Campbell, D. B., Velez, R., Chandler, J. F., Shapiro, I. I., Giorgini, J. D.,and Yeomans, D. K. (1996). “Radar observations of asteroids 1 Ceres,2 Pallas, and 4 Vesta,” Icarus 124, 113–133.

Muhleman, D. O., Grossman, A. W., and Butler, B. J. (1995). “Radarinvestigation of Mars, Mercury, and Titan,” Annu. Rev. Earth PlanetSci. 23, 337–374.

Ostro, S. J. (1993). “Planetary radar astronomy,” Rev. Modern Physics65, 1235–1279.

Pettengill, G. H., Ford, P. G., Johnson, W. T. K., Raney, R. K., andSoderblom, L. A. (1991). “Magellan: Radar performance and dataproducts,” Science 252, 260–265.

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Shapiro, I. I., Chandler, J. F., Campbell, D. B., Hine, A. A., andStacy, N. J. S. (1990). “The spin vector of Venus,” Astron. J. 100,1363–1368.

Simpson, R. A., Harmon, J. K., Zisk, S. H., Thompson, T. W., andMuhleman, D. O. (1992). In “Mars” (H. Kieffer, B. Jakosky, C. Sny-der, and M. Matthews, eds.), pp. 652–685, Tucson, Univ. of ArizonaPress.

Slade, M. A., Butler, B. J., and Muhleman, D. O. (1992). “Mercury radarimaging: Evidence for polar ice,” Science 258, 635–640.

Stacy, N. J. S., Campbell, D. B., and Ford, P. G. (1997). “Arecibo radarmapping of the lunar poles: A search for ice deposits,” Science 276,1527–1530.

Tyler, G. L., Ford, P. G., Campbell, D. B., Elachi, C., Pettengill, G. H.,and Simpson, R. A. (1991). “Magellan: Electrical and physical prop-erties of Venus’ surface,” Science 252, 265–270.

Yeomans, D. K., Chodas, P. W., Keesey, M. S., Ostro, S. J., Chandler, J. F.,and Shapiro, I. I. (1992). “Asteroid and comet orbits using radar data,”Astron. J. 103, 303–317.

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Radio Astronomy, PlanetarySamuel GulkisJet Propulsion Laboratory

Imke de PaterUniversity of California, Berkeley

I. IntroductionII. Basic Concepts

III. Instrumentation for Planetary Radio AstronomyIV. Results—Planets and CometsV. Prospects for the Future

GLOSSARY

Antenna temperature Measure of the noise power col-lected by the antenna and delivered to the radio receiver.Specifically, the temperature at which a resistor, sub-stituted for the antenna, would have to be maintainedin order to deliver the same noise power to the receiverin the same frequency bandwidth.

Blackbody Idealized object that absorbs all electromag-netic radiation that is incident on it. The radiationproperties of blackbody radiators are described by thePlanck function. Planetary radio astronomers use theproperties of blackbody radiators to describe the radi-ation from planets.

Brightness temperature The definition is not unique;great care is needed to decipher the intention of a givenauthor. The temperature at which a blackbody radiatorwould radiate an intensity of electromagnetic radiationidentical to that of the planet for a specific frequency,frequency bandwidth, and polarization under consid-eration is one definition of brightness temperature. Asecond definition is that it is the intensity of radiationunder consideration divided (normalized) by the factor(λ2/2k). The normalization factor dimensionally scales

the intensity to have units of temperature. The two defi-nitions show the largest departures at low temperaturesand high frequencies.

Effective area Equivalent cross section or collecting areaof a radio telescope to an incident radio wave; a measureof a radio telescope’s capability to detect weak radiosignals.

Effective temperature Temperature at which a black-body radiator would radiate over all frequencies anintensity of electromagnetic radiation identical to thatradiated from a planet.

Equivalent blackbody disk temperature Temperatureof a blackbody radiator with the same solid angle asthe planet that gives the same radiation intensity at theEarth as observed from the planet at a specified fre-quency and bandwidth.

Flux density Power per unit area and per unit frequencyof an electromagnetic wave crossing an imaginaryplane surface from one side to the other. In observa-tional radio astronomy, the mks system of units is gen-erally used, and the units of flux density are watts persquare meter per hertz.

Flux unit or jansky Commonly used unit of flux densityequal to 1 × 10−26 W m−2 Hz−1. The size of the unit

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688 Radio Astronomy, Planetary

is suited to planetary radio emissions, which are veryweak.

Nonthermal radio emission Radio emission producedby processes other than thermal emission. Cyclotronand synchrotron radio emission are two examples ofnonthermal radio emission.

Optical depth Atmospheric attenuation is usually ex-pressed by giving the dimensionless quantity “opti-cal depth” along a specified path. A signal that passesthrough an atmosphere whose optical depth is τ is at-tenuated by the factor e−τ .

Thermal radio emission Continuous radio emissionfrom an object that results from the object’s temper-ature. Blackbody radiation is a form of thermal radioemission.

PLANETARY RADIO ASTRONOMY is the study ofthe physical characteristics of the planets in the solar sys-tem by means of the electromagnetic radio radiation emit-ted by these objects. The term is also used more gen-erally to include the study of planetary ring systems, themoon, asteroids, satellites, and comets in the solar system.Radio astronomy generally refers to the (vacuum) wave-length range from about 0.5 mm (600 GHz = 600 × 109

Hz) to 1 km (300 kHz) and longward. There is no wide ac-ceptance of the upper limit frequency. Observations fromthe ground cannot be carried out below a few megahertzbecause of the Earth’s ionosphere, which is opaque tovery low frequency radio waves. At millimeter and sub-millimeter wavelengths, the terrestrial atmosphere defineswindows where radio emissions from cosmic sources canreach the ground. Radio emissions have been measuredfrom all of the planets and some satellites, asteroids, andcomets. The observed continuum emissions from the plan-ets can be broadly classified as quasi-thermal (having thesame general shape as a blackbody emitter) and nonther-mal (i.e., cyclotron, synchrotron). Narrow spectral linesfrom molecules have been observed in the atmospheres ofplanets, satellites, and comets. Planetary radio emissionsoriginate in the solid mantles, atmospheres, and magneto-spheres of the planets. A number of solar system spacecrafthave carried radio astronomical instrumentation.

I. INTRODUCTION

A. Brief History

The science of radio astronomy began with the pioneeringwork of Karl G. Jansky, who discovered radio emissionfrom the Milky Way galaxy while studying the direction ofarrival of radio bursts associated with thunderstorms. Ten

years later, in 1942, while trying to track down the sourceof radio interference on a military antiaircraft radar systemin England, J. S. Hey established the occurrence of radioemission from the sun.

R. H. Dicke and R. Beringer working in the UnitedStates made the first intentional measurement of a solarsystem object in 1945. They observed radio emissionfrom the Moon at a wavelength of 1.25 cm, thus beginningthe first scientific studies at radio wavelengths of theplanets and satellites of the solar system. Subsequent ob-servations revealed that the microwave emission from theMoon varies with lunar phase but the amplitude of thesevariations is much smaller than that observed at infraredwavelengths. This result was interpreted in terms of emis-sion originating below the surface of the Moon, wherethe temperature variations are smaller than at the surface.Within a few years, it was widely recognized that the longwavelengths provided by radio measurements offered anew and important tool for solar system studies, namelythe capability of probing into and beneath cloud layersand surfaces of the planets. However, thermal radio emis-sions from the planets are exceedingly weak and nearly adecade elapsed before system sensitivity was sufficientlyimproved to enable the detection of planetary thermalemission.

Meanwhile, another unanticipated discovery was made.In June 1954, when the angular separation between theSun and a supernova remnant known as the Crab Nebulawas small, astronomers B. Burke and K. Franklin of theCarnegie Institution were attempting to study the effectof the solar corona on radio waves from the Crab Nebula.Occasionally, they observed bursts of radio interference,which they initially thought were due to the Sun. Thathypothesis was discarded when it was discovered thatthe origin of the interference bursts was nearly fixed withrespect to the background stars. Further observations andexaminations of the data revealed that the emissions werein fact originating from Jupiter, which happened to be lo-cated in the same region of the sky as the Sun and the CrabNebula. Because the intensity of the emissions was muchtoo strong to be of thermal origin, Franklin and Burkeconcluded that Jupiter was a source of nonthermal radioemission.

The first successful measurements of thermal emissionfrom the planets were made in 1956 at the Naval ResearchLaboratory in Washington, D. C. C. H. Mayer, T. P. Mc-Cullough, and R. M. Sloanaker scanned Venus, Mars, andJupiter with a 15-m parabolic antenna equipped with anew 3-cm-wavelength radio receiver. They detected weakthermal emission from these three planets when each wasobserved at its closest distance to the Earth.

In the intervening years, thermal emission has beenmeasured from all of the planets in the solar system.



Radio Astronomy, Planetary 689

Because of the faintness of its radio emission, Pluto wasthe last planet to be detected. A few asteroids, satellites,and comets have been measured as well. Nonthermal radioemission has been measured from Jupiter, Saturn, Uranus,Neptune, and Earth. In this article we give an overview ofthe techniques used by planetary radio astronomers anddiscuss what has been learned from the measurements andwhat can be done in the future. In the interest of brevity, wedo not discuss specific observations of asteroids and satel-lites, although they rightfully belong in any discussion ofplanetary radio astronomy.

B. Measurement Objectives

The primary objective of planetary exploration is to deter-mine the physical characteristics of the planets, satellites,asteroids, and comets in order to obtain an understandingof the origin and evolution of the solar system, includingthe origin of life on the planet Earth. One objective asso-ciated with this goal is to determine the composition andphysical characteristics of these bodies and their atmo-spheres. Studies of the energy budget and redistributionof energy within solid surfaces and atmospheres are part ofthis work. Another objective is to investigate the magneticfields and ionized plasmas that surround some of the bod-ies in the solar system and to understand the interactionof the magnetic fields with the solar wind and the cosmicenvironment.

Planetary research involves many scientific disciplinesand requires a variety of instruments and techniques, in-cluding astronomical studies from the Earth, planetaryspacecraft flybys, orbiters, and probes, and eventuallymanned landings. Each of the various approaches usedhas a particular strength that experimenters try to exploit.Thus far, most planetary radio astronomy has been car-ried out from the ground, but the techniques carry over tospacecraft as well.

Planetary radio astronomy measurements provide com-plementary data to other observational techniques. Theyalso provide some unique data. For example, radio mea-surements can be used to provide information about plan-etary atmospheres and planetary subsurface materials tomuch greater depth than other remote-sensing techniques.The greater penetration is a result of neutral gases andsolids being more transparent to radio waves than higherfrequency waves such as infrared or visible light. Also,the scattering from particulate materials in planetary at-mospheres is generally less at radio wavelengths than atshorter wavelengths. The relative transparency of atmo-spheres, clouds, and surfaces to radio waves allows theplanetary radio astronomer to measure thermal profiles ofplanetary atmospheres beneath the cloud layers in the at-mosphere and to measure temperatures beneath the solid

surface of the planet. Taking advantage of this property,radio astronomers were the first to measure the very highsurface temperature of cloud-covered Venus.

Very high resolution spectroscopy is another area inwhich radio astronomy provides a unique capability. It ispossible to achieve very high spectral resolution in the ra-dio and submillimeter spectral region by translating thefrequency of the radio signal under study to a convenientplace in the frequency spectrum where spectrum analysisis easier to achieve with either digital or analog techniques.This process takes place without disturbing the relation ofthe sidebands to the carrier frequency. The process of fre-quency translation is referred to by such names as hetero-dyne, mixing, or frequency conversion. The heterodynetechnique makes it possible to measure absorption andemission line shapes in greater detail than has been pos-sible at shorter wavelengths. Both temperature–altitudeand composition–altitude profile distributions of absorb-ing chemical species (e.g., NH3, H2O, CO) can be deducedfrom spectroscopic measurements.

Finally, we note that both synchrotron and cyclotronradiation from (solar system) planets is confined to theradio region of the spectrum. This circumstance is dueto the range of planetary magnetic field strengths andparticle energies found in the solar system. The exis-tence of Jupiter’s strong magnetic field was first deducedfrom earth-based measurements of its polarized radioemission.

C. Physical Properties of the Planets

The physical characteristics of the planets are required inorder to make qualitative estimates of the radio power fluxdensities expected from them. Table I presents physicaldata for the planets.

II. BASIC CONCEPTS

A. Thermal (Blackbody) Radiation

Any object in thermodynamic equilibrium with itssuroundings (having a temperature above absolute zero)emits a continuous spectrum of electromagnetic radia-tion at all wavelengths, including the radio region. Thisemission is referred to as thermal emission. The conceptof a “blackbody” radiator is frequently used as an ideal-ized standard which can be compared with the absorptionand emission properties of real materials. A blackbodyradiator is defined as an object that absorbs all electro-magnetic radiation that falls on it at all frequencies overall angles of incidence. No radiation is reflected fromsuch an object. According to thermodynamic arguments




TABLE I Physical Data for the Planets

Mean Radius Diameter (arc sec)d

distance Mass (equator) Density Bond(AU)a (Earth = 1) (km) Obl.b (g/cm3) albedoc Min. Max.

Mercury 0.387 0.055 2,440 Small 5.427 0.06 4.7 12.2

Venus 0.723 0.815 6,052 Small 5.204 0.77 9.9 62.2

Earth 1.000 1 6,371 1/298.2 5.515 0.39 — —

Mars 1.524 0.107 3,390 1/156.6 3.934 0.16 3.5 24.6

Jupiter 5.203 317.9 69,911 1/16.7 1.326 0.45 30.5 49.8

Saturn 9.537 95.2 58,232 1/9.3 0.687 0.61 14.7 20.5

Uranus 19.191 14.6 25,362 1/100 1.318 0.42 3.4 4.2

Neptune 30.069 17.2 24,624 1/38.5 1.638 0.42 2.2 2.4

Pluto 39.482 0.0017 1,151 Unknown 1.1 0.55 0.06 0.1

a AU, Astronomical unit = 149.6 × 106 km.b Obl., Oblateness of planet = 1 − (polar radius/equatorial radius).c Bond albedo, ratio of reflected solar radiation to incident solar radiation. Spectral range should be specified, for example, visual bond albedo.d Diameter, angular extent of disk when planet–Earth distance is greatest (min.) and least (max).

embodied in Kirchhoff’s law, a good absorber is alsoa good emitter. The blackbody radiator emits the max-imum amount of thermal radiation possible for an ob-ject at a given temperature. The radiative properties of ablackbody radiator have been well studied and verified byexperiments.

A blackbody radiator is an idealized concept rather thana description of an actual radiator. Only a few surfaces,such as carbon black, carborundum, platinum black, andgold black, approach a blackbody in their ability to absorbincident radiant energy over a broad wavelength range.Many materials are spectrally selective in their ability toabsorb and emit radiation, and hence they resemble black-body radiators over some wavelength ranges and not overothers. Over large ranges of the radio and infrared spec-trum, planets behave as imperfect blackbodies. Later, wewill see how the deviations from the blackbody spectrumcontain information about physical and chemical proper-ties of these distant objects.

An important property of a blackbody radiator is that itstotal radiant energy is a function only of its temperature;that is, the temperature of a blackbody radiator uniquelydetermines the amount of energy that is radiated into anyfrequency band. Planetary radio astronomers make use ofthis property by expressing the amount of radio energyreceived from a planet in terms of the temperature of ablackbody of equivalent angular size. This concept is de-veloped more fully in the following paragraphs.

The German physicist Max Planck first formulatedthe theory that describes the wavelength dependence ofthe radiation emitted from a blackbody radiator in 1901.Planck’s theory was revolutionary in its time, requir-ing assumptions about the quantized nature of radia-tion. Planck’s radiation law states that the brightness of

a blackbody radiator at temperature T and frequency ν isexpressed by

B = (2hν3/c2)(ehν/kT − 1)−1, (1)

where B is the brightness in watts per square meter perhertz per radian; h is Planck’s constant (6.63 × 10−34

J sec); ν is the frequency in hertz; λ = c/ν is the wave-length in meters; c is the velocity of light (3 × 10−8 m/sec);k is Boltzmann’s constant (1.38 × 10−23 J/K); and T is thetemperature in kelvins.

Equation (1) describes how much power a blackbodyradiates per unit area of surface, per unit frequency, into aunit solid angle. The curves in Fig. 1 show the brightnessfor three blackbody objects at temperatures of 6000, 600,and 60 K. The radiation curve for the undisturbed Sunis closely represented by the 6000 K curve over a widefrequency range. The other two curves are representativeof the range of thermal temperatures encountered on theplanets. It should be noted in Fig. 1 that the brightnesscurve that represents the Sun peaks in the optical wave-length range, while representative curves for the planetspeak in the infrared. This means that most of the energyreceived by the planets from the Sun is in the visible wave-length range, while that emitted by the planets is radiatedin the infrared. Radio emissions are expected to play onlya small role in the overall energy balance of the planets be-cause the vast majority of the power that enters and leavesthe planets is contained within the visible and infraredregion of the spectrum.

A useful approximation to the Planck radiation lawcan be obtained in the low-frequency limit where hν

is small compared with kt (hν � kT ). This conditionis generally met over the full range of planetary tem-peratures and at radio wavelengths. It leads to the




FIGURE 1 Blackbody radiation curves at 6000, 600, and 60 K. The 6000 K curve is representative of the solar spectrum.

Rayleigh–Jeans approximation of the Planck law, givenby

B = 2ν2kT/c2 = 2kT/λ2. (2)

The Rayleigh–Jeans approximation shows a linear rela-tionship between physical temperature and the Planckbrightness B. The brightness is also seen to decrease asthe inverse square of the wavelength, approaching infin-ity as the wavelength gets shorter and shorter. The Planckbrightness, on the other, hand reaches a maximum valueat some wavelength and decreases at longer and shorterwavelengths. The Rayleigh–Jeans approximation matchesthe Planck law at wavelengths considerably longer thanthe wavelength of peak brightness. However, for shorterwavelengths, the approximation gets progressively worse.At a temperature of 100 K and a wavelength of 1 mm, theerror is ∼8%.

Planetary radio astronomers estimate the radio poweremitted by the planets by measuring with a radio telescopethe power flux density received at the Earth. Figure 2 illus-trates the geometry involved in the measurement of powerfrom an ideal blackbody radiator. The spectral power (perunit frequency) emitted by an elemental surface elementof the blackbody of area dA into a solid angle d� is givenby B cos(θ ) d� dA, where θ is the angle between the nor-mal to the surface and the direction of the solid angle d�.The total power (per unit frequency interval) radiated by

a blackbody radiator is obtained by integrating the bright-ness over the surface area and over the solid angle intowhich each surface element radiates. The total spectralpower density produced by a spherical blackbody radiatorof radius r at a distance d from the blackbody is given by

S = 1

4πd2

∫ ∫B cos(θ ) ds d� (3a)

= 2πkT (r/d)2/λ2. (3b)

The double integral represents integration over the surfacearea of the emitting body and over the hemisphere intowhich each surface element radiates. The quantity S iscalled “flux density.” Flux density has units of power perunit area per unit frequency. A common unit of flux densityis the flux unit (f.u.) or jansky (Jy), which has the value10−26 W m−2 Hz−1.

If a planet radiates like a blackbody and subtends a solidangle of � steradians at the observer’s distance, then theflux density produced by the planet is given by (using theRayleigh–Jeans approximation)

S = 2kT �/λ2 (4a)

= B� (4b)

The convention generally adopted for calculating � fora planet is to use the polar (PSD) and equatorial (ESD)semidiameter values in the expression




FIGURE 2 Relationship between the brightness and power radiated by a blackbody spherical radiator of radius rand the flux density at a distance d from the blackbody.

� = π × PSD × ESD. (5)

The American Ephemeris and Nautical Almanac (AENA)provides values for PSD and ESD. A web site (http://ssd.jpl.nasa.gov) operated by the JPL Solar System Dy-namics Group also provides these data. Equations (4) and(5) can be combined to yield the expression

S = 5.1 × 10−34T θEθP/λ2 W m−2 Hz−1 (6a)

= 5.1 × 10−8T θEθP/λ2 Jy (6b)

where θE and θP are the apparent equatorial and polardiameters of the planets in seconds of arc andλ is in meters.

Even though the planets do not radiate like a black-body, planetary radio astronomers express the observedbrightness in terms of the temperature of an equivalentblackbody that would produce the same brightness. Thistemperature is called the brightness temperature TB, de-fined as follows [from Eq. (4)]:

TB = Bλ2/2k = (S/�)λ2/2k. (7)

The brightness temperature for a planet can be calculatedonce the flux density S and solid angle � are known. Thebrightness temperature approximates the physical tem-perature the more the planet behaves like a blackbodyradiator.

For problems that deal with the energy budget of theplanets, it is necessary to know the total amount of powerradiated over all frequencies. Once again the concept of theblackbody is useful. The Planck radiation law can be inte-grated over all frequencies and solid angles to obtain therelationship known as the Stefan–Boltzmann law, given by

R = σ T 4, (8)

where R is the rate of emission, expressed in units ofwatts per square meter in the mks system. The constant σ

has a numerical value of 5.67 × 10−8 W m−2 K−4. Usingthe blackbody concept, we can now estimate the energybalance of planets that absorb visible light and radiateenergy into the infrared.

B. Thermal Emission fromAtmospheres and Surfaces

1. Effective Temperatures of the Planets

The amount of thermal radiation expected from a givenplanet depends in detail on the physical characteristics ofthe planet’s atmosphere and surface. A starting point forunderstanding the observed flux densities of the planets isto assume that the planets are blackbodies in equilibriumwith the energy they receive from the Sun and that whichis radiated into free space. The radiation energy incident

http://ssd.jpl.nasa.gov

http://ssd.jpl.nasa.gov




from the Sun on a unit area per unit time is 1.39 × 103

W m−2 sec−1 at the Earth. This quantity is called the solarconstant. The incident solar flux available to heat a planetis given by

(1 − A)S0π R2/d2, (9)

where A is the fraction of the incident solar flux that is notabsorbed, πR2 is the cross-sectional area of the planet,S0 is the solar constant at astronomical unit (AU), andd is the mean distance of the planet from the Sun in as-tronomical units. The quantity A is known as the Bondalbedo or Russel–Bond albedo of the planet. Disregard-ing any significant internal heat sources or heating fromcharged particles, the total flux of absorbed radiation mustequal the total flux of outgoing radiation when the planetis in equilibrium. The Stefan–Boltzmann law provides therelationship between effective temperature TE and the ab-sorbed flux:∫

σ T 4E ds = π R2(1 − A)S0/d2. (10)

If the planet rotates rapidly, equilibrium will be reachedbetween the insulation and the radiation from the entireplanetary surface area, 4πR2. This leads to the estimate

TE = 277(1 − A)1/4d−1/2 K. (11)

If a planet did not rotate and its emitted radiation came onlyfrom the sunlit hemisphere, the effective temperature ofthe sunlit hemisphere would increase by the factor 21/4

because of the reduction in the emission surface area. Theequilibrium temperature for this case would become

TE = 330(1 − A)1/4d−1/2 K. (12)

Figure 3 shows the calculated effective temperatures ofthe planets for the rapidly rotating and nonrotating cases.The albedos and distances used are those given in Table I.Having obtained the effective temperatures, it is possibleto predict flux densities for the planets by using the effec-tive temperatures from Eq. (11) or (12) and the angulardiameter data for the planets in Table I in Eq. (6a) or (6b).

Thus far, we have discussed the ideal model in whichthe planets behave like blackbody radiators. This givesplanetary astronomers a crude model from which theycan estimate flux densities and search for departures. Theplanets would not be very interesting to study if they be-haved like blackbodies since a single parameter, namelythe temperature, could be used to define their radiationproperties. More important, it is the departures from thesimple model that allows radio astronomers to deduce thephysical properties of the planets.

The observed temperatures of the planets departmarkedly from this ideal model for a number of differ-ent reasons. The presence of atmospheres on the plan-ets produces strong perturbations from the ideal model.

Atmospheres modify the amount of heat that enters andleaves the planets over the entire electromagnetic spec-trum. Strong “greenhouse” effects can raise the temper-atures considerably over that calculated from the idealmodels. The presence of internal sources of energy withina planet can modify its effective temperature and affectthe thermal profile of the atmosphere. Surface emissiv-ity effects modify the apparent temperature of the plan-ets. Nonuniform heating of the planets by the Sun due toorbit eccentricity and rotational effects also produces de-partures from the ideal model. Nonthermal emission fromplanetary magnetospheres produces the largest departuresfrom the blackbody model. The role of the planetary as-tronomer is to sort out the various effects that take placeand to measure and infer the actual physical characteristicsof the planets.

2. Radiative Transfer in Planetary Atmospheres

The apparent brightness temperature of a deep atmosphereis related to the physical parameters of the atmosphere,such as pressure, temperature, and composition, throughthe equation of radiative transfer. To a good approximationat radio wavelengths, the equation of radiative transfer fora ray making an angle cos−1 µ with the vertical in a lossymedium is

TB(ν, µ) =∫

T (z) exp

[−

∫α(z′, µ)µ−1dz′

]

× α(z, ν)µ−1 dz, (13)

where α(z, ν) is the absorption per unit length of the atmo-sphere at frequency ν and depth z, and T (z) is the physicaltemperature along the line of sight. This equation statesthat the brightness temperature in any given direction is thesum of the radiation emitted at each point along the trajec-tory, each component being attenuated by the interveningmedium. The equation neglects scattering and variationsof the index of refraction. These effects are important incertain wavelength ranges and for certain ray trajectories.Sometimes it is necessary to add another term to Eq. (13)to account for the presence of a solid surface.

Measurements with single-dish antennas generally haveinsufficient angular resolution to determine the bright-ness distribution across the planetary disk. The mean diskbrightness temperature TD can be calculated by integrationof Eq. (13) over all angles of incidence. This yields

TD(ν) = 2∫ 1

0TB(ν, µ)µ dµ. (14)

This equation is usually used to calculate the average diskbrightness temperature for a model atmosphere for com-parison with observations. Unlike the blackbody radiationmodel, this model predicts a wavelength dependence of




FIGURE 3 Theoretical effective temperatures of the planets for two models. The higher temperature model is forthe case where the planet is not rotating [Eq. (12)]. The lower temperature model is for the case where the planet israpidly rotating [Eq. (11)].

the brightness temperature. The frequency dependence isintroduced by the frequency dependence of the absorptionand the thermal gradients in the atmosphere.

The absorption may either vary slowly with frequencyor exhibit an abrupt change over a narrow frequency range.The two kinds of absorption are referred to as nonreso-nant and resonant absorption, respectively. The standardclassical theory of nonresonant molecular absorption isdue to Debye. Resonant absorption is produced by thediscrete transitions from one energy level to another ina molecule that cause the molecule to absorb or emit atparticular frequencies. The study of resonant absorptionlines in planetary atmospheres is referred to as planetaryspectroscopy.

A brief discussion of the energy levels in the moleculeCO is helpful for understanding resonant absorption andthe usefulness of planetary spectroscopy as a tool forstudying planetary atmospheres. The rotational energylevels in CO are quantized according to the relation

Er = J (J + 1)B, (15)

where J (J = 0, 1, 2, . . .) is the rotational quantum num-ber and B the rotational constant. The rotational constantfor a diatomic molecule is defined by

B = h28π2 I, (16)

where I is the moment of inertia of the molecule aboutthe axis perpendicular to the line connecting the nuclei

and h is Planck’s constant. The transitions between thevarious energy levels are limited by the exclusion principleto �J = ±1. The energy of a quantum emitted or absorbedduring a transition is given by

hν = J (J + 1)B − (J − 1)(J )B = 2JB. (17)

When B is expressed in megahertz, the transition fre-quency ν in megahertz is expressed directly as 2JB. Thevalue of B for CO is 57,897.5 MHz. Thus, CO has tworotational transitions in the millimeter spectrum, a groundstate (∼115 GHz) and the first excited state (∼230 GHz).The ground-state transition corresponds to a transition be-tween J = 0 and 1; the first excited state corresponds toa transition between J = 1 and 2. Both of these transi-tions have been observed in the atmospheres of Venus andMars.

A number of factors cause the energy levels in amolecule to vary slightly and cause the molecule to emit orabsorb over a range of frequencies. The range of frequen-cies or “width” of a spectral line is determined primarily bythree factors: (1) natural attenuation, (2) pressure broad-ening, and (3) Doppler broadening. Pressure broadeningand Doppler broadening are the dominant mechanisms inmost planetary astronomy applications. Natural attenua-tion is interpreted as the disturbance of the molecule byzero-point vibration of electromagnetic fields, which arealways present in free space.




Doppler broadening is caused by the frequency shiftintroduced by the molecule’s motion. The statistical ef-fect of the simultaneous observation of a large number ofmolecules moving at various velocities is to spread thefrequency of the spectral line over a range of frequencies.The spectral line produced by thermal motions in a gas(in thermodynamic equilibrium) is symmetric and has afull-width at half-maximum of

�ν = 7.2 × 10−7(T/M)1/2ν, (18)

where T is the temperature of the gas, M is the molecularweight of the molecule, and ν is the frequency of the spec-tral line without Doppler shift. The Doppler linewidth ofthe ground-state transition (J = 0 to 1) of CO at 200 K is∼200 kHz. A measure of the Doppler width can be usedto estimate the temperature of the gas.

Pressure broadening can be interpreted as the effect ofcollisions disrupting the processes of emission and absorp-tion in a molecule. A number of different theoretical lineshapes have been derived to explain pressure broadening.The one most widely used is the Van Vleck–Weisskopf lineshape. Linewidths due to pressure broadening are propor-tional to pressure, the proportionality constant dependingon the particular molecules involved in the collisions. ForCO broadened by CO2, the linewidth of the ground-statetransition of CO is approximately

�ν = 3.3p(300/T )0.75, (19)

where p is the pressure in millibars and �ν is the linewidthin megahertz. At a pressure of 1 mbar and temperatureof 200 K, the pressure-broadened linewidth of CO is∼4.5 MHz. Observations of pressure-broadened spectrallines can be used to determine the altitude distribution ofa molecule in a planetary atmosphere.

3. Radiative Transfer in Planetary Subsurfaces

While some planets have deep atmospheres, others, suchas Mercury and Mars, have relatively tenuous atmo-spheres. For these planets (and the Moon and satellites) theatmospheres are nearly transparent at radio wavelengths,except possibly in narrow wavelength ranges, where reso-nant absorption lines can produce strong absorption. Ther-mal emission from the surfaces of these planets is easilyobserved at radio wavelengths; it is possible to interpretthe measurements in terms of the physical properties ofthe near-surface materials.

Observations of the thermal radiation at radio wave-lengths provide measurements that are complementary toinfrared measurements of the subsurface materials. Ther-mal emission in the infrared is emitted very close to thesurface of the planet because the opacity of most mineralsis high at infrared wavelengths. Consequently, infrared

thermal emission reflects the physical characteristics ofthe near-surface materials. The opacity of typical plane-tary materials is considerably less at radio wavelengths,and the observed thermal emission originates at greaterdepth.

The interpretation of thermal emission data from a plan-etary surface begins with an analysis of heat transfer insolids. The solid surface receives heat from the incomingsolar radiation and transports it downward, mainly by con-duction and radiation. Boundary conditions are set by theheating of the surface by the Sun, the nighttime cooling,and the internal sources of heat, if any. The surface temper-ature responds to the heating and cooling, being controlledby the “thermal inertia” of the near-surface material. Be-cause the planets are heated and cooled periodically dueto their spin, a thermal wave is set up in the surface layers.The equation of radiative transfer is used to relate the tem-perature structure in the subsurface layers to the observedthermal emission.

The formal solutions of the equations of heat transfer insolids and radiative transfer depend on the following prop-erties of the near-surface material: the complex dielectricconstant ε(λ), thermal conductivity k (ergs per centimeterper second per Kelvin), specific heat c (ergs per gram perKelvin), and density ρ (grams per cubic centimeter). Theanalytic theory of heat transfer at planetary surfaces be-gins by assuming that the temperature at any point on thesurface can be expanded in a Fourier series in time:

Ts(t) = T0 +∞∑

n=1

Tn cos[(nωt) − �n], (20)

where ω (radians per second) is the fundamental heatingfrequency (i.e., rotation rate of the planet as seen from theSun) and t is time. Assuming that the planet is a semiinfi-nite homogeneous slab with constant thermal properties,the equilibrium solution for the subsurface temperaturedistribution is

T (x, t) = T0 +∞∑

n=1

Tn exp(−xβn) cos[(ωt − βn x − �n)],

(21)where x is the depth beneath the surface and βn is givenby

βn = (nωρc/2k)1/2 = β1n1/2. (22)

Equation (21) represents a series of thermal waves propa-gating into the surface and attenuating with distance. Thehigher harmonics are attenuated more rapidly than thelower harmonics since βn increases as the square root ofthe harmonic number n. The attenuation and phase of eachharmonic depend on the quantity β1, which is termed the“thermal absorption coefficient” of the planetary material.The reciprocal ofβ (L t = 1/β1) is termed the “thermal skin




depth.” At a distance of 3–4 thermal skin depths, the fluc-tuations in subsurface temperature are practically zero.

Given the thermal absorption coefficient and the bound-ary conditions on the heating, it is possible to determinethe constants of temperature (T0 and Tn) and phase (�n)in Eq. (21). The inverse problem is faced by the radioastronomer, namely to determine the thermal absorptioncoefficient from measurements of the thermal emission.This is done in the following manner. The temperaturedistribution given by Eq. (21) is used in the equation ofradiative transfer

TB = [1 − RP (ν, θ0)]

×∫ ∞

0T (x) exp(−kνx/ cos θi ) (kν/ cos θi ) dx

(23)

to compute the radio brightness temperatures at any wave-length for comparison with observations. In this expres-sion kν is the power absorption coefficient at frequencyν, θi is the angle of incidence of radiation just below thesurface, and θ0 is the angle of incidence of the observation.The function RP (ν, θ0) is the Fresnel reflection coefficientof polarization P emerging at angle θ0.

After substituting (the series) Eq. (21) for T (x, t) inEq. (23), the integral can be evaluated as a series of inte-grals. Each integral can be put in the form of a standardLaplace transform and integrated directly. The resultingbrightness temperature at time t at a specified point on thesurface is given by

TB(ν, p, t) = [1 − RP ]∞∑

n=1

Tn cos[nωt − �n − �n(θi )]

[1 + 2δn(θi ) + 2δn2(θi )]1/2,

(24)where

δn(θi ) = n1/2β1 cos(θi )/kν, (25)

�n = tan−1{δn[θi/(1 + δn(θi )]}. (26)

Defining l/Kν as the radio absorption length (Le), wehave that δ1 reduces to the ratio of the radio absorptionlength to the thermal absorption length at normal inci-dence. Equations (24)–(26) relate the observational datato the physical parameters of the surface materials. Onlythe first few terms of Eq. (24) are normally important be-cause the higher order terms are small. The most importantterms determined from the observations are δ1 and �1. Theδ1 term defines the reduction in amplitude of the funda-mental diurnal wave component from its surface value.It is best determined from observations at several differ-ent wavelengths spanning a wavelength range of 2:1 ormore. The �1 term defines the phase shift in the diurnalwave at depth. It also can be deduced from measurementsat several wavelengths, but usually with somewhat lessprecision than δ1.

The parameter δ1 can be written in terms of the physicalcharacteristics of the surface material as follows:

δ1 = LeL t = (�ρc/2k)1/2λ[2π√

ε tan(�)]−1, (27)

where tan(�) = 2σ/εrν is the loss tangent, εr is the realpart of the dielectric constant, and σ is the electrical con-ductivity (mhos per meter) of the medium.

Radio observations by themselves do not permit sepa-ration of the physical parameters contained in δ1 and �1.Nevertheless, the radio data, when combined with infrareddata, radar data, and laboratory data for real materials, con-strain the material properties and in some cases allow oneto exclude certain classes of materials in favor of others.

C. Nonthermal Radio Emission

Thermal radio emission in solids and neutral gases arisesfrom the emission of quanta from individual atoms andmolecules in thermodynamic equilibrium with each other.Random collisions between ions and electrons in ther-mal equilibrium with each other in an ionized gas alsoproduce thermal emission. The electrons and ions in thiscase have a Maxwellian velocity distribution. When en-ergy sources are present that produce particles having anon-Maxwellian velocity distribution, the system is not inthermodynamic equilibrium. Efficient processes can ariseunder these conditions that produce large amounts of radioenergy. Nonequilibrium conditions frequently arise in anionized gas or plasma typical of those found in space. Ina fully ionized gas, nonequilibrium conditions can lead tocoherent and incoherent plasma emissions. The radiationthat arises from these mechanisms is called nonthermalemission. Cyclotron emission and synchrotron emissionare examples of nonthermal emission. In the case of ther-mal emission, the blackbody radiation laws limit the ra-diation to an amount corresponding to the temperature ofthe body. For nonthermal radiation, this limit does not ex-ist. The brightness temperature of nonthermal radiationsometimes exceeds millions of degrees, even though theeffective temperature of a planet does not exceed severalhundred degrees.

The classic sources of nonthermal radio emission withinthe solar system are Jupiter’s magnetosphere and the so-lar corona. Nonthermal radio emissions have also beenobserved from the Earth’s magnetosphere and the otherthree giant planets, Saturn, Uranus, and Neptune. Theemissions from the latter planets can only be observedfrom spacecraft near the planets. Cyclotron and coherentplasma emission account for much of the low-frequency(<10 MHz) nonthermal emission from these planets andthe solar corona. This emission is highly variable and thedetails of the generation processes involved are not clearlyunderstood.




Synchrotron radiation is the dominant source of emis-sion from Jupiter from about 50 MHz to 5 GHz; it alsoaccounts for continuum bursts of type IV from the sun.The theory of synchrotron radiation is well developed.A review article on magnetospheric radio emissions byCarr, Desch, and Alexander, contained in the book editedby Dessler (1983), lists a number of references.

High-energy electrons moving in a magnetic field pro-duce synchrotron radiation. Although the observed syn-chrotron radiation from a planet or the sun is the integratedemission from many electrons, an understanding of the ra-diation characteristics of a single electron in a magneticfield is sufficient to understand the qualitative aspects ofthe observations.

A single charged electron moving in a magnetic field isaccelerated unless its velocity is solely in the direction ofthe magnetic field. This causes the electron to emit elec-tromagnetic waves. The nature of these waves depends onwhether the electron is nonrelativistic (velocity�3 × 1010

cm/sec) or relativistic (velocity ∼3 × 1010 cm/sec). Theradiation emitted by nonrelativistic electrons is referredto as cyclotron radiation; radiation emitted by relativisticelectrons is referred to as synchrotron emission.

A nonrelativistic electron with mass m and charge e, inthe presence of a magnetic field (of magnitude B), movesin a helical path with the sense of rotation of a right-hand screw advancing in the direction of the magneticfield. The frequency of rotation about the magnetic field,sometimes called the electron cyclotron frequency or thegyrofrequency, is given by (where B is given in gauss)

fc = Be/2nm = 2.8B(G) MHz. (28)

Cyclotron radiation is emitted in all directions and hasa frequency equal to the gyrofrequency. The radiation ispolarized with the polarization depending on the directionof propagation. The polarization is circular when viewedalong the direction of the magnetic field and linear whenviewed in the plane of the orbit. At intermediate anglesthe polarization is elliptical.

Relativistic electrons radiate not only at the gyrofre-quency, but also at the harmonics. The relativistic massincrease with energy causes the harmonic spacing to de-crease with increasing energy until the synchrotron spec-trum is essentially smeared into a continuum. The radia-tion from a relativistic electron is highly nonisotropic. Theemitted radiation is concentrated within a narrow coneabout the instantaneous direction of the velocity vectorwith an approximate half-cone-width given by

θ ∼= mc2/E rad, (29)

where E is the electron energy. When E is expressed inmillions of electron volts (MeV) and θ in degrees, theexpression becomes

θ ∼= 29/E(MeV) deg. (30)

An observer situated in the plane of the electron or-bit would see one pulse per revolution of the electron.These pulses recur at the relativistic gyrofrequency of theelectron.

A single electron of energy E radiates synchrotronemission with an intensity spectrum that varies as ν1/3

(ν is frequency) up to a critical frequency 0.29νc and de-creases exponentially at higher frequencies. The criticalfrequency is defined as

νc = (3e/4nmc)(E/mc2)B

= 16.08B(G)E2(MeV) MHz. (31)

Thus a 10-MeV electron in a 1-G magnetic field will ra-diate a maximum intensity near 0.29 × 1608 MHz. Thespectral density of the radiation near the frequency of themaximum intensity is

I (ν = 0.29νc) ∼= 2.16 × 10−29 B(G) W/Hz. (32)

The total energy radiated per second (in watts) is given by

P = 6 × 10−22 B2(G)E2(MeV) sin2 α W (33)

where α is the pitch angle of the electrons (α = 90◦ forelectrons with no motion in the direction of the magneticfield).

As in the case of nonrelativistic electrons, the polariza-tion is linear when the electron orbit is seen edge-on andelliptical or circular elsewhere. Since the intensity of theradiated power is beamed in the plane of the orbit, syn-chrotron radiation is predominantly linearly polarized.

It is possible to deduce many properties of Jupiter’smagnetic field and of the high-energy particle environ-ment from radio measurements of Jupiter by judicioususe of the equations given above. Detailed calculations ofsynchrotron emission are complex since they involve in-tegrals over the volume of the emitting electrons and overthe electron energy spectrum while taking into account thecomplex geometry of the magnetic field and polarizationproperties of the radiation.

III. INSTRUMENTATION FOR PLANETARYRADIO ASTRONOMY

A radio telescope is a device for receiving and measur-ing radio noise power from planets, satellites, asteroids,and comets as well as from galactic and extragalacticradio sources. A simple radio telescope consists of an an-tenna for collecting the noise power (in a specified band-width, polarization, and from a limited range of directions)and a sensitive receiver–recorder for detecting and record-ing the power. The antenna is analogous to the objective




FIGURE 4 Basic components of a simple radio telescope.

lens or primary mirror of an optical telescope; the re-ceiver is analogous to the recording medium of the opticaltelescope (i.e., photographic plate, photodetectors, etc.).Figure 4 shows the basic components and configurationof a simple radio telescope. Single antennas may be con-nected together electrically to form an “array” radio tele-scope which has greater sensitivity and directivity than asingle antenna. There are many different types of radiotelescopes in use today and their capabilities and visualappearances show much diversity.

Three important properties of an antenna are its ef-fective area Ae(θ, φ), normalized antenna power patternPN(θ, φ), and gain G. The effective area is a measure ofthe wavefront area from which the antenna can extractenergy from a wave arriving at the antenna from differ-ent directions. It can be thought of as the equivalent crosssection of the antenna to the incident wave front. For mostradio telescopes, the effective area is less than the physicalarea. A working definition of the effective area is given by

P = 1

2SAe dν, (34)

where P is the power the antenna can deliver to a matchedload in bandwidth dν when flux density S is incident on theantenna. The factor 1/2 is introduced because it is assumedthat the radiation is unpolarized and that the antenna isresponsive to only one polarization component.

The effective area of an antenna is a function of thedirection of arrival of the waves. The effective area to asignal from a distant transmitter, as a function of direc-tion, is called the antenna power pattern. The effectivearea normalized to unity in the direction of the maximumeffective area Ae-max is the normalized power pattern ofthe antenna:

PN(θ, φ) = Ae(θ, φ)/Ae-max. (35)

By reciprocity arguments, the normalized power patternis the same for both transmitting and receiving.

A general expression for the power delivered to a ra-dio receiver from a planet is obtained by integrating thebrightness over the solid angle of the planet and over thebandwidth of the receiver as follows:

P = 1

2

∫ ∫ ∫B(θ, φ, ν)Ae(θ, φ, ν) sin(θ ) dθ dφ dν

(36a)

P = 1

2Ae-max

∫ ∫ ∫B(θ, φ, ν)

× PN(θ, φ, ν) sin(θ ) dθ dφ dν. (36b)

A typical antenna power pattern consists of a large num-ber of lobes with one or a few lobes being much larger thanthe others, as shown in Fig. 5. The lobe with the largestmaximum is called the main lobe, while the remaininglobes are called side or back lobes.

The half-power beamwidth of the main lobe, �, is theangle between the two directions in which the receivedpower is half of that in the direction of maximum power.The half-power beamwidth is a measure of the ability ofthe antenna to separate objects that are close together inangle. In optical systems, this is known as resolving power.An estimate of the beamwidth in radians of the main lobeis given by � ∼ λ/D, where D is the linear dimension ofthe antenna in the plane in which the beam is measuredand λ is the wavelength in the same units as D. The re-solving power can be improved by using either a shorterwavelength or a larger diameter telescope.

Two major classifications of large radio telescopes are(1) filled-aperture telescopes and (2) unfilled-aperturetelescopes. Filled-aperture radio telescopes generally con-sist of a single reflecting element that focuses the receivedradio waves to a point or, in some cases, along a line.Examples of filled-aperture radio telescopes are the 64-mparabolic reflector antenna at Parkes, Australia, the 100-m parabolic reflector at Bonn, Germany, and the ∼300-mspherical reflector antenna at Arecibo, Puerto Rico. Thenewest of the large filled-aperture radio telescopes is the100-m Green Bank Telescope (GBT). The surface pan-els of the GBT are supported by motor-driven actuatorsto compensate for the structural deformations of the an-tenna. The GBT is expected to operate at frequencies upto 80 GHz under the most favorable conditions availableat the site.

The resolving power of most filled-aperture radio tele-scopes is generally less than is required for adequate res-olution of the disks of the planets. The few exceptionsare the large telescopes such as the GBT and the 30-mPico Villeta telescope, which operate at short, millimeterwavelengths. The largest single-dish antennas presentlyavailable to radio astronomers are capable of partiallyresolving the disks of the planets of largest angular di-ameter, Venus and Jupiter. For example, an antenna witha maximum dimension of 100 m operating at a wave-length of 10 cm would have a main lobe width of approxi-mately 1/1000 rad or 3.44 arc min. The angular diameters




FIGURE 5 Antenna power pattern and its relation to a measurement of the flux density from a planet.

(Table I) of Venus and Jupiter are approximately 1 arc min;thus an antenna with an aperture of ∼344 is required justto “fill the main lobe.” Adequate resolution of even thelargest planets (at 10-cm wavelength) requires aperturesat least 10 times larger.

Higher resolving power can be achieved by connectingtogether electrically the outputs of two or more filled-aperture antennas to the input of a common radio re-ceiver. The resolving power of such a system dependson the maximum separation between the individual el-ements, even though the space between the elements isunfilled. Multiple-element radio telescopes (arrays) withspaced separations between the elements to achieve highresolving power are termed unfilled-aperture radio tele-scopes. The simplest unfilled-aperture radio telescopeis a total power interferometer with two identical ele-ments, as shown in Fig. 6. The output from the two-element interferometer modifies the power pattern of asingle element with an angular modulation of scale λ/Dsuperimposed.

The Very Large Array (VLA) radio telescope, locatedon the plains of San Augustin west of Socorro, NewMexico, is a classic example of an unfilled-aperture radiotelescope. This instrument, completed in early 1981, isespecially important to planetary radio astronomers. TheVLA consists of 27 antennas, each having a diameter of25 m. The individual antennas are arranged in a huge,Y-shaped pattern. The antennas are mounted on tracksso that they can be moved into four configurations alongthe Y-shaped baseline. This allows the radio telescope tobe custom tailored to a particular kind of measurement.The maximum antenna separation is 36 km across. At thehighest frequency (43 GHz), the VLA has a resolutionof .043 arc sec. The effective sensitivity is equivalent toa filled-aperture telescope having a diameter of 130 m.Continuum, polarization, and spectral line observations ateight wavelength bands (0.7, 1.3, 2.0, 3.6, 6, 20, 90, and405 cm) are supported. The VLA has sufficient resolvingpower to measure the brightness distributions across all ofthe planets at its shortest wavelengths.




FIGURE 6 Total power interferometer. (Top) Geometry of a two-element interferometer. (Bottom) Antenna responsefor a single element of the interferometer (left) and response of the interferometer (right) to a completely unresolvedplanet.

Small arrays at millimeter wavelengths have been op-erational for over a decade and have returned many inter-esting continuum and spectroscopic images of the planets.Major millimeter arrays are the BIMA millimeter array,the Owens Valley Radio Observatory (OVRO) millimeterarray, the Plateau de Bure Observatory, and the NobeyamaMillimeter Array (NMA). The BIMA and OVRO millime-ter arrays are likely to be combined into a single largemillimeter array in the future. The Submillimeter Array(SMA) is an exploratory instrument for high-resolutionobservations at submillimeter wavelengths. The SMA willinitially consist of eight 6-m antennas sited on Mauna Keaat an elevation of 4050 m. A major step in millimetersolar system research will be provided by the construc-tion of very large millimeter arrays. Two large arrays arecurrently in their early phases. The Atacama Large Mil-limeter Array (ALMA) will consist of 64 (or more) 12-mantennas located at an elevation of 16,400 ft in Llano deChajnantor, Chile. This array will provide imaging in allatmospheric windows between 1 cm and 350 µm. Thearray configuration will provide baselines ranging from150 m to 10 km. Spatial resolution of 10 marcsec, 10times better than the VLA, will be possible. A Large Mil-limeter and Submillimeter Array (LMSA) has been pro-posed in Japan. This array will consist of 50 10-m an-tennas and will cover frequencies from 80 to 800 GHz.These new very large arrays will open up many possibili-ties for planetary radio astronomers. Imaging of planetaryatmospheres will be greatly improved and general circula-tion studies will be greatly enhanced. Planetary satelliteswill be easily resolved making temperature and wind mea-

surements possible. Imaging and spectroscopy of cometswill be greatly improved and many new molecules can bestudied.

The performance of a filled-aperture antenna is some-times expressed by specifying the gain of the antenna.The antenna gain is a measure of the ability of the antennato concentrate radiation in a particular direction. Gain isdefined as the ratio of the flux density produced in di-rection (θ, φ) by an antenna when transmitting with aninput power P to the flux density produced by the sametransmitter feeding an antenna that radiates equally in alldirections. The antenna gain, effective area, and beamsolid angle � are interrelated quantities. The relationshipbetween them is given by

G = 4πAe-max/λ2 = 4π/�. (37)

Radio astronomers generally specify the received powerP delivered to the receiver in the frequency bandwidth dν

as the antenna temperature Ta, defined by

Ta = P/k dν, (38)

where k is Boltzmann’s constant. This definition followsfrom the Nyquist theorem, which states that the noisepower delivered from a resistor at temperature T into amatched load in bandwidth dν is

PN = kT dν. (39)

The antenna temperature can be thought of as the physicaltemperature at which a resistor would have to be main-tained to deliver the same power to the receiver as theantenna.




The antenna temperature can be thought of as thephysical temperature at which a resistor would have tobe maintained to deliver the same power to the receiveras the antenna.

The antenna temperature of an unresolved radio sourcecan be calculated directly from the definition of the effec-tive area and the definition of antenna temperature if itsflux density is known. For a planet of known solid angleand temperature, the antenna temperature can be calcu-lated by substituting the Rayleigh–Jeans approximationfor the brightness, B = 2kTp/λ

2, and the relationship be-tween effective area and beam solid angle,

Ae-max = λ2/�, (40)

into Eq. (36). When the planet is unresolved by the mainbeam of the telescope, the antenna temperature is givenby

Ta = (�p/�)Tp, (41)

where �p and Tp are the solid angle and temperature ofthe planet, respectively, and � is the beam solid angleof the telescope. The relationship states that the antennatemperature of a planet is proportional to the brightnesstemperature of the planet, with the constant of proportion-ality being the ratio of the solid angle of the planet to thesolid angle of the beam. This approximation holds when�p � �; consequently, the antenna temperature is alwaysless than the brightness temperature.

The concept of specifying the received power in termsof an equivalent temperature is useful for estimating thesignal-to-noise ratio for a particular measurement sincerandom noise in the receiving equipment is easily ex-pressed as a temperature. A discussion of signal-to-noiseratio follows.

A. Radio Receivers

Radio astronomy receivers, like ratio telescopes, arehighly varied, depending on the type of measurement tobe performed. The function of the receiver is to detect andmeasure the radio emission with as much sensitivity aspossible. The receiver also defines the frequency range orranges of the measurement. Most modern receivers consistof a low-noise amplifier to boost the power of the incom-ing signal (without adding significant noise), followed bya heterodyne mixer and square law detector. The hetero-dyne mixer transforms the signal frequency to a convenient(often lower) frequency for detection or further process-ing. For high-resolution spectroscopic observations, thesquare law detector may be preceded by spectrometer,such as a filter bank, digital autocorrelator, or acousto-optical spectrometer.

The inherent noise fluctuations of a radio receiver usu-ally determine the weakest signal strength that can be mea-sured with a radio telescope. The statistical nature of noiseradiation is such that statistical fluctuations are propor-tional to the noise power itself. Furthermore, the averageof N independent measurements of the noise power is

√N

times more accurate than a single measurement. Notingthat a single independent measurement can be made in theminimum time interval 1/dν, we see that the maximumnumber of independent measurements that can be madein time t is t dν. Thus, the sensitivity equation for an idealreceiver is given by

�T = rms noise power ≈ TS/(t dν)1/2, (42)

where the “system temperature” TS is a measure of thenoise power from the receiver and t is the integration timeof the measurement. The rms noise power is expressedin kelvins and can be directly compared with the antennatemperature to determine the signal-to-noise ratio (SNR)of a particular measurement.

A modern radio telescope may have a system temper-ature of 20 K or less in the frequency range 1–10 GHz,where the radiation from the terrestrial atmosphere andgalaxy are both low. Noise temperatures in the millime-ter and submillimeter bands are substantially higher. Formeasurements of the radio continuum, dν may be chosento be 10 MHz or larger, depending on the characteristicsof the radio receiver being used. If we adopt a value of100 MHz for dν and 20 K for TS, then the rms noisepower obtained in 1 sec of integration is 0.002 K. Forplanetary spectroscopy, dν would have to be reduced to1 MHz or less and the rms noise power would increase to0.02 K. These noise fluctuations can be further reducedby increasing the integration times; however, systematiceffects within the receiving equipment prevent �T frombeing pushed to zero.

B. Spacecraft

Earth-based radio observations of the planets have limita-tions which affect certain types of measurements. Theselimitations include (1) the inability to obtain spatial res-olution on scales of a few meters or less, (2) restrictionson the viewing geometry of the planets, (3) limitations setby the opaqueness and variability of the terrestrial atmo-sphere, (4) the intrinsic faintness of the radio emissionsfrom planetary bodies, and (5) interference from man-made radio noise. The opacity of the terrestrial atmospherevaries with frequency. The atmosphere is opaque at fre-quencies lower than about 5 MHz due to the terrestrialionosphere. Attenuation due to the atmospheric gases, wa-ter vapor, and oxygen affects the centimeter, millimeter,and submillimeter bands, but observations are possible




from the ground by working in the transparent “windows”in the spectrum. Rain, fog, and clouds occasionally limitthe usefulness of the centimeter and millimeter bands.

To overcome these difficulties, a number of spacecraftradio instruments have been proposed, and several haveflown on U.S. spacecraft. The first planetary radio sys-tem on a U.S. spacecraft was a two-channel microwaveradiometer that operated at wavelengths of 13.5 and19.0 mm, flown on the Mariner II spacecraft to Venus in1962. The microwave radiometer system weighed ∼10 kgand used an average power of 4 W. This early system wasdesigned to take advantage of the high spatial resolutionand sensitivity that could be achieved from a spacecraft.Another radio astronomy experiment was placed on theVoyager spacecraft that was launched in the late 1970s tothe outer planets and targeted to fly by Neptune in 1989.This experiment measures the radio spectra of planetaryemissions in the range from 1.2 kHz to 40.4 MHz. The sys-tem was designed to measure planetary spectra below thefrequency range that is cut off by the Earth’s ionosphereand to take advantage of the unique viewing geometryprovided by the spacecraft. The Magellan Venus orbiterspacecraft carried a 12.6-cm radio receiver which allowedover 91% of the surface of Venus to be measured.

In the future, we expect to see many more radio as-tronomy spacecraft experiments. Spacecraft experimentswill allow the submillimeter spectral range to be observedwithout hindrance from the terrestrial atmosphere. Plan-etary spectroscopy in the submillimeter spectral range isexpected to reveal new information about the upper at-mospheres of the planets. The ESA ROSETTA spacecraft

FIGURE 7 (Left) Diurnal path of the Sun about Mercury and (right) representative brightness temperature curvesnear 4-cm wavelengths for “hot,” “warm,” and “cold” regions on Mercury.

will carry a millimeter- and submillimeter-wave spectro-scopic instrument (MIRO) to investigate the nucleus andcoma of a comet.

IV. RESULTS—PLANETS AND COMETS

A. Mercury

Radio measurements of Mercury show no evidence of anatmosphere. Estimates based on other techniques includ-ing spacecraft flyby instruments show the atmosphere onMercury to be extremely tenuous, with a surface pres-sure of ∼5 × 10−15 bar. For the purpose of interpretingthe radio data, it can safely be assumed that Mercury is anatmosphere-less planet. The radio emission from Mercuryis thermal in character, strongly controlled by the high ec-centricity of Mercury’s orbit and the synchronism betweenMercury’s spin period and its period of revolution. Solartidal effects have caused the period of axial rotation ofMercury to be 58.642 days, precisely two-thirds of its or-bital period of 87.97 days. One solar day on Mercury isequal to 3 stellar days or 2 Mercurian years. This periodequals 176 mean Earth solar days. Because of the synchro-nism between spin period and revolution period, the Suntakes a curious diurnal path in the sky as seen from thesurface of Mercury (Fig. 7). At some longitudes, the Sunrises and sets twice a Mercury day. At perihelion the in-solation is approximately twice its value at aphelion. Theinsolation reaches a maximum value of ∼14 × 103 W/m2,10 times the value for Earth. The visual albedo of Mercuryis similar to that of the Moon. The spin–orbit coupling and




eccentricity combine to cause the surface of Mercury tobe heated very nonuniformly in longitude. A pair of longi-tudes 180◦ apart alternatively faces the Sun at perihelion.These longitudes are preferentially heated because theirmidday insolation occurs when the Sun is nearly station-ary on the meridian and the Sun–Mercury distance is ata minimum. At longitudes 90◦ away from these hot lon-gitudes, the heating is identical but much less than thatreceived at the hot longitudes. The longitudinal tempera-ture variations on Mercury are indicated schematically bythe “hot,” “warm,” and “cold” regions shown on the leftin Fig. 7. This pattern of temperature variations is fixedon Mercury because the spin–orbit coupling causes theheating to be cyclic at each longitude (i.e., the same pairof longitudes faces the Sun at perihelion).

The solar heating cycle on Mercury suggests that thetwo longitudes that see the Sun directly overhead at peri-helion (receiving more than twice as much energy as thelongitudes 90◦ away) will be hotter than those 90◦ away.This is borne out by the radio observations. The right-handportion of Fig. 7 shows a schematic representation of thevariation of temperature at “hot,” “warm,” and “cold” re-gions on Mercury at a wavelength near 4 cm. Most of theolder, single-dish microwave observations of Mercury donot have sufficient resolving power to resolve the disk ofMercury, so the reported temperatures are averages overthe entire visible disk.

Radio images of the planet have been obtained withthe VLA and BIMA arrays. Such images clearly show thebrightness variation across the disk of Mercury. At shortwavelengths, where shallow layers are probed, the tem-perature is usually highest at local noon. However, whendeeper layers are probed, the diurnal heating pattern isless obvious, and one sees the two hot regions. Figure 8(left side) shows a radio image at 3.6 cm. At this wave-length one probes ∼70 cm into the crust. The hot regionat longitude 0◦ is clearly visible on the night side, whilethe high temperature on the day side is caused both bythe 180◦ hot longitude and solar insolation. Mercury’s hotand cold longitudes have been modeled in detail. The im-age on the right shows residuals after a thermal modelwas subtracted from the image on the left. Most remark-able here are the negative temperature differences near thepoles and along the terminator, suggesting that the polesand terminator are colder than predicted by the model.This is likely caused by surface topography, which causesa permanent shadowing effect at high latitudes and tran-sient effects in the equatorial regions, where crater floorsand hillsides are alternately in shadow and sunlight asthe day progresses. Some crater floors near the poles arepermanently shadowed, and radar observations have re-vealed evidence for the existence of water ice at such craterfloors.

Radio spectra and images have been together withMariner 10 IR data of the planet used to infer Mercury’ssurface properties. At first glance, Mercury’s surface isquite similar to that of the Moon. Due to the fact thatMercury, like the Moon, is continuously bombarded bysmall meteorites, one would expect the top few centime-ters to have a very low density, while deeper layers aremore compact. Observations indeed show that this is thecase on both bodies. Researchers found that the microwaveopacity on Mercury is roughly a factor of 2–3 smaller thanthat of most lunar samples. This suggests that the ilmenitecontent, which is the most common titanium-bearing min-eral on the Moon [(Fe, Mg)TiO], is much less abundanton Mercury than on the Moon. Ilmenite is also opaque atoptical wavelengths and is largely responsible for the darkappearance of the moon’s maria compared to its highlands.Its absence would explain why Mercury is brighter thanthe Moon at visible wavelengths.

B. Venus

Venus has the densest atmosphere of all the terrestrialplanets. The principal atmospheric constituents are car-bon dioxide and nitrogen (N2); their mixing ratios areapproximately 96.5% and 3.5%, respectively, below, 100-km altitude. Trace constituents below 100-km altitude arein the range of 0.1%. The Venus atmosphere is coveredwith thick clouds composed primarily of sulfuric acid andcontaminants, making the surface invisible from above.The total pressure at the bottom of the cloud layer(∼47 km) is approximately 1.3 atm. Water is highly de-pleted throughout the atmosphere. The mean physicalstructure of the atmosphere (pressure and temperature pro-file) is reasonably well known from the data returned by anumber of space probes. The surface pressure and temper-ature (on a mean surface) are approximately 94 atm and737 K, respectively.

The effective temperature of Venus deduced from mea-surements in the infrared is about 240 ± 8 K, correspond-ing to an altitude of approximately 60 km. Below this level,the temperature distribution generally follows that for anatmosphere that is in convective equilibrium. Convectiveequilibrium implies that the temperature gradient in the at-mosphere is close to the adiabatic value. The temperaturegradient is approximately 8.6 K/km. The high surface tem-perature is believed to be due to the greenhouse effect. Thephysical basis for this is that the visible light from the sunis only partially absorbed by the clouds and atmosphere.Some of the light reaches the surface and warms it. Theheated surface reradiates in the infrared. The atmosphereis highly absorbing in the infrared spectral region to CO2

and perhaps H2O. The atmospheric opacity traps the in-frared radiation, thereby raising the surface temperature.




FIGURE 8 Image on the right shows a 3.6-cm thermal emission map of Mercury observed with the VLA. The beamsize is 0.4 in. (1/10 of a Mercury radius). The direction to the Sun at the time of the observations and the morningterminator (dashed line) are superimposed on the image. The image shows thermal depressions at both poles andalong the sunlit side of the morning terminator. Contours are at 42 K intervals except for the lowest contour, whichis at 8 K (dashed contours are negative). The figure on the right shows the residuals after subtracting a model fromthe observed map. [From Mitchell, D. L., and de Pater, I. (1994). “Microwave imaging of Mercury’s thermal emission:observations and models,” Icarus 110, 2–32.]

The atmosphere of Venus is opaque at millimeter andshort centimeter wavelengths, gradually becoming trans-parent at longer wavelengths. Individual spectral linesare not observable below the clouds because of pres-sure broadening. The total vertical optical depth of theatmosphere of Venus at a wavelength of 1 cm is estimatedto be slightly less than 20 and to vary approximately as λ−2

(optical depth = 1 at ∼4 cm). A little more than half of thetotal opacity is due to collision-induced, nonresonant ab-sorption in CO2; the remaining opacity is produced by theminor constituents in the atmosphere. Other known or sus-pected microwave absorbers in the atmosphere are H2O,SO2, H2SO4, and the sulfuric acid particles in the clouds.Near wavelengths of 6 cm and longward, the atmosphereis sufficiently transparent that it is possible to measurethe surface temperature of Venus using radio astronomi-cal methods. The right side of Fig. 8 shows the continuumspectrum of Venus from a few millimeters wavelength outto approximately 6 cm. The left side of Fig. 9 shows thetemperature versus altitude profile of Venus. The bright-ness temperature is seen to rise from about 225 K at 3 mmto about 700 K near 6 cm. This increase in brightnesstemperature is due to the decreasing opacity of the atmo-sphere with increasing wavelength. The decreasing opac-ity allows radio waves to escape from deeper regions in theatmosphere, where it is warmer due to the adiabatic lapserate. At wavelengths longer than ∼15 cm the brightnesstemperature decreases to ∼600 K.

Radio interferometer data, radar data, and spacecraftdata have been used to study the surface of Venus, inparticular to determine the dielectric constant. Radar re-flectivity data place the dielectric constant in the range4–5. The Magellan radiometer experiment observed the12.6-cm-wavelength radio emissivity of more than 91%of the Venus surface. With its 2-deg beam width, Magel-lan observations achieved surface resolutions that variedfrom 15 by 23 km at periapsis (10◦N latitude) to about 85km at the north pole. The global mean value of emissivityseen using horizontal linear polarization is 0.845, a valuethat corresponds to a dielectric permittivity of between4.0 and 4.5, depending on the surface roughness. Thesevalues are considerably greater than the values for Mer-cury, Mars, and the Moon, which range from 2.0 to 2.5.The higher values are suggestive of a surface composedof dry rock not unlike many rocks of the Earth’s surface.These values are consistent with the dry basaltic mineralsthought to compose the bulk of the Venus surface. Theobservations have confirmed earlier findings that a few re-gions on Venus, primarily located at high elevations, pos-sess unexpectedly low values of radiothermal emissivity,occasionally reaching as low as 0.3.

Carbon monoxide is an important constituent of the up-per atmosphere of Venus. It is formed primarily by thedissociation of carbon dioxide by solar ultraviolet radia-tion and is removed by chemical and transport processesin the atmosphere. The ground and first excited rotational




FIGURE 9 Schematic representation of the spectrum of Venus from 1 mm to 6 cm (right) and temperature versusaltitude profile (left). The figure illustrates how the atmosphere is probed in altitude by changing the wavelength of theobservations.

states of CO (located at very high altitudes in Venus’ at-mosphere) have been observed to absorb the hot contin-uous background of the deeper atmosphere. Examples ofCO spectra on Venus’ day- and night-side hemisphere areshown in Fig. 10. Observed spectral lines have included12CO(0–1), 12CO(1–2), C18O(1–2), and 13CO(1–2). Theseobservations have been particularly useful for exploringthe altitude range from 70 to 110 km.

It has been possible to derive the vertical temperatureand mixing ratio profiles of CO in the upper atmosphereof Venus from such observations. As shown in Fig. 9,the spectra reveal considerable variability of CO abun-dance, which varies with solar phase angle. The variabilityis believed to be the result of large-scale circulation in theupper atmosphere of the planet. Detailed studies of thisvariability have been undertaken with arrays of telescopeswhich operate at millimeter wavelengths. With such ar-rays the planet can be imaged in the CO lines, so the COconcentration and temperature profile at all solar phase an-

FIGURE 10 Observed absorption spectra of J = 0 → 1 transi-tion of CO in the atmosphere of Venus. Line center frequencyis 115 GHz. [Adapted from Schloerb, P. (1985). In “ProceedingsESO-IRAM-ONSALA Workshop on Submillimeter Astronomy.”

gles can be measured simultaneously. In addition, throughmeasurements of the Doppler shift of the lines at variouslocations on Venus’ disk, the winds in Venus’ mesospherecan be studied. For the CO(0–1) transition, a mean windspeed of 100 m/sec in the spectral-line-forming regionproduces a Doppler shift of 38 kHz. Such Doppler shiftshave been observed at altitudes at least as high as 100 km.Continued observations of these spectral lines will leadto a better understanding of the large-scale circulation inVenus’ upper atmosphere.

C. Mars

Mars moves in an orbit slightly larger than the Earth’s, al-ways turning its day side toward the Earth as it approaches.Earth-based measurements of the night side are impossi-ble and phase angle coverage is greatly restricted. The axisof rotation is tilted from the perpendicular to the plane ofits orbit by 25◦, about the same as for the Earth. Radioobservations of the disk brightness temperature of Marsshow it to have a nearly flat spectrum from about 1 mmto 21 cm. The mean disk brightness temperature is about215 K. As seen from the Earth, the average surface disktemperature varies by ±15 K as the sub-Earth point movesfrom afternoon to morning and from midlatitudes to equa-torial latitudes. Most observational data used in thermalmodeling studies have come from infrared measurementsmade from spacecraft. The infrared measurements arelimited to the near-surface properties. Microwave imagesobtained with the VLA have extended the thermal mod-els to the subsurface layers of the planet. Microwave im-ages, in contrast to single-dish observations, also yieldinformation on the spatial variations of the brightnesstemperature. For example, VLA images show the polarregions to be significantly colder than the disk-averagedtemperature.




The centimeter radio brightness temperatures of Marshave been found to vary as a function of the central merid-ian longitude of the planet. Temperature differences aslarge as 5–10 K are observed over the full range of lon-gitudes. The variations are believed to be due to noncon-formity in the Martian surface properties; however, nocompletely satisfactory explanation of the observationsexists.

The Martian atmosphere is very tenuous, having a sur-face pressure some 200 times less than that of the Earth.The primary constituent of the lower atmosphere is CO2.Photolysis of CO2 by solar ultraviolet radiation producesCO and O2. The diatomic molecule CO plays an impor-tant role in determining the millimeter-wave spectrum ofMars.

Both the ground-state and first-excited-state transitionsof CO have been observed in the Martian atmosphere. Thealtitude distribution of CO has been inferred by interpret-ing the observed line shape in terms of pressure broad-ening. A column abundance of CO equal to (2–5) × 1020

molecules/cm2 has been derived from the measurements.This number is very stable over time, even though the COline profiles show significant variability. This variabilityhas been used to monitor Mars’ thermal structure: the at-mospheric temperature rises significantly during globaldust storms, since the dust grains, heated by the Sun, warmup the atmosphere while at the same time preventing sun-light from penetrating down to the surface. Water vapor(from HDO observations at 226 GHz) has also been ob-served on Mars and used to determine water vapor distribu-tion and atmospheric behavior. Clancy and collaboratorsused the VLA at a wavelength near 1.35 cm to image thewater vapor in Mars’ atmosphere. The water vapor showsup in emission around the planet, where the path lengththrough the atmosphere is largest. The data clearly showthe absence of emission over Mars’ polar caps, where theatmospheric temperature is so low that all the water hasbeen frozen out. Note that the ground-based detection ofwater vapor in Mars’s atmosphere could only be achievedbecause of the VLA’s high angular resolution, so that theatmosphere on the limb could be separated from the planetitself.

D. Jupiter

Jupiter was the first planet detected at radio wavelengths.The discovery observations occurred in 1955, at the verylow frequency of 22.2 MHz. Prediscovery observationsof Jupiter were later traced back to 1950. Subsequent ob-servations of Jupiter revealed that its radio spectrum isexceedingly complex, showing both thermal and nonther-mal emission mechanisms. Thermal emission from theatmosphere dominates the Jovian spectrum shortward of

7 cm. Nonthermal synchrotron emission dominates thespectrum from ∼3 m to 7 cm; brightness temperatures ex-ceed 105 K for the synchrotron component. Longward of7.5 m, Jupiter emits strong and sporadic nonthermal radia-tion. The radiation exhibits complex frequency, time, andpolarization structure. The brightness temperature of thiscomponent exceeds 1017 K, suggesting a coherent sourceof emission. The schematic appearance of Jupiter’s spec-trum is shown in Fig. 11.

Observations of Jupiter at high angular resolution withradio interferometers have been used to map the syn-chrotron radiation from Jupiter’s radiation belts and to sep-arate the thermal from the nonthermal synchrotron com-ponents. The nonthermal component is easily identifiablewith a radio interferometer because it is greatly extendedrelative to the optical disk of Jupiter and is strongly lin-early polarized.

The thermal component originates in the Jovian atmo-sphere. The observations are consistent with a deep modelatmosphere, composed mostly of hydrogen and helium, inconvective equilibrium. The principal source of opacity isammonia (NH3), which exhibits very strong absorption inthe microwave spectral region.

In December 1995 the Galileo spacecraft released aprobe into the atmosphere of Jupiter, which relayed itsfindings to the spacecraft via radio signals at a frequencyof 1.4 GHz. By analyzing the attenuation of the probe ra-dio signal, the ammonia abundance in Jupiter’s deep atmo-sphere (at pressures over 8 bar) was derived to be a factorof ∼3.5 larger than the solar N value. Ground-based mi-crowave measurements are most sensitive to layers wherethe clouds form (∼0.5 bar) down to roughly 10–15 bar.The ground-based microwave measurements do not showas much ammonia as the probe. Apparently, the ammoniaabundance in Jupiter’s deep atmosphere is significantlydecreased at higher altitudes, to roughly half the solar Nvalue just below the upper cloud deck. Scientists do not yetunderstand why there is so much less ammonia in the upperregions of Jupiter’s atmosphere compared to deeper layers.

VLA images resolve the disk of Jupiter and show thefamiliar zone-belt structure at 2–6 cm. Figure 12 showsa 1.2-arc sec resolution VLA radio image at 2-cm wave-length. The disk diameter of Jupiter was 32 arc sec atthe time of the radio observations. Radio images, such asshown in Fig. 12, are usually smeared in longitude, sincethe observations are integrated over a substantial time in-terval. The bright (white) beltlike regions are indicativeof a higher brightness temperature, which is likely due toa relative depletion of NH3 gas compared to the darkercolored regions. Since the radio waves originate in andbelow the visible cloud layers, such images contain infor-mation complementary to that obtained at IR and opticalwavelengths. From the images, the latitudinal variation




FIGURE 11 Schematic representation of the spectrum of Jupiter, showing the frequency ranges for which atmo-spheric emission dominates, synchrotron emission dominates, and sporadic nonthermal emission dominates.

of NH3 gas can be obtained, in addition to the altitudedistribution. Such variations must be due to dynamicalprocesses on the planets, for example, zonal winds, up-welling, and subsidence of gas. The zone-belt structure onJupiter is consistent with upwelling gas in the zones andsubsidence in the belts. Images taken in different yearsshow clear variations in the zone-belt structure, indicativeof meteorological changes.

Radio interferometric maps of Jupiter’s synchrotronemission have been made at a number of different wave-

FIGURE 12 Radio photograph of Jupiter at a wavelength of2.0 cm obtained with the VLA. Resolution is 1.2 arc sec. Equatorialdiameter of Jupiter is 32 arc sec.

lengths. It has been possible to deduce a great deal ofinformation about Jupiter’s magnetosphere from the radiomeasurements. The radio astronomical measurementsprovided convincing proof that Jupiter has a strong mag-netic field, and this information was used to design thefirst spacecraft sent to Jupiter. The radio measurementsshow that the magnetic field is primarily dipolar in shapewith the dipole axis tilted about 10◦ with respect toJupiter’s rotational axis. Using the well-developed theoryof synchrotron emission (summarized in Section II.C),it has been possible to determine energies and densitiesof the high-energy electrons that are trapped in Jupiter’smagnetic field.

Figure 13 shows a radio image of Jupiter’s synchrotronradiation. The main radiation peaks are indicated by theletters L and R, and the high-latitude emission peaks by Ln,Ls, Rn, and Rs. Magnetic field lines at jovicentric distancesof 1.5 and 2.5 (from the O6 magnetic field model) are su-perimposed. The resolution is 0.3 Jovian radii, roughly thesize of the high-latitude emission regions. Thermal emis-sion from Jupiter’s atmosphere appears as a disk-shapedregion in the center of the figure.

Figure 14 shows a tomographic map of the emissionregion, obtained by observing Jupiter at all longitudes andreconstructing a three-dimensional map. The emission isseen to be confined to the magnetic equatorial plane outto a distance of ∼4 Jovian radii. Several intriguing fea-tures are visible. The main radiation peaks (L and R on




FIGURE 13 Radio photograph of Jupiter’s synchrotron emission at a jovicentric longitude of 312◦. The image wastaken at a wavelength of 20 cm, using the Very Large Array in June 1994. [After de Pater, I., and Sault. (1998).J. Geophys. Res. Planets 103(E9), 19,973–19,984.]

Fig. 13) are usually asymmetric. One of the peaks ap-pears to be brighter than the other peak. The asymmetryof these main radiation peaks is caused by deviations inJupiter’s magnetic field from a pure dipole configuration.These deviations are evident in Fig. 14, where the mainring of radiation is clearly warped like the surface of apotato chip. If Jupiter’s field were a dipole field, this ringwould be flat, and the radiation peaks (Fig. 13) would al-ways be equal in intensity, though the intensity would vary

FIGURE 14 Three-dimensional tomographic reconstruction ofJupiter’s nonthermal radio emissivity. The planet itself is shown asa black sphere in this visualization. [After de Pater, I., and Sault.(1998). J. Geophys. Res. Planets 103(E9), 19,973–19,984.]

with jovian rotation, such that it would be smallest whenone of the magnetic poles is directed toward us. The sec-ondary emission peaks (Ln, Ls, Rs, Rn in Fig. 13) becomehigh-latitude rings when viewed in a three-dimensionalimage. These peaks are produced by electrons at their mir-ror points, and they reveal the presence of a relatively largenumber of electrons which bounce up and down the fieldlines at a Jovian distance of 2–2.5 Jovian radii. It is be-lieved that these electrons may have been scattered outof the magnetic equatorial plane, perhaps by the MoonAmalthea, which orbits Jupiter at a distance of 2.5 Jovianradii.

The total radio intensity of Jupiter varies significantlyover time (years), and appears to be correlated with so-lar wind parameters. The impact of comet D/Shoemaker-Levy 9 with Jupiter in July 1994 caused a sudden sharp in-crease in Jupiter’s total flux density, by ∼20%. At the sametime the brightness distribution of the radio flux densitychanged drastically. These observations suggest that theimpact and associated phenomena significantly modifiedthe electron distribution and possibly the magnetic fieldas well.




At frequencies below 40 MHz, Jupiter is a strongemitter of sporadic nonthermal radiation. A decameter-wavelength (DAM) component observable from theground is characterized by complex, highly organizedstructure in the frequency–time domain and dependenton the observer’s position relative to Jupiter. The satel-lite Io modulates the DAM emission. The Voyager space-craft added significantly to our knowledge of this low-frequency component when it flew by Jupiter in 1979.A kilometric-wavelength (KOM) component was discov-ered at frequencies below 1 MHz and the observations ofthe DAM component were significantly improved. The ex-tremely high brightness temperatures (>1017 K), narrow-bandwidth emissions, and sporadic nature all suggest thatthe very low frequency emissions from Jupiter are gener-ated by energetic particles acting coherently and interact-ing with the plasma that surrounds Jupiter. The details ofthe emission process are not well understood.

E. Saturn

Radio emission from Saturn has been observed from theEarth over a wavelength range from 1 mm to approxi-mately 70 cm. The emission is thermal throughout thisband, arising in both the atmosphere and the rings. Theatmospheric emission is similar to that observed fromJupiter. Model studies indicate that Saturn, like Jupiter,has a deep convective atmosphere. Hydrogen and heliumform the bulk of the atmosphere, whereas ammonia intrace amounts provides most of the microwave opacity.High-resolution radio images of Saturn also give informa-tion on the latitudinal distribution of NH3 gas. Figure 15shows a VLA image at 6-cm wavelength: the resolution is1.5 arc sec and the disk diameter is 16.8 arc sec. A brightband can be distinguished at midlatitudes, indicative of anaverage lack of NH3 gas over the altitude region probedat this wavelength. The region at midlatitudes is likely aregion of subsiding gas, just like the bright belts seen onJupiter. In the 1990s the zonal patterns on Saturn changeddrastically compared to what was seen in the 1980s, in-dicative of strong dynamical interactions.

As shown in Figs. 15 and 16, interferometer observa-tions of Saturn also detect the thermal emission from thering particles. Most of the radio emission is due to scat-tering of Saturn’s emission off the ring particles. In frontof the planet, the rings are visible as an absorption fea-ture; they block out Saturn’s radio emission. The scatter-ing characteristics of the rings contain information on thering particle sizes and composition.

Interferometer observations of Saturn at centimeter andmillimeter wavelengths have detected thermal emissionfrom the ring particles. The rings have a low brightnesstemperature, approximately 10 K. The presence of ring

FIGURE 15 Radio photograph of Saturn at a wavelength of6.14 cm obtained with the VLA. Resolution is 1.5 arc sec. Equa-torial diameter of Saturn is 16.83 arc sec. [After de Pater, I., andDickel, J. R. (1991). Icarus 94, 474–492.]

particle sizes larger than a few centimeters is suggestedby the radio observations. The observations are consistentwith the bulk properties of the ring particles being thoseof water ice.

The Voyager spacecraft detected two distinct classes ofnonthermal emissions from Saturn at frequencies below

FIGURE 16 Radio photograph of Saturn at a wavelength of 2.0cm obtained with the VLA. Resolution is 1.5 arc sec. Equatorialdiameter of Saturn is 16.83 arc sec. [After de Pater, I., and Dickel,J. R. (1991). Icarus 94, 474–492.]




1 MHz. These emissions are not observable from the Earthbecause of the opaqueness of the Earth’s ionosphere at fre-quencies below a few megacycles. The first class, calledSaturn kilometric radiation, is a relatively narrow bandpolarized emission. The second class is a broadband, im-pulsive emission called the Saturn electrostatic discharge.

F. Uranus

Uranus is unique among the planets in having its rota-tion axis tilted close to the plane of the ecliptic. Thenorth pole of Uranus is inclined ∼98◦ to the ecliptic plane(8◦ south of the plane), and the seasons on Uranus average21 terrestrial years in length. The effect of this geometryon the large-scale circulation of the Uranium atmosphereis not fully understood, but it is expected to be significant.

As in the case of both Jupiter and Saturn, the disk bright-ness temperatures of Uranus significantly exceed the ex-pected equilibrium temperature. The observed tempera-tures are greater than 100 K at wavelengths greater than afew millimeters and longward, whereas the predicted ef-fective temperature is only about 55 K. The radio emissionfrom Uranus is unpolarized within the measurement un-certainties of a few percent. Interferometer observationsof Uranus show the emission to be confined to the solid an-gle of the visible disk, providing evidence that the excessemission is from the atmosphere and is not synchrotronemission. It is believed that the emission from Uranus isthermal, originating in the atmosphere of the planet.

The radio emissions from Uranus arise from sufficientdepths that collision-induced absorption by hydrogen isan important source of opacity at millimeter wavelengths.Ammonia is severely depleted in Uranus’ atmosphere, atleast at pressure levels less than 25 bar. Since, based uponplanet formation theories, nitrogen must be present in atleast solar proportions, it is believed that ammonia gasis abundant at deeper levels, but reacts with H2S to forma cloud of NH4SH. If indeed this process accounts forthe observed depletion in NH3, hydrogen sulfide shouldbe enriched in Uranus’ atmosphere by about an order ofmagnitude over solar S. Such an abundance of H2S itselfwill contribute to the radio opacity in Uranus’ atmosphereand actually help reconcile observed spectra with models.

Another interesting aspect of the radio emission fromUranus is that its total intensity varies slowly over time.With the help of interferometric (VLA) observations, itis well established that the Uranus pole is warmer thanits equator. This will certainly lead to time variations dur-ing Uranus’ orbit around the Sun. It is not known, how-ever, whether this indeed fully explains the observed timevariability.

The Voyager spacecraft detected a wide variety of ra-dio emissions from Uranus during its encounter in January

1986. Most of the emissions were polarized and probablydue to maser-cyclotron emission. The emissions range infrequency from about 20 kHz to 800 kHz, well below thefrequency range that is observable from the Earth. Theemissions suggest a magnetosphere rich in magnetohy-drodynamic phenomena.

G. Neptune

Disk brightness temperature measurements of Neptune atcentimeter and millimeter wavelengths are sparse, but sug-gest a spectrum very similar to that of Uranus. The diskbrightness temperatures exceed the predicted equilibriumtemperature by 50 K or more. High-angular-resolutionmeasurements obtained with the VLA show that the ex-cess emission is not due to synchrotron emission. As inthe case of Uranus, model studies suggest that ammoniamust be depleted on Neptune (as on Uranus) by roughlytwo orders of magnitude compared to solar nitrogen val-ues to explain the high brightness temperatures that areobserved.

This depletion may be caused by a nearly complete re-moval of NH3 gas in the upper atmosphere through theformation of NH4SH, the same process which depletesammonia in the Uranus atmosphere. On Neptune the H2Sabundance must be even larger than on Uranus, about 30times the solar sulfur/hydrogen ratio. Although ammoniagas may be close to the solar N value in Uranus’ deepatmosphere, it must be substantial subsolar throughoutNeptune. Here a problem arises: A subsolar value for ni-trogen gas is inconsistent with theories on planet forma-tion. If a planet forms directly from the primordial solarnebula, the elemental abundances must be equal to thatmeasured on the Sun. Condensable materials accrete assolids, sublime in the protoplanet’s atmosphere and there-fore enhance the elemental abundances above solar values.Carbon, sulfur, and oxygen compounds, present as CH4,H2S, and H2O in the giant planets, are therefore enhancedabove solar values. Similarly, nitrogen is expected to beenhanced above solar N. A subsolar value on Neptune issimply not possible. This dilemma was solved with thedetection of emission lines in the 1- to 3-mm band of COand HCN in Neptune’s upper atmosphere.

Since both lines are seen in emission, CO and HCNmust be located above the tropopause, in Neptune’s strato-sphere. Although CO may be brought up from deep depthsthrough rapid convection, HCN must be formed in thestratosphere from nitrogen and carbon products, sinceHCN, if it existed in Neptune’s deep atmosphere, wouldfreeze out on its way up, well before it could reachthe stratosphere. If, however, much of the nitrogen inNeptune’s atmosphere were present in the form of N2

rather than NH3, the N2 might convect rapidly upward and




form HCN in the stratosphere through chemical reactionswith carbon products. Moreover, if nitrogen existed in theform of N2 rather than NH3, the total nitrogen abundancein Neptune’s atmosphere would be consistent with planetformation theories.

The Voyager spacecraft detected a variety of low-frequency radio emissions from Neptune during its en-counter in 1989. The emissions were similar to thoseobserved from the other major planets.

H. Comets

Prior to the 1960s, comets were investigated primar-ily using visible-wavelength observations. The firstinfrared detection of a comet was achieved in themid-1960s. Although radio astronomers had attempted todetect cometary emissions since the 1950s, the first widelyaccepted radio detection of a comet is that of the 18-cmOH transitions in Comet Kohoutek (1973). Radio obser-vations of comets have been used to study all of the majorcomponents of comets: nucleus, dust, neutral gas, and theplasma.

Continuum observations of thermal emission fromcomets provide information on the nucleus temperatureand on the large dust grains which surround the nucleus.The thermal emission from comets is very weak, andsensitive receiving systems are needed to make a detec-tion. Short centimeter, millimeter, and submillimeter ob-servations have been the most successful for the detectionof thermal emission. In the 1990s sensitive detectors atmillimeter and submillimeter wavelengths came on line,just in time to observe two very bright comets: CometHyakutake in 1996 and Comet Hale-Bopp in 1997. Radiospectra at submillimeter to millimeter wavelengths wereobtained for both comets. The thermal emission is clearlydominated by emission from dust grains rather than thecometary nucleus, and the data have been used to de-rive the dust mass and dust mass production rate for eachcomet. Continuum observations of comets will be greatlyimproved when the new large millimeter and submillime-ter arrays become available and when thermal emissionmeasurements from spacecraft are possible.

Radio astronomy of comets has made its most signifi-cant advances in the area of spectroscopy. Many so-calledparent molecules (molecules which sublimate directly offthe nucleus, in contrast to daughter molecules, which areproducts of the parents) have been observed at radio wave-lengths through their rotation lines in the millimeter andsubmillimeter bands. Observations of these spectral linesgive valuable information on the icy composition of thecometary nucleus, gas production rates, physical condi-tions in coma, and variation of these in time and heliocen-tric distance.

The timely appearance of the bright comets Hyaku-take and Hale-Bopp greatly expanded our knowledgeof cometary volatiles. The number of identified parentmolecules increased by more than a factor of two throughobservations of these comets; most of these new specieswere detected in the millimeter and submillimeter regions.Spectroscopic observations of Comet Hale-Bopp, whichcould be followed in its orbit for several years, yieldedinvaluable data on composition and gas production rates.Gas production rates of different molecules could be fol-lowed over large heliocentric distances (Fig. 17). At dis-tances greater than 3 AU, the sublimation was dominatedby gases more volatile than water. Carbon monoxide, themost volatile species observed, could be detected at aheliocentric distance of 7 AU. It displayed a steady in-crease in brightness while the comet moved in towardthe Sun. This gas clearly must have been key to the

FIGURE 17 Evolution of molecular production rates of cometHale-Bopp as a function of heliocentric distance. Left : Preperi-helion data; right : postperihelion data. [After Biver, N., Bockelee-Morvan, D., Colom, P., Crovisier, J., Germain, B., Lellouch, E.,Davies, J. K., Dent, W. R. F., Moreno, R., Paubert, G., Wink, J.,Despois, D., Lis, D. C., Mehringer, D., Benford, D., Gardner, M.,Phillips, T. G., Gunnarsson, M., Rickman, H., Bergman, P., Jo-hansson, L. E. B., Winnberg, A., and Rauer, H. (1999). EarthMoon, Planets 78, 5–11.]




observed visible brightness of the comet at these largeheliocentric distances. At a heliocentric distance of 3 AU,OH became the most abundant species, confirming thatthe composition of the comet is dominated by water-ice(H2O → OH + H). Inside a heliocentric distance of 1.5AU all species showed a dramatic increase in productionrates. Radio images of various species have been obtainedand have been used to derive the relative importance ofsublimation directly from the nucleus or from grains inthe coma. This varies from gas to gas, and probably differsfrom comet to comet.

As mentioned above, the first radio detection of a cometwas that of the 18-cm OH line. The study of this line hasbeen an important component of cometary research forover 25 years. The 18-cm line is split into four transitionsat 1612, 1665, 1667, and 1721 MHz. The observed in-tensity of the OH line is quite variable. The line is seenin emission or absorption depending on the comet’s he-liocentric velocity. The explanation of this effect is thatit is due to pumping of the OH molecules by solar UVphotons. If the comet’s heliocentric velocity is such thatFraunhofer absorption lines from the Sun shift into theexcitation frequency, the OH molecules are not excited.At all other times they are. This variation in excitation isknown as the Swings effect. When OH is not excited, itis seen in absorption against the galactic background. If itis excited, the emission is actually maser emission ratherthan simple thermal emission.

V. PROSPECTS FOR THE FUTURE

Planetary radio astronomical observations were initiallylimited to measurements of the disk-averaged brightnesstemperatures and to the strong nonthermal radio emis-sion from Jupiter. With improved spatial resolution andhigh-sensitivity receiving systems, it has been possibleto map the planets (and satellites and comets) and carryout high-resolution spectroscopic observations. With therapidly improving instrumentation now on the horizon,eventually it should be possible to study the planets us-ing ground-based and spacecraft instruments in nearly thesame detail in which the Earth is being studied with com-bined sensors on weather satellites and ground stations.As angular resolution improves with time, it should bepossible to map the vertical and horizontal distributionsof certain chemical species within planetary atmospheres,measure wind speeds, and search for local variations insubsurface properties. Both ground-based radio telescopesand spacecraft radio receivers will play a role in future ob-servations. Large ground-based telescopes will have suf-ficient resolution to examine the global properties of theplanets out to Neptune and to study satellites, asteroids,

and comets. The advent of lighter weight and lower powerradio receivers will enhance the possibilities of placing ra-dio experiments on spacecraft. Radio telescopes workingat submillimeter wavelengths are gradually becoming areality as a few mountain-top observatories are nearingcompletion and plans for a submillimeter space telescopeare being discussed in a number of countries. The shorterwavelength region of the spectrum will provide new op-portunities to study the upper atmospheres of the planetswith spectroscopic techniques capable of detecting hereto-fore unobserved transitions that occur in the submillimeterand infrared regions. In addition, the shorter wavelengthswill provide high angular resolution with only moderate-size telescopes. In summary, the future prospects for plan-etary radio astronomy are bright. This optimistic outlookis based on radio astronomical systems currently underdevelopment. The evolution of radio technology will un-doubtedly lead to an even brighter future for planetaryradio astronomy.

ACKNOWLEDGMENT

The portion of the research described in this publication was carried out atthe Jet Propulsion Laboratory, California Institute of Technology, undera contract with the National Aeronautics and Space Administration.


PLANETARY ATMOSPHERES • RADIATION SOURCES •RADIO-ASTRONOMY INTERFEROMETRY • RADIOMETRY

AND PHOTOMETRY • SOLAR SYSTEM, GENERAL

BIBLIOGRAPHY

Berge, G. L., and Gulkis, S. (1976). “Earth-based radio observations ofJupiter: Millimeter to meter wavelengths,” In “Jupiter” (T. Gehrels,ed.), University of Arizona Press, Tuscon, AZ.

de Pater, I. (1990). “Radio images of the planets,” Annu. Rev. Astron.Astrophys. 28, 347–399.

de Pater, I. (1999). “The solar system at radio wavelengths,” In “Ency-clopedia of the Solar System” (P. Weissman, L. McFadden, and T. V.Johnson, eds.), pp. 735–772, Academic Press, New York.

Dessler, A. J. (ed.). (1983). “Physics of the Jovian Magnetosphere,”Cambridge University Press, Cambridge.

Janssen, M. A. (ed.). (1993). “Atmospheric Remote Sensing by Mi-crowave Radiometry,” Wiley, New York.

Lewis, J. S., and Prinn, R. G. (1984). “Planets and Their Atmospheres,”Academic Press, Orlando, FL.

Morrison, D. (1970). “Thermophysics of the planet Mercury,” Space Sci.Rev. 11, 271–307.

Muhleman, D. O., Orton, G. S., and Berge, G. L. (1979). “A model ofthe Venus atmosphere from radio, radar, and occultation observations,”Astrophys. J. 234, 733–745.

Sullivan, W. T., III (ed.). (1984). “The Early Years of Radio Astronomy,”Cambridge University Press, Cambridge.

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Encyclopedia of Physical Science and Technology EN013A-638 July 26, 2001 20:11

Radio-Astronomy InterferometryT. Joseph W. LazioNaval Research Laboratory

I. Theory of InterferometryII. Design of a Radio-Interferometric Array

III. Imaging with Radio-Interferometric ArraysIV. Future Prospects

GLOSSARY

Closure phase Sum of the measured coherence phasearound a triad of array elements; invariant to all ef-fects that factorize per element, e.g., extra path lengthsintroduced into the signal path by the atmosphere.

Coherence Time-averaged product of the electric field attwo different points in space. For a distant incoherentsource the measured coherence is a Fourier transformof the source brightness distribution.

Correlator Computer for calculating the coherence be-tween two antennas, usually realized with digital logic.

Deconvolution Correction for the effects of limited sam-pling of the coherence function. Accomplished by uti-lizing knowledge of the coherence sampling functionand a priori information about the source brightnessdistribution, such as positivity and confinement.

Heterodyne Shift in the frequency of a spectrum accom-plished by adding a carrier wave at an offset frequency,and then passing the signal into a nonlinear device.

Interferometer Device for measuring coherence of theelectromagnetic field.

Self-calibration Calibration of interferometric array us-ing the source of emission being imaged in addition

to an external calibrator; relies on factorization of sys-tematic effects by antenna.

INTERFEROMETERS are used widely in radio as-tronomy for high angular resolution imaging of celestialobjects. An interferometer measures the time-averagedproduct or coherence of the electromagnetic field at twoseparated points. Each measurement corresponds to a sam-ple of the Fourier transform of the brightness distributionof an object. From arrays of such radio interferometersand by exploiting the rotation of the Earth to change theaspect of a single interferometer, many such samples canbe accumulated, and an image formed in a computer. In-terferometers have been formed with antenna separationsexceeding the Earth’s diameter, providing angular resolu-tions of better than a milliarcsecond (∼5 nanoradians), andrecent developments enable ever shorter and ever longerwavelengths to be used.

I. THEORY OF INTERFEROMETRY

At optical wavelengths astronomical imaging is performedalmost exclusively by monolithic telescopes, which either

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676 Radio-Astronomy Interferometry

reflect or refract light to a focal plane. Diffraction lim-its the highest resolution obtained to approximately λ/D,where λ is the observing wavelength and D is the diameterof the aperture. At radio wavelengths (λ ≈ 0.001–10 m)resolutions comparable to those obtained in the opticalwould require telescopes with aperture diameters of tensor hundreds of kilometers. In optical astronomy the desirefor higher angular resolution led to the development ofthe Michelson interferometer, in which light beams fromtwo (widely) separated mirrors are combined to form in-terference fringes. After the initial experiments, opticalinterferometry was not pursued until recently because ofthe numerous practical difficulties including stabilizationof the light paths, atmospheric turbulence, and low signallevels. At radio wavelengths these problems are much sim-plified, especially at moderate resolution of an arcsecond(5 microradians) or more: stabilization of the signal path ispossible for antenna separations up to a few tens of kilome-ters, the effects of the Earth’s atmosphere may be removedthrough calibration, and photon-rich radio signals can bedivided and amplified many times with a negligible impacton the signal-to-noise ratio, unlike typical optical signalswhich consist of relatively few photons and cannot be am-plified coherently. Furthermore, radio frequencies are lowenough that electronic equipment is capable of measuringthe electric field itself and preserving phase information,in contrast to optical interferometers which generally arelimited to measuring the second moment of the electricfield (the intensity).

As a result radio interferometry has been developedvigorously over the past 40 years since Ryle and Vonbergbuilt the first simple Michelson adding radio interferom-eter. Many variants of the Michelson interferometer weretried and discarded, though some turned out to be of im-portance in other fields. (For example, Hanbury Brownand Twiss developed an intensity interferometer in whichinterference fringes were formed from the electric fieldintensity. The utility of the intensity interferometer is lim-ited by poor sensitivity, but it did contribute to the develop-ment of quantum optics, because intensity correlations im-plied the existence of photon bunching, then unknown.) AMichelson interferometer forms fringes by direct additionof the signals, but systematic errors are troublesome. Forexample, a strong, spatially extended background source(e.g., the Galactic radio emission) will magnify the effectsof amplifier gain drifts.

Because the electric field can be measured directly, analternative design—a multiplying interferometer—is usu-ally preferred in order to reduce the contribution of uncor-related components of the signal. A multiplying interfer-ometer forms the electric field coherence or time-averagedproduct of the electric field, E(r, t), at two separate pointsin space and time,

�(ri , r j , ti , t j ) = ⟨E(ri , ti )E∗(r j , t j )

⟩t

where 〈 · · · 〉t denotes an average over time. Because theelectric field can be sampled directly and digitized, themultiplication and averaging can be realized in a special-purpose digital computer.

Given the considerable spatial extent of most celes-tial objects, it might seem surprising that measurementsof the electric field coherence at the Earth could yieldany information about their structures. Indeed, most radiosources emit incoherent radiation: At the source � = 0 un-less ri = r j and ti = t j . Figure 1 illustrates how coherencearises in a distant radiation field. The two point sourcesP1 and P2 are incoherent. However, at the distant pointsQ1 and Q2, the electric field contains contributions fromboth P1 and P2 and is therefore partially coherent. The gen-eralization of this idea leads to the van Cittert-Zernike the-orem. A simple version of this theorem produces a Fouriertransform relation between the sky brightness B(x, y) andthe measured coherence function

�(u, v) =∫

B(x, y) e2π i(ux+vy) dx dy,

where position on (strictly: tangent to) the celestial sphereis measured in radians in a Cartesian system (x, y) cen-tered on the source and antenna separations are measuredin wavelengths in a Cartesian system (u, v) aligned with(x, y). (More general versions of this expression include

FIGURE 1 After propagation through space, a radiation fieldemitted by two mutually incoherent objects, P1 and P2, becomespartially coherent at two distant points, Q1 and Q2. The coherencefunction �(Q1, Q2) contains information about the source of theradiation field.

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temporal lags in � from which spectral information canbe recovered.)

This Fourier relationship between brightness and coher-ence is central to interferometry. It has several importantfeatures. First the coherence measured between a givenpair of points on the ground is a Fourier coefficient ofthe sky brightness, with a spatial frequency given by theseparation of the points (in wavelengths) as seen from theobject. Second, the coherence depends only on the sepa-ration of the two points, not their absolute position. Third,a physical brightness distribution must be real, implyingthat �(ri , r j ) = �(r j , ri ) or �(u, v) = �(−u, −v). Theselast two facts mean that N (N − 1)/2 independent mea-surements of the coherence can be formed from samplesof the radiation field from N antennas, which is importantboth for economy of measurement and for understandingsystematic errors.

In principle, image formation by simple Fourier inver-sion of the measured �(u, v) is possible only if the coher-ence is measured at all separations, u and v. In practice,limited sampling is acceptable provided that some correc-tion is made in the processing. Furthermore, the Earth’srotation usually can be exploited to enhance the samplingproduced by an array. As seen from the object being im-aged, an array will rotate in the u-v plane, each pair of ele-ments following an ellipse. Over a period of up to 12 hr, alarge area in the u-v plane can be sampled without movingthe antennas physically.

A unique aspect of interferometers is that the samplingof the u-v plane limits both the smallest and largest angu-lar scales that can be detected. Like monolithic telescopes,interferometers have an angular resolution of approxi-mately λ/D, where D is the largest separation betweentwo antennas. Objects smaller than this scale appear tohave an angular size of λ/D. Unlike monolithic tele-scopes, interferometers also have a largest angular scale,approximately λ/d where d is the smallest separation be-tween the antennas. As the interferometer measures nospatial frequencies smaller than λ/d , any angular struc-tures on these scales is largely invisible. Information onlargest angular scales can be recovered by mosaicing. Thistechnique incorporates the coherence across the individ-ual antenna elements (which are necessarily smaller thanthe shortest antenna spacing!) into the measured �, but atthe cost of requiring the celestial source to be observedmultiple times at offset pointings.

II. DESIGN OF ARADIO-INTERFEROMETRIC ARRAY

The objective of a radio-interferometric array is to samplethe coherence function over as much of the u-v plane as

possible. At most wavelengths, the radiation is collectedusing parabolic reflectors which focus the radiation to afocal plane; typical antenna diameters are 5–100 m with25 m being a popular compromise between constructioncost and sensitivity. The ability to point the antennas andthe surface accuracy limits the highest practical observ-ing frequency. At wavelengths longer than about 50 cm,dipoles become favored because of the large antenna diam-eter that would be required to produce reasonable antennagains.

Amplification of the radiation is vital at most wave-lengths. Over the years receiver technology has advancedsteadily to decrease the noise introduced at this stage and toincrease the bandwidths feasible. Current state-of-the-artamplifiers use cryogenically cooled field-effect transistors(FETs) or high-electron-mobility transistors (HEMTs) forcentimeter wavelengths, and either Schottky devices orSIS devices at millimeter wavelengths. At meter wave-lengths, cryogenically cooled amplifiers are not requiredbecause the noise introduced by the sky typically domi-nates that introduced by the receiver.

Once the signals have been collected and amplified,they are relayed to a central location for estimation of thecoherence. Often this is more easily done at low frequen-cies, so heterodyne techniques are used to mix the signaldown to an intermediate frequency (IF) for transmissionto the central location. For this conversion an accuratefrequency standard is required at each antenna in order tomaintain coherence throughout the array. This frequencystandard may be either distributed from a central location(via cables, waveguides, radio links, or optical fibers) orderived from an extremely stable clock such as a hydrogenmaser for widely separated antennas. The IF signal is thentransmitted to the central location; for short distances thesame route as the frequency standard can be used, whereasfor long distances (>100 km) the signals are commonlydigitally sampled and recorded on magnetic tapes whichare then shipped to the central location for later process-ing. Bandwidths allowed by current technology exceed100 MHz.

At the central location the signals must be multipliedand integrated (i.e., correlated) to form estimates of thecoherence function. As digital correlators are preferred al-most universally for their lower levels of systematic errors,the signals must be digitized before correlation. One-bitdigitization has been popular for many years and leadsto only a small loss in the signal-to-noise ratio. The ad-vent of cheap, fast samplers has spurred more elaboratedigitization schemes, such as three-level encoding, whichusually are preferred for their lower loss of signal to noise.Before the correlation is performed, the signals must besynchronized to eliminate the continually changing ge-ometric delay of one antenna relative to another due to

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the Earth’s rotation. For digitized signals large buffers ofhigh-speed memory are used to delay the signals.

Even after crude digitization the processing rates re-quired in the correlation step far exceed those feasibleeven with the fastest supercomputers. This problem canbe exacerbated by a need to correlate for a number ofdifferent temporal lags, which is necessary if either thegeometry of the interferometry is poorly known or spec-tral information is desired. For typical sample rates of107 samples/sec for each of 10–30 antennas and up to 512different temporal lags, the required multiplication ratescan approach 1014/sec. Special-purpose hardware is vi-tal, and much effort has been expended in this direction.Most correlators use custom VLSI chips for the crucialmultiplier-accumulator unit. For arrays of many antennas,the conventional correlator design of many multipliers andaccumulators, one per lag per antenna pair, is extremelyinefficient. An FFT chip to transform the signals to the fre-quency domain before multiplication is often preferableas it saves in digital logical and can also allow eliminationof interfering signals.

Earth rotation, while helpful in sampling regions of theu-v plane, complicates correlation. First, as a given pairof antennas traces out its ellipse in the u-v plane, finestructure in the coherence function will be smeared outunless the integration time is short (∼10 sec). Second, therelative motion between the antennas introduces a differ-ential Doppler shift in the received radiation, which mustbe cancelled. The measured coherence samples are usu-ally averaged for as long as possible, within the limitsposed by tolerable smearing of the coherence function orby uncertainties in the interferometry geometry.

The Earth’s atmosphere can be a major source of errorin the final coherence samples. At centimeter wavelengthsthe effect of the troposphere can be ignored for resolutions

TABLE I

Number of MaximumName Location antennas baseline (km) Observing wavelength (cm)

Cambridge low-frequency Cambridge, UK 60 4.6 200synthesis telescope

Very Large Array (VLA) New Mexico, USA 27 35 400, 90, 21–18, 6, 3.6, 2, 1.3, 0.7

MERLIN Jodrell Bank, UK 8 217 200, 75, 18, 6, 2

Westerbork Synthesis Radio Telescope The Netherlands 14 2.7 120–65, 50, 40–25, 21, 18, 13, 6, 3.6

Australia Telescope Compact Array Narrabri, Australia 6 6 20, 13, 6, 3

Molongo Synthesis Telescope Australia 88 1.6 75

Caltech Millimeter Array California, USA 6 0.48 0.3, 0.1

BIMA Millimeter Array California, USA 10 2 0.3, 0.1

Plateau de Bure Interferometer France 5 0.47 0.3, 0.1

Nobeyama Millimeter Array Japan 6 0.35 0.3, 0.2, 0.1

Giant Metrewave Radio Telescope India 30 25 200, 125, 100, 50, 20

Very Long Baseline Array (VLBA) USA 10 8610 90, 50, 21–18, 13, 6, 3.6, 2, 1.3, 0.7, 0.3

poorer than about 1 arcsec. For higher resolutions the aver-aged coherence samples must be calibrated by interleavingobservations of an object of known strength and positionnearby in the sky. In most cases even this procedure isnot sufficient to allow high-quality imaging because theatmospheric variations will be partially decorrelated overeven small antenna separations. The best remedy is thento “self-calibrate” on the source of interest itself (see Sec-tion III). At long wavelengths (>0.1 m) the ionosphereis the dominant cause of phase errors, but self-calibrationcan also remove these effects.

High-quality imaging requires good sampling of the co-herence function. The largest separation of the antennasfixes the highest resolution possible, while the distributionof the samples over the u-v plane determines the complex-ity of the structure than can be imaged. As the informationcollected scales as N 2, it is desirable to have as many el-ements as possible. With a fixed budget one must includeconsideration of a number of factors including the num-ber and diameter of antennas, cost and feasibility of thecorrelator, and ancillary computing costs. Practical con-straints on the placement of antennas include the availabil-ity of land, the signal distribution system, and the mobilityof antennas.

Table I summarizes salient details about radio-astronomical arrays currently in operation around theworld.

III. IMAGING WITHRADIO-INTERFEROMETRIC ARRAYS

Once a correlator has produced the coherence samples,a Fourier inversion is required to produce an image.For this process modern computers have proven to be

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revolutionary. Before electronic computers, man-weekscould be consumed turning a day’s observations into asmall image of the object. Besides facilitating the Fourierinversion, high-speed computers have driven the devel-opment of various algorithms to correct for defects in thecoherence samples, such as poor coverage of the u-v planeand systematic errors due to the time-varying atmosphereabove each antenna. Figure 2 illustrates the advances in fi-delity and dynamic range in radio-interferometric imagingover the past 30 years, using images of the powerful radiogalaxy Cygnus A. As can be seen, imaging has progressedfrom the first crude structural determination in radio inter-ferometry (Fig. 2a), really little more than simple models,

FIGURE 2 The evolution of imaging capability as demonstratedon the strong radio galaxy Cygnus A. (a) Jennison and Das Gupta(1953) first demonstrated double structure. (b) Ryle, Elsmore, andNeville (1965) showed that the radio “lobes” drop off in brightnesstoward the center of the radio galaxy. (c) Hargrave and Ryle (1974)resolved two “hot spots” of bright emission in the lobes, and alsodetected emission from the central galaxy. (d) Perley, Dreher, andCowan (1984) found a jet of emission linking the core and thelobes and also found filaments in the lobes. The energy sourceat the center of the galaxy is likely to be a supermassive blackhole accreting material from its surroundings. [(a) Reprinted bypermission from Nature (London) 172, 996; (b) Nature (London)205, 1259. Copyright ©1953 and 1965, respectively, MacmillanMagazines Ltd. (c) Reprinted by permission from Mon. Not. R.Astron. Soc. 166, 305 (1974). (d) Reprinted by permission fromAstrophys. J. 285, L35 (1984).]

to being able to produce high-resolution images capableof distinguishing fine-scale filamentary structure withinthe lobes and a “jet” tracing the supply of energy from thecentral core to one of the lobes (Fig. 2d). While the 1974image (Fig. 2c) was made from well-sampled coherencemeasurements processed by simple Fourier inversion, the1984 image (Fig. 2d) relied on two new techniques: (1) anonlinear deconvolution algorithm, the maximum entropymethod, was used to correct for the limited sampling of theu-v plane, and (2) a self-calibration algorithm correctedfor the effects of the Earth’s atmosphere on the measuredcoherence functions.

Deconvolution algorithms rely on a priori informationabout the sky brightness to interpolate into portions ofthe u-v plane that were not sampled. The two most com-mon methods are CLEAN and maximum entropy method(MEM). The former assumes that the sky is mostly darkand that sources can be described as a combination ofpoint sources, while the latter assumes positivity for thesky brightness of sources. Figure 3 illustrates deconvolu-tion with the CLEAN algorithm.

Self-calibration also relies on a priori informationabout the sky brightness, but it mainly exploits the factthat the number of systematic errors introduced at eachantenna (N ) is usually much less than the number of sam-pled coherences (∼N 2). The errors can be atmosphericin origin, but any source of error that can be consideredto affect each antenna separately can also be removed.Thus, self-calibration can also correct for slow frequencydrifts in the frequency standard used at each antenna andhas thereby allowed true imaging in very-long-baselineinterferometry (VLBI), in which the frequency standardsare completely independent from antenna to antenna.

Self-calibration is predicated on the concept of phaseclosure developed by Jennison in the earliest days of radiointerferometry. The observed coherence on the i- j base-line, Vij , is assumed to be related to the “true” visibility asVij = gi g j

∗�i j where gi is the complex antenna gain forthe i th antenna. The closure phase is the sum of the ob-served coherence phases around a triad of array elements.Any phase effect that is specific to a specific element oc-curs twice in the sum but with opposite sign and vanishes,and the closure phase is therefore invariant to antenna-based phase errors. An analogous closure amplitude thatis invariant to gain amplitude errors exists for a quartet ofantennas. Self-calibration is closely related to the use ofadaptive optics systems in optical astronomy to counter-act the effects of atmospheric turbulence. [Analogous con-cepts have also been developed by Hauptmann in X-raycrystallography (structure invariants) and by Weigelt inoptical imaging (speckle masks).] Often multiple itera-tions of self-calibration and deconvolution are performed,in order to correct for phase and/or gain amplitude errors

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(a)

FIGURE 3 Deconvolution and self-calibration of an image of the radio galaxy 3C 390.3 at 327 MHz: (a) point-sourceresponse; (b) dirty image corrupted by effects of limited sampling of coherence function; (c) CLEAN deconvolvedimage showing residual phase errors; and (d) the image after a single iteration of self-calibration. Additional self-calibration could be used to reduce further the effects of residual phase errors. All images are shown as negatives,with black being regions of most intense radio emission and white being regions of less intense radio emission, withtransfer functions that are linear between black and white. For images shown in (b), (c), and (d) the intensity levelscorresponding to black and white are held fixed. In order to emphasize low-level intensities, the images are saturated.

on shorter and shorter time scales. Figure 3 illustrates theadditional improvement obtained by combining deconvo-lution and self-calibration.

The net effect of these improvements has been to aug-ment considerably the capabilities of radiointerferometricarrays at the cost of increased computing requirements.

IV. FUTURE PROSPECTS

The driving forces behind radio interferometry for the past50 years have been the quest for higher sensitivity andangular resolution. These principles will continue to driveradio interferometry over the next decade.

A. Sensitivity, Radio Frequency Interference,and Imaging Algorithms

Improved sensitivity can be achieved either by improv-ing receiver characteristics or by increasing the numberof interferometer elements (total collecting area of thearray). Receiver characteristics that can be improved in-clude lowering the noise introduced by the amplifiers orincreasing the bandwidth accepted by the receivers. Un-fortunately, receiver noise is often not the limiting factorat short or long wavelengths and has been decreased gen-erally to an irreducible physical minimum at intermediatewavelengths. Increasing the receiver bandwidth can im-prove the sensitivity to continuum sources of emission

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but does not improve the sensitivity for sources of lineemission.

Efforts to increase receiver bandwidths must be coupledwith strategies for mitigating radio frequency interference(RFI). Radio astronomy (and other passive users of the ra-dio spectrum) has only a limited portion of the spectrumreserved exclusively for its use. Observations outside ofthese reserved spectral regions can be required either in aneffort to obtain a wider continuum bandwidth or becausean astrophysically interesting atomic or molecular transi-tion line has been Doppler shifted by the motion of theemitting source. Previous RFI mitigation techniques haverelied on the remote siting of interferometers and the useof filters. The advent of widespread satellite communi-cations and wide-bandwidth, spread-spectrum broadcastsrequire additional measures. In addition to increased use ofregulatory avenues, measures being investigated by radioastronomers include adaptive nulling. Various techniquesfall under this rubric, but all make use of tracking thesource(s) of RFI so as to remove its effects. For instance,

the power reception pattern (beam) of an array could bealtered continuously so that a null in the sidelobe patternis directed toward the RFI source.

The alternate possibility for increasing the sensitivityof an interferometer is to increase the number of collect-ing elements and thereby the total collecting area. Doingso improves the array’s sensitivity to both continuum andline sources of emission and is at least part of the motiva-tion behind proposed new or expanded arrays across theentire radio spectrum. However, increasing the number ofarray elements also increases the complexity of the cen-tral correlator which scales as N 2. Proposals for arrayscontaining 100 or more elements, compared to a typi-cal number of 10–30 elements in present-day arrays, havebeen made. Perhaps the most ambitious of various propos-als is that for the Square Kilometer Array (SKA) whichwould have 106 m2 of collecting area and operate at leastover the wavelength range 1 cm–1 m. Key to the SKA’sultimate success will be whether such a large amount ofcollecting area can be constructed cheaply. A variety of

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novel possibilities have been suggested to collect andfocus the radiation, many of which forego traditionalparabolic antennas (e.g., Luneberg lenses).

Fully exploiting the capabilities of new interferometerarrays will also require the development of new imagingalgorithms, particularly deconvolution algorithms. Evenfrom existing arrays, the images produced can be limitedas much by errors in existing deconvolution algorithms asby residual (self-)calibration errors. Some recent progresshas been the development of a nonnegative least squares(NNLS) deconvolution algorithm, in which a series of lin-ear equations are inverted with constraints on the positivityof the solutions applied.

B. Millimeter Interferometry

At meter and centimeter wavelengths the primary emis-sion mechanisms of celestial sources are either syn-chrotron or thermal bremsstrahlung, both continuum pro-

cesses, with the 21-cm line of neutral hydrogen andthe transitions from the OH− radical near 18 cm serv-ing as important exceptions. At wavelengths shorter thanabout 1 cm, rotational and vibrational transitions of var-ious molecules become alternate, and often dominant,emission processes. Thus, in addition to the possibilityof higher resolution than at centimeter and meter wave-lengths, there is the possibility of three-dimensional struc-ture information—via the Doppler shift of molecular linesobserved from a source—and chemical information.

Challenges posed by millimeter interferometers includeboth the mechanical stability and tolerances of the anten-nas and the effect of the troposphere. Like antennas atany other wavelength, the surfaces of the antennas mustbe smooth enough that most of the incident radiationis reflected to the focus rather than scattered. Mechani-cal tolerances are particularly demanding given that thetypical millimeter-wave antenna is only a factor of 2–3smaller in diameter than a centimeter-wavelength antenna,

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(d)


but the observation wavelength is an order of magnitudesmaller.

The troposphere introduces two primary difficulties—phase fluctuations and opacity—both of which result pri-marily from atmospheric H2O and O2 molecules. Phasefluctuations can be mitigated by self-calibration, as at otherwavelengths, or by fast calibration switching. The typicalinitial phase calibration scheme described above (§II) in-volves interleaved observations of a calibrator and a tar-get source. If the calibrator can be observed frequentlyenough to track the tropospheric phase fluctuations, thisfast-switching calibration scheme will remove most of thephase fluctuations. At millimeter wavelengths the tropo-sphere can vary on time scales as short as 10 sec, requiringsource switching to be on comparable time scales as well.Thus, the individual antennas must be mechanically sta-ble enough to be driven from source to source this quicklywithout exciting any resonances, and motions must dampquickly enough so that the antennas can point accurately.

The opacity of the troposphere at millimeter wave-lengths is unlike the situation at longer wavelengths (oroptical wavelengths) in that it both attenuates celestial sig-nals and increases the system noise. The latter effect oc-curs because the atmosphere contributes an effective noisetemperature of Tatm(1 − exp[−τatm]) with τatm ∼ 0.1–0.5.One technique for reducing the effects of the troposphereis to place millimeter arrays at as high an altitude as pos-sible so as to be above as much of the atmospheric watervapor as possible.

A crucial imaging problem for millimeter interferome-ters is that the sizes of the celestial sources being imagedare commonly larger than the smallest spatial frequencythey sample (λ/d). Routine use of the mosaicing tech-nique will be required to recover full information aboutthe coherence function.

The most ambitious plan for millimeter interferometryis the Atacama Large Millimeter Array (ALMA, Fig. 4a),a US-European (and potentially Japanese) collaboration

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(a)

(b)

FIGURE 4 Future interferometers. (A) An artist’s conception of the Atacama Large Millimeter Array (ALMA) proposedto be constructed on the (5000-m altitude) Chilean Atacama desert. The array will consist of at least Sixty four 12-mantennas operating between 22 and 350 GHz with the elements capable of being moved to produce baselines rangingfrom 15 m to 10 km. The highest angular resolutions will range from 0.3 arcsec at 22 GHz to 0.02 arcsec at 350 GHz.Image courtesy of the European Southern Observatory. (B) An artist’s conception of a Low Frequency Array (LOFAR)“station.” The array will consist of at least 40 stations of phased-array dipoles with baselines approaching 500 kmand operating between 15 and 200 MHz. The highest angular resolutions will range from 8 arcsec at 15 MHz to 0.6arcseconds at 200 MHz. Image courtesy of the Netherlands Foundation for Research in Astronomy (NFRA/ASTRON).

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that aims to construct a millimeter interferometer in theChilean Atacama desert at 5000 m altitude. ALMA willconsist of at least sixty four 12-m antennas arrayed inmovable configurations with baseline lengths between150 m and 10 km and operating over the wavelength range0.35–10 mm.

C. Long-Wavelength Interferometry

Radio astronomy was discovered at 20 MHz, but the questfor higher angular resolution with the single-dish tele-scopes then available, led quickly to most observations be-ing conducted at higher frequencies. Interferometers wereconstructed to operate at frequencies below 100 MHz,but they had short baselines (<5 km). Short baselineswere motivated by the belief that ionospherically inducedphase fluctuations would destroy coherence on longerbaselines.

The short baselines, and correspondingly limited angu-lar resolution, also contributed to limited sensitivity. Ob-served at low angular resolution, sources overlap leadingto source confusion and sensitivities far worse than ex-pected from receiver noise alone. A crucial assumption ofa two-dimensional Fourier relation between the observedcoherences and the sky brightness is that the interferome-ter’s extent along the line of sight to the source is negligi-ble. The large field of view of meter and decameter instru-ments (>1◦) invalidates this assumption. Approaches todealing with the large field of view include performing thefull three-dimensional Fourier transform or tessellatingthe sky into small facets over which the two-dimensionalassumption is appropriate. Both approaches are computa-tionally intensive. Most work has focused on the latter ap-proach because, if observed at sufficiently high resolution,the sky remains mostly dark at these wavelengths, and theentire field of view does not need to be tessellated: Facetsneed to be placed only on sources. This approach is alsoamenable to parallel computer algorithms as the Fouriertransforms required to produce the facets can be done in-dependently of each other.

The development of self-calibration algorithms in the1980s led to the realization that they could be employedto remove ionospheric phase fluctuations. Subsequently,interferometer baselines have been extended to tens ofkilometers, and the success of these relatively long base-line interferometers (particularly the 74 MHz system onthe Very Large Array, cf. Table I) have spurred plans fora Low Frequency Array (LOFAR, Fig. 4B). This instru-ment will have baselines of order 100 km and a collectingarea of order 106 m2 at 15 MHz, leading to a sensitiv-ity that will be competitive with centimeter-wavelengthinterferometers.

D. Space-Based Very-Long-BaselineInterferometry

The diameter of the Earth presents a limit in improvingthe resolution of centimeter- and meter-wavelength in-terferometers. In order to obtain resolutions better than0.02λ arcsec, with λ in meters, requires placing one ormore antennas in space.

The first successful demonstration of space-based inter-ferometry used a NASA Tracking and Data Relay Satel-lite System (TDRSS) satellite. Although not designed forobserving celestial objects, the TDRSS antenna, whencombined with ground-based antennas, nevertheless re-sulted in the first interferometer that included baselineslarger than the Earth’s diameter. The first dedicated spaceVLBI antenna was onboard the VLBI Space ObservingProgramme (VSOP) satellite (later renamed to the HighlyAdvanced Laboratory for Communications and Astron-omy, HALCA).

Space-based antennas present a number of difficultiesin forming an interferometer. The high launch cost perkilogram of payload means that antennas must be ei-ther fairly small or made of extremely lightweight ma-terials. To date, space-based antennas have been small,requiring large ground-based antennas to be used in orderto have adequate sensitivity. In contrast to well-knownpositions and stable clocks of ground-based antennas,space-based antennas have poorly known locations andclock signals transmitted by uplinks subject to atmo-spheric fluctuations. These differences entail considerableeffort to find and maintain coherence on the baselinesto the space-based antenna. Furthermore, although long,ground–space baselines are often fairly similar. Ratherthan covering a wide range of (instantaneous) u-v values,as is typical of ground–ground baselines, ground–spacebaselines are concentrated in a narrow range at any giveninstant.

One compensating factor, at least for antennas in low-Earth orbit, is that long tracks in the u-v plane can beobtained in relatively short intervals due to the rapid satel-lite motion. There is also a natural limit to the length ofthe baselines that can be used. Plasma density fluctua-tions scatter radio waves propagating through the inter-planetary and interstellar media causing point sources seenthrough these media to be angularly broadened, not unlikethe broadening of stellar images at optical wavelengthsbecause of neutral atmospheric turbulence (“seeing”).The magnitude of the broadening is both direction andfrequency dependent, but roughly a baseline of D Earthradii will be limited by interstellar scattering at wave-lengths below 1 m/D.

The success of HALCA has stimulated more ambi-tious plans, though all still contemplate placing only one

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antenna in space. VSOP2 would be a follow-on missionto HALCA with ten times its sensitivity and operating atfrequencies as high as 43 GHz. RadioASTRON is a long-delayed Soviet/Russian radio telescope slightly larger thanHALCA and operating over a larger wavelength range.ARISE is a proposed NASA mission that would place a25 m diameter antenna in orbit with operating frequenciesas high as 86 GHz.

ACKNOWLEDGMENTS

I thank T. Cornwell, R. Ekers, and K. Weiler for helpful comments.Basic research in radio astronomy at the NRL is supported by the Officeof Naval Research.


ASTROPHYSICS • FIELD-EFFECT TRANSISTORS • GRAV-ITATIONAL WAVE DETECTORS • IMAGE RESTORATION,

MAXIMUM ENTROPY METHOD • MILLIMETER ASTRON-OMY • RADIOCARBON DATING • SIGNAL PROCESSING,DIGITAL

BIBLIOGRAPHY

Hanbury Brown, R. (1974). “The Intensity Interferometer: Its Applica-tion to Astronomy,” Taylor and Francis, London.

Kellerman, K. I., and Thompson, A. R. (1988). “The very long baselinearray,” Sci. Am. 258, 54–64.

Napier, P. J., Thompson, R. T., and Ekers, R. D. (1983). “The very largearray: Design and performance of a modern synthesis radio telescope,”Proc. IEEE 71, 1295–1320.

Sullivan, W. T. (1982). “Classics in Radio Astronomy,” Reidel Publ.,Boston, MA.

Taylor, G. B., Carilli, C. L., and Perley, R. A. (1999). “Synthesis Imagingin Radio Astronomy II,” Astron. Soc. of the Pacific, San Francisco, CA.

Thompson, A. R., Moran, J. M., and Swenson, G. W. (1986). “Inter-ferometry and Synthesis in Radio Astronomy,” Wiley (Interscience),New York.

Vershuur, G. (1987). “The Invisible Universe Revealed—The Story ofRadio Astronomy,” Springer-Verlag, Berlin.

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Encyclopedia of Physical Science and Technology EN016G-534 July 31, 2001 17:4

Telescopes, OpticalL. D. BarrNational Optical Astronomy Observatories (retired)

I. Telescope Size Considerations andLight-Gathering Power

II. Optical ConfigurationsIII. Telescope OpticsIV. Spectral Region Optimization: Ground-Based

TelescopesV. Mechanical Configurations

VI. Considerations of Usage and LocationVII. Observing in Space: The Hubble Space

Telescope

GLOSSARY

Airy disc Central portion of the diffracted image formedby a circular aperture. Contains 84% of the total energyin the diffracted image formed by an unobstructed aper-ture. Angular diameter = 2.44 λ/D, where λ is wave-length and D is the unobstructed aperture diameter.First determined by G. B. Airy in 1835.

Aperture stop Physical element, usually circular, thatlimits the light bundle or cone of radiation that an op-tical system will accept on-axis from the object.

Coherency Condition existing between two beams oflight when their fluctuations are closely correlated.

Diameter-to-thickness ratio Diameter of the mirror di-vided by its thickness. Term is generally used to denotethe relative stiffness of a mirror blank: 6:1 is consideredstiff, and greater than 15:1 is regarded as flexible.

Diamond turning Precision-machining process used toshape surfaces in a manner similar to lathe turning.

Material is removed from the surface with a shapeddiamond tool, hence the name. Accuracies to one mi-croinch ( 1

40 th µm) are achievable. Size is limited bythe machine, currently about 2 m.

Diffraction-limited Term applied to a telescope when thesize of the Airy disc formed by the telescope exceedsthe limit of seeing imposed by the atmosphere or theapparent size of the object itself.

Effective focal length (EFL) Product of the aperturediameter and the focal ratio of the converging lightbeam at the focal position. For a single optic, theeffective focal length and the focal length are thesame.

Electromagnetic radiation Energy emitted by matterwith wavelike characteristics over a range of frequen-cies known as the electromagnetic spectrum. The short-est waves are gamma rays (<1 A) and the longest areradio waves (>40 µm). Visible light is in the interme-diate range.

545

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546 Telescopes, Optical

Field of view Widest angular span measured on the skythat can be imaged distinctly by the optics.

Focal ratio (f/ratio) In a converging light beam, the re-ciprocal of the convergence angle expressed in radians.The focal length of the focusing optic divided by itsaperture size, usually its diameter.

Image quality Apparent central core size of the observedimage, often expressed as an angular image diameterthat contains a given percentage of the available energy.Sometimes taken to be the full width at half maximum(FWHM) value of the intensity versus angular radiusfunction. A complete definition of image quality wouldinclude measures of all image distortions present, notjust its size, but this is frequently difficult to do, hencethe approximations.

Infrared For purposes of this article, wavelength regionfrom about 0.8 to 40 µm.

Optical path distance Distance traveled by light passingthrough an optical system between two points alongthe optical path.

Seeing Measure of disturbance in the image seen throughthe atmosphere. Ordinarily expressed as the angularsize, in arc-seconds, of a point source (a distant star)seen through the atmosphere, that is, the angular sizeof the blurred source. Seeing disturbances arise fromair density fluctuations due to temperature variationsalong the line of sight.

Ultraviolet For purposes of ground-based telescopes, thewavelength region from about 3000 to 4000 A. Theremaining UV region down to about 100 A is blockedby the earth’s atmosphere.

OPTICAL TELESCOPES were devised by Europeanspectacle makers around the year 1608. Within two years,Galileo’s prominent usage of the telescope marked the be-ginning of a new era for astronomy and a proliferation ofincreasingly powerful telescopes that continues unabatedtoday. Because it extends what the human eye can see, theoptical telescope in its most restricted sense is an artifi-cial eye. However, telescopes are not subject to the sizelimitation, wavelength sensitivities, or storage capabili-ties of the human eye and have been extended vastly be-yond what even the most sensitive eye can accomplish.In this article, the word light is used to mean all electro-magnetic radiation collected by telescopes but the prop-erties of astronomical telescopes operating on the groundin the optical/IR spectral wavelength range from 3000 toabout 40,000 A (0.3–40 µm) are the principal subject.The atmosphere transmits radiation throughout much ofthis range. Telescopes designed for shorter wavelengthsare either UV or X-ray telescopes and must operate inspace. The Hubble Space Telescope is the best-known ex-

ample of a UV (and optical) telescope and is discussed inSection VII. Telescopes operating at wavelengths longerthan 40 µm are in the radio-telescope category and arenot considered in this article. Emphasis is placed ontechnical aspects of present-day telescopes rather thanhistory.

I. TELESCOPE SIZE CONSIDERATIONSAND LIGHT-GATHERING POWER

An astronomical telescope works by capturing a sampleof light emitted or reflected from a distant source and thenconverging that light by means of optical elements into animage resembling the original source, but appropriatelysized to fit onto a light-sensitive detector (e.g., the humaneye, a photographic plate, or a phototube). Figure 1 il-lustrates the basic telescope elements. It is customary toassume that light from a distant object on the optical axisarrives as a beam of parallel rays sufficiently large to fillthe telescope entrance, as shown.

The primary light collector can be a lens, as in Fig. 1, ora curved mirror, in which case the light would be shownarriving from the opposite direction and converging af-ter reflection. The auxiliary optics may take the form ofeyepieces or additional lenses and mirrors designed to cor-rect the image or modify the light beam. The nature andarrangement of the optical elements set limits on how effi-ciently the light is preserved and how faithfully the imageresembles the source, both being issues of prime concernfor telescope designers.

The sampled light may have traveled at light speed for ashort time or for billions of years after leaving the source,which makes the telescope a unique tool for studying howthe universe was in both the recent and the distant past. Im-ages may be studied to reveal what the light source lookedlike, its chemistry, location, relative motion, temperature,mass, and other properties. Collecting light and formingimages is usually regarded as a telescope function. Ana-lyzing the images is done by various instruments designedfor that purpose and attached to the telescope. Detectorsare normally part of the instrumentation. The followingdiscussion deals with telescopes.

FIGURE 1 Basic telescope elements. Refractive lens could bereplaced with a curved reflective mirror.

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Telescopes, Optical 547

A. Telescope Size and its Effect on Images

The size of a telescope ordinarily refers to the diameter,or its approximate equivalent, for the area of the first (pri-mary) image-forming optical element surface illuminatedby the source. Thus, a 4M telescope usually signifies onewith a 4-m diameter primary optic. This diameter sets amaximum limit on the instantaneous photon flux passingthrough the image-forming optical train. Some telescopesuse flat mirrors to direct light into the telescope (e.g., so-lar heliostats); however, it is the size of the illuminatedportion of the primary imaging optic that sets the size.

The size of a telescope determines its ability to resolvesmall objects. The Airy disc diameter, generally taken tobe the resolution limit for images produced by a tele-scope, varies inversely with size. The Airy disc also in-creases linearly with wavelength, which means that onemust use larger sized telescopes to obtain equivalent imag-ing resolution at longer wavelengths. This is a concernfor astronomers wishing to observe objects at infrared(IR) wavelengths and also explains in part why radio tele-scopes, operating at even longer wavelengths, are so muchlarger than optical telescopes. (Radio telescopes are moreeasily built larger because radio wavelengths are muchlonger and tolerances on the “optics” are easier to meet.)

Telescopes may be used in an interferometric mode toform interference fringes from different portions of theincoming light beam. Considerable information about thesource can be derived from these fringes. The separationbetween portions of the primary optic forming the im-age (fringes) is referred to as the baseline and sets a limiton fringe resolution. For a telescope with a single, roundprimary optic, size and maximum baseline are the same.For two telescopes directing their beams together to forma coherent image, the maximum baseline is equal to themaximum distance between light-collecting areas on thetwo primaries. More commonly, the center-to-center dis-tance would be defined as the baseline, but the distancebetween any two image-forming areas is also a baseline.Thus, multiple-aperture systems have many baselines.

As telescope size D increases so does the physical sizeof the image, unless the final focal ratio Ff in the converg-ing beam can be reduced proportionately, that is,

final image size = Ff · D · θ,

where θ is the angular size of the source measured onthe sky in radians. With large telescopes this can be amatter of importance when trying to match the image toa particular detector or instrument. Even for small optics,achieving focal ratios below about f/1.0 is difficult, whichsets a practical limit on image size reduction for a givensituation.

Another size-related effect is that larger telescopeslook through wider patches of the atmosphere which usu-

ally contain light-perturbing thermally turbulent (varyingair density) regions that effectively set limits on seeing.Scintillation (twinkling) and image motion are causedby the turbulence. However, within a turbulent region,slowly varying isotropic subregions (also called isopla-natic patches) exist that affect the light more or less uni-formly. When a telescope is sized about the same as, orsmaller than, a subregion and looks through such a subre-gion, the instantaneous image improves because it is notaffected by turbulence outside the subregion. As the sub-regions sweep through the telescope’s field of view, theimage changes in shape and position. Larger telescopeslooking through many subregions integrate or combinethe effects, which enlarges the combined image and ef-fectively worsens the seeing. However, these effects di-minish with increasing wavelength, which means thatlarger telescopes observing at IR wavelengths may havebetter seeing than smaller ones observing in the visibleregion.

Studies of atmospheric turbulence effects have givenrise to the development of special devices to make opticalcorrections. These are sometimes called rubber mirrors oradaptive optics. An image formed from incoming light issensed and analyzed for its apparent distortion. That in-formation is used to control an optical element (usuallya mirror) that produces an offsetting image distortion inthe image-forming optical train. By controlling on a starin the isoplanatic patch with the object to be observed (sothat both experience similar turbulence effects), one can,in principle, form corrected images with a large ground-based telescope that are limited only by the telescope, notthe atmosphere. In practice, low light levels from stars andthe relatively small isoplanatic patch sizes (typically a fewarc-seconds across) have hampered usage of adaptive op-tics on stellar telescopes. One technique, successfully usedin large telescopes, is to split off the visible wavelengthportion of the light beam for image distrotion analysiswhile allowing the longer wavelength (IR) portion of thebeam to pass through to the adaptive optic and to form thefinal corrected image.

B. Telescope Characteristics Related to Size

At least three general, overlapping categories related totelescope size may be defined:

1. Telescopes small enough to be portable. Sizes usu-ally less than 1 m.

2. Mounted telescopes with monolithic primary optics.Sizes presently range up to 6 m for existing telescopes,with many 8 m telescopes either planned or under con-struction. Virtually all ground-based telescopes used byprofessional astronomers are in this category.

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3. Very large telescopes with multielement primary op-tics. Proposed sizes range up to 25 m for ground-basedtelescopes. Only a few multielement telescopes have ac-tually been built.

A fourth category could include telescopes smallenough to be launched into Earth’s orbit, but the possi-bility of an in-space assembly of components makes thisdistinction unimportant.

One cannot, in a short space, describe all of the telescopestyles and features. Nevertheless, as one considers largerand larger telescopes, differences become apparent and afew generalizations can be postulated.

In the category of small telescopes, less than 1 m, onefinds an almost unlimited variety of telescope configura-tions. There are few major size limitations on materialsfor optics. Polishing of optics can often be done manuallyor with the aid of simple machinery. Mechanical require-ments for strength or stiffness are easily met. Adjustmentsand pointing can be manually performed or motorized.Weights are modest. Opportunities for uniqueness aboundand are often highly prized. Single-focus operation is typ-ical. Most of the telescopes used by amateur and profes-sional astronomers are in this size range. Figure 2 illus-trates a 40-cm telescope used by professional astronomers.

In the 1–2 m size range, a number of differences andlimitations arise. Obtaining high-quality refractive opticsis expensive in this range and not practical beyond. Sim-ple three-point mechanical supports no longer suffice forthe optics. The greater resolving-power potential demandshigher quality optics and good star-tracking precision.

FIGURE 2 40-cm telescope on an off-axis equatorial mount.[Courtesy National Optical Astronomy Observatories, Kitt Peak.]

Telescope components are typically produced on large ma-chine tools. Instrumentation is likely to be used at morethan one focus position. Because of cost, the domain ofthe professional astronomer has been reached.

As size goes above 2 m, new issues arise. The need tocompensate for self-weight deflections of the telescope be-comes increasingly important to maintaining optical align-ment. Flexure in the structure may affect the bearings anddrive gears. Bearing journals become large enough to re-quire special bearing designs, often of the hydrostatic oilvariety. The observer may now be supported by the tele-scope instead of the other way around. Support of the pri-mary optics is more complex and obtaining primary mirrorblanks becomes a special, expensive task. Automated op-eration is typical at several focal positions. Star-trackingautomatic guiders may be used to control the telescopedrives, augmented by computer-based pointing correctiontables. Figure 3 illustrates a 4-m telescope with all of thesefeatures.

At 5 m, the Hale Telescope on Mount Palomar isregarded as near the practical limit for equatorial-stylemountings (see Section V). Altitude–azimuth (alt–az)mountings are better suited for bearing heavy rotatingloads and are more compact. With computers, the vari-able drive speeds required with an alt–az telescope canbe managed. Mounting size and the length of the tele-scope are basic factors in setting the size of the enclos-ing building. For technical reasons and lower cost, thepresent trend in large telescopes is toward shorter primary

FIGURE 3 Mayall 4-m telescope, with equatorial horse-shoeyoke mountings. [Courtesy National Optical Astronomy Obser-vatories, Kitt Peak.]

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TABLE I Telescopes 3 Meters or Larger Built Since 1950

Date completed Primary Primary(projected) Telescope and/or institution mirror size (m) focal ratio Mounting style

1950 Hale Telescope, Palomar Observatory, California 5 3.3 Equatorial horseshoe yoke

1959 Lick Observatory, California 3 5.0 Equatorial fork

1973 Mayall Telescope, Kitt Peak 4.0 2.7 Equatorial horseshoe yokeNational Observatory (KPNO), Arizona

1974 Cerro Tololo International Observatory (CTIO), Chile 4.0 2.7 Equatorial horseshoe yoke

1975 Anglo-Australian Telescope (AAT), Australia 3.9 3.3 Equatorial horseshoe yoke

1976 European Southern Observatory (ESO), Chile 3.6 3.0 Equatorial horseshoe yoke

1976 Large Altazimuth Telescope (BTA), 6.0 4.0 Alt–azSpecial Astrophysical Observatory,Caucusus Mtns, Russia

1979 Infrared Telescope Facility (IRTF), Hawaii 3.0 2.5 Equatorial English yoke

1979 Canada-France-Hawaii Telescope (CFHT), Hawaii 3.6 3.8 Equatorial horseshoe yoke

1979 United Kingdom Infrared Telescope (UKIRT), Hawaii 3.8 2.5 Equatorial English yoke

1979 Multiple Mirror Telescope (MMT) Observatory, 4.5a Six 1.8 mb Alt–az at f/2.7Mt. Hopkins, Arizona

1983 German-Spanish Astronomical Center, 3.5 3.5 Equatorial horseshoe forkCalar Alto, Spain

1986 Wm. Herschel Telescope, La Palma, Canary Islands 4.2 2.5 Alt–az

1989 New Technology Telescope (NTT), ESO, Chile 3.5 2.2 Alt–az

(1993) Wisconsin-Indiana-Yale-NOAO (WIYN) Telescope, 3.5 1.75 Alt–azKitt Peak, Arizona

(1992) Apache Point Observatory, New Mexico 3.5 1.75 Alt–az

(1992) Keck Ten Meter Telescope (TMT), Hawaii, 10a 1.75 Alt–azSegmented Mirror Telescope (SMT).36-element (hexagons) paraboloidal primary

Proposed for National Optical Astronomy Observatories (NOAO), 8 1.8 Alt–az DiscHawaii (1987) Arizona& CTIO (1999)

Proposed for Magellan Project Telescope, Las Campanas, Chile 8 1.2 Alt–az DiscChile (1997)

(1998) Japanese National Large Telescope (JNLT), Hawaii 8.3 1.9 Alt–az

(1998) Columbus Project Telescope, Mt. Graham, Arizona, 11.3a Two 8 m at f/1.2b Alt–az “C-Ring”MMT style

(1998) The Very Large Telescope (VLT), ESO, Chile. 16a Four 8.2 m at f/2b Alt–azAn array of telescopes

Proposed Russia, SMT style with a 400-element 25a 2.7 Alt–az(hexagons) spherical primary.

a Equivalent circular mirror diameter with equal light gathering area.b Number, size, and f/ratio of individual primary mirror.

focal lengths and alt–az mounts. This trend is evidentfrom Table I, which lists the telescopes 3 m in size orlarger that have been built since about 1950. Also listedare the major large telescopes proposed for constructionin the late 1980s and the 1990s, which will be discussedin the next section. The largest optical telescope in op-eration today is the Russian 6 m, which incorporates asolid, relatively thick (650 mm) primary mirror that hadto be made three times in borosilicate glass and finally ina low-expansion material before it was successful. Suchdifficulty indicates that 6 m may be a practical limit

for that style of mirror. New approaches are needed togo beyond.

C. The New Giant Telescopes

The desire for greater light-gathering power and imageresolution, especially at IR wave-lengths, continues topress astronomers to build telescopes with larger effectiveapertures. Costs for a given telescope style and imagingperformance have historically risen nearly as the primaryaperture diameter to the 2.5 power. These factors have

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given impetus to a number of new technology telescopedesigns (see Proposed Projects in Table I) that are basedon one or more of the approaches discussed in the fol-lowing. Computer technology plays a strong part in all ofthese approaches.

1. Extending the Techniques for MakingLightweight Monolithic Mirror Blanks

Sizes up to about 8 m are considered feasible, although theRussian 6 m is the largest telescope mirror produced before1985. Further discussion on blank fabrication methods isprovided in Section III. Supporting such large mirrors toform good images will be difficult without some activecontrol of the surface figure and thermal conditions in themirror blank.

Several American universities and the national obser-vatories in the United States and Japan are planning tele-scopes of this variety.

2. Making a Large Mirror from Smaller Segments

This is also known as segmented mirror telescope, or SMT.In principle, no limit exists for the size of a mosaic ofmirror segments that functions optically as a close ap-proximation to a monolithic mirror. For coherency eachsegment must be precisely and continuously positionedwith respect to its neighbors by means of position sen-sors and actuators built into its support. The segmentsmay be hexagonal, wedge shaped, or other to avoid largegaps between segments. Practical limits arise from supportstructure resonances and cumulative errors of the segmentpositioning system. Manufacturing and testing the seg-ments require special methods since each is likely to bea different off-axis optic that lacks a local axis of sym-metry but must have a common focus with all the othersegments.

The University of California and the California Insti-tute of Technology have adopted this approach for theirKeck Observatory 10-m telescope (see Fig. 4), completedin 1992. Russia also has announced plans for a 25-m SMTutilizing a spherical primary to avoid the problems of mak-ing aspheric segments.

3. Combining the Light froman Array of Telescopes

Several methods may be considered:

1. Electronic combination after the light has been re-ceived by detectors at separate telescopes. Image proper-ties will be those due to the separate telescopes, and coher-ent combining is not presently possible. Strictly speaking,

FIGURE 4 Conceptual sketch of a segmented mirror telescope(SMT) using the arrangement adopted for the Keck Ten MeterTelescope, which uses 36 hexagonal mirrors in a primary mirrormosaic to achieve light gathering power equivalent to a single10-m diameter circular mirror. Each mirror segment must be posi-tioned accurately with respect to its neighbors to achieve the over-all optical effect of an unsegmented parabola. The gaps betweenthe segments cause unwanted diffraction effects in the image inproportion to the area they occupy in the primary aperture; hence,they are minimized. Other segment shapes are possible, and thetotal telescope size is limited only by its structural stiffness and op-tics alignment provisions. Thus, very large SMTs are theoreticallypossible.

this is an instrumental technique and will not be consid-ered further.

2. Optical combination at a single, final focus of lightreceived at separately mounted telescopes. To maintaincoherency between separate light beams, one must equal-ize the optical path distance (OPD) between the sourceand the final focus for all telescopes, a difficult conditionto meet if telescopes are widely separated.

3. Placing the array of telescopes on a common mount-ing with a means for optically combining the separate lightbeams. All OPDs can be equal (theoretically), thus requir-ing only modest error correction to obtain coherency be-tween telescopes. This approach is known as the multiplemirror telescope (MMT).

The simplest array of separately mounted individualtelescopes is an arrangement of two on a north–south(NS) baseline with an adjustable, combined focus betweenthem (the OPD changes occur slowly with this arrange-ment when observing at or near the meridian). Labeyriepioneered this design in the 1970s at Centre d’Etudes et deRecherches Geodynamiques et Astronomiques (CERGA)in France, where he used two 25-cm telescopes on a NSvariable baseline of up to 35 m to measure successfully

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numerous stellar diameters and binary star separations,thereby showing that coherent beam combination and theangular resolution corresponding to a long telescope base-line could be obtained. Other schemes for using arrays ofseparate telescopes on different baselines all require mov-able optics in the optical path between the telescopes tosatisfy the coherency conditions, and so far none has beensuccessfully built. However, the European Southern Ob-servatory is building an array of four 8-m telescopes inChile which will be known as the “Very Large Telescope”(VLT) when completed in the late 1990s. One form of theVLT is an in-line array with an “optical trombone” ar-rangement for equalizing OPDs. Other arrangements arealso under consideration.

The MMT configuration was first used by the Smithso-nian Astrophysical Observatory (SAO) and the Universityof Arizona (UA). The SAO/UA MMT on Mount Hopkinsuses six 1.8-m image-forming telescopes arrayed in a cir-cle around a central axis. Six images are brought to a cen-tral combined focus on the central axis, where they maybe incoherently stacked, coherently combined, or usedseparately. The effective baseline for angular resolution(i.e., the maximum separation between reflecting areas) is6.9 m, and the combined light-gathering power is equiv-alent to a single 4.5-m diameter mirror. A two-elementMMT using 8-m mirrors and a 22-m baseline, illustratedin Fig. 5 and called the “Columbus Project,” is under con-struction by the UA in collaboration with the ObservatorioAstrofisico de Arcetri, Italy. Appropriately, this telescopehas been dubbed the “Big Binocular.”

II. OPTICAL CONFIGURATIONS

Light entering the telescope is redirected at each opticalelement surface until it reaches the focal region where theimages are most distinct. The light-sensitive detector iscustomarily located in an instrument mounted at the focalregion. By interchanging optics, one can create more thanone focus condition; this is commonly done in large tele-scopes to provide places to mount additional instrumentsor to produce different image scales. The arrangement ofoptics and focal positions largely determines the requiredmechanical support configuration and how the telescopewill be used.

The early telescopes depended solely upon the refrac-tive power of curved transparent glass lenses to redirectthe light. In general, these telescopes were plagued bychromatic aberration (rainbow images) until the inventionin 1752 of achromatic lenses, which are still used today inimproved forms. Curved reflective surfaces (i.e., mirrors)were developed after refractors but were not as useful un-til highly reflective metal coatings could be applied onto

FIGURE 5 Conceptual sketch of a multiple mirror telescope(MMT) using the arrangement planned for the Columbus “BigBinocular” Telescope, which uses two 8-m diameter telescopesmounted on a common structure with provisions to combine theirseparate output light beams. With careful control of the opticalpath distances in each telescope, the resolving power of the tele-scope is equivalent to that of a single-mirror telescope of a sizeequal to the maximum separation between the primary mirrorsof the two telescopes. Total light gathering power is equal to thesum of the individual telescope powers. There is no theoreticallimit to the number of individual telescopes in an MMT, but thebeam combining and structural provisions become increasinglycomplex.

glass substrates. Today, mirrors are more widely used thanlenses and can generally be used to produce the same op-tical effects; they can be made in larger sizes, and they arewithout chromatic aberration. These are still the only twomeans used to form images in optical telescopes. Accord-ingly, telescopes may be refractive, reflective, or catadiop-tric, which is the combination of both.

A. Basic Optical Configurations:Single and Multielement

The telescope designer must specify the type, number, andlocation of the optical elements needed to form the de-sired image. The basic choices involve material selectionsand the shapes of the optical element surfaces. Commonlyused surfaces are flats, spheres, paraboloids, ellipsoids,hyperboloids, and toroidal figures of revolution.

The optical axis is the imaginary axis around whichthe optical figures of revolution are rotated. Light enter-ing the telescope parallel to this axis forms the on-axis(or zero-field) image directly on the optical axis at thefocal region. The field of view (FOV) for the telescope is

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the widest angular span measured on the sky that can beimaged distinctly by the optics.

In principle, a telescope can operate with just oneimage-forming optic (i.e., at prime focus), but without ad-ditional corrector optics, the FOV is quite restricted. If thetelescope is a one-element reflector, the prime focus andhence the instrument/observer are in the line of sight. Forlarge telescopes (i.e., >3 m) this may be used to advan-tage, but more commonly the light beam is diverted to oneside (Newtonian) or is reflected back along the line of sightby means of a secondary optic to a more convenient fo-cus position. Figure 6 illustrates the optical configurationsmost commonly used in reflector telescopes. In principle,the reflectors shown in Fig. 6 could be replaced with re-fractors to produce the same optical effects. However, thephysical arrangement of optics would have to be changed.

In practice, one tries to make the large optics as simpleas possible and to form good images with the fewest ele-ments. Other factors influencing the configuration includethe following:

1. Simplifying optical fabrication. Spherical surfaces aregenerally the easiest to make and test. Nonsymmetricaspherics are the opposite extreme.

2. Element-to-element position control, which thetelescope structure must provide. Tolerances becometighter as the focal ratio goes down.

3. Access to the focal region for viewing or mountinginstrumentation. Trapped foci (e.g., the Schmidt) aremore difficult to reach.

4. Compactness, which generally aids mechanicalstiffness.

5. Reducing the number of surfaces to minimize lightabsorption and scattering losses.

Analyzing telescope optical systems requires a choiceof method. The geometric optics method treats the incom-ing light as a bundle of rays that pass through the systemwhile being governed by the laws of refraction and re-flection. Ray-tracing methods based on geometric opticsare commonly used to generate spot diagrams of the raypositions in the final image, as illustrated in Fig. 7a. Morerigorous analysis based on diffraction theory is done bytreating the incoming light as a continuous wave and ex-amining its interaction with the optical system. Figure 7b isa computer-generated plot of light intensity in a diffractedimage formed by a circular aperture. The central peak rep-resents the Airy disc. For further detail on the use of thesemethods the reader is referred to texts on optics design.

B. Wide Field Considerations

Modern ground-based telescopes are usually designed toresolve images in the 0.25–1.0-arcsec range and to have

FOV from a few arc minutes to about one degree. In gen-eral, distortions or aberrations due to the telescope opticsexist in the images and are worse for larger field angles.Table II lists the basic types. Space-based telescopes (e.g.,the Hubble telescope) can be built to resolve images inthe 0.1 arcsec region because atmospheric seeing effectsare absent, but compensation must still be made for opti-cal aberrations. Aberrations can also arise from nonidealplacement of the optical surfaces (i.e., position errors) andfrom nonuniform conditions in the line of sight.

To correct distortions produced by optics, the designerfrequently tries to cancel aberrations produced at one sur-face by those produced at another. Extra optical surfacesmay be introduced for just this purpose. Ingenious opticalcorrector designs involving both refractors and reflectorshave resulted from this practice. Many of these designs aredescribed in texts on optics under the originators’ names(e.g., Ross, Baker, Wynne, Shulte, and Meinel). It is possi-ble, however, to cancel some field aberrations by modify-ing the principal optical surfaces or by using basic shapesin special combination. For example, the Ritchey–Cretiantelescope design for a wide FOV reduces coma by modi-fying the primary and secondary surfaces of a Cassegraintelescope. The Mersenne telescope cancels aberrationsfrom the primary (a parabola) with the secondary (anotherparabola).

A spherical mirror with the aperture stop set at its centerof curvature has no specific optical axis and forms equallygood images everywhere in the field. Images of distantobjects have spherical aberrations, however, and the fo-cal region is curved. The Schmidt telescope compensatesfor most of the spherical aberration by means of an as-pheric refractor at the center of curvature. The Maksutovtelescope introduces an offsetting spherical aberration bymeans of a spherical meniscus refractor. Numerous vari-ations of this approach have been devised yielding well-corrected images in field sizes of 10 deg and more. How-ever, large fields may have other problems.

During a long observing period, images formed by atelescope with a very large FOV (i.e., ∼1 deg or more)are affected differently across the field by differential re-fraction effects caused by the atmosphere. Color disper-sion effects (i.e., chromatic blurring) effectively enlargethe images as the telescope looks through an increasingamount of atmosphere. Differential image motion also oc-curs, varying as a function of position in the FOV, lengthof observation, and telescope pointing angle. Partial chro-matic correction can be made by inserting a pair of sepa-rately rotatable prisms, called Risley prisms, ahead of thefocal position. Even with chromatic correction, however,images are noticeably elongated (>0.5 arcsec) at the edgeof a 5-deg field compared with the on-axis image after acontinuous observing period of a few hours.

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FIGURE 6 Basic optical configurations for telescopes.

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FIGURE 7 Examples of image analysis methods. (a) Typical spotdiagrams of well-corrected images in the focal plane of a 1-degfield. Each image represents the ray bundle at that field location.(b) Computer-generated three-dimensional plot of intensity in aperfect image that has been diffracted by a circular aperture.

C. Instrumental Considerations: DetectorMatching and Baffling

At any focal position, the distance measured along theoptical axis within which the images remain acceptablydefined is referred to as the depth of focus. The detectorshould be adjusted to the most sharply focused position inthis region; however, it is more common to adjust the fo-cus (e.g., by moving the secondary) to sharpen the imagesat the detector. Certain instruments containing reimaging

TABLE II Basic Image Aberrations Occurring in Telescopes

Type Condition

Spherical aberrationa Light focuses at different places along theoptical axis as a function of radial positionin the aperture.

Comaa Image size (magnification) varies with radialposition in the focal region.Off-axis flaring.

Field curvaturea Off-axis images are not focused on the idealsurface, usually a plane.

Astigmatisma Light focuses at different places along theoptical axis as a function of angularposition in the aperture.

Distortiona Focused off-axis image is closer to or furtherfrom the optical axis than intended.

Chromatic aberration Shift in the focused image position as afunction of wavelength.

aAlso known as Seidel aberrations.

optics (e.g., spectrographs) require only that the image beformed at the entrance to the instrument (e.g., at a slit oraperture plate). There is a practical limit to the amountof allowable focal position movement obtained by mov-ing the secondary because optical aberrations, especiallyspherical aberration, are introduced when the mirror isdisplaced from its theoretically perfect position.

To view all or part of the focused FOV, it is commonto insert a field mirror into the beam at 45 deg to divertthe desired portion of the field out to an eyepiece or a TVmonitoring camera. The undiverted light to be observedpasses on to the instrument. The diverted light can be usedfor guiding purposes or to make different observations.

The angular size of the focused image (i.e., the imagescale) and its sensitivity to defocusing changes is governedby the effective focal length (EFL) of the optical systemthat formed the image:

image scale = 1

EFL

= radians on the sky

length in the focal plane.

Large EFL values produce comfortable focal depths, butthe image sizes are relatively large. The physical size ofthe detector may place a limit on the FOV that can beaccommodated for a given scale, hence a potential needfor a different focal position or reimaging optics. Thisissue has become quite important with the advent of solid-state image detectors, known as CCDs (Charge CoupledDevices), that have much higher quantum efficiency thanphotographic plates but are difficult to make in large sizes(i.e., approximately 50 × 50 mm is considered large in1990).

Light baffles and aperture stops are important but fre-quently neglected aspects of telescope design. It is com-mon to place a light baffle just ahead of the primary toblock out unwanted edge effects, in which case the bafflemay become the aperture stop. In some cases, the primarysurface may be reimaged further along the optical pathwhere a light baffle can be located. This may be done ei-ther to reduce the size of the required baffle or to locate itadvantageously in a controlled environment (e.g., at cryo-genic temperature to reduce thermal radiation effects). Inother cases, the aperture may be set by undersizing one ofthe optical elements that is further along the optical path.An example is an IR-optimized telescope, where the sec-ondary is made undersized to ensure that the detector can-not see past the edge of the primary mirror. The effectivelight-gathering power of the telescope can be significantlyreduced under these conditions.

Obstructions in the light path further reduce light-gathering power. The most common obstructions are the

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secondary and auxiliary optics along with the mechanicalstruts that support them. It is common for 10–20% of theaperture to be obstructed in this manner. Depending uponthe telescope style and the instrument location, it may benecessary to use a light baffle to prevent the detector fromseeing unwanted radiation. For example, a detector at theCassegrain focus of a two-mirror telescope can see unfo-cused light from stars directly past the perimeter of thesecondary mirror unless obstructing baffles are provided.The size and location of these baffles are generally deter-mined empirically by ray-tracing, and it is a fact that largerFOV requires larger baffles that mean more obstruction.Thus, one cannot truly determine telescope light-gatheringpower until the usage is considered.

III. TELESCOPE OPTICS

Telescope performance depends fundamentally upon thequality of optics, especially the surface figures. That qual-ity in most telescopes is a compromise between what theoptical designer has specified, what the glassmakers andopticians can make, and how well the mechanical sup-porting structures perform. Especially for larger sizes, oneshould specify the optics and their supports at the sametime. How the optics are to be tested should also be con-sidered since the final figure corrections are almost alwaysguided by test results. Optical figuring methods todayrange from simple manual lapping processes to sophis-ticated computer-controlled polishers (CCP) and directmachining using diamond tools. The remarks to followare only a summary of a complex technical field.

A. Refractive Optics

Light passing through the surface of a refractive optic ischanged in direction according to Snell’s law of refraction:

η1 sin θ1 = η2 sin θ2,

where η1 and η2 are the refractive indices of the materialson either side of the surface and θ1 and θ2 the angles withrespect to the surface normal of incidence and refraction.Producing a satisfactory refractor is, therefore, done byobtaining transparent glass or another transmitting mate-rial with acceptable physical uniformity and accuratelyshaping the surfaces through which light passes. Some-times the optician can alter the surface to compensate fornonuniform refractive properties. Losses ordinarily occurat the surface due to scattering and also to the change inrefractive index. Antireflection coatings can be applied toreduce surface transmission losses, but at the cost of re-stricting transmission to a specific wavelength range. Fur-ther losses occur internally by additional scattering andabsorption.

Manufacturing methods for refractive optics are similarto those for reflectors.

B. Reflective Optics

Light reflecting off a surface is governed by the law ofreflection:

θ1 = −θ2,

where θ1 and θ2 are the angles of incidence and reflec-tion, respectively. Controlling the slope at all points onthe reflecting surface is, therefore, the means for control-ling where the light is directed. Furthermore, any part ofthe surface that is out of its proper position, measuredalong the light path, introduces a change at that part of thereflected wavefront (i.e., a phase change) equal to twicethe magnitude of the position error. Surface accuracy isthus the prime consideration in making reflective optics.Achieving high reflectivity after that is usually done byapplying a reflective coating.

The most common manufacturing method is to rough-machine or grind the mirror blank surface and progres-sively refine the surface with abrasive laps. Certain kindsof mirrors, especially metal ones, may be diamond turned.In this case, the accuracy of the optical surface may begoverned by the turning machine, whereas ordinarily theaccuracy limits are imposed principally by the optical testmethods and the skill of the optician. High-quality tele-scope mirrors are typically polished so that most of thereflected light (>80%) is concentrated in an image that isequivalent to the Airy disc or the seeing limit, whicheveris larger.

C. Materials for Optics

Essential material requirements for all optical elementsare related to their surfaces. One must be able to polish ormachine the surfaces accurately, and afterward the blankshould not distort uncontrollably. Residual stresses andunstable alloys are sources of dimensional instability to beavoided. Stresses also cause birefringence in refractors.

1. Refractors

Refractors should transmit light efficiently and uniformlythroughout the operating wavelength region. However,there is no single material that transmits efficiently from0.3 to 40 µm. One typically chooses different materials forthe UV, near-IR (to �2 µm), and far-IR regions. Glass-makers can control the index of refraction to about onepart in 106, but only in relatively small blanks (<50-cmdiameter). In larger sizes, index variations and inclusionslimit the availability of good-quality refractor blanks tosizes less than 2-m diameter.

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2. Reflectors

The working part of a reflector optic is usually the thinmetallic layer, 1000–2000 A thick, that reflects the light.An evaporated layer of aluminum, silver, or gold is mostcommonly used for this purpose, and it obviously mustbe uniform and adhere well to the substrate. Most of thework in making a reflector, however, is in producing theuncoated substrate or mirror blank. The choice of materialand the substrate configuration are critically important tothe ultimate reflector performance.

Reflector blanks, especially large ones, require specialmeasures to maintain dimensional (surface) stability. Theblank must be adequately supported to retain its shapeunder varying gravitational loads. It must also be stableduring normal temperature cycles, and it should not heatthe air in front of the mirror because that causes ther-mal turbulence and worsens the seeing. A mirror-to-airtemperature difference less than about 0.5◦C is usuallyacceptable. The support problem is a mechanical designconsideration. Thermal stability may be approached in anyof several ways:

1. Use materials with low coefficients of thermalexpansion (CTE).

2. Lightweight the blank to reduce the mass andenhance its ability to reach thermal equilibriumquickly (i.e., by using thin sections, pocketed blanks,etc.). Machineability or formability of the material isimportant for this purpose.

3. Use materials with high thermal conductivity (e.g.,aluminum, copper, or steel).

4. Use active controls for temperature or to correct forthermally induced distortion. Elastic materials withrepeatable flexure characteristics are desirable.Provisions in the blank for good ventilation may benecessary.

Materials with low CTE values include borosilicateglass, fused silica, quartz, and ceramic composites.Multiple-phase (also called binary) materials have beendeveloped that exhibit near-zero CTE values, obtained byoffsetting the positive CTE contribution of one phase withthe negative CTE contribution from another. Zerodurmade by Schott Glaswerke, ULE by Corning GlassWorks, and epoxy–carbon fiber composites are examplesof multiple-phase materials having near-zero CTE oversome range of operating temperature. Fiber compositesusually require a fiber-free overlayer that can be polishedsatisfactorily.

One usually considers a lightweight mirror blank to re-duce costs or to improve thermal control. This is particu-larly true for large telescopes. Reducing mirror weight

often produces a net savings in overall telescope costeven if the lightweighted mirror blank is more expensivethan a corresponding solid blank. The important initialstep is to make the reflecting substrate or faceplate asthin as possible, allowing for polishing tool pressures andother external forces. One has three hypothetical designoptions:

1. Devise a way to support just the thin monolithic face-plate. This approach works best for small blanks. Large,thin blanks require complex supports and, possibly, ameans to monitor the surface shape for active control pur-poses. The European Southern Observatory’s 3.5 m NewTechnology Telescope (NTT), commissioned in 1990, is agood example of this approach. The additional complexityof the mirror support is made more worthwhile by using itto correct for image aberrations due to other causes. TheNTT has resolved images of 0.33 arcsec (containing 80%of the focused light and all of the aberrations due to thetelescope and atmosphere), perhaps, the best performanceto date for a large ground-based telescope.

2. Divide the faceplate into small, relatively rigid seg-ments and devise a support for each segment. Segmentposition sensing and control is required: a sophisticatedtechnical task. The Keck Ten Meter Telescope uses thisapproach.

3. Reinforce the faceplate with a gridwork of ribs orstruts, possibly connected to a backplate, to create a sand-wichlike structure. One may create this kind of struc-ture by fusing or bonding smaller pieces, by casting intoa mold, or by machining away material from a solidblock.

All of these approaches have been used to makelightweight reflector blanks. Making thin glass faceplatesup to about 8 m is considered feasible by fusing togethersmaller pieces or direct casting. Titanium silicate,fused silica, quartz, and borosilicate glass are candidatematerials. Castings of borosilicate glass up to 6 m (e.g.,the Palomar 5-m mirror) have been produced; 8 m isconsidered feasible. Structured (i.e., ribbed) fused silicaand titanium silicate mirrors up to 2.3 m have beenproduced (e.g., the Hubble Space Telescope mirror); upto 4 m is considered feasible.

Metals may also be used for lightweight mirrors buthave not been widely used for large telescopes because oflong-term dimensional (surface) changes. The advent ofactive surface control technology may alter this situationin the future. Most metals polish poorly, but this can beovercome by depositing a nickel layer on the surface tobe polished. Most nonferrous metals can also be figuredon diamond-turning machines; however, size is limitedpresently to about 2 m.

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IV. SPECTRAL REGION OPTIMIZATION:GROUND-BASED TELESCOPES

The optical/IR window of the atmosphere from 0.3 to35 µm is sufficiently broad that special telescope featuresare needed for good performance in certain wavelengthregions. Notably, these are needed for the UV region lessthan about 0.4 µm and the thermal IR region centeredaround 10 µm. In the UV, it is difficult to maintain highefficiency because of absorption losses in the optics. Whenobserving in the IR region, one must cope with blackbodyradiation emitted at IR wavelengths by parts of the tele-scope in the light path, as well as by the atmosphere. Dis-tinguishing a faint distant IR source from this nearby un-wanted background radiation requires special techniques.Using such techniques, it is common for astronomers touse ground-based telescopes to observe IR sources thatare more than a million times fainter than the IR emis-sion of the atmosphere through which the source must bediscerned.

A. UV Region Optimization

The obvious optimizing step for the UV region is to putthe telescope into space. If the telescope is ground-based,however, one good defense against UV light losses is to usefreshly coated aluminum mirror surfaces. Reflectivity val-ues in excess of 90% can be obtained from freshly coatedaluminum, but this value rapidly diminishes as the surfaceoxide layer develops. Protective coatings such as sapphire(Al2O3) or magnesium fluoride (MgF2) can be used to in-hibit oxidations. Also, multilayer coatings can be appliedto the surfaces of all optics to maximize UV throughput.However, these coatings greatly diminish throughput atlonger wavelengths, which leads to the tactic of mountingtwo or more sets of optics on turrets, each set being coatedfor a particular wavelength region. The desired set is ro-tated into place when needed. This tactic obviously worksbest for small optics, not the primary.

Many refractive optics materials absorb strongly in theUV. Fused silica is good low-absorbing material. If opticsare cemented together, the spectral transmission of the ce-ment should be tested. Balsam cements are to be avoided.

B. IR Region Optimizations

One cardinal rule for IR optimization is to minimize thenumber and sizes of emitting sources that can be seenby the detector. This includes mechanical hardware suchas secondary support structures and baffles, as well asseemingly empty spaces such as the central hole in theprimary mirror. All of these emit black body radiationcorresponding to their temperatures.

Since the detector obviously must see the optical sur-faces, another cardinal rule is to reduce the emissivity ofthese surfaces with a highly reflective coating. If a coat-ing is 98% reflective, it emits only 2% of the blackbodyradiation that would otherwise occur if the surface weretotally nonreflective. If possible, the detector should seeonly reflective surfaces, and these should be receiving ra-diation only from the sky or other reflective surfaces inthe optical train. Objects that must remain in the line ofsight can also be advantageously reflective provided thatthey are not looking at other IR-emitting objects that couldsend the reflected radiation into the main beam.

Achieving these goals may require one or more of thefollowing special telescope features:

1. Using an exchangeable secondary support structure.This enables elimination of oversize secondaries and baf-fles that might be needed for other kinds of observation.

2. Using the secondary mirror as the aperture stop andmaking it sufficiently undersized that it cannot see pastthe rim of the primary mirror.

3. Putting all of the secondary support (except thestruts) behind the mirror so that none of the hardwareis visible to the detector.

4. Placing a specially shaped (e.g., conical) reflectiveplug at the center of the secondary to disperse radiationemitted from the central hole region of the primary mirror.

A basic technique for ground-based IR observing isthat of background subtraction. This involves alternatingthe pointing direction of the telescope between the object(thus generating an object-plus-background signal fromthe detector) and a nearby patch of sky that has no ap-parent object (thus generating a background-only signal).Signal subtraction then eliminates the background signalcommon to both sky regions. Methods for alternating be-tween positions include (1) driving the telescope betweenthe two positions, usually at rates below 0.1 Hz, (2) wob-bling the secondary mirror at rates between 10 and 50 Hz(called chopping), and (3) using focal plane modulatorssuch as rotating aperture plates (called focal plane chop-ping). With solid state CCD detectors, one may simul-taneously observe the object and a nearby backgroundpatch and electronically remove the measured backgroundthrough appropriate processing of the data from individualpixels on the detector.

V. MECHANICAL CONFIGURATIONS

The mechanical portion of a mounted, ground-based tele-scope must support the optics to the required precision,point to and track the object being observed, and support

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FIGURE 8 Basic telescope mounting styles in popular use. Nu-merous variants on each style are in existence.

the instrumentation in accessible positions. It is custom-ary to distinguish between the telescope (or tube), whichusually supports the imaging optics, and the mounting,which points the telescope and includes the drives andbearings. Tracking motion is usually accomplished by themounting.

Most telescope mountings incorporate two, and occa-sionally three, axes of rotation to enable pointing the tele-scope at the object to be observed and tracking it to keep itcentered steadily in the FOV. In general, the rotating massis carefully balanced around each axis to minimize drivingforces and the location of each rotation axis is chosen tominimize the need for extra counterweights.

Figure 8 illustrates the basic mounting styles that arediscussed in the next section.

A. Mounting Designs

A hand-held telescope is supported and pointed by theuser. The user is the mounting in this case. The mechani-cal mounting for a telescope performs essentially the samefunction, except that a mechanical mounting can supportheavier loads and track the object more smoothly. As arule of thumb, short-term tracking errors in high-qualitytelescopes are less than 10% of the smallest resolved ob-ject that can be observed with the telescope. Smoothness

of rotation is important for long-term observations (i.e.,no sudden movements) which mandates the use of high-quality bearings. Pressurized oil-film bearings (hydrostat-ics) are used in large telescopes for this reason.

Telescope drives range widely in style. The chief re-quirements are smoothness, accuracy, and the ability tomove the telescope rapidly for pointing purposes (i.e.,slewing) or slowly for tracking (i.e., at one revolution perday or less). Electric motor driven traction rollers, wormgears, or variants on spur gears are most commonly used.Position measuring devices (encoders) are often used tosense telescope pointing and to provide input data forautomatic drive controls. Adjustments in tracking ratesor pointing are accomplished either by manual controlfrom the observer or, possibly, by star-tracking automaticguiding devices. Pointing corrections may also be basedon data stored in a computer from mounting flexure anddriving-error calibrations done at an earlier time. Tele-scope pointing accuracies to about 1 arcsec are currentlypossible with such corrections. Once the object is locatedin the FOV, the ability to track accurately is the most im-portant consideration.

1. Equatorial Mounts

Astronomical telescopes ordinarily are used to observestars and other objects at such great distances that theywould appear stationary during an observation period if theearth did not rotate. Accordingly, the simplest telescopetracking motion is one that offsets the earth’s rotation withrespect to “fixed” stars (i.e., sidereal rate) and is done abouta single axis parallel to the earth’s north–south (N–S)polar axis. Equatorial mountings are those that have oneaxis of rotation (i.e., the polar or right ascension axis) setparallel to the earth’s N–S axis. This axis is tilted towardthe local horizontal plane (i.e., the ground) at an angleequal to local latitude. A rotatable cross-axis (also calleddeclination axis) is needed for initial pointing and guidingcorrections, but the telescope does not rotate continuouslyaround this axis while tracking.

The varieties of equatorial mountings are limited onlyby the designer’s imagination. The basic varieties, how-ever, are the following:

1. Those that mount the tube to one side of the polar axisand use a counterweight on the opposite side to maintainbalance. For an example, see Fig. 2. These are sometimescalled off-axis or asymmetric mounts. It is also possible tomount a second telescope in place of the counterweight.

2. Those that support the tube on two sides in a bal-anced way to eliminate the need for a heavy counterweight.Yokes and forks are most commonly used, especially forlarger telescopes. Theses are sometimes called symmetric

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mounts. For an example, see Fig. 3 which shows a horse-shoe yoke mount.

2. Other Mounting Styles

The alt–az mounting is configured around a vertical (az-imuth) axis of rotation and a horizontal cross-axis (thealtitude or elevation axis). The altitude–altitude (alt–alt)mounting, not widely used, operates around a horizontalaxis and a cross-axis that is horizontal when the telescopepoints at the meridian and is tilted otherwise (similar to anEnglish yoke with its polar axis made horizontal). Witheither of these styles, because neither axis is parallel tothe earth’s rotation, it is necessary to drive both axes atvariable rates to track a distant object. Furthermore, theFOV appears to rotate at the focal region, which often ne-cessitates a derotating instrument mounting mechanism,also moving at a variable rate. These factors inhibited theuse of these mountings, except for manually guided tele-scopes, until the advent of computers on telescopes. Com-puters enable second-to-second calculation of the driverates, which is required for accurate tracking. The alt–azconfiguration cannot track an object passing through thelocal zenith because the azimuth drive rate theoreticallybecomes infinite at that point. In practice, alt–az telescopesare operated to within about 1 deg of zenith.

The famous Herschel 20-ft telescope, built in Englandin 1783, was the first large alt–az telescope. Very few werebuilt after that, but the trend today is toward alt–az mounts(see Section I.B and Table I). The ability to support themain azimuth bearing with a solid horizontal foundation isadvantageous, as is the fact that the altitude axis bearingsdo not change in gravity orientation. These are importantconsiderations when bearing loads of hundreds of tonsmust be accommodated. The alt–alt mounting is not assuitable for carrying heavy loads because the cross-axis isusually tilted with respect to gravity.

B. Telescope Tubes and InstrumentConsiderations

Design of the tube begins with the optical configuration.Tube structures are designed to maintain the optics inalignment, either by being stiff enough to prevent exces-sive deflections or by deflecting in ways that maintainthe optics in the correct relative position. The well-knownSerrurier truss first used on the Palomar 5-m telescope isa much-copied example of the latter (see Fig. 9). The tubestructure is normally used to support the instruments at thefocal positions, sometimes along with automatic guiders,field-viewing TV monitors, calibration devices, and fieldderotators. Large telescopes often do not use the Serruriertruss design specifically, but the flexure of the structure is

FIGURE 9 Serrurier truss used to maintain primary-to-secondaryalignment as the tube rotates. Equal deflections and parallelogramaction at both ends keep the optics parallel and equidistant fromthe original optical axis. Similar flexure is designed into most largetelescope tube structures.

usually designed to perform the same function. Moderncomputer-based structural analysis programs, developedsince about 1960 and thus not available to Serrurier, pro-vide the tools to create lighter, stiffer structures withoutambiguity about the positions of the optics.

Focal positions (i.e., instrument mount locations) on thetube obviously move as the telescope points and tracks,which can be a problem for instruments at those locationsthat work poorly in a varying gravity environment. In thosecases, one can divert the optical beam out of the telescopetube along the cross-axis to a position on the mountingor even outside the mounting. Flat mirrors are normallyused for this purpose. To reach a constant-gravity posi-tion with an equatorial mounting, one must use severalmirrors to bring the converging beam out: first along thedeclination axis, then the polar axis, and finally to a focusoff the mounting. This is known as the coude focus andis commonly used to bring light to spectrographs that aretoo large to mount on the telescope tube.

One can reach a constant-gravity focus (instrument lo-cation) on an alt–az telescope by simply diverting the beamalong the altitude cross-axis to the mounting structure thatsupports the tube. This is called the Nasmyth focus afterits Scottish inventor. The instrument rides the mountingas it rotates in azimuth but does not experience a changein gravity direction.

VI. CONSIDERATIONS OF USAGEAND LOCATION

Considering the precision built into most optical tele-scopes, one would expect them to be sheltered carefully. In

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practice, most telescopes must operate on high mountains,in the dark, and in unheated enclosures opened wide to thenight sky and the prevailing wind. Under these conditions,it is not unusual to find dust or dew on the optics, a cer-tain amount of wind-induced telescope oscillation, and in-sects crawling into the equipment. Certain insects flyingthrough the light path can produce a noticeable amountof IR radiation. Observer comforts at the telescope areminimal.

In designing a telescope, one should consider its us-age and its environment. A few general remarks in thisdirection are provided in the following sections.

A. Seeing Conditions

The seeing allowed by the atmosphere above the telescopeis beyond ordinary control. Compensation may be possibleas discussed in Section I.A. but the choice of site largelydetermines how good the imaging is. Seeing conditionsin the region of 0.25 arcsec or less have been measuredat certain locations, but more typically, good seeing is inthe 0.5–1.0 arcsec range. Beyond 2–3 arcsec, seeing isconsidered poor. To the extent possible, one should buildthe telescope to produce images equal to or better than thebest anticipated seeing conditions.

Locating the telescope at high altitudes usually reducesthe amount of atmosphere and water vapor that is in theline of sight (important for IR astronomy), however, thenumber of clear nights and the locally produced thermalturbulence should also be considered. In many locations,a cool air layer forms at night near the ground which canbe disturbed by the wind and blown through the line ofsight. In other cases, warm air from nearby sources can beblown through the line of sight. In either case, telescopeseeing is worsened.

Other seeing disturbances can originate inside the tele-scope enclosure. Any source of heat (including observers)is a potential seeing disturbance. Also, any surface thatlooks at the night sky, and hence is cooled by radiativeexchange, may be a source of cooled air that can disturbseeing if it falls through the line of sight. If possible, it isdesirable to allow the telescope enclosure to be flushed outby the wind to eliminate layers and pockets of air of dif-ferent temperatures. Some telescope buildings have beenequipped with air blowers to aid in the process, but dump-ing the air well away from the building has not alwaysbeen possible even though it should be done.

The study of atmospheric seeing has become a relativelyadvanced science, and the telescope builder is well advisedto consult the experts in choosing a site or designing anenclosure. Having chosen a site, one may be guided by thetruism that seeing seldom improves by disturbing MotherNature.

B. Nighttime versus Daytime Usage

With the advent of IR astronomy, optical telescopes beganto be used both day and night because the sky radiationbackground is only slightly worse at IR wavelengths dur-ing the day compared with night. During the day it is muchharder to find guide stars, and the telescope must oftenpoint blindly (and hence, more accurately) at the objectsto be observed; but much useful data can be obtained.Some problems arise from this practice, however.

A major purpose of the telescope enclosure, other thanwindscreening, is to keep the telescope as close as possibleto the nighttime temperature during the day so that it canequalize more rapidly to the nighttime temperature at theoutset of the next night’s observing. Obviously, this cannotbe done if the telescope enclosure has been open during theday for observation. The condition is worsened if sunlighthas been allowed to fall on the telescope during the day.Accordingly, optical/IR telescopes should be designed forrapid thermal adjustment.

Some of the design options in thermal control are (1) toinsulate heavy masses that cannot equalize quickly, (2) toreduce weights and masses, (3) to provide good ventila-tion (i.e., avoiding dead air spaces that act as insulators),(4) to make surfaces reflective so that radiative coupling tothe cold night sky is minimized, and (5) to isolate or elim-inate heat sources. One should also consider using partsmade from materials with low thermal expansion, but thesehave limited value if their heating effects are allowed tospoil the telescope seeing.

C. Remote Observing on the Ground

The traditional stereotype of an astronomer is a personperched on a high stool or platform, peering through theeyepiece and carefully guiding the telescope. The modernreality is likely to be quite different. Sophisticated elec-tronic detectors replace the eye. Automatic star-trackingguiders take over the guidance chore. The astronomer sitsin a control room sometimes far away from the telescope.A TV monitor shows the FOV or, at least, that part ofthe field not falling on the detector. A computer logs thedata and telescope conditions. The telescope is not evenseen by the astronomer: It can be in the next room or evena continent away if the communication link is properlyestablished.

The advent of space-based astronomy clearly markedthe time when the astronomer and the telescope were sepa-rated. The same separation is taking place in ground-basedastronomy, albeit less dramatically. Numerous demonstra-tions have occurred during the 1970s and 1980s in whichastronomers conducted observing runs on telescopes lo-cated at distant sites. In one case, the astronomer was in

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Edinburgh, Scotland, and the telescope was in Hawaii. The“first light” pictures taken with the European SouthernObservatory’s 3.5-m NTT in Chile were transmitted to as-tronomers in Munich, Germany. In both cases the connec-tion was through a communications satellite. This trendis likely to accelerate as the cost for such connections re-duces and the data transmission rates increase.

VII. OBSERVING IN SPACE: THE HUBBLESPACE TELESCOPE

The Hubble Space Telescope, or HST, named in honorof Dr. Edwin P. Hubble, was launched by the NationalAeronautics and Space Administration (NASA) into or-bit 614 km above the earth on April 24, 1990, from SpaceShuttle “Discovery.” Launch had been delayed more than 3years following the loss of the Space Shuttle “Challenger”in 1986. Figure 10 illustrates the HST and its major com-ponents. Although many other smaller telescopes have

FIGURE 10 Schematic illustration of the Hubble Space Tele-scope (HST), showing its principal components. Light is focusedbehind the primary mirror and directed to the radial and axial bayinstruments. Data are telemetered to the ground from antennasnot shown. HST is optimized for UV region performance down to0.12 µm wavelength and for observation of faint objects in boththe UV and visible wavelength ranges.

previously been used in space, the HST represents such alarge step in observing power and expected lifetime (15years) that, for many astronomers, it marks the matura-tion of space-based astronomy. The discussion to followis about the HST, but many of its operating characteristicsare common to all telescopes operating in space.

The HST differs significantly from ground-based tele-scopes. It can observe throughout the UV region, its prin-cipal scientific justification, and it avoids the image dis-tortions and “sky background” light emission due to theearth’s atmosphere. Thus, very faint, small (presumablyvery distant) objects can be discerned that would be hope-lessly lost in sky background seen from the ground. Toproduce reasonably good images at short UV wavelengths,the optics had to be substantially better than those in eventhe best telescopes on the ground, which results in excel-lent optical region images.

The HST can also observe in all regions of the IR, butits optics and structures are not cooled to minimize radi-ation emission, and its images are diffraction limited atIR wavelengths. In the late 1990s, NASA launched the“Space Infrared Telescope Facility,” a 1-m class telescopethat operates inside an enclosure cooled by liquid heliumto avoid the excess radiation problem.

X-ray telescopes must operate in space like the HST,but their optics consist of near-conical shapes, appearingalmost cylindrical in form, with the central axis pointedat the object. Light reflects at such steep incidence anglesfrom these surfaces that it is not absorbed despite the highenergy of the rays; hence it can be directed to a focus byproperly shaping the optics.

HST operates under remote control in a hostile, highradiation, vacuum environment while producing its ownpower from solar panels. To avoid artificial light scatter-ing, the nearby region of space must not be polluted withgases or debris from the telescope because no helpfulbreeze will blow it away. Since instrument changeoversare not possible except by visiting astronauts, HST mustcarry all of its instruments, essentially ready to work at alltimes. To maintain its orbital altitude, HST completes one“day-night” orbit of the earth every 96 min. Optical align-ment must be maintained despite the rapid hot-to-cold-to-hot temperature cycling. The short observing periods, themultiplicity of instrumentation, the remote location, andthe enormous number of objects to study produced a needto schedule astronomers differently than on the ground.For this purpose, a new organization, the Space TelescopeScience Institute in Baltimore, Maryland, was formed in1981 and is responsible for the scientific operation of thetelescope.

The optical configuration of HST is “Ritchey-Chretien”similar to many ground-based telescopes, with an 18arcmin field of view. The mirrors are held in alignment

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by a special graphite-epoxy truss structure that is nearlydimensionally invariant under changing temperature con-ditions. Light from the focal plane can be diverted into four“radial bay” positions which contain three “fine guidancesensors” (FGSs) and the “wide-field camera” (WFC), aninstrument for recording at all times a portion of any sceneviewed by the telescope. By adjusting the pointing of thetelescope, light from a chosen object can be directed intothe entrance of one of four “axial bay” instruments directlybehind the focal plane. When an object is being observedby an axial bay instrument, the WFC observes an adja-cent region which astronomers hope will result in unex-pected “serendipity discoveries.” The axial bay containsthe “faint object camera,” two spectrographs (high and lowresolution), and a photometer. All of these instrumentsare equipped with electronic detectors for converting lightinto transmittable telemetry data received on the groundby NASA’s global network of radio receiving antennas.

The primary mirror blank for the HST is a sandwichstructure made of Corning’s “zero-expansion” ULE withan “egg-crate” style central core. It weighs about 20%as much as an equivalent solid disc. The low expansionproperties of ULE enabled thin pieces to be assembledby flame welding and fusion bonding in a furnace with-out fear of thermal stress fracture and also avoids dimen-sional changes in the changing temperature environmentof space. The primary mirror was later polished by thePerkin–Elmer Corporation to an accuracy enabling 80%of the focused test light (at 0.63 µm wavelength) to be con-centrated into an image smaller than 0.1 arcsec across, verynear the diffraction limit and an extraordinary achievementfor such a large mirror.

When launched, the 2.4 m HST was the largest opticaltelescope designed for astronomy ever orbited and alsothe costliest ($2 billion). Built in the period 1977–1985,HST cost 200 times as much as typical ground-based tele-scopes of equivalent size built during the same period.Annual operating expenses are expected to be nearly 10%of construction costs, which makes it the world’s most ex-pensive observatory. Thus, the financial commitment bythe U.S. government to HST represents major support ofastronomy and was obtained only after a prolonged effortby hundreds of astronomers during the 1960s and 1970s.

One may imagine the dismay of all concerned when theHST was found soon after launch to have flawed imagingability due to an incorrect curvature of its primary mirror.The images were blurred by spherical aberration 15 timesgreater than the specified 0.1 arcsec image resolution andno ground-controlled adjustment could eliminate the prob-lem. Despite this enormous initial setback, HST has be-come operational. Corrective measures were taken in 1993when a “second generation” instrument package contain-ing a compensating lens was installed by astronauts. Until

then, astronomers used a computer to subtract the aber-ration from the images, a tedious but workable process.Considering the level of quality of the optics when testedindividually and the imaging problems discovered later, afew words about the mirror testing are appropriate.

Testing of the HST primary required compensation ofthe test results for the effects of gravity which the mirror,tested on the ground, would not experience in space. Thiswas done successfully. Additionally, the mirror was opti-cally tested using a “null lens,” which is an optic used tomake the mirror seem to be a sphere that is focusing lightoriginating at or near its center of curvature, a positionthat can be located with precision. In the telescope, themirror functions as a parabola focusing light originatingat infinity, much like an automobile headlamp in reverse.Simulating these conditions in an optical shop is very dif-ficult for large mirrors, so a null lens is used. However, anyerrors existing in the null lens remain in the testing dataand cannot easily be separated from errors in the mirror.Accordingly, opticians generally perform several differenttests for comparison, searching for commonality in theresults. One element of the “most accurate” HST null lenswas incorrectly positioned, which caused the opticians topolish the mirror to a different curvature than was neededto function properly with the secondary mirror. The dis-agreement with other tests (made with other, less accuratenull lenses) was discounted, and no shop tests were madewith both the primary and secondary mirrors workingtogether (as is typical for most telescopes). Unfortunately,the images formed in space by the two-mirror system forHST did contain considerable spherical aberration (theless accurate tests were right), and correction will requirea new secondary mirror or an additional correcting lens.Repolishing the primary mirror would be much moreexpensive.

Pointing the HST, or any orbiting telescope, to a newobject for observation and tracking on it steadily and accu-rately is challenging. Changing position is accomplishedby a “reaction motor” on each of three coordinate axes.Powered acceleration of the motor rotor produces a reac-tive torque on the telescope, causing it to rotate in the oppo-site direction. On reaching the desired rotational velocity,the telescope and rotor “coast.” Motion is stopped by ap-plying power to the rotor to slow its rotation. This “slew-ing” action coarsely positions the telescope, enabling apair of “fixed head” star trackers (small guide telescopeswith relatively large fields of view) to identify a pair ofpreselected, bright, guide stars. Next, the three “fine guid-ance sensors” (FGS), receiving light from the main focalplane as mentioned earlier, begin searching until two have“locked on” to suitable guide stars, presumably faint, butnear the object to be observed and known in position tohigh accuracy. After that, signals from the FGSs are used

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to control the reaction motors for tracking. The system isdesigned to control the 12-ton HST to a pointing accuracyof about 0.01 arcsec, roughly 10 times more accurate thantypical ground-based telescope performance and all donewithout a solid foundation to react against.

Only two FGSs are needed to guide the HST. The thirdFGS can be used to measure star positions (i.e., to do as-trometry) after the other two have locked onto stars withknown position coordinates. Thus, HST is equipped to up-grade its own guide-star catalog to a precision greater thanis possible from the ground. The process of pointing to anew object and locking onto guide stars requires upwardof 30 min, a large penalty in observing time but a tollthat must be paid to operate in space. Ground-based tele-scopes typically perform the same operations in less than5 min.

The HST is an extraordinary telescope and may indeedprove to be the beginning of the era in which most profes-sional astronomy is done in space. Dark skies are becom-ing hard to find on the ground, and ingenious correctionsfor the atmosphere will never be as good as avoiding theproblem altogether, not to mention the loss of wavelengthcoverage on the ground. Many other orbiting telescopesare in progress, and plans already exist at NASA for a10-m class optical space telescope, plus much larger tele-scopes as to operate in the millimeter and longer wave-length range.

Nevertheless, most professional astronomy is still doneon the ground, as the formidable costs of working inspace, exemplified by HST, must be justified, presumablyby new discoveries. The location and special abilities of

the HST (when its optics are finally corrected) assuresthis possibility. The worth of new discoveries is impos-sible to measure in advance, but it seems that a brightfuture for humanity depends upon them. Galileo wouldagree.


ELECTROMAGNETICS • GAMMA-RAY ASTRONOMY • IN-FRARED ASTRONOMY • OPTICAL DIFFRACTION • ULTRA-VIOLET SPACE ASTRONOMY

BIBLIOGRAPHY

Barlow, B. V. (1975). “The Astronomical Telescope,” Wykeham,London.

Bell, L. (1981). “The Telescope,” Dover, New York.Burbidge, G., and Hewitt, A. (eds.) (1981) “Telescopes for the 1980s,”

Annual Reviews, Palo Alto, CA.Driscoll, W. G., and Vaughan, W. (eds.) (1978). “Handbook of Optics,”

McGraw-Hill, New York.King, H. C. (1979). “The History of the Telescope,” Dovehhr, New York.Kingslake, R. (1983). “Optical System Design,” Academic Press,

Orlando, Florida.Kuiper, G., and Middlehurst, B. (eds.) (1960). “Telescopes,” Stars and

Stellar Systems, Vol. 1. University of Chicago Press, Chicago.Learner, R. (1981). “Astronomy through the Telescope,” Van Nostrand

Reinhold, New York.Marx, S., and Pfau, W. (1982). “Observatories of the World,” Van Nos-

trand Reinhold, New York.Schroeder, D. J. (1987). “Astronomical Optics,” Academic Press, San

Diego.

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Encyclopedia of Physical Science and Technology EN017F-33 July 31, 2001 19:45

Ultraviolet Space AstronomyGeorge R. CarruthersNaval Research Laboratory

I. Significance of the ResearchII. Instrumentation for Ultraviolet

Space AstronomyIII. The SunIV. Planetary AtmospheresV. Comets

VI. The StarsVII. Interstellar Gas

VIII. Interstellar DustIX. Extragalactic Objects

GLOSSARY

Blackbody radiator Object that absorbs or emits radia-tion with 100% efficiency at all wavelengths and whoseemission spectrum follows the laws derived by MaxPlanck and others.

Extinction Attentuation of radiation by the processes ofscattering, pure absorption, or both.

Extreme ultraviolet Wavelength range below 1000 A,extending to the X-ray wavelength range below 100 A.

Far ultraviolet Wavelength range below 2000 A, usuallythe range 1000–2000 A.

Flux distribution Radiated energy, in energy units ornumber of photons per unit area or for the total object,per second vs wavelength in a region of the electro-magnetic spectrum.

Ionosphere Region of a planetary atmosphere in whicha significant portion of the atoms or molecules are ion-ized (i.e., stripped of one or more electrons).

Middle ultraviolet Wavelength range 2000–3000 A.Resonance transition Spectral transition of an atom,

molecule, or ion that is between the ground state(state of lowest energy) and an excited state (ofhigher energy), with corresponding emission or ab-sorption of a discrete wavelength of electromagneticradiation.

Subordinate transition Spectral transition between twoexcited states.

ULTRAVIOLET (UV) SPACE ASTRONOMY is thestudy of extraterrestrial objects in the UV wavelengthrange of the electromagnetic spectrum. This portion of thespectrum provides information unavailable in other wave-length ranges, particularly on planetary and stellar atmo-spheres and the interstellar medium. However, because theUV spectrum is inaccessible to ground-based telescopes,UV astronomy must be conducted with instruments on

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290 Ultraviolet Space Astronomy

rockets, Earth satellites, and other space vehicles outsidethe Earth’s atmosphere.

I. SIGNIFICANCE OF THE RESEARCH

One of the primary benefits of doing astronomy in spacerather than from ground-based observatories is the muchwider range of the electromagnetic spectrum that is ac-cessible to observation (Fig. 1). In particular, the entireUV and X-ray wavelength range below 300 nm (3000 A)is absorbed by oxygen and ozone in the Earth’s atmo-sphere and, hence, is totally inaccessible to even the largestground-based telescopes. To observe the sun, stars, andother celestial objects in this wavelength range, the instru-

FIGURE 1 Altitude and fraction of atmosphere remaining overhead that must be reached in order to observe one-halfof the radiation coming from an extraterrestrial source vs wavelength in the electromagnetic spectrum.

ments must be carried above the absorbing atmosphere bymeans of sounding rockets or space vehicles.

The UV spectral range is of importance to astronomyfor a number of reasons. Two of the most significant are asfollows: (1) the primary, or resonance, transitions (thoseinvolving the ground state) of the most common atoms,ions, and molecules occur in the UV spectral range below300 nm; (2) very hot stars, having surface temperaturesin excess of 10,000 K (vs ∼5800 K for our sun), emitmuch or most of their radiation in the ground-inaccessibleUV.

Hydrogen and helium are the most abundant elements inthe universe, accounting for more than 99% of all atoms instars, the interstellar medium, and the giant planets Jupiterand Saturn. Of the heavier elements, the most abundant in



Ultraviolet Space Astronomy 291

numerical order are oxygen, carbon, neon, and nitrogen.For all of these, in atomic or ionic form or in simplemolecules such as H2, N2, and CO, the resonance spectraltransitions occur in the far UV (below 200 nm). The reso-nance transitions (to or from the ground state) are usuallymuch stronger and more quantitatively useful for remotesensing of gas composition and physical state than arethe subordinate transitions (between two excited states).This is particularly true for cool material, such as in theinterstellar medium and in planetary or cometary atmo-spheres, where most of the atoms or molecules reside inthe ground state. Therefore, observations in the far UVprovide information on the composition and properties ofastronomical objects that cannot be obtained at ground-accessible wavelengths.

Stars that are of much higher temperature than our sun(ranging from ∼10,000 K to more than 200,000 K) emitmuch or most of their radiation at wavelengths below the300-nm limit of ground-based observations. Therefore, itis difficult to determine, from ground-based observationsalone, the total energy outputs and energy flux distribu-tions of these stars. Although the flux distributions of hotstars have crude resemblances to those of classical black-body radiators (in that the peak of the distribution shifts toshorter wavelengths as the temperature increases), moredetailed theoretical models predict significant differencesfrom blackbody distributions, particularly at the shortestwavelengths. Comparisons of observations with theoryand accurate determinations of the “effective” tempera-tures of hot stars therefore require accurate measurementsin the far UV.

Even for cooler stars, such as our sun, UV measure-ments are important for detecting and characterizing ener-getic phenomena that occur in their outer atmospheres. Forthe sun, these include the high-temperature solar corona,solar flares, and other manifestations of solar activity.Also, solar UV radiation is largely responsible for themaintenance of the terrestrial and other planetary iono-spheres and for exciting UV emissions observed in plan-etary atmospheres and in comets.

II. INSTRUMENTATION FOR ULTRAVIOLETSPACE ASTRONOMY

The instrumentation used for UV space astronomy is, inmost respects, similar to that used in ground-based as-tronomy. The differences have to do, primarily, with thefollowing: (1) UV radiation is not transmitted as efficientlyby, or by as wide a variety of, transparent materials (usedfor windows, lenses, and other refractive optical elements)as are visible and near-infrared radiation; and (2) reflec-tive coatings for mirrors and reflection gratings are not as

efficient (especially at wavelengths below 120 nm) thanat longer wavelengths.

Categories of instruments can be defined by the types ofmeasurements to be made, such as imagery, photometry(measurement of light intensity), spectroscopy, and spec-trophotometry (measurement of intensity vs wavelength ina spectrum). There is no sharp distinction between thesecategories, and they are not mutually exclusive; it is mainlya matter of emphasis. For example, imagery emphasizeshigh spatial resolution and simultaneous coverage of awide field of view (in comparison to the size of the reso-lution element), but photometric information can also beobtained from images. Traditional spectroscopy empha-sizes the detection, identification, and wavelength mea-surement of spectral features, whereas spectrophotome-try emphasizes measurement of the intensity of spectralfeatures or intensity vs wavelength in a continuum. Bothcan be accomplished with the same instrument, if prop-erly designed. Imagery in a very narrow wavelength range(e.g., by the use of interference filters) can be considered aform of spectroscopy or spectrophotometry, and “imagingspectrographs” or “hyperspectral imagers” are those thatretain spatial intensity resolution in one dimension whileproviding spectral intensity resolution in the transversedimension.

As is true in ground-based astronomy, the type of in-strumentation used depends to some extent on the objectof study; for example, solar studies require different in-strumentation than do observations of stars or nebulae.

Since UV astronomy can be done only at very high al-titudes or in space, its progress has been paced by the de-velopment of rocket vehicles for carrying the instrumentsabove the atmosphere and other payload equipment suchas pointing controls for directing the instruments at theobjects of interest with adequate accuracy and stability.The rate of progress in the various subfields of UV astron-omy has, therefore, depended on both instrumentation andsupporting vehicular developments.

Solar UV astronomy was the first subfield of UV astron-omy to be developed; because the sun is so much brighterthan any other astronomical object, the requirements re-garding both scientific instrumentation and vehicle atti-tude control systems were less stringent than for obser-vations of other celestial objects. Solar UV astronomybegan in the late 1940s with experiments flown by NavalResearch Laboratory scientists on captured German V-2rockets. The initial instruments were unpointed, but never-theless returned new and useful information on the inten-sity and spectral distribution of solar UV radiation. In theearly 1950s, the development of instrument pointing con-trols for Aerobee sounding rockets imparted greater sen-sitivity and higher spectral resolution to UV spectroscopyand photometry.




FIGURE 2 Diagram of the Naval Research Laboratory’s high-resolution telescope and spectrograph used in solarstudies from rockets and Spacelab 2. (a) Diagram of the complete telescope and spectrograph. The optical parametersare as follows. Spatial: field of view, 0.5′′ × 16′; resolution, <1′′. Spectral: range, 1175–1715 A and Hα; resolution,0.05 A. (b) Simplified schematic of the spectrograph. (Naval Research Laboratory illustrations.)




The first measurements of stellar UV radiation weremade from free-spinning Aerobee rockets in the late1950s; the development of inertial attitude control systemsin the early 1960s greatly improved the quality of datareturn. The first satellite vehicles dedicated to space as-tronomy were the Orbiting Solar Observatories (OSOs),the first of which was launched in 1962, and the OrbitingAstronomical Observatories (OAOs), the first successfullaunch of which was in 1968. The advent of satellite ob-servatories tremendously increased the available observ-ing time, in comparison to a typical 5-min sounding rocketflight. This allowed much more comprehensive studies ofthe sun, stars, and other celestial objects than possiblewith sounding rockets. However, the latter still remaineduseful for carrying out special-purpose investigations notsuitable for the long-duration (but technologically moredifficult) satellite observatories.

Some of the unmanned satellites primarily dedicated toUV solar or celestial astronomy include the Solar Max-imum Mission (SMM), the International Ultraviolet Ex-plorer (IUE), the Extreme Ultraviolet Explorer (EUVE),the Far Ultraviolet Spectroscopic Explorer (FUSE), andthe Solar Heliospheric Observatory (SOHO). Ultravioletstudies of the sun are also a significant part of the UpperAtmospheric Research Satellite (UARS) mission, and UVastronomy is an important part of the operations of theHubble Space Telescope.

Ultraviolet astronomical observations have also beencarried out in several manned missions, including Gemini,Apollo, and Skylab, as well as many space shuttle mis-sions. These latter include solar observations, beginningwith the Spacelab-2 shuttle flight in 1985, and celestial ob-servations with the Astro UV astronomy missions flown in1990 and 1995. In addition, the space shuttle was used in1990 as the launch vehicle for the Hubble Space Telescope(HST), a much larger and more comprehensive space ob-servatory, which still remains operational in orbit. TheHST, unlike previous space astronomical observatories,was designed so that it could be revisited by the spaceshuttle for repairs and upgrades (in extravehicular activ-ities by the space shuttle crew members); such missionswere carried out in 1993, 1997, and 1999. The space shut-tle also made upgrades and repairs on the Solar MaximumMission satellite, initially launched on an unmanned Deltarocket. In addition to these, numerous other solar and ce-lestial UV astronomy experiments have been conducted inspace shuttle flights, using instruments carried in the pay-load bay of the space shuttle, or as short-duration, free-flying payloads on carriers such as Spartan (developedby NASA’s Goddard Space Flight Center) and AstroSPAS(developed by the European Space Agency).

There are a large variety of instruments used in UVspace astronomy, and, in general, they are similar to in-

strumentation used in ground-based astronomy. In the UV,the number of optical components (mirrors, gratings, etc.)must be kept to a minimum because of the generallylower efficiencies of optical elements in the UV as com-pared with the visible. However, instruments now in useor planned for near-future missions in UV astronomy arefully comparable in sensitivity, resolution, and other per-formance capabilities to similar visible-light instruments.

In UV astronomy, as in visible-light astronomy, pho-tographic film was initially a major recording techniquefor imagery and spectroscopy, but it has now been almosttotally replaced by electronic imaging detectors. These in-clude image intensifiers and electrographic detectors (hav-ing final images recorded on film) and devices whose fi-nal output is an electronic signal, such as charge-coupleddevices (CCDs) and detectors based on microchannel-plate (MCP) electron-multiplier arrays. Electronic imag-ing detectors can provide much higher sensitivity thanprovided by direct recording on photographic film. Theyalso can be made sensitive only to UV wavelengths, whichis particularly important for studies of objects like thesun, which are much brighter in the visible than in thefar UV. In addition, detectors whose final output is anelectronic signal can send their data back to Earth byradiotelemetry, eliminating the need to recover and pro-cess film (hence making them applicable to long-durationsatellite and deep-space missions). Another potential ad-vantage of electronic detectors vs photography is thatthe information is acquired in a more quantitative form,making it more readily and accurately processed andcalibrated.

We show here some examples of recent or current UVastronomy instruments. Figure 2 shows the Naval Re-search Laboratory’s High-Resolution Telescope and Spec-trometer (HRTS), which has flown on several soundingrocket flights and on Spacelab-2. An improved versionof this instrument uses a CCD detector in place of thephotographic film used previously. The Astro Spacelabshuttle payload consisted of three separate instruments:the Johns Hopkins University’s Hopkins Ultraviolet Tele-scope (HUT), shown in Fig. 3, was used for spectroscopicmeasurements in the 85- to 185-nm wavelength range; theGoddard Space Flight Center’s Ultraviolet Imaging Tele-scope (UIT), shown in Fig. 4, was used for direct imag-ing of celestial objects in far- and middle-UV wavelengthranges; and the University of Wisconsin’s UV photo-polarimeter instrument (WUPPE) was used for studiesof stars and interstellar material in the 140- to 320-nmwavelength range.

A number of UV imaging and spectrographic in-struments have been or will be used on the currentlyorbiting HST, launched in 1990 (see Fig. 5). The HSThas a collecting mirror aperture of 2.4 m diameter, more




FIGURE 3 Diagram of the Hopkins Ultraviolet Telescope (HUT), which was part of the shuttle-based Astro Spacelabmissions in 1990 and 1995. (Courtesy of A. Davidsen, Johns Hopkins University, Baltimore, MD.)

than twice that of the largest previous space astronomytelescope. It operates in the UV, visible, and near-IRwavelength ranges, and of particular importance is thatit has nearly diffraction-limited imaging performance

FIGURE 4 Diagram of the Ultraviolet Imaging Telescope (UIT), which was part of the shuttle-based Astro Spacelabmissions. (Courtesy of T. Stecher, NASA GSFC.)

(better than 0.1 arcsec resolution, or about 10 times betterthan typically achieved, in the visible, with ground-basedtelescopes). This provides not only improved imagingresolution, but also better senstivity in direct imaging,




FIGURE 5 Diagram of the 2.4-m-aperture Hubble Space Telescope, planned for launch by the space shuttle. The sci-entific instruments include imaging cameras, a high-speed photometer–polarimeter, a high-resolution spectrograph,and a faint-object spectrograph. (NASA photograph.)

and imaging spectrometry, of compact and point sources(such as stars).

The HST is also unique among long-duration spaceastronomy missions, in that it was designed so that itsinstruments could be changed on-orbit, in visits by thespace shuttle. This has allowed the “first-generation” in-struments included in the original launch to be replacedwith improved and more advanced instruments, whichhave in turn improved and broadened the HST’s scien-tific capabilities. For example, the first-generation FaintObject Spectrograph (FOS) and Goddard High Resolu-tion Spectrograph (GHRS) were replaced by the SpaceTelescope Imaging Spectrograph (STIS) in a 1997 spaceshuttle refurbishment mission, and a new, improved far-UV Cosmic Origins Spectrograph (COS) is planned forinstallation in a near-future HST refurbishment mission.

III. THE SUN

The sun is the nearest star, the one of most practicalimportance to us, and the only one whose surface fea-

tures can be observed in detail. The visible “surface”of the sun, known as the photosphere, emits a continu-ous spectrum of radiation whose intensity and spectraldistribution crudely resemble those of a classical black-body radiator having a temperature of ∼5800 K. Theintensity of solar radiation is a maximum in the visible(near 500 nm wavelength) and decreases rapidly towardshorter wavelengths and less rapidly toward longer wave-lengths. Thus, in the UV (particularly in the far UV, below200 nm) the solar photosphere is far less bright than in thevisible.

However, the outer atmospheric layers of the sun, abovethe photosphere, have much higher gas temperatures thandoes the photosphere. As seen in Fig. 6, the temperaturerises very sharply in a “transition region” between thelower atmosphere (chromosphere) and the upper atmo-sphere (corona), from ∼10,000 K in the upper chromo-sphere to more than 1,000,000 K in the corona. Highly ac-tive regions in the solar atmosphere, such as solar flares,can have much higher temperatures still. However, be-cause of the very low gas densities in these regions, theenergy content per unit volume is still very much less than




FIGURE 6 Temperature and density in the solar atmosphere vsaltitude. Note that a minimum temperature is reached just abovethe visible-light surface, or photosphere, and temperature risessharply in the transition region between the chromosphere andcorona. [Adapted from Eddy, J. A. (1979). “A New Sun,” NASASP-402. U. S. Govt. Printing Office, Washington, DC.]

in the photosphere, and even the most intense flares con-tribute very little to the visible brightness of the sun.

One of the most important current problems of solarphysics is to explain how the outer atmosphere of the suncan be maintained at million-degree temperatures in con-tact with a 6000-K photosphere. Related problems includeelucidation of the mechanism for the production and ac-celeration of the solar wind, and of the mechanism of, andphysical processes occurring in, solar flares.

In the visible and through the near and middle UV, thesolar spectrum is a continuum with superimposed absorp-tion lines (Fraunhofer lines), due to cool gas in the upperphotosphere and lower chromosphere (the “temperatureminimum” region in Fig. 6). In the far UV, however, thecontinuum fades away and is replaced by an emission linespectrum, produced by the hotter gas in the transition re-gion and corona.

It is particularly noteworthy that, in the far and ex-treme UV, the outer atmosphere of the sun is the pre-

dominant source of radiation, due to its very high tem-perature. This constitutes one of the major advantages ofshort-wavelength observations of the sun: the ability to ob-serve the high-temperature, active regions of the outer at-mosphere without interference from the cooler (but, in thevisible, far brighter) photosphere. Although (with the ex-ception of sunspots) the solar disk appears almost feature-less in white light, observations in far-UV emission lines[and also in narrow wavelength ranges centered on visi-ble absorption lines, such as hydrogen Balmer α (Hα) at656.3 nm] reveal a great deal of detail and time variabilityin the structure of the solar atmosphere. Different emis-sion or absorption features are produced by gas at differenttemperatures and, hence, at different spatial locations inthe solar atmosphere. Therefore, observations from thevisible to the X-ray wavelength range are needed to char-acterize the temperature, density, and time variations in thesolar atmosphere. For example, imagery of the sun in thelight of neutral hydrogen (Lyman α at 121.6 nm) revealsgas having a characteristic temperature of ∼10,000 K,whereas the light of ionized helium (He II) at 30.4 nmis emitted by gas with a temperature of ∼80,000 K.Five-times-ionized oxygen (O VI) emission at 103.2 and103.6 nm reveals material at a temperature of ∼300,000 K.Nine-times-ionized magnesium (Mg X) emission near62.5 nm is characteristic of material at a temperature near1,600,000 K.

Studies of the sun in the UV and X-ray wavelengthranges are also of practical importance, because these ra-diations significantly influence Earth’s upper atmosphereand are primarily responsible for the production and

FIGURE 7 Far-UV spectrum of the sun, obtained in a sound-ing rocket flight, showing the transition to an emission line spec-trum below ∼1800 A. The effective resolution is 5 A. (Courtesy ofG. H. Mount, Naval Research Laboratory.)




maintenance of the ionosphere (which is essential to long-distance radio communications). Ultraviolet radiation be-low 200 nm dissociates molecular oxygen in the upperatmosphere, indirectly resulting in the formation of ozone(O3), which protects life on Earth from the biologicallyharmful middle-UV solar radiation. Lyman α radiationionizes nitric oxide (NO), producing the lower ionosphere,whereas radiations of wavelengths less than 102.6, 91.1,and 79.6 nm ionize molecular oxygen, atomic oxygen, andmolecular nitrogen, respectively.

As mentioned previously, the sun was the first extrater-restrial object to be observed in the ground-inaccessibleUV, in part because of its brightness (even in the far UV,much greater than that of any other celestial object) andits relative ease of acquisition by primitive rocket point-

FIGURE 8 Image of the sun in the light of ionized helium (He II) emission at 304-A wavelength, showing mottledstructure of the transition region, active regions associated with sunspots, and a giant eruptive prominence (at left). Ob-tained with the Naval Research Laboratory extreme-UV spectroheliograph from Skylab. (Naval Research Laboratoryphotograph.)

ing control systems. The first rocket observations wereexploratory in nature, attempting to define the general na-ture and intensity distribution of the solar UV spectrum.Successive experiments gradually improved the spectralresolution and photometric accuracy of the measurementsand extended them toward shorter wavelengths. Also,once strong emission lines (such as hydrogen Lyman α

at 121.6 nm and ionized helium at 30.4 nm) were iden-tified, imaging instruments (such as spectroheliographs)were used to obtain monochromatic images of the entiresolar disk in these emissions.

The advent of long-duration satellite, Skylab, and spaceshuttle-based, Spacelab, observations has allowed notonly more detailed measurements, but also studies of thetime variations of the solar UV output and its correlations




FIGURE 9 Spectrum of the sun obtained with the Naval Research Laboratory high-resolution telescope and spec-trograph in a sounding rocket flight. This stigmatic (imaging) spectrograph reveals spatial variations across the diskof the sun (top to bottom; region covered by the spectrograph slit is shown at the left) simultaneously with the spectralvariations (left to right). (Naval Research Laboratory photograph.)

with other indications of solar activity, such as sunspotsand structure of the white-light corona. Improvements ininstrumentation and observing techniques have resultedin improved spatial, spectral, and temporal resolution inthe measurements. Also, it has become evident that under-standing the physical phenomena taking place in the so-lar atmosphere requires simultaneous or complementarymeasurements over a wide range of wavelengths, from theradio through the X-ray and γ -ray ranges.

Figure 7 is a far-UV spectrum of the sun, obtained ina sounding rocket flight, showing the transition of the so-lar spectrum from a continuum with superimposed ab-sorption lines (Fraunhofer spectrum) to an emission linespectrum below 180 nm. Measurements of this type areuseful for measuring the total solar energy output in spe-cific lines and wavelength ranges in the far and extremeUV. Figure 8 is a monochromatic image of the entiresun in the light of ionized helium (He II) at a wave-length of 30.4 nm, taken with the Naval Research Labora-tory’s extreme-UV spectroheliograph flown on the Skylabspace station in 1973–1974. Images of this type reveal thestructure of the solar atmosphere in various temperatureranges.

Figure 9 is a spectrum of the sun taken in a soundingrocket flight of the Naval Research Laboratory’s HRTSinstrument. Unlike previous instruments, this combinedhigh spectral resolution with high spatial resolutionin the along-slit direction (an imaging spectrograph).Thus, new information on the spatial distributions andvelocity structures of solar active regions was obtained, aswere variations in the spectral intensity and temperaturedistributions.

IV. PLANETARY ATMOSPHERES

Ultraviolet measurements are important for studies ofplanetary atmospheres, including Earth’s upper atmo-sphere. This is due to the fact that the resonance absorp-tion and emission spectral features fall primarily in theUV, making this spectral range much more sensitive fordetection and measurement of the most common atmo-spheric gases than are other wavelength ranges. For ex-ample, O2 absorbs strongly at wavelengths below 200 nm;hence, UV spectroscopy in this wavelength range allowssensitive detection of O2 in other planetary atmospheres




(provided that one observes from above Earth’s O2-richatmosphere). The hydrogen Lyman α emission line at121.6 nm, produced by scattering of solar Lyman α ra-diation by hydrogen atoms, is a very sensitive test for thisgas in the outer atmospheres of planets and comets.

In Earth’s upper atmosphere (and, in planetary probemissions, the atmospheres of other planets), atmosphericcomposition can be measured in situ with mass spec-trometers and related instrumentation. However, UV mea-surements provide a capability for remote sensing of at-mospheric composition and its variation with altitude,geographic location, and time, which supplements andextends in situ measurements where available, and canbe applied to many objects not yet visited by spacecraft(e.g., in observations of other planets by spacecraft in near-Earth orbit). In addition to atmospheric composition, UVmeasurements can remotely sense the atmospheric tem-perature structure and its spatial and temporal variations.Also, information on the fluxes, energies, and spatial dis-tributions of incoming energetic particles (such as thosethat produce Earth’s polar auroras) can be obtained.

Three basic types of UV observations applicable toplanetary atmosphere studies are (1) observations offar-UV emission features, excited by solar radiation orcharged-particle impacts (such as those that cause Earth’spolar auroras); (2) observations of middle-UV absorptionfeatures, superimposed on the reflected solar spectrum (forexample, observations of ozone in Earth’s atmosphere orof sulfur dioxide in that of Venus); and (3) observations ofmiddle-UV or far-UV absorption features superimposedon the solar spectrum or a stellar UV spectrum when thesun or star is viewed directly, with a line of sight pass-ing through the planetary atmosphere (solar or stellar oc-cultation). All of these have been applied to studies ofEarth’s upper atmosphere; various combinations of thesehave been applied (in various wavelength ranges) to stud-ies of the atmospheres of other planets. The pioneeringobservations of both Earth’s upper atmosphere and thoseof other planets were made using sounding rocket vehicles.More recent observations of the other planets have beenmade using both Earth orbiting astronomical observatories(such as the IUE and HST satellites) and planetary flybyor orbiter spacecraft (such as the Mariners, Voyagers, andGalileo).

Figure 10 shows UV spectra of three planets: Earth,Venus, and Jupiter. It is seen that Lyman α (121.6 nm)emission is present in all of these. The atmospheres ofboth Venus and Mars consist mainly of carbon dioxide,and hence, their UV spectra are similar, but there are sub-tle and significant differences. Atomic oxygen emissions(130.4 and 135.6 nm) are present in all but the spectrum ofJupiter, which shows only atomic and molecular hydrogenfeatures. The Earth spectrum is nearly unique, showingstrong features of atomic and molecular nitrogen, although

FIGURE 10 Far-UV emission spectra of three planetary atmo-spheres. (a) Earth’s upper atmospheric day air-glow, observedin a sounding rocket flight. [Reprinted with permission fromTakacs, P. Z., and Feldman, P. D. (1977). J. Geophys. Res. 82,5013.] (b) Day airglow of Venus, observed with the spectrom-eter on the Pioneer Venus Orbiter. [Reprinted with permissionfrom Durrance, S. T. (1981). J. Geophys. Res. 86, 9116.] (c) Anaurora on Jupiter, observed with the International Ultraviolet Ex-plorer satellite. [Reprinted with permission from Durrance, S. T.,et al. (1982). Geophys. Res. Lett. 9, 653.]

these have also been detected in the UV spectrum of Titan,the largest satellite of Saturn. For our moon, the planetMercury, and Ganymede (Jupiter’s largest satellite), UVobservations have set upper limits on atmospheric densi-ties which are far lower than those established by ground-based measurements. As in the case of the sun, imagery




FIGURE 11 Far-UV images of auroras and day airglow on Jupiter and Saturn, obtained with the Space TelescopeImaging Spectrograph (STIS) on the Hubble Space Telescope (HST). Note that the contrast of the aurora to thedayglow and reflected sunlight background is much greater in the far-UV than in the visible spectral range. (Courtesyof B. Woodgate, NASA GSFC.)




FIGURE 11 (continued)




FIGURE 12 Far-UV images of Comet Halley, obtained by the Naval Research Laboratory in a 1986 sounding rocketflight, with exposure times indicated. The images show the great extent of the atomic hydrogen halo surrounding thecomet (many times larger than the sun), which scatters Lyman α (121.6 nm) solar radiation.




of planetary atmospheres in individual spectral lines pro-vides information on the altitude distributions of variousgases, indirectly yielding information on temperature dis-tributions. In addition, it provides information on the plan-etographic distributions of localized phenomena, such asauroras (which Voyager, Galileo, and HST have observedon Jupiter and Saturn). Figure 11 shows HST STIS far-UVimages of auroras on Jupiter and Saturn. It is noteworthythat, as is also true of auroras on Earth, the contrast of theaurora against the daylit lower atmosphere is much greaterin the far-UV than in the visible spectral range.

V. COMETS

Comets are unique, in comparison with the planets andsatellites, in many ways. Of particular significance here isthat they are objects of very low mass (comparable to smallasteroids), but they are composed largely of volatile mate-rials such as water and ice. Thus, when they approach thesun while traveling along their (typically) highly eccentricorbits, a significant portion of their mass is “boiled off” toproduce a gaseous halo, or coma, which is quite prominentin the UV as well as at other wavelengths. As in the case ofplanetary atmospheres, UV observations can provide im-portant information on the volatile composition of comets.They can also be used to determine the vaporization ratesof various cometary materials and to provide informationon the physical interactions between the cometary atmo-sphere and solar UV radiation and the solar wind.

Hydrogen Lyman α and the OH molecular band emis-sion near 310 nm are the two most prominent spectralfeatures in comets. These indicate that water is indeedthe dominant volatile constituent of comets; other ma-terials (which are responsible for the ground-accessiblefeatures, such as CH, CN, C2, and NH band emissions)are only minor constituents. Because of the small mass of

FIGURE 13 Objective-grating far-UV spectrum of Comet Halley, obtained by the Naval Research Laboratory in a 1986sounding rocket flight, which excludes the hydrogen Lyman α emission. The spectrum reveals far-UV emissions ofatomic oxygen, carbon, sulfur, and also carbon monoxide (CO) (unlabeled features between the O I and C I features).

the hydrogen atom, the cometary hydrogen coma is muchlarger than the coma revealed in heavier molecular emis-sions (see Fig. 12); it can be many times larger than thesun. Measurements of the Lyman α brightness distribu-tion in this halo can be used to determine the hydrogenproduction rate and, hence, the vaporization rate of waterand other hydrogen compounds.

Ultraviolet observations of several comets, includingWest (1975) and Halley (1986) (Fig. 13), revealed thatCO is also a prominent cometary constituent. Ultravioletobservations have also resulted in the detection of mi-nor species not previously observed in comets, includingatomic and diatomic sulfur, ionized carbon, and the SHradical. Future, more sensitive observations and ones ex-tending to shorter wavelengths are expected to reveal otherconstituents, such as H2, N2, N, N+, and O+.

VI. THE STARS

A. Hot Stars

Hot stars, meaning those having surface temperatures inexcess of 10,000 K (vs ∼5800 K for our sun), emit much ormost of their radiation in the UV wavelength range below300 nm, the limit for ground-based observations. This waspredicted theoretically, many years before the firstspaceobservations, from models of stellar atmospheres. It wasalso inferred, for the very hottest stars (above 20,000 K),from observations of emission nebulae or ionized hydro-gen (H II) regions; in these regions, ionization of hydrogenis produced by stellar radiation in the extreme UV, below91.2 nm wavelength.

Although the flux distributions for hot stars are rising to-ward shorter wavelengths in the ground-accessible range,the shape of the distribution (or of the theoretical modelcurves) is insensitive to temperature for very hot stars.Hence, it is very difficult to determine temperature or total




radiation output for very hot stars from ground-based ob-servations of their visible/near-UV spectra.

The earliest sounding rocket observations of hot stars inthe UV in the early 1960s indicated much lower UV fluxesthan were predicted by the theoretical stellar atmospheremodels. However, over the following years, improvementsin both the observations and the models resulted in conver-gence of the two, so that now there is reasonable agreementbetween theory and observation.

In particular, the improved models include the effectsof the far-UV absorption lines (line blanketing), omittedin early models, and predict lower far-UV fluxes for agiven temperature. Figure 14 shows a series of model at-mosphere flux distributions, computed by E. Avrett of theHarvard-Smithsonian Center for Astrophysics. As can beseen, the flux distributions of hot stars are far more sensi-tive to temperature in the far-UV range than in the ground-accessible wavelength range.

The first large, self-consistent set of stellar UV spec-trophotometric data was that obtained by the University of

FIGURE 14 Shown are model atmosphere flux distributions, more recent than those in Fig. 13, taking into accountabsorption line blanketing. Effective temperatures for the models are as indicated, from top to bottom. [Reprinted withpermission from Kurucz, R. L. (1979). Astrophys. J. Suppl. 40, 1.]

Wisconsin experiment on the OAO-2 satellite. Figure 15shows measured flux distributions for four hot stars ofdifferent temperatures, a combination of UV observationsby OAO-2 with ground-based spectrophotometry. Simi-lar data sets have been obtained with the European TD-1and ANS satellites and greatly expanded and extended tomuch fainter stars by the IUE satellite spectrometers.

Current efforts include extensions of measurements tomuch fainter stars still (including those in nearby galax-ies, such as the Magellanic Clouds) using HST; moreaccurate and complete measurements in the wavelengthrange below 115 nm, the short-wavelength limit of IUEand HST; using the Extreme Ultraviolet Explorer (EUVE)and the Far Ultraviolet Spectroscopic Explorer (FUSE);and other, special-purpose UV astronomical instruments.

Most stars are not observable at wavelengths below91.2 nm, even from space, because this radiation is ab-sorbed by atomic hydrogen in interstellar space. However,because the distribution of atomic hydrogen in space ishighly variable, EUVE has been successful in observing a




FIGURE 15 Measured flux distributions in the UV and visible for four stars ranging in temperature from about 8000 K(type A7) to 20,000 K (type B2). The UV measurements are from the University of Wisconsin experiment package onOAO-2. (Courtesy of A. Code, University of Wisconsin, Madison.)

number of very hot stars in the extreme-UV range below91.2 nm, some even at relatively large distances, in re-gions in space where the atomic hydrogen column densityis unusually low.

Spectrometric observations of individual hot stars havebeen supplemented by imagery of starfields in moderatewavelength ranges in the UV. The advantage of these imag-ing surveys is that much fainter objects can be measuredand that a very large number of objects can be recorded in asingle exposure. Ultraviolet imagery is particularly usefulas a means of surveying large areas of the sky in order todetect and measure hot stars not previously known to exist(or at least not previously known to be hot). Figure 16 com-pares a far-UV image of the constellation Orion, obtainedin a sounding rocket flight, with a visible-light image. TheUV image shows, at a glance, the distribution of hot starswithout confusion by the far more numerous (and, in somecases, brighter in visible light) stars.

Ultraviolet spectroscopy is useful not only for measur-ing the energy flux distributions of hot stars, but also forgaining insight into the properties and physical processesoccurring in stellar atmospheres. This information is pro-vided by the line features in the spectra. One of the first

major discoveries in stellar UV spectroscopy was that thestrong line features such as C IV (155 nm) and Si IV(140 nm) had what is known as a P Cygni profile: a verystrong, broad absorption feature shifted to shorter wave-lengths (relative to its laboratory, or rest, wavelength) com-bined with an emission feature at, or slightly longer than,the rest wavelength (see Fig. 17). As shown in Fig. 18,the production of such a spectral feature can be explainedas being due to a very strong stellar wind. The observa-tions indicate that some very hot, luminous stars are losingmass at very high rates—of the order of 10−6 solar massper year. Such high mass-loss rates, many orders of mag-nitude greater than that associated with the solar wind,can significantly influence the evolution of a massive hotstar.

In addition, UV line spectra are useful because theycontain the resonance absorption features of most of thecommon ions expected in stellar atmospheres and pro-vide sensitive means of measuring temperature and rela-tive abundances. Since, as discussed later, starlight can beabsorbed or scattered by dust particles in interstellar space,measurements of absorption lines produced in the stel-lar atmospheres can, in some cases, provide more useful




FIGURE 16 Comparison of visible and UV imagery of the constellation Orion. (a) Far-UV (1230–2000 A) image ofOrion obtained by the Naval Research Laboratory in a 1975 sounding rocket flight. (b) Visible-light image, to the samescale. (Hale Observatories photograph.)

temperature information than measurements of the con-tinuum flux distribution.

B. Cool Stars

Cool stars, in the temperature range 3000–9000 K, emitmost of their radiation in the wavelength range accessiblefrom the ground (as does our sun). However, as is truefor the sun, the UV wavelength range reveals energeticprocesses in the outer atmospheres of these stars. Objectsof similar surface temperatures can exhibit quite differentfar-UV spectra, indicative of quite different conditions intheir outer envelopes.

Although some pioneering observations of cool starsin the UV were obtained with sounding rockets, OAO-2,and Copernicus, a truly systematic study covering a widerange of cool star types had to await the higher sensitivityof the IUE satellite. Observations with IUE have revealedthat some giant stars, such as Capella, are much moreactive than our sun (as are also some stars in close binarysystems). Cool supergiant stars, on the other hand, donot show evidence of hot coronas; it is presumed thatthis is due to the presence of strong stellar winds, theenergy of which might otherwise go into heating. Coolclass M stars, having temperatures of only about 3000 Kand being much less luminous than our sun, surprisinglyshow very active chromospheres and coronas—in somecases, with higher far-UV fluxes per unit area than our

sun. These cool stars also sometimes exhibit flare activityfar surpassing that of our sun.

In eclipsing binary systems consisting of, for example,a hot star and a cool giant star, UV measurements can pro-vide information on the outer atmosphere of the cool starby observing the hot star as it is eclipsed by the cool star.

These types of observations with IUE have been sup-plemented by more sensitive observations with the HSTspectrographs and extended to shorter wavelengths by theHUT on the Astro Spacelab shuttle missions and by thenewly operational FUSE. Also, somewhat surprisingly,many late-type stars have been detected by the EUVE(which is most likely seeing EUV emissions from the chro-mospheres and coronas of these stars, as well as occasionalflare activity).

VII. INTERSTELLAR GAS

The space between the stars is not empty, but containshighly rarefied gas and solid particles (dust). The densityand temperature, and to some extent the composition, ofthis interstellar material are highly variable from place toplace in our galaxy. On the average, the interstellar gascontains about one hydrogen atom per cubic centimeter,although it can range from 0.01 or less to more than 106

(in dense molecular clouds). It is this interstellar materialfrom which new stars are formed.




FIGURE 17 Far-UV high-resolution (0.02-nm) spectra of the stars ζ Ophiuchi (spectral type O9.5) and ζ Puppis (typeO4) obtained with the Princeton University spectrometer on the Copernicus satellite. Of interest here are the absorptionfeatures of atomic hydrogen at 121.6 nm (considerably stronger, indicating a larger hydrogen column density, towardζ Ophiuchi) and the absorption features due to four-times-ionized nitrogen (N V) in the stellar atmospheres. The latterfeature exhibits a P-Cygni profile (much stronger in ζ Puppis), indicating high-velocity mass ejection. [Reprinted withpermission from Morton, D. C. (1976). Astrophys. J. 203, 386.]

The composition of the interstellar medium is believedto be similar to that of the sun and the stars: Hydrogenaccounts for ∼90% of all atoms, and helium accounts formost of the remaining 10%. Atoms of all heavier ele-ments make up less than 1%. Much of the heavier elementcomponent is believed to be in the form of dust grainsrather than in gaseous form, although the relative propor-tion is variable. Except in the close vicinity of hot andhighly luminous stars, this interstellar medium is madeevident only by its attenuation of the light of stars seenthrough it. The dust particles produce continuous atten-uation, whereas the gas usually absorbs only in discretespectral lines. Since the resonance transitions of most ofthe common elements occur in the far UV, the composi-tion of the interstellar gas was only poorly known beforethe advent of space UV spectroscopy. Only relatively mi-nor constituents of the interstellar gas, such as sodium andcalcium, can be detected and measured by ground-basedoptical absorption spectroscopy. The far UV allows mea-

surements of the major constituents, such as atomic andmolecular hydrogen, and also atomic oxygen, carbon, andnitrogen.

A. Interstellar Atomic and Molecular Hydrogen

The first observations of interstellar atomic hydrogen, bymeans of its Lyman α absorption line at 121.6 nm, weremade from sounding rockets as early as 1966. Molecularhydrogen was first observed in a 1970 rocket flight. Sur-veys of interstellar atomic hydrogen were made with theOAO-2 satellite spectrometers. However, the instrumentthat produced the most comprehensive studies of theinterstellar gas was the far-UV spectrometer provided byPrinceton University, carried on the OAO-3 (Copernicus)satellite launched in 1972. This instrument observed in thewavelength range 91.2–300 nm with spectral resolutionas good as 0.005 nm. Figure 17 shows spectra of the starsζ Ophiuchi and ζ Puppis, obtained by Copernicus, in the




FIGURE 18 Illustration of the formation of a P Cygni profile (emis-sion line near the “rest” wavelength, with blue-shifted absorption)in a spectral feature, resulting from high-velocity outflow of gasfrom a stellar atmosphere.

region of the Lyman α absorption line. It is apparent thatthere is much more atomic hydrogen in the line of sightto the former star than toward the latter.

Figure 19 shows a higher resolution spectrum of ζ Ophi-uchi, in the region of a molecular hydrogen absorption

FIGURE 19 Copernicus high-resolution (0.005 nm) spectrum of the star ζ Ophiuchi showing absorptions due tointerstellar molecular hydrogen (H2) and HD. [Spitzer, L., and Jenkins, E. B. (1975). Annu. Rev. Astron. & Astrophys.13, 133.]

band. In contrast to atomic absorption spectra, the detaileddistribution of absorption intensity in molecular spectracan be used to determine gas temperature, in the low-temperature range existing in molecular clouds. Here, theH2 absorption features indicate a gas temperature of about80 K, which is consistent with other determinations.

The Copernicus satellite also made the first direct ob-servations of deuterium (“heavy hydrogen”) in the inter-stellar medium, both in atomic form and in the moleculeHD (Fig. 19). Accurate knowledge of the ratio of D to H inthe interstellar gas is of relevance to theories of the originand evolution of the universe.

The Copernicus observations confirmed theoretical pre-dictions that molecular hydrogen is formed by “three bodyrecombination” of hydrogen atoms on dust particles; here,the dust particle acts as a catalyst and takes up the energyof recombination of the two hydrogen atoms. The hydro-gen molecules are broken up, or photodissociated, by UVradiation from hot stars in the interstellar medium outsideof dense dust clouds. Thus, molecular hydrogen is themajor form of interstellar hydrogen in dense dust clouds,whereas in the general interstellar medium, hydrogen isprimarily in atomic form.

Currently, observations of interstellar molecular hydro-gen, as well as of atomic hydrogen, deuterium, and HD,




FIGURE 20 FUSE spectrum of the central star of a planetay nebula, with about 0.004 nm resolution, showing absorp-tion features due to interstellar atomic and molecular hydrogen and atomic oxygen (lower scales) in the 91.2–99.2 nmwavelength range. Features due to the atmosphere of the star itself are marked on the upper scale. [Moos, H. W.,et al. (2000). Astrophys. J. 538, L1.]

are being extended to much fainter and more distant ob-jects by the FUSE satellite mission. Figure 20 shows aFUSE spectrum of the central star of a planetary nebula.Absorption lines due to interstellar H I, O I, and H2 aremarked below the spectrum.

B. Other Constituents of the Interstellar Gas

The Copernicus satellite also observed many other speciesin the interstellar gas, including neutral and ionized car-bon, neutral oxygen, nitrogen, and argon. The moleculesCO and OH were also observed toward some stars. It wasfound that most of the heavier elements were less abundantin the interstellar gas, relative to hydrogen, than expectedon the basis of the relative elemental abundances in thesun and stars. It was conjectured that this “depletion” wasthe result of dust grain formation. Regions of the interstel-lar medium containing less than the usual proportion ofdust showed less depletion than average, whereas the con-verse was true in lines of sight through dense dust clouds.Copernicus also discovered a very hot phase of the inter-stellar gas, revealing absorption lines of O VI characteris-tic of temperatures near 300,000 K. This gas is probablyheated by shock waves in the interstellar medium resultingfrom supernova explosions.

The IUE satellite, launched in 1978, did not have as higha spectral resolution as (or reach wavelengths as short as)the Copernicus spectrometer. However, in the range ofwavelengths longer than 120 nm, IUE was much moresensitive than Copernicus. Therefore, it was able to ob-

serve fainter and more distant stars (including some innearby external galaxies, such as the Magellanic Clouds)and stars whose light is more severely attenuated by inter-stellar dust. It extended studies of high-temperature inter-stellar gas through observations of C IV, Si IV, and N Vabsorption lines. In observations of hot stars in the Mag-ellanic Clouds, it detected interstellar absorption lines at-tributed (because of their Doppler shifts relative to locallyproduced interstellar absorption lines) to a hot “halo” ofgas surrounding our galaxy and also perhaps to similarhalos surrounding the Magellanic Clouds.

More recently, the Goddard High Resolution Spectro-graph (GHRS) and its later replacement, the Space Tele-scope Imaging Spectrograph (STIS) on the HST, havegreatly extended the measurements of the interstellar gasby IUE to fainter and more distant stars and to better spec-trophotometric accuracy. The recently launched FUSEsatellite has also extended the measurements by IUE toshorter wavelengths, and of Copernicus to higher sensi-tivity. In particular, STIS and FUSE have now extendedthese measurements to very large distances in intergalac-tic space, using quasi-stellar objects (quasars) as back-ground light sources. Among other results is the findingthat oxygen has an unexpectedly high abundance, relativeto hydrogen, in intergalactic space.

C. Emission Nebulae

The IUE satellite also provided new information on thecomposition of interstellar gas through observations of




FIGURE 21 Far-UV spectra, obtained with IUE, of diffuse nebulae, (a) Orion nebula, a typical H II region, showingcontinuum due to dust scattering of UV starlight, with nebular emission lines. [Reprinted with permission from Torres-Peimbert, S., et al. (1980). Astrophys. J. 293, 133.] (b) Cygnus Loop, a supernova remnant, showing emission linesdue to shock-heated gas. [Reprinted with permission from Raymond, J. C., et al. (1980). Astrophys. J. 238, 881.]

emission nebulae (H II regions, planetary nebulae, andsupernova remnants), in this case by observations of UVemission lines. Figure 21 shows IUE spectra of the Orionnebula (a typical H II region) and of the Cygnus Loop su-pernova remnant. In particular, the abundance of carbon(difficult to determine from ground-based observations)has been measured by observations of the strong featuresof C II (232.5 nm), C III (190.9 nm), and (in some cases)C IV (155 nm). In these objects, the electron tempera-tures (and, in supernova remnants, shock wave velocities)have also been determined from observations in the farUV. Figure 22 is a HUT spectrum of the Cygnus Loopsupernova remnant, showing the emission line of O VI

(103.2–103.7 nm). The presence of this feature indicatesthat the temperature of the gas is very high (more than200,000 K).

The H II regions are representative of gas from whichstars have recently formed or are in the process of form-ing. Planetary nebulae, on the other hand, are formed fromthe outer envelopes of stars nearing the end points of theirevolutionary life cycles. The collapsed, very hot core of adying star provides the extreme-UV radiation that ionizesthe nebula. Since the gas in the planetary nebula has been“processed” by the star, its composition differs from thatof an H II region; however, it is the gas ejected by oldstars that is recycled to form the next generation of stars.




FIGURE 22 Far-UV spectrum of a filament in the Cygnus Loop supernova remnant, obtained with the HUT in the1990 Astro-1 shuttle mission. Emission features of O VI and other highly ionized species are revealed. [Blair, W. P.,et al. (1991). Astrophys. J. 379, L33.]

Supernova remnants are the result of much more violentdisruptions of (more massive) stars; the shock waves pro-duced by the stellar explosion excite emissions from thegas both in the castoff envelope and in the surroundinginterstellar gas, which is swept up in the expanding shell.Hence, the elemental compositions of supernova remnantsare intermediate between those of H II regions and plan-etary nebulae.

VIII. INTERSTELLAR DUST

Dust particles in interstellar space make themselvesknown by both their attenuation and their reflection ofstarlight. In the visible range, the combined absorp-tion and scattering (extinction) of starlight increases to-ward shorter wavelengths, so that stars seen through dustclouds appear both dimmer and redder in color thanthey would otherwise. In the close vicinity of bright

stars, dust clouds are illuminated and appear as reflectionnebulae.

Ultraviolet measurements of interstellar extinction andof reflection nebulae have the potential to provide addi-tional information on the properties and composition ofthe dust particles. As mentioned, in the visible range, theextinction increases smoothly toward shorter wavelengths.However, early rocket measurements (confirmed by morecomprehensive satellite observations), in which the spec-tra of reddened stars were compared with those of unred-dened stars of the same type, showed that this trend doesnot continue indefinitely into the UV. Instead, the interstel-lar extinction vs wavelength relation reaches a peak near220 nm, following which the extinction decreases towardshorter wavelengths (to ∼160 nm). Below this, the ex-tinction again increases toward shorter wavelengths (seeFig. 23). The peak in the extinction curve near 220 nmmatches that expected, theoretically, to be produced bygraphite particles. However, it has been found that the




FIGURE 23 Interstellar extinction vs wavelength in the UV andground-accessible wavelength ranges. The letters indicate centralwavelengths of ground-based photometric pass bands. Note largevariations in the extinction curve in the UV for different regions ofspace.

UV extinction curve is highly variable in both magnitudeand shape in different directions in our galaxy and in theMagellanic Clouds. Hence, it appears that there must beat least three independent components of the interstellardust, whose relative abundances vary in different wayswith local conditions in the interstellar medium.

FIGURE 24 Comparison of far-UV and visible imagery of the Large Magellanic Cloud, the nearest external galaxy.(a) Image in the wavelength range 1250–1600 A (10 min) obtained with the Naval Research Laboratory S201 cameraon Apollo 16. (b) Visible-light image, to the same scale. (Lick Observatory photograph.)

Observations of the reflection spectrum of interstellardust have also yielded some insights concerning the prop-erties of interstellar dust particles; in particular, it has beenfound that, at least in some reflection nebulae, the particlesare very efficient scatterers of far-UV radiation. Except inthe vicinity of the 220-nm extinction peak, it appears thatmost of the interstellar extinction is due to scattering ratherthan pure absorption.

Most galactic H II regions appear as reflection nebulaein the far UV, as illustrated by the IUE spectrum of theOrion nebula in Fig. 21. This is due to the relatively highdust densities (roughly proportional to gas densities) inthese regions, combined with the presence of UV-brightstars (which both illuminate the dust and excite UV andvisible emission lines). However, the dust in H II regionsis probably not typical of dust in other reflection nebulae(illuminated by somewhat cooler stars) and in the generalinterstellar medium, since the intense radiation fields inregions such as the Orion nebula can significantly modifythe size distributions and compositions of the dust parti-cles. This is evidenced by both their reflection spectra andtheir extinction curves, which differ from those observedin less excited regions of the interstellar medium.

IX. EXTRAGALACTIC OBJECTS

The external galaxies, like our own, are gigantic cluster-ings of stars (as many as 1011 to 1012) and associatedinterstellar material. There is a wide variety of shapes




and stellar content among external galaxies: many arespiral galaxies resembling our own, whereas others arespherical or elliptical and are devoid of obvious spiralpatterns.

As in the case of our galaxy, UV observations are ex-pected mainly to reveal the hot stellar component. How-ever, an advantage in observing other galaxies is that thespatial distribution of the hot stellar population is seenat a glance, whereas this is much more difficult to deter-mine for our own galaxy, which we view from within.The variations in this distribution from one galaxy to thenext, and in comparison with the distribution of coolerstars and of interstellar material in these galaxies, provideinformation on star formation rates and history and onthe overall evolution of galaxies. The ability to detect andmeasure hot stars in the presence of a much larger numberof cool stars, by means of UV observations, is even moreimportant in studies of external galaxies than our own,since in the former individual stars often are not individ-ually resolved and hence problems due to image overlap

FIGURE 25 Comparison of far-UV images (top), taken with the UIT on the Astro-2 shuttle mission, and ground-basedvisible images (bottom) of three spiral galaxies. (Courtesy of T. Stecher, NASA GSFC).

and confusion are more severe. Ultraviolet observationsalso provide more sensitive measurements of the inter-stellar material in observations of starlight extinction orreflection.

Some galaxies, notably the Seyfert galaxies and quasi-stellar objects (quasars), exhibit highly energetic activityin their central regions, which far transcends that whichcan be associated with even the most massive individualstars. The total luminosity of an active galactic nucleuscan greatly exceed the total luminosity of the remainderof the galaxy; quasars are, in fact, by far the most luminousobjects in the universe. Observations of these objects inthe UV can add to the store of knowledge that is neededto acquire an understanding of these objects.

Photometric and spectrophotometric measurements ofa number of external galaxies were obtained with OAO-2and subsequently were supplemented by more sensitiveobservations with IUE. Ultraviolet images of the Magel-lanic Clouds and a number of other galaxies have beenobtained in sounding rocket flights, the Apollo 16 mission




FIGURE 25 (continued).

(see Fig. 24), Astro space shuttle flights of the GoddardSpace Flight Center’s UIT (see Fig. 25), and other UV-imaging space experiments. The HUT on the Astro spaceshuttle flights has been used to obtain far-UV spectra ofquasars and other extragalactic objects at wavelengths asshort as 92 nm.

These observations are being greatly extended usingimaging and spectroscopic instruments on the HST, inparticular the STIS, and with the recently launched FUSE.Among other things, these new instruments have providedmeasurements of the gas and dust in external galaxies andin intergalactic space.

One of the most important objectives of the HSTis to determine more accurately the distance scale ofthe universe; it can do this by observing galaxies atmuch greater distances with the same degree of detailas nearer galaxies are presently observed with ground-based telescopes. Ultraviolet observations are an impor-tant aspect of these studies, because the most luminoushot stars are useful distance indicators, and these aremuch brighter in the UV than in the visible. Also, for

very distant objects, the redshift due to the expansionof the universe allows observations of wavelengths be-low the 91.2 nm short-wavelength limit for nearby ob-jects, set by the absorption due to local interstellar atomichydrogen.


ATOMIC SPECTROMETRY • AURORA • GALACTIC STRUC-TURE AND EVOLUTION • INFRARED ASTRONOMY • INTER-STELLAR MATTER • PLANETARY ATMOSPHERES • SOLAR

PHYSICS • STELLAR SPECTROSCOPY • STELLAR STRUC-TURE AND EVOLUTION • TELESCOPES, OPTICAL

BIBLIOGRAPHY

Bowyer, S., and Leinert, C., eds. (1990). “The Galactic and Extragalac-tic Background Radiation,” IAU Symposium 139, Kluwer Academic,Dordrecht.




Bowyer, S., and Malina, R. F., eds. (1996). “Astrophysics in the ExtremeUltraviolet,” Kluwer Academic, Dordrecht.

Chapman, R. D., ed. (1981). “The Universe at Ultraviolet Wavelengths,”NASA CP-2171, U.S. Natl. Aeronaut. Space Admin., Washington,DC.

Code, A. D., ed. (1972). “The Scientific Results from the Orbiting Astro-nomical Observatory (OAO-2),” U.S. Natl. Aeronaut. Space Admin.,Washington, DC.

Cornell, J., and Gorenstein, P., ed. (1983). “Astronomy from Space,”MIT Press, Cambridge, MA.

Cowie, L. L., and Songaila, A. (1986). “High resolution optical and ul-traviolet absorption line studies of interstellar gas,” Annu. Rev. Astron.Astrophys. 499.

Eddy, J. A. (1979). “A New Sun: The Solar Results from Skylab,” U.S.Natl. Aeronaut. Space Admin., Washington, DC.

Hanle, P. A., and Chambrelain, V. D., eds. (1981). “Space Science Comesof Age,” Smithsonian Institution Press, Washington, DC.

Henbest, N., and Marten, M. (1983). “The New Astronomy,” CambridgeUniv. Press, London and New York.

Kondo, L., Mead, J. M., and Chapman, R. D., eds. (1982). “Advances inUltraviolet Astronomy,” NASA CP-2238, U.S. Natl., Aeronaut. SpaceAdmin., Washington, DC.

Kondo, Y., ed. (1990). “Observatories in Earth Orbit and Beyond,”Kluwer Academic, Dordrecht.

Kondo, Y., Boggess, A., and Maran, S. P. (1989). “Astrophysical contri-butions of the international ultraviolet explorer,” Annu. Rev. Astron.Astrophys. 397.

Lean, J. (1997). “The sun’s variable radiation and its relevance for Earth,”Annu. Rev. Astron. Astrophys. 33.

Lundquist, C. A., ed. (1979). “Skylab’s Astronomy and Space Sciences,”NASA SP-404, U.S. Natl. Aeronaut. Space Admin., Washington,DC.

Noyes, R. W. (1982). “The Sun, Our Star,” Harvard Univ. Press, Cam-bridge, MA.

O’Connell, R. W. (1999). “Far-ultraviolet radiation from elliptical galax-ies,” Annu. Rev. Astron. Astrophys. 603.

Petersen, C. C., and Brandt, J. C. (1995). “Hubble Vision: Astronomywith the Hubble Space Telescope,” Cambridge Univ. Press, Cam-bridge, UK.

Savage, B. D., and Sembach, K. R. (1996). “Interstellar abundances fromabsorption-line observations with the Hubble Space Telescope,” Annu.Rev. Astron. Astrophys. 279.

Spitzer, L., Jr. (1982). “Searching Between the Stars,” Yale Univ. Press,New Haven, CT.

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Encyclopedia of Physical Science and Technology EN017B-829 August 3, 2001 16:52

X-Ray AstronomyM. F. CorcoranNASA, Goddard Space Flight Center

I. OverviewII. Production and Absorption of X-RaysIII. X-Ray Astronomy TechniquesIV. A Brief History of X-Ray AstronomyV. Properties of Cosmic X-Ray Sources

VI. Future Directions

GLOSSARY

Accretion disk A flattened ring of gas surrounding a nor-mal star or compact object. Gas in the ring spirals ontothe central object, which increases the mass of the ac-creting object and may generate X-rays via the conver-sion of gravitational potential energy to heat.

Active galaxy A galaxy whose radiation is dominatedby the emission from a localized region at the centerof the galaxy. This region is thought to consist of amassive torus of gas surrounding a supermassive blackhole about a few million times more massive than thesun.

Black hole A compact object produced by the collapseof a massive object such as a star or star cluster fromself-gravity. The object collapses to such a small sizethat not even light can escape from it.

Corona The outermost part of a stellar atmosphere ofa star like the sun. The temperature of the corona istypically a few million degrees, and thus the corona isthe hottest part of the star that can be directly observed.

Dark matter Matter that does not emit electromagneticradiation detectable at earth. Dark matter is only de-

tectable from its gravitational effect on luminous mat-ter and photons. Dark matter may comprise 90% ormore of the total mass in the Universe.

Electron volt (eV) The change of potential energy ex-perienced by an electron moving from a place wherethe electric potential has a value of V volts to a placewhere it has a value of V + 1 volts. This is a convenientenergy unit when dealing with the motions of elec-trons and ions in electric fields; the unit is also the oneused to describe the energy of X-rays and gamma rays.1 eV = 1.602177 × 10−19 joules.

Neutron star Compact object formed from the death of astar of mass greater than about 10 times the mass of thesun, or from the induced collapse of a white dwarf in abinary system due to mass transfer. Typically neutronstars have a radius of about 10 km and a mass near asolar mass.

Planetary nebula The ejected outer atmosphere of a lowto intermediate mass star that forms a glowing cloud ofgas and dust around the stellar core. This cloud of gasand dust is called a planetary nebula.

Pulsar A rapidly spinning neutron star that emits pulsesof electromagnetic radiation.

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904 X-Ray Astronomy

Solar mass An amount of matter equal to the mass of thesun, i.e., 2 × 1033 g.

Supernova remnant Debris ejected into space as a resultof an explosion of a star whose mass is in excess of 10solar masses.

White dwarf Collapsed remnant of the core of a starwhose mass is near 1 solar mass. The mass of a whitedwarf is limited to 1.4 solar masses, the so-calledChandrasekhar mass. White dwarfs typically have aradius of about 104 km.

X-RAY ASTRONOMY is the study of emission and ab-sorption of high-energy X-radiation produced by cosmicobjects, using space-based detectors. Though a relativelyyoung field of astronomical research, over the last 30 yearsX-ray astronomy has revealed the richness of high energyphenomena in the Universe. X-radiation is produced bynearly all types of cosmic objects, from solar system bod-ies (planets and comets) to stars and galaxies, to largediffuse nebulae. X-ray emission provides an especiallysensitive probe of regions of extreme gravity, extreme tem-perature, and extreme magnetic field strength in the MilkyWay galaxy and in external galaxies.

I. OVERVIEW

The spectrum of electromagnetic radiation is divided intoabout seven discrete regions based on wavelength or en-ergy. The X-ray energy band comprises radiation with en-ergy in the range a few tenths to a few hundred kilo–electron volts (keV). This range roughly corresponds tothe K shell absorption edge of neutral carbon up to therest mass energy of the electron. Since photon wavelengthis inversely proportional to energy, this corresponds to arange in photon wavelength of about one millionth to oneten billionth of a centimeter. For comparison, visible ra-diation comprises a range of wavelength of about fourhundred thousandths to eight hundred thousandths of acentimeter, or energies of about 0.003–0.001 keV. X-rayradiation (first detected by Wilhelm Conrad Rontgen on8 November 1895 at the University of Wurzburg) is thusa form of high energy (short wavelength) radiation usu-ally produced in regions of extreme temperatures or strongmagnetic fields, and is often associated with large changesin kinetic energy produced near extremely strong gravi-tational fields. X-ray astronomy deals with the detectionand analysis of X-radiation produced by stars, collapsedstellar remnants, diffuse hot gas, galaxies, and clusters ofgalaxies. Overall, X-ray emission is an important mea-sure of some of the most energetic physical proceses inthe Universe. Absorption of X-rays by material betweenthe observer at earth and the source is also important as it

gives astronomers a measure of the amount and composi-tion of the intervening material. As in other branches of as-tronomy, X-ray astronomy in particular is concerned withunderstanding the spatial, spectral, and temporal distri-bution of the emitted radiation. However, because X-raysare so energetic, X-ray astronomy must utilize somewhatspecialized detection techniques, though some detectors(like photographic plates and charged-coupled devices)which have been or still are widely used in visible-bandastronomy are also useful detectors of X-rays. Because theatmosphere is mostly opaque to X-rays, X-ray astronomynecessarily requires the X-ray telescope to be placed abovethe bulk of the atmosphere, either carried aloft on a balloonor by a suborbital rocket, or on an orbiting space platform.In the following we discuss how X-rays are produced in thecosmos, and how they are detected and analyzed at earth.

II. PRODUCTION AND ABSORPTIONOF X-RAYS

Electromagnetic radiation is the result of the acceler-ation of charged particles (electron and ions). CosmicX-rays may be produced by both thermal and nonther-mal processes. Thermal processes are those in which thevelocity distribution of the relevant charged particles isdetermined solely by temperature. Hot, optically thick ob-jects (such as planets and stars) will produce “blackbody”radiation in which radiation is emitted as a smooth con-tinuum over a large wavelength range, though the emis-sion peaks near some characteristic wavelength and fallsquickly at shorter wavelengths and less rapidly at longerwavelengths. Wien’s law states that the peak of the black-body continuum occurs at a wavelength λmax given by

λmax = 0.29

Tcm (1)

where T is the temperature of the blackbody in kelvins(K). In order for the continuum peak to occur in theX-ray band, the temperature of the blackbody must beT > 2.3 × 105 K; thus the presence of thermal blackbodyX-ray emission implies high temperatures. For a spheri-cal body of radius R radiating at some temperature T , theblackbody luminosity of the object is given by

Ltot = 4π R2ST 4 (2)

where S is the Stefan–Boltzmann constant. A cloud ofhot, low-density plasma will produce thermal contin-uum emission due to bremsstrahlung (“braking radia-tion”). Thermal bremsstrahlung is produced in opticallythin plasmas by the acceleration of electrons by positivelycharged ions in the plasma. Bremsstrahlung is sometimescalled “free-free” radiation since the radiation is produced



X-Ray Astronomy 905

by motions of unbound charged particles. Optically thinplasmas also produce line emission by collisional excita-tion of electrons to upper atomic bound states and radiativedeexcitation to lower states. In general, all optically thinhot plasmas will produce a combination of X-ray contin-uum bremsstrahlung emission and X-ray line emission.

Nonthermal processes involve the motion of chargedparticles in the presence of magnetic fields. Examplesof nonthermal emission processes are synchrotron andcyclotron emission, in which radiation is produced aselectrons and/or ions accelerate around lines of magneticforce and radiate. Another astrophysically importantnonthermal process is inverse Compton scattering, inwhich photons scatter off a nonthermal population offast-moving electrons, and energy is transferred fromthe electrons to the photons. For sufficiently energeticelectrons (especially those whose velocities approach thespeed of light) enough energy may be transferred to boostthe photon energy into the X-ray (or, conceivably, even thegamma ray) energy band. Production of X-radiation bynonthermal emission processes generally requires largepopulations of electrons moving near the speed of light.Gas near bright sources of X-rays can be photoionized,in which the population of the electronic energy levelsand ionization state is determined by the incident X-rayspectral flux and not the temperature of the gas. Radiativeexcitation and deexcitation in photoinized plasmas canproduce detectable line emission.

Cosmic X-rays are absorbed by intervening materialbetween the source and Earth, either from material as-sociated with the source (as in the case of an accretiondisk, or a stellar wind) or from diffuse nebular gas in ourgalaxy. Absorption is produced by photoionization of hy-drogen and other elements. The photon absorption crosssections of all elements decrease with increasing X-rayenergy; thus in general absorption is important for low-energy or “soft” X-rays (X-rays of energy 0.1–1 keV), butless important for higher energy (or “hard”) X-rays. Typ-ically absorption is unimportant at energies higher thanabout 3 keV for all but the most highly absorbed sources.Since absorption is basically produced by photoioniza-tion, determining the degree to which the X-ray sourceemission is absorbed offers clues to the ionization state,the density, and the chemical composition of the materialalong the line of sight to the source.

III. X-RAY ASTRONOMY TECHNIQUES

A. X-Ray Imaging Systems

Early images of the X-ray sky were produced using col-limated X-ray detectors, where a metal tube (called a

collimator) was placed in front of the X-ray detector torestrict the view direction to some fraction of a squaredegree. Resolving finer spatial detail at X-ray energies isbest accomplished through the use of an imaging systemto bring the X-rays to focus. Unlike visible-band pho-tons, X-ray photons cannot be focused by refraction or bysingle scattering from a mirror at near normal incidence,since X-rays at near normal incidence will penetrate mostmaterials. However, X-rays can be focused by scatteringat near grazing incidence. Use of grazing incidence X-ray optics in astronomy was first proposed by RiccardoGiacconi and Bruno Rossi in 1960. The simplest X-raytelescope mirror configuration is a paraboloid of revolu-tion, in which X-rays along the axis of the paraboloidcan be brought to a focus by scattering at near-grazingincidence from the surface of the reflector. This type of X-ray mirror was used on the SAS-2 (Copernicus) satellite.Simple paraboloids of revolution can only bring on-axisrays to focus, however; off-axis sources suffer aberrationthat severely limits the field of view of the paraboloidmirror.

On-axis and off-axis X-rays can both be focused bymultiple scattering at near grazing incidence. The mostcommon mirror geometry used in X-ray astronomy is the“Wolter type I” configuration (designed by Hans Wolter in1952), which consists of concentric pairs of paraboloid–hyperboloid cylindrical mirror shells, as shown in Fig. 1.The mirrors are typically composed of finely polishedglass coated with a thin layer of dense material such as goldor iridium that has a sufficiently high X-ray reflectivity.In order to maximize the scattering area, the paraboloid–hyperboloid shell pairs are nested so as to provide a max-imum scattering surface for the incident X-rays. X-raysentering the mirror parallel to the mirror axis scatter first

FIGURE 1 Focusing geometry of a Wolter type I grazing inci-dence X-ray telescope constructed by a paraboloid followed by ahyperboloid cylindrical mirror. In X-ray telescopes a number (2, 4,or hundreds) of such shells are “nested,” or placed one inside theother, to improve the X-ray gathering power of the mirror.



906 X-Ray Astronomy

off the paraboloid shells and then are brought to focusby scattering off the hyperboloid shells. The mirror col-lecting area, or “effective area,” depends sensitively onphoton energy and off-axis angle and is typically muchless than 1 square meter in all cases (for example, the X-ray telescope on the XMM-Newton observatory, the largestX-ray telescope yet flown, has an effective area that variesfrom about 0.6 m2 near 0.1 keV down to 0.1 square meternear 10 keV). The mirror focal length depends on pho-ton energy due to the energy dependence of the scat-tering angle. In general the shape of the focal plane iscurved, which means that, for example, images obtainedby a plane parallel detector will show increasing distortionwith increasing off-axis angle. Although the spatial re-solving power of a telescope depends inversely on photonwavelength, the practical difficulty in bringing X-rays tofocus means that the spatial resolution of X-ray telescopesis generally much worse than for an optical telescope ofsimilar collecting area. The Chandra X-ray observatorycontains the finest X-ray imaging telescope yet flown;the absolute limiting resolution of this telescope is about0.5 seconds of arc. For comparison, the theoretical diffrac-tion limit at 1 keV for Chandra is about 2.5 × 10−4 secondof arc.

Wolter type I X-ray mirrors are typically very expensiveto build since they need to be polished to very high toler-ances, and are expensive to launch since they are gener-ally heavy. One means of reducing costs is to approximatethe Wolter type I reflecting surface through use of nestedsets of thin, lightweight, conical aluminum foil shells.Although these thin-foil mirrors sacrifice some angularresolution (typically they can achieve spatial resolutionsof a few minutes of arc), they can provide much greaterthroughput over a large energy range since hundreds offoils can be nested in a single mirror. Thin foil X-raymirrors were used for the first time by the Broad-bandX-ray Telescope (BBXRT) during the ASTRO-1 mission,and later by the Advanced Satellite for Cosmology andAstrophysics (ASCA) X-ray observatories.

B. X-Ray Detectors

Detectors used in X-ray astronomy include proportionalcounters, microchannel plates, and charge-coupled de-vices and other solid-state detectors. Proportional coun-ters were the first type of X-ray detector used in astronomyand are the most common astronomical X-ray detector inuse today. Proportional counters consist of an electricallyneutral gas (usually argon or xenon) in a sealed chamber.As an X-ray enters the chamber, it can photoionize a gasatom, producing a photoelectron that can then be amplifiedand detected. Modern proportional counters can detect theposition of the incident X-ray along with its time of arrival

and energy, since the number of photoelectrons produceddepends on the energy of the incoming X-ray. The rela-tion between the energy of the incident photon and theamplitude of the electron pulse detected in the propor-tional counter is termed the gain of the detector. Exam-ples of X-ray proportional counters include the ImagingProportional Counter (IPC) flown on the Einstein X-rayobservatory, the Position Sensitive Proportional Counteron the Rontgen Satellite X-ray observatory (ROSAT), andthe Proportional Counter Array (PCA) on the Rossi X-RayTiming Explorer (RXTE).

Use of charge-coupled devices (CCDs) is becoming in-creasingly common in X-ray astronomy. X-ray CCDs aresimilar to the more familiar optical CCDs, but have someimportant differences. In each case a photon interacts witha solid layer of material (usually silicon) over which anarray of electrodes has been formed. The electrodes definepotential wells that form the picture elements, or “pixels,”of the image. Like proportional counters, CCDs can beused in photon counting mode to record the time of arrival,location, and energy of the incident X-rays. Because eachpixel in a CCD must be read out by the detector electronics,X-ray CCDs are prone to “pileup,” in which two or morephotons arrive in a single pixel before it is read out and arecounted as a single photon. In addition CCDs are prone to“charge transfer inefficiency” (CTI), in which the inferredenergy of the photon may change during readout, produc-ing a gain that varies spatially over the face of the detec-tor. Examples of charge-coupled devices that have beenused as X-ray detectors include the Solid-State ImagingSpectrograph used on ASCA, the Advanced CCD Imag-ing Spectrometer (ACIS) on the Chandra X-Ray Obser-vatory, and the European Photon Imaging Camera (EPIC)on XMM-Newton.

Microchannel plates are composed of bundles of mil-lions of extremely narrow lead-oxide glass tubes. The inte-rior of each tube is coated with a photoelectrically sensitivematerial. An X-ray entering a tube collides with the inte-rior of the tube wall and produces photoelectrons, whichare then accelerated in an electric field, amplified as theymove down the tube, and detected by an anode grid atthe opposite end of the microchannel plate. Because eachglass tube can be extremely thin (typically each tube isnarrower than a human hair), microchannel plates offerthe best spatial resolution of any type of X-ray detector.While providing extremely fine spatial resolution, the cur-rent generation of microchannel plate detectors is unableto provide any information about the energy of the in-cident X-ray. The first microchannel plate widely usedas an X-ray detector in astronomy was the High Resolu-tion Imager (HRI) on the Einstein observatory. A similarinstrument was flown on ROSAT. The High ResolutionCamera (HRC) on the Chandra X-ray observatory has the



X-Ray Astronomy 907

best spatial resolution of any microchannel plate detectoryet flown.

C. X-Ray Spectrometers

By separating the radiation emitted by astrophysical ob-jects into its component spectrum (the distribution of emit-ted intensity as a function of photon wavelength or en-ergy), astronomers gain greater physical insight into thenature of the emission and the nature of the source ofthe emission. X-ray astronomical spectroscopy consists ofmeasuring the spectrum of the X-rays emitted by a sourcein space. By studying the spectrum of the emitted X-rays,astronomers can determine important source parameterssuch as the temperature of the source, its composition,the magnetic field strength, and/or the relativistic electronpopulation.

Crude spectroscopy can be achieved with proportionalcounters, since the size of the charge cloud induced bythe incident X-ray is proportional to the energy of theX-ray. In practice the size of the charge cloud changesas it migrates to the anode in the counter body, so thatthe detected size of the cloud bears only a very approx-imate relation to the energy of the original photon. Asa result proportional counters typically have very crudeenergy resolving power, E/�E ∼ 1–2 (where �E is theuncertainty in the derived photon energy E). As a re-sult, the analysis of proportional counter spectra involvesan assumption of an incident photon spectrum, which isconvolved with an approximation of the energy smear-ing induced by the proportional counter (which can usu-ally be statistically estimated to fairly high accuracy),and comparison of the “smeared” spectrum to the ob-served spectrum defined by the proportional counter. Ifthe match is not satisfactory, the incident photon spec-trum is modified and the process is repeated until a sat-isfactory match is achieved. In this sense, X-ray spec-troscopy from proportional counter measurements is moreakin to optical broad-filter photometry than it is to opticalspectroscopy.

Higher X-ray energy resolution may be obtained by in-terposing an element in the light path to disperse the inci-dent X-ray flux into its component spectrum. X-ray trans-mission gratings are typically made of a regular pattern offine gold bands, and they operate in the same way as opti-cal transmission gratings, by deflecting incident photonsby an amount dependent on photon energy. The dispersedspectrum is then read out on a position sensitive detector(typically a microchannel plate or CCD). X-ray gratingspectroscopy requires relatively large amounts of X-rayflux in order to generate a detectable signal in a reason-able amount of observing time. Gratings can obtain X-rayenergy resolving powers of 1000.

Gratings work best with point sources, since extendedsources produce complicated dispersed spectra that maybe difficult to analyze. The spectra of extended sources(and faint point sources) can be obtained via nondisper-sive spectroscopy using solid-state detectors. Solid-statedetectors called microcalorimeters can achieve resolvingpowers that equal or surpass the resolving power of trans-mission gratings. A microcalorimeter consists of a ther-mally sensitive absorber such as mercury telluride (HgTe)and a thermistor that changes its resistance when heated.An X-ray incident on the microcalorimeter results in avery slight temperature change (of the order of a fewmicrokelvins) in the absorber; the rise in temperature ofthe absorber, and the resulting change in resistance of thethermistor, is proportional to the energy of the incidentX-ray. Microcalorimeters need to be operated at extremelylow temperatures (typically within a few thousandths ofa degree of absolute zero) in order to measure the verysmall change in temperature produced by the incidentX-rays. To reach temperatures this low, the device needsto be cooled using liquid helium as a refrigerant plus sometype of active magnetic cooling system. Microcalorime-ters that achieve energy resolving powers E/�E ∼ 2000or higher have been constructed.

IV. A BRIEF HISTORY OFX-RAY ASTRONOMY

A. The Discovery of Cosmic X-Ray Sources

Development of reliable launch vehicles at the end ofWorld War II ignited interest in the exploration of space,and especially in the hitherto unexplored regions of theelectromagnetic spectrum that are blocked by the earth’satmosphere. During this period there was an explosiveincrease in curiosity about the possible sources of emis-sion and absorption of cosmic X-rays, especially at en-ergies above 0.5 keV where absorption by the cold gasand dust in the galaxy is not a problem. Groups of scien-tists at the Naval Research Laboratory, American Scienceand Engineering (AS & E), the Massachusetts Instituteof Technology (MIT), and the Smithsonian AstrophysicalLaboratory (to name a few), and at other locations in theUnited States and abroad, began to identify mechanismsby which cosmic objects could emit and absorb X-rays,and to develop detectors and high-altitude and/or space-based platforms to observe this emission. X-ray astro-nomy currently is an international effort, with groupsin the United States, the United Kingdom, Ger-many, Japan, Russia, France, the Netherlands, andother countries all making important contributions. Inthe following we present a brief discussion of some



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important milestones in X-ray astronomy, concentrat-ing on technological developments and observationaldiscoveries.

X-ray emission from the sun was first detected photo-graphically in 1948 by a group from the Naval ResearchLab in Washington, D.C., using as a detector a filtered pho-tographic emulsion carried aloft on an Aerobee rocket. Thesun, though, is a rather weak X-ray source (at least as cos-mic X-ray sources go), and by extrapolation, it was judgedthat other cosmic X-ray sources would be difficult to ob-serve with available detector technology if these sourceswere similarly faint but located at cosmic distances. Itwas already understood though that X-ray sources strongerthan the sun could exist, and that objects such as super-nova remnants, flare stars, and other magnetically pecu-liar stars might be sources of significant and detectableX-ray emission. The first celestial X-ray source outsidethe solar system was detected on 12 June 1962 by a groupfrom AS & E led by Riccardo Giacconi using a set ofgeiger counter X-ray detectors on an Aerobee 150 sound-ing rocket. The primary purpose of this observation was toattempt to measure X-rays from the moon produced by theinteraction of the solar wind with the lunar surface. Dur-ing the course of this rocket flight, the detectors scanneda swath of sky and discovered a surprisingly strong X-raysource (soon dubbed “Sco X-1”) in the constellation Scor-pius, along with nonlocalized X-ray background emissionof unknown origin. If Sco X-1 were a nearby star, its X-rayluminosity would be about 10–100 million times greaterthan the X-ray luminosity of the Sun, and indeed greaterthat the total solar luminosity over all wavelengths. This

FIGURE 2 Map of Uhuru cosmic X-ray sources plotted in galactic coordinates and showing the relative intensity andsource type for several major classes of source.

astonishing result pointed to the existence of a populationof exceedingly bright X-ray sources in the sky. The nextstep was to find them and identify the physical mechanismgiving rise to the emission.

B. The First Surveys

Spurred by the discovery of Sco X-1 and other strongsources, the next step was to try to spatially resolve andidentify the sample of X-ray sources in the sky. The firstsuccessful all-sky survey of the X-ray sky was conductedby the first Small Astronomy Satellite (SAS-1, renamedUhuru after launch). Uhuru was the first orbiting obser-vatory dedicated to the study of X-ray emission. Uhuruwas built by AS & E and launched from a floating plat-form off the coast of Kenya on 12 December 1970. Uhuruscanned the entire sky with two collimated proportionalcounters sensitive to X-rays in the 2–20 keV energy range.The collimators restricted the accuracy of source posi-tions to only about 30 minutes of arc. This rather crudepositional accuracy was sufficient to determine positionsfor all of the brightest X-ray sources in the sky, and todiscover diffuse emission from clusters of galaxies. Dur-ing its 2-year life it obtained positions for 339 X-raysources in the 2–20 keV energy range and measured thetemporal variability of the emission for many of thesesources. Figure 2 shows a map of the Uhuru cosmic X-raysources in galactic coordinates, clearly showing a popu-lation of X-ray sources along the plane of the galaxyalong with a population of fainter sources off the galacticplane.



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The richness of the X-ray sky uncovered by Uhuruignited interest among astronomers to understand thesesources and to discover new ones. In 1977 NASA launchedthe first in a series of large satellite observatories devoted tohigh-energy astronomy. The first High Energy Astrophys-ical Observatory, HEAO-1, was a designed to survey theentire sky every 6 months in the 0.1 keV–10 MeV energyrange. The instruments on HEAO-1 included sets of col-limated proportional counters sensitive to low, medium,and high energy X-rays. HEAO-1 mapped the position ofbright X-ray sources to a precision of ∼30 seconds of arc(compared to ∼30 minutes of arc for Uhuru) with muchhigher sensitivity than Uhuru. HEAO-1 produced a catalogof about 1000 X-ray sources and obtained identificationsof hundreds of these sources because of the improvementin X-ray source position. HEAO-1 produced a sensitive,brightness-limited catalog of sources off the plane of thegalaxy and probed the distribution of extragalactic sourcesas a function of source brightness. In addition to car-rying out the sky survey, HEAO-1 was also operated inpointed mode, enabling sensitive studies of the time vari-ability and energy spectrum of individual bright X-raysources.

C. Imaging the X-Ray Sky

True X-ray images of the sun were first obtained by rocketflights in the 1960s. In the mid-1970s, a group at the

FIGURE 3 Overall layout of the Einstein X-Ray Observatory.

Smithsonian Astrophysical Observatory led by PaulGorenstein produced the first X-ray images of extra-solar objects using two orthogonal one-dimensional X-raymirrors and a proportional counter detector. During rocketflights in March 1975 and December 1975 they used thisinstrument configuration to image the X-ray sky near thestar Algol, and in June 1976 they imaged the extendedX-ray emission around the Virgo cluster of galaxies. Thefirst use of a Wolter nested grazing incidence telescope inX-ray astronomy was the Apollo Telescope Mount, whichflew on Skylab in the early 1970’s and obtained imagesof the solar corona. The first use of Wolter-type opticsin extra-solar X-ray astronomy was by Saul Rappaportof MIT and collaborators who imaged X-ray emissionfrom supernova remnants during the course of two rocketflights.

A major turning point in X-ray astronomy was thelaunch of the second High Energy Astrophysical Ob-servatory (later christened the Einstein observatory) inNovember 1978. The Einstein observatory was an orbit-ing satellite observatory designed to provide the first directimages of large regions of the X-ray sky. Figure 3 showsa schematic drawing of the Einstein observatory. It car-ried the largest Wolter-type 1 X-ray mirror ever launchedto that time, and was equipped with sensitive focal planeimaging detectors. Einstein carried on board two focal-plane cameras, the Imaging Proportional Counter and theHigh Resolution Imager microchannel plate detector. The



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IPC provided spatial resolutions of a few minutes of arcin a 1◦ field along with crude sensitivity to photon en-ergy. The HRI was insensitive to photon energy but couldprovide arcsecond-scale images over a 1◦ field. Einsteinallowed astronomers for the first time to directly imagethe X-ray sky with a sensitivity two orders of magnitudegreater than any previous X-ray observatory. Einstein alsocarried a focal plane spectrometer, the Solid State Spec-trometer (SSS), for improved energy sensitivity in a 6-arcminute field. The highest energy resolution on Einsteincould be obtained through use of the Objective GratingSpectrometer (OGS) or a Bragg crystal spectrometer(called the Focal Plane Crystal Spectrometer or FPCS),though dispersed spectra could be usefully obtained onlyfor the brightest X-ray sources. In addition to the focalplane instrumentation, Einstein also carried a collimatedproportional counter detector, the Monitor ProportionalCounter (MPC). The Einstein mission lasted until April1981. During this time Einstein produced more than5000 images of the X-ray sky in the energy band 0.5–4.5 keV. Einstein revolutionized X-ray astronomy byshowing the ubiquity of X-ray emission for almost allclasses of astrophysical sources (from stars to galaxies),and allowed detailed study of important sources of X-rayemission such as supernovae, solar-type and non-solar-type stars, neutron star systems, and black holes, galaxiesand galaxy clusters, as well as studies of the diffuse X-raybackground.

The European X-ray Satellite observatory EXOSAT waslaunched in 1983, shortly after the end of the Einsteinmission in 1981, and was operational for nearly 3 years.EXOSAT carried two Wolter type 1 X-ray grazing inci-dence mirrors for imaging of low-energy (0.05–2 keV)X-rays from space and a microchannel plate (the Chan-nel Multiplier Array, or CMA) for high spatial resolu-tion studies plus a proportional counter (the Position Sen-sitive Detector or PSD) for imaging studies at coarserspatial resolution but better spectral resolution. UnlikeEinstein, which was placed in a circular orbit a few hun-dred kilometers above the earth, EXOSAT was placedin an elliptical orbit with apogee (maximum distancefrom earth) of 191,000 kilometers (about one-half thedistance to the moon) and perigee (minimum distancefrom earth) of 350 kilometers. This orbit allowed ef-ficient observations of X-ray sources, allowing up to76 hours of uninterrupted observation out of every 90-hour orbit. Studies using EXOSAT showed the first evi-dence of “quasi-periodic oscillations” (QPOs) in the X-rayemission from low-mass X-ray binaries, discovered low-energy X-ray excesses in the emission from active galacticnuclei, and observed for the first time red- and blueshiftedX-ray iron line emission from the low mass X-ray binarySS 433.

D. Expanding the Boundsof the X-Ray Universe

Recent advances in the development and deployment ofX-ray satellite observatories have concentrated on prob-ing the unexplored territory: direct X-ray imaging of largeportions of the Universe, studies of extremely fast vari-ations in X-ray brightness and spectral energy distribu-tions, imaging of sources with extremely high spatial andspectral resolutions, and studies of the population of ex-tremely faint X-ray sources.

1. ROSAT: Large-Scale Spectral Imaging

In 1990 the Rontgen Satellite (ROSAT) was launched.ROSAT was an international X-ray space observatorydeveloped by Germany (who built the X-ray mirror,the spacecraft, and the Position Sensitive ProportionalCounter detector for moderate spectral and spatial reso-lution studies), the United States (who provided a mi-crochannel plate detector similar to the Einstein HRIfor high spatial resolution studies, and who providedthe launch vehicle), and the United Kingdom (who pro-vided an extreme ultraviolet telescope coaligned with theX-ray telescope). The X-ray telescope on ROSAT had veryfine imaging capability, achieving resolutions of about1 minute of arc with the PSPC, and about 5 seconds ofarc with the HRI, in the energy band 0.2–2.4 keV. Thedetectors also had extremely low internal backgrounds,which meant ROSAT was an ideal instrument to observesoft X-ray emission from low surface brightness objects.The observatory continued to make useful science obser-vations up through the end of 1998, more than doublethe lifetime of other X-ray imaging observatories to thattime. This longevity allowed ROSAT to detect more X-raysources than any other X-ray observatory, and also al-lowed astronomers to undertake sensitive studies of X-rayvariability on longer time scales than ever before. Dur-ing the first 6 months after launch ROSAT conducted an“all-sky” survey in which the entire sky was imaged withthe PSPC. After the all-sky survey phase, and for the next8 years, ROSAT obtained deep pointed observations ofparticular regions of the sky containing X-ray targets ofspecial astrophysical interest. ROSAT observations revolu-tionized almost all areas of X-ray astronomy in much thesame way that Einstein did 12 years earlier. In additionto the many discoveries during the all-sky survey phase,in the pointed phase ROSAT made the first ever sensitivedetection of sources in the so-called “Lockman Hole,” alow column density region in the Milky Way, and showedthat much of the hard X-ray background can be resolvedinto emission from active galactic nuclei. ROSAT also ob-tained the first X-ray image of a shadow in the soft X-ray



X-Ray Astronomy 911

background produced by an intervening molecular cloudand so provided the first firm lower limit on the location ofa source of the soft X-ray background. ROSAT discovereda class of X-ray objects called “supersoft sources” andmonitored the brightening of the X-ray emission from Su-pernova 1987A, the closest supernova explosion in morethan 400 years. ROSAT made the first surprising detec-tion of X-ray emission from comets and showed that theimpact of a comet on Jupiter could produce observableX-ray emission. ROSAT also showed the ubiquity of X-ray variability for all classes of stellar X-ray sources. TheROSAT archive contains more than 11,000 pointed obser-vations and a catalog of more than 90,000 X-ray sources,extending the number of known X-ray sources by aboutone order of magnitude.

2. RXTE: Fast Variability Studies

The Rossi X-Ray Timing Explorer (RXTE) was launchedin 1996. RXTE was designed to provide extremely sensi-tive, high-time-resolution (to the microsecond level) stud-ies of the variations of X-ray brightness and X-ray spectrafrom compact objects, active galaxies, and bright stars.A particular strength of RXTE is the capability to sched-ule coordinated observations with other observatories toallow observations of physical processes in astronomicalobjects over a wide range of wavelength regions. RXTE’sinstrumentation includes the Proportional Counter Ar-ray (PCA), a set of six collimated proportional counterscoaligned to point simultaneously at a specified area of thesky of roughly 1 square degree in size. RXTE also carriesthe High Energy X-ray Transient Experiment (HEXTE)designed to study source variability in the 15–250 keVrange, and an All-Sky Monitor (ASM) designed to studyvariability of bright X-ray sources in the entire sky. Oneof the major discoveries of RXTE is the detection of thefastest periodic signals ever observed from an astronomi-cal source. These “millisecond” pulsations (typically thereare roughly 1000 X-ray flashes per second) are producedby some neutron star binary systems and are used to probethe condition of material in the extreme gravity very nearthe surface of the compact object. RXTE also showed thatat least some of the hitherto mysterious objects known assoft gamma ray repeaters show X-ray pulsations as welland that these objects are probably types of compact X-raybinary systems with exceedingly strong magnetic fields.RXTE also produced the first detailed measure of the X-rayvariability of Eta Carinae, a star that many astronomersthink is the most massive star in the Milky Way; theseobservations showed a substantial, periodic eclipse of theX-ray emission every 5 years, probably produced by thepresence of a companion star.

3. BeppoSAX: Solving the Gamma RayBurst Riddle

BeppoSAX is a joint Italian–Dutch X-ray observatory thatwas launched in 1996; it consists of four narrow-fieldX-ray instruments (a set of medium-energy telescopes,a set of low-energy telescopes, a collimated gas scintil-lation proportional counter, and a “phoswich” detectorsystem) plus two wide-field coded-mask cameras. Bep-poSAX has made a major contribution to X-ray astronomyand high-energy astrophysics in general by detecting thefirst X-ray afterglow from a “gamma-ray burst” source.Gamma-ray bursts are brief flashes of gamma rays (a typeof extremely high energy radiation) that occur nearly onceper day. Though they were originally detected by spacesatellites in the 1970s, their origin remained a mysterybecause of the poor angular resolution of gamma-ray de-tectors. The error box of a typical gamma-ray burst posi-tion is generally many minutes of arc, and typically eacherror box contains dozens of candidate sources, makingsource identification difficult. However, in February 1997a gamma-ray burst error box was imaged by the narrow-field X-ray detectors on BeppoSAX, and BeppoSAX dis-covered a bright, fading X-ray source near the gamma-rayburst position. This source was recognized as the X-ray“afterglow” of the gamma-ray burst, and thanks to thehigher spatial resolution of the narrow-field X-ray detec-tors, an accurate position of the source could be obtained.Subsequent follow-up observations using this position byradio and optical telescopes associated this gamma-rayburst with a distant, star-forming galaxy. Because of thisobservation and others like it, it is now thought that somegamma-ray bursts signal incredibly powerful explosionsproduced by the destruction of very massive stars in dis-tant, star-forming galaxies.

4. Chandra: The Finest X-Ray Camera

The Chandra X-ray observatory was launched in the sum-mer of 1999. Chandra, named for the famed astrophysicistSubrahmanyan Chandrasekhar, is the third of the “GreatObservatories” launched by NASA (the Hubble SpaceTelescope and the Compton Gamma Ray Observatory arethe other two) and is designed to image the X-ray uni-verse with the highest spatial and spectral resolution everobtained. Chandra has the finest X-ray mirror ever made.Combined with Chandra’s CCD camera (the AdvancedCCD Imaging Spectrometer) and microchannel plate de-tector (the High Resolution Camera), Chandra can studybrightness and spectral variations on extremely small spa-tial scales (on the order of 0.5–1 second of arc). In addition,Chandra carries aboard three sets of transmission gratingsthat enable the study of X-ray spectra with high resolvingpower (E/�E ∼ 100–2000) over a broad energy range



912 X-Ray Astronomy

(0.1–2.0 keV with the Low Energy Transmission Grat-ing, and 0.4–10.0 keV with the Medium and High EnergyTransmission Gratings). Like EXOSAT, Chandra has beenplaced in a highly elliptical orbit; its apogee takes Chandraabout one-third of the distance to the moon. Near apogee,Chandra is able to observe a large fraction of the X-ray skyfor long intervals uninterrupted by earth eclipses, allowingfor a much more efficient use of observing time. At thevery start of its science life as of this writing, alreadyamong Chandra’s science achievements are the discoveryof a previously unseen collapsed stellar core at the cen-ter of the Cas A supernova remnant, the identification ofthe physical processes by which comets emit X-rays, andsensitive spatial studies of X-ray jets from active galaxiesand galactic neutron star systems.

5. XMM-Newton: Probing ExtremelyFaint Sources

The X-ray Multi-Mirror Mission was launched in Decem-ber 1999 by the European Space Agency; after launch itwas renamed in honor of Isaac Newton. XMM-Newtonconsists of three coaligned, high-throughput X-raymirrors and three sets of focal plane detectors: a CCDcamera (the European Photon Imaging Camera, or EPIC)behind one of the mirror modules, and reflection gratings(the Reflection Grating Spectrometers, or RGS) andcameras to read out the dispersed spectra behind the othertwo modules. XMM-Newton provides for simultaneous0.1–15 keV X-ray imaging (on spatial scales of about15 seconds of arc) with its CCD cameras and X-rayspectroscopy (with a resolving power between 200 and800) in the energy range 0.3–2.5 keV via the reflectiongratings. Because of the high throughput of the X-raymirrors XMM-Newton can study faint sources in unprece-dented detail. At the time of this writing XMM-Newtonis just beginning to take scientific observations after itsinstrumental on-orbit checkout interval. Nevertheless,XMM-Newton has already discovered a cluster of galaxieshidden from previous X-ray observatories by the gasand dust in the plane of the Milky Way, obtained ahigh-resolution X-ray spectrum of the star HR 1099, anddiscovered hundreds of faint, unidentified sources.

V. PROPERTIES OF COSMICX-RAY SOURCES

A. Sources of X-Ray Emission inNormal Galaxies

1. Normal Stars

Nearly all types of normal (i.e., noncollapsed) singlestars generate X-ray emission at some level. Stellar X-

ray emission is thought to be dominated by thermal emis-sion arising from one or more of the following processes:magneto-hydrodynamic heating in the outer stellar atmo-sphere; frictional heating; and shock heating produced byinstabilities in an outwardly flowing stellar wind. The sunis the brightest cosmic X-ray source, yet has a rather mod-est X-ray luminosity compared to other observed stars.The overall flux of X-rays produced by the sun is alsosmall in comparison to the solar emission at other wave-lengths. The solar X-ray flux at earth is about 1 × 10−8 Wm−2 (in the wavelength range 1–8 × 10−8 cm), so that thesolar X-ray luminosity is roughly 3 × 1026 erg s−1. Thisis only one ten-millionth of the solar visible-band lumi-nosity. The X-ray emission can vary by factors of 10,000on short (minutes–hours) time scales. In the sun X-rayemission is produced in the corona, the outermost layer ofthe solar atmosphere. Figure 4 shows an image of the softX-ray emission from the solar corona taken by the Yohkohsatellite. The temperature of the corona is about 2 milliondegrees and varies spatially by about a factor of 3. Thecorona is heated by the interaction of the stellar magneticfield and the ambient gas. The magnetic field is producedby the so-called dynamo mechanism, in which the ro-tation of the convective outer stellar envelope generatessubsurface electric currents that produce a magnetic field

FIGURE 4 Image of the soft (0.25–4.0 keV) X-ray emission fromthe sun, from the the soft X-ray telescope on board the Japanese–U.S.–U.K. Yohkoh solar satellite observatory. X-ray emission fromthe sun is confined to the corona, the outermost layer of the sun’satmosphere. Thermal X-ray emission is produced by conversionof magnetic energy to heat, causing the outer solar atmosphereto reach temperatures of about 2 million degrees. [Credit: ISASand the Yohkoh SXRT team.]



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whose axis is roughly aligned with the rotational axis. Themagnetic field threads the solar surface and the solar atmo-sphere. Heating of the corona is due to twisting of the fieldlines, which locally intensifies the field; magnetic pressureis converted to kinetic gas energy via disruption and recon-nection of the magnetic field lines. Differential rotation inthe outer solar envelope causes the strength of the mag-netic field to vary with an 11-year cycle; this produces acyclical variation in the numbers of sunspots on the solarsurface, and a cyclical variation in solar X-ray emission.At times of sunspot maximum, the solar X-ray flux can in-crease by a factor of 100, and during solar flares, the solarX-ray emission can increase by a factor of 10,000 for briefperiods. Detailed studies of the solar X-ray flux show thatthe spectrum is dominated by emission lines, indicatingthe predominance of thermal emission processes.

Solar-type stars (stars that have masses below aboutfive times the sun’s mass) are also known X-ray sources,though the nature of the emission in these stars is less wellstudied than in the solar case. Since these stars have con-vective outer envelopes and radiative cores like the sun, theemission mechanism is thought to be dominated by mag-netic heating in the stellar coronae in a manner similar tothe solar corona. Generally the spectrum of the emissionhas not been well studied, though modest resolution X-rayspectra show the presence of line emission, again sug-gesting the predominance of thermal emission processes.There is strong evidence that the X-ray luminosity is re-lated to the stellar rotational velocity, indirect evidence ofthe importance of the stellar dynamo in generating X-raysin these stars. No clear periodicity or cyclical variabilityin the X-ray flux from solar-type stars has yet been iden-tified, so it is unclear whether the type of activity cyclerepresented by the sunspot cycle is a general property ofall solar-type stars. X-ray emission from solar-type starsis known to be variable, and rapid brief increases in theX-ray emission have often been seen; presumably these“flares” are similar to the better studied flaring activityseen in the sun.

Very massive stars (stars more massive than about 10 so-lar masses) have radiative envelopes and convective cores,which means that the stellar dynamo is not very effectivein these stars. Naively, one expects that these stars wouldbe weak X-ray sources, so it was somewhat of a surprisewhen the Einstein observatory conclusively detected X-ray emission from a sample of massive stars. It is thoughtthat the emission from these stars is produced, not viamagnetic heating, but via shock heating of a portion ofthe outwardly moving, unstable stellar atmosphere. Verymassive stars produce a large flux of radiation at ultravi-olet wavelengths and longer; matter at the stellar surfaceabsorbs photon momentum from the UV radiation fieldand is driven outward as a massive stellar wind. The ra-

diative driving mechanism is very unstable to velocity per-turbations, and it is thought that such seed perturbationscan steepen into strong shocks, converting wind kineticenergy to thermal gas energy; the relative velocities aresuch that temperatures should reach millions of degreesand produce observable X-rays. As yet, however, there isno predictive, quantitative physical model to describe theobserved emission. Observationally, there seems to be astrong correlation of X-ray luminosity to the total amountof power radiated over all wavelengths, Lx/Ltotal ∼ 10−7.Since the total luminosities of these stars are generallyhundreds of thousands to millions of times larger than thatof the sun, massive stars generate about the same power inX-rays that the sun generates over all wavelength bands.Typically X-ray emission from massive stars shows littleintrinsic absorption from the dense stellar winds, suggest-ing that at least some of the emitting region exists farfrom the photosphere. Generally the X-ray emission isnot strongly variable, again suggesting that the emissionis distributed over a relatively large spatial region.

2. Compact Objects and Accretion

Compact objects generally represent the remains of thestellar core after the rest of the star’s atmosphere has beenejected in either a supernova explosion or by the formationof a planetary nebula. There are three classes of compactobjects, representing increasingly higher maximum den-sities and gravitational fields. White dwarfs are objectsin which approximately 1 solar mass of material is com-pressed to a volume of radius ∼4000 km, with an averagedensity of 106 g cm−3. Neutron stars compress about 1 so-lar mass of material into a sphere of radius of only ∼10 kmand have an average density of 1014 g cm−3. Black holesrepresent the ultimate crushing of matter by gravity, inwhich a singularity, or a region of infinite density, is pro-duced after matter is compressed to greater than nucleardensities (densities in excess of 1014 g cm−3). Though thesingularity represents the greatest possible density achiev-able in nature, the actual average density of a black holecan be modest. The “size” of a black hole is given by the“Schwarzschild radius”

Rsch = 3(M/M)km (3)

where Rsch is the Schwarzschild radius, and M/M theratio of the mass of the black hole to the mass of thesun. Objects within 1 Schwarzschild radius of the sin-gularity cannot communicate with more distant objectsand may be considered “inside” the black hole. Thus theaverage density of a black hole (i.e., the amount of mat-ter within the volume defined by the Schwarzschild ra-dius) is 1.8 × 1016(M/M)−2 g cm−3. For a 1-solar-massblack hole, the average density inside the Schwarzschild



914 X-Ray Astronomy

radius is 1.8 × 1016 g cm−3; however, for a supermassive,100 million solar mass black hole, the average densityinside the Schwarzschild radius is only1.8 g cm−3.

Isolated neutron stars and white dwarfs are initially for-med with surface temperatures representative of the tem-perature of the core of the progenitor star, T ∼ 107–108 K,and as such should be sources of thermal blackbody X-ray emission, though the spectrum may be modified by theresidual atmosphere of the compact object. Detection ofthis emission is difficult since the compact object coolsquickly to temperatures too low to produce X-rays. Thepointlike object at the center of the Chandra X-ray imageof the supernova remnant Cas A shown in F i g . 5 may repre-sent a young, hot isolated neutron star, though the emissionappears too faint to be produced over the entire surface of a10-km-radius neutron star and may rather represent emis-sion from a small hot region on the neutron star surface.

Neutron stars may emit tightly collimated beams of ra-dio radiation near the magnetic poles. If the rotationalaxis is not coaligned with the magnetic axis, these beamscan be detected as pulses of radiation when the beamis directed towards earth. Such radio “pulsars” are of-ten X-ray pulsars as well. Figure 6 shows a Chandra X-ray image of what is perhaps the most famous of thisclass of objects, the Crab Nebula, the remains of a mas-sive star which exploded in our Galaxy in AD 1054. TheCrab Nebula contains a spinning neutron star (which ro-tates 30 times per second) that powers a bright nebula

FIGURE 5 Chandra X-ray Observatory image of the Cas A su-pernova remnant. The point source at the center of the image isbelieved to be either a neutron star or black hole produced by thesupernova explosion. [Credit: NASA/CXC/SAO.]

FIGURE 6 Chandra X-ray Observatory image of the Crab nebula.The source at the center of this image is the 33-ms Crab pulsar.The “rings” surrounding the pulsar are believed to be producedby nonthermal X-ray emission produced by populations of high-energy particles flung out from the pulsar to distances of morethan a lightyear. X-ray “jets” can be seen perpendicular to the“rings.” [Credit: NASA/CXC/SAO.]

surrounding the pulsar. The rotating neutron star is lo-cated at the center of the bright, disk-like rings of X-ray emission seen in the Chandra image. These X-rayrings are thought to represent nonthermal emission fromhigh-energy particles flung outward over a distance of alightyear from the neutron star. X-ray jets from the neu-tron star may be seen emanating from the pulsar perpen-dicular to the “rings.” A subset of these X-ray pulsars,called anomalous X-ray pulsars (AXPs), has recently beenidentified. AXPs are thought to represent isolated neu-tron stars, with extremely high surface magnetic fields andextremely rapid spin rates of up to 1000 revolutions persecond.

Binary systems consisting of a “normal” star plus acompact companion are common sources of X-rays in thegalaxy, and among the strongest galactic X-ray sources.In such systems the X-ray emission is generally pro-duced by accretion of portions of the outer atmosphereof the “normal” star onto the surface of the companion.High-mass X-ray binaries (HMXBs) consist of a com-pact object plus a high mass (M > 5 M) companion star;since such high-mass stars generally possess strong stellarwinds, X-rays can be produced by accretion of the stellarwind material onto the compact object. Low mass X-raybinaries (LMXBs) are systems in which the companionto the compact object is a low-mass star (M < 1 M).



X-Ray Astronomy 915

In LMXBs, the transfer of material from the low-mass(“donor”) star to the compact object usually occurs in theform of a thick stream from the donor to the compactobject, and because of the angular momentum of the sys-tem, the transferred material does not fall directly ontothe surface of the compact object, but instead forms an“accretion disk” around the compact object. Frictionalheating can raise temperatures in the inner part of the diskto millions of degrees, so that the disks can radiate inX-rays. In addition, as material falls from the disk intothe deep gravitational well of the compact object, kineticenergy is efficiently converted into heat, also producing X-ray emission. Accreted material on the surface of the com-pact object can reach sufficient densities and temperaturesto start thermonuclear fusion of the accreted material, pro-ducing a flash of X-rays called an X-ray nova. Hot mate-rial can also be funneled toward the magnetic poles by themagnetic field to produce synchrotron X-rays. By somenot-well-understood mechanism, material near the mag-netic poles can become accelerated in a confined jet. Thematerial in the jet can produce particle/antiparticle pairsthat may produce very high energy X-rays and gammarays. Such an object may be detectable as an X-ray pul-sar if the beam is suitably aligned toward the earth. X-rayemission can also be produced by inverse comptonizationof lower-energy photons as they interact with the accel-erated charged particles near the magnetic poles. Binarysystems in which one of the stars is a compact objectmay also show transient X-ray variability, i.e., flaring ac-tivity and/or fading of the emission, presumably due tothe thermonuclear detonation of accreted material at thesurface of the object. A now famous example of a sin-gle object which shows both regular (pulsing) variabilityand transient variability in X-rays is the so-called “Burst-ing Pulsar,” GRO J1744-28. This system shows pulsesof X-rays produced by a neutron star spinning with aperiod of 0.5 s in an 11.8-day orbit around a low-masscompanion. Irregular bursts of X-ray emission from thisstar lasting from seconds to minutes have been observedby RXTE.

If the compact object is a black hole, emission shouldbe dominated by the emission from the accretion disk,with no observable high-energy radiation from the blackhole itself. Accretion onto black holes can result in the for-mation of collimated jets of material ejected from some-where near the black hole that can produce observableX-ray emission. Low-mass X-ray binary systems contain-ing black holes tend to show transient X-ray variabil-ity, while high-mass black hole X-ray binaries tend toshow relatively constant X-ray emission. Of the 33 brightX-ray transients currently cataloged, 18 are thought tobe LMXBs containing a black hole. On the other hand,the three best studied black hole systems that show

presistent X-ray emission (LMC X-1, LMC X-3, andCyg X-1) are all thought to have high-mass companionstars.

3. Supernova Remnants

A supernova is an extremely powerful explosion thataccompanies the death of a massive star. During theexplosion the stellar envelope and atmosphere of the starabove the core are blasted outward. This ejected materialmoves at very high velocities (approaching 10% of thespeed of light), and as it collides with the ambient gas anddust in the host galaxy, it deposits enormous amounts ofenergy into the galaxy, producing a roughly spherical shellof shock-heated, million-degree gas. Supernova remnantsare generally strong, spatially resolved sources of thermalX-ray emission as exemplified by the Chandra Cas A im-age shown in Fig. 5. The X-ray emissivity of the remnantis expected to vary in the early stages as the remnant firstexpands into a low-density region carved out by the stellarwind of the precursor star prior to the explosion. Eventu-ally the ejecta encounters denser material in the interstellarmedium, producing a strong shock and substantial X-rayemission. With time the shocked material should cool andthe X-ray emission from the remnant will fade. SN 1987 A,a supernova in the Large Magellanic Cloud (a companiongalaxy to the Milky Way) that exploded in 1987, presentsastronomers with a unique opportunity to study the evolu-tion of the high-energy emission from a supernova explo-sion. The first X-ray observation of SN 1987A, by ROSATduring the all-sky survey in 1990, resulted in a rather largeupper limit, though later that same year BBXRT put amuch tighter constraint on the X-ray flux. Monitoring thesource with ROSAT through the 1990s first detected thesupernova as an X-ray source and measured the rise ofits X-ray flux. An observation of SN 1987A with Chan-dra just 12 years after the supernova has already resolveda small ring of emission expanding outward from theexplosion.

Study of the X-ray morphology of supernova remnantsprovides important clues to the poorly understood mecha-nism by which massive stars explode. Observation of theCas A remnant with Chandra suggests the presence ofan asymmetry in the remnant, possibly indicating that theexplosion of the central star was nonspherical. Spatiallyresolved X-ray observations of supernova remnants allowastronomers to measure how the ejected material inter-acts with the local interstellar medium. An ASCA obser-vation of the supernova remnant SN 1006 indicated twosites of nonthermal X-ray emission in the remnant, thefirst strong evidence that supernovae can accelerate par-ticles to extremely high velocities and produce so-called“cosmic rays.” Imaging proportional counter observations



916 X-Ray Astronomy

with Einstein, ROSAT, and ASCA and solid-state detectorobservations with ASCA, Chandra, and XMM-Newtonallow astronomers to map out temperature and col-umn densities in a number of supernova remnantssuch as the Cygnus Loop, the Puppis A remnant, andN132D, while high spatial resolution observations withthe HRI instruments on Einstein and ROSAT, and theChandra HRC, have allowed astronomers to study thefilamentary structure of the hot shock interface in greatdetail.

Supernova explosions pollute their host galaxies withchemical elements heavier than hydrogen, produced bynuclear processing in the core of the star prior to thesupernova, or created in the collision between the su-pernova ejecta and the interstellar medium. Spatially re-solved X-ray spectroscopy is used to determine elementalabundances in the remnant so as to quantify the produc-tion of these heavy elements and to measure their modesof distribution into the galaxy. The Chandra observa-tions of Cas A, for example, have revealed spatial vari-ations in the abundances of iron, calcium, and silicon inthe remnant, which may indicate the importance of mix-ing in the atmosphere of the star prior to the supernovaexplosion.

B. Extragalactic X-Ray Sources

1. Active Galaxies

Active galaxies are those galaxies in which the emissionis dominated not by the sum total of stars and gas, butby a localized region near the center of the galaxy. Suchgalaxies often show tightly collimated jets of emissionstretching for millions of lightyears from the center of thegalaxy, and are often violently variable on short (days orweeks) time scales. Figure 7 shows an X-ray image ofthe jet from the active galaxy Centaurus A obtained bythe Chandra HRC. Because these galaxies are so bright,they can be used as probes of the very distant universe.Active galaxies are divided into two broad classes, quasars(quasi-stellar radio objects) and Seyfert galaxies. Currentideas (the so-called “unified model”) suggest that all thephenomena associated with the various types of activegalaxies are produced by a supermassive black hole (of afew million solar masses) surrounded by an accretion disk(which feeds the black hole) and an “obscuring torus” thatcan hide the black hole for certain viewing geometries; thevarious types of active galaxies are then simply the effectof viewing this system pole on, edge on, or at some inter-mediate angle. Active galaxies are strong X-ray sources,and the X-ray emission provides a means of probing the“central engine” of the active galaxy, referred to as theactive galactic nucleus (AGN).

FIGURE 7 Chandra X-ray Observatory High Resolution Cameraimage of the radio galaxy Centaurus A (NGC 5128), at a distanceof 10 million lightyears from earth, showing an X-ray jet emanat-ing from the active nucleus of the galaxy. The active nucleus ofthe galaxy is also a source of X-rays and presumably houses asupermassive black hole. [Credit: NASA/CXC/SAO.]

X-ray emission was first detected from the quasar3C273 by early rocket and balloon flights. Three addi-tional AGN were detected by Uhuru, and many more byHEAO-1, Einstein, ROSAT, and other modern X-ray ob-servatories. Active galaxies typically show large X-rayluminosities (Lx ≈ 1043), emitting a substantial fractionof their total energy entirely in the X-ray band. The X-rayemission is variable, and typically X-ray variations oc-cur on the shortest observed time scales, an indicationthat the X-ray emission arises from the smallest observ-able volume near the active nucleus. No AGN is knownto show periodic variability (one putative periodic AGN,NGC 6814, was subsequently shown to be confused inearly, low angular resolution observations with a nearbyX-ray binary). The correlation between X-ray variabilityand variability at other wavelengths is not well knownbecause of the difficulties of scheduling long-term near-simultaneous observations on X-ray and optical, ultravi-olet and/or radio telescopes. The best near-simultaneousmonitoring yet obtained is a study of the Seyfert galaxyNGC 7469 over about 1 month starting in June 1996 withRXTE in the X-ray band and the International Ultravio-let Explorer (IUE) in the ultraviolet. This monitoring ef-fort showed that the X-ray variations were correlated withchanges seen in the UV; the UV maxima seemed to pre-cede the X-ray maxima by about 4 days, though the min-ima in each wavelength region were nearly simultaneous.



X-Ray Astronomy 917

The X-ray emission from AGN shows a fairly complexspectral energy distribution, a combination of nonthermaland thermal continuum emission, along with narrowand broadened lines that are useful probes of universalexpansion and the strong gravity environment in whichthe X-ray emitting accretion disk is embedded. An exam-ple of this is the active galaxy MCG-6-30-15, in whichobservations with the ASCA X-ray observatory of the ironline near 6.7 keV showed the line to be contorted intoa “devil’s horn” shape, which has been interpreted as acombination of the effects of motion of the inner edge ofthe accretion disk and gravitational effects just beyond thecentral black hole.

Absorption of the emitted X-rays also provides a usefulprobe of the environment in the galactic nucleus. Absorp-tion edges due to oxygen at low X-ray energies and ironat higher X-ray energies have been detected for some ac-tive galaxies and seem correlated with the AGN subtype,generally in agreement with the “unified model.” Morerecently X-ray absorption in discrete atomic spectral lineshas been resolved by the Chandra transmission gratingsin the active galaxy NGC 3783. The absorption lines inthis system are systematically shifted toward negative ve-locities of about 400 km s−1, suggestive of absorption inan outflowing medium.

2. Galaxy Clusters

Clusters or gravitationally bound groups of galaxies oftenshow extended X-ray emission in addition to the X-raysources that may be associated with individual clustermembers. Figure 8 shows the extended X-ray emissionassociated with the Perseus cluster of galaxies as seen byChandra. Such extended X-ray emission is produced byoptically thin thermal emission from intracluster gas attemperatures of millions of degrees. The heating mecha-nism is not well known, but presumably explosive motionsof gas from supernovae in member galaxies, or heatingdue to the motion of galaxies through the intraclustermedium, or residual heat from the gravitational collapseof the cluster may all play some role. Recent studies ofgalaxy clusters by ROSAT suggest that about one-halfof all nearby clusters show evidence of extended X-rayemission.

The assumption that the hot intracluster gas is gravi-tionally bound to the galaxy provides the means for de-termining a lower limit to the cluster mass from the X-ray emission by equating the gravitational force per unitarea on the X-ray gas to the thermal gas pressure. Clustermasses derived from X-ray measures are typically muchlarger than the masses estimated from the luminous matterin the cluster, suggesting that most of the matter in galaxyclusters is in the form of nonluminous, dark matter.

FIGURE 8 X-ray emission from the Perseus cluster of galaxies,as seen by the ACIS camera on the Chandra X-ray observatory.The image shows a region of about 640,000 by 640,000 lightyears.The most intense X-ray emission is associated with the largestmember of the cluster, the supergiant galaxy Perseus A. Two darkcavities, each about half the size of the Milky Way, are thought tobe buoyant magnetized bubbles of energetic particles producedby energy released from the vicinity of the black hole at the centerof Perseus A. [Credit: NASA/IoA/A. Fabian et al.]

X-ray images of the extended cluster emission ob-tained by Einstein and ROSAT often show that the spa-tial distribution of the intracluster gas is centrally peaked.Such observations indicate a strong condensation of mat-ter in the center of the extended emission, since the X-rayemissivity is proportional to the square of the gas den-sity. These strong central peaks are usually interpretedin terms of a “cooling flow” in which the cooling of thedense gas at the center via X-ray emission produces aslow “infall” of outer material. As material moves intothe center of the intracluster gas, inhomogeneities in theinfalling matter should cause condensations of cool mat-ter to fall out of the flow. Condensation rates of 10–100 solar masses per year are implied by the X-rayobservations.

Since the intracluster medium will become polluted byheavy elements because of the explosion of massive starsin the member galaxies, the amount of heavy elements inthe cluster gas is a clue to the efficiency of this process,and an indirect clue to the heating mechanism. Recentobservations with ROSAT and ASCA suggest that manyobserved clusters have lower than solar iron abundance,suggesting that chemical pollution by supernovae is not soimportant. However, spatially resolved X-ray spectra ofgalaxy cluster emission by ROSAT show that the central



918 X-Ray Astronomy

emission regions tend to have higher iron abundances thanthe outer regions. This may suggest that mixing of pol-luted intracluster gas with primordial, low metal abun-dance gas is important, at least in the outer regions ofthe cluster.

C. The X-Ray Background

The X-ray band, along with the microwave band, arethe only two regions of the electromagnetic spectrum inwhich the energy density of the emission from unresolvedand/or diffuse sources is comparable to (or greater than)the emission from individual resolved sources. Whereasthe microwave background is generally understood as theremnant thermal radiation produced by the Big Bang,the origins of the X-ray background are still somewhatof a puzzle, despite the fact that the X-ray backgroundwas the first cosmic background component to be dis-covered. The X-ray background seems to consist of twodistinct components: hard emission (E > 3 keV) thatis nearly isotropic, and soft emission that is spatiallystructured.

The isotropy of the hard component of the X-ray back-ground suggests that it originates beyond the Milky Way.This background component is currently thought to bemade up of unresolved X-ray emission from active galac-tic nuclei, an idea suggested by early results, especiallywith the HEAO-1 observatory. Later, observations withthe Einstein observatory began to resolve some of the hardX-ray background into point sources. More recently, deepX-ray images with ROSAT have shown that much if notall of the hard X-ray background can be resolved withsufficient angular resolution and sensitivity into point-source emission. Subsequent identifications of the pointsources show that they are indeed primarily associatedwith active galaxies. The hard X-ray sky apparently showsthe effects of “Olbers’ Paradox”, in which the sky glowssince a source lies along the observer’s line of sight re-gardless of direction, and since the number density ofsources increases with look-back time. Observations ofthe hard X-ray background thus provide useful infor-mation about the mass distribution in the Universe asa function of both space and time. Since mass accre-tion onto massive black holes is thought to power theX-ray emission from AGN, the measure of the hard X-ray background also provides a measure of the integratedmass accretion history onto massive black holes in theUniverse.

Because of its sensitivity to low-energy X-rays, its lowinternal background, and its all-sky coverage, observa-tions with the ROSAT observatory have recently played adominant role in the interpretation of the soft X-ray back-ground. At energies below 3 keV the X-ray background

is highly anisotropic. Because absorption is much moreimportant at soft X-ray energies, the soft component ofthe X-ray background traces not only the source of emis-sion but the absorption of this emission by cold materialin the galaxy. The importance of absorption is impliedby an observed anticorrelation between the brightness ofthe diffuse X-ray background at E ∼ 1/4 keV and the ob-served column density through the galaxy. This was bestdemonstrated by ROSAT images in which clear shadowsof cold neutral hydrogen clouds could be seen in silhou-ette against the bright soft background. This anticorrela-tion of X-ray brightness and column density is not ab-solute, however, suggesting either that in some regionsof the galaxy the hot and cold material may be exten-sively mixed, or that the sun is located in an asymmetric“local hot bubble” filled with X-ray emitting gas. Morerecent observations with ROSAT have shown the exis-tence of soft background emission associated with thegalactic halo and may suggest the existence of an ex-tragalactic component to the observed soft backgroundemission.

VI. FUTURE DIRECTIONS

As of this writing both the Chandra and XMM-Newtonobservatories are just beginning to make scientific ob-servations. Even at these early stages the efficiency ofdiscovery (i.e., the number of new results per observa-tion) is extraordinary. Perhaps even more important thanthe unprecedented imaging these observatories can obtainare the high-resolution X-ray spectra they provide. High-resolution spectra of the type produced by the Chandratransmission gratings and by the XMM-Newton RGS willprove an increasingly important diagnostic of the physi-cal conditions in the X-ray emitting region for all typesof X-ray sources. Even higher resolution X-ray spectrawill be obtained in the near future by X-ray calorimeters.Higher spatial resolution observations may be obtainedby fabrication of larger X-ray mirrors, though withoutimprovement in mirror construction technologies, cre-ation of much larger mirrors than the Chandra or XMM-Newton mirrors may remain prohibitively expensive. TheConstellation-X X-ray observatory, scheduled for launchin the first decade of this new millennium, will push theboundaries further by utilizing a system of small X-raysatellites that will work in unison to provide an increasein sensitivity of about two orders of magnitude over anyprevious (individual) X-ray observatory. X-ray interfer-ometry, in which light from two or more X-ray telescopesis combined to give the effective spatial resolution of anX-ray mirror whose aperture size is equal to the separa-tion of the X-ray telescopes, should provide extremely



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high spatial resolution if the significant technologicalchallenges can be overcome. In theory interferometrictechniques can allow astronomers to resolve almostarbitrarily small structures in X-ray sources (to image, forexample, the accretion disk around a black hole). New re-sults provided by Chandra and XMM-Newton along withthe launch of new observatories guarantee that the up-coming decades will be an incredibly exciting time forX-ray astronomy.


DARK MATTER IN THE UNIVERSE •GALACTIC STRUCTURE

AND EVOLUTION • GAMMA-RAY ASTRONOMY • GRAVI-TATIONAL WAVE ASTRONOMY • INFRARED ASTRONOMY

• NEUTRON STARS O PULSARS • QUASARS • SUPERNOVAE

• ULTRAVIOLET SPACE ASTRONOMY

BIBLIOGRAPHY

Aschenbach, B., Hahn, H.-M., and Trumper, J. (1998). “The Invisi-ble Sky: ROSAT and the Age of X-Ray Astronomy,” Copernicus,New York

Barcons, X., and Fabian, A. C. (1992). “The X-Ray Background,” Cam-bridge University Press, Cambridge, U.K.

Bradt, H. V. D., Ohashi, T., and Pounds, K. (1992). Ann. Rev. Astron.Astrophys. 30, 391.

Charles, Philip A., and Seward, Frederick D. (1995). “Exploring theX-Ray Universe,” Cambridge University Press, New York.

Culhane, J. L., and Sanford, P. W. (1981). “X-Ray Astronomy,” TrinityPress, London.

Mushotzky, R. F., Done, C., and Pounds, K. A. (1993). Ann. Rev. Astron.Astrophys. 31, 717.

Rosner, R., Golub, L., and Vaiana, G. S. (1985). Ann. Rev. Astron.Astrophys. 23, 413.

Tanaka, Y., and Shibazaki, N. (1996). Ann. Rev. Astron. Astrophys. 34,607.

Tucker, W. H., and Giaconni, R. (1985). “The X-ray Universe,” HarvardUniversity Press, Cambridge, MA.

Table of ContentsAstrochemistry 2..........................................................................................................................................

Glossary 2..........................................................................................................................Introduction 2.....................................................................................................................Physical Processes 3.........................................................................................................

Basic Molecular Spectroscopy 3...........................................................................Electronic Transitions 3............................................................................Rotational Transitions 3...........................................................................Vibrational Transitions 3..........................................................................

Radiative Transfer: Observational Astrochemistry 4.............................................Line Radiative Transfer 4.........................................................................Masers 5..................................................................................................

Dust 6.................................................................................................................................Molecular Environments 7.................................................................................................

Circumstellar Envelopes 7....................................................................................The Environment of the Interstellar Medium 7......................................................

Chemical Processes 8.......................................................................................................Surface Chemistry: Formation of Molecular Hydrogen 8......................................Gas-Phase Chemistry 8........................................................................................

Reaction Rates 9.....................................................................................Ionization 9...............................................................................................Cooling Processes 10................................................................................Shock Chemistry 10...................................................................................Specific Molecular Reactions 11................................................................

Hydrogen 11..................................................................................Carbon 11.....................................................................................Nitrogen 12....................................................................................Sulfur 12........................................................................................Water as a special case 12...........................................................Isotopic fractionation 13................................................................Polycyclic aromatic hydrocarbons 14............................................

Cosmological Chemistry 14.................................................................................................Conclusion 15......................................................................................................................See also the following articles 15.........................................................................................References 15......................................................................................................................

Celestial Mechanics 16..................................................................................................................................Glossary 16..........................................................................................................................Historical Introduction 16.....................................................................................................Conic Sections and Orbital Elements 19.............................................................................The Dynamical Problem in Gravitational Physics 19...........................................................

The Two-Body or Central Field Problem 19............................................................Gravitational Potential Theory 20............................................................................Perturbation Theory 21...........................................................................................Lunar Theory 22......................................................................................................General Relativity and Celestial Mechanics 23.......................................................The Three-Body Problem 23...................................................................................The Few-Body Problem 24.....................................................................................N-Body Problems 24...............................................................................................

Applications: A Few Interesting Examples 25......................................................................Satellite Dynamics: Transfer Orbits 25...................................................................Solar System 25......................................................................................................Orbital Resonances 25...........................................................................................Planetary Ring Dynamics 26...................................................................................Binary Stars 27.......................................................................................................Stellar and Galactic Dynamics 27...........................................................................Chaos Theory and Celestial Mechanics 28............................................................

Closing Remarks 29.............................................................................................................See also the Following Articles 29.......................................................................................References 29......................................................................................................................

Cosmic Radiation 30......................................................................................................................................Glossary 30..........................................................................................................................Introduction and History 31..................................................................................................Physical Concepts 32..........................................................................................................Energies, Spectra, and Composition 35..............................................................................Origin of Galactic Cosmic Rays 36......................................................................................The Cosmic Rays Between 3 and 50 EeV, the Expected GZK Cutoff 37............................Particles Beyond the GZK Cutoff 39....................................................................................Outlook 41............................................................................................................................Acknowledgments 42...........................................................................................................See also the Following Articles 42.......................................................................................References 42......................................................................................................................

Cosmology 43................................................................................................................................................Glossary 43..........................................................................................................................Issues from Prescientific Inquiries 45..................................................................................

Philosophical Speculations and Myths 45...............................................................Value of Some Early Questions 45.........................................................................

Origins of Modern Cosmology in Science 46.......................................................................Copernican Solar System 46..................................................................................

Newtonian Dynamics and Gravitation 46................................................................Technology of Observational Astronomy 47...........................................................Viewing the Island Universe 47...............................................................................

Revolutions of the Twentieth Century 48.............................................................................New Theoretical Models 48....................................................................................New Observational Evidence 49.............................................................................

Unsolved Classical Problems 50.........................................................................................Finite or Infinite Space 50.......................................................................................Eternal Expansion or an End to Time 51................................................................Observations and Significance of Large-Scale Structure 51..................................Viability of Nonstandard Models 52........................................................................

Interaction of Quantum Physics and Cosmology 53............................................................Answers from Particle Physics 53...........................................................................Constraints from Cosmology 53..............................................................................Singularities and Quantum Gravity 54....................................................................

Thoughts on Sources of Future Progress 55.......................................................................Emerging Observational Technologies 55..............................................................Concepts and Mathematical Tools 56.....................................................................

See also the Following Articles 56.......................................................................................References 57......................................................................................................................

Gamma-Ray Astronomy 58...........................................................................................................................Glossary 58..........................................................................................................................Introduction and Historical Overview 59..............................................................................

Fundamental Concepts and Terminology 59..........................................................The Production of Cosmic Gamma Rays 61...........................................................

Particle–Nucleon Interactions 61...............................................................Nuclear Gamma-Ray Lines 61...................................................................Relativistic Electron Interactions 62...........................................................Electron–Positron Annihilation 62..............................................................

A Brief History of Gamma-Ray Astronomy 62........................................................The Compton Gamma-Ray Observatory 64...........................................................

Sources of Cosmic Gamma Rays 66...................................................................................The Sun 66.............................................................................................................The Solar System 67..............................................................................................Galactic Sources 68................................................................................................

Isolated Pulsars 69....................................................................................Accreting Pulsars 69..................................................................................Black-Hole Binary Systems 70...................................................................

Gamma-Ray Lines of Galactic and Extragalactic Origin 71....................................Nucleosynthesis in Stars and Supernovae 71...........................................Electron–Positron Annihilation Radiation 72..............................................

Diffuse Galactic Gamma-Ray Emission 74.............................................................Active Galaxies 76..................................................................................................Gamma-Ray Bursts 78...........................................................................................The Extragalactic Diffuse Gamma-Ray Emission 81..............................................Unidentified Gamma-Ray Sources 82....................................................................

The Challenge of Observation and Techniques of Detection 84.........................................The Interaction of Gamma Rays with Matter 84.....................................................

The Photoelectric Effect 84........................................................................The Compton Effect 85..............................................................................Pair Production 85.....................................................................................Attenuation and Absorption of Gamma Radiation 85.................................

Sources of Instrumental Background 86.................................................................Atmospheric Gamma Rays 86...................................................................Intrinsic Radioactivity 86............................................................................Cosmic-Ray and Secondary Charged-Particle Interactions 86..................Neutron-Induced Background 86...............................................................

Background Rejection Techniques 87....................................................................Passive Shielding 87..................................................................................Active Shielding 87....................................................................................Pulse-Shape Discrimination (PSD) 87.....................................................Time-of-Flight (TOF) Discrimination 87....................................................Types of Gamma-Ray Telescopes 88.......................................................

Low-Energy (keV to MeV) 88......................................................Medium-Energy (MeV) 88...........................................................High Energy (MeV to GeV) 89....................................................Very High Energy (GeV to TeV, and above) 90..........................

Future Missions and Prospects 91.......................................................................................Concluding Remarks 93.......................................................................................................Acknowledgment 93.............................................................................................................See also the Following Articles 93.......................................................................................References 93......................................................................................................................

Gravitational Wave Astronomy 94.................................................................................................................Glossary 94..........................................................................................................................Introduction to Gravitational Radiation 94............................................................................Observation Techniques 96.................................................................................................

Resonant Mass Detectors 97..................................................................................Ground-Based Interferometers 98..........................................................................

Space-Based Interferometers 98............................................................................Pulsar Timing 98.....................................................................................................Radar Ranging 99...................................................................................................

Data Analysis Methods 99...................................................................................................Detection of Burst Sources 100................................................................................

Interferometers 100......................................................................................Known waveform 100......................................................................Unknown waveform 100..................................................................

Bars 100.......................................................................................................Detection of Continuous Wave Sources 101............................................................Detection of a Stochastic Background 101...............................................................

Astrophysical Sources 102....................................................................................................Supernovae and Neutron Star Formation 102..........................................................

Axisymmetric Supernovae 102....................................................................Nonaxisymmetric Supernovae 102..............................................................Nascent Neutron Star Boiling and Neutrino Emission 102..........................Unstable Modes of Nascent Neutron Stars 103...........................................

Continuous Waves from Neutron Stars 103.............................................................Isolated Pulsars 103....................................................................................Low-Mass X-Ray Binaries 104.....................................................................

Massive Compact Binaries 105................................................................................Binary Neutron Stars 105.............................................................................Binaries With Black Holes 106.....................................................................Binaries with White Dwarfs and Dwarf Stars 106........................................

Cosmological Sources 107.......................................................................................Microwave Background Radiation Measurements 107................................Pulsar Timing Limits 107..............................................................................Limits Based on Nucleosynthesis 107.........................................................Inflation Models 108.....................................................................................Gravitational Waves from Cosmic Strings 108............................................Bubbles from a Phase Transition 108..........................................................

Outlook 108............................................................................................................................Acknowledgments 109...........................................................................................................See also the Following Articles 109.......................................................................................References 109......................................................................................................................

Gravitational Wave Detectors 110...................................................................................................................Glossary 110..........................................................................................................................Introduction 111.....................................................................................................................

Gravitational Waves in General Relativity 111..........................................................Indirect Evidence for Gravitational Waves 111.........................................................

Gravitational Wave Sources 112...........................................................................................Supernovae 113........................................................................................................Pulsars 113...............................................................................................................Black Holes 113........................................................................................................Coalescing Binaries 113...........................................................................................Stochastic Background 114......................................................................................

Interferometric Detectors 114................................................................................................Basic Principles 114..................................................................................................Noise Sources 116....................................................................................................

Photon Shot Noise and Radiation Pressure Noise 116...............................Seismic Noise 117.......................................................................................Thermal Noise 117.......................................................................................Other Noise Sources 118.............................................................................

Technical Requirements 119....................................................................................Interferometric Detectors in Operation 119...............................................................Long Baseline Interferometers under Construction 120...........................................Very Long Baseline Interferometers in Space 121...................................................

Resonant Detectors 121........................................................................................................Basic Principles 121..................................................................................................Noise Sources 122....................................................................................................

Thermal Noise 122.......................................................................................Electronic Noise 122....................................................................................Seismic Noise 123.......................................................................................Disturbances from Cosmic Rays 123...........................................................

Resonant Detectors in Operation 123.......................................................................Gravitational Wave Astrophysics 123....................................................................................

Gravitational Detectors Network 123........................................................................Coincidence with Nongravitational Detectors 124....................................................

Future Developments 124......................................................................................................Interferometric Detectors 124...................................................................................Resonant Detectors 125...........................................................................................

Conclusions 125....................................................................................................................See also the Following Articles 126.......................................................................................References 126......................................................................................................................

Image Restoration, Maximum Entropy Method 127........................................................................................Glossary 127..........................................................................................................................Image Restoration 128...........................................................................................................

Introduction to Imaging 128......................................................................................

Image Restoration 129..............................................................................................“Classical” Image Restoration Algorithms 130..........................................................

Bayesian Inference 130.........................................................................................................Bayes Theorem 130..................................................................................................The Principle of Maximum Entropy 131....................................................................Maximum Entropy Applied to Images 131................................................................

Maximum Entropy Image Restoration in Practice 132...........................................................Data Constraints 132................................................................................................Entropy Measures 133..............................................................................................Combining Data 134.................................................................................................Maximum Entropy Algorithms 134............................................................................General Properties 134.............................................................................................

Some Applications 136..........................................................................................................Hubble Space Telescope 136...................................................................................Radio Interferometric Image Restoration 137...........................................................

Closing Remarks 140.............................................................................................................See also the Following Articles 140.......................................................................................References 140......................................................................................................................

Infrared Astronomy 141...................................................................................................................................Glossary 141..........................................................................................................................Infrared Bands 142................................................................................................................Infrared Observations 143.....................................................................................................

Predominantly Infrared Objects 143.........................................................................Objects Affected by Interstellar Dust 143.....................................................Objects That Radiate Infrared Light 143......................................................Reradiated Light 144....................................................................................Objects That Are Red Shifted 145...............................................................Cosmic Background Radiation 145..............................................................

Normal Objects Studied in the Infrared 146..............................................................Stellar Atmospheres 146..............................................................................Molecular Hydrogen 146..............................................................................Stellar Radiation in Galaxies 146.................................................................Galaxy Morphology 148...............................................................................

Techniques for Observing Infrared Radiation 148.................................................................Detector Arrays 148..................................................................................................

Near Infrared (1–5 µm) 148.......................................................................Midinfrared (8–30 µm) 148.........................................................................Far Infrared 149...........................................................................................

Bolometers 149.........................................................................................................Submillimeter Astronomy 150...................................................................................

Infrared Astronomical Instruments 150..................................................................................Cameras 151............................................................................................................Spectrometers 151....................................................................................................

Ground-Based Infrared Astronomy 152.................................................................................Limitations Due to the Earth’s Atmosphere 152........................................................New Large Telescopes 152......................................................................................Adaptive Optics 153..................................................................................................South Pole Observatory 154.....................................................................................

Space Infrared Astronomy 154..............................................................................................Limitations of Space-Based Observations 154.........................................................InfraRed Astronomical Satellite 155..........................................................................Cosmic Background Explorer 156............................................................................Infrared Space Observatory 156...............................................................................

ISOPHOT 158..............................................................................................ISOCAM 158................................................................................................Short Wavelength Spectrometer 158...........................................................Long Wavelength Spectrometer 158...........................................................

Near Infrared Camera Multiobject Spectrometer on the Hubble SpaceTelescope 158..........................................................................................................Space InfraRed Telescope Facility 158....................................................................

Multiband Imaging Photometer 158.............................................................InfraRed Array Camera 159.........................................................................InfraRed Spectrograph 159..........................................................................

High-Altitude Infrared Astronomy 159....................................................................................Aircraft 159................................................................................................................

The Kuiper Airborne Observatory 159.........................................................SOFIA 159...................................................................................................

High-Altitude Balloons 159........................................................................................Surveys 160...........................................................................................................................

NASA Catalog of Infrared Observations 160............................................................2Mass 160................................................................................................................Deep Near Infrared Southern Sky Survey 160.........................................................Other Infrared Space and Ground-Based Surveys 160............................................

Future 160..............................................................................................................................Large Ground-Based Telescopes and Adaptive Optics 160.....................................Next-Generation Space Telescope 161....................................................................

Acknowledgments 161...........................................................................................................See also the Following Articles 161.......................................................................................

References 161......................................................................................................................Magnetic Fields in Astrophysics 162...............................................................................................................

Glossary 162..........................................................................................................................Introduction 163.....................................................................................................................Observational Techniques for Measuring Cosmic Magnetic Fields 163................................

Measurement of Magnetic Fields in Stars 163..........................................................Atomic Parameters 163...............................................................................Zeeman Polarimetry 164..............................................................................Differential Zeeman Broadening 164...........................................................

Measurement of Magnetic Fields in the Interstellar Medium 165.............................Direct Measurement of Zeeman Splitting for Radio Lines 165....................Faraday Effect 165.......................................................................................Dust and Interstellar Polarization 165..........................................................Synchrotron Radiation 166..........................................................................

Observational Results 166.....................................................................................................Stellar Magnetic Fields 166.......................................................................................

The Sun and Solar-Type Main Sequence Stars 167...................................Magnetic Chemically Peculiar Main Sequence Stars 168...........................Magnetic Activity in Close Binary Stars 168................................................Pre–Main Sequence Stars 169....................................................................White Dwarf Magnetic Fields 169................................................................Neutron Stars and Pulsars 170....................................................................

Interstellar Magnetic Fields 170................................................................................Galactic Scale Magnetic Fields 171..........................................................................

Some Theoretical Developments on Magnetic Field Generation and Decay 172.................Dynamo Generation of Magnetic Fields 172.............................................................Flux-Freezing 173.....................................................................................................Building Dynamos: Differential Rotation and Turbulence 174..................................The Dynamo Number and Scaling Relations 174.....................................................Planetary Magnetic Fields as Tests for Dynamo Mechanisms 175..........................Galactic-Scale Dynamos 176....................................................................................Ambipolar Diffusion 176............................................................................................Magnetic Reconnection 176.....................................................................................

Final Words 176.....................................................................................................................See also the Following Articles 177.......................................................................................References 177......................................................................................................................

Millimeter Astronomy 178................................................................................................................................Glossary 178..........................................................................................................................Millimeter Astronomical Observatories 178...........................................................................Millimeter Astronomical Observing Techniques 179..............................................................

Single Antenna Techniques 179...............................................................................Position Switching 179.................................................................................Beam Switching 179....................................................................................Frequency Switching 179.............................................................................

Interferometric Techniques 180................................................................................Science at Millimeter Wavelengths 181.................................................................................

Star Formation 181...................................................................................................Molecular Clouds 181..................................................................................Measurements of Physical Conditions 182..................................................

Molecular emission as a tracer of physical conditions 183.............Kinematics 186................................................................................Magnetic fields. 186........................................................................

Dust Emission as a Tracer of Physical Conditions 186...............................Classification of Sources and Evolutionary Scenarios 187..........................Isolated and Clustered Star Formation Properties 187................................

Evolved Stars 188.....................................................................................................Chemistry and the Role of Interstellar Molecules 189..............................................

Ion-Molecule Chemistry 189........................................................................Grain Surface Chemistry 189.......................................................................Shock Chemistry 191...................................................................................

Solar System 191......................................................................................................The Sun 191................................................................................................Comets 191..................................................................................................Planets 192..................................................................................................Asteroids 192...............................................................................................

Extragalactic Astrophysics 193.................................................................................Mass Determination in External Galaxies 193.............................................Morphological Studies 193...........................................................................Galactic Evolution 194.................................................................................Galactic Nuclei 195......................................................................................High Redshift Galaxies 195.........................................................................

Cosmology 195.........................................................................................................See also the Following Articles 195.......................................................................................References 195......................................................................................................................

Neutrino Astronomy 197..................................................................................................................................Glossary 197..........................................................................................................................Detecting Neutrinos 198........................................................................................................

Classification of Neutrinos as Elementary Particles 198...........................................

Detection of Neutrinos 199.......................................................................................Interactions with Nuclei 199......................................................................................Interactions with Electrons 200.................................................................................

Neutrinos from the Sun 200...................................................................................................Theoretical Solar Models 200...................................................................................The Chlorine Solar Neutrino Experiment 202...........................................................The Kamiokande-II Solar Neutrino Detector 204......................................................Later Experiments 206..............................................................................................The Gallium Experiments 206...................................................................................The Electronic Detector Experiments 207................................................................SuperKamiokande 207.............................................................................................Results from Solar Neutrino Experiments 207..........................................................

Atmospheric (or Cosmic Ray) Neutrinos 207.......................................................................Neutrino Oscillations 208.......................................................................................................

Interpretation of Data 208.........................................................................................Sudbury Solar Neutrino Experiment 209..................................................................Long Baseline Terrestrial Experiments 209..............................................................

Conclusions 209....................................................................................................................See also the Following Articles 210.......................................................................................References 210......................................................................................................................

Planetary Radar Astronomy 211......................................................................................................................Glossary 211..........................................................................................................................Introduction 212.....................................................................................................................

Scientific Context 212...............................................................................................History 212................................................................................................................

Techniques and Instrumentation 213.....................................................................................Echo Detectability 213..............................................................................................Radar Systems 213..................................................................................................Echo Time Delay and Doppler Frequency 218.........................................................Radar Waveforms 219..............................................................................................

Radar Measurements and Target Properties 220..................................................................Albedo and Polarization Ratio 220............................................................................Dynamical Properties from Delay/Doppler Measurements 221................................Dispersion of Echo Power in Delay and Doppler 222...............................................Topography on the Moon and Inner Planets 224......................................................Angular Scattering Law 224......................................................................................Radar Mapping of Spherical Targets 226.................................................................Radar Evidence for Ice Deposits at Mercury’s Poles 229.........................................Venus Revealed by Magellan 229............................................................................The Radar Heterogeneity of Mars 231......................................................................Asteroids 232............................................................................................................Jupiter’s Icy Galilean Satellites 237..........................................................................Comets 240...............................................................................................................Saturn’s Rings and Titan 242....................................................................................

Prospects for Planetary Radar 243........................................................................................See also the Following Articles 243.......................................................................................References 243......................................................................................................................

Radio Astronomy, Planetary 245.....................................................................................................................Glossary 245..........................................................................................................................Introduction 246.....................................................................................................................

Brief History 246.......................................................................................................Measurement Objectives 247...................................................................................Physical Properties of the Planets 247.....................................................................

Basic Concepts 247...............................................................................................................Thermal (Blackbody) Radiation 247........................................................................Thermal Emission from Atmospheres and Surfaces 250..........................................

Effective Temperatures of the Planets 250..................................................Radiative Transfer in Planetary Atmospheres 251......................................Radiative Transfer in Planetary Subsurfaces 253........................................

Nonthermal Radio Emission 254..............................................................................Instrumentation for Planetary Radio Astronomy 255.............................................................

Radio Receivers 259.................................................................................................Spacecraft 259..........................................................................................................

Results—planets and Comets 260........................................................................................Mercury 260..............................................................................................................Venus 261.................................................................................................................Mars 263...................................................................................................................Jupiter 264................................................................................................................Saturn 267................................................................................................................Uranus 268...............................................................................................................Neptune 268.............................................................................................................Comets 269...............................................................................................................

Prospects for the Future 270.................................................................................................Acknowledgment 270.............................................................................................................See also the Following Articles 270.......................................................................................References 270......................................................................................................................

Radio-Astronomy Interferometry 271...............................................................................................................Glossary 271..........................................................................................................................

Theory of Interferometry 271.................................................................................................Design of a Radio-Interferometric Array 273.........................................................................Imagine With Radio-Interferometric Arrays 274.....................................................................Future Prospects 276.............................................................................................................

Sensitivity, Radio Frequency Interference, and Imaging Algorithms 276.................Millimeter Interferometry 278....................................................................................Long-Wavelength Interferometry 281.......................................................................Space-Based Very-Long-Baseline Interferometry 281.............................................

Acknowledgments 282...........................................................................................................See also the Following Articles 282.......................................................................................References 282......................................................................................................................

Telescopes, Optical 283..................................................................................................................................Glossary 283..........................................................................................................................Telescope Size Considerations and Light-Gathering Power 284..........................................

Telescope Size and its Effect on Images 285...........................................................Telescope Characteristics Related to Size 285........................................................The New Giant Telescopes 287................................................................................

Extending the Techniques for Making Lightweight Monolithic MirrorBlanks 288...................................................................................................Making a Large Mirror from Smaller Segments 288....................................Combining the Light from an Array of Telescopes 288................................

Optical Configurations 289.....................................................................................................Basic Optical Configurations: Single and Multielement 289.....................................Wide Field Considerations 290.................................................................................Instrumental Considerations: Detector Matching and Baffling 292...........................

Telescope Optics 293............................................................................................................Refractive Optics 293................................................................................................Reflective Optics 293................................................................................................Materials for Optics 293............................................................................................

Refractors 293.............................................................................................Reflectors 294..............................................................................................

Spectral Region Optimization: Ground-Based Telescopes 295.............................................UV Region Optimization 295.....................................................................................IR Region Optimizations 295....................................................................................

Mechanical Configurations 295..............................................................................................Mounting Designs 296..............................................................................................

Equatorial Mounts 296.................................................................................Other Mounting Styles 297..........................................................................

Telescope Tubes and Instrument Considerations 297.............................................Considerations of Usage and Location 297...........................................................................

Seeing Conditions 298..............................................................................................Nighttime versus Daytime Usage 298.......................................................................Remote Observing on the Ground 298.....................................................................

Observing in Space: The Hubble Space Telescope 299.......................................................See also the Following Articles 301.......................................................................................References 301......................................................................................................................

Ultraviolet Space Astronomy 302....................................................................................................................Glossary 302..........................................................................................................................Significance of The Research 303.........................................................................................Instrumentation for Ultraviolet Space Astronomy 304............................................................The Sun 308..........................................................................................................................Planetary Atmospheres 311...................................................................................................Comets 316............................................................................................................................The Stars 316........................................................................................................................

Hot Stars 316............................................................................................................Cool Stars 319..........................................................................................................

Interstellar Gas 319................................................................................................................Interstellar Atomic and Molecular Hydrogen 320......................................................Other Constituents of the Interstellar Gas 322..........................................................Emission Nebulae 322..............................................................................................

Interstellar Dust 324...............................................................................................................Extragalactic Objects 325......................................................................................................See also the Following Articles 327.......................................................................................References 327......................................................................................................................

X-Ray Astronomy 329......................................................................................................................................Glossary 329..........................................................................................................................Overview 330.........................................................................................................................Production and Absorption of X-Rays 330.............................................................................X-Ray Astronomy Techniques 331........................................................................................

X-Ray Imaging Systems 331....................................................................................X-Ray Detectors 332.................................................................................................X-Ray Spectrometers 333.........................................................................................

A Brief History of X-Ray Astronomy 333................................................................................The Discovery of Cosmic X-Ray Sources 333..........................................................The First Surveys 334...............................................................................................Imaging the X-Ray Sky 335......................................................................................Expanding the Bounds of the X-Ray Universe 336...................................................

ROSAT: Large-Scale Spectral Imaging 336................................................

RXTE: Fast Variability Studies 337..............................................................BeppoSAX: Solving the Gamma Ray Burst Riddle 337...............................Chandra: The Finest X-Ray Camera 337....................................................XMM-Newton: Probing Extremely Faint Sources 338..................................

Properties of Cosmic X-Ray Sources 338.............................................................................Sources of X-Ray Emission in Normal Galaxies 338................................................

Normal Stars 338.........................................................................................Compact Objects and Accretion 339...........................................................Supernova Remnants 341...........................................................................

Extragalactic X-Ray Sources 342.............................................................................Active Galaxies 342.....................................................................................Galaxy Clusters 343.....................................................................................

The X-Ray Background 344......................................................................................Future Directions 344.............................................................................................................See also the Following Articles 345.......................................................................................Refrences 345........................................................................................................................

Documents

Encyclopedia of Physical Science and Technology (3Rd Ed 2001 Academic Press) - Astronomy