Astrophysics Introductory Coursestaff.on.br/etelles/lectures/bender/chapter5.pdfmolecules can not be detected easily in the radio and, so, these clouds were ﬁrst surveyed based on

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I?M?P?R?S on ASTROPHYSICS at LMU Munich

Astrophysics Introductory Course

Lecture given by

Ralf Bender

in collaboration with:

Chris Botzler, Andre Crusius-Watzel,Niv Drory, Georg Feulner, Armin Gabasch,

Ulrich Hopp, Claudia Maraston,Michael Matthias, Jan Snigula, Daniel Thomas

Fall 2002

Astrophysics Introductory Course Fall 2002

Chapter 5

Interstellar mediumand star formation


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5.1 Interstellar gas and dust

Four Views of the Milky Way : from top to bottom: near infrared, optical, 21 cm, 2.6 mm

Near infrared wavelengths: distribution of stars.

Optical wavelengths: interstellar dust is ’visible’ because it absorbes the star light.

Radio (21 cm): the thin layer of interstellar neutral hydrogen gas (HI gas). The 21cmline corresponds to the forbidden hyperfine structure transition of the H-atom groundstate (parallel to anti-parallel spin of p and e−).

mm-waves (2.6 mm): the very thin layer of cold gas clouds, detected via a CO linetransition. These gas clouds are associated with star-forming regions.


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constituents of ISM where temperature how observedin Milky Way density ...atomic hydrogen in disk, some in halo 50...300K 21cm radio lineHI ≈ 90% of mass, 50% of vol. 1...100cm−3 UV absorption linesmolecular hydrogen dark clouds in disk 3...100K UV absorption linesH2 ≈ 10% of mass, 1% of vol. 102...106cm−3 IR emission linesother molecules dark clouds in disk 3...100K radio andCO, HCN, H2O ... 102...106cm−3 IR emissionionized hydrogen near hot stars, 5000...10000K optical and IR emissionHII emission nebulae 102...104cm−3 lines, radio continuumhot gas everywhere 106...107K X-ray emission

0.01cm−3

dust grains mostly in disk 20...100K reddening/absorption≈ 1% of mass size ≈ 2000A of starlight, IR emission

magnetic fields everywhere µGauss polarization of stars,Zeeman effect,synchrotron radiation

cosmic rays everywhere energies up to air showers1020eV

The total mass of the ISM in the Milky Way amounts to ≈ 15% of the mass in stars, whichis a typical value for spiral galaxies in general.


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5.1.1 Equilibrium configurations of interstellar gas

The interstellar gas forms a multi-phase mediumconsisting basically of three components: hot(> 106K), warm ( 104K) and cold ( 102K). The dif-ferent components are in approximate pressureequilibrium and the spatial transition betweenthe phases can be quite sharp. The equilibriumis established by the balance between heating(e.g. by young stars or shock waves from super-novae) and cooling by radiation (cooling func-tion). Moreover, magnetic fields can help stabi-lizing a cloud by adding magnetic pressure andcosmic rays may contribute as well.The left diagram (from Bowers/Deeming) showsthe cooling rate Λ per n2

H from 10−27 to 10−21 ergcm3 s−1). If the heating rate is called Γ, then thecooling time is:

τcool =3/2NkBT

Γ− Λ


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The above figure shows an example of a two-phase medium (from Bowers-Deeming). Fromthe balance of cooling and heating, we can, e.g., get the above relation between pressureand density for the ISM. For a given pressure Pc three equilibrium configurations exist,


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however only two of these with densities ng and nc are stable. The intermediate one isunstable because, if a volume in this state is distorted towards higher density, the pressurewill be lower than ambient and it will collapse to the density nc. If the distortion is to lowerdensity, the pressure is higher than ambient and it will expand until ng is reached.

The existence of a multi-phase medium is only possible if energy flows in and out of thesystem. An isolated system in equilibrium will develop into a one-phase medium. A mainprocess to inject energy into the ISM are supernova explosions (cf. McKee and Ostriker1977). The hot gas from SN-explosions fills a significant fraction of the interstellar space.In the Milky Way disk the evolution of supernova remnants is altered by evaporation ofcool clouds embedded in the hot medium. Radiative losses are enhanced by the resultingincrease in density and by radiation from the conductive interfaces between clouds andhot gas. Mass balance (cloud evaporation rate = dense shell formation rate) and energybalance (supernova shock input = radiation loss) determine the density and temperatureof the hot medium. The observed pressure of interstellar clouds, the galactic soft X-raybackground, the O VI absorption line observations, the ionization and heating of much ofthe interstellar medium, and the motions of the clouds can be explained by this model.

The figure on the next page is from McKee and Ostriker (1977), APJ 218, 148.


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5.1.2 The cool interstellar medium

The existence of the diffuse ISM was first recognized by the observation absorption lines inbinary stars. Most lines moved back and forth due to the motion of the stars around eachother but some lines didn’t move (like CaI and NaI lines). These were due to interveninggas between the binary and the observer. The analysis of the stationary lines shows thatthey are composed of several narrower lines which shows that the gas is clumpy. Satelliteobservations of blue stars show a large variety of interstellar UV absorption lines ofLyα, N, O, Mg, Si, S, Ar, Fe which allow to determine the metal abundance of the ISM.The abundances in the gas turn out to somewhat lower than in the sun. Moreover, someheavy elements (those with low ionization energies or high condensation temperatures, likeCa and Fe) are significantly depleted. They condense onto dust particles.

Physical state and HI emission

Because the density of the ISM is very low, the particles have a large mean free path. Asthe typical cross section of an atom for collisions is of the order:

σc ≈ 10−15cm−3


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we obtain for the mean free path between collisions:

lc ≈ (nHσc)−1 =

1015

nHcm

The typical velocity v of the particles is:3

2mHv2 = kBT

which results in a collision rate τc:

τ−1c =

v

lc=

(2kBT

3mH

)1/2

nHσc = 7 · 10−12nHT 1/2s−1

with nH in atoms per cm3 and T in K. For low density interstellar HI nH ≈ 1cm−3 andT ≈ 100K, we obtain:

τ−1c ≈ 500years

Because of the low temperatures, the energy available for excitation form collisions is ofthe order ∼< 10−2eV, most atoms will be in their ground state (e.g., H and He need 10eVand 21eV, respectively, for excitation). However, transition between hyperfine levels in theground state can still be excited by collisions. The most important of these transitions isthe hydrogen hyperfine transition :

H : p ↑ e− ↑ −→ p ↑ e− ↓ + γ (6 · 10−6eV)


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This transition is highly forbidden with a life time of 11 million years! Still, as the totalnumber of HI atoms in a column of only 1cm2 area and 1parsec depth is already > 1018 andbecause collisions will ensure that upper and lower level are populated close to equally,there are enough of them to make this transition. The tranisiton corresponds to a photonwavelength of 21cm and is observed in the radio. It was predicted by van der Hulst in 1944and observed in 1951.

Analysis of the velocity distribution of the HI emission is the most important way to deter-mine the rotation velocities of spiral and irregular galaxies.

HI clouds

The typical size of an HI cloud is R ≈ 5pc and a typical mass is M ≈ 500M�. If we calculatethe internal energy of the cloud:

U ≈ 3MkBT

2mH≈ 1046ergs

this turns out to be larger than the potential energy:

EG ≈GM 2

R≈ 3 · 1045ergs


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which implies that the HI clouds are not gravitationally bound (Virialtheorem: |U | = |EG/2|).This means that the clouds can only be stable if they are in pressure equilibrium with theirenvironment.

Molecular clouds

The high density molecular clouds were first detected as dark globules which absorb thelight of stars in the Milky Way. The main content of the molecular clouds, namely H2

molecules can not be detected easily in the radio and, so, these clouds were first surveyedbased on radio emission of the CO molecule (rotational tranisiton from J=1 to J=0 corre-sponding to 2.6mm wavelength). The CO also has the advantage that in very dense clouds,the 13CO isotope which is about 40 times less abundant than 12CO, still allows to observeregions which are optically thick in 12CO.

Other molecules detected range from water (H2O) and cyanide (HCN) to more complexmolecules such as ethyl alcohol (CH3CH2OH). In fact, hundreds of such molecules havebeen found in molecular clouds and identified by comparing their radio emission line spec-tra with radio spectra of the same molecules in laboratories on Earth. By analyzing theratios of radio spectral lines from the molecular clouds, we find that the gas there is ex-tremely cold - ranging from about 3-20 K.


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Example of a small dark cloud which absorbs the light of stars in the background.


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Small dark clouds, as the one on the previous page have masses between 102M� and104M� and radii between 1pc and 10pc. Giant molecular clouds on the other hand havesizes between 10pc and 60pc and masses from 105M� to 106.5M�.

The emission line widths of CO in molecular clouds are typically 3km/s and, so, muchlarger than the thermal velocities at t ≈ 30K. Therefore, the line width must be determinedby turbulent velocities. One finds that the velocity dispersion σv correlates with the sizeof the cloud s like:

σv ≈ 0.8km

s

(s

pc

)0.5

As the pressure associated with the turbulent motions of the clouds is larger than the am-bient pressure, it must be balanced by the gravitational attraction of the cloud itself. Giantmolecular clouds seem to be in aproximate virial equilibrium. For a mass M of amolecular cloud and a typical observed density profile like ρ(r) = ρR/r (R = cloud radius),one obtains:

3Mσ2v =

2

3

GM 2

R(magnetic fields being neglected). In numbers this reads:

M ≈ 1000M�σ2

v

(km/s)2R

pc

This implies that the mean column density NH of the clouds is approximately independent


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of their mass:NH = 1.5 · 1022cm−2

and their visual extinction is AV ≈ 8mag (for a standard dust to gas ratio, see below).


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Interstellar dust

Interstellar dust consists of tiny grains of silicates (much like ordinary beach sand or vol-canic ash) and soot (very similar to the black soot in the exhaust of a diesel engine). Theinfrared emission spectra from dust in interstellar space are almost identical to the labora-tory spectra of tiny grains of sand and soot.

This graph shows a comparison of the infraredspectrum emitted by dust in the Orion Nebula(lower panel) and that emitted by the exhaust ofa diesel truck (upper panel). Both spectra showprominent emission features at 6.2 and 7.6 mi-crometers that we can identify with the laboratoryspectra of ”Polycyclic Aromatic Hydrocarbons”,or ”PAHs” – known carcinogens.


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This graph compares the infrared spectrumfrom dust in the atmosphere of a red gi-ant star (upper panel) with the laboratoryspectrum of coronene, one type of ”Poly-cyclic Aromatic Hydrocarbons”. Observa-tions with infrared spectrometers also showthat the dust grains in the dense molecularclouds are often covered with ices, such asH2O and CO2 (dry ice).

Interstellar dust is produced in the outer atmospheres of red giant stars and expelled intointerstellar space by these stars during the later stages of their evolution. We see in thefigure above that the infrared spectrum of the red giant star HD44179 has emission featuresat 6.2 and 7.8 microns, just as does the spectrum of interstellar dust from the Orion Bar.


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Averaged interstellar extinction curve Aλ according to Savage&Mathis (1979).


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The interstellar dust grains are very effective absorbers of optical and ultraviolet radiation(but in radio, X-rays and infrared they aren’t). The optical depth due to dust shows thefollowing wavelength dependence:

τdust ∝ λ−1

This behaviour is explained by Mie scattering at particles which have about the size ofthe wavelength of the scattered light (atoms or molecules are too small because then wewould expect a dependence ∝ λ−4, i.e. Rayleigh scattering). As the scattered light fromdust is partly polarized, the dust particles cannot be simply spherical.

As the dust is approximately distributed like the gas, column densities of HI (NH) andextinction by dust (as measured by the abosprtion in the V-band AV are well correlated. Inthe Milky Way we observe:

NH = 1.9 · 1021 AV cm−2mag−1

Dust in star formation regions is exposed to strong radiation fields from hot massive stars.The dust absorbes part of the incident UV radiation and reemits it at infrared wave-lengths. This process is important for the cooling of star forming regions. We nowcalculate the expected temperature of dust under these conditions. If we assume that thedust particle is spherical, has a radius a and a temperature Td, and is located at a distanceD from a star with temperature T? and radius r?. The energy dEA absorbed by the dust


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particle per time dt is:

dEA = σBT 4?

r2?

D2πa2εAdt

where εA is the absorptivity of the dust particle (i.e. the fraction of the incident light whichis absorbed). The energy emitted by the particle is:

dEE = σBT 4d 4πa2εEdt

where εE is the particle’s emissivity (not all parts of the particle may radiate equally). Ifthe dust particle has reached an equilibrium state where emitted energy equals absorbedenergy we have:

dEA = dEE

from which we obtain:

Td = T?

(εA

4εE

)1/4 (r?

D

)1/2

If we adopt the parameters of massive stars and distances corresponding to the sizes ofstar forming regions and assume that εa = εE we obtain for a typical dust temperaturevalues between a few 10 to a few 100 K.

Note, that the size of the particle does not enter. With the same calculation we can estimatethe temperature of the earth as heated by the sun and obtain 280K.


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5.1.3 The warm interstellar medium: HII regions

The infrared sky in the direction of Orion. The bright emission comes from dust grainsheated by starlight. The blue dots indicate the positions of the bright stars, with Betelgeuseat the upper center. The Orion Nebula is the bright yellow blob at the lower right, it is atypical HII region . It is associated with a nearby molecular cloud. The green box indicatesthe field of view of the next image.


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Radio emission from cold CO gas in thedirection of Orion. Red and blue indicate Doppler shifts.


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The Orion Nebula in optical light, from the Hubble Space Telescope. The bar at the lowerleft is a wall of gas viewed edge-on. This gas glows because it is ionized by the four hot”Trapezium stars” just to the left of center.


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The Orion Nebula in infrared light. The bar at the lower left is less prominent, but we seea bright nebula in the upper right that is not seen in the visible image before. The orangerepresents infrared line emission from hydrogen molecules being blown away by a powerfulembedded star (see below).


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Left: a closer view of the Orion Nebula in optical light from HST. The trapezium stars areclearly visible. The blue outline shows the field of view of the infrared image. Right: Infraredimage by the NICMOS camera on the HST. We see a cluster of newborn stars buried withinthe dust cloud beneath the optical nebula.


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HII regions are dominated by the warm interstellar medium but also have cool and hotcomponents. HII regions are always found near moelcular clouds. Part of the dense gas ofthe molecular has collapsed and formed stars. The most massive stars (O stars) can ionizehydrogen and heavier elements like oxygen, nitrogen, sulfor etc. The typical spectrum ofan HII region shows strong emission lines . The gas is heated up to a temperature oftypically 5000K and starts to shine in various emission lines. These are excited by thefollowing mechanisms:

Recombination (Hydrogen Balmer lines, He II lines in optical).

Flourescence (eg. recombination of HeII can excite OIII from the ground level to 3d 3P2

which via decay can exite NIII etc..)

Collisions with electrons (these can excite meta-stable levels resulting in forbidden linetransitions like [OIII] lines at 4363A, 4959A and 5007A).

The line fluxes and ratios can be used as diagnostic tools to determine densities,temperatures and abundances of the gas in HII regions (see Osterbrook: Astrophysicsof Gaseous Nebulae and Active Galactic Nuclei). E.g., the [SII] lines at 6716Aand 6731Aallow to constrain the electron density, while the [OIII] lines at 4363A, 4959A and 5007Aconstrain both temperature and electron densities.


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Heating and Cooling mechanisms for HII regions


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5.1.4 The hot interstellar medium: Supernova remnants

The expansion of supernova envelopes proceeds with the explosion speed roughly untilthe interstellar material which has been swept up has about the same mass as the SNenvelope. The size of the SN remanant is then about 1pc. Hereafter, the influence ofthe swept up material starts to dominate, the shock front slows down and the temperaturegoes up to ≈ 107K. At these temperatures, cooling is mostly achieved through thermalBremsstrahlung, a rather inefficient process. The supernova continues to expand almostadiabatically.

A typical example of a supernova remnant is the Crab nebula. It is about a 1000 years oldand still expands with about 1100km/s. It shows radiation from radio to X-ray frequencieswith, e.g. a radio luminosity of 5 cot 1033erg/s. About 20% of the optical light comes fromfilaments with an emission line spectrum. Approcimately 80% of the optical light shows afeatureless spectrum, is diffusely distributed and polarized. This emission is synchrotronradiation of high energy particles in a magnetic field, with energies up to 1011eV. As theparticles loose their energy with a typical time scale of 50yrs, they cannot date back to thesupernova explosion itself but must have been accelerated more recently. The likely sourceof these particles is the Crab pulsar, i.e. the magnetosphere of the neutron star producedin the supernova explosion.


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The Crab nebula, a remnant of a supernova which exploded in 1054. The blue light is dueto the diffuse synchrotron radiation, red is due to gaseous filaments with an emission linespectrum.


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Typical synchrotron radio spectra of two supernova remnants.


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5.2 Star formation

5.2.1 Gravitational instability of interstellar gas clouds

We first discuss under which conditions a gas cloud will collapse. We consider an infi-nite uniform gas cloud in hydrostatic equilibrium with initial conditions: ρ = ρ0 = const.,T = T0 = const and ~v0 = 0.The basic equations of hydrodynamics (without magnetic fields!) which govern the dynam-ics of the cloud are:Continuity equation:

∂ρ

∂t+∇ · (ρ~v) = 0

Equation of motion:∂~v

∂t+ (~v · ∇)~v = −∇P

ρ−∇Φ

Poisson Equation:∇2Φ = 4πGρ

Equation of state for an ideal gas:

P =R

µρT = C2

sρ,


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where Φ is the gravitational potential and Cs is the speed of sound.

We assume that we know an equilibrium solution to which we add a small perturbation:

ρ = ρ0 + ρ1

P = P0 + P1

Φ = Φ0 + Φ1

~v = ~v0 + ~v1

We furthermore assume a constant speed of sound (and temperature!, the gas is assumedto be isothermal). Inserting the perturbed solution into the equation and neglecting allsecond order terms, we obtain differential equations for the perturbations. These can becombined to give a wave equation:(

∇2 − 1

C2s

∂2

∂t2+

4πGρ0

C2s

)ρ1 = 0

which is solved by:ρ1 = A exp i(~k · ~r − ωt)

This represents a planar density wave with wave vector ~k and angular velocity ω fulfillingthe dispersion relation

ω2 = k2C2s − 4πGρ0


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This relation shows that ω is real only when k is larger than a critical value kj =(4πGρ0)

1/2/Cs, or when the wavelength is smaller than a critical wavelength

λj =2π

kj=

(π

Gρ0

)1/2

Cs

In that case the density perturbation is oscillating, but the amplitude will not grow. However,if:

λ > λj,

the frequency ω becomes imaginary, so that density perturbations will grow exponentiallywith time. Thus the region of the density perturbation has to be large enough (and massiveenough) to start collapsing. This is known as the Jeans criterion . The collaps time can beestimated via:

τcollapse ≈λj

Cs=

(π

Gρ0

)1/2

We finally define the critical or Jeans mass as:

Mj = volume · density =4

3πλ3

jρ

or, explicitely

Mj =

(πR

Gµ

)3/2

T 3/2ρ−1/2


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Mj = 1.2× 105M�

(T

102K

)3/2 (ρ

10−24g/cm3

)−1/2

µ−3/2

Therefore, for typical properties of the diffuse ISM, Mj is much larger than the massof a star. Giant molecular clouds, on the other hand, are well above their Jeans mass.However, the temperature of the gas in molecular clouds unterestimates the internal energysignificantly. Most of the internal energy is in the relative motions of the cloudlets which is ofthe order of up to 10km/s (see above). Therefore, giant molecular clouds do not seem to bein a collapse phase yet but rather appear as virialized quasi-stationary systems. Magneticfield pressure can further stabilize a cloud. (Side remark: if all molecular clouds in the MilkyWay would collapse in the time scale estimated 1/

√Gρ, the star formation rate in the Milky

Way would have to be 200M�/yr, observed is only ≈ 1M�/yr).

Collisions between clouds, or tidal forces (e.g. from the Galactic spiral density wave) canhowever finally trigger the collapse. Once the cloud is compressed and the density in-creases, the collapse can start. Also instabilities in the cloud itself may finally cause it tocollapse without external influence.


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5.2.2 Fragmentation of collapsing clouds

From the observations, we know that molecular clouds have complex substructure indicat-ing that fragmentation takes place already in the pre-collapse phase. We now discuss theconditions which determine the size of the fragments. For fragmentation to proceed, Mj

should not be constant during collapse but should decrease with increasing density.

For an isothermal collapse we found

Mj ∝ ρ−1/2 (isothermal collapse)

which means Mj indeed decreases with rising density. The situation is opposite for anadiabatic collapse, where T ∝ P 2/5, so from P ∝ ρT for an ideal gas, or T ∝ ρ2/3, we have

Mj ∝ T 3/2ρ−1/2 ∝ ρ1/2 (adiabatic collapse)

In other words, Mj increases with density in an adiabatic collapse.

To ensure that the collapse is isothermal, the gravitational energy released during the col-lapse of the cloud should be radiated away in order to not increase the internal energyof the gas. Therefore the collapse time τcollapse should be much larger than the thermaladjustment timescale τadj:

τcollapse � τadj


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As we have seen, the collapse time for a cloud(let) only depends on its density and is:

τcollapse ≈ (Gρ)−1/2 ≈ 108y

(ρ

10−24g/cm3

)−1/2

On the other hand, the thermal adjustment timescale for interstellar clouds is found to beof the order τadj ≈ 100y, which obviously fulfills the criterion for isothermal collapse. ThusMj ∝ ρ−1/2 which in turn leads to continued fragmentation during collapse.

We now want to estimate the lower mass limit for fragmentation . For this purpose wehave to know when the collapse will change from isothermal to adiabatic.

We first calculate the energy radiated per second during the isothermal collapse. Thetotal gravitational energy released in the collapse is Eg = GM 2/R during the timescaleτ ≈ (Gρ)−1/2, so that the luminosity is given by

Lg ≈Eg

τ=

GM 2

R/(Gρ)1/2 = (3G3/4π)1/2

(M

R

)5/2

This luminosity should be much smaller than that of a black body with the same temper-ature and volume. Because, if the cloud does emit black body radiation, it means thatit is optically thick, has reached an equilibrium configuration and does not loose energy


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efficiently anymore. The luminosity emitted in the black body case would be:

Lc = 4πR2σT 4

When Lc ≥ Lg the collapse becomes adiabatic because the released gravitational energycannot be radiated away. Obvioulsy, the condition Lc = Lg corresponds to a lower masslimit for fragmentation:

Mj = (π9/9)1/4(σG3)−1/2(R/µ)9/4T 1/4 = 10−2M�T 1/4

where again R = (3/4π)1/3(M/ρ)1/3 has been used. Because of the exponent 1/4 of the tem-perature, the temperature dependence of this mass is small. For temperatures of 1000Kwe obtain 0.05M�, for 5K we get 1.3M�.

This shows why during the transition from diffuse HI clouds to molecular clouds fragmenta-tion already takes place. It is this fragmentation which may actually slow down the furthercollapse of the molecular cloud because the fragments can start to move as individualalmost ’collisionless particles’. This permits relative velocities of the cloudlets which arelarger than what corresponds to their internal thermal motions and helps to stabilize themolecular cloud.

Interstingly, the lower mass limit which we obtain for the cloudlets is similar the lowestmasses which are observed for stars.


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5.2.3 The complexity of the collapse

We have already seen that the collapse of aninterstellar cloud is not a simple process. Thefollowing processes tend to counteract or delaygravitational collapse:1. If a cloud collapses, angular momentum androtation can prevent both a cloud or individualfragments from continuing collapse. The frag-ments may not reach densities which are highenough to start nuclear reactions. Fragmenta-tion into a binary star can be the solution to thisproblem, or, the formation of a planetary system.Also, magnetic fields can transport away angularmomentum.


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2. The cooling problem. If a cold cloud gets denser and cooler, the cooling efficiencydecreases (see cooling curve). Molecular line transitions in the radio and dust emission inthe infrared however continue to provide cooling down to about 5K. The dust also helps toshield the molecules from the UV radiation, which otherwise would dissociate rapidly oncethe first massive stars have been formed. Once the density is high enough that gravitationalcollapse of the fragments proceeds more rapidly, the gas heats up again and it becomesagain easier to radiate away the gravitational energy (cooling curve!).

3. Magnetic pressure. With the collapse of the cloud, the magnetic fields get compressedas well and build up magnetic pressure which tends to resist further collapse. The collapscan however progress further along the magnetic field lines. Moreover, the magnetic fieldcan slowly diffuse out of the cloud.

For these reasons, it takes about 107 years for stars to form in a molecular cloud once thecollaps has started.

The formation of massive stars also is the beginning of the end. The UV light from thehot stars will eventually create an ionized HII region within which further star formation isinhibited. Finally, the UV radiation of the massive stars and their explosion as supernovaewill also disperse the ionized gas.


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However, the explo-sion of supernovaeand the radiationfrom massive starscan also trigger starformation in the neigh-bourhood of an HIIregion by compres-sion of neighbouringmolecular gas whichincreases its coolingrate and causes itto collapse. This iscalled propagatingstar formation .E.g., the Eagle nebulajust experiences thisfate.


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The progression of star formation from a gas cloud in spiral galaxies to newborn stars.


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5.2.4 Protostars and pre-main sequence evolution

We now discuss how finally stars are formed. The collapse passes through the followingstages (the numbers refer to a solar-type mass fragment):

At the end of the fragmentation process, the cloudlets are not in equilibrium and are stillin the process of collapse. The collapse proceeds isothermally (as discussed above)with a temperature of about 10K.

Once the cloudlet has reached a central particle density of about 1011cm−3, it becomesoptically think even in the IR. The contraction proceeds in a quasi-stationary way. Theobject is now called a protostar .

Around a density of 1016cm−3 and temperatures of 1000K, the dissociation of H2 in thecore begins. Gravitaional energy can now be transformed into dissociation energy andthe collapse continues with a dynamical time scale again.

Once the density has reached 1022cm−3 and the central temperature has risen to 104K, asecond quasi-stationary contraction phase of the core begins. The core has a radius of10R� but only a mass of 10−3M�. It is surrounded by extended optically thick envelopewith a radius of about 106R�. Gas from the envelope ‘rains’ onto the core with super-sonic speed and forms an accretion shock front which also heats the core. Rotation


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may lead to the formation of an accretion disk. This phase is reached after a few hun-dred thousend years for a star of 1M�. After this stage the star has been assembledcompletely (it has a mass of 1M�) but nuclear burning has not yet started yet.

The star now contracts in a Kelvin-Helmholtz time scale and transforms contractionenergy into radiation. The star is now called a pre-main sequence star . As the outerlayers of the star are not heated anymore by infalling gas and the opacity is high, asteep temperature gradient develops. The star becomes convective and the luminosityis decreasing. The star moves down the Hayashi line. Low mass stars in this stagehave been observed and are called T Tauri stars (after the prototypical star T Tauri).These stars may still be surrounde by rest gas from the formation, probably in a disk.They show strong magnetic activity on the surface and can emit X-rays. They alsocan produce (magnetically driven) jets which presumably helps in getting rid of excessangular momentum.

Finally a temperature of 107K and a density of 1026cm−3 is reached in the core andnuclear burning starts. The star has reached its place on the main sequence.


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5.2.5 HRDs of stellar clusters at different ages


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5.3 Planet formation and extrasolar planets

5.3.1 Formation of planetary systems

Current theory for the origin of the solar system and other planetary systems has itsorigins in early (1755) ideas by the philosopher Immanuel Kant.

The basic idea is that planets will form out of the protoplanetary disk of gas and dustthat surrounds a newborn star. If the disk is dense enough, the dust grains will tend tostick to each other, bonded by ices, and eventually accumulate into planetesimals.

Comets are thought to be similar to planetesimals. The planetesimals keep growing,eventually becoming massive enough to attract and capture gas from the nearby diskand build up gaseous atmospheres. The giant planets capture the little ones, andsometimes fling them out of the planetary systems. This process is illustrated below.


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Formation of a planetary system: The upper picture shows that the disk has becomethin and is beginning to break into rings of gas and dust. The dust rings will condenseinto rocky ”planetesimals” that will eventually merge to become planets, as shown in themiddle inset. Jets of gas flow out from the newborn star in the polar direction.


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A hydrodynamic simulation, which calculates the evolution of a protostellar disk as agiant protoplanet forms.

The model follows the interaction between the planet and the disk. With the newly


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formed protostar in the center of the disk a Jupiter-mass protoplanet forms at aboutJupiter’s distance to the Sun (seen as a small red sphere).

The protoplanet excites density waves in the gas which propagate away from the proto-planet. These waves, which push the gas away from the protoplanet are also responsi-ble for the planet’s orbital migration . The waves are easily visible in the plot as spiralpatterns. (In the figure, both color and ”height” are used to show the disk surface den-sity - high red bumps indicate high surface density, green is the original, unperturbeddensity, and blue is low surface density.)

The gas-protoplanet interaction clears out a gap in the disk. Once this gap forms, thereis no longer any gas left to accrete onto the protoplanet, and it stops growing. In thisparticular model the surface density in the gap is down by more than six orders ofmagnitude from its original value.


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More than 100 billion rocks and planetesimals seem to be swarming in the disk aroundnearby star HD 100546. The early formation phases of our own planetary system prob-ably was very similar. Ever larger rocks are growing by colliding and accreting dust inthe process of planet formation. The bright light and six-pointed diffraction spikes fromthe central star have been removed from the false-color image. Similar planet-buildingsystems, dubbed proplyds, have been found in Orion.


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Strong evidence that planets are common in our galaxy was provided by this 1994image made with HST, a close-up of the Orion Nebulae. It reveals disks of dust and gassurrounding newly formed stars, called ”proplyds” -infant solar systems in the process offormation. Of the five stars in this field which spans about 0.14 light years, four appearto have proplyds - three bright ones and one dark one seen in silhouette against thebright nebula. A survey of 110 stars in the region found 56 with proplyds.


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5.3.2 Extrasolar planet detection methods

Pulsar Timing

The first widely accepted detection of extrasolar planets was made by Wolszczan(1994).

Earth-mass and even smaller planets orbiting a pulsar can be detected by measuringthe periodic variation in the pulse arrival time.

Doppler Spectroscopy

Doppler spectroscopy is used to detect the periodic velocity shift of the stellar spectrumcaused by an orbiting giant planet (radial velocity method).

From ground-based observatories, Doppler shifts greater than 3m/sec due to the reflexmotion of the star can be measured.

Corresponding minimum detectable mass of 33 Me/ sin i for a planet at 1 AU from a onesolar-mass (1 M�) star, where i is the inclination of the orbital pole to the line-of-sight.

This method can be used for main-sequence stars of spectral types mid-F through M.Stars hotter and more massive than mid F rotate faster, pulsate, are generally more


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active and have less spectral structure, thus making it more difficult to measure theirDoppler shift. The minimum detectable planet mass increases with the square root ofthe planet’s orbital radius, as shown in the figure below (the red ascending line).

Detection Limits for Planets Around Solar-Like Stars


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Astrometry

Astrometry is used to look for the periodic wobble that a planet induces in the positionof its parent star.

The minimum detectable planet mass gets smaller in inverse proportion to the planet’sdistance from the star. For a space-based astrometric instrument, such as the plannedSpace Interferometry Mission (SIM), that could measure an angle as small as 2 micro-arcsec, a minimum planet of mass of 6.6Me could be detected in a 1 year orbit arounda 1 M� star that is 10 pc from the Earth (gray descending line for stars out to 10 pc)and a 0.4 MJ planet in a 4 year orbit (dark-blue descending line for stars out to 500pc). The FAME mission (Full-sky Astrometric Explorer) has an angular resolution of 50micro-arcsec and the minimum detectable planet mass for it at 10 pc is shown by thedescending orange line.

From the ground, the Keck telescope is being equipped to measure angles as small as20 micro-arc seconds, leading to a minimum detectable mass in a 1 AU orbit of 66Me

for a solar-mass star at 10pc.

The limitations to this method are the distance to the star and variations in the positionof the photometric center due to star spots. There are only 33 non-binary solar-like (F,G and K) main-sequence stars within 10 pc of the Earth. The furthest planet from itsstar that can be detected is limited by the time needed to observe at least one orbital


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period. This limit is indicated by the dashed light-blue vertical line chosen to be at 10years in the figure. There are no planet detections that have been confirmed using thismethod.

Transit Photometry

Periodic dimming of the star caused by a planet passing in front of the star along theline of sight

Stellar variability on the time scale of a transit limits the detectable size to about half thatof Earth for a 1 AU orbit about a 1 M� star or Mars size planets in Mercury-like orbitswith four years of observing.

Mercury-size planets can even be detected in the habitable-zone of K and M stars.Planets with orbital periods greater than two years are not readily detectable, sincetheir chance of being properly aligned along the line of sight to the star becomes verysmall.

The KEPLER mission (2005 - 2010) is designed to survey the extended solar neighbor-hood to detect and characterize hundreds of terrestrial and larger planets in or near theHabitable Zone (HZ) (Kasting et al 1993).

Hypotheses to be tested: 1. Most dwarf stars have terrestrial planets in or near the HZ;


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2. On average two Earth-size planets exist in the region between 0.5 and 1.5 AU, basedon our solar system and the accretion model of Wetherill (1996).

Method of Transit Photometry


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Superposed lightcurves of star HD 209458 showing transits occurring on 9 and 16September, 1999 (STARE Project, Ground based Schmidt telescope, Charbonneau etal., 2000)Stellar Parameters: M ≈ 1.1M�, R ≈ 1.1R�Planet Parameter: R ≈ 1.3RJup


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Detection Limits for Planets Around Solar-Like Stars


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5.3.3 Extrasolar planets by the Doppler method


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Results from Doppler Spectroscopy

Planets were found around 67 stars, so far.

Mass range: 0.17 ≤ M sin i/MJup ≤ 17

Semimajor Axes: 0.04 - 3.4 AU

Excentricity: 0.0 - 0.93

Period: 3 - 2500 days

Most of these systems have massive planets in orbits comparable to or smaller than theorbit of Mercury. In one sense this result is not surprising; the heavier the planet is andthe closer it is to its star, the easier it is to find. Moreover, the larger the planet’s orbit,the longer it takes to discover.

In another sense the discovery was very surprising, because such planets were notexpected from theoreticel models. According to current thinking the original theory isstill OK: giant planets can’t form very close to the star. Giant planets will form furtherout, like Jupiter, but seem to spiral in toward the central star while there is still enoughmaterial in the protoplanetary disk to cause frictional drag.


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