The Astronomy and Astrophysics Review, Volume 13

Astron. Astrophys. Rev. (2006) 13(1/2): 1DOI 10.1007/s00159-005-0027-6

EDITORIAL

Thierry J.-L. Courvoisier

Editorial

Published online: 22 February 2006C© Springer-Verlag 2006

A new Editorial Board is taking up its function with the present issue of Astron-omy and Astrophysics Review. This is an opportunity to think about the purposeand the aims of the journal. The board held this discussion over the last monthsand in particular at a meeting that took place in Liege in July 2005 during theannual meeting of the European Astronomical Society.

The Astronomy and Astrophysics Review will aim in the future, as in the pastyears, to publish reviews on all topics of astrophysics. The reviews will be invitedfrom leading researchers in their fields. We intend to visit the fields at regularintervals with a frequency that depends on the progress made. Furthermore, theboard expects the articles to provide a balanced, but where appropriate critical,view on the advances in the field under review. In addition to insisting on authori-tative reviews that serve as a reference in a given subject, the Editorial Board willpay particular attention to obtaining articles that can be read by an audience widerthan the specialists of a given field. Articles published in The Astronomy and As-trophysics Review shall also provide an accessible overview of a given field tolecturers, students and researchers working in other areas of astronomy and as-trophysics. This should allow many of us to find in this review journal first ratematerial for lectures and other forms of communication of astronomy as a wholeand to enhance our understanding of progress further from home.

The new Board is composed of T. Encrenaz, M.C.E. Huber, R. Morganti,C. Norman, M.A.C. Perryman, A. Quirrenbach, J. Surdej and the undersigned.It includes researchers with a broad knowledge in a number of different domainsof modern astronomy. This ensures that all areas will be competently covered bythe journal. As L. Woltjer steps down from his function of Editor we would liketo thank him for having established together with M.C.E. Huber (who stays in theboard for another year) a tool, which already gave the community a set of highquality reviews. We look forward to continue and enhance this tool in the comingyears.

Thierry J.-L. Courvoisier (B)ISDC, 16 ch. d’Ecogia, 1290 Versoix, Switzerland and Observatoire de Geneve,51, ch. des Maillettes, 1290 Sauverny, SwitzerlandE-mail: [email protected]

Astron. Astrophys. Rev. (2006) 13(1/2): 3–29DOI 10.1007/s00159-006-0029-z

PAPER

Rainer Wehrse · Wolfgang Kalkofen

Advances in radiative transfer

Received: 4 January 2005 / Published online: 16 March 2006C© Springer-Verlag 2006

Abstract This review describes advances in radiative transfer theory since about1985. We stress fundamental aspects and emphasize modern methods for the nu-merical solution of the transfer equation for spatially multidimensional problems,for both unpolarized and polarized radiation. We restrict the discussion to two-level atoms with noninverted populations for given temperature, density and ve-locity fields.

Keywords Radiative transfer · Methods of solution for transfer equation ·Specific intensity · Polarization · Many lines

1 Introduction

Radiative transfer is the link between microscopic interactions of photons withatoms and molecules and macroscopic stellar parameters such as the radiative flux.It allows us to examine conditions in the universe far from an observer. Radiativetransfer is therefore of great interest to astronomy. It has become important alsoin environmental and plasma physics, in medicine, and even in movie production,i.e., in all endeavors where light is used as a diagnostic or as a modeling tool. Thefoundations of radiative transfer are in quantum optics. However, the two fieldshave developed in distinctly different directions.

Unfortunately this article was originally published with typesetter’s errors: The correct publica-tion date was 25 February 2006, not 3 January 2006. The content was not in the final form. Thepublishers wish to apologize for this mistake. The online version of the original version can befound at http://dx.doi.org/10.1007/s00159-005-0025-8.

R. Wehrse (B)Institut fur Theoretische Astrophysik der Universitat Heidelberg, Albert-Ueberle-Straße 2,69120 Heidelberg, Germany; Interdisziplinares Zentrum fur Wissenschaftliches Rechnen derUniversitat Heidelberg, Im Neuenheimer Feld 368, 69120 Heidelberg, GermanyE-mail: [email protected]

W. KalkofenHarvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USAE-mail: [email protected]

4 R. Wehrse, W. Kalkofen

The radiative transfer equation has been employed in some form for abouta century. But new observational techniques and very high spectral and spatialresolution for both unpolarized and polarized radiation have made it necessaryto consider much more complicated forms. An example is provided by movingthree-dimensional media. Since the modeling of modern observations is a verychallenging problem, new algorithms for the solution of the transfer equation weredeveloped, driven by advanced computer architectures. In addition, recent devel-opments in numerical mathematics, such as statistical methods that have been usedsuccessfully in other fields, have been fruitful in radiative transfer. It is also note-worthy that the increasing collaboration of astrophysicists with mathematicianshas allowed the interpretation of older methods in a more unified way.

This review reports on developments in the formulation and solution of thetransfer equation since the mid 1980s, and in particular since the book by Oxenius(1986) on the kinetic theory of photons and particles, the monograph by Cannon(1985) on spectral line formation, and by Mihalas and Weibel Mihalas (1984) onthe foundations of radiation hydrodynamics, and since the books on the numericalsolution of transfer problems by Kalkofen (1984, 1987) We discuss briefly thebasics of radiative transfer, with particular emphasis on the formulation of thetransfer equation in terms of the components of the Stokes vector and the specificintensity, as well as new interpretations of the transfer equation. In the main partwe address the impact of several mathematical methods, both old and new, on thesolution of the transfer equation. Our main focus is multi-dimensional transfer andpolarized radiation, two fields that have become important because of the progressin observational techniques. We also provide an overview over particular formsof the transfer equation with respect to geometry, motion, scattering mode andpolarization, discuss its formal solution and make suggestions for its numericalsolution. We also discuss coordinate transformations, which prior to 1996 wereapplied only to the transfer equation itself but not to its formal solution.

We limit the discussion to cases where the velocity field, the absorption andscattering coefficients, and the redistribution function are given functions, i.e., wediscuss 2-level atoms but do not consider the coupling of the transfer equation toother equations (e.g. from hydrodynamics). Furthermore, we do not cover casesin which induced emission plays a dominant role (e.g. in the radio range, or forMASERS), or where space-time is curved (as in the vicinity of massive, denseobjects) or where refraction effects are important (e.g. in dense media). We alsodo not address the inverse problem (“spectral analysis”). The treatment of thesetopics, although important, would require a thorough coverage of many additionalalgorithms and physical details and could not be treated within the framework ofthis review.

The paper is addressed mainly to astronomers interested in recent develop-ments in the field of radiative transfer or to those who want to use radiativetransfer in their modeling. Therefore, whenever possible, we use astrophysicalnomenclature (which differs from that used in environmental physics, for exam-ple). However, because of the use of specialized mathematical expressions that arenot common in astrophysics we include sample references to particular papers andtextbooks.

2 Basic equations

2.1 Definition of radiation quantities

Traditionally (cf. Chandrasekhar 1960; Unsold 1958; Aller 1963; Kourganoff1963), the unpolarized radiation field at position x, time t , frequency ν, and

Advances in radiative transfer 5

direction n is characterized by its specific intensity Iν(x, n, ν, t), defined by theenergy dE of a pencil of radiation in the frequency range ν . . . ν + dν that flowsthrough an area dσ , in the time interval dt , and in the solid angle d� about direc-tion n, making an angle θ with the normal to dσ ,

dE = Iν(x, n, ν, t) cos(θ) dσ dt d� dν. (1)

Note that the index indicates that the specific intensity refers to a frequencyinterval dν = 1 around frequency ν and that it has a transformation behaviordifferent from that of the extinction coefficient, for example.

An alternative definition of the specific, monochromatic intensity is as an en-ergy flux density via the photon distribution function φ(x, n, p, t) (Oxenius, 1986)so that

Iν(x, n, ν, t) = h4ν3

c2φ(x, n, p, t), (2)

where h is the Planck constant, c the speed of light, and p = hνn/c the photonmomentum.

The most satisfactory definition is that of quantum field theory (cf. Grau 1978;Mandel and Wolf 1995; Vogel and Welsch 1994), which describes the radiationfield at time t by means of the electric field (as derived from the vector potentialA),

E(x, t) = ∂A∂t

= E+(x, t) + E−(x, t), (3)

with

E+(x, t) = i∑

σ

√hν

2ε

1√V

eσ a(ν, n, σ ) exp(−i(k · x − ωl t)), (4)

E−(x, t) = (E+(x, t))†, (5)

where ε is the dielectric constant, eσ is the unit vector in the two polarizationdirections, V the volume, k = kn the wave vector, and ωl the correspondingfrequency; and the statistical or density operator ρ(x, t) is defined by

ρ(x, t) =∑

i

Pi |ψi >< ψi |, (6)

where Pi is the probability of a randomly selected particle from the ensemble tobe in the state described by the wave function ψi (cf. Weissbluth 1989; Cohen-Tannoudji et al. 1977). The hierarchy of correlation tensors G(n) with elements

G(n)i1...i2n

(x1, t1, . . . , x2n, t2n)

= Tr(ρE−

i1(x1, t1) . . . E−

in(xn, tn)E

+in+1

(xn+1, tn+1) . . . E+i2n

(x2n, t2n)). (7)

then allows the Stokes vector to be expressed,

I =

I

Q

U

V

=

G(1)11 + G(1)

22

G(1)12 + G(1)

21

i(

G(1)12 − G(1)

21

)

G(1)11 − G(1)

22

, (8)


as well as the degree of polarization 0 ≤ p ≤ 1,

p =√(

G(1)11 − G(1)

22)

)2 + 4(G(1)

12

)2

G(1)11 + G(1)

22

. (9)

Instead of listing the complete set of independent variables in the argumentswe follow astrophysical tradition and suppress all variables except those of im-mediate interest. To single out the frequency for the monochromatic intensity, forexample, we will write I (ν) or Iν .

Quantities related to the specific monochromatic intensity Iν are the photondensity Nν and the corresponding photon flux density cNν ,

Nν = 1

hνcIν, and cNν = 1

hνIν. (10)

Of particular interest are angle averages of the specific (i.e. angle-dependent)intensity. The zeroth angle moment is the mean monochromatic intensity,

Jν = 1

4π

∫

(4π)

Iν(n) d�, (11)

or, in a plane-parallel atmosphere with symmetry about the vertical direction,

Jν = 1

2

∫ 1

−1Iν(µ) dµ where µ = cos θ (12)

The first angle moment is the net monochromatic flux,

Fν =∫

4π

Iν(n)n d�, (13)

(a vector) or, in a plane-parallel atmosphere,

Fν = 2π

∫ 1

−1Iν(µ)µ dµ; (14)

because of symmetry it has the structure Fν = (0, 0, Fν(z)); it is usually writtenas a scalar in this case. Related quantities are the first and second moments of theintensity,

Hν = 1

2

∫ 1

−1Iν(µ)µ dµ

(15)

Kν = 1

2

∫ 1

−1Iν(µ)µ2 dµ

Higher moments play a role only in some theoretical discussions.Mathematically, the definitions require the specific intensity to belong to the

class of normalizable functions, i.e. the L1 class of functions (cf. Adams 1975);however, because of the radiative transfer equation it must also be at least oncecontinuously differentiable with respect to the space variables, i.e. a member ofclass C1. In applications, it is usually assumed that it can be differentiated anarbitrary number of times everywhere except at a finite number of space points,i.e. it belongs to class C∞.


2.2 The transfer equation

The equation of radiative transfer for the monochromatic, specific intensity Iν(µ)can be derived in several different ways:– Proceeding phenomenologically:

The monochromatic intensity varies along a ray defined by the path elementds, subject to the processes of absorption, described by the opacity κν , scatter-ing, described by the coefficient σν , and emission, described by the functionην . The absorption and scattering coefficients may be combined into the extinc-tion coefficient, χν = κν + σν . The inverse of the extinction coefficient is themonochromatic mean-free path, λν = 1/χν .

The intensity along the ray and in an element ds(� λ) is reduced byextinction,

(dI/ds)− = −χ I, (16)and increased by emission,

(dI/ds)+ = η. (17)The intensity I (s) at s along the ray and in the direction defined by the path,due to emission in the interval ds′ near s′, is then given by the intensity emittedinto the ray, η(s′)ds′, reduced by absorption along the path from s′ to s, i.e.,

dI (s) = η(s′) ds′ exp

(−

∫ s′

sχ(s′′) ds′′

), (18)

where the integral is taken over the optical path from s to s′,

τ(s, s′) =∫ s′

sχ(s′′)ds′′ (19)

=∫ s′

s

ds′′

λ(s′′), (20)

the second form indicating that the optical distance is measured along the rayin units of the photon mean free path λ;

– from the Boltzmann equation by linearization (cf. Oxenius 1986);in this derivation we consider the photons as particles that can be localized. Interms of the photon distribution function φ (see Eq. (2)) the kinetic equation(or Boltzmann equation) for the photon gas can be written

∂φ

∂t+ c n · ∇φ =

(δφ

δt

)

+−

(δφ

δt

)

−(21)

where the terms on the right-hand side describe the creation and destruction ofphotons with momentum p. Note that there is no force term since photons havezero rest mass. By means of Eq. (2) Eq. (21) can now be written

1

c

∂ I

∂t+ n · ∇ I = 1

c

(δ I

δt

)

+− 1

c

(δ I

δt

)

−(22)

The first term on the rhs., the creation coefficient, is composed of a spontaneousand a stimulated part

1

c

(δ I

δt

)

+= ε

(1 + c2

2hν3I

), (23)


(ε describes the spontaneous creation only) and the second the destruction term,which for weak fields can be written in terms of the destruction coefficient a(λ)

1

c

(δ I

δt

)

−= a(λ)I ; (24)

– from quantum field theory by means of density matrix formalisms (Sapar 1978;Landi degl’Innocenti 1996);

– by means of a stochastic model (von Waldenfels 2004). This approach shedsnew light on the nature of the transfer equation by showing that it can beregarded as the differential equation for the potential of a Markov process.

Since the last two derivations are very complicated the detailed description isbeyond the scope of this review.

Although it is well known that the transfer equation involves a number of sub-tle assumptions (e.g. the use of the one-particle distribution function and thereforethe neglect of photon correlations, cf. Oxenius 1986) the accuracy that can be ob-tained with solutions of the transfer equation and the range of applicability of thisequation are still uncertain (Mandel and Wolf 1995; Rutily 1999).

2.3 Difficulties in the solution

The determination of the specific intensity from the radiative transfer equationmay be difficult on account of the following complications:

– Depending on the situation to be modeled, the transfer equation can take severaldifferent forms (Table 1 lists 12 widely used cases), representing different typesof equations and requiring different algorithms for the solution.

– All intensities incident on static configurations must usually be given as bound-ary values (except for media of infinite optical depth). For moving configura-tions the distribution of the boundary values depends on the velocity field andmay be quite complicated.

– Except for pure absorption cases, radiative transfer problems are not initialvalue but boundary value problems. An inaccurate formulation of the bound-ary may lead to spurious solutions that let computer codes fail.

– The eigenvalue spectrum of radiative transfer problems extends along the realaxis from −∞ to −1 and from +1 to ∞ for monochromatic problems (for anexample in the angle-discretized case see Fig. 1) and usually from −∞ to +∞for line problems with frequency redistribution, i.e., the problems are very stiffand intrinsically unstable. However, properly given boundary values eliminatethe positive eigenvalues and make the problems physically meaningful. Thesame is true for the discretized equations.

– The particular coupling of the time, space and frequency variables in the trans-port operator and of angle and frequency in the scattering term may prevent theuse of standard methods (and standard program libraries) of numerical math-ematics. Further complications arise from variations of the coefficients in thetransfer equation over many orders of magnitude, with strong gradients andrapid fluctuations with frequency.

– Radiative transfer problems may have high dimension (the Stokes vector maydepend on 3 spatial, 2 angle, 1 time and 1 frequency variable) so the numericalcalculations may require very large memory.


Fig. 1 Example for the distribution of the eigenvalues � of the angle-discretized radiative trans-fer equation for a plane-parallel medium with coherent, isotropic scattering. The figure showsthe eight largest eigenvalues as functions of ε, the ratio of the absorption to the scattering coef-ficient or de-excitation parameter ε for a 16 point Gaussian division of the scattering integral

3 Classification of transfer problems

3.1 Transformation of the transport operator and the formal solution

Time dependence, various geometries, and motions can easily be incorporated inthe transfer equation by considering s as a path element in spacetime·frequencyand by applying suitable transformations in the coordinates by means of the chainrule. Correspondingly, one obtains the formal solution from the original equationby the usual coordinate transformation rule for integrals.

The directional derivative on the left-hand side of Eq. (22) can be written interms of an orthonormal coordinate system x = {x, y, z},

n · ∇xI = nx∂I∂x

+ ny∂I∂y

+ nz∂I∂z

. (25)

It is often convenient (see below) to replace the set of coordinates {x, n, λ} by theset {x(x), n(x, n), λ(x, λ)} which need not be Cartesian but may be particularlysuitable for spherical or moving media. The corresponding transformations arenot the most general ones possible but those of highest practical importance. Inparticular, they include Lorentz transformations and transformations to sphericalcoordinates. Assuming that all relations are invertible, the left-hand side of thetransfer equation now reads according to the chain rule of analysis

n ·(

∂ x∂x

∇xI + ∂n∂x

∇nI + ∂λ

∂x∂I∂λ

)(26)

(the index of the nabla operator indicates the variables with respect to which thedifferentiations have to be performed). By expressing n and the Jacobi matrices interms of the new variables, the old coordinates are completely eliminated.

If the ratio of emissivity and extinction (cf. Eqs. (17) and (16), i.e., thesource function, S, is a given function, the time-independent transfer equation for


unpolarized radiation has the well-known solution

I(s1) = exp(−τ(s0, s1))I(s0) +∫ s1

s0

exp(−τ(s, s1))S(s)χ(s) ds, (27)

with

τ(a, b) =∫ b

aχ(s) ds. (28)

We note that the integrals in Eq. (27) are path integrals in the {x, n, λ} space.The general solutions of Eq. (27) reads in explicit and in parametric forms

I(l1) = exp(−τ(l0, l1))I(l0) +∫

Cexp(−τ(l, l1))S(l)χ(l)

√dx2 + dn2 + dλ2

(29)= exp(−τ(t0, t1))I(t0)

+∫ t1

t0exp(−τ(t, t1))S(t)χ(t)

√(dxdt

)2

+(

dndt

)2

+(

dλ

dt

)2

dt (30)

(l indicates points on the integration curve C, and t is the independent variable inthe parameter representation of C), with

τ(l0, l1) =∫

Cχ(x, λ)

√dx2 + dn2 + dλ2 (31)

=∫ l1

l0χ(x(t), λ(t))

√(dxdt

)2

+(

dndt

)2

+(

dλ

dt

)2

dt. (32)

The simple expression (27) results only in a coordinate system in which the lightrays form fixed angles with the coordinate axes and the wavelengths are consid-ered constant along the ray. In the generalized scheme it is now straightforward tochange the coordinate system according to the above transformations and there-fore get e.g. formal solutions for all cases listed in Table 1.

In the new coordinates, Eq. (29) reads

I(l1) = exp(−τ(l0, l1))I(l0)

+∫

Cexp(−τ(l0, l1))S(l)χ(l)

√(dxdx

dx)2

+(

dndn

dn)2

+(

dλ

dλdλ

)2

(33)

with

τ(l0, l1) =∫

Cχ(x, λ)

√(dxdx

dx)2

+(

dndn

dn)2

+(

dλ

dλdλ

)2

. (34)

The parametric representation follows in an obvious way.

3.2 Scattering

We speak of scattering—as distinct from (true) absorption—if the interacting par-ticle returns to its initial state by a radiative decay immediately after (or after


Table 1 The radiative transfer equation for important geometries and velocity fields as derivedfrom the transformations described in Sect. 3.1

# Geometry Motion Transfer equation

1 2 stream no ± dI ±(s,λ)ds = −(κ(s, λ)

+σ(s, λ))I ±(s, λ) + η(s, λ)

2 plane-p. no µdI (z,λ,µ)

dz = −(κ(z, λ)

+σ(z, λ))I (z, λ, µ) + η(z, λ)

3 spher.-s. no µdI (r,λ,µ)

dr + 1−µ2

r∂ I (r,λ,µ)

∂µ= −(κ(r, λ)

+σ(r, λ))I (r, λ, µ) + η(r, λ)

4 3D no n · ∇ I (x, λ, n) = −(κ(x, λ)

+σ(x, λ))I (x, λ, n) + η(x, λ)

5 2 stream very slow ± dI ±(s,ξ)ds + ∂β

∂s∂ I ±(s,ξ)

∂ξ= −(κ(s, ξ)

+σ(s, ξ))I ±(s, ξ) + η(s, ξ), β = v/c

6 plane-p. very slow µ∂ I (z,ξ,µ)

∂z + µ2 ∂β∂z

∂ I (z,ξ,µ)∂ξ

= −(κ(z, ξ)

+σ(z, ξ))I (z, ξ, µ) + η(z, ξ)

7 spher.-s. very slow µdI (r,ξ,µ)

dr + 1−µ2

r∂ I (r,ξ,µ)

∂µ+ µ2 ∂β

∂r∂ I (r,ξ,µ)

∂ξ= −(κ(r, ξ)

+σ(r, ξ))I (r, ξ, µ) + η(r, ξ)

8 3D very slow n · ∇ I (x, ξ, n) + w∂ I (x,ξ,n)

∂ξ= −(κ(x, ξ)

+σ(x, ξ))I (x, ξ, n) + η(x, ξ)

9 2 stream relativ. ∂I±(s,ξ)∂s ± γ 2 dβ

ds∂I±(s,ξ)

∂ξ

= 1γ (β±1)

(−χ(s, ξ)I±(s, ξ) + η(s, ξ)),

γ = √1 − β2

10 plane-p. relativ. ∂I(z,µ,ξ)∂z − (1 − µ2)γ 2 dβ

dz∂I(z,µ,ξ)

∂µ+ γ 2µ

dβdz

∂I(z,µ,ξ)∂ξ

= 1γ (µ+β)

(−χ(z, ξ)I(z, µ, ξ) + η(z, ξ))

11 spher.-s. relativ. µ+β1+βµ

∂I(r,µ,ξ)∂r + (1 − µ2)

(1r − γ 2 µ+β

1+βµdβdr

)∂I(r,µ,ξ)

∂µ

+(

β1+βµ

1−µ2

r + γ 2 µ(µ+β)1+βµ

dβdr

)∂I(r,µ,ξ)

∂ξ= −χ(z,ξ)I(z,µ,ξ)+η(z,ξ)

γ (1+βµ)

12 3D relativ.

(n0+γ (1+ γ

γ+1 n0·β)β)T

γ (1+n0·β)·(

∂∂x + ∂β

∂x∂n0∂β

∂∂n0

+ ∂β∂x

∂λ0∂β

∂∂λ0

)

I (x, n0, λ0) = −χ(x, λ0) (I (x, n0, λ0) − η(x, λ0))

∂n0∂β = γ

((|n0><n0| −E) + γ

γ+1 (|n0><β| − <n0||β> E)

− γ 2

γ+1 (|β><β| − <n0||β>|β><n0|))

∂λ0∂β = γ

(|n0> + γ 2

γ+1 <n0||β>|β>)

λ0

Note. z, r , x give the geometrical variables in the plane-parallel, spherically symmetric and the 3D cases,resp., the ray directions are indicated by µ and n, wavelengths by λ and the logarithm of the wavelength

by ξ,w = n · ∂βββ∂x · n. When a tensor is to be transposed it is indicated by the superscript T . As usual, E is

the unit tensor and γ = 1/√

1−β2. Note that the expressions for slow velocities are correct to first orderin β = v/c except for the 3D case (entry #8) where aberration and advection terms have been neglectedin addition. For the relativistic 3D case we have used the bra-ket nomenclature of quantum mechanics(cf. Cohen-Tannoudji et al., 1977). Note also that some forms have not yet been published elsewhere andtherefore require additional checking.


passing very few intermediate states) the destruction of the photon. In particu-lar, there should be no interaction with the thermal pool. The intricate kinetictheory of scattering for unpolarized light has been discussed by Oxenius andSimonneau (1994). The corresponding, even more complicated processes for po-larized light are still under investigation (for an account of the present situationsee, e.g., Kerkeni and Bommier 2002; Berdyugina et al. 2002).

Most of the physics of the scattering process can be incorporated in the labora-tory frame redistribution function R121(ν

′, n′, ν, n) (for unpolarized light as willbe assumed subsequently; for polarized light it is a matrix) which gives the prob-ability that after an absorption of a photon from direction n′ at frequency ν′ therewill be a re-emission in direction n at frequency ν. It is given as a convolutionof the atomic redistribution function r121(ν

′, n′, ν, n) and the velocity distributionfunction of the non-excited atoms f1(v)

R121(ν′, n′, ν, n) =

∫r121(ν

′, n′, ν, n) f1(v) dv (35)

with

ν = ν − ν0

cn · v

(36)ν′ = ν′ − ν0

cn′ · v.

It is often assumed that the velocity distribution function is isotropic (i.e. itdepends only on the absolute value of the velocity) and that the atomic redistribu-tion function can be factored into terms that depend only on frequency and onlyangle (“phase function”). Although even in this case the laboratory redistributionfunction may still depend on angle, angle-averaged redistribution functions

Rav121(ν

′, ν) = 1

(4π)2

∫

4π

∫

4π

R121(ν′, n′, ν, n) dω′ dω (37)

are often used. The determination of the atomic redistribution function is straight-forward if (1) coherent scattering (r = δ(ν − ν′)) or (2) complete redistribution(r = φ(ν)φ(ν′), φ = line profile) can be assumed. For the general case of partialredistribution there is unfortunately no completely satisfactory theory since a con-sistent treatment has to involve more than two levels, so that the statistics becomesnon-Markovian (for details see Oxenius and Simonneau 1994).

Note that the use of isotropic laboratory frame redistribution functions oftenfacilitates very much the numerical solution of the transfer equation since onlymean intensities have to be stored (cf. Meinkohn, 2002). However, the availabilityof huge memories in present day computers should make it possible in the nearfuture to treat even the general case for 3D media.

3.2.1 Compton scattering

In Compton scattering the factorization into terms describing the frequency redis-tribution and the phase function is not possible. Since in addition the redistributionfunction has singular planes and prohibited areas, the scattering integral cannot beapproximated by the usual summation formulae. For low energies this problemcan be avoided by expanding the specific intensity to low orders and to evalu-ate the corresponding integrals analytically (Chandrasekhar 1960; Peraiah 2002).For high energies, this approximation becomes inaccurate so that no satisfactorygrid method for the solution of the transfer equation is available, and Monte-Carloapproaches have to be used.


3.3 Polarization

3.3.1 Non-depolarizing media

Non-depolarizing media are media in which fully polarized rays stay fully polar-ized. For such media the extinction matrix has the particular structure of Eq. (38).Since the matrix is dominated by the diagonal elements the theorem of Gershgorin(cf. Golub and v. Loan 1996) guarantees that here basically the same algorithmscan be used as in the unpolarized case (e.g. the method of short characteristics).

χI χQ χU χV

χQ χI rV −rU

χU −rV χI rQ

χV rU −rQ χI

(38)

3.3.2 General media

In the general case, which includes magneto-optical effects, the extinction matrixhas the more general structure of Eq. (39), in which the coefficients obey require-ments such as, e.g., that rotation and reflection of the basis leads to valid Stokesvectors (for details see Nagirner 1993).

χ11 χ12 χ13 χ14

χ21 χ22 χ23 χ24

χ31 χ32 χ33 χ34

χ41 χ42 χ43 χ44

(39)

The diagonal terms have the same sign and dominate so that Gershgorin’s theo-rem also applies here. It should be noted that for negligible scattering the radiativetransfer equation can be solved as an initial value problem for a system of cou-pled differential equations. Although to our knowledge the stiffness of the systemin actual cases has not been investigated, this implies e.g. that for plane-parallelgeometries all standard methods (e.g. Runge-Kutta–Fehlberg, Adams–Bashford,Burlisch–Stoer) can be used provided proper error control is assured. If the con-ditions for the continuity of the derivatives are fulfilled the extrapolation methodsare usually by far the most efficient.

4 Simplifications

4.1 2-stream approximation

The 2-stream approximation, in which I (x, n) is replaced by two discrete inten-sities I ±(x) describing the radiation in two opposite directions, is often usefulfor qualitative insight into the behavior of a solution. With this approximation thetransfer equation for coherent scattering becomes a simple ODE system of twoequations that can be solved analytically in a large number of cases (cf. Kryzhevoiet al. 2001). The solutions show particularly well the behavior for ε = 0 even ifthe system is solved by means of difference equations.


4.2 Optically thin layers

Whenever in a static medium | ∫C χ ds| or | ∫C η ds| (in a suitable norm) becomesmall, a photon emitted in the medium has a very small chance of being reab-sorbed. The emitted intensity can then be obtained simply by integrating the emis-sivities along C

I (s) = I (0)

(1 −

∫

Cχ ds

)+

∫

CεBχ ds, (40)

I(s) = I(0)

(1 −

∫

Cη ds

)+

∫

CεBη ds. (41)

4.3 Optically thick layers: diffusion approximation

The radiative flux at a given point x within a medium can be described by the dif-fusion approximation whenever (i) the boundaries are sufficiently far away so thatthey cannot influence the radiation field at x and (ii) the extinction coefficient is sohigh that the spatial variation of the source function can be well approximated bya linear function. For static configurations it is well known (cf. Rosseland 1924)that, apart from a geometry factor, the diffusive flux is twice the product of themean free path of the photons, 1/χ , and the gradient of the Planck function. Con-sequently, the frequency-integrated flux contains the harmonic mean of the extinc-tion coefficient weighted by the temperature derivative of the Planck function.

A generalization to moving media was obtained by Blinnikov (1996), Pintoand Eastman (2000), and Wehrse et al. (2003):

F(s0, ξ ; w) = 2∂ B(ξ, s)

ds·∫ ∞

0exp

(−

∫ ξ

ξ−w�χ(ζ )dζ

w

)d�, (42)

where ξ = ln λ is the logarithm of the wavelength and

w = n · (βββ · n) = n∂βββ

∂xn (43)

is the projected dimensionless velocity gradient with β being the velocity in unitsof the speed of light. An expansion to second order about the static case gives(Wehrse et al. 2003)

F(s0, ξ ;w) = F(s0, ξ) ·[

1 − ∂

∂ξ

1

χ(ξ)· w + 1

2

∂2

∂ξ2

1

χ(ξ)2· w2

](44)

which shows that the velocities influence the diffusive flux via frequency deriva-tives of the mean free path and its square. Since χ(ξ) may vary very rapidly with ξbecause of lines or continuum edges, the derivatives are usually much larger thanthe extinction coefficients themselves. In addition, they may be positive or nega-tive. It is interesting that a necessary condition that profile functions be positiveand normalizable (i.e. are functions of class L1) leads to the vanishing of the first-order term if the total influence of a narrow line on a flat continuum is considered.The second-order term then turns out to be negative.


Integration of Eq. (44) over direction leads to the flux vector (Eq. (13)) whichreads, after reordering the terms (for details see Wehrse et al. 2003),

Fw(s0, ξ) =[

E + 1

5

(∂

∂ξ

1

χ(ξ)

)�1 + 1

70

(∂2

∂ξ2

1

χ(ξ)2

)�2

]F(s0, ξ), (45)

with the matrices

�1 = Tr

(∂β

∂x

)

sE +

(∂β

∂x

)

s(46)

(E is the unit matrix here) and

�2 =(

Tr

(∂β

∂x

)

s

)2

E + 2 Tr

(∂β

∂x

)2

sE + 4Tr

(∂β

∂x

)

s

(∂β

∂x

)

s+ 8

(∂β

∂x

)

s

2

, (47)

which are functions of the symmetric part of the Jacobian matrix (∂β/∂x)s (theantisymmetric part cancels).

Equation (45) indicates that the generalization of the Rosseland mean opacityis a tensor that is made up of products of terms resulting from hydrodynamics andatomic physics, i.e. one has

χRoss. → χRoss.

[E + 1

5η1 �1 + 1

70η2 �2

]−1

(48)

with

η1(s0) =(

2∂ B(T )

∂T

)−1 ∫ ∞

−∞1

χ(ξ)

∂

∂ξ

(1

χ(ξ)

)∂ B(T, ξ)

∂Texp(ξ), dξ, (49)

=(

∂ B(T )

∂T

)−1 ∫ ∞

−∞∂

∂ξ

(1

χ(ξ)

)2∂ B(T, ξ)

∂Texp(ξ) dξ, (50)

η2(s0) =(

2∂ B(T )

∂T

)−1 ∫ ∞

−∞1

χ(ξ)

∂2

∂ξ2

(1

χ(ξ)

)2∂ B(T, ξ)

∂Texp(ξ) dξ. (51)

Unfortunately, tables for η1 and η2 based on accurate continuous extinction co-efficients and realistic line lists are not yet available so that changes in the timedependence of a nova explosion or in the structure of an accretion disk, for exam-ple, cannot yet be properly estimated.

Note that in a case where the above integrals are not extended over the wholefrequency range the newly found indefinite integral function of the normalizedPlanck function B (Baschek et al. 1997) may be useful,

B(x)

B(T )= 15

π4

∫x3

ex − 1dx

= 15

π4

[− x4

4+ x3 ln(1 − ex ) + 3x2 Li2(e

x ) − 6x Li3(ex ) + 6 Li4(e

x )

],

(52)

where x = hc/(kT λ) = hν/(kT ), B(T ) = σSBT 4/π and where Lis(z) is thepolylogarithmic function (cf. Erdelyi et al. 1953).


4.4 Sobolev approximation

The Sobolev approximation (Sobolev 1957) has become very popular since it al-lows a very fast solution of the transfer equation for line radiation in media withsteep velocity gradients as, e.g., in stellar winds. It utilizes the fact that in mediain which the projected velocity gradient w (see Eq. (43)) does not change signalong a ray, the integration over the spatial coordinate in the solution of the trans-fer equation can be replaced by an integration over frequency (or wavelength).The solution then has the structure

I (z, ξ) =∫ ξ

ξ−wzG(η) dη (53)

with

G(η) = 1

wexp

(− 1

w

∫ ξ

η

χ(ξ ′) dξ ′)

χ(η)S

(z − ξ − η

w, η

)(54)

If the velocity gradient is sufficiently large, G(η) has a narrow peak so that theslowly varying part can be taken out of the integral. The remaining integral canthen be calculated analytically in most cases (cf. Wehrse and Kanschat 1999).

5 Overview of solutions up to 1985

5.1 Analytical solutions

In this early period, interest was focused on plane-parallel media with coherent,isotropic scattering since in this case the total dimensionality of the problem wassufficiently small and by introducing the optical depth it could be simplified fur-ther. In most cases, the solutions were expressed in term of X and Y functions(Chandrasekhar 1960), for which various approximations were developed. Theintroduction of “Case eigenfunctions” in the sixties (for an overview see Cannon1985) marked important progress for obtaining “exact solutions”.

It must also be noted that no formal solutions were available for more complexgeometries and for differentially moving media.

5.2 Numerical methods

Due to limitations in CPU power and memory most transfer calculations referredto 1D geometries. However, non-relativistic velocity fields were frequently in-volved. Except for the moment methods (cf. Sect. 8.2), all algorithms employedline methods (see Schiesser 1991), although this had not become immediatelyclear since for the depth integration very simple schemes have usually been em-ployed (cf. Mihalas 1978; Kalkofen and Wehrse 1982).

Due to the stability of the second-order equations (“Feautrier equations”), ob-tained by adding and subtracting the equations for oppositely directed rays, theuse of its discretized system has become very popular. Similarly popular was the“variable Eddington factor” method, a moment algorithm in which the closing re-lation was obtained iteratively from the formal solution with the source functionprovided by the solution of the moment equations. Both methods, unfortunately,lose most of their advantages if velocity fields or anisotropic scattering are in-volved.


In the “core-saturation-method” for spectral lines (Rybicki 1971), the fre-quency integral in the scattering term is split into two parts, one referring to theoptically very thick parts and one to optically thin parts. In the first, the meanintensity is approximated by the source function, which speeds up a classical it-eration for the source function (cf. Sect. 8.5.1). Although this method has beengeneralized to moving media (Bastian et al. 1980), it is particularly powerful onlyin the static case.

The solution of the transfer equation in the framework of the “dis-crete space theory” (Peraiah 1987, 2002) employs a full discretization of the(frequency)×(angle)×(depth) space. The discretization in depth is stable only forsufficiently small steps. For media of high optical thickness the transmission andreflection operators as well as the source term are generated from the correspond-ing quantities for small optical thickness by doubling.

The very general “matrix exponential method” (Schmidt and Wehrse 1987)comes closest to conventional line methods since after the angle space discretiza-tion the resulting system of ordinary differential equations (ODE) is solved bymeans of the matrix exponential function. Its main advantage is the analyticalelimination of exponentially increasing terms so that no stability problems are en-countered. However, in its classical form it is not very fast since all eigenvaluesand vectors are calculated numerically (application of the new analytical resultscould most probably overcome this problem).

6 Advances in analytical solution

6.1 Closed solution for plane-parallel geometry

For plane-parallel media with coherent, isotropic scattering, Efimov et al. (1995)found a closed solution of the transfer equation in terms of the matrix tangenthyperbolic function. Since this function varies between −1 and +1 only, expo-nentially increasing terms are effectively eliminated analytically. However, thecalculation of function values is quite complicated and involved. The use of anadapted system of orthogonal functions seems to be the fastest way, since in mostcases a few terms are sufficient to reach very high accuracy (Efimov et al. 2005;cf. Richling et al. 2001)

6.2 Formal solutions for various geometries and velocity fields

Formal solutions of the transfer equation for different geometries and velocityfields are easily obtained by the methods described in Sect. 3.1.

6.3 Matrix exponential solution for polarized radiation

Dittmann (1997b) obtained a solution of the transfer equation for polarized radi-ation, which may be used whenever the source vector is given and the absorptionmatrix η is depth independent and has the form (38). The solution of the transferequation can then be formulated in terms of the matrix exponential function (cf.Kincaid and Cheney 1990; Golub and v. Loan 1996)

exp(χτ) =∞∑

n=0

(χτ)n

n! =3∑

i=0

ci (τ ) (χ − χI E)i (55)


with

c0 = exp(χI τ)

x2 − y2(x2 cosh(yτ) − y2 cosh(xτ)) (56)

c1 = exp(χI τ)

x2 − y2

(x2

ysinh(yτ) − y2

xsinh(xτ)

)(57)

c2 = exp(χI τ)

x2 − y2 (cosh(xτ) − cosh(yτ)) (58)

c3 = exp(χI τ)

x2 − y2

(1

xsinh(xτ) − 1

ysinh(yτ)

)(59)

x = 1

2

√2(η2 + ρ2) (60)

y = 1

2

√2(η2 − ρ2) (61)

ρ =√

η2 + 4(ηQρw cos(2θ) + ηU ρw sin(2θ) + ηV ρr )2 (62)

η =√(

η2Q + η2

U + η2V − ρ2

r − ρ2w

)2 (63)

(the last equality follows from the theorem of Cayleigh and Hamilton) and reads

I(0) = exp(−ητ)

(I(τ ) −

∫ τ

0exp(ητ ′)S(τ ′)dτ ′

). (64)

7 Stochastic extinction coefficient

In many cases (as in the calculation of colors or in the coupling to hydrodynam-ics) it is not necessary to consider the radiation field at individual frequencies. Itmay be sufficient to calculate mean values of the intensities, 〈I 〉, i.e., intensitiesaveraged over a frequency interval ν . . . ν+�ν. This could be done by calculatingthe outgoing flux at many frequencies and then integrating over the interval. Un-fortunately, since for reasonable accuracy an enormous number of spectral linesmay have to be included, such calculations are very demanding in CPU time andmemory. It is therefore advantageous to use a statistical description of the extinc-tion coefficient and to determine 〈I 〉 directly. For static media this has been doneby means of opacity distribution functions P(χ) (Strom and Kurucz 1966), whichhave been derived from the statistics of the wavelength-dependent extinction coef-ficient, based on a suitable line list. Using analytic solutions of the transfer equa-tion (see Sect. 6). Baschek et al. 2001 have generalized this approach in a naturalway to moving media by replacing the statistics taken over the extinction coef-ficient itself by the statistics taken over the extinction coefficient averaged overa variable frequency interval. Thus the opacity distribution function in a movingmedium of given chemical composition, thermodynamical state and microturbu-lent velocity is now a function of two variables, namely, the frequency ξ (as fora static medium) and the frequency interval � over which the extinction coeffi-cient is averaged. The depth integration for the specific intensity then involves anintegration over �.


With the ergodic hypothesis, 〈I 〉 can be interpreted as the expectation valueof the monochromatic intensity for a stochastic extinction coefficient, and theexponential term arising in the solution of the transfer equation can be consideredas the characteristic function C of the distribution function of the (monochromatic)extinction coefficient, which coincides with the opacity distribution function. Thissuggests that one may use a stochastic model for treating large numbers of lines.The simplest process that allows this approach is the Poisson point process (cf.Feller 1966), in which it is assumed (i) that the probability for the actual number nof lines in a frequency interval is given by a Poisson distribution with a mean linedensity ρ, (ii) that the frequency positions of the individual lines are independentof one another, and (iii) that the strengths and shapes of the lines follow a(prescribed) distribution. For a given source function, the resulting expressions(Wehrse et al. 1998) can be evaluated conveniently, e.g., by MATHEMATICA,that allow the analytical study of the dependence of the emergent intensities onthe input parameters. For the diffusion limit, e.g., it could be shown (Wehrse et al.2002, 2003), that the flux vector need not be parallel to the temperature gradientand that the radiative flux (in the comoving frame) is a decreasing function ofthe absolute value of the velocity gradient, i.e., that in a given configurationthe flux reaches its maximum value for constant velocity. In addition, such anapproach offers the possibility of estimating the influence of many weak lines onthe emergent radiation, even in cases where specific data are not available fromatomic physics. This might shed new light on the question of the number of linesthat must be considered in a stellar atmosphere model in order to achieve a givenaccuracy.

Since by means of Levy’s theorem (see e.g. Feller 1966) the distribution func-tion P(χ) and the corresponding characteristic function C are connected by meansof a Fourier transform (in the static case, by means of a Laplace transform) it ispossible to calculate the opacity distribution function for the Poisson point pro-cess. This seems to open a way to calculate 〈I 〉 also in cases in which scatteringdominates.

8 Modern numerical methods

8.1 Monte-Carlo-methods

Monte-Carlo-methods are widely used in radiative transfer, with the understandingthat the elementary processes are simulated and the specific transfer equation neednot even be known. However, the methods can also be regarded as a particular wayto solve the transfer equation (Zwillinger 1989) in its statistical interpretation (seeSect. 2.2).

This class of methods has advantages in that

– many physical processes (e.g. scattering mechanisms, curved space time) caneasily be treated

– the geometry of the medium hardly presents a problem– a corresponding code is easily set up and debugged– the code runs well on modern parallel computers– the memory requirement is modest even for physically complicated cases– the convergence rate is often quite acceptable

The disadvantages include

– there is no proper error control (there are only ‘most probable errors’)– it is difficult to obtain reliable derivatives of radiative quantities


8.2 Moment methods

Moment methods are often used when the radiative transfer equation is to besolved in connection with the hydrodynamic equations since they employ justthe quantities needed in the conservation laws of momentum and energy. How-ever, for a rigorous treatment there is no easy way to formulate a closure rela-tion; in particular, it is not clear how an error in the closure at a high momentinfluences the accuracy for low moments. For an accurate treatment, a variableEddington factor has to be calculated for each frequency, which may be quitedemanding.

8.3 Grid methods

8.3.1 Angle discretizations

For 1D media, only one angle is needed (rotational symmetry for the φ coor-dinate is assumed) and therefore usually (see e.g. Peraiah 2002) Gaussian in-tegration schemes are employed. For 2D and 3D media, two angle coordinatesare required and corresponding cubature formulae have to be used for the in-tegration over the unit sphere. The straightforward combination of integrationschemes for θ and φ, unfortunately, has the disadvantage that the mesh pointscrowd in the vicinity of the poles although in most cases they are not of commen-surate importance. Regular polyhedra are much more suitable (see for examplesFig. 3).

8.3.2 Space discretizations

A discretization on a tensor-product grid (i.e. a type of grid as shown in Fig. 2, per-haps with heuristically adjusted distances) is by far the easiest to handle; however,since often a small domain of initially unknown position and extension determinesthe radiation field in a large area, a local refinement that is dynamically adjustedis required. The best way to realize such an adaptive refinement is to calculate

Fig. 2 Examples for integration paths in a 2D medium for the long characteristic method (left)and the short characteristic method (right). In both cases the rays are directed towards the upperright and a tensor-product grid is used. The dots indicate given boundary values. Note that theintensity values at the starting points must be determined by interpolation. When long charac-teristics are used many interpolations along the path are required in addition


Fig. 3 Examples of polyhedra used for the integration of the specific intensity over the unitsphere. Left: 80 grid points, right 320 points

Fig. 4 Example of an unstructured grid constructed by means of an a-posteriori error estimator.From Meinkohn (2002)

the local a posteriori error and—if it exceeds a certain value—to reduce the stepsize by a factor of 2; some details of such a procedure are given in Appendix B.Figure 4 shows an adaptive grid that is constructed in such a way that a densescattering sphere is immersed in a scattering gas of low density and is observedfrom the right.


8.3.3 Characteristics methods

When the source function is given, the transfer equation is a linear partial differ-ential equation (exceptions are the static plane parallel case and the static two-stream-approximation) and can therefore be solved by means of characteristicsmethods. In numerical calculations one usually distinguishes between long andshort characteristics, see Fig. 2. Depending on the integration scheme used, re-sults obtained by means of long characteristics may be very accurate; however,they require a large number of interpolations when the values of the extinctioncoefficient and the source function are given on grid points. In particular, for aspatially multidimensional case, the number of interpolations for short character-istics is reduced, but assumptions about the run of the coefficients between gridpoints must be made; they often reduce the accuracy to first order in the spatialstep width h.

Note that the formal solutions described in Sect. 3.1 involve the analyticalsolutions of the characteristic equations.

8.3.4 Discretization schemes for the transfer equation in differential form

The main schemes here are the Finite Difference Approach (see e.g. Stenholmet al. 1991) and the Finite Element Method (cf. Richling et al. 2001; Meinkohn andRichling 2002), where the former can be considered a special case of the latter.

In the Finite Difference Method the derivatives are replaced by appropriatedifference expressions and the quantities on the rhs. of the transfer equation aretaken at grid points in the up-wind direction. In this way the resulting system isunconditionally stable and leads to the correct intensities in the limit of both smalland large optical depths. If the source function is given, the corresponding matrixis—depending on the direction—either of upper-diagonal or lower-diagonal typeand can therefore be solved by recursion. The paths through static media are usu-ally very easy to choose; in moving media, depending on the sign of the projectedvelocity gradient w, special care has to be taken for the progression, in particularwith respect to the boundary conditions. For an example see Fig. 5.

If the source function is not given it may be iterated by a successive overre-laxation (“SOR”, cf. Kincaid and Cheney 1990) or a Jacobi method (“Lambda

Fig. 5 Examples for first order upwind discretization schemes for a 2D static medium (left)and a 1D moving medium in which the velocity gradient changes sign (right), for details seetext. Large dots indicate given boundary values; small dots, intensities to be calculated. Raydirections φ > 0, θ < π/2 are assumed. The elimination process starts in both cases at thelower left corner. In the static medium it can proceed in the same way throughout the medium,in the moving medium the change in the velocity gradient induces a change in the direction.Note that in this scheme no interpolations are required


iteration”), which—unfortunately—have the well-known convergence problemsfor media with high optical depths and scattering fractions, since the absolute val-ues of some eigenvalues may be very close to unity, cf. Fig. 1. As an alternative,the total block system for all angles and frequencies can be solved globally bya variant of the cg-method (see Golub and van Loan 1996). Here, the iterationconverges usually very well. Note that recursions do not run well on computerswith long pipes so that one may have to use more sophisticated algorithms for thesolution of the upper/lower-diagonal matrices.

The Finite Element Method (for a short introduction to its use in this contextsee Appendix A) is much more flexible since it allows to give a-posteriori errorestimates (see next section) that can be employed to generate locally refined, un-structured grids. In this way it can essentially be guaranteed that the numericalsolution does not differ by more than a prescribed value from the analytical so-lution (which is in fact usually unknown) and that a minimum number of cellsis employed. In addition, angle parallelization can be used (as is the case for theFinite Difference Method) so that high precision results can be obtained with rea-sonable costs in CPU time and memory (Richling et al. 2001). The disadvantageof this method is its high complexity; however, a relatively easy-to-use programpackage for the modeling of resonance lines in slowly moving 3D media that usesthis algorithm in a very sophisticated way will soon be made available to the gen-eral public by the Heidelberg group.

8.3.5 A-priori and a-posteriori errors

In most cases the errors ε(h) in the solution of the transfer equation are estimatedby means of the a-priori estimate εprio(h) = ||Ih − I2h || where h is the step sizein geometrical, angle, frequency space or the inverse of the number of grid points,and the double bars indicate some suitable norm. This error has the advantage thatit can be calculated quite easily. However, in most cases the well known conver-gence problems in the �-iteration for optically very thick, scattering-dominatedconfigurations show that εprio(h) is of very limited value.

Instead, the a-posteriori error εpost(h) = ||Ih − I || with I indicating the ana-lytical solution of the transfer equation is relevant. Unfortunately, I is not knownexcept in some special cases that are not of astrophysical importance. However,by using finite elements and solving the dual problem, i.e., the problem in whichthe sign of the transport operator is changed, one can obtain an upper bound forεpost(h) (Kanschat 1996; for the general approach see Ainsworth and Oden 2000).The mathematics on which the estimate is based is beyond the scope of this review.However, it is to be pointed out that the effort of employing this error estimator isgenerally worthwhile in multidimensional cases since it allows to refine the gridadaptively and to save a very large number of grid points without a reduction inaccuracy (Kanschat 1996; Richling et al. 2001).

8.3.6 Discretization schemes for the transfer equation in integral form

The integral form of the transfer equation is—to our knowledge—used only forstatic problems. It is derived from the differential form, Eq. (22), by multiplicationwith the inverse of the sum of the unit operator and of the transport operator.It is often more suitable for purposes of numerical analysis than the differentialform (cf. Hackbusch 1989); for numerical calculations it has been used only forspatially 1D problems. However, this may change when we have learned to exploitthe stochastic interpretation of the transfer equation (von Waldenfels 2004).


8.4 Methods for 1D polarization problems

As long as scattering can be neglected, one has to deal with initial value problems,i.e., with a system of ordinary differential equations that can be solved by standardmethods, see Sect. 3.3.2.

8.5 Methods for multidimensional polarization problems

Since in the absorption matrix the diagonal elements dominate, the theorem ofGershgorin (cf. Golub and v. Loan 1996) guarantees that the specific intensities Istay positive and that basically the same algorithms (as e.g. of the method of shortcharacteristics, see Dittmann 1997a) as in the unpolarized case can be used.

8.5.1 Solution of resulting system of linear equations

Crucial for the solution of the transfer equation, in particular for multidimensionalgeometries, is the proper solution of the linear system that results from the dis-cretization. Since the corresponding matrices are often huge, it is very important toexploit their structure (as e.g. dominance of elements close to the diagonal, blockstructure, etc). Numerical mathematics has developed a large variety of criticallyevaluated methods for solving such sparse systems. For a general introduction,see Kincaid and Cheney 1990, and for a broad overview, Golub and van Loan1996. Sparse systems, as occur in partial differential equations, are specificallydiscussed by Hackbusch 1993. The latter references stress in addition the use ofan appropriate preconditioner.

8.6 Comparison of methods and recommendations for selection

The optimal choice of the method for the solution of a transfer problem dependson the type of problem (continuum only, line(s), polarization), the opticalthickness and geometry of the configuration, the scattering fraction, the requiredaccuracy, and the effort to be invested. For multidimensional problems, with largescattering fraction and optical depth, or steep gradients, finite-element methodson adaptive, unstructured grids with appropriate linear equation solvers may beused. Unfortunately, these methods are mathematically involved and difficultto implement. Therefore, if the configuration is smooth and has lower opticalthickness, finite-difference and short-characteristics methods may be preferredbecause of their ease of use. Monte-Carlo methods may be employed when thegeometry or the physical interactions between particles and radiation field arecomplicated, but the cost of computing may be high since the accuracy increasesonly slowly with the number of iterations.

9 Open problems

In spite of recent progress in the treatment of radiative transfer problems (as re-ported above), there are still some aspects that require the investment of consider-able effort and—probably—new ideas, as e.g.

– for media with complex 3D geometry that have both large optical thicknessand high scattering fractions, a fast and accurate algorithm for the solution of


the transfer equation has not yet been found. However, such an algorithm isurgently needed, e.g., for understanding (proto-)galaxies or clouds in plane-tary atmospheres. It is conceivable that multi-model approaches with problemadapted preconditioners can provide a fruitful first step (for an initial attempt ofthis kind, see Kanschat and Meinkohn 2005);

– for line problems that depend on general redistribution functions in 3D geome-tries, effective grid methods must be developed since currently-used schemesrequire excessive computer memory when realistic density and temperature dis-tributions are employed. In addition, for Compton scattering at high energies,the difficulties of evaluating the scattering integral due to the forbidden domainsof the redistribution function have to be overcome;

– for media with density or temperature fluctuations on scales much smaller thanthose of the total system, no “homogenized” equation is available (as, e.g.,Darcy’s law for the momentum equation in hydrodynamics, for an overviewsee e.g. Antonic et al. 2002), although it is generally believed that typical mediaof astrophysical interest are not smooth;

– for the numerical treatment of the radiative transfer equation in connection withadditional constraints (as e.g. rate equations, energy and momentum conserva-tion), general algorithms are still not available; in particular, grid generationschemes that are suitable for the total set of equations and that also allow aproper mathematical analysis are urgently needed;

– for the solution of inverse problems, which are the ones most frequently posedin astronomy, algorithms must be developed that indicate the uniqueness ofthe parameter determination, show the resulting errors and are also fast (∼3–5times the CPU time for the forward problem); these algorithms must be adaptedto the peculiarities of radiative transfer (such schemes have been developed innumerical mathematics and applied successfully e.g. in chemical and mechani-cal engineering, cf. Bock et al. 2000).

It can be expected that the solution of such problems may change our view ofradiative transfer and make at least parts of this review obsolete.

Acknowledgements We are indebted to B. Baschek for stimulating discussions and criticallyreading the manuscript. R.W. thanks G.V. Efimov, R. Rannacher, and W. v. Waldenfels for theclarification of many mathematical aspects. W.K. thanks the Kiepenheuer Institut fur Sonnen-physik for its hospitality and the University of Freiburg for a Mercator guest professorshipfunded by the Deutsche Forschungsgemeinschaft. This work has been supported by the DeutscheForschungsgemeinschaft (SFB 359/C2).

Appendix A: basics of the finite element method

Finite element methods require a particular form of the differential equation, the so called weakformulation. It is closely related to the principle of virtual work in theoretical physics, which isone of many possible generalized formulations of boundary value problems. Since these tech-niques have no natural extension to thermodynamics, we will first explain the finite elementmethod in the case of the potential equation.

With every statement of the principle of virtual work it is possible to associate a quadraticfunctional, called the potential energy, and a set, such that the exact solution corresponding tothe statement of principle of virtual work is the minimizing function of the potential energy overthe set. Thus, e.g. the electrical potential u may be characterized by minimizing the potentialenergy in the space of admissible solutions V :

u = arg min ≡ E(w) ≡ 1

2

∫|∇w(x)|2 dx −

∫Q(x)w(x) dx, (65)

w∈V


where Q describes an interior charge distribution. The boundary values are assumed to be zerofor simplicity. Further, we introduce the abbreviation (u, v) = ∫

u(x)v(x) dx . By perturbation,we see that u is a minimizer of (65), if and only if

E(u) ≤ E(u + εv),

for all functions v in the admissible space. Derivation with respect to ε at ε = 0 yields

δE(u) = 0,

which is equivalent to the variational problem

(∇u, ∇v) = (Q, v). (66)

This equation must be satisfied for all test functions v ∈ V . In the case of the virtual workformulation, the test functions are called virtual displacements. Note, that (66) allows for moregeneral solutions than the strong form −�u = f . This form requires second derivatives on u,while the weak form only needs first derivatives.

For the weak formulation (66) of the potential equation there exists a natural function spaceV : it is the space H1

0 , the space of functions with weak derivatives in L2 and zero boundaryconditions. The equation has a solution u in this space and the test functions v are from thisspace, too. Generally, solution space and test space may be different, especially, if the operatoris not symmetric.

In general the dimension of V is infinite and thus in general the problem (66) cannot besolved exactly. The finite element method (FEM) now solves the same weak equation, but thespace V is replaced by a finite dimensional subspace Vh ⊂ V . Therefore, the discrete solutionuh solves

(∇uh, ∇vh) = (Q, vh) ∀ vh ∈ Vh . (67)The aim of the simulation is an approximation uh sufficiently close to the true solution u of

the continuous problem (66).Since test functions vh from the discrete space may be used in the continuous Eq. (66), we

have the fundamental Galerkin-orthogonality relation

(∇u − ∇uh, ∇vh) = 0 ∀vh ∈ Vh, (68)

i.e. the error u − uh is orthogonal to Vh with respect to (·, ·). We may also express this factas follows: The finite element solution uh is the projection with respect to (·, ·) of the exactsolution on Vh , i.e., uh is the element in Vh closest to u with respect to the H1

0 -norm ‖ · ‖H10

. For

abbreviation we write ‖ · ‖ instead of ‖ · ‖H10

. Standard convergence analysis of the FEM usually

leads to the estimate ‖u − uh‖ ≤ C infw∈Vh

‖u − w‖.Consequently, the speed of convergence of the method is determined by the approximation qual-ity of the space Vh . On meshes of size h, this is usually h p+1‖u‖ if p is the degree of polynomialsused for cell-wise approximation.

It is our opinion that numerical methods used to study the quantitative behaviour of a prob-lem should provide estimates of the numerical error. This is the only chance to separate modelerrors from inaccurateness of computation. The exploitation of Galerkin-orthogonality is thecrucial step towards efficient error control. For an overview of these techniques see Beckerand Rannacher (1997) and for applications in fluid dynamics and structural mechanics see e.g.Becker and Rannacher (1995), Suttmeier (1996).

A refined approach to residual-based error control in finite element discretizations is pre-sented. The conventional strategies for adaptive grid refinement in FEM are mostly based ona posteriori error estimates in the global energy or L2-norm involving local residuals of thecomputed solution. The grid refinement process then aims at equilibrating these local error in-dicators. Grids generated on the basis of such global error estimates may not be appropriate incases of strongly varying coefficients and for the computation of local quantities as, for exam-ple, point values or contour integrals. More detailed information about the mechanism of errorpropagation can be obtained by employing duality arguments specially adapted to the quantityof interest. This results in a posteriori error estimates in which the local information derivedfrom the dual solution is used in the form of weights multiplied by local residuals. On the ba-sis of such estimates, a feed-back process in which the weights are numerically computed withincreasing accuracy leads to almost optimal grids for various kinds of error functionals.


Appendix B: error estimation and adaptivity

The simulation of complex radiation fields in astrophysics requires high resolution of parts ofthe domain. Reliable (and sharp) error bounds are necessary to rule out numerical errors incomparison to observed data. Due to the high dimension of the domain of computation, a wellsuited method for error estimation and grid adaptation is necessary to achieve results of sufficientaccuracy even on parallel computers. A first step in this direction was the control of the L2-error(Fuhrer and Kanschat 1997).

Often the computational goals are more specific. In most cases, only the intensity leavingthe domain I in one particular direction is of interest, since the position of earth relative tothe distant object can be considered as fixed. Generally, a measured quantity can be expressedas a linear functional J (.) applied to the intensity function I. Abbreviating e := I − Ih , wehave J (I) − J (Ih) = J (e). J (.) may be well-defined only on a subspace W ⊂ W , in whichcase either u ∈ W or a regularization of J (.) is necessary. In order to construct an accurate aposteriori estimate for the error, we have to solve the dual problem

J (φ) = (φ,A∗z) ∀ φ ∈ W , (69)

with the dual radiative transfer operator

A∗ = −T + κ + Sσ .

The boundary conditions in the dual problem are complementary to those in the primal problem,i.e., I = 0 on �+. This follows immediately by partial integration from the weak formulationof boundary conditions in a(., .).

Assuming I,Ih ∈ W , which means either J ∈ D(A)′ or additional regularity for I, aswell as sufficient regularity of the discrete space Wh , we have the error representation

J (e) = (e,A∗z)= (Ae, z − zi )

=∑

K∈Th

(κ B − AIh, z − zi )K

for arbitrary zi ∈ Wh . Since the dual solution z is unknown, it is a usual approach to applyHolder’s inequality and standard approximation estimates of finite element spaces to obtain theestimate

J (e) ≤ η =∑

K

ηK =∑

K

CK h2K ‖�‖K ‖∇2z‖K , (70)

where the constant Ck is determined by local approximation properties of Wh . The residualfunction � of Ih in the non-discretized equation is defined by

� = κ B − AIh .

Since the dual solution z is not available analytically, it is usually replaced by the finite elementsolution zh to the dual problem (69). This involves a second solution step of the same structureas the primal problem. It is clear, that by this replacement the error estimate (70) is not trueanymore. An estimate of ‖∇2(z − zh)‖K and an according modification of CK are necessaryto recover it strictly. This still has to be done. In computations the estimate has shown to be ofgreat value in its original form.

We briefly discuss how a grid refinement process may be organized on the basis of an aposteriori error estimate. Suppose that some error tolerance TOL is given. The goal is to find themost economical grid Th on which

|J (e)| ≤ η(Ih) =∑

K∈Th

ηK ≤ T O L , (71)

with local error indicators ηK described in (70). There are several strategies of adaptive gridrefinement (for mathematical aspects see Kanschat 1996; Becker and Rannacher 1997). Thestrategy we normally apply is the so-called fixed fraction strategy: Usually, one starts from an


initial coarse grid which is successively refined. In each refinement cycle, the cells are orderedaccording to the size of ηK and a fixed portion ν (say 30%) of the cells with largest ηK is refined.This guarantees, that in each refinement cycle a sufficient large number of cells is refined. It isespecially valuable, if a computation “as accurate as possible” is desired. Then, the parameter νhas to be determined by the remaining memory resources. However, in its pure form, it does notallow for grid coarsening and in certain cases tends to over-refine the grid.

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PAPER

John L. Kohl · Giancarlo Noci ·Steven R. Cranmer · John C. Raymond

Ultraviolet spectroscopy of the extendedsolar corona

Received: 27 October 2005 / Revised: 10 February 2006 /Published online: 22 February 2006C© Springer-Verlag 2006

Abstract The first observations of ultraviolet spectral line profiles and intensi-ties from the extended solar corona (i.e., more than 1.5 solar radii from Sun-center) were obtained on 13 April 1979 when a rocket-borne ultraviolet coron-agraph spectrometer of the Harvard-Smithsonian Center for Astrophysics madedirect measurements of proton kinetic temperatures, and obtained upper limitson outflow velocities in a quiet coronal region and a polar coronal hole. Follow-ing those observations, ultraviolet coronagraphic spectroscopy has expanded toinclude observations of over 60 spectral lines in coronal holes, streamers, coro-nal jets, and solar flare/coronal mass ejection (CME) events. Spectroscopic di-agnostic techniques have been developed to determine proton, electron and ionkinetic temperatures and velocity distributions, proton and ion bulk flow speedsand chemical abundances. The observations have been made during three sound-ing rocket flights, four Shuttle deployed and retrieved Spartan 201 flights, and theSolar and Heliospheric Observatory (SOHO) mission. Ultraviolet spectroscopyof the extended solar corona has led to fundamentally new views of the ac-celeration regions of the solar wind and CMEs. Observations with the Ultravi-olet Coronagraph Spectrometer (UVCS) on SOHO revealed surprisingly largetemperatures, outflow speeds, and velocity distribution anisotropies in coronalholes, especially for minor ions. Those measurements have guided theorists todiscard some candidate physical processes of solar wind acceleration and to in-crease and expand investigations of ion cyclotron resonance and related processes.

J. L. Kohl (B)Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USAE-mail: [email protected]

G. NociDipartimento di Astronomica e Scienza dello Spazio, Universita di Firenze, 50125 Firenze, Italy

S. R. Cranmer · J. C. RaymondHarvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, USA

32 J. L. Kohl et al.

Analyses of UVCS observations of CME plasma properties and the evolution ofCMEs have provided the following: temperatures, inflow velocities and derivedvalues of resistivity and reconnection rates in CME current sheets, compressionratios and extremely high ion temperatures behind CME shocks, and three di-mensional flow velocities and magnetic field chirality in CMEs. Ultraviolet spec-troscopy has been used to determine the thermal energy content of CMEs allowingthe total energy budget to be known for the first time. Such spectroscopic obser-vations are capable of providing detailed empirical descriptions of solar energeticparticle (SEP) source regions that allow theoretical models of SEP accelerationto be tailored to specific events, thereby enabling in situ measurements of freshlyemitted SEPs to be used for testing and guiding the evolution of SEP accelera-tion theory. Here we review the history of ultraviolet coronagraph spectroscopy,summarize the physics of spectral line formation in the extended corona, describethe spectroscopic diagnostic techniques, review the advances in our understandingof solar wind source regions and flare/CME events provided by ultraviolet spec-troscopy and discuss the scientific potential of next generation ultraviolet corona-graph spectrometers.

Keywords Solar wind · Sun: corona · Sun: coronal mass ejections (CMEs) ·Sun: UV radiation · Techniques: spectroscopic · Telescopes

1 Introduction

Ultraviolet spectroscopy of the extended solar corona (defined here as 1.5 to 10solar radii, R�, from Sun-center) has become a powerful tool for obtaining de-tailed empirical descriptions of coronal holes, streamers, and coronal mass ejec-tions (CMEs). Ultraviolet spectroscopy uniquely determines the velocity distribu-tions and outflow velocities of protons and minor ions near the Sun, it providesabsolute chemical abundances, and it is capable of determining the velocity distri-butions and densities of electrons. Polarization measurements of H I Lyman seriesemissions are believed to be capable of determining vector magnetic fields forcertain geometries.

The empirical models resulting from ultraviolet spectroscopy provide the con-straints needed to test and guide theoretical models of solar wind acceleration,CME heating and acceleration, and solar energetic particle (SEP) acceleration.Ultraviolet spectroscopic instruments on sounding rockets, the Shuttle-deployedSpartan 201 spacecraft, and the ESA/NASA Solar and Heliospheric Observatory(SOHO) spacecraft (Domingo et al. 1995; Fleck & Svestka 1997) have led to newinsights regarding the physical processes that control these phenomena, and moreadvanced instruments are envisioned that are capable of providing a much deeperunderstanding.

The first ultraviolet images of the extended solar corona were obtained on7 March 1970 when a rocket borne objective grating spectrograph was flown intothe path of totality of a natural solar eclipse (Speer et al. 1970; Gabriel et al.1971). The observations revealed H I Lyα emission extending outward to beyondρ = 1.5 R�.1 Gabriel (1971) determined that this emission occurred primarily

1 In this paper we use r to represent the true radial distance from Sun-center, and ρ to repre-sent the radial distance from Sun-center projected on the plane that passes through Sun-center

Ultraviolet spectroscopy of the extended solar corona 33

through the resonant scattering of chromospheric H I Lyα from the small fractionof coronal protons that exist as a component of neutral hydrogen. In addition, 30coronal lines were observed at lower heights.

Prior to these observations, coronal ultraviolet imaging had been confinedto heights within a few tenths of a solar radius from the solar surface, andhigh-resolution ultraviolet spectroscopy was also limited to that region. Remotesensing observations of larger heights consisted primarily of broadband mea-surements of the electron-scattered visible-light corona, limited observationsof visible forbidden emission lines and measurements at radio wavelengths(Newkirk 1967). Visible polarimetry provided the overall electron densitystructure, revealed large-scale coronal structures and substructures and inferredthe shape of the magnetic field.

Several approaches were taken to determine temperatures in the extendedcorona. Estimates from the observed density gradient required an assumption ofhydrostatic equilibrium, which the presence of a solar wind demonstrates to beuntrue, and this method yielded only a single temperature for the electron/protonplasma. Ion kinetic temperatures for Fe9+ and Fe13+ could be determined fromspectral line widths. Type III radio bursts were used to estimate temperaturesabove active regions. Type II bursts are an indicator of the presence of shocks,and coronal density models have been used to infer the location of the shocks.Thermal radio emission was also used to determine the electron temperature ofthe low corona, but it gave only a lower limit for the temperature in the extendedcorona (see reviews by Noci 2003a, b).

Later, observations obtained with the High Altitude Observatory’s white lightcoronagraph on Skylab allowed the determination of the three-dimensional densitystructure within a polar coronal hole, and the bulk outflow velocity was inferredby assuming that the particle fluxes were similar to those in high-speed solar windstreams measured by in situ methods in the ecliptic plane at 1 AU (Munro &Jackson 1977). The Skylab instrument provided the first observations of CMEs,and the High Altitude Observatory’s instrument on the Solar Maximum Missionprovided a large body of such data. The most extensive set of visible corona-graphic data has been provided by the Naval Research Laboratory’s Large AngleSpectroscopic Coronagraph (LASCO) instrument on SOHO. Its field of view ex-tends out to ρ = 30 R� and provides several images per day of the density struc-ture and dynamic characteristics of the extended corona (Brueckner et al. 1995).Sheeley et al. (1997) used LASCO data to infer solar wind speeds near the Sunby tracking density structures in the corona called blobs. The LASCO C1 channelprovided images of the corona out to ρ ≈ 2 R� in narrow wavelength bands cen-tered on several visible spectral lines. The wavelength of these images could bescanned to provide information about the spectral line shapes over a wide field ofview (e.g., Schwenn et al. 1997).

Radio interplanetary scintillation measurements have been used to infer prop-erties of coronal plasma turbulence, including the drift speed of fluctuations inthe solar wind and the spatial scales of density inhomogeneities (see, e.g., Bird& Edenhofer 1990; Coles et al. 1991; Mullan & Yakovlev 1995; Bastian 2001).Woo & Habbal (1997) found evidence for fine density structure in the extended

and is perpendicular to the line of sight (i.e., the “plane of the sky”). This latter quantity mayalso be denoted as an observed height or a projected heliocentric height.


corona using radio occultation measurements. In addition to the remote sensingobservations, in situ measurements have provided a wealth of information aboutsolar particle emissions that can be combined with remote sensing measurementsto place additional constraints on coronal plasma parameters.

It can be seen from the above summary, which is not intended to be complete,that it is possible to obtain a large amount of information about the extended solarcorona without high-resolution ultraviolet spectroscopy, but that body of data isnot sufficient in itself to provide the detailed empirical descriptions of solar windsource regions and CMEs near the Sun that are needed to test, evaluate and guidetheoretical models aimed at identifying the physical processes that control thesephenomena.

The complexity of the extended coronal plasma is a result of its decreasingdensity with height that leads to a transition from a collisionally dominated plasmato one that is nearly collisionless. As a result, every ion species tends to have itsown unique temperature, its own departure from a Maxwellian velocity distri-bution, and its own outflow speed. The protons and electrons also have uniquetemperatures and an outflow speed that is different from those of the minor ions.The elemental abundances vary widely in different structures, and the ionizationdistribution in various species can be much different from structure to structure.

In order to observe most of the extended corona, it is necessary to observe res-onant scattered radiation, which varies according to the first power of the electrondensity rather than the second power dependence of collisionally excited spectrallines whose intensities fall rapidly with height. The resonance lines of hot coronalions tend to have wavelengths in the extreme ultraviolet (EUV), and thus requireobservations in this range.

As described in Sects. 5 and 6 below, empirical temperatures, densities, abun-dances, and outflow speeds of the protons, electrons and various minor ion speciesderived from EUV spectroscopic observations can provide constraints on theorythat are needed to identify the physical processes that control the production of thesolar wind and CMEs. Although the source regions of SEPs are not known, thereare several regions in the extended corona that are likely candidates. They includeCME shocks that tend to form above ρ ≈ 2 R� and flare/CME current sheets thatare found at ρ ≈ 1.3–2.5 R�.

Interest in developing instrumentation to observe the extended corona atultraviolet wavelengths grew out of the 1970 eclipse observations. At theHarvard-Smithsonian Center for Astrophysics, Robert Noyes, Edmond Reeves,and William Parkinson foresaw a need to carry out such observations in the ab-sence of a natural eclipse in order to vastly increase the time available to observethe diverse phenomena of the region. The initial idea was to design a rocket-bornecoronagraph that would make images of the extended corona in H I Lyα radiationusing a circular external occulter. Such an instrument would only measure the lineintensity of H I Lyα, which could be used to investigate hydrogen outflow veloci-ties with the Doppler dimming analysis (see Sect. 2.2.3) proposed for this purposeby Giancarlo Noci (1973a). However, outflow velocity predictions at the time in-dicated that solar wind speeds would not reach levels in the sensitivity range ofthis technique until ρ ≈ 10 R�. John Kohl suggested that the design include pro-vision for spectral line profile measurements to determine kinetic temperatures,that the observable spectral lines not be limited to H I Lyα but ultimately be


Fig. 1 Timeline of ultraviolet observations of the extended solar corona from 1970 to 2005,compared with the monthly international sunspot number (http://sidc.oma.be/)

extended to the entire EUV wavelength range, and that an unconventional lin-ear external occulter be used since its occulting geometry is well matched withthe linear geometry of a spectrometer entrance slit.

Laboratory tests with a solar simulator and a mock-up of the instrumentindicated that internal occultation was also needed to prevent diffracted lightfrom the external occulter from being specularly reflected by the telescope mir-ror into the spectrometer entrance slit. This, together with a sunlight trap andan entrance slit baffle, was added and the basic concept for the rocket ultravio-let coronagraph spectrometer was established (Kohl, Reeves, & Kirkham 1978).This rocket instrument yielded high-quality observations of spectral line profilesfor ρ = 1.5–3.5 R� in coronal holes and brighter coronal regions. The samebasic optical design has been used for all of the ultraviolet coronagraph spec-trometer instruments to follow including the one on the Shuttle-deployed Spar-tan 201 spacecraft and the Ultraviolet Coronagraph Spectrometer (UVCS) in-strument on the SOHO spacecraft (see Fig. 1). John Kohl took responsibility forthe program in 1974 and was formally designated the Principal Investigator in1978.

In addition to the instrument development, an equal effort was placed onidentifying and developing a set of spectroscopic plasma diagnostic techniquesthat could determine the most important parameters of both the electron/protonplasma and the minor ions. George Withbroe was involved in the program at thispoint and he and Kohl worked together to identify and develop the diagnostictechniques and refine the scientific goals of the program (e.g., Withbroe et al.1982b).

This paper provides a review of ultraviolet spectroscopy of the extendedcorona. In Sect. 2, the processes responsible for the formation of ultravioletemissions are described and an overview of the spectroscopic plasma diagnos-tic techniques is provided. In Sect. 3, the instrument design for past, current,and future instruments is discussed. Section 4 reviews the rocket and Spartan201 flights and the technical and observational aspects of the UVCS investiga-tion. The scientific results from UVCS are presented in Sect. 5 and 6, with theformer addressing fast and slow solar wind source regions and the latter describ-ing the investigation of CMEs. Section 7 provides a brief description of obser-


vations of non-solar objects with UVCS and Sect. 8 provides some concludingremarks.

2 Formation of ultraviolet emission in the extended corona and associatedspectroscopic diagnostic techniques

2.1 Formation of ultraviolet emission in the extended corona

UVCS/SOHO has detected spectral lines from neutral hydrogen and coronal ionswith a broad range of ionic charge states. Detectable spectral lines depend stronglyon the observed coronal structure, the heliographic height and in the case of dy-namic structures, on the time of observation. Table 1 is a list of spectral linesobserved by UVCS. The wavelengths are given in nanometers, and structures inwhich they have been observed are indicated by CH (coronal holes, e.g., Kohl et al.1997a), ST (quiescent streamers, e.g., Raymond et al. 1997), AR (active regions,e.g., Ko et al. 2002; Ciaravella et al. 2002), CME (coronal mass ejections, e.g.,Ciaravella et al. 1997; Akmal et al. 2001), C (comets, e.g., Povich et al. 2003),and FC (helium focusing cone, e.g., Michels et al. 2002).

The strongest emission in essentially all structures is H I Lyα. As originallypointed out by Gabriel (1971), it is somewhat surprising that a spectral line ofa neutral atom would dominate the spectrum of a plasma with an electron tem-perature on the order of 1 × 106 K. Gabriel considered the contributions of fivephysical processes in explaining the strong H I Lyα emission in the 1970 eclipseobservations. They are the following:

1. Electron impact excitation of the residual coronal hydrogen2. Photo-excitation of the residual coronal hydrogen3. Thomson scattering of chromospheric radiation from free coronal electrons4. Rayleigh scattering of chromospheric radiation from coronal ions5. Scattering of chromospheric radiation from interplanetary dust particles (the

so-called F-corona).

He concluded that the primary contribution to H I Lyα is process 2, which is theresonant scattering of chromospheric H I Lyα by the small fraction of protonsin the corona that exist at any instant of time with an attached electron. In ad-dition, electron impact excitation can make a significant contribution to Lyα inCMEs, and typically makes a significant contribution to the spectral line inten-sities of coronal ions. Thomson scattering of chromospheric H I Lyα by coronalelectrons results in a broad spectral line component that is several orders of mag-nitude weaker than the resonant scattering component. Processes 4 and 5 provideeven smaller contributions. Observations through the Earth’s exosphere and in-terplanetary space can have measurable contributions from resonant scattering ofchromospheric H I Lyα in those regions. Those emissions can usually be identi-fied by their narrow line widths and relatively weak intensities. The exosphericneutral hydrogen also absorbs coronal H I Lyα near line center.

UVCS has observed several ions in the extended corona that have their chargestate fraction peak at electron temperatures much lower than those of the extendedcorona. For example, the second brightest spectral line tends to be O VI 103.2 nmwhose charge state balance peak is at about 2.9×105 K (e.g., Arnaud & Rothenflug1985). Since, in the case of resonant scattering the emission is proportional to the


Table 1 Spectral lines detected by UVCS/SOHO

Wavelength (nm) Ion Transition Obs. (see text)

94.974 H I Lyδ ST,CH,AR,CME,C97.254 H I Lyγ ST,CH,AR,CME,C

102.572 H I Lyβ ST,CH,AR,CME,C121.567 H I Lyα ST,CH,AR,CME,C

52.221 He I 1s2 1S0 −1s4p 1P1 CME58.433 He I 1s2 1S0 −1s2p 1P1 FC

103.634 103.702 C II 2s22p 2P1/2,3/2 −2s2p2 2S1/2 CME,C97.702 C III 2s2 1S0 −2s2p 1P1 CME,C

108.458 N II 2s22p2 3P1 −2s2p3 3D2 CME98.979 99.158 N III 2s22p 2P1/2,3/2 −2s2p2 2D3/2,5/2 CME

123.882 124.280 N V 2s 2S1/2 −2p 2P3/2,1/2 ST,AR,CME98.877 99.020 O I 2p4 3P2,1 −2p33s 3D3,2 C

102.816 O I 2p4 3P0 −2p33d 3D1 C59.960 O III 2s22p2 1D2 −2s2p3 1D2 CME62.973 O V 2s2 1S0 −2s2p 1P1 ST,CME

121.385 [O V] 2s2 1S0 −2s2p 3P2 CME121.839 O V] 2s2 1S0 −2s2p 3P1 CME103.191 103.761 O VI 2s 2S1/2 −2p 2P3/2,1/2 ST,CH,AR,CME

99.927 100.579 Ne VI] 2s22p 2P3/2 −2s2p2 4P5/2,3/2 CME124.81 Ne IX 1s2s 3S1 −1s2p 3P2 AR60.976 62.493 Mg X 2s 2S1/2 −2p 2P3/2,1/2 ST,CH,AR,CME55.001 Al XI 2s 2S1/2 −2p 2P3/2 ST,AR

120.651 Si III 3s2 1S0 −3s3p 1P1 CME130.332 Si III 3s3p 3P2 −3p2 3P1 CME

94.438 94.923 [Si VIII] 2p3 4S3/2 −2p3 2P3/2,1/2 ST,AR95.008 [Si IX] 2p2 3P1 −2p2 1S0 ST49.937 52.066 Si XII 2s 2S1/2 −2p 2P3/2,1/2 ST,AR,CME

119.913 S V] 3s2 1S0 −3s3p 3P1 CME94.452 S VI 3s 2S1/2 −3p 2P1/2 CME

119.625 [S X] 2p3 4S3/2 −2p3 2D5/2 ST,AR49.146 S XIII] 2s2 1S0 −2s2p 3P1 AR,CME

101.879 105.485 [Ar XII] 2p3 4S3/2 −2p3 2D5/2,3/2 ST,AR49.020 Ar XIII] 2s22p2 3P2 −2p2p3 5S2 AR94.588 99.444 [K XIII] 2p3 4S3/2 −2p3 2D5/2,3/2 AR55.774 Ca X 3s 2S1/2 −3p 2P3/2 ST,AR94.361 [Ca XIV] 2p3 4S3/2 −2p3 2D3/2 AR,CME

109.844 [Ca XV] 2p2 3P1 −2p2 1D2 AR,CME96.887 [Ti XVI] 2p3 2D3/2 −2p3 2P3/2 AR,CME

102.804 [Fe X] 3d 4D7/2 −3d 4F7/2 ST,AR124.200 134.938 [Fe XII] 3p3 4S3/2 −3p3 2P3/2,1/2 ST,AR

48.708 51.008 Fe XIII] 3s23p2 3P1,2 −3s3p3 5S2 ST,AR48.149 Fe XV 3s3p 1P1 −3p2 1D2 ST,AR

115.320 Fe XVII 3s 1P1 −3s 1P0 AR97.486 [Fe XVIII] 2p5 2P3/2 −2p5 2P1/2 AR,CME

127.723 [Ni XIII] 3p4 3P1 −3p4 1S0 AR103.488 117.472 [Ni XIV] 3p3 4S3/2 −3p3 2P3/2,1/2 AR103.304 [Ni XV] 3s23p2 3P1 −3s23p2 1S0 AR,CME


chromospheric intensity as well as the chemical abundance, charge state fraction,and atomic parameters, the charge state fraction of a species in itself is not nec-essarily a good indicator of the electron temperature in the region of formation.Other atomic processes that can produce atomic line emission in the extreme ul-traviolet (EUV) include radiative decay following charge transfer into an excitedstate and emission of a stabilizing photon following dielectronic recombination.The contribution of these processes can usually be ignored.

Ionization balance is an important consideration in determining the intensity ofemission lines in the extended corona. In the upper regions of the corona the densi-ties are sufficiently low that the ionization balance for various particle species maybecome decoupled from the local electron temperature (Withbroe et al. 1982b).For this reason, it is highly desirable to eliminate the sensitivity to uncertainties inthe ionization balance by utilizing line ratios of spectral lines from the same ioncharge states to deduce physical parameters.

The neutral hydrogen motions should be representative of the proton motionsin much of the extended corona. This is a result of rapid charge transfer betweenthese species. Olsen et al. (1994) and Allen et al. (1998, 2000) find that below∼2.5 R� in coronal holes and considerably larger heights in more dense struc-tures, there should be little decoupling between neutral hydrogen and proton ve-locities and temperatures. At larger heights in coronal holes, though, the neutralhydrogen atoms may have a substantially larger perpendicular temperature thanthe protons because of increased frictional dissipation between the neutrals andtransverse magnetohydrodynamic wave motions. The protons, however, exhibit“nonthermal” transverse motion due to their response to the oscillating electricand magnetic fields of the waves. In some cases, the frictional heating for theneutrals and the nonthermal broadening for the protons are of the same order ofmagnitude, and the resulting kinetic or effective temperatures of the two species(see Eq. (11)) are very nearly equal (see also Cranmer 1998).

Because most structures in the extended solar corona are optically thin, theobserved radiation is emitted over a line of sight (LOS) that may subtend morethan one large scale structure. Therefore, the data analysis must account for theproperties of the foreground and background plasma. In general, LOS effects tendto contribute about 10% to the plasma parameter uncertainties. In some cases suchas polar coronal holes at solar minimum, the LOS is dominated by the structureof interest and a spherically symmetric geometry – or a similarly straightforwardaxisymmetric superradial geometry – can be used without introducing significantadditional uncertainties in the analysis (Cranmer et al. 1999b). In all cases, contri-butions from structures in the plane of the sky tend to dominate because the LOSsamples such structures at lower heights (and thus higher densities) than those forthe foreground and background structures. For stable structures such as quiescentequatorial streamers at solar minimum, a tomographic reconstruction can be usedto model the LOS (Panasyuk 1999; Strachan et al. 2000; Frazin 2000; Frazin &Janzen 2002; Frazin et al. 2003).

Miralles et al. (2001a) produced an empirical model of an equatorial coro-nal hole near solar maximum. The first step in that empirical modeling processwas to define the exact volumes of the coronal hole and the surrounding regionswith respect to five radial axes. The radial dependence of the electron density wasconstrained using several days of UVCS white-light channel measurements of po-


larization brightness (pB).2 As the coronal hole rotated into and out of the planeof the sky, the relative decrease and increase in pB allowed the densities in thetwo regions to be determined. Each of the O VI 103.2 and 103.7 nm spectral lineswere curve fit to broad and narrow Gaussian components that were found to result,respectively, from the coronal hole and surrounding regions.

In the case of CMEs, Raymond (2002) made a three-dimensional reconstruc-tion of a CME plasma by utilizing UVCS measurements of Doppler shifts versustime to probe the LOS direction, and intensity measurements to model the perpen-dicular plane.

In the remainder of this subsection, additional information about line forma-tion by electron impact excitation (Sect. 2.1.1), resonant scattering (Sect. 2.1.2),and Thomson scattering (Sect. 2.1.3) will be provided.

2.1.1 Line formation by electron impact excitation

For most EUV and XUV spectral lines, the emergent intensity is a combinationof collisionally excited and resonantly scattered components. The collisionallyexcited component has an intensity (e.g., Withbroe 1970)

Ic(λ) = 1.7 × 10−16∫ ∞

−∞dx Ael Ri N 2

e C12φλ (1)

where Ne and Np, respectively, are the number densities of electrons and protons(cm−3), Nel is the number density of ions summed over all stages of ionizationof the atomic species producing the ion i , Ael = Nel/Np, C12 is the electronimpact excitation rate coefficient, Ri = Ni/Nel is the ionization balance term,Ni is the number density of the ion species producing the line, and φλ is the lineprofile function (e.g., a Gaussian for a Maxwellian particle velocity distribution).The integration in Eq. (1) is taken over the LOS distance x . For most ions, elec-tron impact excitation dominates in the low corona, while at larger heights it iscomparable to resonant scattering.

2.1.2 Line formation by resonant scattering

Gabriel (1971) and Beckers & Chipman (1974) derived equations for the intensityand profile of the resonantly scattered H I Lyα spectral line. The intensity andprofile of the resonantly scattered components of minor ions are given by a similarexpression. Here we will describe resonant scattering for the case of H I Lyα.

Following Withbroe et al. (1982b), the number of coronal hydrogen atoms withvelocities between v and v+dv excited per second from level 1 (the ground level)

2 The so-called polarized brightness pB is the linearly polarized component of thewavelength-integrated white-light (400–600 nm) spectral radiance of a ray passing through thesolar corona. It is often given in units of B�, the unpolarized spectral radiance of the solardisk, similarly integrated in wavelength. In some papers B� is given as the disk-center radianceand in others it is given as the disk-averaged radiance (see Minnaert 1930; van de Hulst 1950;Altschuler & Perry 1972).


to level 2 (the first excited level) by a beam of chromospheric radiation with wave-lengths between λ′ and λ′ + dλ′ and angular direction between ω and ω + dω is

d N2(v) = N1(v)h B12λ−10 I�(λ′, ω)

× δ

(λ′ − λ0 − λ0

cv · n′

)dω dλ′ dv, (2)

where B12 is the Einstein absorption coefficient, h is Planck’s constant, andI�(λ′, ω) is the intensity of the chromospheric radiation. The only photons thatcan be scattered by a hydrogen atom moving with a velocity v are those with λ′ =λ0 + (λ0/c)v ·n′ where λ0 is the central wavelength of the Lyα transition and n′ isthe vector describing the direction of the incident chromospheric radiation; hencea Dirac delta function was introduced in Eq. (2). (The effect of the natural Lyα linewidth can be ignored for scattering at coronal temperatures; see Cranmer 1998).

The number of photons scattered per second in the direction n toward an ob-server is

d N = d N2(v)

4π

[11 + 3(n · n′)2

12

]δ

(λ0 − λ + λ0

cv · n

), (3)

where the term in square brackets is the effective angular dependence of the H ILyα scattering process. (This term takes on a different form for other spectrallines.) The Dirac delta function transforms the scattered wavelength from theatom’s frame to the observer’s frame. Employing a rectangular coordinate system,taking Np/Ne = 0.8 for a fully ionized plasma with 10% helium, where f (v) isthe velocity distribution function of the hydrogen atoms, and the observer’s LOSis the x-axis, we have:

Is(λ) = 0.8 h B12

48πλ0

∫ ∞

−∞dx Ne R

∫ω

dω [11 + 3(n · n′)2]

×∫ ∞

0dλ′ I�(λ′, ω)

∫ ∞

−∞dv f (v) δ

(λ′ − λ0 − λ0

cv · n′

)

× δ

(λ0 − λ + λ0

cv · n

)(4)

where Is(λ) is the intensity of the scattered radiation, R = NH I /Np, and v · n =vx is the LOS velocity of a hydrogen atom. The velocity distribution f (v) containsinformation about the mean flow velocity u (i.e., the bulk solar wind velocity) aswell as the temperature.

2.1.3 Line formation by Thomson scattering

The electron scattered component of a spectral line emanating from the extendedsolar corona is produced by Thomson scattering of radiation from lower helio-graphic layers. The problem of determining the scattering of monochromatic ra-diation by coronal electrons was addressed by Dirac (1925), van Houten (1950),and others concerned with the photospheric white light spectrum. In the case ofsolar radiation with intensity I�(λ′, ω), wavelength between λ′ and λ′ + dλ′ and


angular direction between ω and ω + dω, the number of incident photons cm−3

s−1 scattered by coronal electrons with velocities between ve and ve + dve is:

d N = Ne(ve) σ I�(λ′, ω) dλ′ dω dve (5)

where σ is the Thomson scattering cross-section. The fraction of these photonsscattered toward an observer is:

d N (λ) = d N

4π

3

4[1 + (n · n′)2] δ

[(λ′ − λ′

cve · n′

)−

(λ − λ

cve · n

)](6)

where 3[1 + (n · n′)2]/4 is the angular dependence of Thomson scattering and n′and n are the directions of the incident and scattered photons. Since these photonsmust have the same wavelength in the rest frame of the electrons, the Dirac deltafunction specifies which incident photons will be scattered at wavelength λ mea-sured by the observer. Hence the intensity (photons cm−2 s−1 sr−1) of the electronscattered component is given by:

Ie(λ) = 3σ

16π

∫ ∞

−∞dx Ne

∫ω

dω [1 + (n · n′)2]∫ ∞

0dλ′ I�(λ′, ω)

×∫ ∞

−∞dve f (ve) δ

[(λ′ − λ′

cve · n′

)−

(λ − λ

cve · n

)](7)

where x is the distance from the observer along the LOS. Because of the highthermal velocity of the electrons, the solar wind flows and turbulence on the elec-trons can be ignored. It is important to note that the shape of the electron scatteredcomponent of H I Lyα depends on the scattering geometry and is not simply aGaussian. The profile width depends on the angle between the vector from Sun-center to the plasma element and the vector defined by the LOS. Other expressionsfor the Thomson scattered and resonantly scattered intensities are given by Nociet al. (1987), Cranmer (1998), Li et al. (1998a) and Noci & Maccari (1999).

2.2 Ultraviolet spectroscopic diagnostics for the extended solar corona

The ultraviolet emission lines present a rich and varied source of diagnostic infor-mation about the solar corona. The shapes of lines formed by resonant scatteringand collisional excitation are direct probes of the LOS distribution of electron,atom, and ion velocities. Integrated line intensities of resonantly scattered spectrallines are sensitive to bulk outflow velocities near the Sun. The electron velocitydistribution can be determined directly by observing the spectral line profile ofThomson scattered H I Lyα and the angles of polarization of H I Lyα and Lyβ aresensitive to the coronal vector magnetic field for certain geometries. The inten-sities of collisionally dominated EUV lines can constrain electron temperatures,densities and elemental abundances in the extended corona. In the case of spectrallines of, for example, Li-like species with comparable resonantly scattered andcollisionally excited components, intensity ratios can be sensitive to bulk outflowvelocities and to the anisotropy of particle velocity distributions.

Although spectroscopic diagnostic techniques yield values of coronal plasmaparameters directly, more accurate and self consistent values for the various


plasma parameters can be obtained by producing an empirical model of the plasmaconditions in the various structures of the extended corona. The modeling proce-dure is initiated by deducing various physical quantities directly from the obser-vations in a fashion similar to that used by Kohl et al. (1997a). These values areused as initial estimates in an empirical model of the observed structure. Althoughparticular coronal plasma parameters (e.g., outflow velocities), tend to dominantlycontrol particular observable quantities (e.g., line intensities), other plasma param-eters (e.g., temperatures) can also affect those same observables. Hence, syntheticobservables such as line profiles, line intensities and line ratios, which are gener-ated with models that are based on the initial estimated parameters, are normallynot fully consistent with those observed. Repeated comparison with the data pro-vides guidance on how to iterate the derived quantities until there is optimal agree-ment between the empirical model and all of the observed spectroscopic observ-ables. For many parameters, the initial diagnostic estimates and the final iteratedempirical model results differ by about 10–20% (see Cranmer et al. 1999b). Forsome parameters, though, the initial diagnostic estimates can be misleading andthe final iterated results differ from them by a large relative amount.

Since the goal of ultraviolet spectroscopic observations is to determine a de-tailed empirical description of the observed structure that will ultimately be usedto test and guide theory, it is important that the empirical models do not spec-ify the processes that control and maintain the coronal plasma. There must beno constraints on the models and no inclusion in the models of any mathematicaldescription of a physical process that might control coronal heating, particle accel-eration, waves and turbulent motions, and magnetic field structures. The modelsand ultimately the final iterated plasma parameters must only depend on obser-vations and well-established theory, such as the radiative transfer inherent in theline formation process. The empirical models can, of course, also depend on otherkinds of direct observations – e.g., white-light pB diagnostics of the electron den-sity, in situ mass flux constraints, and coronal magnetic field extrapolations fromphotospheric field measurements (see Sect. 5.2). For some plasma parameters, itmay not be possible to derive precise empirical values, and in such cases, rea-sonable limiting ranges for their values should be used. The uncertainties in allobservable quantities and the limits in the ranges of imprecisely known parame-ters should be taken into account in specifying the uncertainties in each plasmaparameter that results from the empirical modeling process. All of the resultingcoronal parameters, then, are either derived straightforwardly and unambiguouslyfrom measurements or, in a few cases, specified with a range of values determinedfrom limited empirical evidence. The outcome is a data set that can be utilizedeffectively to constrain and guide theoretical models.

In the following subsections, the relationships between particular plasma pa-rameters and the observable quantities most sensitive to those parameters will bedescribed. These relationships will be described in terms of the plasma diagnostictechniques that are used to determine the initial estimates of plasma parametersfor the empirical models described in the preceding paragraph.


2.2.1 Line of sight velocities

In the case of a particle emitting a photon at wavelength λ, its velocity componentvx relative to the observer and along an observational LOS x is given by the non-relativistic Doppler formula:

vx = (λ − λ0)c/λ0 (8)

where λ0 is the theoretical or laboratory value of the wavelength of the transition.Hence, a spectral line profile consisting of an array of intensity versus wavelengthvalues can be converted to an array of intensity versus LOS velocity values. How-ever, since the line profile shape of resonantly scattered radiation depends on thegeometry of the scattering (Sect. 2.1.2) and on Doppler dimming (Sect. 2.2.3),and many spectral lines of the extended corona have resonant scattering contribu-tions, the plot of intensity versus velocity is not exactly the velocity distribution.Nonetheless, it is reasonable in most cases to use the first moment m1 of thisdistribution as the characteristic bulk velocity for emitters along the LOS, where

m1 ≡ vc = 1

n

∑i

vi I (vi ), (9)

and vc is the center velocity, n is the number of points across the profile I (vi )(see also Noci & Maccari 1999). To put vi on an absolute scale, it is necessary tohave an absolute wavelength reference. Otherwise, only relative velocities can bedetermined.

2.2.2 Hydrogen and ion kinetic temperatures

Determination of particle temperatures from spectral line profiles in the extendedcorona has been discussed by, for example, Withbroe et al. (1982b). In the case ofa collisionally excited spectral line or resonant scattering at right angles, the widthof an optically thin spectral line in a low-density plasma such as the extendedsolar corona depends on the kinetic temperature Tkin of the plasma where the lineoriginates. If the line has a shape which is Gaussian or nearly Gaussian, one candefine the kinetic temperature by the relation

�λ1/e = λ0V1/e

c= λ0

c

(2kTkin

mion

)1/2

, (10)

where Tkin includes the effects of both thermal and nonthermal motions, k isBoltzmann’s constant, mion is the mass of the particle species producing the spec-tral line, and �λ1/e is the 1/e Gaussian half-width. Line widths can also be ex-pressed equivalently in velocity units as V1/e. Note that the kinetic temperature isa quantity determined directly from the line width. If one wishes to separate theeffects of thermal and nonthermal line broadening, then one can define

�λ1/e = λ0

c

(2kTion

mion+ ξ2

)1/2

, (11)


where Tion is the ion’s thermal temperature – indicative of “microscopic” randommotions – and ξ is the root-mean-square velocity component due to plasma mo-tions that occur on spatial scales much larger than the particle mean free path,but smaller than the path length over which the spectral line is formed. For ex-ample, Alfven waves propagating through the corona may cause plasma motionsof sufficient amplitude to significantly broaden spectral lines, perhaps even bethe dominant source of broadening for spectral lines of heavy ions. By observ-ing lines from ions of different masses one can obtain empirical constraints onthe magnitude of mass-dependent and mass-independent motions (see, e.g., Esseret al. 1999; Frazin et al. 1999). Line profiles can also be affected by the LOScomponents of bulk outflow velocities.

Temperature is a convenient parameter, but the line profile gives much moreinformation, namely a direct determination of the velocity distribution of the par-ticles along the LOS. A static isothermal plasma with a Maxwellian particle ve-locity distribution produces Gaussian profiles, whereas a multi-temperature ornonthermal plasma with a non-Maxwellian particle velocity distribution functionyields non-Gaussian profiles. Thermalization times in the extended solar coronaare long. As a result, plasma heating, acceleration and/or transport processes thatare mass or charge-to-mass dependent can produce differences in thermal temper-atures and/or non-Maxwellian velocity distributions among different species ofparticles.

The profile of the resonantly scattered component of H I Lyα provides a mea-surement of the kinetic temperature of protons in regions where the coronal expan-sion time is much greater than the lifetime of the hydrogen atoms (see Sect. 2.1).

In general, the width of a profile produced by resonant scattering from aplasma element in the LOS depends on the angle between the vector from Sun-center to the plasma element and the vector defined by the LOS. The greater theamount of geometric information available, the lower the uncertainty in the de-rived temperatures and velocity distribution.

It will be shown in Sect. 2.2.3 that information about the velocity distribu-tion in the radial direction for certain ions can be determined from the ratio ofthe intensities of the ions’ resonance doublet. This can yield constraints on thetemperature anisotropy (T‖ = T⊥) in the collisionless extended corona.

2.2.3 Hydrogen and ion outflow velocities

It can be seen from Eq. (4) that the intensity of a purely resonantly scattered spec-tral line depends on the number of particles in the LOS capable of scattering radi-ation in the line, and also depends on the intensity of the incoming radiation fromlower levels of the solar atmosphere. The number of scatterings is a function ofthe outflow velocity of the emitting species. In a static corona, the central wave-length of the coronal scattering profile would be identical to that of the disk profile.However, in a region with solar wind flow, the scattering profile is Doppler-shiftedwith respect to the disk profile and the less efficient scattering results in a reductionin intensity of the scattered radiation. This effect is known as Doppler dimming(Hyder & Lites 1970; Noci 1973a; Beckers & Chipman 1974; Withbroe et al.1982b; see also Fig. 2). A similar diagnostic of mass motions in comets from


Fig. 2 Noci’s (1973a) illustration of the overlap between the disk H I Lyα profile and the broadercoronal scattering profile, which drives the Doppler dimming effect

visible-light molecular lines was described by Swings (1941) and Greenstein(1958).

In order to determine the outflow velocity using Eq. (4), it is necessary tohave independent knowledge of the electron density and the ionization balancealong the LOS, the velocity distribution of coronal hydrogen in the directions ofthe incoming radiation, various atomic constants, and the intensity of ultravioletemission from lower atmospheric layers (i.e., the solar disk). In the case of spectrallines of elements other than hydrogen, the elemental abundance is also needed.

Approaches for modeling LOS variations were discussed in Sect. 2.1. Electrondensities can be determined from measurements of pB and by measurements ofelectron scattered H I Lyα as discussed in Sect. 2.2.5. The ionization balancedepends on the electron density and the electron temperature whose measurementis discussed in Sect. 2.2.4. The intensity of ultraviolet emissions from the solardisk also can be measured (for a recent discussion of the variability of the H I Lyαdisk intensity, see Auchere 2005).

The velocity distribution of coronal hydrogen along the LOS can be measured,but the LOS tends to be nearly perpendicular to the direction of the incomingradiation. UVCS has provided strong evidence that coronal velocity distributionsare often anisotropic, especially in coronal holes. It was shown by Cranmer et al.(1999b) that meaningful bounds on the hydrogen outflow speed can be obtainedwith the Doppler dimming method by placing reasonable higher and lower limitson the hydrogen velocity distribution in the radial direction. The usual approach isto set the lower limit of the width of the hydrogen velocity distribution in the radial


direction to the value corresponding to the measured electron temperature (seeSect. 2.2.4) and set the upper limit to the measured hydrogen velocity distributionalong the LOS.

The resulting values for hydrogen outflow velocity as a function of height canbe used to specify the hydrogen particle flux. This in turn can be used with esti-mated flux tube expansion factors, based on the macroscopic geometry of the ob-served structure, to derive values of the particle flux at the location of spacecraftcapable of in situ measurements. Cranmer et al. (1999b) found consistency be-tween the predicted particle fluxes and the in situ measurements. H I Lyα Dopplerdimming is sensitive to outflow velocities larger than about 100 km s−1.

There are a variety of techniques that can be used to obtain an estimateof the outflow velocity for use as a starting value in self-consistent empiricalmodels. These methods depend on comparing the intensity of a spectral line thatis affected by Doppler dimming to the intensity of an observable quantity that isnot. For example, Noci (1973a) suggested a method that makes use of the ratioof the intensity of the resonantly scattered component of a spectral line to thepolarized radiance of broad band visible light. Withbroe et al. (1982b) illustratedthis technique by using the following simplified expression for the resonantlyscattered component:

Ires = const ×∫ ∞

−∞Ael Ri Ne I� dx (12)

where

I� =∫ ∞

0dλ I�(λ) φ(λ − δλ), (13)

and I�(λ) is the intensity of the disk radiation at wavelength λ, φ is the normal-ized absorption profile, δλ ≡ (λ0u/c) is the Doppler shift introduced by the solarwind flowing at speed u. If one assumes an isothermal corona,

Ires = const × Ael 〈Di (u)〉 Ri

∫ ∞

−∞Ne dx (14)

where Di (u) is the Doppler dimming term (see Eq. [4] for a more accurateexpression). The intensity of the polarized radiance of visible light is givenapproximately by

pB = C∫ ∞

−∞Ne dx (15)

where C is a constant. It follows that:

Ires

pB∝ Ael Ri 〈Di (u)〉. (16)

The Doppler dimming term can be expressed as

Di (u) =∫ ∞

0dλ I�(λ − δλ) φ(λ − λ0) (17)

If the outflow velocities are sufficiently high to produce significant Dopplerdimming, then the ratio Ires/pB as a function of height can be used to determine


the amount of Doppler dimming and, therefore, to estimate the bulk outflowvelocity of, in this case, coronal hydrogen.

With the exception of emission from CMEs, the intensity of H I Lyα in theextended corona is comprised almost entirely of the resonantly scattered compo-nent. Most other spectral lines have contributions from both resonant scatteringand electron impact excitation. Kohl & Withbroe (1982) pointed out that if theratio of the resonant scattering component to that of the collisionally excited com-ponent can be determined, then the outflow velocity for the emitting ion can bederived. This can be seen from the following simplified expression:

Ires

Icoll= const × 〈Di (u)〉

∫Ne dx∫N 2

e dx. (18)

The resonance line doublets produced by Li-like and Na-like ions are wellsuited to empirical determinations of the relative intensities of their collisionallyand radiatively excited components. Examples of such spectral lines are O VI103.2 and 103.7 nm, Ne VII 77.0 and 78.0 nm, Mg X 61.0 and 62.5 nm, Si XII49.9 and 52.1 nm, and Fe XVI 33.5 and 36.1 nm. The collisionally excited compo-nents of these lines are proportional to the collision strengths while the radiativelyexcited components are proportional to the Einstein coefficient times the intensityof the disk radiation that provides the radiative excitation (see Eq. [4]).

Kohl & Withbroe (1982) described a simple example for identifying the col-lisional and radiatively excited fractions. In the case they considered, the coronalions are excited through the same Li-like ionic species and same energy transi-tions that produce the solar disk radiation. The coronal collisional componentsthen will be in the ratio of the collision strengths (i.e., 2:1) and the radiative com-ponents will be in the ratio of their Einstein coefficients (2:1) times the ratio ofthe intensities of the disk radiation pumping each transition. Since the disk ra-diation is collisionally excited, it too would be in the ratio 2:1, and so the ratioof the resonantly scattered component of the coronal lines is 4:1. Therefore, theobserved ratio of the intensities of the coronal lines, in this simplified example,can be used to determine the fraction of the total intensity that is attributable toresonant scattering – for each member of the doublet – and the fraction due tocollisional excitation. Then Eq. (18) can be used to determine the outflow velocityof those coronal ions.

The sensitivity range of outflow velocities depends on the spectral line widthsof the solar disk radiation and on the widths of the absorption lines in the corona(i.e., the velocity distribution of the coronal ions in the direction of the incomingradiation). The Doppler shift due to the outflow velocity must be large enough tocause a significant decrease in the overlap between the pumping and absorbingprofiles, and it must be small enough to not reduce the overlap to near zero. Inthe case of O VI 103.2 and 103.7 nm, this limits the useful range of the “pure”Doppler dimming effect to about 30 km s−1 to 80 km s−1.

Noci et al. (1987), however, pointed out that determinations of an arbitrarilylarge range of velocities is possible when pumping by neighboring lines is consid-ered. They provided several examples of resonance doublets with nearby spectrallines capable of pumping one of the spectral lines at outflow velocities of interest.Their examples included the following: O VI 103.19 nm and 103.76 nm pumped


Fig. 3 Modeled O VI line ratio at ρ = 3 R� plotted as a function of ion outflow speed u for aseries of anisotropic models with a model for T⊥(r) constrained by O VI line widths measuredby UVCS and a range of trial T‖ values. Adapted from Cranmer et al. (1999b)

by C II 103.70 nm at a velocity of 173 km s−1, Fe XVI 33.5407 nm pumpedby Mg VIII 33.50 at 364 km s−1 together with Fe XVI 36.0798 nm pumped byFe XII 35.97 nm at 913 km s−1 and pumped by Si XI 35.9 nm at 1500 km s−1,and Mg X 60.976 pumped by O IV 60.80 nm at 866 km s−1 together with Mg X62.493 nm.

Li et al. (1998a) investigated how the component of the kinetic temperaturein the direction perpendicular to the magnetic field, for both isotropic andanisotropic temperatures, affects both the amount of Doppler dimming andpumping. Since the velocity distribution perpendicular to the radial directionwill have a component along the direction of the incident radiation from thewhole solar disk (except from Sun-center), the so-called perpendicular kinetictemperature T⊥ (which in the plane of the sky corresponds mainly to the LOStemperature) will also contribute to the resonant scattering. Li et al. (1998a) alsofound that for cases where the anisotropy of the O VI doublet is very large, it isnecessary to consider also pumping of O VI 103.76 nm by C II 103.63 nm.

An example of the application of the Doppler dimming and pumping techniqueapplied to the O VI doublet was reported by Cranmer et al. (1999b). Figure 3 isa plot of the observed intensity ratio R of O VI 103.2 nm to O VI 103.7 nm,versus bulk ion outflow velocity u for modeled O VI emissivity integrated over apolar LOS at ρ = 3 R�. The function R(u) is modeled here for a range of valuesfor u and T‖, the latter quantity being the kinetic temperature in the direction ofthe incoming radiation, along with an observationally constrained function for theradial variation of perpendicular kinetic temperature T⊥(r).

It is evident from Fig. 3 that smaller values of T‖ produce ratios R that havelower minimum values. This fact can be exploited to put a firm upper limit onT‖ when the measured O VI intensity ratio is less than ∼1.7. For example, in the


Fig. 4 Modeled profiles of the Thomson scattered component of H I Lyα computed with aspherically symmetric isothermal corona viewed through a LOS at distance ρ = 3 R�. Profilesfor 4 coronal temperatures (in units of 106 K) are shown. From Withbroe et al. (1982b)

figure, it is impossible for the models with parallel kinetic temperatures largerthan about 3 × 107 K to ever agree with the observations of R ≈ 0.95 at thatheight, no matter the outflow speed (see also Kohl et al. 1997a, 1998; Li et al.1998a; Antonucci et al. 2000; Zangrilli et al. 2002; Frazin et al. 2003). Using thisconstraint, a threshold for T‖ can be computed above which the intensity ratiocould never reach the indicated observed value of ∼0.95. This provides a firmupper limit for the parallel velocity distribution that can be used in comparisonto the more observable perpendicular distribution to determine the degree ofanisotropy T⊥/T‖. As can be seen from Fig. 3, the plot of R versus u togetherwith the observed value of R also determines the outflow velocity for O5+ ions. Insome cases, a range of values for u might be compatible with the observations ata particular height, but measurements at several heights are helpful in narrowingthe range of values for each height.

2.2.4 Electron temperature

It was suggested by Hughes (1965) that the electron temperature of a coronalplasma could be determined directly by measuring the spectral line profile ofelectron-scattered H I Lyα in the extended corona. The formation of this Thomsonscattered radiation is governed by Eq. (7) in Sect. 2.1.3. Withbroe et al. (1982b)used Eq. (7) to produce plots of profiles for the electron scattered component ofcoronal Lyα for a spherically symmetric isothermal corona with a typical radialelectron density distribution (see Fig. 4). These profiles show the sensitivity of thewidth of the electron scattered component to the magnitude of the coronal electron


Fig. 5 Modeled widths of Thomson scattered profiles for plasma elements at different scatteringangles ψ and a range of observing heights ρ, where the widths are given in units of the electronthermal width: �λe = (λ0/c)(2kTe/me)

1/2. From Withbroe et al. (1982b)

temperature. Due to the low mass of the electrons, the width of this componentis much larger than the resonantly scattered component of Lyα. The Thomsonscattered profiles can also provide information on the velocity distribution of theelectrons along the LOS, which determines the shape of the profile.

The shape of the electron scattered component of H I Lyα depends on thescattering geometry as well as the electron distribution. In particular, it dependson the angle ψ between the vector from Sun-center to the plasma element andthe vector defined by the LOS. It was shown by van Houten (1950) that the widthof the profile �λe ≈ 2�λ0 sin(ψ/2). For ψ = 90◦ the profile is Gaussian witha characteristic width that is a factor of 21/2 larger than the Doppler width �λ0.For plasma elements on the observer’s side of the plane of the sky, the width �λedecreases as sin(ψ/2) with increasing angular distance, while on the opposite side,the width increases with increasing angular distance. This is illustrated in Fig. 5,which presents curves showing the variation of the width of profiles from plasmaelements at different angular distances ψ from the plane of the sky. Curves areplotted for several values of ρ. For large values of ρ where the angular size ofthe solar disk is small as viewed from the corona, these curves approach the value�λe = 2�λ0 sin(ψ/2).

Figure 6 illustrates the effect of the above ρ dependence on the shape of theprofile of the electron scattered H I Lyα line. Theoretical profiles for an isothermalcorona with Te = 1.5 × 106 K are given for several values of ρ. The profiles havebeen normalized to have the same central intensity. Since the observed intensity ofthe scattered radiation measured at a given spatial location is an integral over thecontributions of plasma elements distributed along the LOS, one cannot simplyfit a Gaussian curve to a measured profile and determine the electron temperaturefrom the width. A model must be used.


Fig. 6 Modeled profiles (solid lines) of the Thomson scattered component of H I Lyα computedfor several values of the observing height ρ (units of R�) using an isothermal coronal modelwith Te = 1.5 × 106 K. For comparison, a Gaussian curve with a width corresponding to thethermal width is also plotted (dashed line). From Withbroe et al. (1982b)

The line intensity of the electron scattered component of coronal H I Lyα isabout three orders of magnitude weaker than the resonant scattered componentand also about 40 times wider so that the count rate per unit area for the electronscattered component at a spectrometer focal plane is more than 4 orders of magni-tude below the peak intensity of the resonance line. Fineschi et al. (1998) made thefirst direct measurement of electron temperature in the extended corona by usingUVCS observations of a streamer. The removal of grating stray light and diffractedlight was marginal and resulted in large uncertainties. An improved arrangementfor making this measurement is described in Sect. 3.4.

Other spectroscopic methods can be used to estimate electron temperaturesin the extended corona, but none of those can determine the departures from aMaxwellian. For example, Noci et al. (1997b) described a method whereby theelectron temperature could be determined indirectly through the hydrogen ioniza-tion ratio, either by comparison of the Lyα total intensity with the intensity in thevisible continuum, or by a comparison of the collisional and radiative componentsof Lyβ (see also Fineschi & Romoli 1994; Maccari & Noci 1998). Methods forderiving electron temperatures from the ionization states of observed ions is de-scribed in Sect. 6.1.3.


2.2.5 Electron density

It can be seen from Eq. (7) that the integrated line intensity of electron scatteredH I Lyα is proportional to the electron column density. This is the same quantitythat is determined by the white-light pB. However, the H I Lyα measurementdoes not require a polarization measurement to distinguish the electron-scatteredK-corona from the dust-scattered F-corona, which can be removed because of itsmuch narrower line profile. The electron scattered Lyα measurement also avoidsany assumption that the F-corona is unpolarized above a given height (typicallyr ≈ 5 R�). Hence, the Lyα method is expected to provide new information aboutelectron densities at heights where the assumption of an unpolarized F-corona isuncertain.

Spectral line ratios are sensitive to local electron densities. Akmal et al. (2001)derived electron densities in a CME using the ratio of O V 121.385 to O V121.839 nm lines (see Sect. 6.1.2). Comparisons to column densities determined,in that case, with polarized radiance of broadband visible light provided infor-mation about the size of the observed structures. If the collisional and radiativecomponents of a spectral line can be separated, Eq. (18) can be used to put con-straints on both the electron density and the ion outflow speed (see, e.g., Mariska1977; Parenti et al. 2000; Ko et al. 2002; Zangrilli et al. 2002; Antonucci et al.2004).

2.2.6 Magnetic field

In the optically thin extended solar corona, the resonant components of spectrallines are linearly polarized due to the anisotropic illumination from the disk. If amagnetic field is present in the scattering volume, then the linear polarization ismodified by the Hanle effect (Hanle 1924; Mitchell & Zemansky 1934).

In the extended corona, the measurement of ultraviolet resonance line polar-ization and its interpretation through the Hanle effect is expected to provide, forcertain geometries, a diagnostic of the strength and direction of coronal magneticfields (Bommier & Sahal-Brechot 1982). The first consideration of the ultravi-olet coronagraphic instrumentation required for such measurements in H I Lyα,Lyβ, and Lyγ was described by Strachan (1984) in a report submitted to the Har-vard University Astronomy Department with John Kohl serving as the academicadvisor. Fineschi et al. (1993) carried out a study of an all-reflecting ultravioletcoronagraph polarimeter to make such measurements in H I Lyα.

In preparation for proposals for advanced ultraviolet coronagraphic spectro-scopy, S. Fineschi worked out a method whereby the difference in polarizationdirection between H I Lyα and H I Lyβ could provide a sensitive measurement ofthe magnetic field in coronal loop structures (Fineschi et al. 1999).

In the solar corona, the presence of a magnetic field induces a change in rota-tion of the zero-field polarization vector and a change of the degree of polarizationin the zero-field linear polarization of the resonantly scattered component of coro-nal line-emission. If P0 is the zero-field linear polarization, then the change of theresonance line polarization, P , due to the Hanle effect is given by

P

P0= 1√

1 + (2ωL/A12)2, (19)


Table 2 Hanle effect in coronal lines

Spectral line λ (nm) A12 (107 s−1) Bmin – BHanle (G)

H I Lyγ 97.2 6.8 1 – 6H I Lyβ 102.5 16.7 2 – 16H I Lyα 121.6 62.7 6 – 60O VI ( 2 P3/2 −2 S1/2) 103.2 41.6 4 – 40

Fig. 7 Illustration of the rotation of the polarization vector P by an angle β from the zero-fieldpolarization vector P0. The magnetic field vector B is oriented away from the LOS direction byangle χB

where ωL is the Larmor frequency and A12 is the Einstein coefficient for sponta-neous emission of the [1 → 2] line transition.

The rotation angle, β, from the zero-field direction, tangent to the limb, is

β = 1

2tan−1(2ωL/A12). (20)

The Hanle effect is most useful for determining the strength, B, and the componentalong the LOS of the magnetic field when (ωL/A12) ≈ 1. Therefore, the bestsensitivity to the Hanle effect occurs at a critical magnetic field strength BHanle,such that

BHanle ≈ 10−7 A12 (21)

where A12 is given in s−1 and BHanle in G. The lower limit of the domain of sensi-tivity of the Hanle effect extends to fields such that B ≥ Bmin ≈ 0.1BHanle (Sahal-Brechot 1981). Table 2 gives the domain of sensitivity of the brightest coronalultraviolet resonance lines.

A simulated measurement is illustrated in Fig. 7 where a magnetic field of 5 Gat the top of a coronal loop lies in a plane that is parallel to the limb tangent. Themagnitude of B is best determined from a measurement of the angle of polariza-tion of H I Lyα relative to that of H I Lyβ. In this case, the polarization angle ofH I Lyα will be rotated by 4.6◦ and that of H I Lyβ will be rotated by 17.2◦. If theangles of polarization are measured to an accuracy of ±1◦, then a magnetic fieldof 5 G would be determined with an uncertainty of ±1.5 G (S. Fineschi, personalcommunication).

Additional information on the direction of the field may be obtained from ul-traviolet polarimetric observations interpreted in terms of linear resonance linepolarization modified by the Doppler-dimming effect (Sahal-Brechot et al. 1998;Fineschi 2001).


Fig. 8 Diagram of the rocket Lyman alpha coronagraph (Kohl, Reeves, & Kirkham 1978)

3 The ultraviolet coronagraph spectrometer design

3.1 Overview

A suitable ultraviolet coronagraph spectrometer design must provide high respon-sivity to allow detection of the weak coronal emission, and it must suppress thestrong solar-disk radiation to less than 10% of the coronal line intensities of inter-est. It must also provide sufficient spatial, spectral, and time resolution.

The basic optical concept for ultraviolet coronagraph spectrometers (seeFig. 8), which has been used for all such instruments to date, was first describedby Kohl et al. (1978). It consists of one or more articulated telescope mirrorsplaced in the shadow created by a linear external occulter, which forms one sideof a rectangular entrance aperture. The mirror is used to image a portion of theextended solar corona onto the entrance slit of an ultraviolet spectrometer. Alinear internal occulter (originally called a secondary occulter), placed near thetelescope mirror, intercepts and removes that solar disk light that is diffractedtoward the mirror by the external occulter, and would otherwise be specularlyreflected through the spectrometer entrance slit. This externally and internallyocculted telescope design provides the stray light suppression at the wavelengthof interest that is needed to observe the relatively faint ultraviolet extendedcorona. Stray solar disk light at wavelengths outside the wavelength of interestis suppressed by a combination of the occulting system, the optical coatings,the dispersive action of the diffraction grating and the wavelength dependentsensitivity of the detector. A sunlight trap intercepts and absorbs solar disk lightthat passes through the entrance aperture, past a series of light baffles and past thetelescope mirror. The spectrometer entrance slit is shielded from the illuminatedsurfaces of the trap by an entrance slit baffle and the telescope mirror.

In the remainder of this section, the ultraviolet coronagraph spectrometer de-sign is described in terms of the UVCS/SOHO instrument (Kohl et al. 1995a).


Fig. 9 Optical layout of the UVCS/SOHO H I Lyα channel. From Kohl et al. (1995a)

An advanced concept developed for future space mission opportunities is also de-scribed.

3.2 Occulted telescope design

The UVCS instrument includes two optical channels with very similar designs. Inan optimized instrument, the primary differences would be in the optical coatingsand perhaps in the surface finish of the mirrors. Figure 9 is an illustration of theoptical layout of the H I Lyα channel. The optical rays are for the case wherethe center line and roll axis of the instrument are pointed at Sun-center. The pri-mary optical components of each occulted telescope are the linear external occul-ter, which comprises one side of the rectangular entrance aperture, the entranceaperture itself, the telescope mirror, the internal occulter, the entrance slit baffle,the spectrometer entrance slit, and the sunlight trap. There are also a series oftelescope baffles and a Sun sensor consisting of four shadow edge sensors. Mech-anisms open and close the door on the entrance aperture, control the orientationof the telescope mirrors in the solar radial direction and control the position ofthe internal occulter, whose optimal location depends on the orientation of themirror. The entrance aperture is rectangular and consists of three knife edges anda serrated edge that acts as the linear external occulter; the knife edges limit thefield of regard and the amount of light entering the instrument. The approximately32′ divergent beam from the solar disk enters the instrument through the entranceaperture, passes through a series of three baffles, and passes by the telescope mir-ror at 1.6 mm from its edge. That light then enters the sunlight trap where it isattenuated.

The telescope mirror was originally intended to be an off-axis section of aparaboloidal mirror, but difficulties in polishing the non-spherical surfaces led toa decision to use spherical mirrors with a focal length of 750 mm. The rectan-gular mirror surface is placed such that the coronal light rays from ρ = 1.2 R�that nearly graze the external occulter edge, impinge upon the edge of the tele-scope mirror that is nearest the shadow line. Hence, rays from ρ = 1.2 R� arefully vignetted and can not be observed. The useful area of the mirror depends onthe observed height in the corona with the practical lowest height with standardpointing for UVCS/SOHO being ρ = 1.5 R�. The mirrors are filled at a height ofρ = 10 R�.

In the original design of a white light coronagraph (Lyot 1939), the telescopemirror was re-imaged and scattered light from the edges of the mirror was blockedby the Lyot stop. This function is accomplished in the ultraviolet coronagraph by


Fig. 10 The field of view of UVCS/SOHO. From Kohl et al. (1995a)

rounding and polishing the edges of the mirror. This approach increases respon-sivity by reducing the number of reflections.

The telescope mirror focuses the coronal light onto the spectrometer entranceslit, which accepts a segment of the coronal image that defines the instantaneousfield of view (see Fig. 10). The mirror is rotated to scan the coronal image acrossthe entrance slit in the solar radial direction. The telescope mirror also images theexternal occulter inside the spectrometer. This results in an out of focus image ofthe external occulter edge in the region of the entrance slit. Most of the solar disklight diffracted and scattered by the external occulter onto the telescope mirror isblocked by the entrance slit jaws.

The purpose of the internal occulter is to intercept that portion of the diffractedand scattered light from the external occulter that would otherwise be specularlyreflected by the telescope mirror through the entrance slit. That light follows thesame path as light rays from the observed radial height that nearly graze theexternal occulter edge. It falls on a narrow rectangular patch of the telescope thatis located at the edge of the portion of the telescope mirror that has access to raysfrom the observed coronal height. As the mirror is rotated to place the image ofother heights on the entrance slit, the internal occulter also must be repositioned.The location of the internal occulter defines the unvignetted aperture for each ob-servation.

The sunlight trap includes two regions that are illuminated by direct solar diskradiation and a dark un-illuminated region. The entrance slit baffle and the tele-scope mirror shield the entrance slit from the illuminated portions of the trap.Baffles separate the regions and a secondary baffle shields the dark region fromlight diffracted by the central baffle. Multiple specular reflections off the low re-flectance surfaces of the trap attenuate the radiation that enters the trap.

The surface finish is the most critical specification of the telescope mirrors. Inan optimized design, it is non-specular scattering off the surfaces of the telescopemirrors that is the primary contributor to scattered light. The origin of this light issolar disk light diffracted off the external occulter. The optical coatings are alsocritical and must be optimized for the wavelengths to be observed by each opticalchannel.


Fig. 11 Isometric display of the imaging properties between the two stigmatic points of theUVCS/SOHO spectrometer

3.3 Spectrometer design

Each channel of an ultraviolet coronagraph spectrometer instrument includes aspectrometer channel that is optimized for spectroscopic measurements in a spe-cific wavelength band. The ideal spectrometer for each channel would have alarge radiometric throughput for the wavelengths of interest, stigmatic imageryover the entrance slit length for the primary spectral lines of that channel, goodimage quality for other spectral lines of interest and a dispersion and detectorpixel size that is compatible with the required spectral and spatial resolution el-ements. It is highly desirable to provide some redundancy in the capability todetect radiation needed to determine the highest priority plasma parameters. Inpractice, compromises must be made. In the case of UVCS/SOHO, the two pri-mary spectral features were H I Lyα and the O VI 103.2/103.7 nm doublet,which are imaged stigmatically in the H I Lyα and O VI channels, respectively(Pernechele et al. 1997). Both ultraviolet channels are capable of detecting H ILyα, which was the only spectral line in the extended corona that had been de-tected and analyzed at the time the instrument was designed. In the O VI chan-nel, a grazing incidence mirror is used to divert and focus the Lyα line onto thedetector.

Each spectrometer channel consists of an entrance slit, a toric diffractiongrating and a crossed delay line detector (see Fig. 11). These components weremounted in a Johnson (1952)–Onaka (1958) configuration. Grating mechanismsallowed the spectrum from each channel to be scanned across its detector. Themaster diffraction grating for the Lyα channel was ruled holographically andthe master grating for the O VI channel was ruled with a conventional me-chanical ruling engine. The original grating rulings were produced on spheri-cal surfaces and the toric surfaces were generated as part of the grating repli-cation process (Huber et al. 1988). The widths of the entrance slits could bevaried in order to select the spectral resolution. A filter could be inserted intoeach optical path to provide an attenuation of 1 × 10−3 at Lyα for solar diskmeasurements. The detectors are two-dimensional photon counting, centroiding,microchannel plate sensors with electronic readout (Siegmund et al. 1994). AKBr coated, low resistance Z stack of microchannel plates provides detection


Fig. 12 Schematic optical diagram of a spectrometer design optimized to measure Thomson-scattered H I Lyα photons, and thus to accurately measure the LOS electron velocity distribution

and amplification, and a multilayer cross delay line anode accomplishes positionreadout.

3.4 Electron temperature channel concept

The UVCS/SOHO Lyα detector included a blocking strip that could be used tointercept the resonantly scattered core of the H I Lyα line and allow observation ofthe much weaker and broader line wings that result from electron scattering in thecorona of chromospheric Lyα. That combined with the good stray light propertiesof the holographically ruled grating allowed a successful attempt to measurethe width of the electron scattered line profile and determine the electron tem-perature. However, stray light in the spectrometer from the resonantly scatteredLyα component together with Fraunhofer diffraction of that light could onlymarginally be removed (Fineschi et al. 1998). Both of these sources of stray lightcan be sufficiently suppressed with the crossed dispersion double spectrographconcept shown in Fig. 12. The spectrometer is fed with an externally and inter-nally occulted ultraviolet telescope with the usual design. A concave grating in thefirst stage forms a spectrally dispersed image of the entrance slit at its focal plane.This grating can be rotated in order to center H I Lyα on this plane. An optical flatmirror is located in the first stage focal plane. It has a hole in it that passes the im-aged line core into a light trap. The mirror acts as the entrance slit for the secondstage, directing the radiation from outside the line core image to the second stagegrating, which has its dispersion direction perpendicular to that of the first stage.At the first dispersion focus, the line wing will include the dispersed electronscattered radiation, but it will also include grating scattered stray light, whichis dominated by wavelengths of the line core, and the wings of the Fraunhofer


Fig. 13 Concept for an in-line extreme ultraviolet (EUV) polarimeter design

diffracted profile resulting from the finite aperture. The Fraunhofer diffracted lightis also dominated by the wavelengths of the bright core. This line core radiationthat enters the second stage is imaged by the second grating onto a horizontal lineon the detector, while the electron-scattered photons that are used to determine thevelocity distribution of the electrons are dispersed vertically and lie on a diagonalline on the detector (see Fig. 12). This separates the electron-scattered photonsfrom the unwanted photons and allows the electron scattered line profile to bemeasured.

3.5 Extreme ultraviolet polarizer concepts

The depolarization of resonantly scattered H I Lyα and Lyβ radiation and thechange in the angle of polarization for these two spectral lines due to precessionof the hydrogen atom’s magnetic moment about the magnetic field during thelifetime of the excited state (see Sect. 2.2.6), provides a means to measure the localmagnetic field (Hanle 1924; Fineschi & Habbal 1995). There are two approachesto the instrumentation needed for this measurement. One possibility is to introducethree reflective optics (see Fig. 13) in the light path of the spectrometer channelused for this radiation. Two of the reflections serve to direct the radiation along thenominal optical path and the third is a polarization sensitive element consisting ofa single reflecting surface placed at the Brewster angle with respect to the incidentbeam (Samson 1967; Hunter 1978). The device is to be rotated about the opticalaxis in order to pass plane polarized components of the original beam. Care mustbe taken to keep the spectral line of interest in acceptable focus when this deviceis inserted in the optical path.

Another approach is to place a polarizer device near the spectrometer focalplane (see Fig. 14). A focal plane mask selects the spatial/spectral element ofinterest. Polarizations of the H I Lyman series lines are individually directed to thepolarizer by selecting the grating orientation. The polarizer comprises the maskand a polarizer and detector that rotate together. The polarization sensitive elementis a single reflecting surface at the Brewster angle. The radiation at the detectorcovers a blur circle, and so only one spatial/spectral element can be examined ata time. The detector could consist of a stack of microchannel plates with a KBrphotocathode and a discrete anode array in a “bull’s eye” pattern.

3.6 Large aperture ultraviolet coronagraph spectrometer concept

The spatial resolution in the radial direction and the effective area are severelylimited in ultraviolet coronagraph spectrometers such as UVCS/SOHO. For ex-


ample, the 1.8 m separation between its external occulter and its telescope mir-rors, together with the need to further occult with the internal occulter, results inan unvignetted telescope width of 0.8 mm when observing at ρ = 1.5 R�. Thislimitation can be greatly improved with a remote external occulter supported byan extendable boom. Space qualified booms of 13 m and longer are available thatcan provide 14.7 m separation between the linear external occulter and the tele-scope mirrors. This arrangement provides an unvignetted mirror width of 27 mmfor observations at ρ = 1.5 R�. This advantage together with improvements inmirror reflections and detector sensitivity provide the gain in effective area shownin Fig. 15. A mechanism is required to translate and rotate the external occulterin order to align the occulted telescope system. The basic optical arrangement issimilar to that of UVCS/SOHO and the earlier instruments, but in this case themirrors are positioned so that coronal light from ρ = 1.1 R�, which passes by theexternal occulter, just reaches the outer edges of the mirrors. A spacecraft conceptthat accommodates a large aperture ultraviolet coronagraph spectrometer and alarge aperture visible coronagraph is shown in Fig. 16.

Fig. 14 Concept for a focal-plane EUV polarimeter design

Fig. 15 Ratio of efficiencies of an advanced large-aperture ultraviolet coronagraph spectrometerto those of UVCS/SOHO for observations with the same spatial and spectral resolutions at H ILyα and O VI 103.2 nm


Fig. 16 Spacecraft concept for advanced large-aperture coronagraphs. The inset shows a dia-gram of an advanced ultraviolet coronagraph spectrometer

4 History of ultraviolet spectroscopy of the extended solar corona

4.1 Rocket Lyman alpha coronagraph spectrometer investigation

4.1.1 Rocket flights

A rocket-borne ultraviolet coronagraph spectrometer of the Harvard-SmithsonianCenter for Astrophysics was flown jointly with a white light coronagraph of theHigh Altitude Observatory on Nike boosted Black Brant V sounding rockets fora series of three suborbital flights. The primary purpose was to demonstrate thefeasibility of ultraviolet spectroscopic observations of the extended corona in theabsence of a natural solar eclipse. These flights verified the design and perfor-mance of the ultraviolet instrument in space including stray light suppression, anddemonstrated that potential peripheral problems such as particulate contaminationwere overcome. Basic ultraviolet coronagraphic/spectroscopic observing tech-niques were developed, tested, and verified.

The observational goals for the joint payload were to obtain H I Lyα intensitiesand spectral line profiles that were spatially co-registered with values of broadbandvisible polarized radiance at projected heliocentric heights (ρ), from 1.5 to 3.5 R�.These observations were to be made in coronal streamers, coronal holes, and quietcoronal regions. Ultraviolet spatial and spectral resolution elements for the firsttwo flights were 0.6′ (radial) × 4.0′ (parallel to the limb tangent) and 0.034 nm,respectively, as determined by laboratory calibrations before and after the rocketflights. Absolute radiometric calibrations for H I Lyα were made before and aftereach flight. The spatial resolution element was increased to 5.0′ for the third flight.

The launch for the first flight was from White Sands Missile Range in NewMexico on 13 April 1979, which was about one year prior to solar maximum. Thespecific objective of this flight was to measure H I Lyα spectral line profiles inboth low intensity and higher intensity coronal structures over as large a range ofheights as practicable and evaluate the instrument design and performance. Con-


Fig. 17 Empirical proton temperature derived from H I Lyα line widths (solid line), and temper-atures determined from EUV emission gradients by Mariska & Withbroe (1978) (dashed line)and from Fe XIV line widths by Liebenberg et al. (1975) (points). From Withbroe et al. (1982a)

sequently, shorter integration times were used than for the later flights. The ultra-violet coronagraph spectrometer performed flawlessly, measuring H I Lyα profilesat ρ = 1.5, 1.8, 2.0, 2.5, 3.0, and 3.5 R� in a quiet coronal region and at 1.5, 1.8,and 2.0 R� in a coronal hole at the south solar pole. In addition, measurementsmade in a coronal hole at ρ = 3.5 R� indicated that the stray light level was morethan a factor of ten below the measured coronal intensities and in agreement withlaboratory stray light tests (Kohl et al. 1980). The second flight occurred on 16February 1980 about 6.5 hours prior to a natural solar eclipse in India. The targetfor this flight, near solar maximum, was a coronal hole located near the south solarpole. H I Lyα profiles were measured at ρ = 1.5, 2.5, and 3.0 R�. The third flighton 20 July 1982 measured H I Lyα profiles at ρ = 1.5, 2.0, and 3.5 R� along aradial line at a position angle of 5◦ east of heliographic north in a coronal hole.Measurements were also made near the boundary between the hole and a helmetstreamer.

4.1.2 Primary scientific results from the rocket flights

Withbroe et al. (1982a) analyzed observations from the 1979 rocket flight. Imagesof the visible corona from the companion white light coronagraph and a whitelight image of the 26 February 1979 natural eclipse, which occurred about 1.5 so-lar rotations later, indicated that observations along one of the observed radial lineswere made in a quiet coronal region (i.e., a region without an obvious streamer oran underlying coronal hole). Care was taken to remove the effects of geocoro-nal emission and absorption with a geocoronal model, which was consistent with


Fig. 18 H I Lyα intensity as a function of ρ. The points are the observed values, and the linesgive values calculated for models with different solar wind particle fluxes that are parameterizedhere by the wind velocity at r = 4 R�. From Withbroe et al. (1982a)

observations at ρ = 3.5 R� in a coronal hole where geocoronal emission was ex-pected to dominate. A spherically symmetric coronal model was used to accountfor temperature and density variations along the line of sight (LOS) and provideinformation about the heights of formation of the line profiles. The results of theline profile analysis are provided in Fig. 17. Coronal hydrogen kinetic temper-atures, which are expected to be equal to proton temperatures because of rapidcharge transfer collisions, were found to decline fairly rapidly with height imply-ing that the heating of protons in quiet coronal regions over the observed rangeof heights was not large. Fe XIV kinetic temperatures derived from line profilesat 530.3 nm by Liebenberg et al. (1975), and temperatures derived by Mariska &Withbroe (1978) from Skylab extreme ultraviolet (EUV) emission gradients, bothfrom similar quiet coronal regions, are also shown. The agreement between theFe XIV and proton kinetic temperatures was surprising since one might expecta relatively large non-thermal contribution to the Fe XIV profiles. The tempera-tures derived from emission gradients depend on ionization balance and shouldrepresent the electron temperature, which was expected to be near the proton tem-perature in the low corona. The authors concluded that the three sets of data areconsistent with the proton temperature passing through a maximum at r = 1.5 R�in quiet coronal regions.

A Doppler dimming analysis of the quiet Sun observations from the first flightindicated that proton outflow velocities were subsonic out to at least r = 4 R�.Fig. 18 is a plot of the observed H I Lyα line intensities versus ρ. The curvesrepresent modeled values with different solar wind particle fluxes that are param-eterized according to the solar wind velocity at r = 4 R�. The models used anelectron density model of Allen (1963) with Te = T0(r/r0)

−0.3 and the variation


Table 3 Empirical hydrogen temperatures from the 1980 rocket flight

ρ (R�) 〈r〉 Vrmsa(km s−1) Tkin,H(K) Tkin,H

b(K)

1.5 1.6 142 ± 5 1.22 × 106 1.20 × 106

2.5 2.8 111 ± 13 0.75 × 106 0.70 × 106

3.0 3.4 108 ± 13 0.71 × 106 0.63 × 106

3.5 4.0 106 ± 15 0.68 × 106 0.57 × 106

a Vrms = (2kTkin,H/mH)1/2, assuming Tkin,H at distance 〈r〉 is the same in all directions perpendicularto radius vector.b Hydrogen kinetic temperatures corrected for effects of outflow (see Withbroe et al. 1985).

Fig. 19 A comparison of measured (points) and calculated (curves) H I Lyα intensities as afunction of projected distance from the Sun. The curves give values calculated for models withdifferent solar wind fluxes parameterized here by the wind velocity at r = 4 R�. From Withbroeet al. (1982b)

of flow velocity with radius was specified by the conservation of particle flux.The curves for u(4 R�) < 85 km s−1 give good agreement with the observations.These models correspond to particle fluxes < 2 × 1035 particles s−1 in agreementwith typical values of 1 to 2 × 1035 particles s−1 from in situ measurements nearthe Earth.

Analysis of the data from the 1980 flight concentrated on the coronal holeobservations (Withbroe et al. 1982b, 1985). Table 3 provides information aboutthe hydrogen/proton r.m.s. velocities caused by a combination of thermal motions,turbulence, waves and bulk flow velocities. The value of ρ is given in the firstcolumn and the mean height of formation is provided in the second column. Thefourth column provides the kinetic temperature, which is determined directly fromthe line width. The fifth column provides the kinetic temperature after removalof the contribution from the component of the outflow velocity along the LOS.Outflow velocities were determined from a Doppler dimming analysis. Figure 19


Fig. 20 Predicted LOS intensities (solid curves) vs. outflow velocity at ρ = 2.0 R�. Dashedcurves on either side are ±1σ uncertainties in the model. Horizontal lines indicate measuredLOS (solid line) and ±1σ uncertainties (dashed lines). Upper and lower limits for predictedoutflow velocity at ρ = 2.0 R� are shown along with the best value. From Strachan et al. (1993)

shows observed intensities and modeled intensities for outflow velocities from 0.0to 300 km s−1 at r = 4 R�. The data are most consistent with a flow in which thevelocity increased with radius to a value of ∼100 km s−1 at 4 R�. Given that thesound speed for a corona with Te = 1 to 1.5 × 106 K is 130 to 160 km s−1, theobservations suggested that the proton outflow speed was subsonic for r < 4 R�for the observed polar coronal hole at solar maximum.

The first clear evidence of proton supersonic outflow velocities within r =4 R� came from a Doppler dimming analysis of the polar coronal hole observedon 20 July 1982 (Kohl et al. 1984; Strachan 1990; Strachan et al. 1993). Atr = 2 R� electron densities were found to be about 33% of those in the polarcoronal hole observed in 1980 (see Withbroe et al. 1986; Strachan et al. 1993),but comparable to those measured in other polar coronal holes observed at solarminimum (Guhathakurta & Holzer 1994; Fisher & Guhathakurta 1995). The pro-ton radial outflow velocity at ρ = 2 R� was determined to be 217 km s−1 with anuncertainty range of 153 to 251 km s−1 at a confidence level of 67% (see Fig. 20).This value for the outflow speed was two standard deviations of uncertainty abovethe calculated sound speed (146 km s−1) at the observed height. The wavelengthshift of the line center corresponded to a LOS velocity of 37 km s−1, which wouldbe expected if the coronal hole were tilted 9◦ away from the observer. He I 1083nm data (Coffey 1982) indicated that most of the coronal hole base was behindthe limb.

Although the Strachan et al. (1993) values for radial outflow velocity wereindependent of the assumed flux tube divergence model, divergence parameterswere inferred by requiring a single Doppler dimming model to be consistent withobserved intensities at all observed heights. The best-fit to the Kopp and Holzerdivergence model (Kopp & Holzer 1976) resulted in fmax = 7 with rm = 1.0, σ =0.9 and A(r0) ≈ π R2�, where A(r) is the cross-sectional area of the flow tube,A(r0) is its value at the coronal base, and fmax A(r0)(r/r0)

2 is its asymptotic value;


the superradial growth of A(r) occurs between rm − σ and rm + σ . Extrapolationof the flux density from 2 R� (where the uncertainties are smallest) to 1 AU withthese divergence parameters predicts a proton flux density of 1.42×108 cm−2 s−1

at 1 AU.The analysis assumed that the coronal H I Lyα absorption line profile in the

approximately radial direction was identical to the coronal profile observed alongthe LOS, which was approximately in the perpendicular direction. A test of thatassumption, which also depends on the accuracy of the other plasma parametersused in the coronal model, is to extrapolate the particle flux to 1 AU and compareit to in situ data. Although such a comparison was not possible at the time of theStrachan et al. (1993) publication, measurements with the SWOOPS instrumenton the ESA/NASA Ulysses spacecraft, between 13 September 1994 and 31 July1995, determined the particle flux densities at 1 AU for high latitudes above polarcoronal holes to be in the range from about 1.4×108 cm−2 s−1 to about 2.6×108

cm−2 s−1 (e.g., Goldstein et al. 1996) in reasonable agreement with the valuederived from the rocket Doppler dimming measurements of the large polar coronalhole observed in 1982. This level of uncertainty allows for some anisotropy inthe H I Lyα velocity distribution, but it tends to confirm the Doppler dimmingdeterminations of supersonic outflow speed at ρ = 2.0 R�.

4.2 Spartan 201 ultraviolet coronal spectrometer investigation

4.2.1 Spartan 201 flights

The Spartan 201 scientific payload consisted of an ultraviolet coronal spec-trometer (UVCS/Spartan) of the Harvard-Smithsonian Center for Astrophysicsand a white light coronagraph (WLC) of the High Altitude Observatory and ofthe Goddard Space Flight Center. The instruments were similar to those flowntogether on three sounding rocket flights, but they had refinements that tookadvantage of Spartan’s 40 hour observing period. The two instruments wereco-aligned and housed in the pre-evacuated instrument carrier of the Spartan201 service module. The service module provided on-board data storage, power,thermal control, attitude control and an observing program sequencer. Spartan201 was carried into orbit by NASA’s Space Transportation System (STS), anddeployed from the Orbiter’s cargo bay. For each flight, it spent about 27 orbits inan autonomous detached mode before it was recovered and returned to the groundfor data retrieval, post-flight calibration and preparation for reflight.

Spartan 201 was deployed successfully during four STS missions. Coronalregions of interest were selected by orienting the ultraviolet instrument’s telescopemirrors and by rolling the spacecraft to look at selected position angles. Provisionfor storing and executing observing sequences for four coronal targets wereimplemented in the UVCS/Spartan flight software, which controlled the observ-ing configurations of the instrument. While the exposure times and instrumentsettings were decided in advance, the roll of the spacecraft was not decided untila few hours before Spartan 201 was deployed. Target selection was based on solarimages from a combination of ground based and space based telescopes. The pro-cedure to select the first target position angle about the Sun used the Orbiter’s re-mote manipulator system to fix the Spartan orientation with respect to the Orbiter,


and a maneuver to select the orientation of the Orbiter at the time of Spartan’srelease. The other position angles were selected according to three Spartan rollmaneuver parameters that were placed into the memory of the Spartan attitudecontrol system by a crew member prior to deployment. The coronal images andultraviolet spectral data were recorded onboard for later analysis on the ground.

Spartan had a much longer observation period than sounding rocket flights,and it provided opportunities for both preflight and post-flight characterizationsand calibrations, thus determining in-flight performance with high reliability.Also, its reusability allowed the instruments to be employed on several differ-ent occasions. The 40 hours of observations during the STS-56 mission in 1993provided for a much more extensive application of H I Lyα spectroscopy in theextended solar corona than had been possible with the combined 15 minutes of ob-servations afforded by the three sounding rocket flights. Spartan 201 flights duringthe STS-64 and STS-69 missions in 1994 and 1995, respectively, were coordinatedwith the passes of the Ulysses spacecraft over the south and north solar poles. Thefinal flight, which occurred during the STS-95 mission, was used to update theradiometric calibration of UVCS/SOHO and intercompare the spectrometric andstray light characterizations of the two instruments.

The primary observational goals of the Spartan flights were to obtain H I Lyαintensities and spectral line profiles with the ultraviolet coronal spectrometer andto obtain spatially co-registered broadband visible polarization brightness (pB)measurements with the WLC. The ultraviolet measurements were made over aheight range of ρ = 1.5–3.5 R�. The primary ultraviolet spatial resolution ele-ment was 0.5′ (radial) × 2.5′ (parallel to the limb tangent), and the spectral res-olution elements had a FWHM of 0.037 nm as determined by laboratory mea-surements of the instrument profile. Absolute radiometric calibrations were madebefore and after each flight. The discrete anode microchannel array detector pro-vided simultaneous measurements for 48 pixels with 0.025 nm resolution elementsin the spectral direction.

In addition to coronal measurements, there were center to limb scans (from–8.0′ to the limb) of the H I Lyα disk profile and there were measurements of theH I Lyα geocorona at five orientations between 95◦ and 160◦ from the Sun-centerdirection. Background measurements were made while the instruments were inthe Earth’s umbra and facing the Earth. For these measurements, data were ac-cumulated with two very different unvignetted areas of the ultraviolet telescopemirrors in order to distinguish between the light signal and instrument inducedbackground.

In addition, initial attempts were made to detect emission at the observedheights from N V 123.8 nm, Fe XII 124.2 nm, and the O VI doublet at 103.2 and103.7 nm. The spatial resolution elements for N V and Fe XII were 4.0′ (radial)by 5.0′ (parallel to the limb tangent), and were 2.5′ (radial) for O VI.

Spartan 201-1 was deployed from the Space Shuttle on 11 April 1993 andcarried out about 40 hours of observations. The four primary targets were thenorth polar corona, the south polar corona, a helmet streamer at position angle135◦ and an active region above the west limb. Figure 21 indicates all of thesolar spatial elements observed during the mission. Concentrating on the smallestspatial elements, which indicate the H I Lyα profile measurements, it can beseen that the four targets were sampled extensively, but not completely. The mostcomplete coverages were for the helmet streamer and for the south polar region.


Fig. 21 Spatial elements observed by UVCS/Spartan during the Spartan 201-1 mission are il-lustrated. At any instant, the instrument observed three spatial elements (e.g., the group of threerectangles at the extreme top of the figure). The smallest and largest rectangles are, respectively,for observation of the line profile and integrated line intensity of H I Lyα, and the intermediatesized one is for the intensity of O VI lines. Telescope motions are used to vary the heliocentricheight and the entire spacecraft is rotated to vary the position angle. Also shown are an X-rayimage of the solar disk from the Yohkoh Soft X-ray Telescope (SXT) and a white-light imagefrom the Mark III coronagraph of the Mauna Loa Solar Observatory (MLSO)

Observations by the Spartan WLC indicated that the north and south polar regionswere coronal holes with substructures consisting of polar plumes extendingoutward to heliocentric heights in excess of 5 R� (Fisher & Guhathakurta 1995).

The evaluation of the in-flight performance was based, in large part, on theobservations at ρ = 3.52 R� in the north polar hole, the geocorona observation at95◦ to the Sun, and the background measurements in the Earth’s umbra. In-flightperformance was also inferred from the preflight and post-flight calibrations. Inthe case of the radiometry, the agreement between preflight and post-flight cali-brations indicated that the instrument retained its sensitivity during the mission.The spectral resolution profile was checked by comparing the FWHM of the ob-served geocoronal H I Lyα dominated observation of a coronal hole at ρ = 3.5 R�to laboratory measurements. The geocoronal profile width is known to be muchsmaller than the instrument profile width (see, e.g., Withbroe et al. 1982b). Laterrefinements of the laboratory instrument profile measurements provided improvedprecision that was needed to analyze the complex shapes of the observed coronalline profiles. An upper limit on the instrumental stray light in-flight was deter-mined from curve fits to the coronal hole observation at ρ = 3.52 R�. Sincethe stray light has the spectral profile of chromospheric H I Lyα, it was apparent


Fig. 22 Spatial elements observed by UVCS/Spartan during the Spartan 201-2 mission aresuperimposed on solar images from Yohkoh/SXT and the MLSO/Mark III (see caption ofFig. 21)

that the stray light level was well below the integrated intensity of the geocoro-nal emission. The average background rate per pixel was determined to be about0.013 counts per second. Detector pixel to pixel cross talk and flat field variationswere measured in the laboratory before and following the flights.

Spartan 201-2 was deployed on 13 September 1994 and retrieved on 15September after about 47 hours of observations. Four coronal targets were se-lected for observation including the north and south polar coronal holes and twostreamer regions (see Fig. 22). The primary target was the south polar coronalhole which produced the fast solar wind streams sampled by Ulysses at 80◦ he-liographic latitude and 2 AU from the Sun. No distinct and clearly isolated hel-met streamers were seen in the preflight planning images, and so the H I Lyαprofile slits were placed on the regions of maximum visible light brightness in thestreamer belt. Those observations covered active region streamers and possibly anequatorial coronal hole located near the west limb. The instrument performancewas nominal.

Spartan 201-3 was deployed on 8 September 1995 and retrieved on 10 Septem-ber 1995. Observations were made during 25 orbits. The final two planned or-bits were lost when an “End-of-Mission” command was issued by the spacecraft.The observing program was designed to optimize the coordinated science datato be obtained during the Ulysses north polar passage. The two coronal hole tar-get sequences were both placed in the north polar coronal hole to give a morecomplete coverage spanning from the center of the coronal hole to its easternedge (see Fig. 23). There were two streamer target sequences lasting for four or-bits each. Observations of H I Lyα were made at several locations on the solar


Fig. 23 Spatial elements observed by UVCS/Spartan during the Spartan 201-3 mission aresuperimposed on solar images from Yohkoh/SXT and the MLSO/Mark III (see caption ofFig. 21)

disk in order to characterize the input source for resonant scattering. Observationsof the geocorona were made while Spartan 201 was in the Earth’s umbra withUVCS/Spartan pointed 95◦, 110◦, 140◦, 150◦, and 160◦ away from the Sun. Theinstrument performance was nominal.

Spartan 201-4 was deployed on 21 November 1997. The spacecraft failed toexecute a scheduled pirouette maneuver several minutes after release, suggestingthere was a problem with the attitude control system. After a plan was formulatedto retrieve the spacecraft, two astronauts captured Spartan 201 by hand during anearly eight-hour duration activity outside the pressurized compartments of theOrbiter. The scientific instruments were not activated during this mission.

Spartan 201-5 was deployed on 1 November 1998 and retrieved on 3 Novem-ber 1998. Observations were carried out during a 38 hour time interval. UVCS/Spartan was used to update the calibration of UVCS/SOHO and also provideinformation on the physical conditions of the solar corona during the rising phaseof the solar activity cycle. The cross-calibration also provided continuity betweenthe earlier results of Spartan 201 and the later results from SOHO. Preplannedobservational sequences were designed for four primary coronal targets (seeFig. 24). The first target was a coronal streamer above the northeast limb of theSun. H I Lyα profiles and intensities were measured at ρ = 1.7 and 2.1 R� onthe streamer axis. The second target was a coronal streamer above the southwestlimb. Measurements of the H I Lyα profile were made along the streamer axisat ρ = 1.7, 2.1, 2.5, 3.0, and 3.5 R�. Target three was the north polar coronalhole. Observations were made near the axis of the coronal hole at ρ = 1.7, 1.8,


Fig. 24 Spatial elements observed by UVCS/Spartan during the Spartan 201-5 mission are su-perimposed on an EIT/SOHO Fe XII 19.5 nm image of the solar disk and a UVCS/SOHO O VI103.2 nm image of the extended corona (see also the caption of Fig. 21)

1.9, 2.1, 2.5, 3.0, and 3.5 R�. The final coronal target was the south polar coronalhole, which was observed at a single height (ρ = 1.7 R�). In addition to theobservations of the solar corona, there were solar disk observations made in twoorbits and background/geocoronal measurements made during the night timeportions of each orbit. The instrument performance was nominal.

4.2.2 Primary scientific results from the Spartan 201 ultravioletcoronal spectrometer

Perhaps the greatest benefit from the Spartan 201 flights was the ground work itprovided for the UVCS/SOHO investigation. Spartan 201 provided experience inplanning ultraviolet spectroscopic observations of the extended corona includingestimates of count rates, it provided opportunities for extensive application ofspectroscopic diagnostic techniques that would be used to analyze UVCS/SOHOobservations and it provided additional verification of the basic ultravioletcoronagraph spectrometer design and characteristics, which formed the basis ofthe UVCS/SOHO optical design. The Spartan 201 experience enabled a rapid sci-entific interpretation of the UVCS/SOHO observations and rapid presentation andpublication of the results. This led to a resurgence in theoretical investigations ofenergy deposition and solar wind acceleration in the extended corona with an em-phasis on the role of minor ions and ion cyclotron resonant waves (see Sect. 5.2.4).

However, the UVCS/Spartan, together with WLC/Spartan, made several im-portant discoveries that were later confirmed and amplified by UVCS/SOHO.Those discoveries are described in the remainder of this section.

Detailed knowledge of the instrument resolution profile is of critical impor-tance in the interpretation of the observations. The original laboratory measure-ments of the instrument profile were ultimately found to be unsatisfactory foranalyzing the observed H I Lyα profiles with high confidence. The interpretationwas particularly sensitive to the FWHM of the narrow instrument-profile core,


and was also highly sensitive to the profile wings. This became apparent duringthe Spartan 201-5 flight when simultaneous H I Lyα observations were made withboth UVCS/Spartan and UVCS/SOHO. Nonetheless, the early publications of theSpartan 201 results were essentially correct and therefore will be included here. Ahigh precision measurement of the instrument profile for UVCS/Spartan and theanalysis of the simultaneous and nearly co-spatial Spartan 201 and UVCS/SOHOobservations are described in Sect. 4.2.3.

The initial results for Spartan 201-1 concentrated on observations of the northpolar coronal hole (Kohl et al. 1994). The WLC/Spartan indicated that this coronalhole was centered at a position angle of 0◦ and extended from −40◦ to +40◦. Itappeared to have a substructure consisting of polar plumes or rays, which extendedoutward along nearly radial lines (Fisher & Guhathakurta 1995). One H I Lyαmeasurement at ρ = 2.13 R� was at a position angle of −8◦. The analysis as-sumed that the line profiles only depended on the velocity distribution of neutralhydrogen along the LOS, and ignored effects of resonant scattering on the lineshapes because they were known to be small (Withbroe et al. 1982b). The pur-pose of this initial analysis was to provide an indication of data quality, but it alsoprovided some interesting discoveries about the profile shapes. While the Dopplerdimming analysis of the H I Lyα intensities from the rocket observations had pro-vided startling information about the height in the coronal holes where the solarwind reached supersonic velocities, the statistical accuracy of the line profiles lim-ited the rocket observations to determinations of the apparent FWHM.

The Spartan 201-1 observation at ρ = 2.13 R� in the north polar coronal holeappeared to consist of at least three components. The H I Lyα emission and ab-sorption in the Earth’s outer atmosphere was treated as one component. Since theintrinsic line profile of this geocoronal emission/absorption is extremely narrow,its observed contribution was assumed to have the shape of the instrument reso-lution profile. It was found that the remaining profile, after the geocorona contri-bution was removed, could not be fit satisfactorily with a single Gaussian shapedcurve such as that to be expected for a purely thermal velocity distribution. It ap-peared instead that the coronal profile consisted of a narrow component with a halfwidth at 1/e of 0.04 nm, which corresponds to a kinetic temperature of 5.8×105 Kand a broader component with a half width at 1/e of 0.091 nm, which correspondsto a kinetic temperature of 3.0 × 106 K. It was known at the time that the coronalH I Lyα line profile at this observed height should be representative of the protonvelocity distribution as well as the neutral hydrogen velocity distribution. This isbecause charge transfer between neutral hydrogen and protons is much faster thanany process that would change their velocity distribution (Withbroe et al. 1982b).Hence, this was the first indication that some region in the extended corona has aproton kinetic temperature that is much higher than that of the electrons.

Four explanations for the complex line shapes were described at the time. Onepossibility was that one of the coronal components results from a foreground orbackground structure and the other from the coronal hole. Another explanationwas that the polar plumes or rays observed by WLC/Spartan may be the source ofeither the narrow or wide component. It was also possible that waves propagatethrough the corona and across the LOS. The waves might occupy some fractionof the LOS leaving the rest as undisturbed corona. Transverse wave velocitiescould then account for the broad components. There were several possibilities


Fig. 25 The H I Lyα profile derived from the difference between the coronal profiles observedby Spartan 201-1 in a line of sight that included a polar plume and an interplume region. Thesolid points are the differences and have ±1σ statistical uncertainties. The curves represent atwo-component fit to the data with two Gaussian curves. The narrow and broad componentshave 1/e widths of 0.049 and 0.120 nm, respectively. From Kohl et al. (1995b)

for accounting for the complex shapes with a single distribution. For example,one could envision a coronal hole with a flow geometry that is highly nonradialwith a bulk outflow velocity from the near side of the coronal hole that flowsnearly directly at the observer, while that from the other side flows nearly directlyaway. Another explanation was a highly non-Maxwellian velocity distribution ina predominantly single component plasma. Models of the latter type had beendescribed by Scudder (1992).

The first indication that polar plumes or rays have H I Lyα profiles that are nar-rower than those of the interplume regions of coronal holes resulted from an anal-ysis of the H I Lyα profile observed in the south polar coronal hole at a positionangle of 209◦ and ρ = 1.8 R� (Kohl et al. 1995b). It was observed that the H I Lyαintensity was particularly high at that position angle and appeared to correspondto the location of one of the polar plumes or rays observed in visible light. Obser-vations for that height at other position angles (e.g., 199◦) had lower intensitiesand appeared to fall between the observed plume or ray structures. After removalof the geocoronal contribution, the remaining profile for the 199◦ position anglewas subtracted from the profile from 209◦ (see Fig. 25).

The authors assumed that the coronal hole contribution to the profile at 209◦was identical to the profile observed at 199◦, that the geometry of the coronal holealong both lines of sight were the same, and that the plume occupied a negligiblefraction of the coronal hole along the LOS. Within those assumptions, the authorsattributed the difference profile to the plume. The difference profile was foundto have a complex shape with enhanced wings over a Gaussian profile. Treating


the difference profile as a single component, the r.m.s. velocity was found to be137 km s−1. The profile for the interplume region at 199◦ had an r.m.s. velocityof 150 km s−1. Hence, the authors concluded that the observed polar plume atρ = 1.8 R� is cooler than the interplume region of the coronal hole or has smallernon-thermal velocities.

A more extensive analysis of the Spartan 201-1 polar observations wasreported by Kohl et al. (1996a). The geocoronal component was assumed to bea Gaussian with the FWHM of the instrument resolution profile. As will be seenin Sect. 4.2.3, the curve fits to the Spartan 201-1 observations were affected bythe differences between the high-precision instrument profile and the assumedinstrument profile, but the basic conclusions were not changed. The line centerof the observation at ρ = 3.52 R� together with knowledge of the spacecraftvelocity provided an absolute wavelength scale.

The observed profiles were fit to three Gaussian curves, one constrained torepresent the geocoronal contribution and the other two representing the coronalcontribution with no constraints on amplitude, width, or central wavelength.

It was clear that the velocity distribution along the LOS in the polar regionswas not a single Gaussian as might be expected for an approximately isothermalLOS. The polar coronal profiles were well fit to two Gaussians. The average bestfit profile widths for the narrower component and the widths for the broader com-ponent for individual polar regions did not vary much with the observed height.To investigate the possibility that foreground and background structures were re-sponsible for the narrow component, the LOS for the observation at ρ = 1.83 R�in the south polar coronal hole was modeled. There was clear evidence in MarkIII coronagraph data from MLSO (Real 1993) that the LOS intersected a streamerarcade in the background at a height of ρ = 3.5 R�, but the streamer arcade didnot appear to be present along the LOS in the foreground. Using Spartan 201-1observations of this streamer at ρ = 3.5 R�, it was determined that the streameraccounted for only half the intensity of the narrow component. The best fit forthe narrow component width and the streamer width at ρ = 3.5 R� were differ-ent by 20%, which was probably within the uncertainty of the curve fits. In anycase, both the widths and the intensities supported the conclusion that a signifi-cant part, but not all, of the narrow component at ρ = 1.83 R� was due to thestreamer. There was no bright streamer observed in the north hemisphere, and soa much smaller contribution from foreground and background features was ex-pected for the observation at ρ = 1.83 R�. This was consistent with the muchsmaller intensity of the narrow component in the north. Although this analysisaccounted for some of the narrow component intensity with foreground and back-ground structures, it did not rule out the possibility that at least some of the nar-row component came from substructures in the coronal hole or that the velocitydistribution along the LOS was not Maxwellian. There was nothing along theLOS, other than the coronal hole, that could account for the intensity of the broadcomponent.

The curve fits also provided a central wavelength for each coronal compo-nent. In the south polar coronal hole, the narrow profile components showed smallline shifts corresponding to small LOS flow velocities that were probably not dis-tinct from zero within the uncertainties. The small expected outflow speeds in thestreamer were consistent with the idea that a major fraction of the narrow com-


ponents was due to the streamer. The broad components had positive line shiftsthat increased steadily with height. This is consistent with the south polar coro-nal hole being tipped slightly away from the observer, and having an increasingoutflow speed with height. The broad components for the north polar region hadsmall shifts indicating that the coronal hole is centered on the plane of the sky andis fairly symmetric. Interestingly, the line shifts for the narrow components in thenorth corresponded to velocities of about 27 km s−1 toward the observer, and didnot vary much from ρ = 1.83 to 2.52 R�. Those components accounted for about30% of the observed intensity at each height. Therefore, the narrow components inthe north appeared to have a different source than the broad components attributedto at least some part of the coronal hole (Kohl et al. 1996a).

The work concluded that at least the broad components and perhaps some ofthe narrow components were due to the polar coronal hole. The width of the broadcomponent corresponded to four times the expected H I Lyα width for a protonplasma at the expected electron temperature. Although the broad profile widthswere consistent with the suggestion of McKenzie et al. (1995) that the protonswere preferentially heated by ion cyclotron resonance, transverse proton motionsinduced by non-dissipative waves (Leer 1987) could not be ruled out. Since thegeometry of the outflow velocity was not known with certainty, and since Dopplerdimming determines only the radial outflow, some contribution to the observedprofile width from nonradial outflows was not completely ruled out, although rea-sonable models of the geometry indicated that the contribution was small. Thevelocity filtration model (Scudder 1992), which predicted a non-Maxwellian ve-locity distribution for the protons, also remained a possibility.

Both the south and north polar coronal holes were observed during the Spartan201-2 flight in September 1994 and the north polar coronal hole was observed dur-ing the Spartan 201-3 flight in September 1995. Dobrzycka et al. (1999) reportedthat the coronal hole profiles for these flights were very similar to the profilesobserved in the north coronal hole during the first flight in April 1993. The onlyexception was that the profile widths at ρ = 1.83 R� may have increased slightly.That may indicate that the kinetic temperature perpendicular to the expected mag-netic field in polar coronal holes increases as we approach solar minimum. Thebroad components for the Spartan curve fits at ρ = 2.1 R� had a similar widthto profiles measured with UVCS/SOHO near solar minimum as fit with a singleGaussian curve (Kohl et al. 1997a, 1997b).

The Spartan 201 flights provided observations of several streamers and bound-aries between streamers and coronal holes. Observations included a streamer in thesoutheast in 1993, a streamer in the northeast in 1994, a streamer in the southwestin 1995 and their respective boundaries with neighboring coronal holes.

The 1993 streamer appeared to be well isolated. Observations with the MarkIII coronagraph of MLSO indicated the presence of a streamer near the plane ofthe sky with the same approximate latitude for at least a half-rotation before andafter the Spartan 201 observations. It appeared that the streamer nearly encircledthe Sun, and was shaped like an archway along an observed neutral line that ex-tended from Carrington longitude −180◦ to +30◦ (Real 1993). Spartan 201 whitelight images (Fisher & Guhathakurta 1995) indicated that the streamer was not ra-dial. The geocoronal contribution was removed by curve fitting two Gaussians tothe observed profile. The Gaussian representing the geocoronal contribution was


Table 4 Proton kinetic temperatures in streamers

Heliocentric Tkin (MK) Tkin (MK) Tkin (MK)height (R�) (Spartan 201-1) (UVCS, Oct. 1996) (UVCS, Feb. 1997)

1.5 2.6 2.0 –1.8 2.9 2.2 2.02.1 3.2 2.3 1.92.5 3.0 2.1 1.73.0 2.7 1.9 1.63.5 2.2 1.7 1.54.0 – 1.7 1.44.5 – 1.5 1.4

assumed to have the shape of the instrument profile. The streamer kinetic temper-ature versus height was derived from the 1/e half width of the wider componentprofile using the Doppler broadening expressions given in Sect. 2. The kinetic tem-peratures versus heliocentric height are shown in Table 4 (Strachan et al. 1994).Also shown in Table 4 are kinetic temperatures derived from helmet streamer ob-servations by UVCS/SOHO in 1996 and 1997 (Kohl et al. 1997a).

Strachan et al. (1994) pointed out that the H I Lyα profile widths observed bySpartan 201-1 were nearly constant with height, but the derived kinetic temper-ature did rise to a slight peak at ρ = 2.1 R� and then decreased slightly towardlarger heights. A similar behavior can be seen in the UVCS/SOHO observationsfrom October 1996. However, the SOHO observations from February 1997 showa small but steady decline from ρ = 1.6 R� to 8 R�.

The 1994 streamer observed by Spartan 201-2 seemed to be a combinationof an active region and a quiescent streamer or streamers. Multiple streamer axeswere present in both the 1994 streamer and the 1995 streamer observed by Spartan201-3. Transitions from the streamers observed by Spartan to the neighboringcoronal holes could be seen in the observations from all three flights, but thetransition was clearest in the 1993 data. In those data, the H I Lyα intensity atρ = 1.8 R� dropped by a factor of 31.6 from the center of the helmet structureto the boundary with the south polar coronal hole. For each observed height, anintensity minimum was found between position angles 132◦ and 157◦ near theboundary between the streamer and the south coronal hole (Miralles et al. 1999).The minimum appeared to be outside the streamer edge as observed in pB byWLC/Spartan. The H I Lyα intensity also appeared to pass through a minimumbetween the streamers and coronal holes observed by Spartan in 1994 and 1995,although the transition was less distinct. Similar intensity minima are present inUVCS/SOHO observations of streamer/coronal hole boundaries taken during so-lar minimum (e.g., Strachan et al. 1997). The minimum in the H I Lyα intensityhas never been fully explained, but it appears to be associated with Doppler dim-ming or the hydrogen ionization balance since no similar minimum is found in thevisible polarization brightness. Reductions in H I Lyα intensity could be due to anincrease in the proton radial outflow speed, a decrease in the proton radial velocitydistribution width, or an increase in the electron temperature, which would reducethe neutral hydrogen population fraction.

In addition to observations of the line profile and absolute intensity of H I Lyα,UVCS/Spartan was designed to measure the intensity of O VI 103.2 and 103.7 nm


and also the intensity of Fe XII 124.2 nm. Spartan 201 detected these spectral linesfor the first time in the extended solar corona outside a natural solar eclipse. Theobservations proved the feasibility of observing these emissions, but the data werenot suitable for detailed analysis.

4.2.3 UVCS/Spartan calibration of UVCS/SOHO and reanalysisof Spartan observations

Spartan 201-5 provided an opportunity to carry out simultaneous and coreg-istered observations of coronal holes and streamers in November 1998 withUVCS/ SOHO and the freshly calibrated UVCS/Spartan. The Spartan 201-5 flightoccurred just after SOHO was recovered from an extended period without ob-servations. At the time of the Spartan 201-5 flight, SOHO was rotated from itsnominal orientation. Since this was not known by the Spartan team, the overlap ofthe Spartan and SOHO observations was not ideal, but enough overlap was presentto allow comparisons of H I Lyα profiles for nearly the same spatial regions.

These co-registered observations were used for two purposes. One purposewas to update the UVCS/SOHO radiometric calibration for wavelengths near121.6 nm. The other purpose was to verify that the coronal line profiles extractedfrom observations of the same spatial region by the two instruments agreed withinthe uncertainties after instrumental effects were removed from both observations,and the geocorona contribution to the Spartan observations was taken into account.

A key to removing the instrumental effects was the instrument resolution pro-files. The UVCS/SOHO profile had been measured in the laboratory and also dur-ing the flight using fairly narrow C II profiles from the solar disk (see Sect. 4.3.2).This light was scattered into the spectrometer by the occulted telescope system.Additional in-flight characterization was carried out to describe an effect with thedetectors whereby a small fraction of detected photons were assigned to neigh-boring pixels. This effectively removed photons from the line core and redis-tributed them into the line wing. Data reduction procedures for UVCS/SOHO take

Fig. 26 Spartan 201 instrument resolution profile, normalized to unity at the central peak


Fig. 27 UVCS/Spartan measurement of H I Lyα in a north polar coronal hole at ρ = 3.5 R�on 2 November 1998. The solid points represent the absolute intensity corresponding to thecount rate measured at each detector pixel. The dotted lines denote the coronal and stray lightcomponents. The geocoronal absorption can be seen as the notch in the coronal component. Thesolid line is the combination of the geocoronal emission (not shown) and the other components,all convolved with the instrument resolution profile. The triangles are the modeled intensitiescorresponding to each of the discrete detector pixels

the instrument profile, including the detector effect, into account. In the case ofthe Spartan instrument, the original laboratory measurements did not include thewings of the instrument resolution profile, and the core of the profile was mea-sured with the entrance slit under-filled. This had the effect of under-determiningthe FWHM of the central core of the instrument profile. The UVCS/Spartan reso-lution profile was re-measured after the Spartan 201-5 mission. For this measure-ment, a platinum hollow cathode lamp with extremely narrow intrinsic line widthswas used, and care was taken to illuminate the full width of the entrance slit. Also,the wings of the instrument profile were precisely measured. The resulting instru-ment resolution profile is provided in Fig. 26.

The UVCS/Spartan observation of the north coronal hole at ρ = 3.5 R� isshown in Fig. 27. This profile is dominated by the geocoronal emission. It alsoincludes a small contribution from the coronal hole that has a narrow absorptionfeature due to geocoronal absorption. There is a small component resulting frominstrumental stray light, which has the shape of chromospheric H I Lyα. The curvefitting procedure used the following starting values: geocoronal emission and ab-sorption from a geocoronal model, the nearly co-spatial UVCS/SOHO coronalprofile and laboratory measurements of UVCS/Spartan stray light. The curve fit-ting search was constrained to values within the uncertainty limits of the start-ing values. The fitting procedure combined the test component profiles, appliedthe geocoronal absorption and then attempted to minimize the normalized chi-square by varying the components within the above limits. This analysis of theρ = 3.5 R� observation established the absolute wavelength scale for the mission,the geocoronal emission for the mission, and the stray light level for ρ = 3.5 R�relative to the disk intensity for all Spartan 201 missions.


Fig. 28 UVCS/Spartan measurement of H I Lyα in a southwest streamer at ρ = 2.12 R� on 2November 1998. The lines show the coronal component (solid), geocoronal absorption (dotted),stray light from the solar disk (dot-dashed), and the final convolved profile (dashed line withopen triangles) as compared to the observed data points (solid circles with ±1σ error bars)

The UVCS/Spartan observation of a southwest streamer at ρ = 2.12 R� isshown in Fig. 28 and the comparison to the nearly co-spatial UVCS/SOHO obser-vation is provided in Fig. 29a. The curve fits for this line followed the same pro-cedure used for the coronal hole observation at ρ = 3.5 R�, except the absolutewavelength scale and the geocoronal emission were fixed to the values resultingfrom the ρ = 3.5 R� observation. Since the ρ = 3.5 R� observation was not verysensitive to the geocoronal absorption, which, unlike the geocoronal emission, isnot affected by uncertainties in the disk intensity, it was allowed a small variationfrom the geocoronal model as corrected by the ρ = 3.5 R� analysis. The coronalprofiles from UVCS/SOHO and UVCS/Spartan were found to be in good agree-ment with an identical 1/e half width of 0.062 nm and integrated line intensitiesof 6.8 × 1010 photons s−1 cm−2 sr−1 and 7.4 × 1010 photons s−1 cm−2 sr−1,respectively. Differences in the observed heights together with the radiometriccalibrations and the procedures for removing instrument effects and geocoronaleffects are believed to account for the differences in the derived coronal profiles.

The curve fit to the UVCS/Spartan observation of the north coronal hole atρ = 2.12 R� is provided in Fig. 30. The curve fitting procedure for this line wasthe same as that for the streamer. This profile is more sensitive to stray light thanthe streamer observation. The resulting stray light value was within the uncertaintyrange of the laboratory stray light measurements, and established the stray lightlevel at ρ = 2.12 R� relative to the disk intensity for all the Spartan missions. Un-like the streamer profile at ρ = 2.12 R�, the coronal hole profile at ρ = 2.12 R�was not well fit to a single Gaussian. It was found that the coronal components forboth the UVCS/Spartan and the nearly co-spatial UVCS/SOHO observations weremuch better fit to two Gaussians. The individual narrow and broad components for


Fig. 29 Comparison of UVCS/Spartan and UVCS/SOHO H I Lyα coronal emission profiles for(a) the streamer observation of Fig. 28, and (b) the coronal hole observation of Fig. 30. Bluelines denote Spartan measurements at ρ = 2.12 R� and red lines denote SOHO measurementsat (a) ρ = 2.14 R�, and (b) ρ = 2.18 R�. In the coronal hole, dashed [dotted] lines showindividual broad [narrow] Gaussian components and their sum is a solid line

Fig. 30 UVCS/Spartan measurement of H I Lyα in a north polar coronal hole at ρ = 2.12 R�on 2 November 1998. Line types are described in caption of Fig. 28

the two instruments are in reasonably good agreement as can be seen in Fig. 29b.The broad components have an identical width of 0.095 nm and integrated lineintensities of 2.9 × 109 photons s−1 cm−2 sr−1 and 2.2 × 109 photons s−1 cm−2

sr−1, for SOHO and Spartan respectively. The narrow components have widths of0.045 and 0.044 nm and integrated line intensities of 4.8 × 109 photons s−1 cm−2


Fig. 31 UVCS/Spartan measurement of H I Lyα in a north polar coronal hole at ρ = 2.12 R�on 12 April 1993. Line types are described in caption of Fig. 28

sr−1 and 6.2 × 109 photons s−1 cm−2 sr−1, for SOHO and Spartan respectively.The total coronal line intensities are in agreement to within 9%. This is well withinthe radiometric uncertainties. The differences in the observed spatial regions forthe two instruments may contribute to the differences in the coronal profiles de-rived from the two instruments. In addition, comparisons of UVCS/SOHO andUVCS/Spartan in 1998 were key to determining the onset and the rate of respon-sivity degradation in UVCS/SOHO (see Sect. 4.3.2).

Because earlier publications of coronal hole observations with Spartan 201 didnot have the benefit of the high precision instrument profile, observations from thefirst three flights are being re-analyzed. Figure 31 represents the re-analysis of thenorth polar coronal hole observation at ρ = 2.12 R� on 12 April 1993 duringthe Spartan 201-1 mission. Prior to this fit, an observation at ρ = 3.5 R� wasused to determine the geocoronal emission and the absolute wavelength scale forthe mission. The curve fitting routine used in this case was identical to that used forthe 1998 streamer, except there was no independent starting value for the coronalcomponent. Once again, it was found that curve fits that assumed a single Gaussianfor the coronal component could not match the peak intensity of the observationsnor the line wings. When the coronal component was fit with two Gaussians, theprofile parameters were similar, but not exactly the same as the original analy-sis reported by Kohl et al. (1996a). Comparing the original result to that of there-analysis, the line widths for the broad component were 0.090 and 0.094 nm,the line widths for the narrow component were 0.040 and 0.035 nm, the ratio ofthe broad component line intensity to the total line intensity was 0.73 and 0.70,the line shifts for the broad components relative to the geocoronal line center were–0.002 and –0.006 nm, and the line shifts for the narrow components relative tothe geocoronal line center were –0.008 and –0.025 nm, respectively. Hence, thegeneral conclusions from the original analysis hold. Additional results from theSpartan missions are reported by Miralles et al. (2006).


Fig. 32 The SOHO spacecraft in launch configuration prior to acoustic tests at Intespace inToulouse, France. From Domingo et al. (1995). UVCS is the large gold-colored instrumentmounted on the forward-facing side of the spacecraft

4.3 SOHO ultraviolet coronagraph spectrometer investigation

4.3.1 Instrument development

The UVCS instrument is shown mounted on the SOHO spacecraft in Fig. 32.UVCS was developed through a collaborative effort of the Smithsonian Astro-physical Observatory, the University of Florence, the University of Padua, the Uni-versity of Turin, and a group of scientists in Switzerland. The program was con-ducted in cooperation with and under the auspices of the NASA Goddard SpaceFlight Center (GSFC), Agenzia Spaziale Italiana, and the ESA PRODEX program(Swiss Contribution). The major industrial participants were Ball Corporation,Electro-Optics and Cryogenics Division, Alenia Spazio, Officine Galileo, andBrusag. The crossed delay-line detectors were provided by the Space SciencesLaboratory, University of California, Berkeley.

An ultraviolet coronagraph spectrometer was first considered for SOHO dur-ing an ESA assessment study conducted between February and August 1983. JohnKohl served as a consultant to ESA for that study and also served as a member


of the Science Team for ESA’s Phase A study, which was conducted betweenJuly 1984 and October 1985. The UVCS team responded to a joint ESA/NASAAnnouncement of Opportunity for the SOHO and Cluster missions in 1987, andUVCS was selected along with the other SOHO scientific investigations in March1988. SAO together with Ball Corporation and NASA Goddard Space Flight Cen-ter was responsible for the overall instrument system, the development of the oc-culted telescope unit, the experiment controller and the flight and ground software.Agenzia Spaziale Italiana together with the Italian university scientists, AleniaSpazio and Officine Galileo had the primary responsibility for the spectrometerassembly. The Swiss scientists together with Brusag were responsible for provid-ing the diffraction gratings, which were manufactured by Messrs. Bernhard W.Bach and Kirk G. Bach. GSFC was responsible for procuring the ultraviolet sensi-tive array detectors. Cleanliness was an issue of major significance during the fab-rication, integration and testing of UVCS. The primary concern was degradationof the ultraviolet responsivity due to photopolymerization of molecular contami-nation on sunlit optical surfaces. A formal contamination control program was inplace for all phases of the hardware development. The flight model of UVCS wasdelivered, initially, to ESA in 1994, and was later removed to upgrade several crit-ical components. The end-to-end functional test and instrument radiometric cali-bration, characterization and stray light tests were completed at SAO in July 1995.UVCS was then shipped to the Kennedy Space Center where it was re-installed onthe SOHO spacecraft. The launch was 2 December 1995. (For additional historyof the SOHO mission, see Domingo et al. 1995; Huber et al. 1996.)

4.3.2 Characterization and radiometric calibration

The laboratory calibration and characterization of UVCS is described by Gardneret al. (1996). The general arrangement for the UVCS radiometric calibration isshown in Fig. 33. The instrument was supported in the test vacuum chamber on anoptical bench that could be articulated to achieve alignment with the chamber op-

Light Trap System

Collimating Mirror

Light Source

Monochromator

Thermal Shroud

Scavenger Plate

Photodiode SystemTQCMs

Pumping Station

Pumping Station

Roughing System

Cryopump

Cryopump

UVCS on Instrument Support

1 meter

Neutral Density Filters

UVCS Remote Electronics

Fig. 33 The arrangement for the UVCS system-level laboratory calibration and characterization.This vacuum chamber and its peripheral units included light sources, a predispersing monochro-mator, the collimating mirror, standard photodiodes and instrument support. Mechanisms facil-itated remote control of the in-vacuum devices. From Gardner et al. (2002)


tics. Radiation at the desired wavelength from a windowless glow discharge lightsource was selected by a monochromator and collimated by a 4.6 m focal lengthmirror, which was remotely adjustable. The light was directed onto the telescopemirrors, which focused the light onto and through the spectrometer entrance slits.The UVCS radiometric response was measured against photodiodes that servedas radiometric transfer standards calibrated by the National Institute of Standardsand Technology (NIST). The portion of the light incident on each telescope mirrorcould be measured by scanning the appropriate photodiode over the portion of thebeam illuminating the mirror. The spectrometer slits were set wide enough to passthe entire light bundle. A total relative standard uncertainty of 16% was computedfor the laboratory calibration. Prior to flight, this calibration could only be carriedout for the instrument aperture to be used for observations at ρ = 2.7 R� becausethe internal occulter mechanism could not be operated in a 1 g environment. Theresponsivity for other apertures to be used for other heights had to be determinedduring the flight. The schedule allowed only enough time to do the first diffractionorder calibration.

Fig. 34 Aperture averaged measurements of the UVCS O VI channel responsivity determinedfrom observations of stars. The identification of the various points is noted in the legend on theplot. Data from 1996 and 1997 are normalized to the laboratory values, which have the samerelative variation with mirror width. The later data are put on a common scale through ratiosof count rates observed at the same aperture values and the same wavelength for the same star.To connect different stars and thereby extend trends into later years, the relative scales are es-tablished using the demonstrated conclusion that the aperture averaged responsivity at aperturesbeyond 49 mm has changed very little in time. The consistency of the results for a mirror widthof 30 mm implies that the irradiances of the stars are nearly constant in time. The smooth colorcurves, red-dashed, red-dash-dot, and blue-dash-dot, are third-degree polynomial fits to the 1999ρ Leo, 1999 θ Oph, and 2001 θ Oph data, respectively. All three fits are constrained by the twohighest aperture points of the 1999 θ Oph data set. From Gardner et al. (2002)


In-flight radiometric calibration has been determined using specially designedobservations of four source types: (1) stars, (2) the solar disk, (3) the corona atρ = 1.5–5.0 R�, and (4) the H I Lyα emission of the interplanetary medium(Gardner et al. 2002).

Observations have been made with UVCS of 15 stars when they were in theUVCS field of view for 4 or 5 days once per year. The spectrometer entrance slitswere set sufficiently wide that the entire stellar images could pass through them.Some of these stars (typically B stars) were considered stable enough to be usefulfor determining the changes in the radiometric calibration over time. Examplesof the results from these measurements are shown in Fig. 34. The UVCS O VIchannel has lost responsivity over the mission. The loss is greatest at the edge ofthe aperture that is used for observations at the lowest heights and is progressivelylower for the portions of the aperture used for increasingly larger heights, whichare less frequently used. Similar measurements for the Lyα channel and for theredundant Lyα path together with appropriate analyses (e.g., Valcu et al. 2006)were carried out.

Although those analyses established the amount of degradation inUVCS/SOHO responsivity for wavelengths near H I Lyα between the timeof the laboratory calibrations and star observations in 2000, it was not clear fromthose measurements when the degradation started. However, since the amount ofdegradation depends on the aperture used for observations at various heights, thecomparison of UVCS/Spartan and UVCS/SOHO observations at different heightscould be used to check the consistency of the degraded vignetting functionswith test cases that assume different start-dates for the degradation. It was foundthat the Spartan and SOHO comparison in November 1998 was consistent withthe un-degraded laboratory calibration, establishing that the degradation beganjust after the recovery from the SOHO mission interruption in November 1998(Gardner et al. 2006).

Observations of the solar disk were used to inter-compare the UVCS andSUMER radiometric calibrations. The calibrations were in agreement to withinthe known uncertainties.

The system responsivity as a function of unvignetted aperture was determinedby observing a stable coronal structure at a particular height. H I Lyα and O VIradiations were then measured for several different internal occulter positions andthus different unvignetted apertures. The results in 1996 were consistent with lab-oratory measurements of flight-like replica gratings. Similar measurements weremade for larger apertures using interplanetary Lyα. These measurements also wereconsistent in 1996 with the laboratory measurements. Such measurements havealso been used to track the changes in the responsivity as a function of aperture.The effective area of the redundant Lyα path is a function of both grating angle andthe unvignetted grating aperture width. These dependences have been character-ized by using a combination of coronal measurements with different unvignettedgrating apertures as described above and different grating angles.

For the stray light tests, a solar divergent beam was produced that was largeenough to fill the UVCS aperture. This was accomplished by placing a circularaperture at the focal surface of the collimating mirror and illuminating it with amicrowave discharge light source. A band pass filter was used to select the wave-length. The instrument was oriented to place the image of the aperture center onthe entrance slit, and calibrated attenuation filters were inserted in the beam to re-


duce the radiance to an acceptable level so the simulated disk center could be ob-served. The instrument response was recorded. The center of the instrument fieldof view was then re-oriented to ρ = 2.7 R�. A light trap similar to the one usedin the UVCS instrument was placed on the ρ = 2.7 R� LOS. This was used tosimulate an essentially zero radiance corona. The attenuation filters were removedand the instrument response was recorded. In this way, the stray light backgroundrelative to the disk-center intensity at the wavelength of interest was measured.

Since some of the stray light signal could have been a result of scattering in thetest chamber, this measurement provided an upper limit to the stray light signalexpected for a given Sun-center spectral radiance. The effects of center-to-limbvariations were considered in the analysis, but no correction was made. The Lyαchannel response to stray light relative to its response to the Sun-center intensitywas found to be < 1 × 10−8.

The instrument response to stray light from off band wavelengths was also de-termined and found to be acceptable. The off band stray light suppression is animportant consideration since the wavelength-integrated near ultraviolet radianceof the Sun is many orders of magnitude greater than the on-band disk radiance.The off band rejection is provided by a combination of the occulted telescopesystem, the off band rejection of the spectrometer and the long wavelength insen-sitivity of the detectors.

The stray light signal also was measured during the mission. This was doneby measuring the signal at the detector pixels corresponding to the Si III 120.6nm line in the Lyα channel and in the redundant Lyα path, and the signal forthe C III 97.7 nm line in the O VI channel direct path. Neither of these spectrallines are normally expected to be produced in the extended solar corona. Hence,any observed signal can almost always be attributed to stray light. Since the diskintensities of these spectral lines relative to the disk intensities of spectral lines ofinterest are known or can be estimated, the Si III and C III signals can be scaled todetermine the stray light signals at the wavelengths of the extended corona lines.The stray light has the line shape of the disk spectrum.

In practice, the low stray light level of UVCS has only yielded measurableSi III and C III intensities for observations between ρ = 1.5 and 2.0 R�. How-ever, these signals can be scaled for observations at other heights by using modelsof the variation with angle of non-specular reflection off the telescope mirrors.Non-specular reflection of light diffracted by the external occulter onto the tele-scope mirrors is the dominant source of ultraviolet stray light in UVCS. The straylight level is expected to drop off exponentially as the scattering angle increasesfrom the specular direction (Romoli et al. 1993). The extrapolations to nearbywavelengths and to larger heights take variations in the intensity over the solardisk into account. As expected, the measured levels for observations at less thanρ = 2 R� are larger than those determined in the laboratory for observations atρ = 2.7 R�. In the cases of both the Lyα channel and the paths of the O VIchannel, extrapolations to larger heights of in-flight stray light measurements areconsistent with the laboratory measurements.

A Ne-Pt hollow cathode lamp with a MgF2 window was used for the laboratoryspectrometric calibration of the Lyα channel. The lamp provided a rich spectrumof narrow spectral lines for wavelengths from the MgF2 cutoff to well above therange of the Lyα channel. The entrance slit width was set at 25 µm. Data were


Fig. 35 Lines observed in-flight in the O VI channel. Shown is a composite coronal spectrummade from UVCS observations at several grating angles. From Gardner et al. (1996)

collected for several grating angles. A calibration for wavelength versus detectorpixel number was determined as a function of grating angle. A similar calibrationwas done for the redundant Lyα path of the O VI channel. The spectrometriccalibration for the direct path of the O VI channel was determined in a similarfashion with an Al-Xe hollow-cathode lamp.

Wavelength scales have been determined during the mission by observing andidentifying spectral lines emitted from the corona. Figure 35 is an example of thecoronal spectrum used for the in-flight wavelength calibration. Wavelength scaleswere also determined with stray disk light by deliberately spoiling the occultingsystem to increase the stray light level.

The spectral resolution was measured in the laboratory with the hollow-cathode lamps that were used for the spectrometric calibration. Instrument spectralline profile functions were determined for each optical path and several grating ori-entations. These measurements were limited to the instrument aperture to be usedfor observations at ρ = 2.7 R�, as were all laboratory characterizations. An ex-ample of a Lyα channel line profile for the Pt II 121.95 nm spectral line is shownin Fig. 36, where pixel to pixel separations correspond to 0.014 nm. The spec-tral resolution during the mission was measured using observations of disk andcoronal emission from heavy ions. The results are consistent with the laboratorycalibration.

The variation in response over the area of the two detectors was sampled inthe laboratory by illuminating the primary and redundant Lyα paths with the largeaperture microwave discharge source, which was also used for the stray light char-acterization. Because of schedule constraints, measurements were not made overthe entire active area of the detectors. Instead, representative portions were char-


Fig. 36 High-resolution spectrum in the Lyα channel from a Ne-Pt hollow cathode lamp. Shownis an expanded view of the Pt II 121.95 nm emission line with a simple Gaussian fit to the data.The FWHM of the fit is less than 2 pixels, indicating spectral resolution elements of less than0.028 nm. From Gardner et al. (1996)

acterized so that the characterization could be extended to the rest of the detectorduring the flight with grating scans. The variations in response along the slit lengthdirection (i.e., the spatial direction) were determined by scanning the image of thelight source along the entrance slits. This was accomplished by stepping the col-limating mirror gymbal in the test chamber and taking exposures (see Fig. 33).The variation in response was also measured in-flight by orienting the instrumentso that a star’s path in the sky traveled along the length of the slit. The resultingcharacterization was extended to the spectral direction with grating scans.

The spatial resolution elements for each of the optical paths were determinedin-flight by analyzing the images of observed stars. The spatial resolution in thespatial direction (i.e., along the length of the entrance slits) depends on the fol-lowing: the figures of the spherical telescope mirrors and the toric gratings, theoptical alignment, the illuminated apertures of the telescope and spectrometer, theangles of incidence and reflection at the telescope mirror, the angle of incidenceand diffraction at the grating and the effective size of the detector pixels. Althoughthere are configurations where the FWHM approaches the value corresponding tothe size of the detector pixels, most instrument configurations have FWHM be-tween 24′′ and 60′′, which has been adequate for most UVCS scientific purposes.With UVCS, the count rates usually require summing over several pixels in orderto obtain adequate statistical precision.

The pointing calibration of UVCS has been described by Frazin (2002). Thiscalibration is based on UVCS observations of the star ρ Leo whose position in thesky relative to the Sun can be determined with an uncertainty of 1′′. The pointingconsists of two parts: the position of the reference axis of the instrument, whichis defined by the instrument roll axis, and the actual telescope mirror angle be-tween the reference axis and the direction of a fiducial point in the corona whoseimage falls near the center of the fixed edge of the O VI channel spectrometer en-trance slit. The angular relationships to the other UVCS channels were measuredin the laboratory prior to launch and confirmed in-flight by tracking a star (e.g., ρLeo) in all three channels. In-flight determination of the pointing angles requires


knowledge of the star’s trajectory from the SOHO vantage point, which can becalculated. The direction of the reference axis relative to the disk center directionis determined by four items: the pointing and roll of the spacecraft, the positionsof the instrument pointing stages, the slightly non-circular shape of the UVCS rollring, and thermal changes in the instrument, which were shown to be negligible.UVCS has alignment diodes that are placed in the shadows of the entrance aper-ture edges. A combination of instrument rolls and pointing stage adjustments canminimize the deviation of the reference axis from the Sun-center direction. Themirror angle is controlled by the mirror mechanism and so the mirror angle cali-bration is a characterization of the mirror mechanism. The mirror angle dependson the commanded mirror angle, but it also depends on the orientations of thegratings. This is due to an electronic cross talk that was characterized by Fineschiet al. (1997). Once the trajectory of the star is determined in solar coordinates,UVCS could be pointed so that the star image passed through its slits at a numberof points along the star’s trajectory. The position of the star at these times yieldsthe pointing calibration information.

4.3.3 Science operations

UVCS science operations are conducted in the SOHO Experiment Operations Fa-cility (EOF) at GSFC. Each week a Lead Observer is designated to lead the prepa-ration of a series of daily observing plans aimed at achieving scientific goals pro-posed to the Principal Investigator. The UVCS resident operations team at the EOFassists the lead observer, prepares the observation command scripts, tests the se-quences on an instrument simulator program, issues the commands, and displaysthe “quick look” data. The flight operations team is required to follow sanctionedoperation procedures and guidelines. Any unusual situation requires the approvalof the Instrument Scientist and Principal Investigator before the operations teamis permitted to proceed with the resolution.

The flight software provides the operations team with the capability to oper-ate the instrument interactively during contact periods or to upload observationsequences for autonomous execution. Most UVCS observations have been per-formed by executing observation sequences stored in onboard memory. New se-quences are uplinked as needed. The UVCS command workstations at the EOFcontain the software tools needed to generate, uplink and verify new sequencesand associated parameter data.

Commands from the UVCS workstations are routed to the SOHO MissionOperations Control Center and uplinked to the spacecraft in a near real time or,occasionally, delayed commanding mode. The most common mode of operationis to uplink an onboard stored procedure and then issue a command to start theprocedure in real time or at a specified later time. Guidelines require certain com-mands to only be issued in near real time so that the response of the instrumentcan be monitored and appropriate action taken immediately.

Near real time and playback telemetry data are received at the EOF, while finalflight data are sent to the UVCS Data Reduction and Analysis Facility (DRAF) atSAO where the data quality is verified, the level one data are produced, stored anddistributed to the users and to the SOHO Data Archive. Data products distributedto users include spectral data files containing uncalibrated data from the ultraviolet


channels, instrument configuration data and exposure timing data. Data files fromthe white light channel (see, e.g., Kohl et al. 1995a), calibration data files, dataanalysis software, example model codes and a tutorial designed to familiarize newusers with the analysis of UVCS data, are also provided. A web site is maintainedthat provides interested parties with a large body of current information regardingthe UVCS program.

5 UVCS/SOHO solar wind results

The hot plasma in the extended solar corona expands continuously into interplan-etary space as a bulk outflow known as the solar wind. The history of pre-SOHOobservations of the extended corona and solar wind was summarized in Sect. 4,and further details can be found in reviews by Parker (1963, 2001), Dessler (1967),Hundhausen (1972), Leer et al. (1982), and Tu & Marsch (1995). More recent re-views include Cranmer (2002a), Marsch (2004), and Holzer (2005). In this sectionwe focus on the increased understanding of physical processes responsible for thesolar wind that has come from the past decade of UVCS/SOHO observations andrelated observations and theoretical work.

5.1 Large-scale magnetic structure of the extended corona

The earliest in situ measurements of solar wind plasma revealed that the windexists in two relatively distinct states: a high-density, low-speed (300–500 km s−1)component and a low-density, high-speed (600–800 km s−1) component. The twotypes of solar wind are associated with similarly distinct features in the corona.Magnetic flux tubes carrying fast wind tend to coincide with large coronal holes.The flux tubes carrying slow wind are associated with bright “quiet Sun” regionsand active regions on the solar disk, small coronal holes, and streamers in theextended corona. These correlations point to a deep connection between the solarmagnetic field and the properties of the solar wind.

Before the late 1970s, the slow wind was believed to be a relatively calm back-ground state, and the fast streams were seen as occasional disturbances. This viewwas bolstered by the successful application of the initial Parker (1958) solar windmodel to the slow wind, but not to the fast wind. However, we know now that thisidea came from the limited perspective of spacecraft that remained in or near theecliptic plane. It gradually became apparent that the fast wind is indeed the more“ambient” steady state and the slow wind is more variable and filamentary (e.g.,Feldman et al. 1976; Bame et al. 1977). The polar passes of Ulysses in the 1990sconfirmed this revised paradigm (Gosling 1996; Marsden 2001).

Figure 37 illustrates the solar cycle dependence of the large-scale magneticstructure of the corona and the associated solar wind. At the minimum of the Sun’s11-year activity cycle (Fig. 37a), large coronal holes exist at the north and southheliographic poles and their associated open field lines expand into a large frac-tion of the volume of interplanetary space. Fast solar wind is accelerated in theseregions (e.g., Goldstein et al. 1996). We use the term “coronal hole” both for thedark patches seen on the solar surface in ultraviolet and X-ray images and forthe low-density off-limb extensions of these patches observed by coronagraphs.


The bright equatorial streamer belt is evident as mainly closed magnetic fieldsnear the solar surface and open fields beyond 2–4 R� that contain slow-speedwind. There is also strong evidence for wind outflow in the open field lines thatborder streamers (e.g., Strachan et al. 2002); the term “streamer” is used here todenote the collection of open and closed flux tubes that give rise to relatively iso-lated (high-density) helmet or fan shaped structures.

As solar activity increases above the minimum state, the magnetic field beginsto lose its simple axisymmetric character. On the largest scales, the solar dipolemust “flip” from one solar minimum to the next, but this does not manifest as asimple rotation of the dipole axis. Solar maximum is a complex mixed-polaritystate that witnesses a substantial amount of magnetic flux transport over the solarsurface (Fig. 37b; see also Wang 1998a; Sanderson et al. 2003). At solar maxi-mum, active regions emerge at all latitudes, and their stronger field strengths giverise to “active-region streamers” in the extended corona (see, e.g., Newkirk 1967;Bohlin 1970; Liewer et al. 2001; Ko et al. 2002). Active-region streamers tendto be narrower and brighter than their quiescent equatorial counterparts at solarminimum. As discussed in Sect. 4.1.2 above, there also seems to be evidence foran intermediate plasma state between dark coronal holes and bright streamers inthe extended corona that may have some connection to the “quiet Sun” regionsviewed on the solar disk (see also Habbal et al. 2001). Some of this diffuse fanned-out emission may, however, come from flattened streamer belts that happen to beviewed nearly face-on (e.g., Wang et al. 1997).

During the approach to solar maximum (Fig. 37b), the large polar coronalholes disappear as magnetic flux of the opposite polarity is advected toward thepoles (see, e.g., Wang & Sheeley 2003). Also, smaller coronal holes can appearat all latitudes and last for several solar rotations (Nolte et al. 1976; Harvey et al.1982; Miralles et al. 2004). Because of the omnipresent active-region streamersand other high-density structures in the corona (including, perhaps, the smallestcoronal holes), the interplanetary medium is dominated by highly variable slow-speed wind (Smith & Marsden 2003). During the decline from solar maximum tothe next minimum, polar coronal holes of the new cycle’s polarity begin to growin size and strength. The growth phase of new coronal holes lasts about twice aslong as their pre-maximum decay (Waldmeier 1981; Fisher & Sime 1984).

(a) (b)

Fig. 37 Schematic illustration of the large-scale solar magnetic field at (a) solar minimum and(b) solar maximum, with bright streamers shown as dark gray and coronal holes on the solarsurface as black; see text for discussion. Inspired by Fig. 3 of Suess et al. (1998)


Fig. 38 Normalized total intensity of the O VI 103.2 line measured by UVCS, sampled once per23 days from late 1996 to early 2005, and interpolated to a common height of 1.6 R�. The northand south poles are at position angles 0◦ and 180◦, respectively, and the east and west equatoriallimbs are at 90◦ and 270◦. Intensities have been rescaled so that the dimmest (brightest) latitudesat each time are shaded black (white), with a color scale ranging from black to red to yellow towhite. Periods when no data are available are indicated by white rectangles

A significant fraction of the UVCS/SOHO observation time has been devotedto a synoptic program that provides long-term monitoring of the large-scale evo-lution of the plasma properties of the extended corona (see, e.g., Strachan et al.1997, 2000). The 27-day solar rotation provides a slow sampling of many lines ofsight through the optically thin plasma, and it is possible to use these large datasets to tomographically reconstruct the three-dimensional distribution of plasmaproperties (e.g., Davila 1994; Frazin 2000). Panasyuk (1999) produced a globalreconstruction of H I Lyα and O VI 103.2, 103.7 nm emissivities between 1.5 and3 R� during the first SOHO Whole Sun Month campaign (August–September1996). Further insights concerning the global wind structure from all three WholeSun Month campaigns are presented by Gibson (2001).

In Fig. 38 we display a qualitative summary of the first eight years of theUVCS synoptic program, with data extracted from the “daily images” publishedonline. This plot shows the latitudinal dependence of the O VI 103.2 nm inten-sity as a function of time, with observations sampled approximately once every23 days (≈ 7/8 of a rotation) to not be biased by structures at specific longi-tudes. The position angle plotted on the vertical axis is measured counterclockwisefrom the north heliographic pole. Instead of showing the absolute intensity (e.g.,Fig. 4 of Cranmer 2002a), which would be swamped by an overall factor-of-tenincrease from solar minimum to solar maximum, we renormalize the intensitiesto the minimum and maximum of each observation. This allows the relative lat-itudinal structure at all epochs to be seen clearly. The large polar coronal holesand bright equatorial streamers at solar minimum (1996–1998) are evident, as arehints of abundance-linked dimming in the central “cores” of the streamers (seeSect. 5.3.1). Interestingly, with this kind of plot it is clear that even at solar max-imum (1999–2001) the north and south poles remain somewhat dimmer than the


equator. This result is not anticipated by traditional solar maximum images likeFig. 37b, which would predict a more random distribution of brightness as a func-tion of position angle. Despite the existence of high-latitude streamers, though,the brightest features at solar maximum are associated with active regions, whichtend to appear near the equator at the most active phases of the cycle.

5.2 Coronal holes and fast solar wind

The existence of coronal holes was first recognized by Waldmeier (1957, 1975),who noticed long-lived regions of negligible intensity in coronagraph images ofthe [Fe XIV] 530.3 nm green line. Waldmeier called the features that appearedmore-or-less circular when projected onto the solar disk Locher (holes), and elon-gated dark features were called Rinne (grooves) or Kanal (channels). Coronalholes were effectively rediscovered in the 1970s as discrete dark patches on theX-ray and ultraviolet solar disk, and their connection with the fast solar wind soonbecame clear (Krieger et al. 1973; Noci 1973b; Zirker 1977).

UVCS has made significant progress toward identifying the physical processesthat heat and accelerate the plasma in coronal holes. Below, we review the mea-sured mean properties of large polar coronal holes at solar minimum (Sect. 5.2.1),differences between dense polar plumes and tenuous interplume regions withinpolar coronal holes (Sect. 5.2.2), coronal hole structure and variability through-out the solar cycle (Sect. 5.2.3), and the theoretical advances in understanding thefast solar wind that have been spurred by the past decade of UVCS observations(Sect. 5.2.4).

5.2.1 Solar minimum: Mean properties of polar holes

Polar coronal holes at solar minimum have the lowest ultraviolet intensity of anystructure seen off-limb over the entire solar cycle. Thus, UVCS observations arelimited to only the brightest emission lines: H I Lyα, the O VI 103.2, 103.7 nmresonance doublet, and Mg X 62.5 nm. In this section we summarize the UVCSobservations of these lines in solar-minimum coronal holes, with emphasis ondetermining the “mean” large-scale plasma properties of these regions.

The H I Lyα line had been observed in the extended corona for several yearsprior to the launch of SOHO (see Sect. 4) but UVCS/SOHO allowed greater spa-tial coverage and resolution, as well as a much longer timespan for observations.Earlier observations indicated relatively large proton temperatures compared toelectrons (i.e., Tp > 2 MK; Kohl et al. 1996a) and supersonic outflow speedsclose to the Sun (Strachan et al. 1993). The UVCS results confirmed both of thesetrends and put much firmer limits on the values of the temperature and outflowspeed (Kohl et al. 1997a, 1998; Cranmer et al. 1999b). Figure 39 shows the de-rived range of hydrogen temperatures in the extended corona, along with othertemperature quantities to be described below. The upper H0 curve, which flattensout at ∼3.5 MK at large distances from the Sun, is the upper limit on the kinetictemperature derived from H I Lyα line widths using a three-dimensional empiricalmodel of the plasma emissivities. The kinetic temperature is likely to be a sum ofsmall-scale random thermal motions and larger-scale (but still unresolved in either


Fig. 39 Summary of the radial dependence of temperature in polar coronal holes and the high-speed wind at solar minimum, from both remote-sensing and in situ measurements: electrontemperatures (solid lines), neutral hydrogen and proton temperatures (dotted lines), and ion-ized oxygen temperatures (dashed and dot-dashed lines). Paired sets of curves in the extendedcorona (1.5 < r < 10 R�) denote different empirical models derived from UVCS emissionline properties; statistical uncertainties are not plotted for clarity. Dashed regions in the lowcorona (r < 1.5 R�) correspond to lower and upper limits on the O5+ kinetic temperature fromSUMER line widths (see text)

space or time) nonthermal motions, the latter the result of waves, turbulent eddies,or shocks. The lower H0 curve, which peaks below 2 MK and begins to decreaseat large distances, is a lower limit on the hydrogen temperature without nonther-mal broadening by waves. A model of Alfven wave action conservation, with alower boundary amplitude of 30 km s−1, was convolved with the empirically de-termined kinetic temperature in order to compute this curve (see also Esser et al.1999; Cranmer 2002a, 2004b).

Suleiman et al. (1999) presented UVCS H I Lyα line widths measured at largeheights in polar coronal holes (ρ = 3.5–5 R�). These measurements were takenon 5–11 January 1998, which was near the end of the time period of the nearly ax-isymmetric solar-minimum corona. By carefully removing the contribution frominterplanetary H I Lyα emission – which was assumed to dominate the measuredprofiles at ρ = 6 R� – the coronal line widths were determined to decrease withincreasing height similar to the lower dotted curve of Fig. 39. At ρ = 5 R�, theH0 kinetic temperature was found to be (4.1 ± 1.2) × 105 K. Note that at largeheights the H0 and proton properties are expected to be decoupled from one an-other (Olsen et al. 1994; Allen et al. 1998, 2000).

Figure 39 also shows estimates for the electron temperature in polar coronalholes. The short and long solid curves are determinations of Te from SUMERspectroscopy (Wilhelm et al. 1998) and freezing-in models of in situ charge statesmeasured by Ulysses (Ko et al. 1997), respectively. No direct measurements ofTe at large heights in coronal holes yet exist, and discrepancies between the spec-troscopic and freezing-in temperatures are only beginning to be understood (e.g.,Esser & Edgar 2000, 2001). Although it is highly likely that Tp > Te, the un-certainties on both quantities are considerable and we cannot state unequivocallythat the protons are hotter than the electrons in coronal holes. Note, though, thatthe ranges of values for both Tp and Te in the corona seem to connect reason-


Fig. 40 (a)–(d) UVCS/SOHO observations of the O VI 103.2, 103.7 nm doublet in four types ofcoronal structure (see, e.g., Kohl et al. 1997a; Frazin et al. 1999; Miralles et al. 2001a, 2004). (e)SUMER/SOHO observations of the quiet solar disk in the same range of the spectrum (Warrenet al. 1997)

ably smoothly to the in situ values for each, plotted here for distances greater than60 R� (where in the fast wind it is clear that Tp > Te). The latter curves wereconstructed by Cranmer (2002a) from an overview of Helios, IMP, Ulysses, andVoyager particle data.

Prior to the launch of SOHO it was expected that minor ions in the coronawould have similar temperatures as the protons and electrons. (Indeed, many pre-1990 theoretical models of the solar wind did not differentiate between the tem-peratures of heavy ions and the “background” plasma temperature.) Thus, UVCSwas designed with spectral resolution sufficient to detect the narrow O VI 103.2,103.7 nm emission lines that would appear for oxygen temperatures of order 1 to2 MK. It was therefore a surprise that the O VI profiles in polar coronal holes wereat least an order of magnitude broader than expected – implying ion temperaturestwo orders of magnitude larger than expected (Kohl et al. 1996b, 1997a, 1997b).Figure 40 displays measured O VI profiles from a variety of coronal regions. InFig. 40a we show representative polar coronal hole profiles with 1/e Doppler half-widths of order 400–600 km s−1. The narrower emission components at the cen-ters of the two lines have been interpreted as solar-disk stray light scattered by theinstrument (Fig. 40e; see also Kohl et al. 1997a).

Figure 39 shows the radial dependence of O5+ ion temperatures that werederived from UVCS measurements (Kohl et al. 1998; Cranmer et al. 1999b). Fora nearly radial magnetic field viewed through an off-limb line of sight (LOS), theline width is most sensitive to the ion temperature component T⊥i perpendicularto the magnetic field. As described in Sect. 2, the relative intensity ratio betweenthe 103.2 and 103.7 nm components of the O VI doublet is sensitive to motionsin the radial direction, and these provide constraints on both the bulk ion flow


speed u and the parallel ion temperature T‖i . Near the Sun (r < 1.3 R�), we showrepresentative values of T⊥i for O VI lines measured by SUMER (Tu et al. 1998).At heights above r = 1.5 R�, the oxygen temperatures rise dramatically past 10MK and T⊥i exceeds 100 MK above 2–3 R�. These temperatures are so high thatthey would not be substantially reduced by subtracting any realistic amount ofnonthermal wave broadening (see, e.g., Esser et al. 1999).

Judging by the observed differences between the O5+ and proton temperatures,it seems clear that there is preferential heating of heavy ions in coronal holes, andthat the amount of heating leads to an ion-to-proton temperature ratio that exceedsthe ion-to-proton mass ratio mO/m p = 16 (see Sect. 5.2.4 for how this puts strongconstraints on theoretical models). Note that the in situ oxygen temperatures in thefast wind are approximately mass-proportional compared to the protons (see, e.g.,Marsch 1999), but in the highest-speed flows measured by the Wind spacecraft theions exhibited temperatures higher than traditional mass-proportionality (Collieret al. 1996). Thus, even though the ∼108 K ion temperatures measured by UVCSare extreme, they seem to be consistent with known trends in the in situ data.

As shown in Fig. 39, the empirical models of O VI Doppler dimming andpumping indicate that there must be a temperature anisotropy in the extendedcorona, in the sense that T⊥i > T‖i above r ≈ 2.2 R� (Kohl et al. 1997a, 1998;Li et al. 1998a; Antonucci et al. 2000; Zangrilli et al. 2002). Protons in the innersolar wind (between 60 and 200 R�) exhibit a temperature anisotropy in the samesense (Marsch et al. 1982b), and the strength of the anisotropy seems to keep in-creasing as one moves closer to the Sun. Recently, Raouafi & Solanki (2004a,b)have suggested that it may be possible to explain the UVCS O VI line propertieswith isotropic ion velocity distributions (i.e., T⊥i = T‖i ). However, the publishedisotropic models do not seem able to produce simultaneously the wide observedline profiles (with V1/e of order 500–600 km s−1) and the low 103.2 to 103.7 in-tensity ratios (below 0.9). Cranmer et al. (2005) have investigated the new regimesof parameter space implied by Raouafi & Solanki (2004a,b) and have put firmerlimits on the magnitude of the O VI anisotropy; above 2.5 R� there must be aminimum T⊥i/T‖i anisotropy ratio between 3 and 10 in order to reproduce the fullrange of observed line profiles.

UVCS also made test measurements of the Mg X 62.5 nm emission line inpolar coronal holes, but the observational uncertainties (including second-orderdisk-scattered stray light) were larger than for O VI and H I Lyα. However, Kohlet al. (1999a,b) presented line widths between ρ = 1.3 and 2.0 R� that reflectthe LOS velocity distribution of Mg9+ ions. Below ρ ≈ 1.8 R�, both the O VIand Mg X line widths are smaller than the H I Lyα line widths, thus indicating thepossibility that the ions and protons could have equal temperatures plus a commonwave broadening (see Eq. [11]). Above this height, we saw that the O VI widthsbegin to increase rapidly and become increasingly larger than the H I Lyα widths.The Mg X width, though, rises to just meet the H I Lyα width (∼200–230 kms−1) at the largest observed height of ρ = 2.0 R�. This implies either mass-proportional heating for the Mg9+ ions or line profiles strongly dominated bywave broadening. In Sect. 5.2.4 we discuss how the very different behavior for twominor ions having similar charge-to-mass ratios can be understood theoretically.

The Doppler dimming method (Sect. 2.2.3) also allows the determination ofplasma outflow speeds. In Fig. 41 we display a collection of mean solar wind


Fig. 41 Measured outflow speeds in polar coronal holes. (a) Proton speeds derived by massflux conservation, from density models of Doyle et al. (1999) (solid lines), Guhathakurta &Holzer (1994) (dotted lines), Sittler & Guhathakurta (1999) (dash-dotted lines), and Cranmer &van Ballegooijen (2005) (dashed lines). For each density model there are 3 assumptions for thesuperradial expansion factor. From bottom to top (for each style of curves), these are: spherical,Kopp & Holzer (1976) with fmax = 6.5 (see Cranmer et al. (1999b)), and Banaszkiewicz etal. (1998). Doppler dimming speeds for (b) H0 and (c) O5+ are shown from Cranmer et al.(1999b) (dashed curves), Antonucci et al. (2000) (solid vertical bars), Zangrilli et al. (2002)(open boxes), Teriaca et al. (2003) (dotted bars and gray region in panel [c]), and Giordano etal. (2000) (triangle: plume, X: interplume lane, diamond: off-axis background)

outflow speeds in polar coronal holes that have been derived from both Dopplerdimming diagnostics and from other constraints.

Figure 41a shows proton speeds u p derived from mass flux conservation, i.e.,the constancy of the product n pu p A along a steady-state magnetic flux tube. Theproton number densities n p were derived from electron densities ne that in turnwere determined from white-light polarization brightness (pB) measurements,and a 5% concentration of helium was also assumed (thus, n p = ne/1.1). Thecross-sectional area A of the polar flux tube was estimated using three independentassumptions: (1) spherical symmetry (thus, A ∝ r2), (2) the superradial geometryderived by Cranmer et al. (1999b) for the 1996–1997 solar minimum using theKopp & Holzer (1976) functional parameterization, and (3) the semi-empiricalpolar magnetic field model of Banaszkiewicz et al. (1998). Each of the threechoices for A(r) was combined with four different choices for ne(r) (see Fig. 41caption for references) to obtain the 12 plotted curves for u p(r). The constant fast-wind mass flux was normalized at 1 AU using the mean value of n pu p = 2 × 108

cm−2 s−1 measured during the first polar pass of Ulysses (Goldstein et al. 1996).The wide range of outflow speeds seen in Fig. 41a arises from uncertainties in

both the number density and the area factor. The main source of variation betweenthe four sets of ne(r) curves seems to be the varying fraction of dense polar plumesthat occur along the observed lines of sight (see also Sect. 5.2.2). Some pB obser-vations have been optimized to avoid bright concentrations of plumes, and othershave purposefully averaged over the full range of coronal hole substructure. Con-


cerning the range of variation in A(r), the spherical and Kopp & Holzer (1976)curves remain close to one another because the latter becomes nearly sphericalrelatively low in the corona (r ≈ 2.5–3 R�). The Banaszkiewicz et al. (1998) po-lar flux tube, on the other hand, does not begin to expand spherically until at least∼10 R�.

In Figs. 41b and c we collect a number of outflow speeds derived from UVCSobservations of H0 and O5+ in polar coronal holes. Vertical bars in these plotsgenerally denote ±1σ uncertainty limits. These speeds were derived using theDoppler dimming technique for H I Lyα and the Doppler dimming/pumpingtechnique for O VI 103.2, 103.7 nm (see Sect. 2). A major source of uncertaintyin determinations of the outflow speed via Doppler dimming and pumping isthe adopted value of the temperature in the direction parallel to the flow (i.e.,equivalent to T‖ near the Sun where the flow and the magnetic field are aligned).In simple derivations of Doppler dimming for H I Lyα (Cranmer 1998; Noci &Maccari 1999), the outflow speed and parallel temperature appear together infactors of the form exp(−u2/T‖). Because these two parameters are essentiallyconvolved together, the Doppler dimming technique has been applied in twogeneral ways: (1) mass flux conservation was used to determine u p so thatDoppler dimming gives T‖, and (2) various limiting values were used for T‖(e.g., T‖ = Te and T‖ = T⊥, with the latter constrained by the line width) sothat Doppler dimming then gives u p. The results were checked against measuredflows at 1 AU for consistency. The second method was preferred for the derivedproton outflow speeds shown in Fig. 41b (see caption for references).

For oxygen, the additional diagnostic responsiveness provided by the C IIpumping lines allows simultaneous constraints to be placed on u and T‖ by mea-surements of the intensity ratio of the two O VI lines. Combined with the linewidth, we have seen above that the temperature anisotropy ratio T⊥/T‖ can beconstrained as well. Figure 41c shows O5+ outflow speeds that were derived invarious ways, but all with the same general Doppler dimming/pumping physicsincluded. The empirical models of Kohl et al. (1998), Cranmer et al. (1999b), andZangrilli et al. (2002) came to the same conclusion that the oxygen outflow speedsmust exceed the hydrogen outflow speeds above r ≈ 2 R� by a substantial amount(see also Li et al. 1998a). Ventura et al. (1999) found that models with equal protonand oxygen outflow speeds could not simultaneously reproduce the observed H ILyα and O VI intensities. Antonucci et al. (2000), however, derived roughly sim-ilar oxygen and hydrogen outflow speeds at all heights (see also Antonucci et al.2004). From the collected values in Figs. 41b and c, though, it seems more likelythan not that oxygen does flow somewhat faster than hydrogen – at least around2.5 R�. Above ∼3 R� the observed O VI intensity ratios and line widths are seento have increasingly large uncertainties, and the comparisons between oxygen andhydrogen grow less definite with increasing height.

5.2.2 Plumes versus interplume regions

Polar plumes are bright ray-like features in coronal holes that appear to trace outthe superradial expansion of the open field lines (e.g., Newkirk & Harvey 1968;Ahmad & Withbroe 1977; Suess 1982; see also Fig. 37a). These dense strandsare often observed to stand out distinctly from the ambient “interplume” corona,


April 6–9, 1996:

Left: O VI intensity

Right: O VI line width

Fig. 42 Composite illustration of polar plumes at solar minimum. The two images are O VI103.2 nm intensity (left) and line width (right); in both images, white is high and dark is low(see Giordano et al. 1997). The solar disk illustration, lined up with the O VI intensity grayscaleimage, shows a map of the polar coronal hole boundary made from publicly available Kitt PeakHe I 1083 nm data (see, e.g., Harvey & Recely 2002). The off-limb magnetic field lines werecomputed from the potential field source surface coefficients published by the Wilcox SolarObservatory for Carrington Rotation 1908 (e.g., Hoeksema & Scherrer 1986)

though it is not clear to what extent off-limb observations (which integrate overlong optically thin lines of sight) ever see only one component. Plumes seem tooriginate on the solar disk in small (1000–4000 km) magnetic flux concentrationsalong network cell boundaries, and to expand outward to angular diameters of 2◦to 4◦ measured from Sun-center. Although some plumes are still discernible atthe outermost heights observable with the LASCO/SOHO coronagraph (30–40R�; see DeForest et al. 2001a), the plume/interplume density contrast becomestoo low to measure in interplanetary space. However, indirect and possiblyplume-related signatures in the in situ data have been reported by Thieme et al.(1990), Reisenfeld et al. (1999), and Yamauchi et al. (2002). The disappearanceof plumes is probably due to some combination of simple pressure balance (i.e.,dense plumes expanding to fill more of the heliospheric volume; see Del Zannaet al. 1998) and various magnetohydrodynamic (MHD) instabilities that can mixthe two components (Parhi et al. 1999; Andries et al. 2000).

UVCS/SOHO has measured the plasma properties of polar plumes in the ex-tended corona and put new constraints on where and how the fast solar wind isaccelerated. Figure 42 shows scanned images of the intensity and width of theO VI 103.2 nm line made at solar minimum. The densest concentrations of po-lar plumes along the LOS exhibit smaller line widths, and thus they have lowerion kinetic temperatures than the lower-density interplume plasma (see, e.g., Kohlet al. 1997a; Noci et al. 1997a; Giordano et al. 1997; Corti et al. 1997). SUMERhas also measured lower ion temperatures in plumes than in interplume regionsbetween the solar limb and ρ ≈ 1.5 R� (Wilhelm et al. 1998, 2000; Banerjeeet al. 2000). However, earlier EUV sounding rocket observations at the limb werefound to imply larger electron temperatures for plumes than for interplume regions(Walker et al. 1993).


UVCS synoptic measurements have also been used to put constraints on theplume/interplume density contrast and the filling factor of polar plumes in coronalholes. This was done using a statistical approach that does not depend on the pre-cise positions and properties of individual plumes (Cranmer et al. 1999b, 2001).Because plumes have been seen to evolve substantially on one-day time scales,and because solar rotation brings new flux tubes into a specified LOS on a similartime scale, the daily UVCS synoptic scan over the north pole provided a quasi-random sampling of the full range of plume and interplume properties. Cranmeret al. (1999b, 2001) thus measured the means and standard deviations of the dis-tributions of pB and H I Lyα intensity, and compared these in detail to simulateddistributions of plumes placed randomly in a model coronal hole (see also Wang &Sheeley 1995). For example, at ρ = 1.7 R�, the simulated and observed statisticaldistributions agreed best with one another for a plume/interplume density ratio of2.0 and an area filling factor of 25% plume material and 75% interplume (cor-responding to ∼40 plumes distributed throughout the coronal hole). Earlier mea-surements made closer to the limb (e.g., Saito 1965; Orrall et al. 1990; Walkeret al. 1993) revealed a higher density contrast (factors ranging from 5 to 50) andlower filling factors (∼< 10%). The UVCS measurements are consistent with a lat-eral expansion of polar plumes with increasing distance from the Sun, resulting ina decreasing density contrast and a larger filling factor. UVCS observations havebeen crucial in bridging the gap between near-Sun (high contrast) and interplane-tary (almost zero contrast) measurements of plume properties.

There have been various measurements of the solar wind outflow speed inplumes with UVCS, and the consensus (at least for O5+ ions) is that the densestconcentrations of plumes exhibit lower flow speeds than low-density lines of sightdominated by interplume plasma (e.g., Giordano et al. 2000; see also Fig. 41c).Closer to the solar limb, though, the measurements are not so definitive. For obser-vations below about 1.3 R�, there is still substantial disagreement about whetherthe fast wind is accelerated more in plumes (Walker et al. 1993; Gabriel et al.2003) or more in the interplume lanes (Wilhelm et al. 1998; Teriaca et al. 2003).We still do not know how much of the mass, momentum, and energy flux of thefast solar wind comes from polar plumes, or indeed if the mass loss is best mod-eled using a two-phase (plume/interplume) paradigm or as a more complex – evenfractal – distribution of states (Llebaria et al. 2002).

Despite the above uncertainties, there have been several reasonably success-ful models of polar plume formation. Wang (1994a, 1998) presented models ofpolar plumes as the extensions of concentrated bursts of added coronal heatingat the base – presumably via microflare-like reconnection events in X-ray brightpoints (see also DeForest et al. 2001b). In these models, the extra heat input atthe base is balanced by conductive losses to produce the larger plume density. Theheating rate in the extended corona is unaffected by the basal burst, but the largerdensity in the flux tube implies less heating per particle, which leads to lowerion temperatures in the extended corona and a lower gas pressure force for solarwind acceleration. This model is consistent with the smaller plume outflow speedsdetermined from UVCS measurements in the extended corona, and the bursty na-ture of the plumes may be responsible for the differences in the interpretation ofobservations at lower heights.


Polar plumes are observed to vary substantially on a range of time scales.Plumes are not always “filled” with dense plasma, though their magnetic fluxtubes have been seen to retain their identity over several solar rotations (e.g., Lamyet al. 1997). Intensity oscillations measured with EIT and the UVCS white lightchannel seem to imply the presence of compressive MHD waves channeled alongpolar plumes (DeForest & Gurman 1998; Ofman et al. 1999, 2000). Sporadic os-cillations of the H I Lyα intensity were also reported in coronal holes and otherregions of the extended corona (Morgan et al. 2004). If such oscillations take theform of slow-mode magnetosonic waves, they are expected to steepen into shocksat relatively low coronal heights (Cuntz & Suess 2001).

UVCS made the first spectroscopic measurements (Dobrzycka et al. 2000) ofpolar jets, which were discovered by EIT and LASCO to originate at EUV brightpoints and expand rapidly into the fast solar wind (see also Wang et al. 1998). Polarjets and polar plumes have roughly similar angular sizes and intensity contrastsnear the solar limb. A detailed study of polar jet properties with UVCS, EIT, andLASCO (both at solar minimum and during the rising phase of solar cycle 23)found that the jets have higher densities, faster outflow, and lower temperaturesthan the surrounding coronal hole plasma (Dobrzycka et al. 2002). Other than thedifferences in outflow speed between plumes and jets (which may be related to thegrowth and decay phases of jets and not to differences in solar wind acceleration),these observations seem to be consistent with the idea that jets and plumes aresimilar kinds of phenomena. Polar jets seem to be the result of short-lived burstsof basal heating, whereas polar plumes seem to be the result of base-heating eventsthat last longer than several hours.

5.2.3 Solar cycle dependence of coronal hole properties

It was fortunate that the first observations of UVCS/SOHO occurred at solar min-imum, when the extended corona exhibited a comparatively simple geometry andany questions regarding the interpretation of lines of sight passing through mul-tiple structures were easily addressed. As the maximum of solar cycle 23 ap-proached (1999–2000), though, the morphology of the extended corona becamemore complex. The presence of bright streamers at a wider range of latitudes hadan impact on UVCS coronal hole observations, because the streamers often actedas foreground and background contaminants in the emission line data. Fortunately,at heights above ρ ≈ 1.75 R�, the widely different ion temperatures of the holesand streamers resulted in O VI profiles that have a clear two-Gaussian shape. Per-forming various tests – such as scanning in position angle with the slit and usingsolar rotation to probe the starting and ending longitudes of the coronal hole – so-lidified the identification of the wide O VI components with coronal holes and thenarrow components with the foreground/background streamers (see, e.g., Miralleset al. 2001a).

As of early 2005, UVCS had measured the properties of at least 140 large coro-nal holes. Some of these were multiple re-appearances of a single quasi-stablecoronal hole over several solar rotations. We count these as separate events be-cause the magnetic geometry of coronal holes tends to vary substantially from onerotation to the next (at least far from solar minimum; see, e.g., Harvey & Recely2002). Thus, it is worthwhile to treat each new “incarnation” as an independent


sample of the plasma parameter space spanned by all possible coronal holes. Itis important to have as large as possible a database of coronal hole properties inorder to explore this parameter space; i.e., to see the full range of possibilitiesregarding potential source regions of the fast solar wind.

UVCS tends to observe only the largest coronal holes, since when the small-est ones are on the solar limb, their ultraviolet line profiles tend to be heavilycontaminated by foreground and background streamer plasma. This selection ef-fect naturally screens out small coronal holes that give rise to slow-speed solarwind in interplanetary space (Nolte et al. 1976; Neugebauer et al. 1998). In thecases where UVCS and in situ measurements were made of the same coronal-hole-related plasma, high speeds in excess of 600 km s−1 were found in interplanetaryspace (e.g., Miralles et al. 2004).

During the rising phase of solar cycle 23 (i.e., 1998–2000), UVCS measuredthe plasma properties associated with several large equatorial coronal holes.Miralles et al. (2001a) found that the outflow speed in an equatorial hole inNovember 1999 was approximately three times lower than in the polar coronalholes in 1996–1997, at corresponding heights of ρ = 2–3 R�. This was consistentwith SUMER measurements of the same equatorial hole (on the solar disk)that indicated blueshifts about three times smaller in magnitude than for asolar-minimum polar hole (Buchlin & Hassler 2000; see also Xia et al. 2003).Given, though, that both kinds of coronal hole plasma are eventually acceleratedto similar speeds (600–750 km s−1) at 1 AU, this shows that the bulk of thewind acceleration must occur above r = 3 R� in the case of the equatorial hole.UVCS also found narrower O VI line widths at ρ = 2–3 R� in the equatorialcoronal hole compared to the polar hole, implying perpendicular ion temperaturesabout an order of magnitude smaller than above the poles at solar minimum (seeFig. 40b). Poletto et al. (2002) observed another large equatorial hole in December1998 and derived similar ranges of outflow speed and perpendicular temperature.

Miralles et al. (2001b) reported the resurgence of very broad O VI profiles in ahigh-latitude coronal hole that was observed nearly simultaneously with the large-scale magnetic polarity reversal of solar cycle 23 (see, e.g., Wang et al. 2002). Thereappearance of ion plasma parameters approaching those seen at the last solarminimum, at a time when the new polar coronal holes were only beginning tomanifest, was a surprising and interesting development. Even so, the O VI linewidths measured above the poles between 2001 and late 2005 did not reach theextremely large values seen at the last solar minimum.

Figure 43 shows a sample of the distribution of coronal hole O VI measure-ments made by UVCS over the last decade (here shown for observations at a com-mon height of ρ = 2.4 R�). This plot shows that the O VI line width tends to beclearly anticorrelated with the 103.2/103.7 intensity ratio, which indicates that linewidth is more-or-less positively correlated with O5+ outflow speed (see Fig. 3). Asimilar plot with pB as the abscissa shows that the lowest density coronal holeshave the largest perpendicular ion temperatures (see Kohl et al. 2001; Miralleset al. 2002, 2004). The pattern that is beginning to emerge is that of a single one-parameter “main sequence” of coronal hole properties, with lower densities at agiven heliocentric height tending to correspond to a more rapid solar wind accel-eration and stronger ion heating. (This is also consistent with the differences be-tween plumes and interplume regions measured by UVCS in the extended corona;


Fig. 43 Observed anticorrelation between the O VI 103.2 to 103.7 intensity ratio (which isinversely correlated with outflow speed) and the O VI 103.2 line width V1/e for various kindsof coronal holes that appear over the solar cycle, all measured at ρ = 2.4 R�. Plotted symbolsrepresent: polar coronal hole at solar minimum (circle), high-latitude hole near solar maximum(diamond), equatorial holes (crosses), and mid-latitude holes (squares)

see Sect. 5.2.2.) Any successful theoretical explanation of the production of thehigh-speed solar wind must reproduce this kind of locus of parameter variation.

5.2.4 Theoretical advances: Coronal holes

The UVCS measurements of surprisingly extreme plasma conditions in coronalholes have led to many new theoretical studies of how the fast solar wind plasma isheated and accelerated. Specifically, the anisotropic temperatures of oxygen ions(T⊥ > 108 K) have guided theorists to discard some candidate physical processesand further investigate others. Hollweg & Isenberg (2002) stated in a review paperthat “We have seen that the information provided by UVCS has been pivotal indefining how research has proceeded during the past few years.”

A large fraction of research into understanding coronal heating has been de-voted to the so-called “basal” coronal heating problem; i.e., the physical origin ofthe heat deposited below a heliocentric distance of r ≈ 1.5 R�. At these heights,different combinations of mechanisms (e.g., magnetic reconnection, turbulence,wave dissipation, and plasma instabilities) are probably responsible for the var-ied appearance of coronal holes, quiet regions, isolated loops, and active regions(Priest et al. 2000; Aschwanden et al. 2001; Cargill & Klimchuk 2004). In theopen magnetic flux tubes that feed the fast solar wind, though, additional heat-ing at distances greater than r ≈ 2 R� is needed to produce the measured in situproperties at 0.3 AU and beyond (e.g., Hartle & Sturrock 1968; Leer et al. 1982;


Parker 1991; Feldman & Marsch 1997; Cranmer 2002a; Holzer 2005). In coro-nal holes, the protons and heavy ions above r ≈ 2 R� are almost completelycollisionless. Thus, the ultimate energy dissipation mechanisms at large heightsare likely to be qualitatively different from the smallest-scale collision-dominatedmechanisms that dominate near the coronal base (i.e., resistivity, viscosity, andion-neutral friction).

The range of possible physical processes responsible for heating the extendedcorona is limited by the nearly collisionless nature of the plasma. Also, there ex-ists a stringent requirement to predict the observed properties of ion, proton, andelectron temperatures (Tion � Tp > Te) as well as the temperature anisotropies(T⊥ > T‖). Most of the suggested mechanisms involve the transfer of kinetic andmagnetic energy from propagating fluctuations (e.g., waves, shocks, and turbulenteddies) into an increased thermal energy in particle velocity distributions. Thisfocus on wave damping, at the expense of other kinds of popular coronal heatingmechanisms (e.g., reconnection), has gained broad acceptance for the extendedcorona because the ultimate source of energy must be the Sun itself, and theenergy must somehow propagate out to the distances where the heating occurs(see, e.g., Hollweg 1978; Tu & Marsch 1995). Collisionless wave-particle inter-actions are natural alternatives to collisional damping processes and have beenstudied in the context of the solar wind for several decades (Barnes 1968; Toichi1971; Abraham-Shrauner & Feldman 1977; Hollweg & Turner 1978; Marschet al. 1982a; Isenberg & Hollweg 1983; Hollweg 1986; Tu 1987, 1988; Axford& McKenzie 1992).

The UVCS observations discussed above have given rise to a resurgence ofinterest in collisionless wave-particle resonances (typically the ion cyclotron reso-nance) as potentially important mechanisms for damping wave energy and prefer-entially energizing positive ions (e.g., McKenzie et al. 1995; Tu & Marsch 1997,2001; Hollweg 1999a, 1999b, 2000b, 2005; Axford et al. 1999; Cranmer et al.1999a; Li et al. 1999; Cranmer 2000, 2001, 2002a, 2002b; Hollweg & Isenberg2002; Vocks & Marsch 2002; Gary et al. 2003; Marsch et al. 2003; Cranmer &van Ballegooijen 2003; Gary & Nishimura 2004; Gary & Borovsky 2004; Marsch2004).

The ion cyclotron heating mechanism is a classical resonance between left-hand polarized Alfven waves and the Larmor gyrations of positive ions. In the heli-cally accelerating frame of a resonant ion, the sinusoidally oscillating electric andmagnetic fields due to the wave are no longer felt by the ion to be oscillating. Theparticle in such a reference frame is thus accelerated by what it sees as a DC elec-tric field, and to zero order it is spun up into a faster/wider Larmor gyration aroundthe background field direction (i.e., its perpendicular energy is increased at the ex-pense of the wave energy). If there is a continuous distribution of wave energywith frequency – with random phases – the positive ions tend to experience bothacceleration and deceleration due to the cyclotron resonance, and thus on averagethe energization can be thought of as a net diffusion in velocity space (see, e.g.,Rowlands et al. 1966; Dusenbery & Hollweg 1981; Isenberg et al. 2000, 2001;Galinsky & Shevchenko 2000; Isenberg 2001, 2004; Shevchenko et al. 2004).Figure 44 shows an example of how an initially Maxwellian velocity distributionof O5+ ions becomes distorted due to this ion cyclotron diffusion (Cranmer 2001).The dominant effect is perpendicular heating, but the conservation of energy in the


Fig. 44 Contour plots of a modeled O5+ velocity distribution undergoing ion cyclotron reso-nance at r = 2 R� (see Cranmer 2001). Times in the model evolution are, from left to right,0, 100, 1000, 2000, 5000, and 50000 s, and velocities are shown in units of 100 km s−1. Thedarkest regions correspond to the core of the velocity distribution, and the levels of the 5 con-tours correspond to 1–5 standard deviations away from the peak (computed for correspondingMaxwellian distributions)

wave frame tends to produce nearly circular “shells” centered on the phase speedof the Alfven waves in the extended corona (Vph ≈ u + VA ≈ 2000 km s−1).

One potential obstacle to this mechanism is that the resonant wave frequenciesrange between 104 Hz, in the low corona, and 1–10 Hz, in interplanetary space.The Sun, though, is expected to emit Alfven waves at much lower frequencies(∼< 0.01 Hz, corresponding to periods of several minutes to several hours) thatare not expected to evolve strongly with distance. This discrepancy has led to twogeneral ideas:

1. Basal generation: Axford & McKenzie (1992) suggested that high-frequencyoscillations could be generated during small-scale reconnection events in thechaotic “furnace” of the supergranular network. These waves would propagateup through the corona until they reached heights where they became cyclotronresonant with various positive ions, then they would damp over a very shortdistance (see also Schwartz et al. 1981; Tu & Marsch 1997, 2001; Ruzmaikin& Berger 1998).

2. Extended generation: There have been numerous “local” wave generation sce-narios proposed that involve the Sun launching low-frequency Alfven or fast-mode waves that are gradually converted into ion cyclotron waves in the ex-tended corona. Examples of suggested mechanisms include MHD turbulentcascade, kinetic plasma instabilities (driven by non-Maxwellian velocity dis-tributions or spatial gradients), and wave mode conversion driven by reflectionor refraction (e.g., Hollweg 1986; Matthaeus et al. 1999; Kaghashvili & Esser2000; Dmitruk et al. 2001, 2002; Cranmer & van Ballegooijen 2005).

There remains some controversy over which of the two above ideas is likely tobe dominant in coronal holes (for a summary, see Hollweg & Isenberg 2002).


The basal generation scenario has been called into question for several reasons.Cranmer (2000, 2001) argued that the collected effect of the resonances of manyminor ion species may be strong enough to damp out a base-generated spectrumof cyclotron waves before they can become resonant with the observed species.Hollweg (2000a) noted that a base-generated cyclotron wave spectrum should ex-hibit a very different appearance in interplanetary radio scintillations compared towhat is measured. Leamon et al. (2000) compared the relative rates of “frequencysweeping” (required in the base-generated picture) and MHD turbulent cascadeand found that the latter process always seemed to be more efficient than the for-mer. Micro-scale kinetic simulations of the resonance process itself (e.g., Ofmanet al. 2001) also give some credence to ideas that require active driving over arange of heights, rather than passive sweeping of the resonance across a basalspectrum.

Measuring the plasma properties of more than one ion species (with a rangeof charges and masses) is one possible way of distinguishing between the manyproposed scenarios. The existing UVCS measurements of O5+ and Mg9+ are in-triguing because these two ions have charge-to-mass ratios Z/A that are relativelysimilar (i.e., 0.31 and 0.37 in units of proton charge/mass), and the large observeddifference in their widths was not expected. Two possible explanations have beenproposed. Esser et al. (1999) noted that the rate of Coulomb collisions betweena heavy ion species and the (cooler) protons is proportional to Z2/A, and thusthe Mg9+ ions (with Z2/A = 3.3) should be more strongly coupled to the pro-tons than should the O5+ ions (with Z2/A = 1.6). Thus, collisional temperatureequilibration may explain the lower Mg9+ temperatures. Cranmer (2000), though,noticed that Mg9+ has nearly exactly the same value of Z/A as O6+, the thirdmost abundant ion in the corona. If the ion cyclotron waves are damped in pro-portion to their relative number densities, there may be substantially lower wavepower at the combined Mg9+/O6+ resonance than at the slightly offset O5+ reso-nance. Observing a larger number of ions can resolve the ambiguity between theabove two possible explanations (see Cranmer 2002b).

MHD turbulence has been proposed as a natural means of transforming fluc-tuation energy from low frequencies (i.e., periods of a few minutes; believed tobe emitted copiously by the Sun) to the high frequencies required by cyclotronresonance theories. A strong turbulent cascade is certainly present in interplan-etary space (Goldstein et al. 1995), and there is evidence from radio soundingobservations that the corona is similarly turbulent (e.g., Harmon & Coles 2005).However, both numerical simulations and analytic descriptions of turbulence incoronal plasma conditions indicate that the cascade from large to small lengthscales occurs most efficiently for modes that do not increase in frequency (for arecent survey, see Oughton et al. 2004). In the corona, the expected type of tur-bulent cascade would tend to most rapidly increase the electron T‖, not the ionT⊥ as observed (Leamon et al. 1999; Cranmer and van Ballegooijen 2003). Re-cently there have been several ideas proposed to explain this apparent divergencebetween theory and measurement:

1. Despite prior expectations about the anisotropic nature of the wavenumber cas-cade in a coronal plasma, there may exist unanticipated mechanisms of “fre-quency cascade” to produce ion cyclotron waves from low-frequency Alfvenwaves (e.g., Medvedev 2000; Gomberoff et al. 2004).


2. If the plasma conditions in the corona become sufficiently inhomogeneous,the plasma becomes susceptible to local microinstabilities that damp the fluc-tuations and can lead to rapid growth of ion cyclotron waves. These in-homogeneities could take the form of cross-field drift currents associatedwith large-amplitude MHD waves (Markovskii 2001; Zhang 2003), intermit-tent bursts of parallel electron heat flux from microflares in the low corona(Markovskii & Hollweg 2004a,b), or perpendicular magnetic eddies associ-ated with large-amplitude kinetic Alfven waves (Voitenko & Goossens 2003,2004; Markovskii et al. 2005).

3. If there are Alfven waves propagating both outward and inward along openmagnetic field lines, there could exist additional interactions that drive ahigher-order form of velocity-space diffusion (compared to the straightfor-ward cyclotron resonance of unidirectional waves) between resonant shellsthat cross over one another. This could provide additional perpendicular ionheating, and it is akin to the random walks that energize particles in second-order Fermi acceleration (e.g., Terasawa 1989; Isenberg 2001; Gary & Saito2003).

4. On the smallest spatial scales, MHD turbulence has been shown to developinto a collection of narrow current sheets undergoing oblique magnetic recon-nection (i.e., with the strong “guide field” remaining relatively unchanged).Dmitruk et al. (2004) performed test-particle simulations in a turbulent plasmaand found that protons can become perpendicularly accelerated around theguide field because of coherent forcing from the perturbed fields associatedwith the current sheets.

Note that the above ideas can be essentially conceived as “ion cyclotron reso-nance” (i.e., coherent spinup of ion gyromotions around the strong backgroundmagnetic field), even if the mechanisms are more complicated than believed pre-viously.

Other proposed ideas for the preferential heating and acceleration of heavyions in the extended corona include the following:

1. The low-frequency kinetic Alfven waves that are believed to be generated fromMHD turbulence may give rise to substantial electron beams when they damp.Sufficiently strong beamed distributions would then be unstable to the gen-eration of parallel Langmuir waves. Evolved Langmuir wave trains exhibit aperiodic electric potential-well structure in which some of the beam electronscan become trapped. Adjacent potential wells may then merge with one an-other and form isolated “electron phase space holes” of saturated potential.Ergun et al. (1999), Matthaeus et al. (2003), and Cranmer & van Ballegooijen(2003) described how these tiny (Debye-scale) electrostatic structures can heations perpendicularly via Coulomb-like “collisions.”

2. Lee & Wu (2000) suggested that small-scale reconnection events at the so-lar surface could fill the extended corona with fast collisionless shocks. Forthin enough shocks, ions that cross from one side to the other remain “nonde-flected” by the rapid change in direction of the magnetic field and thus mustconvert some of their parallel motion into perpendicular gyration. Mancusoet al. (2002) suggested this mechanism may be applied to understandingUVCS measurements of ion heating in large-scale CME shocks (see Sect. 6).


3. There are several speculative “passive” mechanisms of producing ion temper-atures exceeding 100 MK in the corona. Pierrard & Lamy (2003) and Pierrardet al. (2004) have shown that Scudder’s (1992) velocity filtration mechanismcan produce extremely hot ions in the corona if they had suprathermal tailsin the chromosphere. However, the anisotropy ratios of such filtered veloc-ity distributions are likely to have T‖ � T⊥, which is not what is observed.Another idea involves the interaction between Spitzer-Harm conductivity andcollisional equilibration in the low corona. It is well known that without heatconductivity to transport coronal energy down to the transition region, thecoronal heating would lead to plasma temperatures in excess of 108 K (e.g.,Owocki 2004). The proton conductivity is substantially smaller than the elec-tron conductivity, and that of heavy ions is much smaller still. It is generallybelieved that the electron conductivity remains strong in regions where the par-ticle temperatures are equilibrated via rapid Coulomb collisions. If, however,the naturally lower conductivities for positive ions can affect the energy bal-ance at heights where collisional equilibration breaks down, the protons andheavy ions would naturally heat up to higher temperatures than the electrons(see also Holzer & Leer 1997; Lie-Svendsen & Esser 2005).

Although the UVCS ion measurements represent strong constraints on theheating and acceleration of the fast solar wind, we do not yet have closure onthe exact kinetic microphysics of the heavy ions. Nonetheless, it has been possibleto make progress in understanding other global aspects of wave heating. Cranmer& van Ballegooijen (2005) presented a comprehensive model of how incompress-ible Alfven waves are generated in the photosphere, how they propagate up theflaring and merging open flux tubes, how they are linearly reflected to seed the tur-bulent cascade (which requires counterpropagating waves), and how the cascadeflux determines the gross properties of the damping (see also Dmitruk et al. 2002;Verdini et al. 2004). The models above were constrained by having to match thelow-frequency Alfven wave amplitudes determined from UVCS line width mea-surements (e.g., Esser et al. 1999). Other recent studies focus on the self-consistentcomputation of fast solar wind models using a simpler Kolmogorov version of theturbulent damping (e.g., Hu et al. 1999; Li 2003), and on the ability of variouskinds of waves to steepen into shocks and heat open-field regions (Suzuki 2004;Suzuki & Inutsuka 2005). (See also Sect. 5.4 for further discussion of global heat-ing constraints on the final solar wind state.)

It is clear from the above summary of theoretical work that UVCS has pushedthe envelope of the known into new regimes of kinetic plasma physics and en-abled the community to formulate more focused questions. For example: Howand where are ion cyclotron fluctuations generated and damped? What are therelative contributions of the various kinds of wave-particle interaction? Is a wave-like (i.e., linear or quasilinear) description of the fluctuations even applicable inregions of strong MHD turbulence? Are “classical” collisional processes (e.g.,viscosity, thermal conductivity, ion-neutral friction, electrical resistivity) impor-tant in the low-density extended corona? Is the generation of suprathermal tailsin particle velocity distributions a necessary part of the bulk plasma heating andwind acceleration?

One straightforward way to make progress in answering many of the abovequestions would be to measure the plasma properties of additional ions having a


wider range of charges and masses. Cranmer (2002b) gave a set of predictions forthe widths of 12 emission lines (corresponding to He+, N4+, O4+, Ne7+, Si7+,Si8+, Si10+, Si11+, S5+, S9+, Fe11+, and Fe12+) that would be observable withthe next-generation ultraviolet coronagraph spectrometer concept described inSect. 3.6. The distribution of derived kinetic temperatures as a function of the ioncharge-to-mass ratio Z/A puts a firm constraint on not only the shape of the powerspectrum of cyclotron-resonant fluctuations (see also Cranmer 2002a), but also onthe identification of dominant wave modes, on the local degree of wave damp-ing, and on the amount of local collisional temperature equilibration. Once thesequantitative determinations of high-frequency wave properties are made from theheavy ion observations, the impact of these waves on the bulk plasma (via protonsand He2+) can be found. The derived heating rates can then be compared directlyto empirical heating rates that come from measurements of, e.g., H I Lyα and He II30.4 nm emission lines. This gives a clear indication of the relative contributionof phenomena such as ion cyclotron resonance to the heating of the bulk plasmaof the fast solar wind. Other aspects of the questions listed above, such as the ex-istence of suprathermal tails, can also be addressed with the improved capabilitiesof a next-generation instrument (see Sect. 8).

5.3 Streamers and slow solar wind

The slow-speed component of the solar wind is believed to originate (at least inpart) from the bright “helmet streamers” seen in white-light coronagraph images.However, since most of the streamer appears to have a closed magnetic field andthe streamer “legs” appear to have an open but convergent geometry, it is uncertainhow the plasma expands into a roughly time-steady flow. Does the slow wind flowmainly along the open regions (i.e., legs) neighboring the closed central cores ofstreamers? Do the closed fields occasionally break open and release plasma intothe heliosphere? Do there exist intermediate-brightness regions of “quiet” openfield (in the extended corona) that cannot be classified as either coronal holes orstreamers? SOHO has provided varying levels of evidence for all of the abovephenomena, but an exact census or mass budget of slow-wind source regions hasnot yet been constructed. Below we review the following: the measured propertiesof the large-scale equatorial “streamer belt” that persists for several years aroundsolar minimum (Sect. 5.3.1), the variations in slow wind source regions over thesolar cycle (Sect. 5.3.2), and recent theoretical advances in understanding theseregions (Sect. 5.3.3).

5.3.1 Solar minimum: Quiescent equatorial streamers

It was evident from the very first UVCS/SOHO observations of equatorial stream-ers that the bulk plasma (as sampled by H I Lyα and white-light pB) has a qual-itatively different appearance than the emission in heavy ions (e.g., O VI 103.2,103.7 nm). Figure 45 illustrates these differences by showing raster images of totalline intensities built up from multiple-height scans with the UVCS slit. The Lyαintensity pattern is similar to that seen in LASCO visible-light images; i.e., thestreamer is brightest along its central axis. In O VI, though, there is a darkening in


Fig. 45 Equatorial streamer observed off the west solar limb with UVCS in April 1997.Wavelength-integrated intensities are shown for (a) O VI 103.2 nm and (b) H I Lyα. Blackdotted lines show the plane of the ecliptic. Arrows show the computed wind speed, with lengthproportional to speed, and circles indicate no measurable speed (see Strachan et al. 2002)

the central core whose only interpretation can be a substantial abundance depletion(Noci et al. 1997b). For solar-minimum equatorial streamers, the oxygen abun-dance along the streamer edges, or legs, was ∼0.3 times the photospheric value.In the presumably closed-field core, though, the oxygen abundance ranged be-tween 0.01 and 0.1 times the photospheric value (Raymond et al. 1997; Marocchiet al. 2001; Vasquez & Raymond 2005). Low FIP (first ionization potential) el-ements such as Si and Fe were enhanced by a relative factor of 3 in both cases(Raymond 1999; see also Uzzo et al. 2003, 2004). Abundances observed in thelegs are consistent with abundances measured in situ in the slow wind. This is astrong indication that the majority of the slow wind at solar minimum originatesalong the legs of streamers. The extremely low abundances in the streamer core,on the other hand, are evidence for gravitational settling of the heavy elements inlong-lived closed regions, a result that was confirmed by SUMER (Feldman et al.1998, 1999).

UVCS measurements have also been used to derive the wind outflow speedsin streamers. Kohl et al. (1997a) reported O5+ doublet intensity ratios above aquiescent equatorial streamer from ρ = 1.5 to 8 R�; they constrained the ionoutflow speed at ρ = 7 R� to be between about 175 and 205 km s−1. Habbalet al. (1997) examined the latitudinal morphology of the O5+ intensity ratio ina solar-minimum streamer. Relatively sharp gradients were found in the inferredoutflow speed between the central axis of the streamer belt at large heights (i.e.,the “streamer stalk”) and the neighboring streamer/coronal-hole boundary region.For the same 1997 data analyzed by Habbal et al. (1997), Strachan et al. (2002)


found no detectable outflow at various locations inside the central core region ofthe equatorial streamer. Measurable outflow speeds were found outside (i.e., athigher latitudes than) the bright legs. Slow-wind speeds were also found alongthe streamer axis (i.e., the stalk) above the probable location of the magnetic cuspbetween about 3.6 and 4.1 R� (see also Fig. 45). Abbo & Antonucci (2002) andAntonucci et al. (2005) found similar results, but with a slightly lower cusp radius(2.3–2.7 R�).

As implied above, the precise latitudinal location of the boundary betweenopen and closed magnetic field is not known with certainty. At heights below thecusp, the local latitudinal maxima in O VI total intensity that define the streamerlegs appear to be connected to the merged radially outflowing region above thecusp (i.e., they join together at the Y-shaped cusp to form the stalk). However,Doppler dimming measurements of the outflow speed tend to show substantialoutflow only at latitudes 10◦ to 20◦ higher than this intensity maximum, and theyshow that outflow along the bright legs is below the detectable level with currentmethods (i.e., less than about 30 km s−1; see Strachan et al. 2002; Spadaro et al.2005; Antonucci et al. 2005). Nevertheless, the agreement of the elemental abun-dances between the streamer legs and the in situ slow-speed wind seems to implythat the slow wind accelerates in the legs and reaches measurable levels of outflowspeed above the cusp. At the time of this writing, there has not been an abundancedetermination in the region outside the legs and so it is not known if the observedoutflowing plasma in this region has the abundance pattern of the fast or slow solarwind.

There are other potential explanations for the low outflow speeds in thestreamer legs. The bright legs may correspond to the last few closed field lines,but they could exhibit higher abundances than in the core because of enhancedcross-field diffusion (via, e.g., Coulomb friction) between the static O5+ ions andoutflowing particles on neighboring open field lines (Ofman 2000). Conversely,the bright legs may indeed coincide wholly with open field lines, but the slow-speed solar wind along these flux tubes could exhibit a deep local minimum inoutflow speed (possibly with u < 50 km s−1) due to mass flux conservation inthe flared flow-tube geometry near the cusp. Thus the wind speed in the legs be-low the cusp would not be measurable with the Doppler dimming diagnostic (e.g.,Vasquez et al. 2003).

Before leaving the topic of streamer magnetic connectivity, it is importantto note that another interpretation exists. Rather than a dipole-like (Y-shaped)cusp, both Noci et al. (1997b) and Wiegelmann et al. (2000) suggested more ofa �-shaped cusp, with open flow emerging between latitudinally separated sub-streamers. This picture has some support from LASCO/C1 observations of mid-latitude quadrupolar loops near the solar limb (Schwenn et al. 1997) that even-tually seem to merge into a single equatorial streamer at heights above ∼2 R�(see also Waldmeier 1957; Banaszkiewicz et al. 1998). Even at solar minimum,there are times when the in situ slow solar wind seems to map back down to sur-face footpoints at low latitudes – some near active regions, but many not (e.g.,Luhmann et al. 2002). Although SOHO has led to significant improvements in ourunderstanding, it is clear that a full accounting for the coronal source regions ofthe slow solar wind is not yet in place.


UVCS temperature measurements in solar-minimum streamers generallysupport the idea that high-density closed-field regions are in collisional thermalequilibrium. At low heights below the cusp, the proton and oxygen temperaturesdetermined from H I Lyα and O VI line widths, respectively, agree with electrontemperatures determined both from ionization balance models (e.g., Raymondet al. 1997; Raymond 1999) and from a UVCS measurement of Thomson-scattered H I Lyα, which is sensitive to the LOS component of the electronvelocity distribution (Fineschi et al. 1998). At ρ = 1.5 R�, consistent values ofTe ≈ Tp ≈ Tion between 1.1 and 1.5 MK have been found.

A somewhat surprising result, in view of the general assumption that thecorona is a low-β plasma, was derived from a comparison of solar-minimumstreamer densities and temperatures measured with UVCS and potential fieldextrapolations of the surface magnetic field. The plasma β is defined as theratio of gas pressure to magnetic pressure. Using the above measurements, Liet al. (1998b) showed that β ≈ 1 in the equatorial streamer belt at a height ofρ = 1.5 R� (see also Suess & Nerney 2002). This result has direct implicationsfor the heating of the streamer plasma since the dissipation of some MHD wavestends to produce preferential heating of either electrons or protons depending onthe plasma β (e.g., Habbal & Leer 1982; Gary & Borovsky 2004).

For heights above the streamer cusp, UVCS has found evidence for a loss ofcollisional equilibrium similar to that seen in coronal holes (Kohl et al. 1997a).Frazin et al. (2003) determined that O5+ above 2.6 R� in an equatorial solar-minimum streamer have significantly higher kinetic temperatures than hydrogenand exhibit anisotropic velocity distributions with T⊥ > T‖ (see also Parenti et al.2000; Strachan et al. 2004). However, the oxygen ions in the closed-field core ex-hibited neither this preferential heating nor the temperature anisotropy. The anal-ysis of UVCS data has thus led to evidence that the fast and slow wind may sharesome of the same physical processes.

Evidence for a time-variable component of slow wind in streamers came fromSOHO white-light coronagraph images. The increased sensitivity of LASCO overearlier instruments revealed an almost continual release of low-contrast densityinhomogeneities, or “blobs,” from the cusps of streamers (Sheeley et al. 1997;see also Tappin et al. 1999). These features are seen to accelerate to speeds oforder 300–400 km s−1 by the time they reach ρ ≈ 30 R�. Because of their lowcontrast, though (i.e., only about 10–15% brighter than the rest of the streamer),the blobs themselves cannot comprise a large fraction of the mass flux of theslow solar wind. This is in general agreement with the above UVCS results thatshowed that the plasma in streamer cores (presumably the origin site of the blobs)has significantly different abundances from the slow solar wind at 1 AU, implyingthat the blobs, at most, only provide a small contribution to the slow solar wind.

5.3.2 Solar cycle dependence of slow wind source regions

Even after a decade of SOHO observations, there is general disagreement concern-ing the various coronal sources of the slow-speed solar wind. Two regions that arefrequently cited as sources of slow wind are the boundaries between coronal holesand large streamers undergoing strong superradial expansion and narrow plasmasheets that extend out from streamer cusps (Wang et al. 2000). However, during


active phases of the solar cycle, many contend that most of the slow wind em-anates either from small coronal holes (e.g., Nolte et al. 1976) or active regions(Hick et al. 1995; Liewer et al. 2004). During the rising phase of solar activity,there seems to be an abrupt (∼< 6 month) change in the magnetic connectivity be-tween field lines in the ecliptic plane and the Sun (see Fig. 5b of Luhmann et al.2002). At minimum, a large fraction of field lines map into the high-latitude north-ern and southern polar hole/streamer boundaries, but at maximum nearly all fieldlines map into low-latitude active regions and small coronal holes. Unfortunately,the majority of the most recent transition was not observed by SOHO because ofthe 4-month mission interruption in 1998.

As summarized in Sect. 5.1 above, many active regions are associated withbright and compact “active-region streamers” that tend to be denser than the largerquiescent streamers seen at solar minimum (see, e.g., Ko et al. 2002; Venturaet al. 2005). At low heights, active-region streamers have higher electron tem-peratures than quiescent streamers (Foley et al. 2002) and UVCS has shown thatthis trend continues to larger heights (up to ρ ≈ 1.6 R�); the evidence comesfrom both line-specific determinations of Te and from the shapes of differentialemission measure curves that were constructed from the intensities of many lines(Parenti et al. 2000). Ion temperatures, however, exhibit the opposite trend as elec-tron temperatures. Frazin et al. (1999) found that O VI lines were narrower in anactive mid-latitude streamer than at corresponding heights in a quiescent equato-rial streamer. Strachan et al. (2004) extended this study to compare the line widthsof 7 UVCS observations of solar-minimum (1996) streamers to four observationsof solar-maximum (1999) streamers. Both proton and O5+ kinetic temperatureswere found to be smaller, for comparable heights, at solar maximum than at mini-mum. For O5+, the difference can be as large as a factor of two; i.e., at ρ = 4 R�,the kinetic temperature is ∼10 MK at minimum versus ∼5 MK at maximum. Atall epochs, the proton and O VI kinetic temperatures reach their peak values atsubstantially larger heights than where the electron temperature is a maximum.These trends imply that the energy deposition sites of positive ions are spatiallyseparated from the dominant regions of electron heating (Strachan et al. 2004).

As opposed to quiescent equatorial streamers, which tend to almost alwaysdisplay depleted ion abundances in their cores, the smaller streamers that appearat solar maximum often do not show this depleted core at the heights observedby UVCS (e.g., Uzzo et al. 2003, 2004). The lack of a depleted core could beexplained either by the existence of cusps that fall below r = 1.5 R� – implyingthat UVCS sees only the open-field regions – or by a sufficiently complex or tiltedmagnetic configuration so that there is no alignment favorable to show the internaldepletion. Uzzo et al. (2004) observed an active-region streamer that had a centralabundance depletion, then was disrupted by a CME, and then reasserted its orig-inal depletion pattern only about one hour after the CME eruption. This presentsa challenge for models of streamer abundances, which all tend to require abouta day for the depletion to manifest itself (e.g., Raymond et al. 1997; Noci et al.1997b; Schwadron et al. 1999).

It is difficult to distinguish open from closed magnetic regions solely fromimages of streamers in the extended corona (see also Ventura et al. 2005). Bycombining ultraviolet spectroscopy with various in situ measurements, though,


unique additional constraints can be placed on the coronal origins of solar windstreams. Two general techniques have been used:

1. Coordinated Abundance Mapping: Measurements of elemental abundancesboth in the corona and in interplanetary space are valuable constraints onwhere various solar wind features originate. A broad consistency betweenUVCS and in situ abundances has been found using Ulysses (Parenti et al.2001; Bemporad et al. 2003), ACE (Ko et al. 2001), and CELIAS/SOHO(Uzzo et al. 2003). However, there are many cases where there seems to besubstantial radial evolution of the abundances between the heights sampledby UVCS and the in situ measurements. It should also be noted that SUMERhas put constraints on the helium abundance in the low corona (Laming &Feldman 2001, 2003) that imply consistency with in situ number density ra-tios (nHe/nH ∼< 0.05) and also seem to rule out the large spikes in heliumabundances predicted in some models of the corona and solar wind (e.g., Burgi1992; Hansteen et al. 1997).

2. Spacecraft Quadrature Studies: The optimum type of coordinated observa-tion is one that samples the same plasma both close to and far from the Sun.This is achievable only with a combination of remote-sensing observationsand in situ instruments that are in quadrature with the line joining the Sun andthe remote-sensing instruments. The only spacecraft currently in this kind ofconfiguration is Ulysses, and as of early 2005 there have been 12 coordinatedobservation campaigns between SOHO and Ulysses. UVCS and LASCO ob-servations of the boundary between coronal holes and streamers have led tothe determination that the boundary between fast and slow wind in 1997 wasessentially radial and nondiffusive between 5 R� and 5 AU (Suess et al. 2000).The rotation-tracking of coronal holes and CMEs with UVCS has produced anaccurate calibration of ballistic “feature mapping” of in situ data back to thesolar disk (Poletto et al. 2002). At least two CMEs observed in the corona havebeen measured later in situ with Ulysses – one that was a result of a streamerblowout (Suess et al. 2004) and one that exhibited a hot (Te ∼> 6 MK) trailingcurrent sheet (Poletto et al. 2004; Bemporad et al. 2005b); see Sect. 6.3.

UVCS also has observed various kinds of time variability (in addition toCMEs) above active regions. For example, Ko et al. (2005) made detailed mea-surements of a coronal jet in a coordinated campaign with UVCS, CDS, EIT,TRACE, and other ground-based instruments. Jets are often observed in X-raysand are associated with Hα surges, bright points, flares, and photospheric fluxcancellation (e.g., Shibata et al. 1992; Alexander & Fletcher 1999). EUV and X-ray imaging highlights the hottest parts of these transient features (which often lastonly for tens of minutes), whereas UVCS has been shown to probe a cooler com-ponent that can last for several hours. Ko et al. (2005) found that this componentwas heated rapidly at the onset of the event (with a H I Lyα kinetic temperature of0.3 MK), then it cooled rapidly to ∼0.1 MK over 2 hours. Ion abundances and H ILyα widths measured with UVCS implied collisional temperature equilibration(Te ≈ Tp) in the cool component. Also, UVCS observed the jet at a height of 1.6R�, but not at or above 2.3 R�. This implies the jet may have been ballistic innature, arching up then falling back down in a manner similar to spicules. Coronaljets may also be related to “narrow CMEs” that also have been observed by UVCS(see Sect. 6.6; see also Dobrzycka et al. 2003).


5.3.3 Theoretical advances: Streamers

Despite the new observational constraints from SOHO, the overall energy budgetin coronal streamers is still not well understood, nor is their temporal magneto-hydrodynamic stability. Modeling of the partially open magnetic field associatedwith streamers began with iterative approaches that, in some cases, were notguaranteed to yield self-consistent or time-steady solutions (see Pneuman & Kopp1971; Sakurai 1985; Wang et al. 1993). Simple magnetostatic potential-fieldmodels are often used to estimate the geometry of the axisymmetric (solarminimum) field, but these can exhibit a wide range in physical parameters whereobservations have been limited – e.g., the modeled streamer cusp may be too low(Banaszkiewicz et al. 1998) or too high (Charbonneau & Hundhausen 1996)when compared to the UVCS measurements. Recent models run the gamut fromsimple, but insightful, analytic studies (Suess & Nerney 2002; Nerney & Suess2005) to time-dependent multidimensional simulations (e.g., Suess et al. 1999;Wiegelmann et al. 2000; Usmanov et al. 2000; Wu et al. 2000; Ofman 2000, 2004;Lionello et al. 2001, 2005; Roussev et al. 2003; Hu et al. 2003; Li et al. 2004).

In Sect. 5.4 we discuss theoretical explanations for why streamers give riseto slow-speed solar wind (as opposed to high-speed wind streams from coronalholes). Here we briefly summarize theoretical models of the dynamical stability– or instability – of streamers, as well as possible theoretical explanations for theFirst Ionization Potential (FIP) effect.

Wang et al. (2000) reviewed three proposed scenarios for the production ofthe “blobs” seen emerging from the tips of streamers in LASCO images (seeSect. 5.3.1): (1) “streamer evaporation” as the loop-tops are heated to the pointwhere magnetic tension is overcome by high gas pressure; (2) plasmoid forma-tion as the distended streamer cusp pinches off the gas above an X-type neutralpoint; and (3) reconnection between one leg of the streamer and an adjacent openfield line, transferring some of the trapped plasma from the former to the latterand allowing it to escape. Wang et al. (2000) concluded that all three mechanismsmight be acting simultaneously, but the third one seems to be dominant (see alsoWu et al. 2000; Fisk & Schwadron 2001; Lapenta & Knoll 2005). Einaudi et al.(1999, 2001) performed multidimensional simulations of the narrow shear layerabove the streamer cusp and found that “magnetic islands” can form naturally asthe nonlinear development of a tearing-mode instability. There may be some sim-ilarity between these scenarios and older models of diamagnetic acceleration ofthe solar wind via buoyant plasmoids that may fill some fraction of the corona(e.g., Schluter 1957; Pneuman 1986; Mullan 1990).

A two-fluid MHD study by Endeve et al. (2003, 2004) showed that the stabil-ity of helmet streamers may be closely related to the kinetic partitioning of heatbetween protons and electrons. When the bulk of the heating goes to the protons,the models evolve to a state with a large transverse pressure difference betweenthe closed and open field regions. This leads to an instability and the periodicejection of massive plasmoids. When the electrons are heated more strongly, theincreased heat conduction reduces the transverse pressure difference between re-gions and the streamers are stable. It is possible that the observed (small) massfraction of the blobs observed by LASCO can be used to help constrain the rel-ative amounts of proton and electron heating. However, in order to conclusively


determine the energy deposition rates for the two major particle species, one wouldneed to measure both Tp and Te from the coronal base to past the streamer cusp,and as a function of latitude and longitude. UVCS/SOHO has shown the potentialfor ultraviolet coronagraph spectroscopy to make such measurements, but futureinstrumentation would be needed to carry out such a detailed characterization ofthe plasma.

The factor of three enhancement in the abundances of low FIP elements seenin essentially all UVCS streamer observations has been important in establishingthe connection between streamer legs and the slow solar wind. The theoretical un-derstanding of the FIP enhancement, though, is still open to debate. Various earlymodels relied upon steady-state or time-dependent diffusion in the chromosphere(Marsch et al. 1995; Wang 1996; Peter 1998), but McKenzie et al. (1998) pointedout that these models rely critically on boundary conditions. Other models (vonSteiger & Geiss 1989; Vauclair 1996; Henoux & Somov 1997) rely upon mag-netic fields. In a model related to the nanoflare picture of coronal heating, Arge& Mullan (1998) considered reconnection regions in the chromosphere where theionized low-FIP elements were driven more effectively into the current sheet. Themost recent models (Schwadron et al. 1999; Laming 2004) are based on Alfvenwave heating and ponderomotive forces. The model by Laming may also explainan “inverse FIP effect” seen in some active stars.

5.4 Why are there two phases (fast/slow) of solar wind?

This section is concerned mainly with understanding the dichotomy between thefast solar wind streams that emerge from the central regions of large coronalholes and the slow streams that are associated with streamer legs, stalks, andstreamer/coronal-hole boundary regions. More work is needed to apply the ideaspresented below to other potential slow-wind source regions (e.g., small coronalholes and active regions; see Nolte et al. 1976; Wang 1994b; Neugebauer et al.1998; Liewer et al. 2004).

There is a strong empirical relationship between the solar wind speed u mea-sured in situ and the inferred lateral expansion of magnetic flux tubes near the Sun.Levine et al. (1977) and Wang & Sheeley (1990) found that the asymptotic windspeed is inversely correlated with the amount of transverse flux-tube expansionbetween the solar surface and a reference point in the mid-corona (Arge & Pizzo2000; Poduval & Zhao 2004). As illustrated in Fig. 46, the field lines in the centralregions of coronal holes undergo a relatively slow and gradual rate of superradialexpansion, but the more distorted field lines that coincide with the streamer legsand the hole/streamer boundary regions undergo more rapid expansion. It shouldbe noted, though, that the eventual flux tube expansion (i.e., between the Sun and1 AU) for polar coronal holes is likely to exceed that of the streamer structures,despite the opposite trend seen when the expansion factor f is measured betweenthe solar surface and a coronal source surface.

Several potential explanations for the observed anticorrelation between windspeed and flux-tube expansion have been proposed (see below). However, it isworthwhile to begin examining such a relationship from the standpoint of the


equation of momentum conservation along a solar wind flux tube:(

u − a2‖u

)du

dr= d F

dr(22)

where, for a plasma dominated by protons and electrons, the effective one-fluidmost-probable speeds are defined as a2‖/⊥ = kB(Tp ‖/⊥ + Te)/m p and collisionsand external sources of momentum are neglected. The function F(r) appearing onthe right-hand side is defined as

F(r) ≡ G M�r

− a2‖ +∫ r

R�dr ′a2⊥

(2

r ′ + 1

f

d f

dr ′

)(23)

and f (r) is the dimensionless flux-tube expansion factor (which is proportional toB−1r−2 measured along a flux tube; see also Kopp & Holzer 1976).

Local extrema in F(r) satisfy the Parker (1958) critical point condition. Kopp& Holzer (1976) and Vasquez et al. (2003) found that only the global minimumin F(r) gives a sonic/critical point location that allows a consistent and continu-ous solution for u(r) over the full range of distances from the Sun to 1 AU. Formonotonically increasing expansion factors like those over the poles, F(r) tendsto exhibit a single minimum in the low corona (r ≈ 2 R�). For streamer-like ex-pansion factors that peak near the cusp, another minimum in F(r) appears at aheight well above the cusp; this new point tends to be the global minimum. Thelatter kind of flux tube – i.e., one that allows a more distant critical point radius– seems to correspond directly to the slow-speed wind measured in situ (see alsoBravo & Stewart 1997; Chen & Hu 2002; Cranmer 2005).

(a)(b)

(c)

Fig. 46 (a) Idealized solar-minimum magnetic field from the model of Banaszkiewicz et al.(1998), with selected field lines labeled A to D in all 3 panels. (b) Superradial flux-tube expan-sion factors (normalized to f = 1 at the solar surface) for 4 selected field lines. (c) Possibleradii of the sonic/critical point computed from local minima in F(r), shown for a fine grid offield lines in the Banaszkiewicz et al. model (not all shown in [a–b]). Colatitudes of field lines(measured from the pole) at r = R� and at infinity are plotted on the left and right verticalscales, respectively


Figure 46c shows the radial locations of minima in F(r) along individuallymapped flux tubes that range from the pole to the edge of the streamer belt (seecorresponding labels A→D in the other panels). Cranmer (2005) solved Eq. (23)using the magnetic field model of Banaszkiewicz et al. (1998) and an isothermalcorona (Tp‖ = Tp⊥ = Te = 1.75 MK) for simplicity. The outer critical point ap-pears only for field lines having latitudes at r →∞ less than about 23◦ above andbelow the equator. In more physically realistic models that include radial and lati-tudinal temperature variations (e.g., Vasquez et al. 2003), the outermost minimumin F(r) is the global minimum, and thus as one moves from the centers of coronalholes to their edges, the critical point moves outwards abruptly from < 2 R� to> 4 R� at a latitude still rather far removed from the streamer cusp.

Why does the height of the critical point matter? Physically, the critical orsingular point (equivalent to the sonic point for a hydrodynamic pressure-drivenwind) is the location where the subsonic (i.e., nearly hydrostatic) coronal atmo-sphere gives way to the kinetic-energy-dominated supersonic flow. Whether thecritical point lies above or below the regions where most of the energy depositionoccurs is a key factor in determining the nature of the wind:

1. If substantial heating occurs in the subsonic corona, its primary impact is to“puff up” the scale height, drawing more particles into the accelerating windand thus increasing the mass flux. Roughly, the increase in energy flux due tothe heating can be balanced by the increase in mass flux, so that the eventualkinetic energy per particle is relatively unaffected and the wind speed maynot change (relative to an unheated model). In some scenarios the mass fluxincrease can be stronger than the energy flux increase, and the asymptotic windspeed decreases.

2. If substantial heating occurs in the supersonic corona, the subsonic tempera-ture is unaffected and the mass flux is unchanged. The local increase in energyflux has nowhere else to go but into the kinetic energy of the wind, and theflow speed increases.

See, for example, Leer & Holzer (1980), Pneuman (1980), and Leer et al. (1982).The above dichotomy is often modeled by changing the height at which the bulkof the energy is deposited, but it can also occur if the heating remains the sameand the height of the critical point changes (as discussed above).

A natural link can be made between geometry-related changes in the flowtopology and the heating-related changes in the wind. Wang & Sheeley (1991)proposed that the observed anticorrelation between u and f is a by-product ofequal amounts of Alfven wave flux emitted at the bases of all flux tubes (see alsoearlier work by Kovalenko 1978, 1981). Near the Sun, the Alfven wave flux FAis proportional to ρVA〈δV⊥〉2. The density dependence in the product of Alfvenspeed VA and the squared Alfven wave amplitude 〈δV⊥〉2 cancels almost exactlywith the linear factor of ρ in the wave flux, thus leaving FA proportional mainly tothe radial magnetic field strength B. The ratio of FA at the critical point to its valueat the photosphere thus scales as the ratio of B at the critical point to its value atthe photosphere. The latter ratio of field strengths is proportional to 1/ f , where fis the coronal expansion factor as defined by Wang and Sheeley. For equal wavefluxes at the photosphere for all regions, coronal holes (with low f ) will thus havea larger flux of Alfven waves at and above the critical point compared to streamers(that have high f ).


There is another phenomenological piece of evidence from UVCS that maybe related to where the heating occurs in the acceleration region of the fast andslow solar wind. Kohl et al. (2001) compared the heights at which significant O5+heating occurs in coronal holes and streamers (both at solar minimum and solarmaximum) to the densities of these structures, and found a definite correlation.The lower-density regions exhibit preferential O5+ heating at lower heights (seealso Frazin et al. 2003; Miralles et al. 2004). This could be the result of collisionaldecoupling that occurs below some critical density, but it also works in the samesense as the above-cited links between flux-tube geometry, critical point location,and the regions of substantial Alfven wave flux.

To summarize, for streamers [coronal holes], more of the Alfvenic energy fluxshould be deposited below [above] the critical point. This effect is complementaryto the change in height of the critical point discussed above; i.e., for streamers[holes] the critical point is higher [lower]. However, whether waves primarily givemomentum to the solar wind (via wave pressure gradient forces) or energy (viadamping) is still a debated topic; in coronal holes, it is likely that both processesact with roughly comparable importance. Cranmer (2004b, 2005) provided illus-trations of both effects for a specific model of non-WKB Alfvenic turbulence, andthe UVCS H I Lyα line widths acted as strong constraints in both cases.

When examining predictions for the relative amounts of heating in coronalregions that give rise to fast vs. slow solar wind, it is worthwhile to comparewith different, but potentially complementary ideas. Fisk (2003) and Schwadron& McComas (2003) discussed the origins of correlations between the asymptoticwind speed and observed properties of emerging loops in the low corona (see alsothe related footpoint diffusion model of Fisk & Schwadron 2001). Their predictionof more basal coronal heating (and a higher mass flux) in the slow wind seems tobe in accord with the results discussed above. There still seems to be a disconnect,though, between theories of coronal heating via flux emergence and theories thatinvoke magnetic footpoint shaking (which in turn generates waves). The relativecontributions of these processes in various coronal regions need to be quantifiedfurther.

6 UVCS observations of coronal mass ejections

Coronal mass ejections (CMEs) are dramatic eruptions of prominence and coronalplasma at speeds ranging from 100 to 2500 km s−1, and typical masses are 1015

to 1016 g (e.g., Sheeley et al. 1999; Vourlidas et al. 2000; Yashiro et al. 2004).They are observed to occur quite frequently, varying from once in three days atsolar minimum to more than three per day at solar maximum (St. Cyr et al. 2000).While there have been attempts to divide CMEs into slower, gradually acceleratingevents and faster events that seem to reach constant speed by the time they areobserved with coronagraphs (e.g., Sheeley et al. 1999; Moon et al. 2002), recentresults suggest a more continuous distribution (Vourlidas & Patsourakos 2004;Yurchyshyn et al. 2005). CMEs are triggered by magnetic field eruptions, but thereis no consensus yet regarding the magnetic field configuration that causes a CME.

CMEs are often associated with solar flares, though some CMEs arise fromfilament eruptions without detectable flares (Moon et al. 2002). When CMEs andflares occur together, the CMEs seem to precede the flares in many cases, and


+

flare ribbon

evaporation

shock enhanced cooling

Mach 2 jets

Hα loops (104 K)

conduction front

x -ra

yloo

ps(10

7 K)

super hot (hard X-ray) regions(> 108 K)

chromosphere

current sheet

isothermal Petschek shock

post shock flow

condensation inflowUV loops (105 K)

condensation downflow

chromosphericdownflow

reconnection inflow

termination shock

solar surface

reconnectioninflow

reconnectioninflow

current sheet &reconnection outflow

plasma + magneticflux ejected

electric field inthe current sheet

magnetic field line

magnetic field line

plasma flow plasma flow

separatrix bubbleflux rope

Fig. 47 Schematic field configuration and flow pattern for CME-flare system (Lin & Forbes2000; Lin et al. 2004; Lin & Soon 2004). The geometry of the Lin & Forbes model is simplifiedfor mathematical convenience (see Sect. 6.2)

the CMEs generally contain more kinetic energy than the energy radiated by theflare (e.g., Emslie et al. 2004b). There has been some dispute as to whether flarescause CMEs or vice-versa, but it is more appropriate to consider a unified modelthat accounts for both (e.g., Gosling 1993). Figure 47 is a schematic from Linet al. (2004) that depicts the scenario that has developed over the past 20 years(e.g., Svestka & Cliver 1992; Svestka 1996; Svestka & Farnık 1998; Lin & Forbes2000). In this “standard” picture, a stressed magnetic arcade that may contain atwisted rope of magnetic flux at its core begins to rise. A current sheet developsbeneath it as external pressure causes oppositely directed magnetic field lines toreconnect. Some of the energy liberated helps to heat the CME plasma and driveit upward, at the same time adding mass and magnetic flux to the CME structure.


The rest of the energy is directed downward in the form of energetic particles orrapidly moving plasma. When it encounters the low-lying magnetic loops or trav-els on to the chromosphere, this energy produces the solar flare. In some cases,especially if a prominence lifts off slowly, there may be too little energy depositedin underlying loops to produce a detectable flare. In other cases, a different mag-netic topology might produce a flare without a detectable CME. However, mostsizable events seem to have both.

CMEs often show apparently helical structures, for instance the events shownby Wood et al. (1999a) and Plunkett et al. (2000), but it is difficult to derive thethree-dimensional structure from a two-dimensional image obtained by a whitelight coronagraph. These helices are attributed to helical magnetic flux ropes.While there is debate about whether the flux ropes are pre-existing or are formedduring the course of the eruption (Gosling 1996; Antiochos et al. 1999; Lin &Forbes 2000), there is a possibility that conservation of magnetic helicity plays animportant role in the evolution of CMEs (Kumar & Rust 1996). It has also beenproposed that CMEs play an important role in the solar dynamo by shedding mag-netic helicity that would otherwise build up in the convection zone (Low 2001;Blackman & Field 2000; Brandenburg & Sandin 2004). While filaments on theSun show a definite difference in handedness between the northern and southernhemispheres (e.g., Pevtsov & Canfield 1999), we are just beginning to connect thehandedness of CMEs with that of the pre-CME filaments (see Sect. 6.2.4).

As CMEs expand into the heliosphere, they often take the form of magneticclouds – smoothly varying structures of twisted magnetic flux containing rela-tively low pressure plasma (Osherovich & Burlaga 1997). A sheath of swept-upsolar wind plasma may enclose the magnetic cloud, and if the CME is fast enougha shock wave forms at the leading edge of the sheath. Energetic particles are accel-erated by CME shocks, but some of the solar energetic particles (SEPs) associatedwith flare/CME events are believed to originate in the flare itself (Reames 1999)or in the current sheet (Litvinenko 2000).

CMEs can produce intense space weather effects when they encounter theEarth’s magnetosphere, both by direct bombardment of SEPs and by disturbingthe magnetic field (e.g., Lanzerotti 2001). They have been known to disrupt powergrids and disable satellites. The SEPs can endanger astronauts. A good summaryof CME physics is contained in AGU monograph 99 (Feynman et al. 1997).

Few ultraviolet spectra of CMEs were available before the launch of SOHO.Schmahl & Hildner (1977) observed a prominence eruption with the SO55 experi-ment aboard Skylab. They were able to trace the density and temperature structureas the prominence rose to ρ = 1.3 R�, finding little change from the pre-CMEvalues. They concluded that most of the CME mass originated in the low corona.Fontenla & Poland (1989) also observed a prominence eruption in chromosphericand transition region lines with the UVSP experiment aboard SMM. They foundsignificant heating of the prominence plasma below ∼1.5 R�, at least up to tem-peratures near 105 K.

SOHO has greatly extended the possibilities for ultraviolet spectroscopy ofCMEs. CDS has observed the velocity signatures of a rapidly untwisting helix(Pike & Mason 2002) and rotating columns of plasma in jets or sprays (Harrisonet al. 2001). Smaller velocities are also seen over larger scales in CMEs, and theyindicate evacuation of the corona that leads to dimming as seen by EIT (Harra &


Sterling 2001). SUMER has measured density sensitive line ratios in an eruptingprominence (Wiik et al. 1997) and measured high velocities in species as disparateas C+ and Fe20+ (Innes et al. 2001, 2003). The remainder of this section willconcentrate on UVCS observations at larger heights.

UVCS has observed several hundred CMEs, generally at heights betweenρ = 1.5 and about 5 R�. This is the region where CMEs typically experiencetheir maximum acceleration, acquiring most of their mass and kinetic energy(e.g., Zhang et al. 2004). In addition, reconnection in the wake of the CME addspoloidal magnetic flux to the structure, creating a helical magnetic flux rope(Gosling 1996). Even in the case of a pre-existing magnetic flux rope, this processcan roughly double the size and magnetic flux of the CME (Lin, Raymond & vanBallegooijen 2004). Thus a CME attains all the major properties that determineits geoeffectiveness in the altitude range observed by UVCS.

CMEs usually appear as sudden brightenings in lines of low ionization speciesin narrow intervals along the UVCS slit. H I Lyα, for example, may brightenby a factor of 1000 over the course of 10 minutes. The bright emission may beDoppler shifted by as much as 1000 km s−1, and the line profile is usually quitenarrow. In other CMEs, the signature in UVCS data may be very high-temperatureemission or simply a dimming as streamer material is blown away. The wide rangeof CME properties detectable with ultraviolet spectroscopy allows many differentconstraints on the parameters and physical processes in CMEs to be determined.

The following subsections outline the specific diagnostics available from ultra-violet spectra (Sect. 6.1), then present some UVCS results regarding CME struc-ture (Sect. 6.2), current sheets (Sect. 6.3), bulk plasma heating (Sect. 6.4), CME-driven shock waves (Sect. 6.5), jets (Sect. 6.6), and SEP acceleration (Sect. 6.7).

6.1 Ultraviolet spectral diagnostics of CMEs

Many physical parameters are needed to describe CMEs in sufficient detail to en-able a study of their dominant physical processes. To understand the triggeringand evolution of CMEs, one needs to know the pre-CME configuration of thecoronal magnetic field and plasma and to measure the mass, density, temperature,and velocity field in the CME itself. To understand the production of SEPs, thepre-CME coronal conditions must be understood: density and temperature, ionicand elemental composition, magnetic field strength and direction, and the veloc-ity distributions of particles to be accelerated (seed particles). It is also necessaryto know the shock speed, compression ratio, and angle between the shock nor-mal and the line of sight (LOS). Some of these parameters can be measured byUVCS as described below, while others will require a more advanced ultravioletcoronagraph spectrometer.

6.1.1 Velocity

Coronagraphic ultraviolet spectra measure velocities. The LOS component is mea-sured directly from the Doppler shift. In the case of radiatively excited lines, theDoppler shift may be weighted toward the centroid of the exciting chromosphericline (Noci & Maccari 1999), but at high outflow speeds most lines are primarily


Fig. 48 Intensity and velocity as functions of position along the UVCS slit (horizontal axis) andtime (vertical axis) for the 12 December 1997 event. From left to right, the panels show H I Lyαintensity, C III 97.7 nm intensity, O VI 103.2 nm intensity, and H I Lyα Doppler shift, with thelatter velocity scale (in km s−1) given in the color-bar on the right. The three threads analyzedby Ciaravella et al. (2000) can be seen in all panels

excited by collisions. Of the lines commonly observed by UVCS (see Table 1),only the Lyman lines of H I and the O VI lines have substantial radiative compo-nents in CMEs. Figure 48 shows the Doppler velocities as functions of space andtime for the event on 12 December 1997 (Ciaravella et al. 2000). The panel on thefar right indicates LOS speeds ranging from –170 to +40 km s−1, while the otherpanels show the brightness in H I Lyα, C III 97.7 nm, and O VI 103.2 nm (left toright).

The Doppler shift can be combined with speeds in the plane of the sky, ob-tained either from white light images or from time sequences of spectra, in orderto obtain the three-dimensional structure of the expanding CME (for an example,see Raymond 2002). This is especially important in establishing the helical natureof a structure and in determining whether a helix is unwinding or simply expand-ing. The Doppler speeds are also important in determining the nature of steadyflows, such as those along the thin vertical strands that persist along the sides ofthe CME well after the eruption.

The radial component of the velocity can be measured by Doppler dimmingand by radiative pumping of O VI 103.76 nm by the C II lines at 103.63, 103.70nm (at 172 km s−1 and 369 km s−1, respectively; Li et al. 1998a), as discussedabove (Sect. 2). The use of the Doppler dimming/pumping technique in CMEs isnot as straightforward as in coronal holes and streamers, though. In the latter, theelectron temperature is reasonably well constrained to vary relatively smoothly asa function of radius. In CMEs, though, Te can change abruptly between nearbysubstructures. Thus, for individual measurements of CMEs it is difficult to sepa-rate the radiative and collisional contributions to the lines.

The C II pumping process is apparent when the intensity ratio of the O VI linesfalls below its collisional value of 2:1. Figure 49 shows an example from a study of“narrow” CMEs (Dobrzycka et al. 2003). The ambiguity between speeds near 172and 369 km s−1 can generally be resolved by considering the Doppler shift and the


Fig. 49 Theoretical O VI doublet ratios as a function of outflow speed compared with observedratios (yellow bars) for a narrow CME (Dobrzycka et al. 2003). Solid, dashed, and dotted blackcurves correspond to electron densities of 1, 5, and 15 times fiducial coronal-hole values at thetwo heights, and Te = 0.5 MK. The red curve corresponds to the density of the solid black curve,but Te = 1.2 MK

Fig. 50 The O VI 103.2 intensities, inferred Doppler pumping speeds, and electron densitiesderived for different bright strands in the event of 28 June 2000 (Raymond & Ciaravella 2004).Heliocentric distances listed vertically on the right denote the radii at which the features wouldappear at the latest time in the observation sequence (01:54 UT on 29 June); i.e., converting thetime sequence at 1.7 R� into a spatial image using the derived outflow speeds


apparent speed in the plane of the sky and its variation with height and time. At thehigher speeds of fast CMEs, additional pumping mechanisms can come into play.Pumping of O VI 103.76 nm by O VI 103.19 nm (1650 km s−1) and pumping ofO VI 103.19 nm by H I Lyβ 102.57 nm (1810 km s−1) provide additional velocitydiagnostics. As with the C II pumping mechanism, these pumping processes man-ifest themselves through O VI intensity ratios different from the 2:1 collisionalvalue. Figure 50 shows the velocities determined for the CME of 28 June 2000(Raymond & Ciaravella 2004). It has also proven possible to determine when anobserved plasma structure passes through zero velocity relative to the Sun. Koet al. (2005) observed a ballistic jet at ρ = 2.3 R�. The intensity of C III 97.7 nmpeaked sharply without any corresponding change in density or temperature, justwhen the Doppler shift passed through zero. This indicated the time when C IIIions in the flow reached the top of their arc and resonantly scattered C III photonsfrom the solar disk.

6.1.2 Density

White light coronagraph images provide the electron column density, which givesan average density along the LOS. as opposed to the local density. Given the greatuncertainty in the depth of a CME structure along the LOS, local density diagnos-tics are quite important. Ultraviolet spectra provide two types of diagnostics forthe local density.

First, classical line ratio techniques that have long been applied to the solartransition region can be used, though different lines must be chosen because ofthe generally lower densities at large heights in the corona. This leads one to ratiosthat depend on forbidden rather than intercombination lines. Among the density-sensitive line ratios, the ratio of the O V forbidden and intercombination lines,at 121.385 and 121.839 nm respectively, is especially useful because the criticaldensity is about 106 cm−3 (Akmal et al. 2001). Figure 51 shows the line ratioobserved at one position in the 23 April 1999 event plotted against the densitydependence of the ratio predicted by CHIANTI (Young et al. 2003). Uncertaintiesin the measured line ratio and the atomic rates lead to density determinations withuncertainties ranging between ±10% and ±50%, depending on the specific linesused. It is worth noting that many density-sensitive line ratios have some sensi-tivity to the electron temperature as well, and it is not always straightforward todetermine reliable values for Te. The O V ratio is relatively insensitive to varia-tions in Te.

Second, CME studies also make use of densities derived by comparing thecollisionally excited component of a line, which is proportional to ni ne, to theradiatively excited component, which is proportional to ni (see Sect. 2.1). Theycan generally be separated by simple algebra given the ratio of two lines of an ionand the known ratios of collisional and radiative components. This technique canbe used to obtain pre-CME coronal densities (e.g., Raymond et al. 2003) or to ob-tain densities when the CME outflow velocity provides resonance with a pumpingtransition (e.g., Dobrzycka et la. 2003). Along with the velocities, Raymond &Ciaravella (2004) obtained density estimates for the 28 June 2000 event shown inFig. 50.


6.1.3 Ion, electron, and ionization temperatures

Ion temperatures can be obtained from line profiles provided that one can separatethermal from bulk velocities. H I Lyα and C III 97.7 nm have proven useful inthis regard (e.g., Ciaravella et al. 2000). In many cases only an upper limit canbe derived, but in some cases that limit is quite stringent. The H I Lyα profilein CME cores is usually much narrower than typical coronal profiles for otherspectral lines, and depending on the spectral resolution (determined in part by theslit width chosen), the observations frequently imply proton temperatures below105 K.

Electron temperatures can be derived from line ratios (e.g., Si III 120.65,130.33 nm; Ciaravella et al. 2000), but in existing analyses they are more oftenconstrained by the ionization states present and the excitation rates needed to ac-count for the observed emission line intensities.

The ionization state is determined from the range of ions observed. In general,spectra of CMEs show extremely bright emission of low temperature species suchas H0, C2+, and O5+, faint emission or none at all from species found at coro-nal temperatures such as Mg9+ and Si11+, and emission from high-temperaturespecies such as Fe17+ in powerful CMEs and in the current sheets behind moreordinary CMEs (e.g., Ciaravella et al. 2002; Ko et al. 2002; Raymond et al. 2003;Bemporad et al. 2005b). Higher ion charge states are observed at lower heights inflare structures by X-ray spectrometers and by SUMER (Innes et al. 2001, 2003).They have not been detected in the corona above ρ = 1.5 R�, but they are some-times detected by in situ measurements of CMEs (e.g., Lepri et al. 2001; Lynchet al. 2003; Lepri & Zurbuchen 2004). Recently Poletto et al. (2004) observed aCME on 26 November 2002 while the Ulysses spacecraft was at quadrature. Theywere able to observe the same highly ionized plasma with UVCS at ρ = 1.7 R�and with Ulysses at 4.3 AU. The combination of remote and in situ observationsof a CME opens the possibility of tightly constraining the thermal evolution of

Fig. 51 O V 121.385/121.839 nm intensity ratio and derived electron densities for the firstexposure in the 23 April 1999 CME (Akmal et al. 2001). The individual line intensities werecomputed in units of erg s−1 cm−2 sr−1


Table 5 Spectral lines observed by UVCS in CMEs

Line Wavelength (nm) log10 Tmax Comments

H I Lyα 121.567 4.3 radiative pumpingH I Lyβ 102.572 4.3 radiative pumpingH I Lyγ 97.254 4.3 radiative pumpingH I Lyδ 94.974 4.3 radiative pumpingC II 103.634, 103.702 4.3C III 97.702 4.9N II 108.456 4.4N III 98.979, 99.158 4.8N V 123.82, 124.280 5.3O III 59.782 4.9O V 62.973 5.4[O V] 121.385 5.4 density-sensitiveO V] 121.839 5.4O VI 103.191, 103.761 5.5 radiative pumpingNe VI] 100.584 5.6Mg X 60.976, 62.493 6.1Si III 120.651, 130.332 4.4 temperature-sensitiveS V] 119.918 5.2Si XII 49.937, 52.066 6.3[Fe XVIII] 97.486 6.8

the ejected plasma by combining density, temperature and velocity measurementsnear the Sun with detailed charge state and abundance measurements in interplan-etary space.

6.1.4 Composition

Only a modest number of lines has been detected in UVCS observations of CMEs(Table 5), mostly because nearly all of the existing UVCS observations of CMEspertain to fairly narrow wavelength ranges centered on the bright lines. It is rela-tively easy to detect lines formed at transition region temperatures because thereis little coronal background in these lines. In addition, it appears that the densestCME material, presumably originating in erupting prominences, tends to be foundat these temperatures.

Given the modest number of lines and the large range of temperatures overwhich they are spread, it has so far only been feasible to obtain ratios of C, N andO abundances. In the best-determined case, a modest nitrogen depletion relative tocarbon suggests a moderate First Ionization Potential (FIP) bias, consistent with aprominence origin for at least some CME plasma (Ciaravella et al. 1997). In somecases the elemental composition helps to determine where material in the CMEleading edge or current sheet originated (Ciaravella et al. 2002, 2003).

6.2 CME structure

The classic picture of a CME is a three-part structure consisting of a bright leadingedge, a dark, low density void, and a bright core, generally identified with ejected


Fig. 52 Composite illustration of a generic CME/flare system and the multi-part structure fromLASCO (red image) with the magnetic field structure of the Lin & Forbes (2000) model (blueoverlay). The LASCO image has been laterally offset for clarity. The CME/flare system com-prises: (a) the bright core, (b) the dark void, (c) the outward-moving leading edge, (d) the shockfront, (e) the current sheet, (f) the arcade of magnetic field loops in the low corona, and (g) theirfoot points which form the two-ribbon flare

prominence material (see Fig. 52). The Lin & Forbes (2000) model depicted inFigs. 47 and 52 assumes a geometry whereby the prominence, the flux rope, andthe CME core are colocated. This is done for mathematical convenience, althoughin some observed CMEs these structures do seem to be colocated. Other observedCMEs appear to have a separation between the prominence and the flux rope,where the latter is often seen to be identified with the dark void. Even so, the Lin& Forbes model is well-suited for describing the evolution of flare/CME events.

It is often difficult to see a clearly defined three-part structure in corona-graph images because the leading edge may be faint or because projection of thethree-dimensional structure onto a two-dimensional image confuses the interpre-tation. For CMEs viewed nearly side-on, one part of the projection problem isdetermining the angle of the CME axis to the LOS. This can be partially addressedby assuming radial expansion from the site of the CME eruption on the solar disk(if observed). Another technique is to use the polarization fraction of the whitelight image of the CME and the known dependence of polarization fraction onscattering angle (Moran & Davila 2004). Doppler shift measurements provide theangle through a comparison of the LOS speed with the speed in the plane of thesky determined from a series of white light coronagraph images (e.g., Ciaravellaet al. 2000).


In contrast to CMEs viewed mainly from the side, there are also halo CMEsthat occur near the center of the solar disk (as viewed by an observer) andexpand into a circumsolar ring in coronagraph images. They generally show faint,somewhat diffuse borders that presumably indicate compression or deflectionof coronal material along the flanks of the CME. Halo CMEs are generallypowerful events, and they often show red-shifts or blue-shifts of order 1000 kms−1, giving a quick indication of whether or not they will strike the Earth. UVCShas observed several halo CMEs, as well as many other oblique “partial halo”events (Ciaravella et al. 2005b), and the strong measured Doppler shifts wereused to constrain the small angular separation between the direction of radialCME expansion and the Sun-Earth direction. The fact that measurable H I Lyαintensities are seen in these high-velocity events indicates that large densities(and collisional excitation) are present, since Doppler dimming is expected todrastically reduce the resonantly scattered component of this line.

Jets or sprays may be a physically distinct category from other CMEs(Sect. 6.6). In these events, reconnection between open and closed field lines is be-lieved to create high-speed flows of hot or cool plasma guided by the pre-existingmagnetic field lines. In these cases, the expanding CME as observed in the ex-tended corona would be much narrower and have a much simpler morphologythan other kinds of CMEs.

In the subsections below we describe observations of the three main partsof many CMEs: the leading edge (Sect. 6.2.1), void (Sect. 6.2.2), and brightcore (Sect. 6.2.3). We also summarize UVCS observations of the thin, helicallythreaded strands that tend to follow the vertical edges of some CMEs (Sect. 6.2.4).

6.2.1 Leading edge

The CME leading edge is often pictured as a region where the expanding CMEmagnetic bubble has compressed the overlying coronal gas. If the CME is fastenough, this compression happens by way of a shock wave. The gas can be com-pressed by at most a factor of four in the ordinary MHD case, but if SEP accelera-tion is efficient, the plasma may be compressed by a factor of seven or even more(e.g., Ellison et al. 2004). However, it is often not clear whether a structure seenin white light coronagraph images actually reveals compressed coronal gas, orwhether the leading edge is simply a magnetic loop or arcade that was filled withdense gas that expanded with the CME, maintaining a high density relative to thecorona it traveled through (e.g., Sime et al. 1984). Maia et al. (2000) present anexample of a type II radio source that seems to be coincident with the leading edgeseen in coronagraph images, and Sheeley et al. (2000) show that CMEs can causemoving kinks in nearby streamers hit by shocks. Vourlidas et al. (2003) show anexample in which the observed electron density increase matches that predicted byan MHD model of a CME with appropriate velocity and angular width. However,they assumed an explicit radial variation of the polytropic index, increasing fromγ = 1.05 to 1.45, in order to model the observed deceleration of the leading edge.Their assumed nonadiabatic dissipation may correspond to highly efficient SEPacceleration, but more realistic energy equations are needed to better understandthe balance between CME heating, dynamics, and SEP production.


We discuss UVCS diagnostics of collisionless shocks below (Sect. 6.5), butUVCS observations also bear upon the important question of the geometricalstructure of the leading edge. It is generally assumed to correspond to a thin spher-ical shell or else to a toroidal magnetic loop. Ciaravella et al. (2003) used the 50km s−1 variation in Doppler shift along the leading edge of a 11 February 2000CME and the lack of red- and blue-shifted components of H I Lyα in the CMEvoid to show that the leading edge was not a spherical shell, but a loop or ribbon-like structure. The leading edge was denser, cooler and more depleted in both Oand Si than the pre-CME streamer, leading to the conclusion that the leading edgewas a loop or arcade from the closed field core of the pre-CME streamer that hadlain below the height of the UVCS slit. This particular CME was slow enough thatthe lack of a shock front was not surprising.

6.2.2 Void

The void is clearly a low density region, and since it is expanding and pushingcoronal material aside, it must have a high magnetic pressure. A likely way ofproviding an increased magnetic pressure in this region is the continual injec-tion of magnetic flux from below via magnetic reconnection in the current sheet(Lin et al. 2004). It is thus generally agreed that the void corresponds to a regionof strong magnetic field, quite likely identified with the magnetic clouds seen ininterplanetary space. It is therefore imagined to be a helical flux rope (or somepart of a flux rope). In the 11 February 2000 CME analyzed by Ciaravella et al.(2003), the void showed a high intensity ratio of Si XII 52.1 nm to O VI 103.2nm, suggesting a temperature higher than the typical coronal temperature of 106.2

K. Within the void, variations in Doppler dimming implied substantial differencesin outflow speed. A particularly dark region in H I Lyα was interpreted as a localhigh velocity region, rather than a part of a smoothly expanding magnetic region.

6.2.3 Core

The CME core is the brightest part of the CME in ultraviolet emission, mainlybecause of the higher densities and the n2 dependence of the emissivities of col-lisionally excited lines. In addition, the low ionization temperatures favor speciessuch as H0, C2+, and O5+ that have high elemental abundances and intrinsicallylarge excitation rates. The brightness in the Lyman lines can increase by threeorders of magnitude over the course of a few minutes when CME core materialreaches the UVCS slit.

The core plasma is believed to originate in the erupting prominence because ofits high density and its morphological similarity to events seen in Hα. Measuringelemental abundances in CME cores provides a potentially powerful way to de-termine whether this material originated in the chromosphere or the corona. Caremust be taken, though, to account for the broad temperature range and small-scaleinhomogeneities when determining the uncertainties in derived elemental abun-dances of CME cores. Even without precise absolute abundances, UVCS mea-surements of the lack of a strong FIP enhancement in a CME argue against a coro-nal origin for the core material (Ciaravella et al. 2000). It would also be difficult


to explain the low ionization states observed if the gas originated at coronal tem-peratures, as the coronal ionization state would be frozen in for the faster events(Akmal et al. 2001; Ciaravella et al. 2001).

The core plasma usually takes the form of long, slender filaments seen bestin the low ionization species. The cooler lines, such as those of H I and C III,seem to be found in narrower cores within somewhat more diffuse structures seenin O VI. Proton temperature upper limits obtained from the widths of the Lymanlines are as low as 104.8 K in some cases (e.g., Ciaravella et al. 2000), and inother cases the existence of bulk velocity gradients can put large uncertainties onthe derived values of Tp. Ciaravella et al. (2000) used a ratio of Si III lines toshow that Te in the Si III emitting regions fell between 104.4 and 104.6 K in anevent on 12 December 1997, or about where the ion would be found in ionizationequilibrium. The presence of ions ranging from C+ to O5+ suggests a range oftemperatures from 104.6 K or lower to 105.5 K or somewhat higher, but the plasmacan be far from ionization equilibrium at the heights observed by UVCS. OtherCMEs show only a narrow range of ionization states, such as an event on 6 March1997, in which only ions found near 105.4 K were observed (Ciaravella et al.1999). Higher temperature emission is less frequently observed, but Ciaravellaet al. (2003) reported prominence material bright in Mg X 61.0 nm and Si XII52.1 nm near the top with a gradual shift to cooler ions in the trailing regions.

6.2.4 Helical structure

Not only are helical magnetic structures observed in the interplanetary medium(e.g., Osherovich & Burlaga 1997), but they play a crucial role in many modelsof CME eruption (e.g., Chen 1996; Gibson & Low 1998; Wu et al. 1999; Amariet al. 1999; Lin & Forbes 2000; Krall et al. 2001; Manchester 2001). Even CMEmodels that do not initially contain a twisted flux rope can develop one duringthe course of the eruption by reconnection between opposite sides of the magneticarcade (Antiochos et al. 1999; Roussev et al. 2004; Amari et al. 2003). One im-portant test is the comparison between the handedness of the coronal helix andthat of the pre-CME structure. Better yet, the chiralities can be compared if themagnetic fields are known. Martin & McAllister (1997) present a set of signaturesfor left-handed and right-handed filament and arcade structures observed on thesolar disk, and Pevtsov & Canfield (1999) have shown that left-handed chiralitypredominates in the northern hemisphere and right-handed in the south. Antonucciet al. (1997) found evidence for rotational motion in the first CME observed byUVCS. Ciaravella et al. (2000) analyzed the morphology and Doppler shifts ofthe event shown in Fig. 48 to show that it was a left-handed helix untwisting overa 1 hour time scale. Because the event occurred near the limb, the handednessof the pre-CME structure was not known, but the CME did agree with the senseexpected in the northern hemisphere. This was a relatively slow CME, and therotational motion was correspondingly slower than that observed in a much fasterevent by CDS (Pike & Mason 2002).

Suleiman et al. (2005) studied a CME on 12 September 2000. Magnetogramand Hα images of the pre-CME filament showed a right-handed structure. UVCSobserving sequences at ρ = 3.5 and 6.0 R� showed the inclination of the filamentsof cool plasma, and separate groups of filaments were seen with blue-shifts of ∼


300 and ∼ 600 km s−1. The filaments lay on the surface of an expanding, roughlytoroidal structure, and the –600 and –300 km s−1 components corresponded to thenearer and farther surfaces respectively. The combination of the inclination of afilament on the plane of the sky and the knowledge of its position on the toroidalsurface yields the handedness, which in this case was right-handed, in agreementwith the pre-CME structure.

6.3 Current sheets

Reconnection current sheets play a major role in all CME models. As indicatedin Fig. 47 they allow the CME to escape and power the solar flare beneath it.The models of Priest & Forbes (1990), and Lin & Forbes (2000) are particularlyexplicit in predicting the extent and evolution of the current sheets. Some combi-nation of turbulence and electric fields in current sheets may produce the powerlaw distributions of SEPs inferred from X-ray and gamma ray observations and de-tected in interplanetary space (e.g., Martens 1988; Litvinenko 2000; Emslie et al.2004a). Existing models of current sheets do not yet reliably predict the recon-nection rate or the fractions of the dissipated energy that emerge as heat, kineticenergy, and nonthermal particles, but considerable theoretical progress is beingmade (e.g., Priest & Forbes 2000; Bhattacharjee 2004).

There have been attempts to identify current sheets from white light corona-graph data (Webb et al. 2003), but it is difficult to be certain from morphologyalone whether a structure is a current sheet. UVCS has observed several structureswhose densities, compositions and temperatures support the current sheet identifi-cation and provide diagnostics for physical conditions near the reconnection layer.Most of those analyzed so far are bright, narrow features that are visible thanks totheir end-on orientations to the LOS.

On 23 March 1998, Ciaravella et al. (2002) detected a very narrow feature inthe [Fe XVIII] 97.4 nm line formed near 106.8 K on the line connecting brightpost-flare loops and the core of a CME. The post-flare loops extending up to r =1.2 R� were most clearly visible in Si XI emission in the EIT 30.4 nm band andin Yohkoh soft X-ray images. The [Fe XVIII] line appeared as a narrow intensitypeak along the slit and at ρ = 2.55 R�, suggesting an edge-on view of a thinsheet corresponding to the current sheet in Figs. 47 and 52. Figure 53 shows acomposite of EIT and LASCO C2 images with the UVCS slit image superposed.Several other high temperature lines of [Ca XIV], Fe XVII, and Ne IX were visibleat the same location, particularly when the UVCS entrance slit was placed 0.15R� lower. Cooler lines did not show the same peak, but they were detectable atnearby locations along the slit. The [Fe XVIII] to Fe XVII intensity ratio indicateda temperature of 106.8 to 106.9 K, and the Doppler width of the [Fe XVIII] linewas consistent with that temperature. An upper limit to turbulent line broadeningwas 60 km s−1. A density of 6 × 107 cm−3 was computed by comparing theemission measure with the hydrogen column density derived from the H I Lyαprofile. There was some evidence for enhanced elemental abundances comparedwith the nearby active region corona, but it was not conclusive. The [Fe XVIII]feature lasted for a remarkably long time, fading over a 20 hour time scale. Thisis probably related to the very slow CME that produced it.


Ko et al. (2003) observed a similar long-lasting feature on 9 January 2000.The temperature derived from the high ionization states was 106.5 to 106.6 K,and a FIP enhancement similar to that of the neighboring corona is consistentwith the expected inflow of coronal plasma into the current sheet. The outflowvelocity at ρ = 1.53 R� is below about 50 km s−1, as judged by the lack ofO VI Doppler dimming, but individual blobs of dense gas seen in LASCO movedoutward with constant acceleration to as much as 550 km s−1 by the time theyreached ρ = 6 R�. The long duration of this current sheet and its gradual motionin latitude (20◦ over the course of a day) indicate a slow relaxation of the magneticfield structure at a small Alfven Mach number.

Faster relaxation was observed in the wake of a CME on 18 November 2003(Lin et al. 2005). In this case, blobs in the LASCO images moved along the currentsheet at speeds ranging from 460 to 1065 km s−1, and the inward motion towardthe current sheet, which was measured from changes in the width of the gap seen inH I Lyα emission at ρ = 1.7 R�, ranged from 10 to 100 km s−1. Figure 54 showsthe H I Lyα intensity as a function of position along the slit, and the width of thecentral dip (coincident with the current sheet) decreases in time, indicating densematerial flowing into the reconnection region. Combining the outflow and inflowmeasurements yielded a value for the Alfven Mach number, which was between0.01 and 0.23 based on the assumption that the speed of the blobs measured above2.9 R� equals the Alfven speed. Yokoyama et al. (2001) reported inward motionsnear the cusp of an event on 18 March 1999 seen with EIT (though Chen et al.2004 have questioned this interpretation). They estimated Alfven Mach numbersbetween 0.001 and 0.03 based on a model for the magnetic field. The AlfvenMach number of the reconnection flow is closely related to the plasma resistivity,

Fig. 53 Composite of EIT and LASCO images showing the post-flare loops and CME core,respectively. The white rectangle containing a bright spot (between the larger images) containsthe UVCS slit image showing the position of the [Fe XVIII] 97.4 nm emission


and it is a key parameter in models such as that of Lin & Forbes (2000). It mustbe remembered that the Alfven Mach number probably varies with position alongthe current sheet and with time, but the Alfven speed can also be constrained byestimates of the magnetic field based on pressure balance.

One face-on current sheet has been reported (Bemporad et al. 2005b). In thatcase, a diffuse region of [Fe XVIII] emission appeared in the wake of a CME.Highly ionized plasma in the interplanetary CME (ICME) detected by Ulysses in-dicated that part of the current sheet material was ejected into interplanetary space,perhaps as part of the CME bubble (Lin et al. 2004). Bemporad et al. (2005b) werealso able to determine the temporal evolution of the current sheet temperature andto estimate the density and elemental composition.

6.4 Plasma heating

While the CME eruption can dissipate a great deal of magnetic energy, it is notclear how much of this energy takes the form of heat, and it is not clear wherethat heat would be deposited. Flares clearly liberate large quantities of heat at lowaltitudes, and flare studies have provided many examples in which the location andtransport of energy can be constrained. Much less is known about the heating ofCME plasma after the initial ejection. Obvious heating mechanisms are thermalconduction from the hot coronal plasma of the flare, kinetic energy of plasmainjected by the current sheet and then dissipated (possibly in shocks), nonthermalparticles from the flare site, and continued dissipation of magnetic energy withinthe CME as the stressed magnetic configuration relaxes. Most theoretical modelsof CMEs simply assume a polytropic equation of state, avoiding the need to solvean energy equation. The polytropic index is typically taken to be γ ∼ 1.1, because

Fig. 54 Five H I Lyα intensity profiles along the UVCS slit taken at ρ = 1.7 R� over 10minutes. The width of the central dip decreases with time and indicates inflow to the currentsheet. From Lin et al. (2005)


adiabatic expansion with a perfect gas index γ = 5/3 would lead to temperaturesmuch lower than observed in ICMEs at 1 AU. The choice of a smaller value of γtacitly implies a heating rate that balances much of the adiabatic cooling, but doesnot specify the heating process.

One CME model that does predict a heating rate is that of Kumar & Rust(1996). They assumed that conservation of magnetic helicity governs the evolu-tion of the CME as it travels through interplanetary space, and they found thatconservation of helicity in an expanding flux rope implies dissipation of magneticenergy. While their model does not predict the mechanism of that dissipation ex-cept to make a reference to turbulent cascade, it does predict that the heating rateis a significant fraction, of order 2/3, of the rate of increase of kinetic energy. Asmany CMEs are observed to accelerate strongly at heights of a few R�, the heatingmight be expected to be strong at these heights as well (e.g., Zhang et al. 2004).

With the help of quite general models, UVCS observations have been ableto constrain the heating rates in the cores of two CMEs. The technique is simi-lar to the empirical modeling procedure described in Sect. 2.2, in that the rangeof possible plasma states is determined iteratively by comparing predicted andobserved emission line properties. Akmal et al. (2001) constructed a large grid ofmodels with different assumed “initial” temperatures and densities (i.e., values as-sumed to exist at the coronal base), then evolved a plasma parcel up to the heightobserved by UVCS assuming different expansion laws and different parameter-izations for the heating rate. Each of these models involves the computation ofthe time-dependent electron temperature, density, and ionization state, and fromthese one can compute trial predictions for the ultraviolet emission line proper-ties. Models that are not consistent with the UVCS spectra and LASCO electroncolumn densities were rejected. In these models the time-dependent ionizationstate must be computed and used to compute the radiative cooling rate. While thisprocedure would seem likely to allow almost any value for the heating rate, therange of acceptable models is much smaller than might be expected. Models thatstart at very high densities suffer severe radiative and adiabatic losses, while thosethat start at low densities and high temperatures fail to recombine to the observedionization states.

Akmal et al. (2001) applied this technique to a CME on 23 April 1999. Thatevent was observed at ρ = 3.5 R�, and it was chosen for this analysis because the[O V] 121.385 nm to O V] 121.839 nm line ratio provided an especially good den-sity determination. The above modeling procedure was applied to a bright “knot”of emission that seemed to comprise a substantial part of the bright core of thatCME. The density was allowed to vary as t−1, t−2, or t−3, the heating was allowedto vary as density or density squared, as an exponential with height with a scaleheight similar to that of the solar wind, or in the manner prescribed by the Kumar& Rust (1996) model. Intial densities and temperatures covered the range fromcoronal to prominence values, 109 to 1011 cm−3 and 1.6 × 104 to 2.5 × 106 K.

Figure 55 gives an overview of the successful models in the grids of initial Teand ne for t−1 expansion and heating proportional to density or density squared.(For the precise definition of “successful,” see Akmal et al. 2001.) When heatingis proportional to density, only small ranges of the initial Te and ne values are con-sistent with the measured line intensities in the O V-bright knot, and both requireheat inputs of about 177 eV per proton, or 1.4 × 1014 ergs per gram to match the


constraints. Figure 56 shows the density, temperature and ionization fractions ofseveral ions for one of the acceptable models. When the heating varies as densitysquared, a larger region in the parameter space of initial conditions is acceptable,and the heat input of those models ranges over a factor of 2. When other expansionlaws and heating parameterizations were considered (see Akmal et al. 2001), therange of allowable thermal energy deposition is about a factor of 4.

Akmal et al. (2001) analyzed the heating required for three knots, one brightin C III, one in O V, and one in O VI. Ciaravella et al. (2001) performed a similaranalysis for a CME on 12 December 1997. Table 6 shows the energy budgets forthese two events. It is important to note that the thermal energy at the heightsobserved by UVCS is relatively low because of radiative losses and adiabaticexpansion, but a substantial amount of heat must be added as the plasma expandsto maintain even the modest temperatures observed. In fact, the total heating iscomparable to the kinetic energy and gravitational potential energy of the CMEplasma, and it should therefore be considered in CME models. The rough equalityof the kinetic energy and integrated heating agrees with the prediction of theKumar & Rust (1996) model. In detail, that model predicts too much heating at

Fig. 55 Initial densities and temperatures (at the coronal base) of models that produced accept-able emission line intensities of the O V-bright knot in the 23 April 1999 CME for heating ratesproportional to n and n2 (Akmal et al. 2001)

Table 6 CME energy budgets (in units of 1013 erg g−1)

23 April 1999 3.5 R�Knot C III O V O VI 12 December 1997 1.7R�Kinetic 180 180 180 9.5Gravitational 78 78 78 65 ?Ionization 1.9 2.1 2.1 1.5Thermal 1–3 2–5 3–10 4.5Total Heat 10–50 50–200 10–500 13–400


Fig. 56 Left panel shows the radial variation of electron temperature (in K) and electron density(in cm−3), both plotted versus modeled radius r , for one of the acceptable models of a brightO V knot in the 23 April 1999 CME (Akmal et al. 2001). Right panel shows dimensionlessionization fractions for relevant ion species

the very early stages of the eruption. However, one probably should not applytheir self-similar solution to the very early stage of the event.

Another interesting consequence of extended heating in the CME plasma is theionization state. Depending on the density and speed of the CME, the ionizationstate is usually expected to be frozen in somewhere around r ≈ 1.5 R�. Severaladditional effects may produce variations in the ionization state at larger heights.First, for slow and dense CMEs, the plasma could remain in a collisionally coupledregime far into the extended corona, thus allowing the ionization state to reflectlocal conditions at large heights. Second, the continual injection of kinetic andthermal energy (as well as nonthermal particles) from the CME current sheet mayproduce high ionization states in regions of the “separatrix bubble” that may endup being indistinguishable from the cool innermost flux rope in the ICME mag-netic cloud (see, e.g., Lin et al. 2004). These two effects could help to explain thedifference between the low ionization species that dominate UVCS observationsand the high ionization states prevalent in in situ measurements.

6.5 CME-driven shock fronts

Evidence of shock fronts driven by CMEs is seen in the in situ measurements ofdensities, temperatures, magnetic fields, and SEPs in interplanetary space. Theyare also known to occur in the solar corona, where they produce type II radio bursts(e.g., Pick et al. 2005). The radio bursts provide accurate estimates of the densitywhere the shock occurs, but little other information. Many of the SEPs associatedwith CMEs are believed to be produced as the shock passes through the corona,


so it is important to obtain diagnostic observations of CME shocks within a fewsolar radii of the Sun.

Comparison of the timing and density variation of type II bursts with the evo-lution of radio and plasma wave measurements on the Wind spacecraft leads tothe conclusion that most of the type II events are “blast waves” perhaps driven byX-ray ejecta, rather than shocks just ahead of the bulk of the CME ejecta (e.g.,Gopalswamy et al. 2001; Leblanc et al. 2001), but in most cases the location ofthe shock cannot be reliably determined. Shocks are expected to form when theCME speed exceeds the local fast mode speed V f in the corona, where

V 2f = V 2

A

[1 + β

2+

√(1 + β)2 − 4β cos2 θ

2

], (24)

and VA is the Alfven speed, β = (Vs/VA)2 is a factor of 1.2 smaller than thestandardly defined plasma beta (where Vs is the sound speed), and θ is the anglebetween the magnetic field and the propagation direction of the wave or shock.For the low-beta corona (β � 1), V f is very close to VA, which declines withincreasing distance after peaking in the low corona. Therefore, as the CME accel-erates and as the Alfven speed drops, it is likely that the CME can drive a shockwhen the leading edge speed exceeds the local value of V f . This tends to occurfor CMEs faster than ∼ 1000 km s−1 once they pass a height of order 2 R�.

There have been various attempts to identify shocks from white light corona-graph data. Sheeley, Hakal & Wang (2000) used kinks in streamers deflected byCMEs to infer the existence of shocks on the flanks of CMEs. Mancuso & Abbo(2004) used a bifurcation in the type II dynamic spectrum to determine the natureof a shock interacting with a streamer. Vourlidas et al. (2003) showed evidence fora shock based on the morphology of the sharp, bright rim and comparison withMHD models. In those models, though, a small value of the adiabatic index hadto be assumed in order to match the observations.

Ultraviolet spectra provide an unambiguous means to observe coronal shocksand to determine their properties. Shock compression causes an immediate in-crease in the emissivity of dominant ions, such as Mg9+. The bulk motion of theshocked plasma causes immediate Doppler dimming of the H I Lyman lines andO VI lines. Electron heating causes a more gradual change in the ionization state,so that lower ions such as H I and O VI decline, while those whose concentra-tion peaks at temperatures above the ambient coronal temperature, such as Si XII,increase. Heating of the ions can be measured through the increase in line width.

Because the shocked gas passes quickly through the UVCS slit, thesesignatures are only briefly visible. Nevertheless, four shocks have been reported(Raymond et al. 2000; Mancuso et al. 2002; Raouafi et al. 2004c; Ciaravellaet al. 2005a). In all cases broad O VI profiles were detected, and the kinetictemperatures of oxygen were above 108 K (see Fig. 57). Since the shock speedswere about 1000 km s−1, which would produce only 1.4 × 107 K if the electronsand ions shared a common temperature, the high temperature of oxygen requiresa lack of thermal equilibration among particle species. In the 11 June 1998 event,the time-dependence of O VI and Si XII emission implies only a modest electronheating (Raymond et al. 2000). Raouafi et al. (2004c) report similar observationsof an event on 27 June 1999. These results are similar to trends seen in supernova


remnant shocks (Ghavamian et al. 2001; Korreck et al. 2005). Inefficient electronheating and preferential heavy ion heating are also seen in heliospheric shocks(e.g., Schwartz et al. 1988; Berdichevsky et al. 1997), but there are still a varietyof models available for the plasma processes in fast collisionless shocks (e.g.,Cargill & Papadopoulos 1988; Hull et al. 2001; Lee & Wu 2000).

Ultraviolet spectra are also valuable in establishing the conditions in thecorona before the shock passes. This helps to determine the compression in theshock and hence its Mach number. Coupled with the coronal density and temper-ature and the speed determined from the times the event is seen by EIT, UVCS,and LASCO, this constrains the magnetic field strength (Raymond et al. 2000).The densities can help to establish the relationship to type II bursts in some cases,though the complex structure of type II bursts can make this difficult. Even whenUVCS does not observe the shock, the coronal conditions can be combined withtype II burst observations to place limits on the coronal magnetic field (Mancusoet al. 2003; Mancuso & Raymond 2004).

6.6 Jets

Coronal jets are generally believed to occur when closed field loops reconnectwith open field lines and material from both the open and closed regions is ejectedand channeled along open field lines (Wang et al. 1998; Shimojo & Shibata 2000;Wang & Sheeley 2002; see also Sect. 5.3.2). While there is a clear difference be-tween the prevailing physical pictures of jets and CMEs, it is not always easyto tell the difference from observations. Polar jets occur in coronal holes, andare generally seen in coronal emission lines and LASCO images (Gurman et al.1998). Their velocities can be partly explained by ballistic trajectories as mightbe expected for impulsive ejection along open field lines, but some subsequent

Fig. 57 UVCS O VI observations of a CME at ρ = 1.7 R� on 3 March 2000 (crosses). Thecurve fit utilized two Gaussians for each line in the doublet plus a constant background. Thebroad components (dashed curves) represent kinetic temperatures in excess of 108 K and thusindicate the passage of shocked gas through the UVCS slit. From Mancuso et al. (2002)


acceleration is also needed (Wood et al. 1999b). Dobrzycka et al. (2000, 2002)analyzed UVCS observations of 11 jets in coronal holes, most of which had si-multaneous EIT or LASCO observations. They found density enhancements ofabout a factor of 2 and speeds of about 200 km s−1. Temperatures dropped to aslow as 1.5 × 105 K. There was some evidence that continued heating after theejection was required to counteract adiabatic cooling in order to maintain eventhose modest temperatures.

Gilbert et al. (2001) used white light coronagraph data and EIT images toinvestigate CMEs with opening angles less than 15◦, and Dobrzycka et al. (2003)analyzed UVCS observations of several of these events. The UVCS observationsindicate that the temperatures, densities and outflow speeds were similar for the5 events, with the densities somewhat lower than is typical for CMEs. One eventshowed continuing acceleration, which fits better with a CME model than with thestandard jet model.

The jet event with the most complete diagnostic information was observed dur-ing the Whole Sun Month campaign on 26 August 1999 (Ko et al. 2004). It wasobserved by LASCO, EIT, CDS, and UVCS aboard SOHO, along with TRACEand the CHIP and PICS instruments at Mauna Loa. This jet emerged from an ac-tive region, and like other active region jets (e.g., Alexander & Fletcher 1999), itshowed coronal temperature plasma as indicated by TRACE emission in the 17.1nm and 28.4 nm bands and detections of Mg X and Si XII emission by CDS.UVCS observed the event at ρ = 1.64 R�, and at that height only cooler emis-sion lines of H I, C III, N III, and O VI were detected. The UVCS observingsequence contained interleaved sets of exposures at ρ = 1.64, 2.33, and 2.66 R�,but the jet material never reached the larger heights. The most remarkable featureof this event was that the Doppler velocities at low heights from CDS and CHIPprogressed gradually from 300 km s−1 red-shifts to 200 km s−1 blue-shifts overthe course of about 50 minutes, while UVCS observed the opposite trend, with aprogression from a 150 km s−1 blue-shift to 100 km s−1 red-shift over the courseof an hour. Analysis of the Doppler dimming of the C III and O VI lines showedthat the outflow speed of the jet material passed through zero at the same timethat the LOS speed passed through zero, indicating that the jet plasma came to acomplete stop. All the velocity measurements, as well as the trends in density andbrightness, are consistent with a ballistic model in which plasma is ejected fromthe Sun with a range of speeds from about 120 to about 500 km s−1, with someacceleration between the CDS and UVCS heights. The gas is seen on both theupward and downward parts of its trajectory. The difference between red to blueand blue to red velocity shifts at the two heights requires that the plasma travelalong curved field lines that are directed away from the Earth close to the Sun,but toward the Earth at r = 1.64 R�. It is not clear whether the magnetic field isultimately open or part of a very large closed field structure.

6.7 SEP acceleration in CME shocks and current sheets

Ultraviolet coronagraphic spectroscopy has the ability to determine the detailedplasma properties in the source regions of SEPs in the solar corona. The precedingsections have shown how UVCS/SOHO observations provided new diagnostics ofthe properties of some potential SEP source regions (e.g., shock waves and cur-


rent sheets). Here we briefly summarize future remote-sensing observations thatwould better determine the physical conditions and mechanisms that govern SEPproduction. Such observations would provide determinations of the parametersgoverning SEP emission that are needed to tailor theoretical models to specificSEP events and thereby predict the emitted SEP properties accurately.

In the case of CME shocks, the following pre-shock coronal quantities must bedetermined in order to constrain the eventual SEP production: suprathermal seedparticle populations, ion and electron densities and temperatures, charge states andchemical abundances, and the radial dependence of the fast-mode speed V f (seeEq. 24). Although the magnetic geometry can be determined from photosphericmagnetic field measurements and MHD models, empirical samples of the mag-netic field strength at larger heights are needed to constrain and verify the modeledfield. In addition, the following post-shock quantities must be measured: the shockspeed, the CME plasma speed (e.g., of the prominence core and leading edge), theion and electron temperatures, and the compression ratio (post-shock/pre-shockdensity). This information is probably sufficient for fully constraining theories ofSEP shock acceleration and predicting SEP emission for specific events. Uncer-tainties in all measured quantities need to be included and propagated into themodeled plasma properties. If a parameter in the model cannot be measured withcontemporary capabilities, a range of values should be used (see, e.g., the limitingranges on T‖ in coronal-hole empirical models; Cranmer et al. 1999b). The middleof the range would then be used as the best estimate and the limits of the rangewould be used as the uncertainty limits.

So far, only one shock observed by UVCS has been connected to a discreteSEP event (28 June 2000; Ciaravella et al. 2005a), but in that case the UVCSspectra had a low signal-to-noise ratio, and they only covered a portion of theshock. Higher sensitivity and greater spectral coverage would greatly help in suchtests (see Sect. 3.6), as would implementation of the next-generation concepts formeasuring the electron velocity distribution along the LOS via Thomson-scatteredH I Lyα (Sect. 3.4) and measuring the magnetic field strength in selected regionsvia the Hanle effect (Sect. 3.5).

Current sheets are believed to represent the main region of reconnective en-ergy conversion in the CME eruptive processes. They are believed to be relatedto so-called impulsive SEPs (e.g., Reames 1999), which are known to be accel-erated when CME-driven shocks have not formed; i.e., other mechanisms mustplay the main role in the particle acceleration. The reconnecting current sheet isan important, if not unique, region where such acceleration may occur.

Information about current sheet plasma parameters – and their ability to pro-duce SEPs – is usually deduced indirectly by observing the dynamic behaviorsof the products of magnetic reconnection, such as the separating flare ribbons onthe solar surface (Poletto & Kopp 1986; Qiu et al. 2002, 2004; Wang et al. 2003)and growth of the flare loops in the corona (Sui & Holman 2003; Sui et al. 2004).However, earlier observations were not able to provide information regarding theplasma density and temperature, the spatial scale of the current sheet (mainly thethickness), the rate of magnetic reconnection, or the strength of the magnetic fieldnear the front of the CME and the current sheet. Such information is related notonly to the energy conversion on large scales, such as the plasma heating and CME


acceleration, but also to that on the smallest, kinetic scales, such as the productionof SEPs.

UVCS observations made it possible for the first time to allow measurementsto be made of the plasma properties inside the current sheet (see Sect. 6.3). Suchmeasurements have important theoretical consequences; they allow the electricalresistivity (conductivity) in the reconnection region to be determined. This param-eter is essential for understanding the detailed physics of reconnection occurringinside the current sheet during the eruption. Several mechanisms, including thestrong turbulence due to the tearing mode instability inside the current sheet, havebeen proposed to explain the highly efficient energy conversion in solar eruptions,but none of them is decisive. Results obtained from UVCS and other remote-sensing instruments can provide the value of the electrical conductivity of theplasma inside the current sheet in an ongoing eruption for the first time since theimpetus of applying reconnection theory to solar eruptions began six decades ago(Giovanelli 1946; see also Priest & Forbes 2000).

With improved knowledge of the dynamical processes inside the current sheet(e.g., constraints on specific turbulence modes, the dispersion relation, and thepower distribution), we are further able to investigate the SEP acceleration tak-ing place in the current sheet. In a current sheet, a strong electric field is inducedby magnetic reconnection. For typical events, the electric field strength can reachvalues of order 5 to 50 V/cm (e.g., Wang et al. 2003; Qiu et al. 2004; Xu et al.2004). In principle, such a strong electric field is able to accelerate SEPs of awide range of energy. Second, electrons and protons are accelerated in oppositedirections, and their separation inevitably causes two-stream (Buneman) instabili-ties that further excite ion-acoustic turbulent waves. Additional turbulence modesmay then appear as a result of wave-particle and particle-particle interactions (e.g.,Tsytovich 1977). Thus, the current sheet is an assembly of waves and electric field,and accelerations can occur in various ways (see also Miller & Roberts 1995;Litvinenko 2000).

Further progress in understanding the above processes occurring in the currentsheet depends on the accurate measurement of the thickness of the current sheet,plasma parameters in the current sheet (including electron and ion velocity distri-butions and densities), the speeds of reconnection inflow/outflow near the currentsheet, as well as electric and magnetic fields in and around the current sheet. Ul-traviolet coronagraphic spectroscopy is uniquely suited to these requirements, andthe next-generation capabilities described in Sects. 3.4–3.6 would add powerfulnew tools to what is available with UVCS.

7 Observations of non-solar objects

7.1 Comets

UVCS has observed several comets per year, both sungrazers of the Kreutz groupand ordinary comets. Photodissociation of H2O produces an expanding cloud ofhydrogen atoms which scatter H I Lyα photons. Spatial, spectral, and temporalprofiles of the scattered H I Lyα provide the outgassing rates of the comets alongwith a novel probe of solar wind speed and density at points along the comettrajectory. In the case of Comet C/1996 Y1, the H I Lyα line width was used to


determine the parameters of the comet bow shock, which in turn led to a constrainton the speed of the fast solar wind at r = 6.8 R�, a region difficult to observeby any other means (Raymond et al. 1998). The comets C/2000 C6 and C/2001C2 provided density determinations in the slow wind that differ from other remotesensing density measurements in that the comets probe the density at a point alongthe trajectory rather than averaging along the LOS (Uzzo et al. 2001; Bemporadet al. 2005a).

The UVCS observations also constrain properties of the comets themselves.The outgassing rates lead to estimates for the diameters of the nuclei ranging from5 to 20 meters. Changes in the outgassing rates with distance from the Sun indicatethat the nuclei of comets C/2000 C6 and C/2001 C2 fragmented at r = 4 to 5 R�,indicating that the tensile strength of the nuclei is approximately 104 to 105 dyncm−2 (Uzzo et al. 2001; Bemporad et al. 2005a).

Normal comets observed by UVCS near perihelion at 0.1–0.3 AU includeComet 2P/Encke (Raymond et al. 2002), Comet Kudo-Fujikawa (Povich et al.2003), and Comet Machholz. The outgassing rates and the changes near perihe-lion were determined, but the most interesting feature was detection of the doublyionized species C2+ in Kudo-Fujikawa and Machholz. The existence of such ahigh ionization state probably results from the high photoionization rate close tothe Sun. The carbon produced by Kudo-Fujikawa exceeds that produced in theform of CO, leading to the conclusion that the carbon originates in grains thatsublimate in the cometary coma. One of the two images in the C2+ reconstructedfor Kudo-Fujikawa showed a disconnection event that apparently occurred whenthe comet crossed the heliospheric current sheet (Povich et al. 2003).

7.2 Stars and planets

UVCS has observed many UV-bright stars which pass within ρ = 10 R� of theSun. In addition to providing observations in a wavelength range extending belowthat covered by IUE or HST, stellar observations are useful for tracking changesin the radiometric responsivity of the instrument (see Gardner et al. 2002; Romoliet al. 2002; see also Sect. 4.3.2). Stars observed in the first several years of op-eration include 38 Aqr, TT Ari, 53 Tau, 103 Tau, 121 Tau, τ Tau, ζ Tau, α Leo(Regulus), ρ Leo, HD 142883, θ Oph, β Sco, δ Sco, ω Sco, α Vir (Spica), HD164794, HD 164492, and HD 164816. The bright B0.3IV star δ Sco is a long-period binary that underwent an outburst of circumstellar gas during its last peri-astron passage in July 2000 (Miroshnichenko et al. 2001). UVCS observed δ Scoin November of every year from 1996 to 2004, but there was no marked change inthe ultraviolet spectrum between 99.0 and 104.0 nm after the 2000 event. To ourknowledge, the yearly UVCS monitoring of this star represents the only consistentset of pre-outburst and post-outburst observations of such an event at wavelengthsshorter than 130 nm.

UVCS also observed several planets. Venus was observed in June 1996 whenit passed close to the Sun, but UVCS only saw a dimming of the coronal H I Lyαemission because the night-side of Venus was presented towards SOHO. Jupiterwas observed twice near conjunction (January 1997 and June 2001) and was usedas a useful photometric calibration source for the UVCS white light channel (Ro-moli et al. 2002).


7.3 Helium focusing cone

Interstellar helium atoms penetrate the heliosphere, and solar gravity focuses theirtrajectories on a line in the downwind direction from the Sun. UVCS has observedHe I 58.4 nm photons scattered from this focusing cone inside 1 AU (Michelset al. 2002), though at a lower brightness than expected from models of the he-lium density based on the photoionization rate measured by the CELIAS/SEM.The brightness of the focusing cone faded by an order of magnitude between min-imum and maximum of the solar cycle, and it began to recover in 2005. Boththe initial brightness level and about half of the drop with solar activity are at-tributed to collisional ionization by solar wind electrons as the hotter, denser slowsolar wind fills the heliosphere at solar maximum. Detailed models of the UVCSobservations through the end of 2000, combined with in situ measurements ofthe helium density and CELIAS/SEM measurements of the photoionizing fluxes,yield the collisional ionization rate in the inner solar wind through half the solarcycle (Lallement et al. 2004a,b).

8 Conclusions

Ultraviolet coronagraph spectroscopy has led to fundamentally new views of theacceleration regions of the solar wind and CMEs. As described in this paper, sig-nificant progress has been made toward identifying and characterizing the physicalprocesses that heat the extended corona, accelerate the various plasma compo-nents of the solar wind, and produce a wide range of nonequilibrium phenomenain CMEs. Perhaps most notably, the surprisingly extreme plasma conditions ob-served by UVCS in coronal holes have guided theorists to discard some candidatephysical processes and to further investigate others. The UVCS observations ofcoronal holes – and subsequent theoretical investigations of ion cyclotron reso-nance – have been cited increasingly in literature devoted to other plasma envi-ronments, such as the Earth’s aurora (Gavrishchaka et al. 2000), and they haveguided new investigations in pure plasma physics (e.g., Mizuta & Hoshino 2001;Chen et al. 2001). The UVCS observations of CME plasma properties have high-lighted the importance of studying the evolution of CMEs in the extended corona(including regions such as shocks and current sheets that may be key to under-standing SEP production) rather than just their initiation at the solar surface. Ul-traviolet spectroscopy allows the thermal energy content of CMEs to be uniquelydetermined, and thus the total energy budget of CME plasma to be elucidated.

Despite the advances outlined above, though, the diagnostic capabilities ofUVCS/SOHO were limited and fundamental questions have not yet been an-swered. New instrumentation, as described in Sects. 3.4–3.6, would provide sub-stantial improvements in our understanding (see also Cranmer 2002b; Gardneret al. 2003; Kohl et al. 2005). For example, a next-generation instrument couldmeasure the line of sight component of the electron velocity distribution via theThomson-scattered component of H I Lyα. This, in combination with the existingproton heating diagnostic from the resonantly scattered H I Lyα line, would allowthe total plasma heating rate in different coronal structures to be determined withunprecedented accuracy. Also, if the kinetic properties of many additional ionswere to be measured in the extended corona (i.e., a wider sampling of charge/mass


combinations), we could much better constrain the specific kinds of plasma fluc-tuations that are present as well as the specific collisionless damping modes.

New measurements such as those described above would be enabled by greaterphoton sensitivity, an expanded wavelength range, and the use of additional diag-nostics that heretofore have only been utilized in a testing capacity (e.g., Thomson-scattered H I Lyα and the use of EUV polarimetry and the Hanle effect to obtainconstraints on the magnetic field). Ultraviolet spectroscopic diagnostics like theserepresent a unique doorway into the detailed physics of solar wind acceleration,CME eruption and evolution, and SEP acceleration deep inside coronal shocksand current sheets.

Acknowledgements The development of ultraviolet spectroscopy of the extended solarcorona has been the work of many individuals and organizations. The primary scientificaccomplishments achieved up to the time of this writing are summarized in this review andthe names of the scientists who carried out the research can be found in the references. Theorganizations, managers, administrators and lead engineers who developed the UVCS/SOHOinstrument are listed in the acknowledgements of the paper describing the UVCS programat the time of the launch (Kohl et al. 1995a). We thank the following persons for valuablediscussions and contributions to the preparation of this manuscript: Silvano Fineschi, LarryD. Gardner, Jun Lin, Mari Paz Miralles, Alexander Panasyuk, Leonard Strachan and Aad vanBallegooijen. The authors are pleased to acknowledge the following engineers and scientistswho were instrumental in designing and building the Rocket Lyman Alpha Coronagraph: JamesCrawford, Larry Coyle, Frank DeFreze, Stanley Diamond, Vesa Kuosmanen, William “Chip”Milliken, Ed Thompson, Frank Rivera, Leonard Solomon, Darrell Torgerson, Peter Warren,Barry Kirkham, William H. Parkinson, Edmund M. Reeves, Heinz Weiser and Carlos Zapata.We are also indebted to the following additional engineers, manager and administrator whoupgraded the rocket instrument to become the UVCS/Spartan: David Boyd, Edward Dennis,Gerry Gardner, Richard Goddard, Roger Hauck, Frank Licata, George Nystrom, Robert Rasche,Peter Sozanski and Brenda Bernard. We thank the UVCS/SOHO science operations team,including Carlo Benna, Angela Ciaravella, Silvio Giordano, Yuan-Kuen Ko, Salvatore Mancuso,Joseph Michels, Andrea Modigliani, Daniel Phillips, Marco Romoli, and Chi-Rai Wu. We alsoacknowledge the engineering and management team responsible for the conceptual design ofnext-generation science payloads, especially Peter Daigneau, Mark Ordway, Tom Gauron, TimNorton, and Joe Swider. This work would not have been possible without the skills and effortsof the managers and engineers from the NASA GSFC Sounding Rockets Branch and SpecialPayloads Division including the following: Robert Weaver, Don Carson, Frank Collins, JohnLane, Jack Pownell, Dave Shrewsburg, Craig Tooley, Tom Budney, Stewart Meyers, RobertPincus, and Fred Witten. We thank Bernhard Fleck and Joseph Gurman, the ESA and NASASOHO Project Scientists, respectively, who served in those roles for most of the operationsphase. We also thank the SOHO Science Operations Coordinators, the Flight Operations Team,and the ESA, NASA, and Matra Marconi engineers who recovered SOHO from the missioninterruption. Special thanks to Giuseppe Tondello, Piergiorgio Nicolosi, Giampiero Nalettoand Claudio Pernechele of Universita di Padova for the UVCS/SOHO spectrometer opticaldesign, alignment and test, and Martin C. E. Huber for his many contributions to the program.This work has been supported by the National Aeronautics and Space Administration (NASA),the Smithsonian Astrophysical Observatory, Agenzia Spaziale Italiana and by ESA PRODEX(Swiss Contribution). SOHO is a project of international cooperation on the part of NASAand the European Space Agency. The preparation of this paper was supported by NASA grantNNG05GG38G to the Smithsonian Astrophysical Observatory and by Universita di Firenze.

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Astron. Astrophys. Rev. (2006) 13(3): 159–228DOI 10.1007/s00159-006-0028-0

PAPER

Ingrid Mann · Melanie Kohler ·Hiroshi Kimura · Andrzej Cechowski ·Tetsunori Minato

Dust in the solar system and in extra-solarplanetary systems

Received: 7 January 2006 / Published online: 27 April 2006C© Springer-Verlag 2006

Abstract Among the observed circumstellar dust envelopes a certain population,planetary debris disks, is ascribed to systems with optically thin dust disks andlow gas content. These systems contain planetesimals and possibly planets and arebelieved to be systems that are most similar to our solar system in an early evo-lutionary stage. Planetary debris disks have been identified in large numbers bya brightness excess in the near-infrared, mid-infrared and/or submillimetre rangeof their stellar spectral energy distributions. In some cases, spatially resolved ob-servations are possible and reveal complex spatial structures. Acting forces andphysical processes are similar to those in the solar system dust cloud, but the ob-servational approach is obviously quite different: overall spatial distributions forsystems of different ages for the planetary debris disks, as opposed to detailed lo-cal information in the case of the solar system. Comparison with the processes ofdust formation and evolution observed in the solar system therefore helps under-stand the planetary debris disks. In this paper, we review our present knowledgeof observations, acting forces, and major physical interactions of the dust in thesolar system and in similar extra-solar planetary systems.

Keywords Solar system: general · Solar system: formation · (Stars:) planetarysystems · Interplanetary medium · Meteors · Meteoroids

I. Mann (B) · M. Kohler · T. MinatoInstitut fur Planetologie, Westfalische Wilhelms-Universitat, Wilhelm-Klemm-Str. 10,48149 Munster, Germany

H. KimuraInstitute of Low Temperature Science, Hokkaido University, Sapporo, Japan

A. CechowskiSpace Research Center, Polish Academy of Sciences, Warsaw, Poland

160 I. Mann et al.

1 Introduction

Discoveries and studies of second-generation dust disks around main-sequencestars started two decades ago, when measurements of the spectral energy distribu-tion of Vega revealed a faint excess compared to the spectrum of the stellar pho-tosphere in the infrared brightness (Aumann et al. 1984). This excess was foundfor a number of stars and was attributed to circumstellar dust with lifetimes signif-icantly shorter than the age of the star. These systems do not necessarily containplanets, but the existence of planetesimals is certain. Like in the solar system, theplanetesimals are the major source of the dust. In contrast to dust around youngstars, these dust particles are produced from destruction or erosion of the parentbodies. These systems are called circumstellar debris systems, second-generationdust clouds or Vega-type objects or planetary debris disks. We will use the termplanetary debris disk because it accounts for the fact that the dust is produced fromplanetesimals and is influenced in its dynamics by planetesimals. These systemsdo not necessarily contain planets, but systems which contain planets (i.e. ‘real’extra-solar planetary systems) are expected to form and develop in similar ways.From our later discussion, it will become clear that the direct influence of possi-bly existing planets on the overall dust cloud is small compared to the influence ofplanetesimals. In contrast to young circumstellar systems, the dust in planetary de-bris disks is produced by larger parent bodies; the gas component in the planetarydebris disks is tenuous and does not influence the dynamics of dust; and the plan-etesimals induce dust relative velocities that cause catastrophic dust collisions. Itis assumed, that among the objects currently accessible to astronomical observa-tions, these planetary debris disks resemble our solar system most closely. At leastsome of them contain planets. This makes them interesting targets for research.

While the formation of stars can be studied from astronomical observations,studies of the conditions of the formation and evolution of planets were for a longtime limited to the case of our solar system and to classical planetology, meaningstudies of meteorites and lunar samples, studies of craters on planetary surfaces,observations of planets, and recent space exploration of planets and minor solarsystem objects. Planet formation around other stars was hidden in dense proto-planetary clouds and planet evolution was not observable due to the large distanceand faint brightness of these systems. The discoveries of extra-solar planets andfollowing revision of the models of planet formation showed how the perceptionof the solar system (from earth) limits our view of the solar system and even moreso of planetary systems in general.

A topic of special interest within the topics of astronomical and planetary re-search is that of the formation of terrestrial planets and among those the evolutionof habitable planets like earth. The role of debris disks in this context is mani-fold: Planetary debris provide a local flux of material onto a planet, i.e. deliveringsolids and volatiles onto the surface or into the atmosphere. For the planetarydebris disks that are currently observed around other stars, impacts in most caseswould be catastrophic for terrestrial planets, significantly altering their surface andatmosphere. Therefore, the evolution of habitable planets is closely connected tothe evolution of the planetary debris disks that they are embedded in. As far as ob-servations are concerned, the spatial distribution of the planetary debris allows toinfer the distribution of planetesimals as their parent bodies and as their perturbers.

Planetary debris disks 161

The spatial distribution of debris may also reveal the presence of earth-mass plan-ets; these cannot be observed directly but their gravity shapes the structure of theobserved dust cloud.

We note that even for future improved dedicated observation facilities the ex-istence of planetary debris disks hampers the astronomical observation of extra-solar earth-like planets.

The similarity of the planetary debris disks to the solar system dust cloud hasbeen pointed out before. The latter is less dense than the currently observed cir-cumstellar debris disks, but the acting forces and major physical processes areidentical. In contrast to circumstellar systems, studying the solar system dust cloudis easier, since we can derive many of the influencing quantities directly from ob-servations, from laboratory studies of returned samples, and from space measure-ments. On the other hand, we will see that our view is limited to measurementsnear earth orbit. A comparative review of the solar system dust cloud and the plan-etary debris disks should therefore provide the current knowledge of the physicalprocesses of the solar system dust in order to allow its extrapolation to the othersystems.

A further important topic of planetary and astrophysical research is the evo-lution of dust material within the interstellar medium and the connection be-tween dust in the interstellar medium and dust in a planetary system. Observationsrange here from the dust properties in the interstellar medium (ISM), propertiesof circumstellar dust in systems of different evolutionary stages, to properties ofcometary dust. They permit a comparative study of the optical and thermal prop-erties of dust in these different systems. Dust material evolution in the planetarydebris disks is similar to the evolution of dust and small bodies in the outer solarsystem. Dust measurements from spacecraft and laboratory analysis of collectedsamples support the observational studies of cometary dust as primitive solar sys-tem dust with further complementary information.

In this paper, we review present knowledge of the dust in the solar system andin extra-solar planetary debris disks. We first present observation methods and re-sults about dust in the solar system (Sect. 2) and planetary debris disks (Sect. 3). InSect. 4, we describe the main acting forces and effects. The spatial distributions ofdust are discussed in Sect. 5, and this is partly related to the collisional evolutionand the observation of gas components (Sect. 6). We then introduce the concept of‘astrospheres’ (Sect. 7) being the regions of influence of the stellar wind aroundstars. They are of interest for estimating stellar wind fluxes and for conditionsof interstellar dust entering the planetary debris disks. The optical properties andthermal properties of dust (Sect. 8) are important for interpreting observationaldata and for understanding the material evolution in planetary systems. We sum-marize the review in Sect. 9.

2 Dust in the solar system

2.1 Observations

Detection methods of dust and meteorites in interplanetary space are limitedto certain size ranges and biased by particle characteristics (orbital parameters,albedo, composition, etc.) (see Fig. 1). Most methods are limited to the near-earth

162 I. Mann et al.

photographic &visual meteors

impact ionizationPVDF trajectory measurement

Zodiacal light

thermal emission

micro - meteorites

atmospheric collectionradar meteors

0.01 0.10 1.00 10 100 1000

a (µm)

m (g)

head echoobservation

-17 -12 -710 10 10 10-2

Fig. 1 Detection methods: Shown are different detection methods of dust near earth and theapproximate size (i.e. radii) or mass range over which these methods detect particles. The darkbars denote detection methods that provide orbital information, the grey bars denote methodsthat provide brightness information integrated along the line of sight, the light grey bars denotedetection of single particles or events where the orbital information is not clear. Conversionbetween sizes shown on the upper scale and masses shown on the lower scale are made assumingspherical particles with bulk density 2.5 g cm−3 (Mann et al. 2004a)

environment. Thermal emission and scattered light brightness of the zodiacal lightdescribe the size range of particles from 1 to 100 µm. They provide informationaveraged over large spatial regions mainly between 0.3 and 1.7 AU distance fromthe Sun and close to the ecliptic plane. Only few studies exist about dust in theouter solar system and near the Sun. In-situ measurements best describe parti-cles that yield a large flux rate, i.e. particles with sizes below 1 µm. Aside fromthe measurements near comet Halley and recent measurement with the Cassinimission, in-situ measurements gave no direct information about dust composition.The observation of meteors provides total fluxes as well as some information aboutthe composition of the in-falling bodies. Atmospheric collection of interplanetarydust particles (IDPs) and collection of micrometeorites allow a direct analysis inthe laboratory.

2.1.1 Zodiacal light measurements

Brightness observations The observed brightness is produced by solar radiationscattered at dust and thermal radiation emitted from dust particles along the lineof sight (LOS). The brightness observed for a given longitude (λ − λ�) and agiven latitude (βlos) in geocentric coordinates of the LOS is the signal integratedover the entity of dust particles in a given volume element in space. Brightnessobservations yield a good data set of the visible zodiacal light brightness from


about 15◦ latitude and longitude from the Sun out to the Gegenschein as well asinfrared observations, usually at elongation larger than 60◦, where the elongationdenotes the angle of the LOS from the Sun-ward direction (Leinert et al. 1998).The visible brightness decreases smoothly with increasing elongation of the LOSfrom the Sun and increases again by a factor of 2 at elongations larger than 170◦(the Gegenschein). As opposed to the solar radiation, the zodiacal light is polarisedas a result of the scattering properties of dust particles. Detailed descriptions ofthe brightness analysis and the LOS integrals have been given before (Dumont1973; Roser and Staude 1978; Giese et al. 1986). The coordinates describing thedust distribution are given in heliocentric coordinates, solar distance r and helio-ecliptic latitude β�. The number density of dust in a given volume in space is

n(r, β�) =∫ s2

s1

dn

dsds, (1)

where dn/ds is the differential size distribution of dust and s1 and s2 denote theminimum and maximum sizes of the dust.

Due to the decreasing number density and low solar illumination, the outerregions of the dust cloud have only a small contribution to the brightness seenfrom earth. Based on different models to describe the zodiacal light, it is possibleto estimate from which region dust particles contribute to the observed brightness(Giese et al. 1986). At 45◦ as well as at 90◦ latitude of the LOS the contributionfrom distances >2.6 AU is less than 1%, with the contribution to the brightness at90◦ elongation dropping more steeply than at 45◦.

First thermal emission observations of the solar system dust over a wide rangeof elongations have been made from ballistic rocket Murdock and Price (1985).Satellite observations cover smaller ranges of elongations than these rocket obser-vations or than visible observations (Levasseur-Regourd et al. 2001). Initial analy-sis of infrared measurements in terms of absolute brightness was difficult and didnot agree with the analysis of visual zodiacal light data (Kneissel and Mann 1991).Major progress of the infrared satellite measurements, as will be discussed laterin the paper, was to reveal spatial structures and spectral features in the emissionbrightness.

Some optical observations were carried out from spacecraft away from 1 AU:after the Helios spacecraft measured the zodiacal light brightness for fixed elonga-tions as function of the distance of observation from the Sun, the data were used toderive the radial slope of the zodiacal light brightness to be close to B(r) ∝ r−2.3,as well as to invert the average scattering function of particles (Leinert et al.1982a). The zodiacal light at medium elongations is not very sensitive to the exactslope of the scattering function and its variation predominantly reflects the spatialvariation of dust number density which was shown to be r−n with n = 1.0–1.3(Leinert and Grun 1990).

The Pioneer 10 and 11 spacecraft also carried a photopolarimeter to map thezodiacal light and background starlight in two broad bandpasses centred at 0.44and 0.64 µm (Pellicori et al. 1973). The change in brightness of the zodiacal lightwith Sun–spacecraft distance, r , allowed to derive the radial gradient of the spa-tial density distribution of the zodiacal particles. The best fit radial gradient, r−n ,was found to be n = 1.0–1.5, with a cut-off at 3.3 AU. No further decrease inbrightness with distance was detected beyond the asteroid belt (r > 3.3 AU). The

164 I. Mann et al.

Fig. 2 The zodiacal light: The zodiacal light is produced by scattering of Sunlight at interplan-etary dust particles distributed in the solar system along the ecliptic plane and under good con-ditions is visible to the bare eye. This image is taken from Mauna Kea, Hawaii with an analogue(35-mm film) camera with fish-eye lens (focal length = 8 mm). The brightness of the zodiacallight forms a faint, almost horizontal band. The left-hand side of the band shows a bright spot ofthe Sun-ward direction and the right-hand side shows a slight enhancement of the Gegenschein.The brightness of the Milky Way ranges from the lower left to the upper right of the imageshowing how the ecliptic is tilted relative to the galactic plane. Four meteors relevant to Leonidshower are seen in the lower part of the image. The faint brightness at the lower right partand upper left part of the image is due to OH-airglow emission (courtesy of Masateru Ishiguro,JAXA, Japan)

lack of a radial gradient between 3.3 and 5.0 AU and comparison of the measuredbackground with predicted integrated starlight indicate that the residual scatteringfrom outer solar-system dust is smaller than 10−7 Wm−2 µm−1 sr−1 at 0.4 µm(Hanner et al. 1981). This puts a limit to the dust density as discussed in the con-text of in-situ measurements given later in the paper.

Polarisation observations As opposed to the intensity, the polarisation of thezodiacal light describes the local polarisation of interplanetary dust and is onlyweakly dependent on the spatial distribution. The linear polarisation of the zodia-cal light is a smooth function of elongation with a maximum of approximately20% around elongation ε = 60◦ and a negative branch at backscatter direc-tion with a minimum of a few percent along the ecliptic plane (Leinert 1975;Leinert et al. 1998; Levasseur-Regourd 1996). This dependence of polarisationhas been established with ground-based, balloon-borne, aircraft-borne, rocket-borne and space-borne telescopes (Behr and Siedentopf 1953; Blackwell 1956;Blackwell and Ingham 1961a,b,c; Dumont and Sanchez 1975a,b, 1976; Frey et al.


1974; Leinert et al. 1974). The linear polarisation at the anti-solar point is found tobe zero (Frey et al. 1974; Dumont 1965; Dumont and Sanchez 1975a). The polar-isation of the zodiacal light in the ecliptic is nearly constant within the error barsin the wavelength range λ = 260–900 nm but tends to increase toward the red andthe ultraviolet (Peterson 1961; Pitz et al. 1979; Van de Noord 1970; Weinberg andHahn 1980).

In the early 1970s, Wolstencroft and Bandermann (1973, 1974) claimed thedetection of significant angular structure and day-to-day variations in the polari-sation of the zodiacal light near the anti-solar point and stirred up further discus-sions (Sparrow and Weinberg 1975; Bandermann and Wolstencroft 1977). Suchvariations in the polarisation were not detected at smaller elongation by the Helios1 and 2 measurements discussed later. Detections of significant circular polari-sation in the zodiacal light were reported by Wolstencroft and Rose (1967) andWolstencroft and Kemp (1972), while Staude and Schmidt (1972) showed fromtheir observations that circular polarisation is zero within the accuracy of 0.1%.

Helios 1 and 2 measured the polarisation of the zodiacal light in U, B andV spectral bands between 0.3 and 1.0 AU from the Sun. The polarisation mea-sured by Helios along the ecliptic latitudes of 16◦ and 31◦ is a smooth func-tion of elongation with a maximum around ε = 52◦ and reaches zero aroundε = 161◦ Leinert et al. 1981, 1982a. The polarisation shows the highest value inthe B band and the lowest value in the U band, irrespective of heliocentric distance(Leinert et al. 1981). The polarisation is stable with time between 1974 and 1981and is found to increase with heliocentric distance approximately proportional tor = 0.3, where r denotes the heliocentric distance (Leinert et al. 1982a,b).

Cosmic Background Explorer (COBE) observed the polarisation at wave-lengths of 1.2, 2.2 and 3.5 µm (Berriman et al. 1994): The polarisation at ε = 90◦along the ecliptic plane showed blue colour, namely, and it decreases with wave-length.

F-corona and Sungrazing comets observations The zodiacal light brightnesssmoothly continues to small elongations of the LOS into the solar corona (Mann1998b; Levasseur-Regourd et al. 2001). Scattering of solar radiation at electrons,ions and dust particles produces the coronal brightness. Analysis of the F-coronaproduced from dust is especially hampered by the signal of the K-corona producedby scattering at electrons near the Sun. Moreover, the observations are hamperedby the presence of coronal and atmospheric stray light and therefore F-corona ob-servations are preferably made in the near-infrared and during solar eclipses orwith coronagraphs from space.

The brightness from dust particles (F-corona) is the predominant componentof the corona brightness beyond 4 R� distance from the centre of the Sun, whichcorresponds to an elongation of about 1◦ of the LOS from the centre of the solardisk. The ambiguities of the LOS inversion also limit the results that can be derivedabout near-solar dust from the remote observations. The diffraction part in theforward scattering at a small scattering angle is very effective, the light scattered(with small scattering angles) by obstacles near the observer is very intense andyields a strong contribution to the brightness (depending on the size distributionof dust), as pointed out already by van de Hulst (1947). The polarisation of thezodiacal light decreases smoothly at small elongations toward the solar F-corona(Blackwell and Petford 1966). The average polarisation and albedo, as well as

166 I. Mann et al.

the spectral variation of the albedo, change with distance from the Sun and withlatitude possibly indicating a change of particles properties as well as of the dust-cloud composition (Kneissel and Mann 1991; Mann 1998a).

Early observations with space coronagraphs (Michels et al. 1982) reported theappearance of Sungrazing comets in the corona. During the Solar and HeliosphericObservatory (SOHO) mission, Sungrazing comets are frequently observed withthe SOHO/Large Angle and Spectrometric Coronagraph Experiment (LASCO)(Biesecker et al. 2002). The number of comets observed with a limit of ninth mag-nitude is about 60 comets per year and the extrapolated total is 180 comets peryear. Most of these comets have sizes of the 10–100 m range and are associated tothe Kreutz group Sungrazing comets that originate from the same parent body thatfragmented when it encountered the Sun (Marsden 1967; Biesecker et al. 2002).The H2O outgassing of Sungrazers was observed with the Ultraviolet Corona-graph Spectrometer (UVCS) aboard SOHO: the cometary hydrogen Ly-α signalwas interpreted in terms of interactions of coronal protons with atoms created bythe photodissociation of water (Bemporad et al. 2005). Additional Ly-α emissionhas been ascribed to the sublimation of dust particles, whose end products neu-tralize coronal protons via charge exchange processes (Bemporad et al. 2005).

2.1.2 Cometary dust observations

Cometary dust is observed from its light scattering and thermal emission directlyin the coma. Regardless of the difference in the properties of comets, the dust par-ticles have common characteristics in their optical properties that are distinctly dif-ferent from interplanetary dust: they have a lower albedo and often show strongeremission features than those observed in the zodiacal light. Cometary dust is usu-ally assumed to be more pristine than other dust components in the solar systemand it is often used for comparison to dust observations around other stars. Thecometary dust properties will be further discussed in Sect. 8.

2.1.3 Meteor observations

The flux of small solid bodies into the earth atmosphere is known for a long timefrom the existence of meteors, so-called shooting stars. A meteoroid that entersthe earth atmosphere and atoms ablated from the meteoroid collide with atmo-spheric constituents. Meteoroid and atmospheric atoms and molecules undergodissociation and ionisation and form an expanding column of partially ionisedplasma along the trajectory of the meteoroid. This plasma cloud that is generatedin the atmosphere produces the brightness that is commonly ascribed as meteor.The physics of the meteor phenomenon was recently reviewed by Ceplecha et al.(1998). Some meteors occur in streams, indicating that they are fragments of thesame parent body, but the majority of meteors belong to the class of sporadicmeteors. It should be noted that the orbital distribution of the sporadic meteorsderived from observations is different from the orbital distribution of dust derivedfrom zodiacal light inversion (Kneissel and Mann 1990). The difference in orbitaldistributions is plausible, since zodiacal light observations are biased to dust withhigh albedo (Mann et al. 2006).


2.1.4 Laboratory measurements of collected samples

Direct laboratory analysis of cosmic dust particles has been, up to now, only fea-sible for collected samples. Depending on a variety of different parameters con-nected to the entry velocity and to the conditions of re-radiation of the entry heat,these collected particles have survived the entry un-melted or only partly melted.Cosmic dust particles collected in the stratosphere by high-flying aircraft cover thesize range from 5 to 50 µm, these particles are often denoted as interplanetary dustparticles (‘IDPs’) (Brownlee 1978; Jessberger et al. 2001; Rietmeijer 1998). Cos-mic dust particles that are collected from Antarctic Ice and Greenland ice samplesas well as from the ocean floor have typically sizes of 20 µm to 1 mm (Mauretteet al. 1991; Kurat et al. 1994) (often denoted as ‘micrometeorites’).

The presence of solar wind noble gases confirms the extraterrestrial nature ofthe IDPs (Hudson et al. 1981). Also nuclear tracks, in majority generated by solarenergetic particles (‘solar flare tracks’), have been identified in collected strato-spheric cosmic dust and indicate their exposure age to be approximately 10,000years (Bradley et al. 1984).

Simulating the heating of dust particles with typical entry velocities showedthat the entry processes depend on the orbits of the dust particles: Theatmospheric-entry conditions inferred for the major fraction of the collectedstratospheric cosmic dust is consistent with parent bodies in the main asteroidbelt (Flynn 1989).

While for the single particle it is not possible to use the heating history asindicator of the parent bodies, for the case of two specific particles, the density ofsolar flare tracks clearly exceeded the values that are typical for dust from cometsor asteroids, suggesting that they originate from the Kuiper belt (Flynn 1996).There is evidence that some of the materials in the collected samples are verypristine. The so-called anhydrous chondritic IDPs are thought to be among themost primitive samples, among them cluster IDPs are thought to be cometarydust, since their enhanced D/H ratio suggests a pristine nature (Messenger 2000).These interplanetary dust particles contain GEMS (glass with embedded metal andsulphides) with high abundances. It is suggested that GEMS are either interstellarsilicate grains or they would be the oldest known solar nebula solids.

Although the number of dust particles collected and analysed is limited, wecan infer from the analysis of dust samples the presence of silicates, carbon com-pounds, sulphides and metals. We can moreover assume that although fluffy, themajority of dust particles in the solar system show only moderate porosity. Thereis no evidence for largely elongated particles. Particles of irregular structure recomposed of submicrometre constituents.

2.1.5 Direct measurements from spacecraft

Instruments on spacecraft measure dust, predominantly of sizes below 100 µmlimited by statistics of the low flux rates. Most in-situ experiments from spacecraftmake use of the large speed of impacting particles: They detect the material ofthe dust particle and of the target, evaporated and ionised upon impact (impactionisation detectors). The interplanetary dust has been measured near ecliptic bythe Helios spacecraft from 1 AU to a distance as close as 0.3 AU from the Sun. A

168 I. Mann et al.

Fig. 3 Dust measurements in the outer solar system: Shown are data from Voyager measure-ments for masses m > 1.2 × 10−14 kg and for Pioneer measurements for masses m > 10−13 kg(note that the channels have different mass thresholds). The dashed horizontal lines denote aconstant flux of interstellar dust that a spacecraft moving in interstellar upwind direction woulddetect if moving approximately 10 AU per year. Note that these fluxes are for large interstellarparticles that are not influenced by the solar and interstellar magnetic fields. The shaded areasdepict the range of possible fluxes due to the dust component in the Kuiper belt and due to thedust in the interstellar medium beyond the heliopause (Mann et al. 2004a)

number of spacecraft (Pioneer 8/9, HEOS 2, Hiten, etc.) measured the dust near1 AU, covering a broad mass range down to 2 × 10−19 kg (HEOS 2). The surfacesof atmosphere-less bodies in the solar system provide a natural area for the indirectdetection of dust: Analysis of micro-craters on samples of the lunar surface thatwere brought back to earth with the Apollo flights enabled detailed studies of thedust flux near 1 AU (Fechtig et al. 2001).

Measurements outside of 1 AU are shown in Fig. 3. Ulysses at distance1.7–5 AU measured an average flux of 1.5 × 10−4 m−2 s−1 (Grun et al.1994), where about half of the particles had impact speeds correspondingto dust in hyperbolic orbits (β-meteoroids). The flux of β-meteoroids wasstudied in detail for three selected suitable parts of the Ulysses orbit: Thestudy showed that the β-meteoroids cover a broad range of dust massesand a wide range of orbital perihelia, which agrees with β-meteoroids be-ing produced by collisional fragmentation (Wehry and Mann 1999). Firstdata of the interstellar dust flux were derived from Ulysses measurements(Grun et al. 1994).

In-situ dust measurements at heliocentric distances >5 AU were made aboardPioneer 10 and 11, detecting dust up to 18 AU (Humes 1980). The resulting flux,4 × 10−6 m−2 s−1 for particles with masses of 8 × 10−13 kg, was nearly con-stant between 3 and 18 AU. These measurements are possibly hampered by sat-uration of the detectors and the derived dust fluxes are too high to be in agree-ment with optical measurements (see Sect. 2.1.1) onboard the same spacecraft(Mann and Hanner 1998). Aside from Pioneer measurements, the plasma wavedetectors aboard Voyager 1 and 2 detected plasma clouds produced by dust im-pacts onto the spacecraft, showing dust impacts from 6 to 51 AU (Voyager 1) and


Fig. 4 The sources of dust in our planetary system: The main sources of dust in the solar systemare comets, asteroids, Kuiper belt objects and interstellar medium dust. The solar system objectsare produced from cold molecular cloud dust that is processed in the protoplanetary nebula. Incontrast to the cold and dense molecular cloud environment, the local interstellar cloud dust thatstreams directly into the solar system is embedded in a warm tenuous gas (Mann et al. 2006)

33 AU (Voyager 2). The detected average flux amounts to 5 × 10−4 m−2 s−1 withthe mass threshold of ∼10−14 kg (Gurnett et al. 1997). Note that the Voyagermeasurements are from instruments designed for measuring plasma parametersand therefore data interpretation is difficult. The fluctuations of measured Voy-ager fluxes, like those of Pioneers, exceed statistical limits, but do not show aclear trend in the variation with heliocentric distance. It should be noted that thePioneer and Voyager dust measurements may include both interstellar dust as wellas dust produced in the Kuiper belt (Mann and Kimura 2000).

2.2 Sources of solar system dust

The main sources of dust in the solar system are comets, asteroids and Kuiperbelt objects. The dust particles are released with the activity of cometary nuclei,produced by collisional fragmentation either of the parent bodies or by collision oflarger meteoroids that originate from these parent bodies. A further source of dustare particles entering the solar system from the interstellar medium and impactejecta generated by impact of interstellar dust onto the Kuiper belt objects. Therelative contributions of these different sources are uncertain and vary with size ofthe particles and with location within the solar system dust cloud.

2.2.1 Asteroids

The number of asteroids as well as their relative velocities show that catastrophiccollisions must take place in the asteroid belt. This is supported by observation ofasteroids with similar orbital parameters: they are the fragments of the same parent

170 I. Mann et al.

body (Hirayama 1918). Collisional models of asteroids and their debris (Dohnanyi1969) show the mass distribution of fragments produced by catastrophic colli-sions, this is in accordance with the mass distribution derived from observations.These collisions produce meteoritic fragments over a broad mass range. Estimatesof the absolute dust production rate from asteroids range from 109 to 1011 kg peryear (Mann et al. 1996). These values are either comparable with, or less than, thedust supply by comets.

A clear indication for the dust production from asteroids is observed with dustbands. Dust bands were firstly noticed in the data of the Infrared AstronomicalSatellite (IRAS) as pairs of slight, symmetrically placed enhancements superim-posed to the background of the zodiacal emission brightness measured at 12 and25 µm. The dust bands are explained with particles that move in orbits with sim-ilar orbital elements and that are fragments produced upon collision of asteroidalbodies. In some cases, the derived orbital parameters indicate the connection ofthe dust band to an asteroid family (Sykes 1990).

2.2.2 Comets

The production of dust by comets is obvious from the observation of dust tails.The estimates of the dust production rate in comets are listed in Tables 1 and 2.Most of the estimates of the dust production rate are, as a result of the wavelengthof observation, limited to a certain size range of particles as well as they are validfor a narrow range of the orbit of the parent body. Variation of cometary activityand uncertainties in determining the size distribution of ejected particles make itdifficult to estimate the total mass production from a single comet. The maximumvalue of mass loss rate for short-period comets is 144000 kg/s for comet Hal-ley and for a long-period comet the maximum value is 1800000 kg s−1 for cometHale–Bopp. The mass loss rates derived from observations are listed in Tables 1and 2. For the cases of Hyakutake and Hale–Bopp it is nicely seen that the derivedmass loss rate increases with the wavelength of observations. This indicates thatthe observed larger particles determine the total mass loss rate.

A significant amount of the small dust particles that generates the brightnessof the tail are in hyperbolic orbits after release from the comet and therefore donot significantly contribute to the solar system dust cloud. Larger dust particlesand meteoroids stay in bound heliocentric orbits and are subsequently fragmentedby mutual catastrophic collisions. Meteoroid streams that cross the earth orbitcause meteor showers, some of which directly can be traced back to their parentcomets. Moreover, the observation of cometary “dust trails” with IRAS revealedthe existence of larger cometary fragments (Sykes et al. 1986): These spatiallyconcentrated trails of dust particles with sizes larger than the typical zodiacal dustare associated with short-period comets. The age of a typical trail is of the orderof 100 years. More recent dust trails were also detected in optical observations,and the data indicate the albedo of dust in the trails is low (Ishiguro et al. 1999).

2.2.3 Interstellar medium

The motion of the Sun relative to the local interstellar medium causes a flux ofinterstellar matter in the form of neutral gas and dust into the solar system. The


Table 1 Estimates of dust mass loss rate from observations of short-period comets

Comet Qdust (kg s−1) rh (AU) Data References

1P/Halley 11.4–1,44,000 0.90–2.84 VIS (1), (2), (3), (4), (5)1P/Halley <52,000 0.89 VISa (6)1P/Halley 100–15,000 0.89–2.81 IR (7), (8), (9)1P/Halley 1500 0.89 radio (10)1P/Halley 5000–10,000 0.89 direct (11), (12)2P/Encke 0.76–2000 0.33–1.89 VIS (13), (2), (14), (15)2P/Encke 22–230 0.35–1.17 IR (16), (17), (9)4P/Faye 125 1.59–1.60 VIS (18)6P/d’Arrest 1.3–382 1.16–2.19 VIS (19), (15)8P/Tuttle 3.67–29.22 0.78–1.89 VIS (2)9P/Tempel 1 <390 1.49 IR (9)10P/Tempel 2 2.72–64.63 1.39–1.74 VIS (2)10P/Tempel 2 50–500 1.3–2.9 IR (20)16P/Brooks 2 7.69–9.25 1.86 VIS (2)19P/Borrelly 140–341 1.34–1.52 VIS (2), (4), (21), (22)21P/Giacobini- 16.7–1253 1.03–1.73 VIS (2), (23), (4),

Zinner (24), (5)21P/Giacobini-Zinner 80–380 1.03–1.57 IR (17), (25)22P/Kopff 453.6 1.68 VIS (2)22P/Kopff 130 1.59 VIS (26)22P/Kopff 1000 1,91 IR (9)23P/Brorsen-Metcalf 100–300 0.72–0.97 VIS (24)23P/Brorsen-Metcalf 300 0.51 IR (27)26P/Grigg-Skjellerup 4.43–4.54 1.04 VIS (2)26P/Grigg-Skjellerup 200 1 VIS (28)26P/Grigg-Skjellerup 20 1.02 IR (17)27P/Crommelin 130 1.01 IR (29)27P/Crommelin 1200 1.02 IR (17)29P/Schwassmann- 600 ± 300 5.77 VIS (30)

Wachmann 138P/Stephan-Oterma 22.63–226.1 1.73–3.04 VIS (2)38P/Stephan-Oterma 0–250 1.57–2.17 VIS (24)45P/Honda-Mrkos- 1 0.96–0.98 VIS (31)

Pajdusakova46P/Wirtanen 4–20 1.06–2.45 VIS (32), (33)46P/Wirtanen 1.5 ± 0.5–2 ± 1 2.0–2.5 IR (34)55P/Tempel-Tuttle 210 1.15 IR (9)59P/Kearns-Kwee 18.52–40.46 2.22–2.27 VIS (2)64P/Swift-Gehrels 12.76–15.19 1.36–1.53 VIS (2)65P/Gunn 100–300 2.6–2.9 IR (34)67P/Churyumov- 20–170 1.35–1.88 IR (17)

Gerasimenko73P/Schwassmann- 1.67 1.440 VIS (15)

Wachmann 373P/Schwassmann- ∼120 0.97 IR (35), (9)

Wachmann 378P/Gehrels 2 20.79 2.36 VIS (2)81P/Wild 2 19.8–545 1.49–2.62 VIS (15)81P/Wild 2 570–2000 1.58–1.88 IR (9), (36)86P/Wild 3 24.49–24.96 2.41 VIS (2)103P/Hartley 2 100 1.03 VIS (14)

172 I. Mann et al.

Table 1 Continued


109P/Swift-Tuttle 5000 ± 3000 1–2.5 VIS (37)109P/Swift-Tuttle 300–1500 0.98–1.13 IR (38)126P/IRAS 300 3.3 IR (9)D/1993 F2 Shoemaker-Levy 9 6–22 5.39–5.41 VIS (39)

Note. (1), Suto et al. (1987); (2) Newburn Jr. and Spinrad (1989); (3) Rozenbush et al. (1989); (4) Singhet al. (1992); (5) Singh et al. (1997); (6) Thomas and Keller (1991); (7) Tokunaga et al. (1986); (8) Hanneret al. (1987b); (9) Lisse (2002); (10) Edenhofer et al. (1987); (11) Mazets et al. (1986); (12) Mazets et al.(1987); (13) Sekanina and Schuster (1978b); (14) Epifani et al. (2001); (15) Sanzovo et al. (2001); (16)Ney (1982); (17) Krishna Swamy (1991); (18) Lamy et al. (1996); (19) Sekanina and Schuster (1978a);(20) Fulle (1996); (21) Lamy et al. (1998b); (22) Weaver et al. (2003); (23) Landaberry et al. (1991);(24) Sanzovo et al. (1996); (25) Hanner et al. (1992); (26) Lamy et al. (2002); (27) Lynch et al. (1992);(28) Fulle et al. (1993b); (29) Eaton and Zarnecki (1985); (30) Fulle (1992); (31) Lamy et al. (1999);(32) Lamy et al. (1998a); (33) Fulle (2000); (34) Colangeli et al. (1998); (35) Lisse et al. (1998); (36)Hanner and Hayward (2003); (37) Fulle et al. (1994); (38) Fomenkova et al. (1995); (39) Hahn and Rettig(2000).aAt Giotto encounter.

majority of interstellar dust particles of sizes below 0.1 µm are deflected from en-tering the solar system and move around the heliopause (Czechowski and Mann2003a), which is an asymmetric structure formed by interaction of the solar windand interstellar medium ionised gases. The conditions for particles to enter thesolar system depend on the dust charging (Kimura and Mann 1998a) and plasmaconditions (Linde and Gombosi 2000; Czechowski and Mann 2003b). The dustfluxes in the inner heliosphere depend on the influence of radiation pressure, so-lar gravity and Lorentz forces on the interstellar dust (Mann and Kimura 2000).All the listed effects are correlated to the dust properties. The first observationalevidence of interstellar dust came from an earth-orbiting satellite measuring a vari-ation in the dust flux along the earth’s orbit. This variation was explained by grav-itational focussing of interstellar dust by the Sun (Bertaux and Blamont 1976).Measurements aboard the Ulysses spacecraft have detected both interstellar dustparticles (Grun et al. 1994) and neutral interstellar helium (Witte et al. 1993). Thein-situ experiments have detected particles with masses beyond 10−20 kg. Inside,3 AU interstellar particles have been detected up to masses of 10−12 kg and be-yond 3 AU up to masses slightly above 10−14 kg. The mass density is determinedby the upper end of the distribution and amounts to 2.8 × 10−23 kg m−3 (Mannand Kimura 2000). The initial direction of the flux is almost parallel to the eclipticplane at 72◦ ± 2.4◦ ecliptic longitude and −2.5 ◦ ±2.7◦ ecliptic latitude (Grunet al. 1994).

2.2.4 Kuiper belt objects

Shortly after the discovery of the first Kuiper belt objects, it was suggested thatKuiper belt objects may serve as a source of dust in the solar system. Collisionsof predominantly those Kuiper belt objects that are below the present limit ofdetection should create a dust disk in the trans-Neptunian’s region (Jewitt andLuu 1995). Estimates for the total dust production rate range from 9 × 105

to 3 × 108 kg s−1 (Stern 1995, 1996). It was further proposed that impacts of


Table 2 Estimates of dust mass loss rate derived from observations of long-period comets


C/1956 R1 Arend-Roland 75,000 0.32 VIS (1)C/1969 Y1 Bennett 1400–13,000 0.64–1.1 IR (2), (3)C/1973 E1 Kohoutek 12–48,000 0.85–1.33 VIS (4)C/1973 E1 Kohoutek 161.6 0.96 VIS (5)C/1973 E1 Kohoutek 490–25,000 0.15–0.96 IR (2)C/1974 C1 Bradfield 46–1900 0.51–0.83 IR (3)C/1975 N1 Kobayashi-Berger- 78–2600 0.43–1.02 IR (2), (3)

MilonC/1975 V1 West 690–1,20,000 0.20–1.12 IR (2), (3)C/1979 Y1 Bradfield 1.63–441 0.57–1.75 VIS (5), (6)C/1980 E1 Bowell 500–3244 3.39–5.55 VIS (6)C/1980 V1 Meier 57.18 2.19 VIS (5)C/1980 Y1 Bradfield 1500–8300 0.28–0.79 IR (3)P/1980 Y2 Panther 577.8 1.86 VIS (5)C/1983 H1 IRAS-Araki- 200–22,000 1.01 IR (3), (7)

AlcockC/1983 J1 Sugano-Saigusa- 0 1.06–1.08 VIS (5)

FujiwaraC/1983 J1 Sugano-Saigusa- <2 1.04–1.08 IR (8), (3)

FujiwaraC/1984 V1 Levy-Rudenko 0.9–16.9 1.40–2.17 VIS (9)C/1985 R1 Hartley-Good 0.044–0.0874 1.25–1.28 VIS (10)C/1985 R1 Hartley-Good 4.47–14.5 0.98–1.27 VIS (11), (12)C/1985 T1 Thiele 58.2–96.2 1.48 VIS (11)C/1986 P1 Wilson 8.4–500 1.36–3.74 IR (14), (3)C/1986 P1 Wilson 683–1080 1.28–1.36 VIS (11)C/1987 P1 Bradfield 2120–2870 0.94–1.01 VIS (11)C/1987 P1 Bradfield 400–2000 0.87–1.45 IR (13)C/1988 A1 Liller 5000 0.9 VIS (15)C/1988 A1 Liller 529–2160 1.08–1.54 VIS (11)C/1989 Q1 Okazaki-Levy- 450 0.95 IR (16), (7)

RudenkoC/1989 X1 Austin 30,000 0.36 VIS (17)C/1989 X1 Austin 300 0.78 IR (18)C/1989 X1 Austin 510+510

−205 0.94 IR (19)C/1989 X1 Austin 2400 0.94 IR (16), (7)C/1990 K1 Levy 500–11,000 1.05–3.01 VIS (6)C/1990 K1 Levy 8700–9300 1.52–1.57 IR (20)C/1990 K1 Levy 6100 1.14 IR (16), (7)C/1995 O1 Hale–Bopp 500–58,800 2.4–13 VIS (21), (22)C/1995 O1 Hale–Bopp 30,000–1,50,000 2.54–4.58 IR (23), (24), (7)C/1995 O1 Hale–Bopp 1,00,000–18,00,000 0.91–3.17 submm (25)C/1995 O1 Hale–Bopp 15,00,000 0.91–1.01 mm (26)C/1996 B2 Hyakutake 1000–8000 0.5–1.5 VIS (27)C/1996 B2 Hyakutake 1860–3445 1.14–1.18 IR (28)C/1996 B2 Hyakutake 13,000 1.03 IR (7)C/1996 B2 Hyakutake 28,000 1.06–1.08 submm (29)

174 I. Mann et al.

Table 2 Continued


C/1999 S4 LINEAR 6300 1.07 IR (7)C/1999 S4 LINEAR 90 0.77 radio (30)C/1999 T1 McNaught-Hartley 100–300 1.20–1.27 VIS (31)C/2001 A2 LINEAR ∼900 1.30 IR (7)

Note. (1) Finson and Probstein (1968); (2) Ney (1982); (3) Krishna Swamy (1991); (4) Fulle (1988); (5)Newburn Jr. and Spinrad (1989); (6) Sanzovo et al. (1996); (7) Lisse (2002); (8) Hanner et al. (1987a);(9) Sanzovo et al. (2001); (10) Landaberry et al. (1991); (11) Singh et al. (1992); (12) Singh et al.(1997); (13) Hanner et al. (1990); (14) Hanner and Newburn (1989); (15) Fulle et al. (1992); (16) Lisseet al. (1998); (17) Fulle et al. (1993a); (18) Hanner et al. (1993) ; (19) Lisse et al. (1994); (20) Lynchet al. (1992); (21) Fulle et al. (1998); (22) Rauer et al. (1997); (23) Lellouch et al. (1998); (24) Grunet al. (2001); (25) Jewitt and Matthews (1999); (26) de Pater et al. (1998); (27) Fulle et al. (1997); (28)Sarmecanic et al. (1997); (29) Jewitt and Matthews (1997); (30) Altenhoff et al. (2002); (31) Morenoet al. (2003).

interstellar dust particles onto Kuiper belt objects are an efficient source of ejectaparticles with radii smaller than 10 µm. For this, the dust production rate rangesfrom 4 × 102 to 3 × 104 kg s−1 (Yamamoto and Mukai 1998). The latter dustproduction by impacts depends critically on the assumed surface properties of theicy Kuiper belt objects.

3 Circumstellar planetary debris dust

Discoveries and studies of planetary debris disks started two decades ago, whenmeasurements of the spectral energy distribution of Vega revealed a faint excessin the infrared brightness. The excess is attributed to circumstellar dust and thedust lifetime is below the age of the central stars. The debris shells are observedaround main-sequence or “old” pre-main-sequence stars younger than the Sun.The circumstellar structure cannot clearly be determined from the infrared excessalone. Measurements at far-infrared and submillimetre range, as well as observa-tions of emission features allow to estimate the size distribution of the dust and todistinguish the dust from interstellar dust. Some relatively nearby systems can bestudied with spatially resolved observations.

3.1 Detection of planetary debris disks from spectral energy distributions

3.1.1 Mid-infrared excess

Vega observations with IRAS showed the first infrared excess of circumstellar dustaround a main-sequence star ( Aumann et al. 1984). IRAS firstly measured the in-frared excess also around other stars. Observations were made in spectral intervalscentred around wavelengths of 12, 25, 60 and 100 µm; for further discussion ofIRAS observations see Backman and Paresce (1993).


3.1.2 Search for near-infrared emission from near-star components

The majority of observations of circumstellar dust describe “cold” dust compo-nents that cause a far-infrared excess brightness. Some data of stars with “warm”dust components have been derived from ISO observations (Fajardo-Acosta etal. 1998): For eight systems, a 12 µm excess emission produced by dust that islocated between 1 and 10 AU (angular radius 0.0028–0.074 arcsec, distances 70–250 pc) was observed. The dust temperatures range from 200 to 500 K and arebelow the average temperature for the solar system zodiacal cloud. The observedflux densities (0.085–0.155 Jy at 12 µm) exceed the flux estimate for a solar sys-tem type zodiacal dust cloud seen from 10 pc (0.0001 Jy at 10 µm). These ‘warm’dust components are of special interest, since they are in regions where the habit-able zones of these planetary systems are expected. In future, VLTI observationsmay allow searching for such near-star dust components.

3.1.3 VLTI observations

Interferometric measurements in the near-infrared are of special interest, sincethey can possibly resolve the most inner 10 AU of a planetary debris disk andtherefore the regions of possible habitable planets as well as, even further inwardthe regions of dust sublimation. High-resolution observations of the stellar photo-sphere also allow confining stellar evolution models and determining the ages ofthe host stars of the planetary debris disks: Di Folco and collaborators have usedthe VLTI during commissioning period to study five nearby Vega-type stars in theK- and H bands (Di Folco et al. 2004). By direct size measurements of the stel-lar photospheres, they could improve estimates of the age of the stars, which willhelp understanding the time evolution of the planetary debris disks. They furtherobtained information about two of the dust disks.

3.1.4 Millimetre and submillimetre observations

Stars that harbour very cold disks may not reveal an observable excess of mid-infrared brightness, and moreover the detection of emission at large wavelengthprecludes the contribution of small dust particles, which could be interstellardust. This shows that submillimetre observations are beneficial for analyzingspectral energy distributions not only by extending the observed spectral range.The advantage of the positional accuracy in comparison to the infrared data ismentioned later. Several searches have been carried out with the SubmillimeterCommon-User Bolometer Array (SCUBA) at James Clerk Maxwell Telescope(JCMT). They concentrated on different samples of stars with known infrared ex-cess (Sylvester et al. 1996, 1994; Wyatt et al. 2003; Sheret et al. 2004). Sheretet al. (2004) carried out new observations and compiled the submillimetre obser-vations, which were photometric and in some cases mapping observations: Thephotometric fluxes range from 0.066 to 1.925 Jy at 450 µm and between 0.0024and 0.384 Jy at wavelength 850 µm. In roughly half of the 21 objects, only upperlimits of the flux could be derived. The total amount of mass contained in the dustin these systems is estimated with between about 1/1000 and several earth masses.While these observations are of A-, F-, G- and K-type stars, recently some M-type

176 I. Mann et al.

Fig. 5 The dust mass versus age of the star derived from submillimetre searches for planetarydebris disks. Detected debris disks are shown as large letters in boxes; the letters denote thespectral type of the star. The small letters denote the non-detections and the given dust massesare upper limits, assuming 30 K dust temperature in interpreting the 850 µm non-detections.Observational data are from Wyatt (2003); Sheret et al. (2004); Liu et al. (2004) and this figureis from the latter reference

stars were observed (Liu et al. 2004). The observed dependence of debris massand age of the stars is shown in Fig. 5.

3.1.5 Correlation of infrared excess and planet detection

For a long time, the direct observation of both a planet and a dust disk around astar was limited to one case only and it seems that only few stars host both innergiant planets and detectable planetary debris disks. Beichman et al. (2005) havesearched for infrared excesses toward 26 field stars of type F-, G-, and K knownto have one or more planets and have detected 70 µm excesses (but no excess at24 µm) around six stars. The excesses are consistent with the presence of Kuiperbelt analogues with 100 times more emitting surface area than in the solar system.A search for debris disks in the submillimetre regime around nearby stars that hostgiant planets resulted in no positive detection, implying that typical dust massesin these systems are less than 0.02 earth masses (Greaves et al. 2004a).

3.1.6 Need for spatially resolved observations

Measurements of the spectral energy distribution are a good tool to find evidencefor circumstellar dust and planetary debris disks in surveys. It is interesting to notethat the irregular structure of the dust disks may even be detected by photometryof the stars: Variations of the β Pictoris brightness from 1999 to 2002 were foundto have a weak long-term variation of −0.8 × 10−3 mag per year (Lecavelier DesEtangs et al. 2005). The authors note that similar variations of the star have beenobserved before and suggest that they are caused by either dust inhomogeneitiestransiting the star or by variations of the dust structure. Nevertheless, observa-tions of the infrared excess alone may not provide enough information to clearlyidentify a planetary debris disk and/or to study its properties.


Kalas et al. (2001) point out that in some cases of Vega-like stars, the dust re-sponsible for excess thermal emission may originate from the interstellar mediumrather than from a planetary debris system. They carried out coronagraphic opticalobservations of six Vega-like stars with reflection nebulosities. For five of themthey found the emissivity is similar to that of the Pleiades, and concluded thatthey are caused by interstellar dust. Also, the confusion with background bright-ness components is possible. Sheret et al. (2004) have observed stars with knowninfrared excess in the submillimetre regime with SCUBA in order to confirm theirorigin from a circumstellar dust and to constrain the spectral energy distributions.Compared to the IRAS measurements, the SCUBA observations have a smallerpositional uncertainty and therefore can be used to confirm whether the observedinfrared brightness is really associated to the star and not to a background source.For the case of HD 123160, the existence of a dust disk could be rejected becausethe thermal emission brightness was detected with an offset of 10 arcsec from thestar Sheret et al. (2004).

3.2 Spatially resolved observations of planetary debris disks

By far the best explored Vega-type object is β Pictoris, for which detailed imagesboth in the visual and infrared have been obtained (Table 3). Resolved in visual–near-infrared (i.e. in scattered light) is also the disk around HR 4796A, which hasa M companion star. Resolved in infrared and submillimetre (i.e. thermal emis-sion) are more stars such as Vega (α Lyrae), ε Eridani and Fomalhaut (α PiscisAustrini) and 55 Cancri, which is known to host both a disk, resolved in the near-infrared, and a planet (Trilling and Brown 1998; Dominik et al. 1998; Trilling et al.2000). Detailed information for some systems is given in the following sectionsand further discussion of the spatial distribution will follow in Sect. 5.

3.2.1 β Pictoris

Probably the most massive debris disk is observed around β Pictoris (HD 39060),a young main sequence star of spectral type A5 IV (Weinberger et al. 2003). Earlystudies assumed its distance from the Sun as 16.4 pc (Lanz 1986) and early studiesof the dust disk refer to this value. According to measurements of the Hipparcossatellite, the distance is 19.28 ± 0.19 pc (Crifo et al. 1997). Also, various num-bers for the stellar photospheric temperature exist such as Teff = 8250 K (Wahhajet al. 2003) and Teff = 8500 K (Heinrichsen et al. 1999). The age of the star is as-sumed by Crifo et al. (1997) as 8 × 106 years, while other authors assume 2 × 108

years (Wahhaj et al. 2003) and 1–3×108 years (Kalas and Jewitt 1995), respec-tively. The stellar radius is 1.46 R� (Heinrichsen et al. 1999), the luminosity is8.7 times the solar luminosity L� (Crifo et al. 1997) and its mass 1.7–1.8 M�. Itsproximity to the Sun and the high number density of the dust debris disk allowedfor detailed imaging observations over a wide spectral range (see Table 3). Theyrevealed the heterogeneity of the spatial distribution and allowed to infer the sizesof dust particles. Also some gas component are observed (see Sect. 6.1).

178 I. Mann et al.

Table 3 Observations of the dust disk around β Pictoris and the distance of the observed dustfrom the star

Reference Wavelength Range (AU)

(1) 0.67 µm (R filter) 100–400(2) B, R, V, I filter 100–800(3) R linear polarised 300–600(4) B, V, R filter 40–300(5) 0.67 µm (R filter) 40–100, 100–300(6) 10 µm <90(7) 0.67 µm (R filter) 50–100, 100–800(8) B, V, R, I linear polarised 150–350(9) 1.2 µm (J filter) 20–80(10) 2.2 µm (K filter) 24–100(11) 2.4–45.2 µm <100(12) 25 and 60 µm(13) 6–13 µm <70(14) 10–200(15) 790 µm ca. 500–800(16) 0.67 µm (R filter) 120–1834(17) 11.7 µm, 17.9 µm Up to 77(18) 17.9 µm Up to 100(19) 1.2 mm Up to 1050(20) 12 µm <90(21) 12 µm <90(22) 12 µm <200(23) K linear polarised 50–150

Note. The listed distances are those given by the authors. (1) Smith and Terrile (1984); (2) Paresce andBurrows (1987); (3) Gledhill et al. (1991); (4) Lecalvelier Des Etangs et al. (1993); (5) Golimowskyet al. (1993); (6) Lagage and Pantin (1994); (7) Kalas and Jewitt (1995) ; (8) Wolstencroft et al. (1995) ;(9) Mouillet et al. (1997b); (10) Mouillet et al. (1997a); (11) Pantin et al. (1997); (12) Heinrichsen et al.(1999); (13) Lagage et al. (1999); (14) Heap et al. (2000) ; (15) Kalas et al. (2000); (16) Larwood andKalas (2001); (17) Weinberger et al. (2003); (18) Wahhaj et al. (2003); (19) Liseau et al. (2003); (20)Liseau et al. (2003); (21) Okamoto et al. (2004); (22) Telesco et al. (2005); (23) Tamura et al. (2006).

3.2.2 Fomalhaut

Fomalhaut (HD 216956) is a A3V main-sequence star at a distance of 7.69 pc(Holland et al. 1998) from the solar system. Its photospheric temperature isabout Teff = 9000 K (Backman and Paresce 1993) and its luminosity as 13L�(Dent et al. 2000) to 16L� (Holland et al. 1998). The stellar radius and massare assumed to be 1.7 R� and 2.3 M�, respectively, the age is of the order of100 Myr. Early observations at 0.87 and 1.3 mm show brightness excess but donot allow for reliably estimating the extension of the disk (Chini et al. 1990).Further submillimetre observations revealed a disk-like structure (Holland et al.1998). Mapping at 450 and 850 µm with SCUBA showed a close to edge onnarrow ring of dust around 150 AU from the star, with possibly azimuthal densityvariations along the ring: Observations at 450 µm, where the telescope beamsize is equivalent to a resolution of 50 AU, reveal the existence of a clump ora ring arc (Holland et al. 2003). No gas disk was observed around Fomalhaut(Liseau 1999).


3.2.3 Vega

Vega (HD 172167) is a bright A0 V main sequence star at distance 7.76 pc fromthe Sun with an age of approximately 350 Myr ( Aumann et al. 1984), luminosityof 60L�, mass of 2.5M� and effective photospheric temperature of the order ofTeff = 9500 K (Ciardi et al. 2001) (see also for detailed discussion). Photometrywith ISOPHOT shows excess brightness of a factor of 1.7 at 25 µm, a maxi-mum excess factor of 21 at 120 and 150 µm, and excess factor of 15 at 200 µm(Heinrichsen et al. 1998). Spatially resolved ISOPHOT data were obtained at 60and 90 µm. Observations at 2.2 µm wavelength (K-band) show small, hotter dustparticles located close to the star: With model calculations, the observed flux con-tribution of 3–6% can be reproduced by dust within 4 AU from the star (Ciardiet al. 2001). Observations at 0.87 and 1.3 mm show brightness excess beyond thestellar photospheric flux fitted with a blackbody curve by a factor of 3.7 and 1.7,respectively (Chini et al. 1990). These initial observations at 0.87 and 1.3 mmshowed that the excess brightness is offset from the star and indicated that thedust cloud lies between 40 and 74 AU distance (Chini et al. 1990). Further sub-millimetre observations of emission peaks offset from the star indicated a possibledisk-like structure (Holland et al. 1998; Dent et al. 2000). Mapping observationsat 1.3 mm provided an image of several emission enhancements located along acircumstellar ring of 95 AU radius (Koerner et al. 2001). Observations with higherresolution and sensitivity showed that a large fraction of the observed emissionis due to two dust emission peaks northeast and southwest from the star (Wilneret al. 2002). A search for planets showed that planetary companions in the debrisdisk can be excluded to a level of 6–8 Jupiter masses (Macintosh et al. 2003).

3.2.4 ε Eridani

ε Eridani (HD 22049) is a nearby 0.5–1 Gyr (730 Myr (Macintosh et al. 2003),800 Myr (Henry et al. 1996)) old K2V star with a stellar mass of 0.8 M� (Quillenand Thorndike 2002). The star has a distance of 3.22 pc from the Sun (Greaveset al. 1998), and a stellar luminosity of 0.33 L� (Dent et al. 2000), an effectivetemperature of 5050 K (Saar and Osten 1997). Images of ε Eridani at 850 µmshows a signal out to about 115 AU radius (35 arcsec offset) with an emissionpeak at 60 AU and a reduced emission at 30 AU, which possibly indicates the inneredge of a ring-like dust distribution (Greaves et al. 1998). The dust ring is seenalmost face-on. These results are confirmed with more recent observations, whichalso achieved the first imaging at 450 µm (Greaves et al. 2005). Asymmetries andbright peaks are also observable in the image. From observations of the excessemission at 100 µm Chini et al. (1990), in contrast, derive an inner and outerradius as 4 and 25 AU for dust particles of sizes between 162 and 486 µm, a totaldust mass of 4.2 × 10−9 M�, and temperatures at the inner and outer edge as135 and 45 K, respectively. From ISO observations (60 and 90 µm mapping andlow-resolution spectroscopy between 5.8 and 11.6 µm), Walker and Heinrichsen(2000) give a total mass of the dust disk of 1.1 × 10−9 M�. A search for planetsshowed that planetary companions in the debris disk can be excluded to a levelof 5 Jupiter masses (Macintosh et al. 2003). The gas component in the dust ringaround ε Eridani (mgas/Mdust < 10−3) seems negligible (Liseau 1999).

180 I. Mann et al.

3.2.5 AU Microscopii

With AU Microscopii (HD 197481), the first imaging of planetary debris aroundan M-type star was achieved. From SCUBA observations of the 850 µm excessemission Liu, Kalas and Mathews inferred the presence of a debris disk and con-firmed this with spatially resolved observations using an optical stellar corona-graph (Liu et al. 2004; Kalas et al. 2004). Initial imaging revealed a dust signalbetween 50 and 210 AU where the dust lifetime exceeds the age of the star. TheSCUBA data further suggest that the system is gas-poor, and that the inner diskvoid extends to approximately 17 AU, if the spectral energy distribution is ex-plained with blackbody temperature of dust. The system appears in age similar tothe β Pictoris disk (Kalas et al. 2004). Further imaging observations of scatteredlight show that the inner disk is asymmetric with various substructures; a changein the radial slope of the surface brightness profile is seen in the data at 35 and33 AU, respectively (Liu 2004; Metchev et al. 2005). H-band imaging observa-tions exclude the existence of planets larger than Jupiter-mass at distances largerthan 20 AU from the star (Metchev et al. 2005).

3.2.6 HD 32297

A system that possibly reveals an asymmetric structure as consequence of interac-tions with the interstellar medium is the planetary debris disk around the A0 starHD 32297 (see also Sect. 7). IRAS observations indicated the existence of a dustdisk and a nearly edge-on disk was imaged with HST in scattered light at 1.1 µmthat extends to at least 400 AU (3.3 arcsec) along its major axis (Schneider et al.2005). Optical stellar coronagraph observations from Mauna Kea show the duststructure from 560 to 1680 AU distance from the star is extremely asymmetrictowards the southern wing which is in the vicinity of a relatively dense interstel-lar gas cloud and comparison to the HST data indicates the dust is probably blue(Kalas 2006).

3.2.7 τ Ceti

With 850 µm observations of τ Ceti (HD 10700), the first dust disk around aSun-like (G8V) star of late main-sequence age was recently confirmed by imaging(Greaves et al. 2004b). The debris disk extends out to a radius of about 55 AUcomparable to the Kuiper belt, but the dust mass is at least an order of magnitudegreater than in the Kuiper belt.

3.2.8 η Corvi

For η Corvi (HD 109085) first spatially resolved observations of dust around amain-sequence F star were achieved in the submillimetre and mid-infrared withSCUBA (Wyatt et al. 2005) as two peaks in the emission brightness offset from thecentral star at projected distance of 100 AU. The observations at 450 and 850 µmare explained with a disk of radius 150 ± 20 AU seen at 45◦ ± 25◦ inclination.The inner zone of the disk within 100 AU appears to be cleared of dust emitting inthe submillimetre regime. When fitting the spectral energy distribution taking into


account mid-infrared data this is, in contrast, best explained with an additional hotdust component corresponding to a distance of only 1–2 AU (Wyatt et al. 2005).

3.2.9 HD 141569

An example for a relatively young system (<5 Myrs) for which the dust dynam-ics is still influenced by remnant gas is HD 141569. Spatially resolved obser-vations of scattered light of its circumstellar dust disk were obtained with theHubble Space Telescope at 1.1 and 1.6 µm wavelength (Augereau et al. 1999a,b;Weinberger et al. 1999). Refined observations with higher signal-to-noise ratioand spatial resolution reveal the heterogeneity of the disk with two ring-like struc-tures at distances of about 200 and 325 AU from the star as well as an arc-likestructure and a change of the tilt of the symmetry plane (Mouillet et al. 2001). Ad-ditional ground-based near-infrared (2.2 µm) observations allowed to constrainminimum grain size and size distribution in the disk (Boccaletti et al. 2003). Mid-infrared imaging at λ = 12.5, 17.9 and 20.8 µm fit to a flat radially symmetricinner dust disk indicating that near- and mid-infrared brightness picture the innerand outer parts of a common disk structure (Marsh et al. 2002). Both, the influenceof a planet and the influence of stellar companions are discussed as possible per-turbations to cause the observed structures (Wyatt 2005; Augereau and Papaloizou2004).

3.3 Polarization measurements of planetary debris disks

Gledhill et al. (1991) measured the linear polarization in the R-band of the diskaround β Pictoris in the range 15–30 arcsec from the star (i.e., roughly 300–600 AU). The degree of linear polarization along the mid-plane was 17 ± 3%with a dip around 24 arcsec in the northeast direction and a dip around 20 arcsecin the southwest direction. Linear polarization outward from about 150 AU in theB-, V-, R- and I-band confirmed the overall trend of the previous R-band data(Wolstencroft et al. 1995). Krivova et al. (2000) modelled the polarization of thedisk using Mie theory and concluded that grains smaller than micrometre sizesare depleted in comparison to a power-law size distribution; in particular, in thesouthwest side of the disk. Tamura et al. (2006) measured the linear polarizationof the inner K-band brightness and explain the polarization data with a model ofice-filled fluffy aggregate particles (see Fig. 6).

3.4 Dust sources in planetary debris disks

For the spatially resolved observations of the disks, their wide extension indi-cates that planetesimal-size objects are present and act as perturbers (Backman andParesce 1993). These are also expected to feed the dust disks by collisional frag-mentation. Moreover, there is some evidence for phenomena similar to cometaryactivity: Doppler shifted circumstellar components (Lagrange et al. 1989) ob-served in stellar photospheric UV absorption lines of the β Pictoris are explainedwith comets falling onto the star (Beust et al., 1989, and references therein). It is

182 I. Mann et al.

Fig. 6 The observed linear polarization as function of offset from β Pictoris: filled circles denoteR-band data (Gledhill et al. 1991), open circles denote B-, V-, R-, and I-band data (Wolstencroftet al. 1995), and squares denote K-band data (Tamura et al. 2006). The solid line gives the modelcalculation (Tamura et al. 2006). This figure is adapted from Tamura et al. (2006)

suggested that the comets may have been brought to star-grazing orbits by per-turbations of (yet unknown) planets (Beust and Morbidelli 1996; Levison et al.1994).

4 Forces and effects

The major forces on the dust particles are the gravitational force and radiationpressure force of the central star. In some cases, stellar wind forces can be equallyimportant as radiation pressure force, but the parameters of the stellar windsare uncertain. Surface charges of dust in planetary debris disks are expectedto be slightly higher than that in the solar system. This is a result of enhancedphotoionization. Lorentz force is important for small particles only and thereforehas no significant influence on the observed dust components. Dust destruction bysublimation occurs far inward from 1 AU for refractory particles in the consideredsystems. Ices sublimate at several astronomical units distance and also UV


radiation can cause chemical alteration and erosion of the particles. The maindestruction mechanism for dust in these systems is collisional fragmentation.

4.1 Gravitational forces

The gravity of the central star is the dominant force for most objects in circum-stellar systems and their motion is roughly approximated as Keplerian orbits. Forsmall dust particles, forces due to the stellar light and wind and Lorentz force cansignificantly affect their motions. This is because the gravity is proportional to thevolume of dust particles, the forces caused by impact of photons and stellar windparticles are roughly proportional to the cross-section, and Lorentz force is pro-portional to the radius of the dust particles, provided that the particles are chargedto the same potential.

The gravitational force, Fg, acting on a body with mass, m, is expressed as

Fg = −GM∗m

r2(2)

where G is the gravitational constant, M∗ is the mass of the star, and r is helio-centric distance of the body from the star.

Dust is further influenced by the gravitational force of the planets. Distant,non-resonant interactions cause small periodic oscillations of the orbital elementsof the dust particles on long timescales. These are the most common planetaryperturbations and they cause the rotational symmetry of the dust cloud, as wellas of those meteoroids that are associated to the sporadic meteors. More severeperturbations occur for close encounters with the planets. Resonant perturbationsoccur when the orbital periods of planets and dust particles are such that the planetimposes a periodic perturbation, which will be discussed in Sect. 5.

4.2 Radiation pressure forces

The absorption and scattering of stellar light by dust particles lead to the radiationpressure on the dust, which is usually the most important non-gravitational forcethat determines the orbital evolution of dust. The resulting radiation pressure force,FPR, is expressed as the product of momentum flux of the incident light and thecross-section:

FPR = L∗4πr2c

A〈QPR〉 (3)

where L∗ is the stellar luminosity, c the speed of light, A the geometrical cross-section of dust and 〈QPR〉 the radiation pressure coefficient averaged over thestellar spectrum F∗(λ) defined as

〈QPR〉 =∫ ∞

0F∗ (λ) QPR(m∗, λ) dλ∫ ∞

0F∗ (λ) dλ

. (4)

The cross-section A〈QPR〉 is similar to the geometrical cross-section A when thesize of dust is much larger than the wavelength of typical incident light (geometri-cal optics). For small particles, 〈QPR〉 strongly depends on the wavelength of light,

184 I. Mann et al.

Fig. 7 Calculated β values for astronomical silicate. Left, for spherical grains in different sys-tems; right, for BCCA and BPCA aggregates (symbols) in the solar system, compared to spher-ical grains (solid line) (Kohler 2005). The dashed line and the dashed-dotted line give the esti-mated extrapolations curves for the β values for larger aggregates. The horizontal lines in bothfigures indicate the limit of particles in bound and unbound orbits. The upper line for parti-cles released by parent bodies on circular orbits and the lower line for particles released byparent bodies on high eccentric orbits (e = 0.9). Note that results are similar for small BPCAand BCCA particles. The particle model and light scattering calculations will be explained inSect. 8

shape of dust and material composition of the particle through its optical constantm∗. For dust much smaller than the incident wavelength of light, the cross-sectionis proportional to the volume of dust (Rayleigh limit); A〈QPR〉 ∝ V .

The importance of the radiation pressure is commonly measured by the ratioof radiation pressure to gravity of the star as

βPR = FPR

FG= L∗ A〈QPR〉

4πG M∗mc. (5)

Note that the ratio βPR is independent of heliocentric distance r . As seen inEq. (5), βPR is inversely proportional to the radius of the large dust where ge-ometrical optics is applicable. For small dust, i.e. in the Rayleigh limit, βPR isconstant with size. Figure 7 shows that for some systems, βPR > 1 applies for allsmall particles, while for other systems, β can be below 1 again for particles in theRayleigh limit. If the radiation pressure overcomes the stellar gravity, the dust isnot in bound orbit around the star. Large bound-orbiting dust particles can suffermutual collisions and produce small fragments, which are then blown out. Theseparticles in hyperbolic orbits are called β-meteoroids. Radiation-induced ejectionis one of the major fates of dust. Calculation of βPR have been done for sphericallyshaped dust and various compositions using Mie theory. According to calculatedβPR, dust in our solar system and β Pictoris is not in bound orbits if their sizeis smaller than ∼0.1 and 1–10 µm, respectively (Burns et al. 1979; Artymowicz1988). For dust around AU Mic, which is a M-type star of low luminosity, theradiation force is not sufficient to blow out the dust of any size (Plavchan et al.2005).

Unless the radiation pressure is strong enough to eject dust, the force due tostar light decelerates the dust and gradually decreases the heliocentric distance ofthe dust. This effect is known as Poynting–Robertson effect and comes from a


finite aberration angle between direction of light and moving dust. A small, non-radial component of the radiation pressure force is exerted on the orbiting dust.The more correct expression of the radiation force on dust having velocity v canto order v/c be written as (Burns et al. 1979)

FPR = FPR

[(1 − v · r

c

) rr

− vc

]. (6)

The non-radial term in Eq. (6) is opposed to the velocity vector of the dust, andthus dissipates the energy and angular momentum of dust. The falling time of dustwith circular orbit from heliocentric distance r to the star is given as

τPR = r2 c

2 G M∗ β. (7)

The falling timescale of ∼µm sized dust from 1 AU to the Sun is several thousandyears. In our zodiacal cloud, the observed radial distribution of dust ∝ r−1 canbe roughly explained by the result of the inward migration due to the Poynting–Robertson effect.

Due to the higher stellar fluxes, radiation pressure force in most of the cir-cumstellar systems exceeds those in the solar system (see Fig. 7). Recently, theprogress in optical theories and computational facilities makes it possible to calcu-late optical properties of more realistic irregularly shaped dust that are comparableto collected IDPs. The β values calculated for irregular dust models are shown onthe right-hand side of Fig. 7, they can significantly differ from those of compactparticles. It should be noted that in certain cases it may not be sufficient to approx-imate the stellar brightness in Eq. (4) with the Planck function B∗(T ), but rather toconsider the observed spectrum F∗(λ) of the star (Lamy 1976; Artymowicz 1988).

Circumstellar disks around other stars observed until today have a much higherdust density than the zodiacal cloud and timescales of mutual collisions are ex-pected to be much shorter than τPR. Inward migration of dust by Poynting–Robertson drag is inefficient in such dense disks (e.g. Wyatt 2005).

4.3 Stellar wind forces

Like stellar light gives rise to the radiation pressure forces, the impacts of solarwind particles, mainly of protons and α particles, exert both a radial force and anon-radial drag force. The effects of the force, FSW, on the dynamics of dust aresimilar to that of the electromagnetic radiation force, FPR, given by Eq. (6). Theexpression of FSW is given as

FSW = FSW

[(1 − v · r

vSW

)rr

− vvSW

]. (8)

where FSW is the force on the dust for v = 0 and vSW the bulk velocity of thewind. The non-radial term in Eq. (8) is referred to as plasma or pseudo-Poynting–Robertson drag force. The force FSW is expressed as

FSW = M∗vSW

4πr2A〈QSW〉 (9)

186 I. Mann et al.

where M∗ is the mass loss rate of the central star and A〈QSW〉 the momentumtransfer cross-section averaged over the wind species. For the stellar wind force,we can define βSW as

βSW = FSW

FG= M∗vSW A〈QPR〉

4πG M∗m. (10)

The ration βSW is independent of the heliocentric distance except near the star(vSW = const) and outside the astrosphere.

In our solar system, the wind’s radial force is negligible compared to the ra-diation pressure; FSW/FPR ∼ 10−3. Although the momentum flux of the solarwind is 3 orders of magnitude smaller than that of the electromagnetic radiation,the plasma Poynting–Robertson drag is not negligible. From Eqs. (6) and (8), theratio of plasma Poynting–Robertson drags force to (photon) Poynting–Robertsondrag force can be written as

FSW

FPR

c

vSW� 0.3

(M∗M�

) (L∗L�

)−1 ( 〈QSW〉〈QPR〉

)(11)

where L� and M� are solar luminosity and mass loss rate, respectively. The factorc/vSW comes from the difference in the aberration angles.

In the case of dust disks around other main-sequence stars, the lack of clearknowledge about the stellar wind has made it difficult to discuss the wind’s forceson dust. From recent HST observations, Wood et al. (2002) and Wood et al.(2005a,b) infer that the mass loss rate M∗ of Sun-like stars decreases as the age ofthe stars increase and that in their young stages the star is up to ∼100 times moremassive than the current solar value. If one combines this high mass loss rate andEq. (11), the plasma Poynting–Robertson drag becomes much stronger than(photon) Poynting–Robertson drag and thus the timescale of inward migrationcan be by far shorter than previously thought (Plavchan et al. 2005). The wind’sradial force can overcome the stellar gravity for small dust (smaller than ∼0.01–0.1 µm) around the high mass loss rate (M = 100–1000 M�) stars even if onesimply assumes 〈QSW〉 ∼ 1.

Beyond the earlier simple estimations, more detailed studies of the force havebeen done especially for the solar system. Distant encounters between the solarwind particles and the dust particles cause dynamical friction described as theindirect or Coulomb solar wind drag (Morfill and Grun 1979). The dynamic effectsof the Coulomb drag are the same as those of the direct drag, but its strength isabout 3 orders of magnitude less. Mukai and Yamamoto (1982) showed that theeffect of sputtering on the dust increases the drag force by a factor of <0.5. Minatoet al. (2004) studied the effect of the passage of the impinging ions through smalldust grain and showed that the dependence of the cross-section A〈QSW〉 on dustsize is analogous to that for the electromagnetic radiation force. For dust smallerthan the range of impinging ions (0.01–0.1 µm), the cross-section is proportionalto the volume of dust A〈QSW〉 ∝ V , and for the larger dust, the cross-section isnearly its geometrical cross-section.

For small dust particles the neutral-gas drag force on dust particles in the outersolar system was shown to cause significant changes in the semimajor axes andeccentricities, leading to lifetimes of only ∼5 × 105 years for 1 µm dust particles(Scherer 1999).


Fig. 8 The scales for photon Poynting–Robertson lifetime, plasma Poynting–Robertson lifetimeand collision lifetime for dust in the solar system at present and at 0.7 Gyrs. The variation of thesolar photon flux over this time is almost constant compared to variation of stellar wind flux.As a result, the plasma Poynting–Robertson effect is more important in the early solar system(Minato et al. 2006)

4.4 Lorentz force

The Lorentz force reads

FL = qV × B, (12)

where q is the electric surface charge, V = v−vSW is the velocity of the dust rela-tive to the solar wind, and B the magnetic field vector carried with the solar wind.As the dust particles move through the sectored magnetic field of the Sun with al-ternative polarities, the Lorentz force changes its direction. For particles in boundorbit, this causes changes in a, e and i (Morfill and Grun 1979; Consolmagno1979, 1980; Barge et al. 1982a,b; Wallis and Hassan 1985).

Submicrometre particles, in particular when they reach the strong magneticfield near the Sun, can be ejected from the system by the Lorentz force (Hamiltonet al. 1996; Mann et al. 2004b). Nanometer-sized particles are even ejected nearearth orbit and by interaction with the solar wind are accelerated to solar-windvelocity (Mann et al. 2006).

4.5 Dust erosion and surface alteration

4.5.1 Dust surface charging

Photoelectron emission, sticking and recombination of plasma particles, sec-ondary electron emission, thermionic emission and field emission electricallycharge dust particles in space. The dust particle charge depends on the size, shape

188 I. Mann et al.

Table 4 The zone of sublimation calculated for different materials

Sphere Fluffy References

Graphite ≤5 R� ≤2 R� (2), (3), (6), (8), (9)Glassy carbon 4 R� 3–4 R� (10), (11)Magnetite 10–40 R� – (7)Iron 11–24.3 R� – (4), (5)Water ice 1–2.8 AU – (2), (5), (7)FeO-poor obsidian 1.9–7 R� 2.5–3 R� (4),(6),(7),(8), (9), (10), (11)FeO-rich obsidian 2.9–6 R� — (6), (9)Andesite 9–10.5 R� – (3), (4), (5)Basalt 6 R� – (9)Quartz 1.5–4 R� – (1), (2), (5)Astronomical silicate 14 R� – (9)Crystalline Mg-rich olivine 10 R� 9.5–11 R� (12)Amorphous Mg-rich olivine 13.5–15.5 R� 12–15 R� (12)Crystalline Mg-rich pyroxene 5 R� 5 R� (12)Amorphous Mg-rich pyroixene 5.5–6.5 R� 5–6.5 R� (12)

Note. (1) Over (1958); (2) Mukai and Mukai (1973); (3) Mukai et al. (1974); (4) Lamy (1974a); (5) Lamy(1974b); (6) Mukai and Yamamoto (1979); (7) Mukai and Schwehm (1981); (8) Mann et al. (1994); (9)Shestakova and Tambovtseva (1995); (10) Kimura et al. (1997); (11) Krivov et al. (1998); (12) Kimuraet al. (2002).

and structure of the particles, UV flux, their velocity relative to the plasma and theplasma temperature, which defines the velocity distribution of in-falling plasmaparticles. (To our knowledge, no detailed studies on the influence of the dust shapeand structure on the charging have been carried out so far.) Since photoelectronemission, secondary electron emission and thermionic emission vary with the ma-terial, the dust surface charge also depends on the dust composition. As a result ofthe dominating photoelectron emission caused by the solar radiation, dust parti-cles in the interplanetary medium, as opposed to dust in denser plasmas such as inplanetary magnetospheres, are usually positively charged. The calculated chargeof dust in the interplanetary medium corresponds to surface potentials relative toinfinity of between 5 and 10 V (Mukai 1981). The equilibrium surface charge ofdust particles of ∼µm size in the solar system is attained in timescales of around104 seconds or less, i.e. in less than a day. Temporal variations of the solar windparameters yield fluctuations of the surface charge of 20% and less (Kimura andMann 1998b). For particle sizes of the order of 10 nm and below, charge fluctua-tion are important compared to the dynamical timescales (Mann et al. 2006).

The charging of dust grains in extra-solar circumstellar systems can be esti-mated by considering the photoelectron emission. So far, the information aboutstellar winds are very rare. The energy of the photons can be estimated from stel-lar spectrum. In the case of β Pictoris, Vega and Fomalhaut the maximum of thestellar spectrum lies at about 0.33 µm (compared to solar system ∼0.5 µm). As aresult, the surface charges are possibly higher than those derived for dust in thesolar system.

4.5.2 Sputtering

Bombardment of energetic particles onto dust particles results in sputtering ofatoms and molecules from the surface of the dust particles. The mass loss rate


per surface area due to sputtering is found to be size independent and bom-bardment of solar wind particles causes stronger sputtering than that of cosmicrays of higher energies but lower fluences (Mukai and Schwehm 1981). The ero-sion by sputtering is mostly independent of the temperature of dust particles,though for ice particles its sudden increase close to the sublimation tempera-ture is measured (Lanzerotti et al. 1982). For magnetite particles of 1 and 10 µmsize at 0.5 AU, Mukai and Schwehm (1981) calculate lifetimes of 1 × 1011 s and1 × 1012 s (3000–30,000 years) respectively. By comparison to the Poynting–Robertson lifetime, they conclude that most interplanetary dust particles foraverage solar wind conditions drift toward the Sun under moderate erosion bysputtering.

4.5.3 UV alteration

The stellar UV radiation deposits energy in the grains, which can, aside fromheating, cause chemical alteration of the volatile and semi-volatile dust material.In particular, the desorption and chemical alteration of ices and organics are in-terrelated, and together with the release of light elements, the refractory organicscan also form, as the structure of dust particles is changed (Mukai et al. 2001). Forthe photosputtering of water ice in β Pictoris, Artymowicz (1997) shows that theresulting lifetime of water ice is of the order of Kepler orbital period and belowother relevant lifetimes.

4.5.4 Collisional fragmentation

Relative velocities of dust in the solar system and in extra-solar planetary systemsare of the order of fractions of the orbital velocities and typically in the range ofkilometre per second. Mutual collisions are therefore catastrophic and lead to thedestruction of particles. Fragmentation occurs at speeds exceeding about 1 km s−1

and fragments are distributed according to a power-law size distribution n(s) =s−p with p = 3.5 derived from laboratory measurements (Fujiwara et al. 1977).Values of p slightly greater than 3 are derived from an analytical theory basedon estimates of the propagation of shock waves in solids (Jones et al. 1996). Theexact critical velocities for fragmentation and vaporization of materials dependon the impact speed, on the size of target and projectile and on the material. Theamount of vaporized material is typically small but notable in the interplanetarymedium (Mann and Czechowski 2005).

4.5.5 Sublimation

The sublimation of dust particles depends on the temperature and the physicaland chemical properties of the dust. It was estimated for typical dust analoguematerials, such as silicates, metal oxides and different forms of carbon. Dustparticles composed of pure water ice are estimated to sublimate at a few astro-nomical units from the Sun (Mukai and Mukai 1973; Lamy 1974a; Mukai andSchwehm 1981). Contaminated water-ice dust particles attain higher temperaturesand thus sublimate at larger heliocentric distances (Mukai et al. 1985). Refrac-tory dust particles consisting of silicates, carbons and metals sublimate closer to

190 I. Mann et al.

Table 5 Plane of symmetry of the zodiacal cloud derived from visual (VIS) and infrared (IR)observations

i (◦) (◦) Data Reference

<2 – VIS Robley (1975)3.7 ± 0.6 66 ± 11 VIS Leinert et al. (1976)1.5 ± 0.4 96 ± 15 VIS Dumont and Levasseur-Regourd (1978)3.0 ± 0.3 87 ± 4 VIS Leinert et al. (1980)1.0 ± 0.3 20 ± 6 VIS Winkler et al. (1985)2.03 ∓ 0.5 57+7

−3 VIS Mukai et al. (2003)1.6–3.0 77–110 IR Murdock and Price (1985)2.3 ± 0.1 70 ± 5 IR Deul and Wolstencroft (1988)1.71 ± 0.01 77.1 ± 0.4 IR Reach (1988)1.1 ± 0.1 79 ± 1 IR Rowan-Robinson et al. (1990)1.45 ± 0.1 53 ± 1 IR Reach (1991)1.54 ± 0.01 40.9 ± 0.4 IR Vrtilek and Hauser (1995)2.03 ± 0.017 77.7 ± 0.6 IR Kelsall et al. (1999)

the Sun (Mukai and Mukai 1973; Lamy 1974a,b; Mukai et al. 1974; Mukai andYamamoto 1979; Mukai and Schwehm 1981). The location of sublimation zonesdepends not only on the size and composition of the dust particles, but also ontheir porosities (Mann et al. 1994; Kimura et al. 1997). If dust particles are ag-gregates of small constituent monomers, sublimation becomes less dependent ontheir overall sizes but rather on the size of the constituent dust particles (Kimuraet al. 2002). Table 5 gives a compilation of sublimation zones estimated for a va-riety of dust particles with different assumptions for composition and structure(Mann et al. 2004b).

In a different approach, Mann and Murad (2005) consider the sublimation se-quence of typical meteoritic and cometary silicates and show that metal oxides(here MgO) survive up to very close distances from the Sun, while silicon oxidessublimate at lower temperatures already and pure silicon is unlikely to form. Thestudy is based on the material parameters of enstatite but a typical and commonmeteoritic material. Knowledge about organic refractory components, as they areexpected to be present in the cometary dust, is poor. Since the chemical appear-ance is not yet understood, sublimation temperatures or zones near the Sun cannotbe calculated. There is also no direct evidence for the fractional sublimation ofsome of the dust constituents. Observations of pick-up ions in the solar wind in-dicate the presence of an inner source, which peaks near the Sun (0.1 to about0.3 AU) and contains the elements present in the solar wind up to Mg as well assome molecular ions (Gloeckler et al. 2000). The inner source was recently ex-plained with ion species that are produced by the vaporization of dust materialupon mutual collisions (Mann and Czechowski 2005). The presence of the carbonsource at small distances from the Sun possibly indicates that some of the organicrefractories are heat resistant and sublimate inward from 0.1 AU.

5 Spatial distributions

The presence of planets shapes the dust distribution in the solar system, but thiseffect is comparatively small. More pronounced structures in the solar system dust


cloud are observed due to the uneven distribution of the parent meteoroid popula-tion. Consequently, the dust cloud is structured in the regions where it is locallyreplenished. The smooth appearance of the dust cloud near 1 AU may indicatethere are less local sources than in the asteroid belt or in the inner solar system.Similarly, for the planetary debris disks, one might conclude that orbital reso-nances of the dust particles are smeared out, since the forces acting on the dustparticles depend on the dust size. The resonances, if they are the cause of thespatial structures, may act more efficiently on the meteoroid sized parent bodies.

5.1 Spatial distributions of solar system dust

5.1.1 The spatial distribution of dust in the inner solar system

The different zodiacal models, such as those of Leinert et al. (1977), Murdock andPrice (1985), Giese et al. (1986) and Good et al. (1986) converge near 1 AU intheir relative slopes of the density distribution (Giese et al. 1986), but the valuesderived for absolute dust number densities vary. The radial slope agrees with thepicture that particles are in orbits with low eccentricity and drift to the Sun underPoynting–Robertson effect. The smooth structure and the rotational symmetry ofthe overall dust cloud near 1 AU relative to an axis through the Sun is confirmedby zodiacal light observations. In terms of orbital evolution, it can be explainedby the randomisation of the orbital elements argument of perihelion ω and of theascending node . The rotationally symmetric number density distribution n isgiven as a function of solar distance r and helio-ecliptic latitude (or the latitudefrom the plane of symmetry, respectively) β�, radial and latitudinal dependenceare often assumed to be separated: n(r, β�) = n0 f (r)g(β�). The zodiacal lightcontinues smoothly into the solar F-corona, but since the coronal brightness isstrongly influenced by forward scattering at dust near 1 AU this does not proofa smooth continuation of the dust distribution. Findings about dust in the innersolar system will be further discussed in the next section discussing the collisionalevolution.

5.1.2 Spatial distributions of dust in the outer solar system

The small number of measurements, together with the low density of the dustcloud in the outer solar system make it difficult to assess the present data. Therecent studies of the interstellar dust show that the order of magnitude of detecteddust fluxes in the outer solar system can well be explained with the flux of inter-stellar dust that is confirmed from measurements inward from 5 AU (Mann andKimura 2000). Nevertheless, there is some experimental evidence for other dustcomponents in the outer solar system. The variation of the Voyager flux rates isabove statistical limits and hence is better explained with Kuiper belt object dustparticles rather than with interstellar dust (Mann and Kimura 2000). Although thePioneer in-situ measurements are not in agreement with the optical observationsaboard the same spacecraft, they showed that the existence of dust particles be-yond 5 AU is not limited to the direction of the interstellar dust flux. While Humes(1980) initially explained the Pioneer data with dust in orbits with high eccentric-ity and high inclination, Grun et al. (1994) suggested the flux to originate from

192 I. Mann et al.

large interstellar particles that are focused in the solar gravity field. This was laterstudied in detail by Landgraf et al. (2002). Still the disagreement with the opticalobservations aboard Pioneer remains (see Sect. 2.1.5). Therefore, these limitedexperimental results should be treated with some caution.

The thermal emission brightness of the Kuiper belt object dust populationis near or below observational limits set by the foreground zodiacal emission(Backman et al. 1995; Stern 1996). The optical depth of the Kuiper belt objectdust is predicted between 2 × 10−7 and 2 × 10−5 (Yamamoto and Mukai 1998;Stern 1996). If Kuiper belt object dust particles are predominantly composed oficy material, they effectively sublimate between 3 and 8 AU (Mukai 1986). Theejection of Kuiper belt object dust (Liou et al. 1996) will be further discussed laterin the context of resonances.

5.1.3 Plane of symmetry

The zodiacal dust is concentrated in a plane that shows a slight tilt relative to theecliptic. Since the symmetry plane is expected to reflect the dominant perturbingforces, such as the perturbation of the planets, it should be close to the invariableplane of the solar system with inclination i = 1.6◦ and ecliptic longitude of theascending node = 107◦, but different values are derived from the observations(see Table 5).

From ground-based visible light observations, Dumont and Levasseur-Regourd (1978) find the inclination of the cloud symmetry plane i = 1.5◦ ± 0.4◦and the ecliptic longitude of the ascending node = 96◦ ± 15◦. Visible light ob-servations at small elongations from the Helios spacecraft between 0.3 and 1 AUgive i = 3.0◦ ± 0.3◦, = 87◦ ± 4◦ (Leinert et al. 1980). Infrared observationsgive values of i = 1.7◦ ± 0.2◦, = 79◦ ± 3◦ and i = 3.0◦ ± 0.1◦, = 55◦ ± 4◦as listed in (Leinert et al. 1998). It should be noted that the symmetry plane isnot always derived directly from the data, but may also depend on the brightnessmodel used to fit the data. Moreover, even if we consider observations only from1 AU, the brightness at different wavelengths and elongations originates fromdifferent locations along the LOS, and hence does not always describe the samepart of the cloud.

Closer to the Sun, the Lorentz force acting on the small dust particles, may leadto the alignment of the cloud with the solar equator: i = 7.3◦, = 75.7◦. Thiscan be especially the case for micrometre-size and smaller dust particles (Mannet al. 2000). Whether these small dust particles have a noticeable contribution tothe LOS brightness is not clear. A change in the cloud symmetry plane closer tothe Sun can also be attributed to the gravitational perturbations from Venus, theorbital plane of which has i = 3.4◦, = 76◦ (Gustafson 1985; Gustafson andMisconi 1986).

5.2 Local density variations

5.2.1 Dust bands and dust trails

IRAS observations in 1983 revealed the existence of several solar system dustbands, brightness enhancements caused by dust particles with similar orbital


parameters (see Sykes 1990). In some cases, the orbital parameters are similarto those of the asteroid families, but many asteroid families have no associateddust bands. Nesvorny et al. (2003) suggest this is due to the advanced age of theseasteroid families and that the dust bands are primarily by-products of recent aster-oid break-up events.

Narrow trails of dust coincident with the orbits of periodic comets have beenfound in the IRAS data (Sykes et al. 1986). The particles are in orbits close to thatof the parent comet and seen both ahead and behind the comet. The trails werestudied in detail for eight comets and more than 100 faint dust trails are suggestedby the IRAS data (Sykes and Walker 1992). Based on this survey, the authorsconclude that the trail phenomenon is common to short-period comets.

Recently, Ishiguro et al. (2002) have found the visible dust trail existed alongthe orbit of comet 22P/Kopff. The trail consists of large (a few centimetre) anddark (albedo of 0.01) dust grains ejected from parent comet. Ongoing observa-tional programs show that dust trails are a common feature of comets. Similarspatial variations can be expected for planetary debris disks, but most authors con-centrate on the discussion of orbital resonances to explain the spatial structures inplanetary debris disks.

5.2.2 Resonances

Resonances occur when a periodic perturbation is imposed to a system that is ableto oscillate, such as an object orbiting a central star. In that case, orbital reso-nances occur for objects in orbit whose orbital period is in (small) integer ratios tothe period of a planet. Since even small perturbations tend to grow, objects may beejected from these resonances; on the other hand, they can be trapped in the orbitalresonance at least for a certain time. The most obvious case of orbital resonancesin the solar system is that of the asteroids: within the asteroid belt, asteroids avoidthe zones where orbital periods are in ratios 1:3, 2:5, 3:7, or 1:2 with the orbitalperiod of Jupiter (Kirkwood gaps), while an accumulation of asteroids is seen inthe range of the 1:1 resonances, for instance, (Trojans). Long-term trapping isexpected for the outer mean motion resonances and for instance, for a particle ap-proaching earth, passing the resonance gradually increases the eccentricity of theorbit until the particle reaches a planet-crossing orbit from which it is expelled byclose encounter with the planet. A set of particles in librating orbits with the orbitaleccentricity enhanced by this resonance would form a density enhancement thatrotates with the planet (Kuchner et al. 2000). Thus, the mean motion resonancescan form density wave patterns, some of which may show in circumstellar disksobservable orbital periods (Ozernoy et al. 2000). The resonances can also causea depletion of the dust inward from the orbit of the planet. The mechanism forclearing up the inner region is a temporary trapping of grains by the planet in outerresonances, which act as barriers, stopping the inward motion of dust toward thestar.

Dermott et al. (1994) suggest this structure formed for interplanetary dustreaching earth orbit. As a result, faint signals due to such a local dust enhance-ment leading and trailing the earth were found in the COBE infrared observationsof the zodiacal light (Reach et al. 1995). It is suggested that in a similar way thepresence of planets would form clearance zones in planetary debris disks.

194 I. Mann et al.

Liou et al. (1996) calculated the orbits of dust grains of diameters 1–9 µm andfind that due to resonances with the outer giant planets only 20% of the grainsevolve to the inner solar system. Since the zodiacal dust covers a broad size in-terval, where in particular the small grains might be influenced by other forcesbesides gravity, the features that result from resonances are possibly smeared out.A search in infrared observations for a wake of dust trailing Mars and for dust inthe Trojan region near Jupiter was not successful (Kuchner et al. 2000).

Nevertheless, the resonance structures in circumstellar dust disks are possiblystronger that those observed in the solar system. The resonant structure that buildup in a dust cloud depends among other on the lifetime of the particles (Ozernoyet al. 2000). Modelling a distribution of test particles shows that presence of aplanet influences a dust disk via resonances and gravitational scattering and alsothat for a rather massive planet the arising structure may have a high contrast rel-ative to the background dust cloud, if the lifetime of the particles is limited bycollisions (Ozernoy et al. 2000). Kuchner and Holman (2003) discuss the reso-nant structures caused in a dust cloud by single planets in orbit with eccentricitye < 0.6. They find that four different types of typical resonance geometries canarise. They suggest that three of them are similar to the structures observed inthe solar system dust cloud or around Vega, ε Eridani and Fomalhaut, but the en-hancements are not quantified. It is also quite possible that the observed structuresin the planetary debris disks are a combination of the dust band phenomenon andthe resonance effect. In a model to describe the observed structure of the β Pictorisdisk, Augereau et al. (1999b) suggest those do not form due to the resonances aris-ing for the dust: rather planetesimals are perturbed by a giant planet and provide asource of the collisionally produced dust.

5.3 Spatial distributions of dust in planetary debris disks

5.3.1 Inner depletion zones

An important feature of the spatial distribution is the radial dependence of thedust spatial density. Many observed Vega-type stars have disks with the densityfirst increasing and then increasing slower or even decreasing with decreasingdistance from the star (Backman and Paresce 1993). For instance, β Pictoris wasinitially assumed to show an inner depletion zone at about 40 AU, and outsidethis distance the number density of the cross-section-dominating grains slopes asr−2.7 to r−3.4. For two other resolved systems – HD 141569 and HR 4796A –the brightness also increases outward from the star, reaches a maximum and thendecreases (Augereau et al. 1999a,b; Schneider et al. 1999; Weinberger et al. 1999).The existence of planets and the collisional destruction of dust can both cause theinner depletion zones.

5.3.2 The β Pictoris disk observations

Aside from the existence of an inner zone of reduced dust density, spatially re-solved observations show a number of spatial structures in the β Pictoris disk (seeTable 6). Kalas and Jewitt (1995) used observations in the 0.67 µm (R filter) wave-length with 0.41 arcsec per pixel spatial resolution to describe five asymmetries in


Table 6 Parameters derived for the density enhancements detected around β Pictoris (Kalaset al. 2000; Wahhaj et al. 2003)

Kalas et al. (2000) Wahhaj et al. (2003)

SurfaceRadius brightness Enhancement Radius Optical

Ring (AU) (mag arcsec2) (%) Ring (AU) i (◦) depth

A 785 23.5 >20 A 14 ± 1 −32 ± 2 5.9 × 10−3

B 710 23.7 10 B 28 ± 3 +25 ± 2 2 × 10−3

C 647 24.1 5 C 52 ± 2 −2 ± 2 7.7 × 10−3

D 608 24.0 5 D 82 ± 2 +2 ± 2 2.3 × 10−2

E 575 24.0 5F 543 24.0 5G 506 24.0 5

the β Pictoris disk. The radial extension of the disk is 790 AU in northeast direc-tion, while it is only 650 AU in southwest direction. Later observations allowedto detect the disk further out to 1062 AU in southwest direction and 1835 AU innortheast direction (Larwood and Kalas 2001). The disk in northeast directionoutside of a radius of 330 AU is brighter than that at the same distances fromthe star in southwest direction. The width of the disk outward from 150 AU fromthe star is larger in the southwest direction compared to the northeast direction.The northeast wing is more extended to the north from the symmetry axis, whilethe southwest wing is more extended to south from the symmetry axis (‘butter-fly asymmetry’). The position angle of the northeast wing differs from that of thesouthwest wing by 1.3◦. Further imaging observations of β Pictoris were madeby Kalas et al. (2000) and Wahhaj et al. (2003). Both groups observe features thatindicate the existence of rings: Kalas et al. (2000) in the outer disk at 785–506 AU,while Wahhaj et al. (2003) detect features inward of 85 AU.

5.3.3 β Pictoris disk models

Kalas and Jewitt (1995) attempted to explain the asymmetries with the presenceof a massive body in the disk. The required parameters were a mass of 0.3 stel-lar masses moving in orbit with inclination 30◦ to the disk at minimum distance700 AU from the star. The resulting ring structure would be pronounced in oneside of the disk, as is observed (Kalas et al. 2000). Also the influence of stellerencounters was considered. This encounter would also change the orbital inclina-tion within the disk which could account for the “butterfly asymmetry” (Kalas andJewitt 1995).

Refined calculations (Larwood and Kalas 2001) give a value of 0.5 M�, pro-grade orbit and small inclination toward the disk axis for the perturber. The smallvelocity would suggest it be in bound orbits around the star, while the simulationsshow that the perturber would destroy the formed structure during subsequent or-bital periods. If the structure were formed by a single encounter then it happened105 years ago (Larwood and Kalas 2001).

The same group checked for stars that have encountered the β Pictoris systemduring the past 106 years and found that 22 stars could have possibly influencedthe system. While most of the encounters would generate a cloud of planetesimals

196 I. Mann et al.

to fall into the inner parts of the system, only six encounters within 0.1 pc possiblyhad a direct influence on the structure of the dust disk (Kalas et al. 2001).

Wahhaj et al. (2003) discovered features in the 17.9 µm spectral regime at dis-tances inward from 85 AU, which seen in both wings of the disk so that they mightare be explained with dust rings. Table 6 lists the observed density enhancementsas well as the optical depth that is associated to these rings. The outer ring, denotedas D, is generated by dust in high-eccentricity orbits, while others have circularorbits. Some of the gaps between the rings are different for the southwest and thenortheast direction (Wahhaj et al. 2003).

Models to explain these rings suggest gravity perturbations due to the presenceof a planet, dust ring formation due to radiation pressure, collisions or interactionswith the gas component, or again the perturbations caused by the encounter of astar or massive body. Models that assume the presence of a single planet can ex-plain the observed inner ring structure (see discussion by Wahhaj et al. (2003)),but they cannot explain the complex structure of the entire observed system(Wahhaj et al. 2003), which rather is explained with a system of planets. In thiscase, the rings would be located in the resonance zones of the planets. The obser-vation of the inner system also shows inclination relative to the symmetry planewhich is opposite to that of the outer dust disk.

Lecavelier Des Etangs et al. (1996) show how an asymmetric structure in theβ Pictoris disk can form due to the presence of a planet and can be maintainedin spite of collisional destruction. Earlier calculations had shown a horseshoestructure of dust enhancement in the resonance zones (Roques et al. 1994). Thehorseshoe structure varies with the size of particles and therefore is not seenin the more recent simulation, which assumed a size distribution of particles(Lecavelier Des Etangs et al. 1996). From recent studies, it appears more likelythat it is the heterogeneity in the distribution of larger objects that cause thedensity variations in the dust cloud. Telesco et al. (2005) note from imagingobservations an asymmetry in the brightness at 12 µm wavelength inward from200 AU around β Pictoris. They suggest local dust production by catastrophiccollisions of resonantly trapped planetesimals leads locally to a different sizedistribution of dust and therefore local brightness variations.

5.3.4 AU Microscopii disk models

Even for systems where both, the measurements of the spectral energy distri-bution and spatially resolved observations exist, the dust number density andsize distributions cannot be unambiguously derived. This can be seen from adetailed model to describe the smooth brightness component in the dust disk ofAU Microscopii (Metchev et al. 2005): Metchev et al. calculated the scatteredlight assuming spherical grains in an optically thin disk. They adapt a power-lawsize distribution and a dust material mixture that are typically assumed forinterstellar medium dust. They constrain the absolute mass in the disk fromsubmillimetre data and subsequently use colour and absolute flux of the scatteredlight to constrain the minimum and maximum size of the particles. The scatteredlight data indicate a possible lack of small particles inward from 50 AU and theauthors suggest this is either due to grain growth or due to destruction by thePoynting–Robertson effect. The change in the radial slope of surface brightness


Fig. 9 Keck adaptive optics imaging of the radial substructure in the AU Microscopii disk: theupper part shows the brightness in the northwest wing and the mirrored image in the southeastwing, the pixel brightness has been weighted in order to highlight the structure. The lower partshows the entire image with the vertical axis expended by a factor of 5 showing the heightdifference in the northwest and the southeast wing as well as the disappearance of one of thefeatures (Liu 2004)

that is observed near 33 AU indicates the existence of an inner void. The authorssuggest the void is generated in similar ways in the AU Microscopii disk and theβ Pictoris disk and results in both systems from the collisional evolution or theinfluence of the Poynting–Robertson effect.

5.3.5 HD 141569 disk models

The influence of companions on the structure of a dust disk has been recentlystudied for HD 141569 A. The star has two low mass stellar companions HD141569 B and HD 141569 C. In order to explain the brightness observed aroundHD 141569, Augereau and Papaloizou (2004) study the evolution of a collision-less circumstellar dust disk under gravitational perturbation by a companion onbound eccentric orbit. Imposing the perturbations onto an initially axisymmetricdisk generates a spiral structure, a wide gap in the disk and a broad faint outerextension. The simulations match the observations and the star age if the perturber

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is on an elliptic orbit with a periastron distance of 930 AU and an eccentricitybetween 0.7 and 0.9.

5.3.6 Models of the spectral energy distribution

Models of the spectral energy distribution are of special interest for analyses ofthermal emission spectra that new and future observation facilities will provide,but the information that can be derived from the spectral energy distributions islimited.

For many of the data of excess infrared emission, it is not possible to determinethe dust distribution unambiguously, since there is no additional information aboutthe spatial distribution of dust (Kohler 2005). For systems where spatially resolveddata are available in addition to submillimetre data, Sheret et al. (2004) modelledthe spectral energy distribution with dust emission. They showed that the dustmodels to describe the emission differ and possibly are correlated to the age ofthe stars. The authors note a tendency possibly indicating that the dust aroundolder stars is less porous than the dust in the disks around younger stars. Fromthe diversity in their models for the spatially resolved disks they conclude it is notpossible to determine the size of an unresolved disk solely based on measurementsof the spectral energy distribution.

In some cases, the spatial distribution was assumed from spatially resolved ob-servations to estimate the dust composition from the spectral slope of the thermalemission. Li and Lunine introduced two alternative models to describe the circum-stellar dust as porous aggregates. In one case, they describe the dust as aggregatesof unprocessed interstellar grains; in the other case, they assume it consists ofgrains that are recondensed in the protostellar nebula. Both models provided agood fit the dust emission around HD 141569A. From the data they further de-rived the presence of a dust component with minimum size of 0.35 nm consistingof PAH molecules and confine the mass fraction of crystalline silicates to less than10% (Li and Lunine 2003a). The same model was successful to describe the dustaround HR 4796A (Li and Lunine 2003b) and around the more evolved star εEridani, assuming dust porosities as high as 90% (Li et al. 2003).

6 Size distribution and disk evolution models

The size distribution of particles in a dust disk is closely connected to the sources,sinks and dynamics of the particles. Mutual collisions of dust in the systems con-sidered here occur with relative velocities of kilometre per second and more andare catastrophic. Particles are both destroyed through collisions and generated ascollision fragments. The currently observed planetary debris disks have highernumber densities than the solar system dust cloud and collisions are thereforemore important. In most cases of planetary debris disk, collisions determine thelifetime of the dust. Also the existence of central clearance zones can partly resultfrom collisional destruction.

Some of the observed gas emissions, especially in the case of the β Pictorisdisk are not yet understood. For one, time-variable red-shifted components in thestellar spectra indicate the existence of fast evaporating bodies falling into the star.


These are explained as comet-like objects. Aside from that a component of gas inKeplerian motion is observed and its density and origin not yet understood. Whatcomes clear from other investigations is that the gas content does not influence thedust dynamics.

6.1 Size distribution and collision evolution of solar system dust

For the asteroid belt Dohnanyi (1969) derived a power-law size distribution of

n(m) ∝ m− 116 or accordingly n(s) ∝ s−3.5. These distributions result when as-

suming equilibrium between the mass gain and mass loss of the particles overthe considered size interval. When regarding the mass distribution of the flux ofinterplanetary meteoroids near 1 AU, this slope can be seen in the data for largeparticles while there is a change in the slope at masses of approximately 10−6gwhere the Poynting–Robertson drag effectively removes particles by deceleratingthem toward the Sun. Later studies applied a similar approach to the interplanetarydust cloud (Dohnanyi 1978; Leinert et al. 1983).

A more detailed study to investigate the evolution from 5 AU inward to thevicinity of the Sun, included estimates of the dust production from cometaryand asteroidal sources, and considered the Poynting–Robertson transport of dustparticles as well as their collisional evolution (Ishimoto 1999; Ishimoto 2000).The latter calculations indicate that mutual collisions of dust inward from 1 AUshift the size distribution towards smaller particles (Ishimoto and Mann 1998;Ishimoto 2000). Collisional evolution causes a narrowing of the mass spectrum,i.e. the number of particles with masses m < 10−9 kg is reduced. Small fragmentsare removed by radiation pressure and dust production inside 1 AU is neededin order to explain the interplanetary dust cloud. The most plausible sources ofdust inside 1 AU are meteoroids originating from comets, while the dust supplyof the frequently observed sungrazing comets is small compared to the totalmass that is contained in inner solar system dust cloud (Mann et al. 2004b). Itis quite possible that these sources are not homogeneously distributed and thatthe inner solar system dust cloud shows some temporal and/or spatial variations.Observations of the infrared F-corona brightness in 1966–1967 revealed anenhancement of the coronal brightness near 4R� (MacQueen 1968; Peterson1967, 1969), which pointed to the possible existence of a dust ring near the Sun.The formation of a feature in the near-infrared brightness does not necessarilyrequire the presence of a dust ring but a peak feature can be explained as ageometric effect that occurs from the sharp decrease of the thermal emissionbrightness at the point where the LOS crosses the beginning of the dust-freezone (Peterson 1963; Mann 1992). The hump features in the brightness have notalways been observed subsequently, but the correlation between the appearanceor disappearance of a peak feature and the solar activity cycle is unlikely (Kimuraand Mann 1998a; Ohgaito et al. 2002). It is suggested that variations of theF-corona brightness rather than indicating the presence or absence of a dust ringare due to variations of the dust cloud composition. This is in accord with theassumption that the dust cloud is locally replenished in the inner solar system(Mann et al. 2004b).

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Fig. 10 Sungrazers and gas components: The left-hand side of the figure shows the Doppler shiftof absorption lines in the spectrum of β Pictoris in the lower part and above a sketched modelof fast evaporating bodies causing this Doppler-shifted component (from Grady et al. (2000)).The right-hand side of the figure shows observations of NaI indicating the presence of a coolgas component in orbital motion about the star (from Olofsson et al. (2001)): as opposed to thefast evaporating bodies component which is only seen moving toward the star as a red-shiftedcomponent, this gas component is seen in emission with an offset from the star both red-shiftedand blue-shifted relative to the stellar spectrum. This data also show the stellar absorption lineand a weak feature of (terrestrial) atmospheric gas. Finally, the middle lower part of figureconsists of a LASCO C3 image showing two comets approaching the Sun, they do not reappearon the other side (Courtesy of SOHO/LASCO consortium. SOHO is a project of internationalcooperation between ESA and NASA.) The Sungrazers that are observed as often as once everysecond day with SOHO are in majority generated from one parent comet that was fragmentedduring a previous passage near the Sun. Further Sungrazers occur, but since they can only bedetected with space coronagraphs their frequency is not known

6.2 Size distribution and collision evolution in planetary debris disks

The size distributions of circumstellar debris disks have been studied especiallyin the context of the β Pictoris system, but results are applicable to other systemswith low gas contents and similar optical depths as well (Krivov et al. 2000; Arty-mowicz and Clampin 1997). As distinct from the solar system case β-meteoroids,for systems with higher stellar flux extend to larger sizes, and due to higher dustnumber densities collisions are more frequent. As a result the collision models sep-arately consider the dust in bound orbits (α-meteoroids) and the dust in hyperbolicorbits (β-meteoroids) and the collisions between these two different populationsincrease the collisional fragmentation. Moreover, due to higher radiation pressure,also particles in bound orbit may have high eccentricities, which increases therelative velocities in the disks and therefore the collision rates (Artymowicz andClampin 1997). The fragmentation of α-meteoroids by impacts of β-meteoroids


flattens the distribution of α-meteoroids in the size regime adjacent to the blow-out limit and changes the derived size distribution (Krivov et al. 2000). The latterdistribution has three different slopes: steeper ones for both small β-meteoroidsand large alpha-meteoroids and a gentler one in between for α-meteoroids withsizes just above the blow-out limit. The size distribution also changes within thedisk.

Yet, an approximation for the size distribution n(s) ∼ s−q is justified for sim-ple approximations. While initially q = 3.5 was applied to β Pictoris (Backmanand Paresce 1993), Heinrichsen et al. (1999) assume q = 4.1 to explain infraredobservations.

However, the collision products can explain the amount of small grains thatare required to explain observational data. Since β-meteoroids are continuouslyreplenished by collisions, at any time the disc contains a substantial populationof small particles. Spatially resolved observations indicate the variation of thesize distribution within the disk: Weinberger et al. (2003) observed the southwestwing at wavelength 8–13 µm and detected emission features which they attributeto amorphous and crystalline silicate outward to 1 arcsec (20 AU). The featuresdisappear at larger offset angles and the authors suggest that be explained by ahigh abundance of small silicate grains in the inner disk compared to the outerregions.

The collisional evolution can also explain a depletion of dust in the inner re-gions of planetary debris disks. Estimates of the inner depletion zone for the βPictoris disk were derived from the spectral variation of the infrared brightness.Backman and Paresce (1993), assume 38 AU, other estimates are 50 AU (Roqueset al. 1994), 20 AU (Kalas 1998) and 1 AU by Li and Greenberg (1998).

Gas observations The observation of neutral and singly ionised gas is possiblycorrelated to the dust collisional evolution: Liseau et al. (2003) observed in the βPictoris disk emission the neutral sodium resonance line at distances from 30 AUto at least 140 AU from the central star. This atomic gas is coexistent with the dustparticles and the Doppler shift suggests the gas is in Keplerian rotation. Recentresults of spatially resolved spectroscopic observations of the disk around β Pic-toris in the spectral range from 0.3 to 1 µm revealed a large number of detectedlines extending over the entire field of view (i.e. distances of 8 or 12 arcsec fromthe star) in a disk that is significantly higher than the extension of the dust disk(Brandeker et al. 2004). The sources and mechanisms to generate these gas com-ponents are still not fully understood. Studies of the dust distribution indicate thatthe gas does not influence the dynamics of dust (Thebault and Augereau 2005).

6.3 Disk evolution models

Planetary debris disks evolve in the later stage of the planetary system formation:after initial growth of planetesimals in a circumstellar disk of dust and gas the rel-ative velocities of dust and planetesimals increase so that catastrophic collisionsoccur. The increase of relative velocities is caused by a lack of gas and togetherwith the presence of perturbing planetesimals, which also causes an extension ofthe disks in height. This stage is expected to be reached after 10 Myrs (see for in-stance Kenyon and Bromley 2001) and the presence of planets will cause further

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perturbations. Further time evolution of the planetary debris disks is influencedby the Poynting–Roberson drag, by the possible presence of planets and by catas-trophic collisions. A decrease in mass as t−1 is obtained for systems dominatedby Poynting–Robertson drag and a decrease as t−2 for a system dominated bycollisions (Dominik and Decin 2003).

The recently found similarities of planetary debris disk around AU Micro-scopii and β Pictoris motivated discussions of their disk evolution. Both systemsare observed in scattered light over a large spatial extension and have similar spa-tial structures. In addition to this similarity AU Microscopii belongs to the groupof young stars of similar age that are moving together with β Pictoris (Zuckermanet al. 2001) and therefore it is discussed whether these systems have a similar evo-lutionary stage (Liu 2004; Metchev et al. 2005). By comparing the timescales formutual collisions of dust and Poynting–Robertson drag between the two systems,Metchev et al. argue that the breaks in the radial slopes of both systems are linkedto one or both of these processes. Older systems, in contrast seem to have ring-like structures. Those structures are often detected in the submillimetre regimethough and therefore more biased towards large dust particles. From consideringthe perturbing forces it is plausible that the smaller dust tends to form homoge-nous distributions faster, which would explain the smoother structures observed inscattered light. Estimating the time evolution from the limited spatially resolveddata seems difficult and only observations of excess brightness provide a largesample of stars.

The age dependency of infrared excesses should therefore provide us withsome information of the time evolution in planetary debris disks. From analy-sis of submillimetre observations Liu and co-workers derive the total dust massdrops by about a factor of 1000 within 10 Myrs and then decreases with t−γ , withγ = 0.5 − 1 (Liu et al. 2004) (see Fig. 5). Several analyses based on the mid-infrared observations of stars with infrared excess have been made in terms of thefractional luminosity, i.e. the amount of the excess brightness given as fractionalluminosity L IR / L�. They suggested there is a global power law describing theamount of dust seen in debris disks as a function of age of the stars (see for in-stance Holland et al. 1998). Decin and co-workers reconsidered the observationaldata and come to a different conclusion not supporting this power law (Decinet al. 2003). They re-evaluated fractional luminosity and stellar age data and con-clude they are widely spread for stars of most ages. The excess is more commonin young stars than in old stars but there are a few very young stars with inter-mediate or small excesses and there seems to be a common upper limit of theinfrared excess. This upper limit is possibly due to dust collisional avalanches thatquickly reduce high density dust clouds (Artymowicz and Clampin 1997; Krivovet al. 2000; Dominik and Decin 2003). Several scenarios have also been suggestedto explain the lack of young stars with low fractional luminosity and need to bechecked with future improved observational data (Dominik and Decin 2003).

7 Interstellar dust entry and astrospheres

The entry of interstellar dust provides a further dust constituent to the planetarydebris disks. It can also increase collision rates and enhance dust production inthese disks. While large interstellar grains are mainly influenced by stellar gravity


and radiations pressure force when they enter the systems, the small (typical)interstellar dust particles are also influenced by the interstellar and circumstellarplasma and magnetic field configuration.

In analogy to the heliosphere around the Sun, the region around a star filledwith the stellar wind plasma is called the astrosphere. The parameters of stellarwinds of the systems considered here are not accessible to direct observations.In some cases, the presence and size of the astrosphere can be inferred from theenhanced density of neutral hydrogen (‘hydrogen wall’) that builds up in front ofthe astrosphere. From observations of hydrogen walls it is possible to estimate thestellar mass loss. Values derived for observed cases, lie between 0.15 and 100 ofthe solar mass loss.

7.1 Interstellar dust entry and astrospheres

The stellar wind outflowing from stars creates the astrospheres (the heliospherefor the case of the solar system): the regions in space from which the interstellarplasma and the interstellar magnetic field is kept out (Lallement 2001). Instead,the astrospheres contain the stellar wind plasma and the magnetic field of stellarorigin. Since the stars move with respect to the interstellar medium (ISM), theastrospheres have an asymmetric structure. In the direction of the star motion rel-ative to the ISM the outer boundary of the astrosphere (the astropause) is pushedclose to the star by the pressure of the ISM. The interstellar plasma flow (but notthe neutral component of the ISM) cannot cross this boundary and must re-directitself to go around the obstacle. In result, in front of the astrosphere there is a re-gion where the flow velocities of the neutral and ionised components of the ISMbecome different. This leads to an increase in the charge exchange rate betweenthese components and results in a “hydrogen wall”: the region of enhanced densityand temperature of neutral hydrogen in front of the astrosphere, first predicted forthe case of the heliosphere by Baranov and Malama (1993). A number of “hydro-gen walls” were discovered for nearby stars (including the Sun) by observing theDoppler shift caused by the Ly-α radiation passage through the “wall” (Linsky andWood 1996; Wood and Linsky 1998; Wood et al. 2002; Wood 2004; Wood et al.2005a,b). As the astrospheres are tenuous extended structures, “hydrogen wall”observations are at this time the only means of discovering them. By now this hasbeen achieved for 13 stars which are listed in Table 7. The method of observationrequires that the ISM hydrogen column density is not too large along the line ofsight (Wood 2004). In consequence, all but three of the detected astrospheres arewithin 10 pc from the Sun. Wood et al. (2005b) give results of analyses of the Ly-αdata from Hubble Space Telescope Archive for 62 stars.

In the direction opposite to the star’s velocity the astrosphere develops an ex-tended ‘tail’. In the case of the Sun, numerical simulations show that the ‘tail’ doesnot dissolve in the interstellar medium at least for several thousand astronomicalunits.

The size of the astrosphere depends first of all on the strength of the stel-lar wind. The observation of “hydrogen walls” is in fact the main method bywhich the mass loss (and therefore the stellar wind outflow) can be estimatedfor solar-like stars. This is done by fitting the amount of absorption by the“hydrogen wall” using the available information about the ISM, the star velocity

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Table 7 List of stars for which astrospheres have been detected (based on Wood (2004); Woodet al. (2005b)

Star Spectral type Distance (pc) Mass Loss (M�) RH (AU)

α Cen G + K 1.35 2 220–400ε Eri K 3.22 30 800–175061 Cyg A K 3.48 0.5 20–30ε Ind K 3.63 0.5 30–4036 Oph K + K 5.99 15 300–600λ And G + M 25.8 5 150–200EV Lac M 5.05 1 60–10070 Oph K + K 5.09 100 1000–1700ξ Boo G + K 6.7 5 300–50061 Vir G 8.53 0.3 300–450δ Eri K 9.04 4 200–300HD 128987 G 23.6 – –DK UMa G 32.4 0.15 200–400

Note. RH denotes the estimated distance range to hydrogen wall in the ISM apex direction.

Fig. 11 The components of the heliosphere shown for the Sun moving from the right to theleft relative to the surrounding interstellar medium plasma. Thin lines indicate the direction ofthe interstellar magnetic field (Bism), the dashed lines the interstellar plasma flow. The shadedregion behind the bow shock indicates the accumulation of neutral hydrogen (‘hydrogen wall’)in front of the heliosphere. The motion of two small interstellar dust particles is indicated withsolid lines: they gyrate and slide along the magnetic field lines carried by the plasma flow

and a gas-dynamical model of the astrosphere (Wood 2004; Wood et al. 2005a).The distances to the inner and outer boundaries of the “hydrogen wall” are listed inTable 7 (RH). Of the stars in the list, two have the estimated mass loss much higherthan the Sun: ε Eridani (30 · solar value) and 70 Ophiuchi (100 · solar value). Thesizes of their astrospheres are supposed to be about order of magnitude larger thanthe heliosphere.

The other factor determining the size of the astrosphere is the ISM. In denseclouds, the size of the astrosphere would contract drastically. The effect of pas-sages through dense clouds on the heliosphere and the solar system is discussedin Yeghikyan and Fahr (2003, 2004).


The astrospheres have a possible, although minor, role in processing of theinterstellar dust. The probability of a dust grain encountering an astrosphere is low.The astrosphere of the star moving at 20 km/s relative to ISM through a interstellarcloud of 10 pc size would sweep up about 10−8 of the cloud volume (assuming theastrosphere cross-section π ·(300 AU)2) within the crossing time of 5 × 105 years.With 103 stars in the cloud, about 10−5 of the dust grains will be affected withinthis time, 2 × 10−4 within 107 years and some few percent during the total grainlifetime of 109 years.

7.2 Interstellar dust entry

The behaviour of the dust grain encountering the astrosphere depends on two pa-rameters. One is the radiation pressure force to gravity ratio (β). The other isthe strength of the grain coupling to the magnetic field, which depends on thegrain charge-to-mass ratio. For the stars hotter and more luminous than the Sun,including A and B type stars, in particular β Pictoris, the radiation pressure isthe dominant force, with β > 1 for a wide range of the grain sizes. Accordingto Artymowicz and Clampin (1997), the radiation pressure keeps the grains of0.1 µm size from approaching closer than 765 AU to β Pictoris and closer than3530 AU to Vega (estimation for porous silicate and graphite grains). Only thelarger grains (above ∼few µm for β Pictoris and ∼10 µm for Vega) have β < 1and are not repulsed by radiation.

For the solar type stars, the values of β are smaller and the main force acting onsmall grains approaching the astropause is the Lorentz force. The strength of thegrain coupling to the magnetic field can be expressed by its Larmor rotation timeτL, the inverse of the Larmor frequency L = Q|B|/mc, where Q and m are thecharge and the mass of the grain and B the magnetic field. If τL is much smallerthan the characteristic time L/V (where L is the size of the astrosphere and Vthe speed of the grain, or of the interstellar flow relative to the astrosphere) thegrains are coupled to the interstellar plasma flow and do not enter the astrosphere.This is the case of very small grains (∼ 0.001 µm for the case of the heliosphere)with large charge-to-mass ratio. Large grains (> few 0.1 µm for the heliosphere)with τL large compared to L/V , enter the astrospheres freely (Linde and Gombosi2000). The larger of the middle sized grains (∼ few 0.01 µm for the heliosphere)can enter the astrosphere but are deflected from closer approaching the star bythe magnetic field of the star (Linde and Gombosi 2000; Landgraf 2000) althoughthe structure of the astrospheric magnetic field may sometime allow particles toapproach close to the star (Czechowski and Mann 2003a). The smaller of those(up to ∼0.01 µm for the case of the heliosphere) with τL/(L/V ) ∼ 0.1 stay out-side the heliosphere but their velocity distribution is modified by the encounter(Czechowski and Mann 2003b). The stellar bow shock, which will form in theISM if the star velocity is supersonic with respect to ISM, has an interesting effecton the grain dynamics: since crossing the shock slows down the plasma but notthe dust grain, the grains downstream from the shock acquire the velocity differ-ence relative to the ISM plasma (Czechowski and Mann 2003b) equal to the dropin plasma velocity across the shock. The velocity distribution of these grains istherefore significantly modified near the astrospheres. The “draping” of the inter-stellar magnetic field at the astropause may cause streaming of those grains along

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Fig. 12 Trajectories of dust grains of ∼0.01 µm size in the vicinity of the astrosphere. Theinterstellar magnetic field is perpendicular to the velocity of the star relative to the interstellarmedium and lies in the plane of the figure. The grains with the initial trajectories passing closeto the boundary of the astrosphere are caused to stream away from it along the magnetic fieldlines (Czechowski and Mann 2001, 2003b)

the magnetic field lines, away from the astrosphere (Czechowski and Mann 2001,2003b). This is illustrated in Fig. 12.

In distinction to the small effect on the grains in the ISM, the astrosphereaffects strongly the dust that enters it: dust particles that can enter into the outerpart of the astrosphere, are deflected from the inner part by the star’s magnetic fieldand radiation pressure. Only the bigger grains can pass into the vicinity of the star.In the case of the Sun, the dust particles of interstellar origin were detected byULYSSES with dust at masses <10−16 kg suppressed compared to the interstellardust mass distribution derived from extinction measurements (Grun et al. 1994;Grun and Landgraf 2000; Kruger et al. 2001).

An interesting question is the effect of the astrosphere on the dust in largecircumstellar disks. Artymowicz and Clampin (1997) have considered the possi-bility of ‘sandblasting’ of the circumstellar disk by the grains from the interstellarmedium for the stars known to have large circumstellar disks. They found thatthe radiation pressure prevents these grains from entering the disks, except for theperipheral parts. For the stars closer to the solar type, a similar shielding couldbe provided by the astrosphere. If the large dust disk extends outside of the astro-sphere, the interaction with the interstellar dust would be stronger.

A possible example: HD 32297 The dust around HD 32297 that was recently im-aged is a system that possibly shows both, the planetary debris dust and interstellarmedium dust. Kalas (2006) points out in his analysis that the blue colour indicatedfrom the observations would agree with Raleigh scattering at interstellar mediumdust. However, he points out that the inner structure shows typical characteristicsof a debris disk: it is relatively symmetric and has a radial brightness decreasewith distance that is comparable to other systems. The asymmetry in the disk thatoccurs at large distances from the star may result from overlap with interstellardust signal at distances beyond 190 AU (Kalas 2006). It is quite possible that the


structure is not a result of the erosion of the planetary debris due to interstellar dustimpacts, but rather a result of the local accumulation of interstellar dust: either asa result of the radiation pressure acting on the interstellar dust or as a result of in-terstellar dust deflection at the astrosphere. Unfortunately, there is no informationabout the astrosphere of HD 32297.

8 Optical properties and the evolution of matter

The properties of dust that are derived from observations are albedo, emissivityand polarisation. These properties can be used to compare dust in different sys-tems. Comparison to light-scattering models allows the study of the dust propertiesby means of these observational data. Comparison of thermal emission measure-ments shows similarities of planetary debris dust to cometary dust in the solarsystem.

8.1 Light scattering

The typical shape of an empirical scattering function is shown in Fig. 13. It de-scribes the average scattering cross-section as a function of the scattering angleθ . The scattering function has its maximum for small angles (forward scattering),is nearly isotropic for scattering angles between 45◦ and 160◦ and then increasesagain by a factor of 2. The polarization of scattered light is in a similar way givenas a function of scattering angle.

8.2 Albedo

The albedo of dust particles is inferred from the comparison of thermal emis-sion and scattered light brightness, while the geometric albedo is derived from thebrightness data under assumptions of the dust geometric cross-sectional area byintegration of the differential size distribution of dust. We discuss the geometricalbedo of dust particles given as the generalized geometric albedo for 90◦ scatter-ing angle (see Hanner et al. 1981 for definition). Based on the comparison of thevisible zodiacal light to IRAS data, the albedo was determined to be 15% at max-imum for particles at 1 AU, applying thermal emission data from the rocket pho-tometry by Murdock and Price (1985) gives values less than 10%. The differencebetween the data sets may be explained by the uncertainty of the absolute calibra-tion in the IRAS measurements. Laboratory experiments with irregular particlesof meteoritic as well as terrestrial samples of dark opaque material yield albedovalues between 5 and 9% and could also reproduce the empirical scattering func-tion derived from Helios observations (Weiss-Wrana 1983). Values for the albedoof cometary dust are typically lower (see Kolokolova et al. 2004 for a review)which is often discussed as evidence that the cometary dust is more pristine.

Aside from the absolute value, the values derived from one data set show atrend to an increasing albedo with decreasing distance from the Sun. In a similarway the polarisation at 90◦ scattering angles derived for the distances from theSun decreases with decreasing distances from the Sun. This reflects either the

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Fig. 13 Scattering properties of dust: A typical sketch of intensity, I , and linear polarization,P , of scattered light as a function of scattering angle θ . The incident solar/stellar light is un-polarized. Some observers discuss the scattering properties as function of the phase angle α, α=180◦ −θ , that is also shown. The intensity of scattered light (marked with ‘A’) has a maximumat small scattering angles, a broad minimum (marked with ‘B’) at medium scattering angles anda slight enhancement at backscattering for scattering angles close to θ = 180◦ (marked with‘C’). The linear polarization is zero for θ = 0◦, has a maximum at medium scattering anglesand turns to negative polarization (‘D’) at θ > 160◦. The scattering properties of dust dependon the material composition, described by its index of refraction, on the size, s, and shape andcharacteristic subshape sizes s′ of the particles. Some of the theoretical approaches to describethe light scattering at dust particles that are discussed in the text are depicted in the upper partof the figure: Mie theory provides rigorous solutions of the light-scattering problem for particlesof certain defined shape. Mie theory can be combined with the Maxwell–Garnett mixing rule(Mie & MG) to simulate particles consisting of different materials. Particles can be approxi-mated as an array of dipoles (discrete dipole approximation, DDA) in order to calculate the lightscattering of particles of arbitrary shape. The scattering properties are also an important param-eter to determine the temperature of particles and to determine the appearance of characteristicemission features

gradual change of dust optical properties while they drift to the Sun or the changein the composition of the dust cloud. While data between 0.3 and 1 AU describemoderate changes of albedo and polarisation the change at distances <0.3 AUfrom the Sun cannot be explained by gradual changes of particle properties (Mann1993).

8.3 Polarisation

8.3.1 Observations

The local polarisation of interplanetary dust and its variation with scattering an-gle has been derived from zodiacal light observations. The polarisation function,i.e. degree of linear polarisation of the scattered natural light, has a negative branch


at large scattering angles, a neutral point around 160◦ followed by an approx-imately linear increase. The minimum of polarisation for interplanetary dust de-rived from Gegenschein observations is −2±1% (Levasseur-Regourd et al. 2001).The absolute value of the maximum polarisation decreases for particles close tothe Sun, while the albedo increases. Linear polarisation of comets is a smoothfunction of phase angle α with a maximum of typically 10–30% around α = 90◦and a negative branch at α ≤ 20◦ with a minimum of a few percent, and increaseswith wavelength (Dobrovolsky et al. 1986; Dollfus et al. 1988; Kolokolova et al.2004). These dependences of linear polarisation on phase angle and wavelengthare consistent with visible and near-infrared observations of a number of comets(Chernova et al. 1993; Dollfus and Suchail 1987; Ganesh et al. 1998; Hadamcikand Levasseur-Regourd 2003; Kikuchi et al. 1989, 1987; Kiselev and Velichko1997; Manset and Bastien 2000; Sen et al. 1991b). The spatial distribution of thepolarisation in the coma is highly inhomogeneous. In the jets, the polarisationis higher and positive irrespective of the phase angle (Hadamcik and Levasseur-Regourd 2003). Sun-ward side of coma of Hale–Bopp shows higher degree of lin-ear polarisation than anti-Sun-ward side (Hadamcik and Levasseur-Regourd 2003;Kiselev and Velichko 1997). A decrease in the polarisation with distance from thenucleus was observed along the dust tail of comet Hale–Bopp at the projected dis-tance of approximately 4 × 104 km and outward, while the polarisation closer tothe nucleus was nearly independent of the distance (Manset and Bastien 2000).This tendency was observed along Sun-ward direction but the polarisation in anti-Sun-ward direction was nearly constant (Hadamcik and Levasseur-Regourd 2003).The Optical Probe Experiment onboard Giotto measured in situ the local polarisa-tion of dust from comet Halley (Levasseur-Regourd et al. 1999). The polarisationof 10–30% gradually increases with distance from the nucleus in the 103–105 kmrange. Spatially resolved observations at comet Encke show variations in colour ofalbedo that are explained with particle properties changing on time scales of hours(Jewitt 2004). Faint circular polarisation less than 1% with both signs was detectedfor comets Halley and Hale–Bopp (Dollfus and Suchail 1987; Manset and Bastien2000) and interpreted with the presences of partially aligned non-spherical dustparticles or multiple scattering in the innermost coma.

It was suggested that according to the values for the maximum polarisation,comets could be classified into two groups (Dobrovolsky et al. 1986; Levasseur-Regourd et al. 1996). Comets in the high and low polarisation classes are knownto be dust-rich and gas-rich, respectively. However, observations of comet Hale–Bopp revealed the polarisation higher than expected for dusty comets belonging tothe high-polarisation class (Hadamcik and Levasseur-Regourd 1999; Kiselev andVelichko 1997; Manset and Bastien 2000). Hence the distinction into two groupsmay also arise from observational biases.

8.4 Light-scattering models and laboratory measurements

8.4.1 Particle model

While first model calculations to describe optical properties of cosmic dust weremade with Mie theory describing spherical (or in some cases cylindrical) particles,it became more and more evident, that dust particles in many cases are irregularly

210 I. Mann et al.

shaped. As a tool to describe irregular particles with reproducible properties, so-called ballistic particle cluster aggregates (BPCA) and ballistic cluster aggregates(BCCA) are used (see cf. Mukai et al. 1992), and references there). BCCAs arenumerically produced by randomly shooting cluster of monomers onto each other:starting with two monomers that form a cluster, then followed by collision of twoof the two-monomer clusters, then four-monomer clusters and so forth. As a resulta relatively open structure is formed. For BPCA on the initially formed cluster,further single monomers are attached, so that a more closed structure evolves. Fora small number of monomers these clusters look quite similar but for larger num-bers of monomers the differences are significant, and it is especially questionablewhether the BCCAs do resemble any of the dust components observed in our solarsystem. Still this is a model to describe very porous grains and also to systemat-ically study variations of properties with the size and structure of particles. Inmany cases, the BPCAs and BCCAs are used as a model to reproducibly describeirregular particles, irrestistive of their path of formation.

8.4.2 Numerical simulations

Exact theoretical results are given for some particular cases such as a homoge-nous sphere where the Mie formalism describes the interaction of electromagneticwaves with an obstacle of given index of refraction. This formalism holds for par-ticles of well-defined shape and size parameters x = 2πs/λ (see van de Hulst1957; Bohren and Huffman 1983), it is valid for any sizes of particles. Effectivemedium approximations are often applied to describe the effective refractive indexof irregular dust particles as aggregates that consist of building stones of submi-crometre sizes (cf. Mukai et al. 1992): this is described by a porous medium asillustrated in Fig. 13. The approach is valid as long as the size of the inclusionsis small compared to the wavelength of scattered light. In this case it means theaggregates of approximate sizes of 0.01 µm.

The Discrete-Dipole Approximation (DDA) originally proposed by Purcelland Pennypacker (1973) provides the opportunity of studying light scattering byarbitrarily shaped particles (Draine 1988; Draine and Flatau 1994).

The superposition T-matrix method (TMM) rigorously provides solutionsfor light scattering by a cluster of spheres (Mackowski and Mishchenko 1996).Petrova et al. (2000) applied the TMM to compute light scattering by small clus-ters of spheres that are located on a lattice. Because linear polarisation of eachcluster shows oscillations with phase angle, reasonable results could be obtainedonly with averaging over different sizes of clusters.

Mie theory allows to compute light scattering by a sphere of arbitrary size(Bohren and Huffman 1983; Mie 1908). Therefore, it has often been used to com-pute the degree of linear polarisation of cometary dust. Mukai et al. (1987) werethe first to successfully reproduce the phase-angle and wavelength dependencesof linear polarisation observed in the range 0–20◦ for dust in comet Halley bynumerical calculations on the basis of Mie theory. They used the size distributionof dust in comet Halley derived from in situ measurements (Mazets et al. 1986).The complex refractive indices estimated in the visible wavelength range are con-sistent with a mixture of ice and silicate. Sen et al. (1991a) used the same methodfor the same comet to obtain almost the same values for the refractive indices.


Fig. 14 Aggregates with 32 monomers consisting of two different arrays of dipoles; left: ballisticcluster–cluster aggregates; right: ballistic particle–cluster aggregates (Kohler et al. 2005). Thisillustrates how DDA is applied to aggregate particles: mkd denotes the distance with which thedipoles are located on the grid in order to describe the particle. Note that for small numbers ofmonomers, shown here, BPCA and BCCA look similar

Sen et al. (1991b) applied the same method to polarimetric observations of dustfrom comet Austin and obtained similar refractive indices, but a steeper sizedistribution.

Mukai and Mukai (1990) took into account light scattering by large particleshaving rough surface to explain the data observed at 0◦–65◦ for linear polarisationof dust in comets Halley and Bradfield. The fits of the numerical results to the datawere improved, in particular, at 0◦–20◦ with the consideration of rough-surfaceparticles consisting of a mixture of ice and silicate.

Lumme and Rahola (1994) showed from their numerical calculations withDDA that linear polarisation of highly absorbing aggregates averaged over sixsizes with a power-law size distribution resembles the phase-angle dependenceobserved for cometary dust. DDA calculations of the light scattering by frac-tal aggregates (Kozasa et al. 1993) provide results that are similar to Raleighscattering showing no negative polarisation at small phase angle and a largemaximum near 90◦. This apparently results from the assumption of small con-stituent dust particles, which are 10–30 nm in radius. Light scattering by ag-gregates of different shapes and compositions described by DDA (Xing andHanner 1997) results in oscillations in the phase function of linear polarisa-tion, which are inconsistent with observations. These oscillations arise from theuse of large constituent dust particles, which are 250–500 nm in radius. Vari-ous types of non-spherical shapes for compact dust particles were used to com-pute their light-scattering properties, but none of the results were successful(Yanamandra-Fisher and Hanner 1999a).

Lumme et al. (1997) were able to show using DDA that the phase-angle de-pendence of linear polarisation observed for cometary dust can be qualitativelyexplained with light scattering by aggregates consisting of water ice or silicatewithout averaging over different sizes and compositions. Levasseur-Regourd et al.

212 I. Mann et al.

Fig. 15 Calculated lifetime of dust particles in the solar system at 1 AU due to the Poynting–Robertson effect (dashed line) and collisions (solid line)

(1997) and Haudebourg et al. (1999) showed a large difference in the light-scattering properties between highly fluffy and relatively compact fractal aggre-gates from their DDA calculations, but their results were not confirmed by Kimura(2001) who utilized both the TMM and DDA to study light scattering by largefractal aggregates consisting of silicate or carbon. Quantitatively best result wasobtained with the aggregates consisting of silicate dust particles whose radius is150 nm, based on the TMM computations. Recently, Kimura et al. (2003) achievedqualitatively best result for the phase-angle and wavelength dependences of notonly polarisation but also brightness for cometary dust. They used the TMM withthe fractal aggregates consisting of absorbing materials derived from a mixture ofsilicate, iron, organic refractory and amorphous carbon with the elemental abun-dances of Halley’s dust.

8.4.3 Laboratory measurements

Microwave analogue experiments showed that large fluffy absorbing particles ac-count for the phase-angle dependence of linear polarisation observed for the zo-diacal light (Giese et al. 1978) and also the influence of an absorbing mantlematerial was measured (Zerull et al. 1993). Gustafson and Kolokolova (1999)used microwave analogue technique to study the wavelength and phase-angle de-pendences of polarisation and intensity for a variety of aggregates with differentsizes, shapes, and compositions of the constituent particles. They obtained properdependences with fluffy aggregates consisting of wavelength-size absorbing con-stituents. Weiss-Wrana (1983) used electrostatic levitation and a laser beam tostudy light scattering by single dust particles. The phase-angle dependence oflinear polarisation consistent with zodiacal light observations was achieved withfluffy dark particles in the size range of 20–120 µm. Munoz et al. (2000) stud-ied scattering matrices for olivine and Allende meteorite particles using lasers attwo wavelengths. Their results with micrometre-size olivine particles show the


phase-angle and wavelength dependences of polarisation that are similar to thoseobserved for cometary dust particles.

8.5 Temperature and thermal emission

Dust particles in interplanetary space usually attain their equilibrium temperatureof absorbed radiation integrated over the solar spectrum and the emitted radia-tion determined by the optical properties of the particles. The conditions for theequilibrium temperature, Tdust, are given by

π

(R

r

)2 ∫ ∞

0F(λ)Cabs(s, λ) dλ = 4π

∫ ∞

0B(λ, Tdust)Cabs(s, λ) dλ, (13)

where Cabs is the absorption cross-section and B denotes the Planck function, F

the brightness of the stellar photosphere, R the radius of the star, r , the distanceof the particle from the star and λ the wavelength of absorbed and emitted radia-tion. Further smaller contributions to the energy budget (neglected in the previousequation) are the sublimation energy and kinetic energy from the impact of plasmaparticles (Mukai and Schwehm 1981).

By approximating the stellar spectrum with the blackbody emission and as-suming particles with constant albedo, A, (i.e. the ratio of the in-falling and scat-tered radiation is constant with λ) one can estimate the temperature of particlesby approximating with the Stefan–Boltzmann law both the in-falling stellar radia-tion at distance r from the star and the thermally emitted radiation of the dust andobtains the relation:

Tdust = T

(1 − A

4

)1/4 (R

r

)1/2

(14)

where T is the temperature of the stellar photosphere. The dust temperature variesapproximately as r1/2 in a given system and for a given distance increases propor-tionally with the temperature of the stellar photosphere. Assuming T = 5800 Kfor the solar photosphere and A = 0 for a blackbody results in the dust tempera-ture in the solar system of 280 K at 1 AU.

Note that the real solar and stellar spectra deviate from the blackbody emissionthat is assumed in this equation (see also the discussion of the radiation pressureforce in Sect. 4.2). Moreover, the dust properties are different from the blackbody.The absorption cross-section varies with wavelength and depends on the size andthe composition of the dust particles. “Small” particles show typical emission fea-tures such as the features around 10 µm attributed to the emission from silicate.Even if these features are not observed, the low absorptivity of silicates in thevisible and higher absorptivity in the near infrared lead to temperature profiles(i.e. variation of temperature with distance from the star) that are different fromthose of a blackbody. Large dust particles, especially when they consist of differ-ent materials, show only a weak wavelength dependence of the absorptivity overwavelength and reach approximately blackbody temperature.

214 I. Mann et al.

8.6 Emission features

Silicate mineralogy of the cosmic dust is revealed in observational data by thecharacteristic vibration and rotation bands of the molecules that influences thespectral slope of the thermal emission brightness. While thermal emission fea-tures are small in the zodiacal light, they are clearly seen in some comets and incircumstellar systems. They provide information on dust composition, size andstructure.

8.6.1 Zodiacal light

Early infrared photometry of the zodiacal light by rocket experiments have notshown any features at a spectral resolution of 0.1 ≤ �λ/λ ≤ 0.4 (Murdock andPrice 1985). The first attempt of detecting spectral infrared features in the wave-length range of 5–16.5 µm using the mid-infrared camera (ISOCAM) on the In-frared Space Observatory (ISO) was also unsuccessful at a level of 15% of the con-tinuum (Reach et al. 1996). Later ISOCAM observations have revealed a weak ex-cess in the wavelength range of 9–11 µm at a level of 6% of the continuum (Reachet al. 2003). Description of the features with spherical particles was possible withknown size distributions of the interplanetary dust cloud slightly enhanced forsmall particles, while size distributions of cometary or interstellar dust due to thehigher amount of small grains produced too strong features (Reach et al. 2003).The features were best described with a mixture of Mg-rich olivine, dirty crys-talline olivine and hydrous silicates. The authors note a slight tendency towardsenhanced features above the ecliptic and toward the Sun.

We suggest this tendency possibly indicates that in those regions there is ahigher amount of cometary dust. Cometary dust is assumed to be darker than as-teroidal dust and moreover is likely to have a fluffy structure which enhances theappearance of features for larger particles.

8.6.2 Cometary dust

Maas et al. (1970) suggested the excess emission from comet Bennett overblackbody-like continuum at wavelengths of 10 µm, likely originated from silicatedust particles. In the infrared spectra from comet Halley, Bregman et al. (1987)identified the presence of crystalline olivines and Campins and Ryan (1989) con-firmed a strong peak at 11.3 µm attributed to crystalline olivine as well as anotherstrong peak near 9.7 µm. The peak feature of crystalline olivine and the broadmaximum around 9.7 µm, which may originate from amorphous olivine, havealso been detected in infrared spectra from comets C/1987 Bradfield, C/1993aMueller, C/1990 Levy and Hale–Bopp, while no feature of crystalline olivinehas been detected in comets C/1973 Kohoutek, C/1987 Wilson, C/1989 Okazaki-Levy-Rudenko, C/1989 Austin, 23P/Brorsen-Metcalf, P/Borrelly, 4P/Faye, and19P/Schaumasse (Hanner et al. 1994a,b, 1990; Wooden et al. 1999). From spectraof comet 103P/Hartley 2 measured by ISO, Crovisier et al. (1999) detected a peakat 11.3 µm while Colangeli et al. (1999) found no feature of olivines.

The appearance of features may also vary along the orbit of the comet. Forcomet Hale–Bopp, Wooden et al. (1999) note that the postperihelion dropping of


Fig. 16 Example for transmission spectra (left) for olivine with a magnesium content of100 mol% (Fo100) (bottom), of 80 mol% (Fo80) (middle) and of 60 mol% (Fo60) (top) and py-roxene spectra (right) obtained by laboratory measurements of meteoritic samples. Shown arespectra for pyroxene with a magnesium content of 100 mol% (En100) (bottom), of 80 mol%(En80) (middle) and of 75 mol% (En75) (top): intensity and position of the features change withthe magnesium content of the silicates (Kohler 2005; Morlok et al. 2005)

the feature happens more rapidly than expected from preperihelion spectra. Theysuggest that the relative abundance of submicron-sized grains decreased duringthe perihelion passage and also note that the temperature of the different dustcomponents may play a role for the material that is then seen in the comet.

8.6.3 Circumstellar dust

With its large IR excess and its relative proximity to the solar system β Pictorisis one of the best studied stars. Observations with the IRTF telescope indicate afeature at 10 µm attributed to a silicate component of the dust (Telesco and Knacke1991). Subsequent observations (Knacke et al. 1993) of the dust disk of β Pictorisagain with IRTF showed that the spectrum of β Pictoris is in good agreement withthe features in the spectrum of comet Halley (Fig. 17).

Low spectral resolution ISOPHOT measurements also indicate a rise in emis-sion from 9 to 11.6 µm (Heinrichsen et al. 1999). Observations with the ISO SWS(de Graauw et al. 1996; Pantin et al. 1999; Malfait and Waelkens 1999) were madein the wavelength range from 2.4 to 45.2 µm (Reach et al. 2003) and then com-pared with the ISOPHOT data (Heinrichsen et al. 1999), IRAS data and IRTFdata (Knacke et al. 1993). IRTF, ISOCAM and SWS data are clearly different, thedifferences begin around 8 µm and increase to longer wavelength. This indicatesthat the dust composition varies within the disk: CAM and IRTF observe the innerdisk, while SWS and PHOT observe the entire disk including colder emission. Thesouthwest part of the disk was observed with the Keck Long Wavelength Spectro-graph (LWS) in a wavelength range of 8–13 µm (Weinberger et al. 2003). Features

216 I. Mann et al.

Fig. 17 Comparison of the infrared spectra from the dust disk around β Pictoris with cometHalley (solid line) and comet Levy 1990 XX (dashed line) (Knacke et al. 1993)

are observable outward to 1 arcsec. The authors conclude that within 20 AU parti-cles must be smaller than 10 µm to produce the features.

The circumstellar dust observations were also compared to model calculations.Li and Greenberg (1998) compared observations in the wavelength range from 2.6to 1300 µm with their model calculations. They calculated the emission bright-ness for two types of particles: amorphous silicate core-organic refractory mantelgrains and crystalline silicates grains. The particles are assumed to have an icemantle at distances larger than 100 AU from the star and to have porosities of 0.95up to 0.975. Three different size distributions were applied within the disk. On thebasis of the model they suggest that both components: amorphous silicate core-organic refractory mantle aggregates and crystalline silicate aggregates occur inthe material composition of the dust particles.

Heinrichsen et al. (1999) compared the ISOPHOT and IRAS observations witha model of silicate grains in the 1 µm to 5 mm size range with a size distributionn(s) ∝ s−4.1, where s is the grain radius. They reproduced the spectrum with amixture of thermal black body emission (T = 300–500 K) and a silicate emissionfeature which confirms previous work (Knacke et al. 1993).

Features are currently observed for many young circumstellar dust systems,but not so much for Vega-like systems: The photosphere of ε Eridani, for in-stance, dominates the spectrum out to 11.6 µm such that silicate features are notdetectable. For Vega it is suggested that a dip in the spectrum around 34 µm iscaused by forsterite (Mg-rich olivine) dust (Min et al. 2004).

8.7 Influence of dust size and structure on the emission features

Aside from material composition the appearance of features depends on the size,shape and structure of particles. Recent studies show that the appearance of sharppeaks in the infrared does not necessarily mean a large contribution from small


dust particles to the brightness. When Mukai and Koike (1990) computed thermalemission from compact olivine spheres having the size distribution derived fromin situ measurement of comet Halley, they could not reproduce the twin peaksof olivines seen in the observations. Okamoto et al. (1994) computed the thermalemission of fractal aggregates of small (10 nm) monomers and could find the peakstructure. They have shown that the prominent twin peaks of olivines observedfor several comets are easily obtained with highly fluffy aggregates, irrespectiveof their sizes. Yanamandra-Fisher and Hanner (1999b) showed that the thermalemission peak at a wavelength of 11.2 µm can be matched with submicrometretetrahedrons, moderately elongated bricks, aggregates of spheres and aggregatesof tetrahedrons of magnesium-rich olivine, but not with spheres. Moreno et al.(2003) used DDA and a combination of Mie theory and Maxwell–Garnett effec-tive medium approximation to calculate thermal radiation over wavelengths of8–40 µm from aggregates of a mixture of crystalline and amorphous olivines andglassy carbon with a power-law size distribution. They obtained reasonable fitsto the infrared spectra of comet Hale–Bopp measured with ISO from heliocentricdistances from 2.8 to 3.9 AU.

The refractive index of a material is usually obtained from laboratory measure-ments. The exact position and relative intensities of emission bands change withthe microscopic structure of the sample materials as well as with the temperatureof the samples. The laboratory spectra in mid- and far-infrared region obtained forolivine particles that were continuously cooled down to 10 K show for instancethat the peaks become stronger and narrower with decreasing temperature (Koikeet al. 2005). Recent studies of silicates extracted from meteorite material showsimilar infrared spectra compared to previous measurements at synthetic or ter-restrial minerals (Kohler 2005). The spectra of silicates vary with their Fe/Mgcontent (Fig. 16), which allows using the observation of the features for studies ofthe material evolution of silicates.

8.8 Evolution of matter

Dust particles provide the opportunity to study the evolution of matter in the solarsystem and in planetary debris disks as indicated in Fig. 18. During the evolutionof a planetary system dust is either formed by accumulation of primordial dust, bycondensation out of the gas phase, or by a combination of both. It is accumulatedin large objects and subsequently released during their fragmentation caused byheating and collisions. Cometary material, as well as the material in the typicallyobserved outer regions of planetary debris disks is assumed to be relatively pris-tine: it contains condensed volatiles and therefore may still contain unprocesseddust material, though the present location is not necessarily the region of formationof these objects. Understanding the composition of the dust and the planetesimalsand comparing them to other dust populations helps to trace down the evolutionof the planetary systems. An important issue in this context is the evolution ofsilicates.

First detection of crystalline silicate came from observations of features at-tributed to crystalline olivine in comet Halley (Bregman et al. 1987; Campins andRyan 1989). Crystalline silicate features were also observed in other comets, inevolved stars, in some young stellar objects as well as crystalline silicates were

218 I. Mann et al.

Fig. 18 The evolution path of dust in planetary systems: A sketch of the dust evolution duringplanetary system formation: interstellar dust is partially melted and recondensed in the proto-planetary nebula and then incorporated in larger solar system objects. From those it is releasedand further processed during fragmentation and by physical processes occurring in the interplan-etary medium

detected in IDPs. A fraction of crystalline silicate was also found in the zodia-cal light spectra (Reach et al. 2003). No crystalline silicates were observed in theISM, in molecular clouds and in young stellar objects in their early stage (Hanner1999, 2003 for a review). The features are observed in both hot and cold regions,and they are similar in shape. Hence a mixture model of cometary dust assumesthat part of the silicates is amorphous in the solar nebula while portions of the dustare either annealed at high temperatures or are recondensed from the gas phase inthe solar nebula. This model requires a process to mix crystalline and amorphoussilicates. It is also plausible to assume that some amounts of crystalline silicatesexisted in the interstellar dust cloud out of which the solar system was formed.

Dust particles that are condensed in supernovae or AGB stars may be formedas crystalline. Interstellar dust particles, due to processing in the ISM mainly con-sist of amorphous silicate. Irradiation in the ISM leads to amorphisation of initialcrystalline silicates. Nevertheless dust particles that were recently formed did ex-ist in the proto-solar nebula and are in some cases still observed as presolar dustparticles. Presolar dust particles exist in meteorites and IDPs. They are formedbefore formation of the solar system and attributed to different sources, since theirmeasured isotope ratios differ greatly. The existence of short-lived radionuclidesin presolar dust particles indicates those were formed shortly before the formationof the solar system (<107 years) and hence were not greatly processed in the ISM.


This points to the possible existence of crystalline silicate dust in the ISM at thetime of the solar system formation.

The amount of amorphous versus crystalline silicates at the time of the forma-tion of the solar system depends on the amount of typical ISM dust versus freshlyproduced dust in the ISM plus solar nebular condensates at the time of the so-lar system formation. Comparison to dust in different planetary debris disks willshow to what extent the ISM conditions at the time of the formation of the hoststar influence the appearance of the silicates in the planetary systems.

9 Summary

The past decade has brought a wealth of information about the spatial structures ofat least some of the planetary debris disks and progress was made in understandingthe influence of planets on the spatial distribution of dust and planetesimals. Plan-etary debris disks were first discovered by the infrared excess that their host starsreveal relative to the typical spectral energy distribution of a star of that type andevolutionary stage. Studying planetary-debris disks by their infrared excess aloneis difficult and spatially resolved observations or sub-mm data are extremely im-portant.

The planetary debris disks surround main-sequence stars or late pre-main-sequence stars of ages that clearly exceed the lifetime of dust in those systems.The lifetimes of dust particles are limited by catastrophic collisions, orbital per-turbations induced by planets, photon Poynting–Robertson effect due to radiationpressure force and/or plasma Poynting–Robertson effect due to momentum trans-fer from stellar wind particles. We compare these systems to the dust cloud inour solar system where all the listed effects occur as well. While observationalmethods at first glance appear to be more sophisticated for the case of our solarsystem, we show that detailed observational results there are limited to the regionnear 1 AU. However, in contrast to other systems, it is possible to study actualdust samples in the laboratory. Moreover, cometary dust observations give directinformation about relatively pristine material within the dust cloud.

Major sources of our solar system dust cloud are asteroids and comets. Theplanetary debris disks are sustained by fragmentation of planetesimals. The oc-currence of fast evaporating bodies in the β Pictoris system shows some similarityto the Sungrazing comets, but is more frequent. The fast evaporating bodies in-dicate the existence of cometary activity. The fast evaporating bodies, as well asthe extension of the spatially resolved disks from their symmetry planes indicatethe presence of perturbing objects in the disks. The spatial distribution of the dustin planetary debris disks in general is less homogenous than appears to be in thesolar system and is influenced by the presence of planetesimals and possibly plan-ets. A closer look at the solar system dust cloud, indicates, however, that it is un-evenly distributed outside from several astronomical units distance from the Sunand possibly also near the Sun, i.e., at distances smaller than 0.5 AU. Recently, itwas found that, rather than direct influence of orbital resonances on the dust par-ticles, uneven distribution of parent bodies can cause spatial density variations ofdust in the planetary debris disks, similar to the dust trails and bands observed inthe solar system.

220 I. Mann et al.

Aside from the gravitational forces, the major forces on the dust particles arethe radiation pressure of the central star and, in some cases, stellar-wind forceswhich can be as important as the force resulting from radiation pressure. Radiationpressure is typically stronger than in the case of the solar system dust cloud, aswell as the surface charge of grains and therefore the Lorentz force. Similar to thesolar system, the dust size distribution of the planetary debris disks is determinedby the interplay of collisional fragmentation of particles and ejection of particlesby radiation pressure. Collisions also cause a dust depletion in the inner zones ofthe disks, so that the observation of inner depletion zones, does not necessarilyrequire the presence of a planet. There is no direct observation of the stellar windin the planetary debris disks. The parameters of stellar winds in some cases canbe inferred from measurements of the enhanced density of neutral hydrogen (theso-called ‘hydrogen wall’) at the boundary region between stellar wind and theplasma of the interstellar medium, and give values of the mass loss between 0.1and 20 solar mass loss rates. The entry of interstellar dust provides a further dustconstituent to the planetary debris disks, and it can also stir up the dust productionin these disks. Neutral and singly charged gas components observed in Keplerianorbits about β Pictoris still lack a final explanation.

The properties of dust that are derived from observations are albedo, emissivityand polarisation. These optical properties can be used to compare dust in differentsystems. From observations of thermal emission features, the dust in planetarydebris disks appears similar to cometary dust in our solar system, rather than tozodiacal dust.

Further progress in understanding planetary debris disks will be made by com-bining the dynamical considerations with other findings about the material prop-erties as well as the interactions with the gas component. While the presence ofplanets is certainly of high interest, the study of the observed planetary debrisdisks provides far more information, which – in contrast to the planet detection– cannot be given otherwise. By measuring particle size, particle properties, andcomposition, the material properties can be compared to solar system dust as wellas to dust in the interstellar medium. For this, infrared and polarization measure-ments are of great interest. Their interpretation needs improved models of opticaldust properties as well as supporting laboratory measurements. A further open is-sue is to understand the presence or absence of gas components, which may givefurther clues about the evolutionary stage of the systems. Advanced observationalprograms will allow to study the infrared spectra as well as the gas content ofplanetary debris disks.

Acknowledgements We thank Martin Huber for his suggestion to write this article and for hispatience with the authors. A significant part of the preparations for this review was carried outduring I.M.s stay at ESA Space Science Department and was funded by the European SpaceAgency under ESTEC/Contract 14647/00/NL/NB. We wish to thank Sabine Dude for assis-tance in preparing the manuscript. Parts of this research have been supported by the GermanAerospace Center, DLR (project ‘Rosetta: MIDAS, MIRO, MUPUS’ RD-RX-50 QP 0403)and by the Japanese Ministry of Education, Culture, Sports, Science and Technology, MEXT,(Monbu Kagaku Sho) under Grant-in-Aid for Scientific Research on Priority Areas “Develop-ment of Extra-Solar Planetary Science” (16077203).


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Astron Astrophys Rev (2006) 13:229–315DOI 10.1007/s00159-006-0001-y

PA P E R

The electron–cyclotron maser for astrophysicalapplication

Rudolf A. Treumann

Received: 15 March 2006 / Published online: 5 July 2006© Springer-Verlag 2006

Abstract The electron–cyclotron maser is a process that generates coherentradiation from plasma. In the last two decades, it has gained increasing attentionas a dominant mechanism of producing high-power radiation in natural high-temperature magnetized plasmas. Originally proposed as a somewhat exoticidea and subsequently applied to include non-relativistic plasmas, the electron–cyclotron maser was considered as an alternative to turbulent though coherentwave–wave interaction which results in radio emission. However, when it wasrecognized that weak relativistic corrections had to be taken into account inthe radiation process, the importance of the electron–cyclotron maser rose tothe recognition it deserves. Here we review the theory and application of theelectron–cyclotron maser to the directly accessible plasmas in our immediateterrestrial and planetary environments. In situ access to the radiating plasmashas turned out to be crucial in identifying the conditions under which the elec-tron–cyclotron maser mechanism is working. Under extreme astrophysical con-ditions, radiation from plasmas may provide a major energy loss; however, forgenerating the powerful radiation in which the electron–cyclotron maser mech-anism is capable, the plasma must be in a state where release of susceptibleamounts of energy in the form of radiation is favorable. Such conditions are

R. A. Treumann (B)Geophysics Section, Ludwig-Maximilians-University Munich, Theresienstr. 37-41,80333 Munich, Germanye-mail: [email protected]

Present Address:R. A. TreumannThe International Space Science Institute Bern, Bern, Switzerland

R. A. TreumannDepartment of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA

230 R. A. Treumann

realized when the plasma is unable to digest the available free energy thatis imposed from outside and stored in its particle distribution. The lack ofdissipative processes is a common property of collisionless plasmas. When, inaddition, the plasma density becomes so low that the amount of free energyper particle is large, direct emission becomes favorable. This can be expressedas negative absorption of the plasma which, like in conventional masers, leadsto coherent emission even though no quantum correlations are involved. Thephysical basis of this formal analogy between a quantum maser and the elec-tron–cyclotron maser is that in the electron–cyclotron maser the free-spaceradiation modes can be amplified directly. Several models have been proposedfor such a process. The most famous one is the so-called loss-cone maser. How-ever, as argued in this review, the loss-cone maser is rather inefficient. Availablein situ measurements indicate that the loss-cone maser plays only a minor role.Instead, the main source for any strong electron–cyclotron maser is found inthe presence of a magnetic-field-aligned electric potential drop which has sev-eral effects: (1) it dilutes the local plasma to such an extent that the plasmaenters the regime in which the electron–cyclotron maser becomes effective; (2)it generates energetic relativistic electron beams and field-aligned currents; (3)it deforms, together with the magnetic mirror force, the electron distributionfunction, thereby mimicking a high energy level sufficiently far above the Max-wellian ground state of an equilibrium plasma; (4) it favors emission in the free-space RX mode in a direction roughly perpendicular to the ambient magneticfield; (5) this emission is the most intense, since it implies the coherent resonantcontribution of a maximum number of electrons in the distribution function tothe radiation (i.e., to the generation of negative absorption); (6) it generates alarge number of electron holes via the two-stream instability, and ion holes viathe current-driven ion-acoustic instability which manifest themselves as subtlefine structures moving across the radiation spectrum and being typical for theelectron–cyclotron maser emission process. These fine structures can thus betaken as the ultimate identifier of the electron–cyclotron maser. The auroralkilometric radiation of Earth is taken here as the paradigm for other manifes-tations of intense radio emissions such as the radiation from other planets inthe solar system, from exoplanets, the Sun and other astrophysical objects.

Keywords Electron–cyclotron maser · Non-thermal radiation · Coherentradiation · Radio emissions from magnetized planets · Auroral kilometricradiation · Jupiter radio bursts · Solar radio bursts/spikes · Coherent radiationfrom stars · Coherent radiation from Blazar jets

1 Introduction

It is common place that astronomy and astrophysics live from the observationof radiation and that there is no window anywhere in astronomy for makingobservations in situ. Nevertheless, space plasma physics opens up a windowin near-Earth space, where on the one hand, some astrophysical concepts of

The electron–cyclotron maser 231

processes, small-scale models, and theories can be put to test and, on the otherhand, new concepts can be developed. These concepts range from the phys-ics of collisionless shocks, over the acceleration of particles, to the merging,breaking-off, and reconnection of magnetic lines of force. And that these con-cepts have not yet been ultimately settled shows the enormous complexity ofthe physics involved.

The generation of radiation, spanning the whole range from the longest radiowaves through the infrared, optical, ultraviolet, X- and γ -rays up to cosmicrays, where the physics of particle acceleration enters directly, has always beenthought of as being quite well understood. This holds certainly true for mostof the optical emission and absorption processes including coherent emissions.It holds also true, though in a more complicated way, for the infrared and sub-millimeter bands, for bremsstrahlung generation of X-rays and for the nuclearprocesses involved in the γ -ray emission. However, at radio wavelengths thesituation has become much more complex. Indeed, gyro- and synchrotron emis-sion processes in magnetic fields, although providing excellent results on map-ping large-scale structures, have turned out to be of value only on large spatialand long temporal scales. Depending on the magnetic field strength and theenergy of the radiating plasma component, radio emission processes may even‘pollute’ the electromagnetic spectrum deep into the optical and even into theγ -ray domains. When it comes to the observation of short-time radiation events,which for the time being can be detected only from objects located close-by inour galaxy or from extremely violent remote emitters, these simple classicaltheories fail. One is then thrown back to the consideration of plasma emissionprocesses, which are accessible either under grossly non-astronomical condi-tions in the laboratory or with somewhat better correspondence in near-Earthspace. This is where progress in understanding those mechanisms has beenachieved and with what we will deal in this review.

Over the last few decades, it has been realized in observational space plasmaphysics that radio emission from the magnetized planets in the solar systemcan occasionally become so intense that the conventional theories of emissionat radio wavelengths are unable to account for it. The concerted efforts oftheorists to explain the extraordinarily high inferred emissivity (or in the lan-guage of radio astronomy: TB, the brightness temperature1) of these sourcesinitially concentrated on non-linear wave-evolution which, in a perturbationalapproach, becomes important at large wave amplitudes, and which includesnon-linear wave-particle interaction processes. However, these non-linear ap-proaches, as well as those based on non-perturbational techniques invoking thenon-linear evolution of the waves, failed in many respects to provide the properunderstanding of how natural plasmas could generate the excessively high ob-served radiative powers. The situation became even more mysterious when hightime- and frequency-resolution techniques became available, and showed thatthe radiation occurred in narrow bands, varied with time and reached peak

1 For the definition of the brightness temperature in plasma see, e.g., Melrose (1980).

232 R. A. Treumann

power levels of up to several percent of the available kinetic plasma energy.Indeed, brightness temperatures many orders of magnitude higher than plasmatemperature and sometimes reaching values above 1020 K were observed. Suchbrightness temperatures pointed to an unknown coherent emission mechanism2

that had to be responsible for the generation of such radiation. The mechanismultimately identified was the direct linear amplification of the free-space elec-tromagnetic modes by a non-thermal (energetic) electron population presentin the plasma. In some of its properties this kind of direct amplification of radi-ation resembles the well-known molecular masers or lasers where populationinversion leads to stimulated emission of coherent radiation of high yield, aphenomenon that has found wide application not only in technology but also inastrophysics. In fact, molecular maser processes have been identified in manyastrophysical objects such as the environment of oxygen-rich late-type giants,dust clouds and H-II regions where various rotational lines of OH, H2O, SiO ...have been attributed to molecular masers. In these masers the pumping is pro-vided by either chemical processes, collisions, or infrared and ultra-violet radia-tion. (For a recent review the reader may consult the proceedings volume in Mi-genes and Reid 2002.) The resemblance between molecular masers and plasmaemissions of high brightness temperature led to the somewhat unfortunate name‘electron–cyclotron maser’ for the radiation mechanism. This name is mislead-ing, since neither quantum effects, nor energy levels, nor elementary populationinversions are involved, and no electrons jump coherently down from an ex-cited energy level onto some lower level.3 In fact, the emission mechanismof the electron–cyclotron maser is simply based on a linear instability of free-space modes in the presence of a non-thermal electron population, which undersome special conditions can be excited in a plasma. Such special conditions are,however, not so rare. They occur in many space plasmas, and it is reasonableto assume that they also occur in astrophysical plasmas. The main remainingsimilarity to a maser is that the plasma must contain a substantially abundantnon-thermal electron component as the carrier of an excess of free energy.

Depending on whether this electron component is mono-energetic or hasa broad velocity spread corresponding to high temperature, one distinguishesbetween ‘bunching maser’ and ‘genuine maser’ mechanisms, respectively. For

2 ‘Coherent emission’ is defined as emission with brightness temperature TB > T or TB > We/kBthat is much larger than the temperature T of the plasma or electron kinetic energy We/mec2 =γ − 1, where γ is the relativistic factor. Such high brightness temperatures cannot be explainedin terms of thermal emission. Thermal emission, on the other hand, has brightness temperatureTB < T, We/kB, where kB is Boltzmann’s constant.3 Le Quéau (1988) has attempted a quantum mechanical treatment of the electron–cyclotronmaser emission based on the pumping of Landau levels WL = hωce(l + 1

2 ) in magnetized plasma.However, this analogy can be considered only metaphorically since under conditions in space and inmost astrophysical plasmas, which are subject to electron–cyclotron maser emission, the prevalentmagnetic field strengths are so weak that the Landau levels form a featureless continuum. For exam-ple, in the auroral kilometric radiation — the paradigm of an electron–cyclotron maser discussedbelow in depth — the energy spacing between adjacent Landau levels is �W = hωce ≈ 10−29 J or≈ 10−10 eV which when compared to the auroral electron temperature, where kBTe lies between1 and 10 keV, is entirely negligible.


2 4 6 80kc /

fX

fuh

fpe

fZ

X-mode

O-mode

Z-mode

f = kc/2

2 4 6 80kc /

fR

fce

fpe

fL

R-mode

L-mode

whistler-mode

f = kc/2

ωce ωce

π

π

Fig. 1 The dispersion relations of the magneto-ionic wave modes in a plasma for perpendicu-lar (left) and parallel (right) wave propagation with respect to the ambient magnetic field. f isthe frequency given on the ordinate, and k = 2π/λ is the wave-number vector component givenon the abscissa in terms of the product kc of wave number and velocity of light c. The repre-sentation with respect to kc (instead of k) has been chosen since then the dispersion relationof light waves becomes the diagonal of the figure. For perpendicular propagation the X-modeis the ‘fast’ branch of the right-hand polarized wave, the Z-mode the ‘slow’ branch of the right-hand polarized wave, and the O-mode the left-hand polarized wave. The X-mode propagates onlyabove the X-mode cutoff fX , the Z-mode between the Z-mode cutoff fZ and the upper hybridfrequency fuh, and the O-mode above the plasma frequency fpe. For parallel propagation theX-mode becomes the right-circular polarized R-mode, the O-mode the left-circular polarized L-mode, and the Z-mode the right-circular polarized whistler mode which is confined below theelectron–cyclotron frequency fce

a recent review of the former one may consult Chu (2004). It forms the basisfor laboratory attempts of generating intense slow-wave4 cyclotron emissions.Application to astrophysical problems is still missing as one does not expectthe special conditions of strong bunching to occur under most incoherent nat-ural plasma conditions. Therefore, we will discuss the mechanism of bunchingonly briefly in context with cyclotron radiation. Nevertheless, the distinctionbetween the bunching maser instability and the genuine maser instability is nota fundamental one: Winglee (1983) has shown that they are just two differentlimiting cases of the same basic cyclotron instability.

When one calculates the absorption coefficient of a plasma that contains anon-thermal component, negative values are obtained in this volume. Thus, theplasma turns into a macroscopic radiator, which is just the global property ofa maser. Melrose and Dulk (1982) have formulated the theory in terms of theabsorption coefficient in order to demonstrate the similarity to quantum masers.Loosely spoken, the electron–cyclotron maser is a classical maser for which wewill, therefore, retain the now generally adopted name of a maser. In fact, the

4 For the definition of ‘fast’ and ‘slow’ waves in plasma, see Fig. 1 and the caption to that figure.

234 R. A. Treumann

electron–cyclotron maser is a linear plasma instability which directly pumps thefree-space electromagnetic modes in the presence of a non-thermal electronpopulation; and this is the view we adopt in the presentation of the theorybelow rather than the more ambitious absorption-coefficient representation.We note, however, that both representations are equivalent.

Generation of intense radiation is one way, though not the only way, forthe plasma to get rid of a substantial part of the excess energy stored in thenon-thermal electron component. This happens, when other conventional waysof dissipating the free electron energy by heating, particle acceleration, andgeneration of anomalous transport are slow. Such conditions are best satisfiedwhen the thermal plasma component is dilute or absent and the non-thermalcomponent dominates, or when the plasma is immersed into a very strong mag-netic field. In the latter case, all plasma waves are confined to low frequenciesfar below the cyclotron frequency. They are not involved in the radiation.

Provisionally, we can provide a rule of thumb: with ne the plasma density, andB = |B| the strength of the ambient magnetic field B, the necessary condition forplasma hosting the electron–cyclotron maser can be written as f 2

pe/f 2ce � 1. Here

fpe = e√

ne/meε0/2π , fce = eB/2πme are, respectively, the electron plasma andthe electron–cyclotron frequencies. Handy formulas for these two frequenciesare fpe ≈ 9

√ne kHz and fce ≈ 28B kHz, where the density ne is in cm−3, and the

magnetic field B is measured in gauss. The above inequality is, in fact, slightly toostrong. The electron–cyclotron maser will also work under the weaker conditionf 2pe/f 2

ce ≤ 1, when it will only be less efficient.However, only under the most extreme conditions would all the free energy

go into radiation. Such conditions are barely realized in magnetized plasmas.Efficiencies of up to several percent are already very close to being extreme.The remaining ∼90% free energy may still be dissipated in the plasma in otherways. How this can be achieved will be mentioned when discussing the elec-tron–cyclotron maser mechanism in the main body of this review.

The review is structured as follows: in the next section we briefly discuss thehistory of the electron–cyclotron maser theory, thereby we include parts of thehistory of the bunching theory, since the two are closely related. The main in situobservations of the electron–cyclotron maser emission in near-Earth space arereviewed in Sect. 3, and Sect. 4 deals with the elementary theory of the electron–cyclotron maser mechanism in a cold-plasma fluid-approximation including thevarious hitherto proposed models. Section 5 describes the warm-plasma rela-tivistic-electron cyclotron maser and the long favored loss-cone maser and thenturns to the ring-shell maser. We will stress that the latter is the most impor-tant one and that radiation generation requires the presence of an electric fieldcomponent that is aligned with the ambient magnetic field. Hence electron–cyclotron maser radiators are high-probability systems where strong magneticfield-aligned currents have been generated. Section 6 provides arguments formechanisms which generate such fields, discusses the stability of such fields, andpresents the most recent ideas about the generation of maser fine-structures andtheir informational content about the radiation-source regions. Section 7 will


discuss a number of astrophysical applications, and in Sect. 8 we present someconclusions.

2 History

The possibility of an electron–cyclotron maser emitting radiation at frequenciesclose to the electron cyclotron frequency and its harmonics was first envisagedabout simultaneously but independently by Twiss (1958), Gaponov (1959a),and Schneider (1959). Bekefi et al. (1961) refined the theory. All these authorsrealized that it should be possible to directly amplify the high-frequency elec-tromagnetic waves in a plasma (cf., Fig. 1) by a resonant interaction betweenthe wave and energetic electrons at the Doppler shifted electron–cyclotronfrequency:

ω − k‖v‖ = lωce

γ, γ =

(1 − v2

c2

)− 12

. (1)

Here ω = 2π f and ωce = 2π fce are the angular frequency of the emittedwave and the angular cyclotron frequency, respectively, v is the resonant elec-tron velocity with components v‖, v⊥ parallel and perpendicular to the ambi-ent magnetic field B0, respectively, and l is the cyclotron harmonic number.k = (k‖, k⊥) is the wave number of the free-space wave which in magnetizedplasmas is related to the frequency via the dispersion relation

N2 ≡ k2c2

ω2 = ε(ω, k). (2)

The quantity N is the index of refraction , and ε = I +σ/iωε0 is the dielectrictensor (its projection k · ε · k onto the direction of k is the response function) ofthe plasma, and I is the unit tensor. Explicit expressions for the linear plasmaconductivity tensor σ have been given in (Montgomery and Tidman 1964; Bekefi1966; Melrose 1980; Baumjohann and Treumann 1996) and by others. A generalform is

σ

2π iωε0= ω2

pe

ω2

∞∫0

p⊥dp⊥∞∫

−∞dp‖

∞∑l=−∞

S/γ

ω − k‖p‖/meγ − lωce/γ, (3)

where the tensor S is represented by the following matrix

S =

v⊥U(

lJlx

)2iv⊥U

lJlJ′l

x v⊥WlJ2

lx

−iv⊥UlJlJ′

lx v⊥U(J′

l)2 −iv⊥WJlJ′

l

v‖UlJ2

lx iv‖UJlJ′

l v‖WJ2l

. (4)

236 R. A. Treumann

The parameter x is defined as x = γ k⊥v⊥/ωce, Jl(x) are Bessel functions oforder l, and the operators U, W are given through

U = meγω∂p⊥f0 + k‖(p⊥∂p‖ − p‖∂p⊥)f0, (5)

W = meγω∂p‖f0 − melωce

p⊥(p⊥∂p‖ − p‖∂p⊥)f0. (6)

In all these expressions p = meγ v is the relativistic momentum of the electrons,and v the velocity. p has the components p‖ and p⊥ parallel and perpendicularto the magnetic field. In the magneto-ionic (cold plasma) limit the propagat-ing free-space solutions of this dispersion relation (cf. Fig. 1) are the (fast) RXand LO free-space modes propagating above the respective cutoff frequen-cies ωX (8) and ωpe, and the (slow) RZ (or simply Z) mode which cannotleave the plasma, since it is confined below the upper-hybrid frequency ωuh ≡(ω2

pe +ω2ce)

12 < ωX (Bekefi 1966; Budden 1988; Melrose 1980; Baumjohann and

Treumann 1996). The RX and Z modes are polarized right-hand, while the LOmode has left-hand polarization. Figure 1 gives a graphic representation of thedispersion relations of these modes for the two main directions of propagation:perpendicular and parallel to the ambient magnetic field.

For the electron–cyclotron maser including the relativistic factor γ — evenin very weakly relativistic plasmas — is important. This was, however, realizedonly later.

Hirshfield and Bekefi (1963) pointed out that coherent mechanisms could beat work in planetary magnetospheres such as that of Jupiter when they endeav-ored to explain the observation of Jovian decametric radiation. Hirshfield andWachtel (1964) actually demonstrated the emission in a laboratory experimentwith relativistic electrons. Non-relativistic versions of electron–cyclotron maseremission had been developed in other papers by Gaponov (1959b), Harris(1959) (who suggested that certain non-thermal electron-velocity distributionsfavor the emission) and Sagdeev and Shafranov (1960). These theories were fur-ther developed by Melrose (1973, 1976), who assumed a bi-Maxwellian electrondistribution function and found from quasilinear theory that coherent emissionclose to the fundamental harmonic l = 1 in the X-mode would dominate butcan occur only in highly underdense plasma with ω2

pe � ω2ce, for temperatures

(kBT⊥)2| cos θ | > 12 mec2kBT‖, (7)

where θ is the angle of propagation with respect to the ambient magnetic field.The second condition (7) is very severe as, in particular for very oblique emis-sion θ ≈ π/2 close to the perpendicular, it requires very high temperatureanisotropies T⊥/T‖ of the order of > 102 which are hard to achieve. Emissionat harmonics faces weaker restrictions on the plasma density. Melrose (1976)also pointed out that all emissions are subject to the constraint that the radia-tion should be able to escape from the plasma. Since in magnetoionic theory(Budden 1988) there are only the above-mentioned two free-space modes LO


and RX which can escape, escaping radiation must be above the respectivelower cutoff frequencies ω > ωpe for the LO-mode, or for the RX-mode

ω > ωX = 12

[ωce +

(ω2

ce + 4ω2pe

) 12

]. (8)

The radiation has to choose between these two conditions. It turns out thatit favors the RX-mode even though its cutoff is at much higher frequency thanthat of the LO-mode. Hence escaping radiation should exhibit right-hand polar-ization in the RX-mode. The (slow) Z-mode — or low-frequency RX-mode —is confined to the plasma and is thus not accessible to remote sensing. Theseescape restrictions remain valid even under relativistic conditions. All theserestrictions temporarily drove the interest away from further consideration ofthe electron–cyclotron maser in space and astrophysical applications.

Wu and Lee (1979) achieved major progress. They realized that (similar tothe importance of the relativistic correction in the bunching maser) includ-ing relativistic effects in the electron component — even in the very weaklyrelativistic case — has a decisive effect on the efficiency of the amplificationof the emitted wave. The reason is that the resonance condition (1) taken inthe non-relativistic limit γ = 1 is independent of v⊥ and yields a straight linev‖ = (ω − ωce)/k‖ in velocity space.5 Along this line only very few resonantelectrons contribute to radiation.

The exact solution of (1) yields an ellipse in the plane (v⊥, v‖) which can bepositioned on the particle distribution in such a way that it visits many of the res-onant particles which carry the available free energy. Wu and Lee (1979) foundthat including the weakly relativistic correction for electrons in the Earth’sauroral region, which cover the energy range from 0.3 to 10 keV, substantiallyenhanced the growth rate of the RX-mode over the rates found earlier in thenon-relativistic approach. They proposed that natural emissions of the kind ofthe auroral radio emissions could be generated by the semi-relativistic electron–cyclotron maser instability. Such terrestrial radio emissions had been detectedand described by Benediktov et al. (1965) in 1965, and had been investigatedmore closely and confirmed by Gurnett (1974). Gurnett (1974) was able to inferthe bandwidth of the terrestrial radio emission and its average intensity whichhe found to be between 1 and 10% of the total energy supplied to the Earth’smagnetosphere during a substorm. By 1985 investigations of the direction fromwhich the radiation was emitted (Mellott et al. 1984, 1985) had demonstratedclearly that the emission resulted from the auroral zone just above the auroralionosphere at altitudes of a few 1,000 km. Later investigations and refinementsfound that the emission came from the nightside of the magnetosphere and thisrelated it to processes in the Earth’s magnetotail, which are now believed tocome from the violent reconnection process taking place in the Earth’s plasmasheet during substorms.

5 See the detailed discussion of the resonance condition in Sect. 5.2.

238 R. A. Treumann

The paper by Wu and Lee (1979) was immediately followed by a vast activityin the calculation of various models of the electron–cyclotron maser mecha-nism for different electron-distribution functions and for different objects. TheSun largest number of models concerned the Sun [for an intermediate reviewof solar observation and theory see McLean and Labrum (1985), Dulk (1985),Bastian et al. (1998)], followed by models for the Earth’s auroral radio emis-sions and Jupiter’s radio radiation. The idea of Wu and Lee (1979) had been thatthe electron-distribution function, which is responsible for the electron–cyclo-tron maser instability, and the excitation of the terrestrial radio emission, whichwas now called ‘auroral kilometric radiation’ (AKR), is a so-called loss-conedistribution on the precipitating and trapped hot auroral electron component.The loss-cone is dug out from the initially isotropic distribution in pitch angle θ6

by the collisions of the nearly parallel electrons with the dense and cold upperionospheric plasma component.

A loss-cone distribution indeed satisfies the condition that electrons virtuallyreside in a higher energy state than the (isotropic and pitch-angle independent)‘ground state’ of the equilibrium distribution function. This means that the dis-tribution function in a certain region around the loss cone is anisotropic andlacks the parallel particle component required to isotropize it. This formallycauses a positive derivative on the electron-distribution function f (v‖, v⊥) withrespect to the perpendicular velocity of the electrons, viz. ∂f/∂v⊥ > 0. Now,since these electrons which are residing along the edge of the loss cone carrythe free energy by contributing to the positive derivative, it would be desirableto draw the resonance line (1) along the positive gradient of the distributionfunction. Indeed, this becomes possible by exploiting the aforementioned rel-ativistic deformation of the resonance line from a straight line into an ellipse,the position of which in velocity space (v‖, v⊥) can be chosen in such a way thatit covers most of ∂f/∂v⊥ > 0.

The loss-cone maser theory7 was further expanded by Melrose and Dulk(1982), Melrose et al. (1982), Melrose et al. (1984), and Hewitt et al. (1982) andwas applied also to solar-system radio emissions, including planetary radiation,solar microwave spikes in impulsive flares, radio emission from binary systems,and narrow-band emissions from dwarf M flare stars. By including the relativis-tic correction into the electron–cyclotron maser mechanism, the very disturbingearlier requirement of extreme temperature anisotropies Melrose (1973) in thenon-relativistic cyclotron maser had now been removed. Realistic small tem-perature anisotropies became sufficient for letting the maser work. However,the growth rates still remained comparably small and, in addition, the emissionturned out to have large bandwidth. This was less disturbing until observa-tion of the fine structure of the AKR revealed that the auroral radio radiationconsists of very many narrow emission features (Gurnett and Anderson 1981)

6 The pitch angle θ = arccos (v · B/|v||B|) is the angle between the velocity vector v of a particleand the magnetic field B.7 An extended summary of the linear theories of the loss-cone maser can be found in Wu (1985).A short introduction into the maser theory is given in Treumann and Baumjohann (1997).


which move in an irregular fashion on top of a comparably weak backgroundradiation across the dynamical frequency-time spectra. Moreover, these narrowemission features turned out to be very intense. Interpretation of such prop-erties was very difficult when sticking to the loss-cone maser. Models requiredextremely steep perpendicular velocity gradients on the distribution functionat the edge of the loss cone which neither were supported by observationnor could be justified theoretically. The information needed for developing arealistic model mechanism was clearly stored in conditions that could only beexplored in situ, i.e., within the radiation source region.

In the early 1980s, then, it turned out that the loss-cone maser theorywas not supported by observation of the AKR. Moreover, two-dimensionalparticle simulations based on measured electron loss-cone distributions(Pritchett 1984a,b; Pritchett and Strangeway 1985) had failed as well. Omidi andGurnett (1982a,b, 1984), guided by the observations of the polar-orbiting space-craft S3-3 high above the aurora at 8,000 km altitude, undertook to determinethe maser growth rate for the Earth’s AKR from experimental data. Investigat-ing the weakly relativistic cyclotron resonance condition as it had been given byWu and Lee (1979) and had been elaborated in depth in particular by Melroseand Dulk (1982) and Melrose et al. (1982), they tried to determine the resonanceellipse (see the discussion below) in the auroral electron distribution. They con-cluded that for the weakly relativistic auroral energies between 0.1 and 10 keVthe resonance ellipse could be approximated by a resonance circle that was dis-placed from origin and that, however, this circle covered at least a few electronsin resonance lying mostly inside the loss-cone. So they concluded, sticking to thethen general philosophy, that the loss-cone is the main source of AKR emissionby the maser mechanism. Under this assumption they numerically determinedthe growth rate of the maser by integrating the electron distribution along theresonance ellipse and found very small and non-acceptable growth rates, whichthey tried to justify with the quasi-linear saturation of the emission and thequasi-linear depletion of the loss-cone by energy loss to the radiation.8 In fact,the resolution of the electron measurements was not good enough to let themrealize that the distribution was closer to a ring or shell distribution with onlya small and negligible loss-cone component present. Nevertheless, this attempt

8 Such a depletion of the loss-cone was considered by many authors in application to various solarradio bursts and their fine structures (cf., for instance, Aschwanden 1990a,b; Aschwanden and Benz1988a,b, Melrose 2002 and others) as the dominant saturation mechanism. The idea is that the loss-cone would be very vulnerable to energy losses of the electrons at the boundary of the loss-cone,and that the small energy loss to the radiation would be sufficient to fill in the loss-cone. However,this assumption requires that the radiation does not escape from the source region, an assumptionbarely satisfied in the source region of the AKR. Moreover, here the loss-cone is very wide, and it ishard to believe that weak pitch-angle diffusion, due to the small energy loss to the radiation, couldbridge its entire width. In contrast, it is easy to understand that at equatorial altitudes the loss-conecan be filled due to pitch-angle diffusion in the resonant interaction of electrons with whistler waves,as Kennel and Petschek (1966) argued in their classic paper on the stability of the radiation belts,because here the loss-cone is extremely narrow and the growth rate of the resonant whistlers isvery large. However, in the equatorial region the electron–cyclotron maser instability cannot beexcited. This argument also applies to other systems like Jupiter, Saturn, and solar coronal loops.

240 R. A. Treumann

demonstrated that the theory could be tested by exploiting the in situ measure-ments. Clearly, without such measurements the generation mechanism of theauroral kilometric radiation would still lay in darkness.

Failure of the loss-cone mechanism thus became obvious already early on,even though the overwhelming majority of investigators was still favoring it.It was instead suggested in 1986 that ‘ring’ or ‘shell’ distributions produced byfield-aligned electric fields may drive the electron–cyclotron maser Winglee andDulk (1986). A study based on the Swedish Viking satellite9 observations sug-gested that the loss-cone itself is insufficient as a reason for emission of auroralkilometric radiation. Louarn et al. (1990) found in these observations manycases with pronounced loss-cones with no auroral kilometric radiation. Instead,they found that the free energy for the growth of auroral kilometric radia-tion comes from electron-distribution functions exhibiting a positive gradientwhich was not necessarily located inside the loss cone. This led to speculationthat the emissions, at least as observed in situ in the Earth’s environment, donot draw their energy from a loss-cone instability. Rather the energy comesfrom a deformed distribution which is the result of the action of magnetic-field-aligned electric fields10 as it had already been proposed by Pritchett andStrangeway (1985) based on the electric-field model investigated by Chiu andSchulz (1978).

The missing fact in the theory of the electron–cyclotron maser of the auro-ral kilometric radiation was indeed the neglect of the role that is played by afield-aligned electric field in the auroral dynamics. The presence of magnetic-field-aligned electric potential drops to accelerate the auroral electrons in theauroral magnetosphere was a long suspected though mysterious fact. It hadalready been anticipated by Hannes Alfvén (1958) in the fifties and had sincebeen promoted by his collaborators and others, but did not receive the attentionit deserved. In the practically collisionless plasma of the auroral region, paral-lel potential drops were believed not to occur over the length of time that issufficient for generating auroral electron beams. The first indication on the realimportance of field-aligned potentials in the auroral region had been providedearly on in a widely neglected paper published by Calvert (1981a). Calvert(1981a) had observed that the auroral region is practically void of thermal

9 Viking (Hultqvist 1990) was a Swedish auroral spacecraft that was launched on February 22, 1986from Kiruna, Sweden, into a polar orbit at roughly 8,000 km distance from Earth, measuring thereuntil December 1986. It was particularly tailored for the exploration of the properties of substormsand the auroral radio emission.10 The first very simple model of such electric fields by Knight (1973) was based on thermal equi-librium and had nothing to do with the real physical process that keeps a field-aligned electric fieldalive. This model was followed by more recent attempts to construct stationary electric fields alongthe magnetic field provided by Lyons (1980), Vedin and Rönnmark (2005) and others. Measure-ments of such auroral electric fields have been reviewed Weimer et al. (1985) and more recentlyby Hull et al. (2003). Earlier, Föppl et al. (1968) and Haerendel et al. (1976) injected a Bariumion cloud into the upper ionosphere and, from observation of emission lines of Barium atoms andBarium ions in the visible, inferred a sudden upward acceleration of the ions along the Earth’sauroral magnetic field-lines at high altitude of a few 1,000 km. They concluded that the accelerationhad been provided locally by an upward electric field along the Earth’s magnetic field.


plasma, and proposed that radiation in this region, where the plasma frequencyis much lower than the electron–cyclotron frequency, should be generated by theenergetic plasma component and should be bouncing back and forth betweenthe walls of the ‘auroral density trough’ that acts as a wave guide. Thereby theradiation would be amplified before it leaked out from the trough to free space.Calvert (1981a) did not address the question of how the trough would be pro-duced. However, Chiu and Schulz (1978) had already shown 3 years earlier thatsuch a trough would occur, provided a magnetic-field-aligned electric potentialdrop existed in the auroral region. Mechanisms that generate potential dropsand field-aligned electrostatic fields are under consideration even today becausefinding conditions for maintaining them in a collisionless plasma presents seri-ous difficulties. But Chiu and Schulz (1978) had shown that such drops oncethey are established deform the original trapped electron-distribution functionin a certain characteristic way which much later turned out to be crucial forthe maser mechanism. Under the combined action of these electric fields andthe mirror effect of the converging magnetic field-lines, the electron-distribu-tion function assumes the shape of a ring in (v‖, v⊥)-phase space. This wasultimately demonstrated in particle simulations (Winglee and Pritchett 1986).

In order to understand how this situation arises, one may assume that a sta-tionary electric field exists along a magnetic field-line pointing upward. Such afield accelerates electrons down into the converging magnetic field. While theelectrons move down into the stronger magnetic field, the first adiabatic invari-ant µ = meγ c2 sin2 θ/B (the magnetic moment of the particles) is conserved,and as a consequence the electrons assume larger pitch angles θ . This causesa peak in the electron distribution at the larger pitch angles and, by removingelectrons from smaller energies due to acceleration in the electric field, pro-duces a hole at small energies, and thus causes a positive perpendicular-velocitygradient, ∂f0/∂v⊥ > 0, in the distribution function. Thus, in the presence of afield-aligned electric field component, there should exist an inner region in thedistribution function at low energies that is void of particles (Chiu and Schulz1978).

This latter prediction is not in agreement with observations which showed,instead, that the electron distribution exhibits a well-pronounced plateau atsmaller velocities. Explaining this plateau involved considerable difficulties. Itis clear by now that the plateau is not caused by a quasi-linear relaxation of thedistribution through energy loss by electron–cyclotron maser emission. Instead,it was found to be caused by wave-particle interaction between the energeticelectrons and low-frequency waves in the Very low-frequency range (LaBelleand Treumann 2002). These low-frequency waves are bound to the plasma andhave no way to escape from it. Their excitation is unavoidable; it is intrinsicto the positive perpendicular velocity gradient in the undisturbed distributionfunction. Their intensity grows high enough to imprint on the electrons whichare in resonance with the VLF waves and to deplete the gradient and gen-erate the plateau. In fact, artificially inhibiting the depletion of the gradientby taking out the VLF waves retains the gradient and leads to larger maseremissivity. Escaping free-space modes of the maser radiation are not intense

242 R. A. Treumann

enough to deplete the gradient, unless the radiation would be kept inside themaser source by some mechanism of confinement. Thus electric fields, particleacceleration, and VLF waves work together in producing auroral kilometricradiation as a most intense emission which can be understood only on the basisof the electron–cyclotron maser mechanism in the presence of a field-alignedelectric potential drop. This has been a most important realization of the lastdecade, and its consequence for astrophysical plasmas has yet to be exploited.

Stimulated by all these investigations, Pritchett (1984a,b), developed theelectron–cyclotron maser theory for ring distributions of the kind describedabove. The important point he realized was that the resonance condition (1)becomes a perfect circle in phase space for strictly perpendicular free-spacemode propagation. Positioning the resonance line for perpendicular emissionis thus ideally adapted to the ring distribution. It follows from the propagationproperties of the RX modes that in this case only the extraordinary wave willbecome resonantly amplified.11

Interestingly, due to the relativistic mass increase the emitted resonantfrequency for perpendicular propagation falls below the (non-relativistic) elec-tron–cyclotron frequency, ω < ωce. An estimate of the dependence of the lineargrowth rate of the radiation brought the result that maximum growth is attainedjust for strictly perpendicular emission of the fundamental harmonic at such fre-quencies below ωce. Of course, higher harmonic emission is possible as well butits growth is much slower and thus radiation in these harmonic modes should beweaker. On the other hand, escaping from the density trough is no problem forthem. Under certain conditions, when the fundamental, most intensely excitedradiation cannot leave the plasma, one may thus expect to observe harmonicradiation instead.

Calvert (1981a) claim that multiple bouncing of the fundamental radiationinside the density cavity will amplify the radiation before escape will, how-ever, in most cases be barely realized simply because the conditions for suchan amplification require that the length of the ray path between the bound-aries is a multiple of the radiation wavelength. This does not preclude thatunder fortunate conditions and for broadband amplification of the RX-mode,the macroscopic density trough may filter out a particular wavelength, amplifyand release it to free space. Radiation of this kind will clearly be narrow band.Such a model has been proposed by Louarn and Le Quéau (1996a,b) who con-sidered the auroral density trough as an imperfect wave guide and showed thatthe resonantly amplified RX-mode is not only amplified but also couples to theexternal LO-mode outside the walls. The latter leaves the plasma without anyproblem. A model of this kind could explain the sometimes observed imperfectpolarization of the radiation.

Pritchett (1984a,b) theory turned out to provide the relevant tool forinterpreting the Earth’s auroral kilometric radiation when in the late eight-ies and early nineties in situ measurements of plasma and radiation above the

11 This is explained in detail in Sect. 5.2.


Earth’s auroral zone from the Viking and FAST12 satellites became available.The measurements demonstrated that the earlier suspected field-aligned poten-tial drops do exist and are accompanied by ringlike particle distributions withonly moderate loss-cones. In situ crossings of the generation region of the auro-ral kilometric radiation by the FAST satellite showed, in addition, that the mostintense emissions occurred below the local electron–cyclotron frequency andin the regions of highly diluted plasma density that contained accelerated hotelectrons. An enormous fine structuring of the radiation found in the source re-gion suggested that the fine structure observed earlier by Gurnett and Anderson(1981) had not been created at large distance from the source by propagation northrough selection by wavelength but was a property of the source itself. Closerinvestigation of the plasma properties of the source yielded the result that thesource region is filled with small-scale parallel electric field structures, eithermicroscopic solitary waves or so-called electron holes in phase space which ac-tively contribute to the generation of radiation. They possibly even cause the finestructure of the radiation by a mechanism which until the time of writing has notbeen clarified. The observations indicated that almost all of the radiation con-sists of narrow-band ‘elementary’ radiators of microscopic size. These act likepoint-like sources of the radiation moving both in real space and in phase space.

As mentioned before, astrophysical applications of the electron–cyclotronmaser mechanism outside the solar system are still sparse. Application to solarradio emission dominated the field from the very beginning just until the dis-covery of the intense terrestrial auroral radio emission in 1974 (Gurnett 1974).Attempts to explain the solar radiation in the radio band from the longestwavelengths down to microwaves abound in the literature. Solar type IV andtype V bursts, solar radio spikes, and various fine structures in the solar radioemission have been proposed to be the result of maser activity. Application toJupiter and radiation from the other magnetized planets followed, and specula-tions about radiation emitted from extrasolar planets when they are magnetizedstrongly enough have been published as well (Bastian et al. 2000; Zarka et al.2001a,b). Radiation of this kind, because it would be much stronger than anyother radio emission, would allow not only to detect ‘radio-loud’ extrasolarplanets but also to infer their magnetic field strengths and plasma properties.Its identification is therefore of vital interest. However, given the experiencewith the Sun which is a strong radio emitter it may be more realistic for the timebeing to apply the theory to other stellar systems. The proposals of this kindhave been around since the earliest application of the electron–cyclotron masermechanism (Louarn et al. 1986) and have been renewed meanwhile in view ofthe modern theories (Ergun et al. 2000; Bingham and Cairns 2000; Binghamet al. 2001). Applications of the theory to exotic objects like pulsars (Ma et al.

12 FAST is the mnemonic for NASA’s Fast Auroral Snapshot (FAST) Explorer spacecraft, whichhas been launched into a 350 km by 4,180 km altitude polar orbit on August 21, 1996, the firstof NASA’s small spacecraft. FAST was tailored to improve substantially and complement Vikingobservations with very high-resolution in situ measurements at lower altitudes in the auroral plasmacavity (Pfaff et al. 2001).

244 R. A. Treumann

1998) and Blazar jets (Begelman et al. 2005) have recently been attempted aswell. These more speculative theories have of course to await more detailedobservations afforded by the much higher spatial and temporal resolutions offuture instrumentation. In this respect, space plasma physics has a tremendousadvantage over astrophysics as near-Earth or planetary space offers the possi-bility to undertake in situ measurements of the very conditions of emission. Inthe following section, we review the most relevant observations that supportthe very existence of the natural electron–cyclotron maser in space.

3 Observing the space plasma in situ

Since the radiation generated in the electron–cyclotron maser mechanism isclosely related to the plasma configuration in the radiation source, a review ofthe relevant observations supporting its existence cannot avoid to go into somedetailed discussion of the connected plasma observations. This is possible onlyfor the region very close to the Earth (and sporadically as well but with muchhigher uncertainty for other planets like Jupiter). We therefore start in this sec-tion, after briefly reviewing the first observational papers, with the descriptionof the observational properties of the Earth’s auroral kilometric radiation thesource of which is the upper auroral ionosphere between, roughly, 1,000 and8,000 km altitude, a region which has turned out to be so far the only accessibleand in any case the closest to Earth electron–cyclotron maser source. Othermuch less accessible and still quite uncertain sources are the auroral regions ofthe large planets Jupiter, Saturn, Uranus, and Neptune and, of course, the solarcorona of which it has been most frequently speculated that electron-maseremission is one of the dominant mechanisms generating radio emission in therange from meter to micro waves. This concentration on Earth’s environmentcannot be avoided in this discussion as only there ideas, theory, and simulationscan be compared with the hard facts of observation.

3.1 Large-scale properties of auroral kilometric radiation

Figure 2 shows the first crude measurement (Gurnett 1974) of the full spectrumof the auroral kilometric radiation recorded by the Interplanetary MonitoringPlatform Imp 6 spacecraft flying far above the ionosphere and seeing the radia-tion coming from the entire Earth13. Terrestrial radio emission had already beendetected earlier. The earliest observation by Benediktov et al. (1965) showednatural radio radiation leaving the Earth’s upper atmosphere but covered onlypart of the spectrum at high frequencies. Nevertheless, these authors alreadyidentified the observed radiation correctly as ‘terrestrial radio noise’. Other

13 The Interplanetary Monitoring Platform spacecraft Imp formed consecutively numbered seriesof early scientific spacecraft. Other similar series were the Explorer spacecraft, the Orbiting SolarObservatory OSO spacecraft, the Orbiting Astronomical OAO spacecraft and others.


10-18

100 101 102 103

10-16

10-14

10-12

10-10

Frequency [kHz]

Pow

er F

lux

[Wat

ts m

-2 k

Hz-

1 ]

AKR

Noise Level

Galactic Radiation

Fig. 2 The first measurement of the auroral kilometric radiation spectrum obtained from theImp 6 spacecraft. Included into the figure are the instrumental noise level for comparison and thespectrum of the galactic cosmic background. The latter becomes important at frequencies above afew hundred kilohertz. The striking fact of this first still relatively crude observation of the auroralkilometric radiation spectrum is that the spectrum is orders of magnitude stronger than the galacticbackground radiation. It is a rather broad emission spectrum, covering the frequency range abovebackground (noise level and real near-Earth background) from ∼1 kHz to a few MHz with a steepmaximum around a few hundred kilohertz (after Gurnett (1974), with permission by the AmericanGeophysical Union)

parts of the auroral kilometric spectrum had been observed on the OrbitingGeophysical Observatory OGO 1 (Dunckel et al. 1970) and on Imp 6 (Brown1973), and were followed by the Hawkeye 1 spacecraft (Kurth et al. 1975) (whocoined the name ‘auroral kilometric radiation’), Imp 8 (Gurnett 1975), and theRadiation Astronomy Explorer Rae 2 (Alexander and Kaiser 1976), the Inter-national Satellite for Ionospheric Studies ISIS 1 (Benson and Calvert 1979;Benson 1982, 1985), the Swedish spacecraft Viking (Bahnsen et al. 1987), andmost recently (Carlson et al. 1998; Ergun et al. 1998a,b,c) by FAST and theCluster14 mission (Mutel et al. 2006).

The first rough measurement of the full auroral kilometric spectrum in Fig. 2exhibits a pronounced maximum at a few hundred kHz, exceeding the near-Earth radio level between about 20 kHz and a few GHz by orders of magni-tude. Comparison with the galactic radio noise spectrum shows that the auroralkilometric emission dominates even at the frequencies of the galactic noise.This is clearly only the case if one is close enough to Earth. In addition, the

14 Cluster is a European Space Agency (ESA) mission comprising four satellites – which werelaunched in pairs on Soyuz launchers from Baikonur on 16 July and 9 August 2000 — to fly information with separation distances ranging from 200 to 10,000 km (Escoubet et al. 1997). TheCluster orbit is 4 by 20 Earth radii with an inclination of 90◦. Cluster is currently scheduled tooperate until 2009.

246 R. A. Treumann

galactic noise can be distinguished from the auroral kilometric radiation by itsstationarity while the auroral kilometric radiation exhibits fast variations bothin time and frequency since it strongly depends on auroral activity.

The typical total power radiated in the auroral kilometric radiation is of theorder of 107 W during small substorms, while peak power levels can be as high as109 W during strong substorms, caused by the intense disturbance of the Earth’smagnetic field resulting from its interaction with the super-alfvénic solar wind.The ultimate energy source of a substorm is the solar wind flow with velocityvsw > vA,sw and the solar wind magnetic field Bsw, the latter acting through thesolar wind convection electric field E = −vsw × B, and hence the solar wind isalso the ultimate energy source of the auroral kilometric radiation. The mech-anism of energy transfer from the solar wind to the geomagnetic field consistsof a combination of the mechanical compression of the geomagnetic field bythe solar wind ram pressure psw = nswmpv2

sw,n, with nsw the solar wind den-sity, vsw,n the solar wind velocity component normal to the boundary betweenthe geomagnetic field and the solar wind (i.e., the magnetopause), and mp theproton mass — an approximation based on the composition of the solar windwhich is ∼95% protons and ∼5% helium — a possible but so far unidentifiedfriction force acting at and along the magnetopause and, as the main mecha-nism, reconnection between magnetic fields carried by the solar wind and thegeomagnetic field. Substorms are the elementary disturbances through whichthe large geomagnetic storms are built. The former occur in the wake of theinteraction between solar coronal mass ejections and the geomagnetic field, andlast over days and play an important role in the effects which are of interest inspace weather prediction. During a typical substorm of duration of ∼ 103 s atotal energy of between 1011 and 1014 J corresponds to a power of between 108

and 1011 W that is transferred to the magnetosphere. Accordingly, the energyemitted in auroral kilometric radiation is typically several percent of the totalsubstorm energy. The resulting brightness temperatures lie between 1010 K forthe weakest events and 1024 K or more for the strongest events, i.e., many ordersof magnitude higher than what may be expected from incoherent gyro or syn-chrotron mechanisms of radiation (Jackson 1962; Rybicky and Lightman 1979).Auroral kilometric radiation — and in the same spirit the highly time-variableradio emissions of the outer large magnetized planets of the solar system — isthus seen to be far from being generated by an incoherent emission process.The measured intensities require a strongly coherent process.

The polarization measurement of the AKR based on Hawkeye spacecraftobservations (Gurnett and Green 1978) indicated that the radiation is emittedmostly in the free space RX mode and that OL mode emission or slow Z modeemission may be present but are in general much weaker.

The direction finding measurements of AKR (Jones 1976; Green et al. 1977;de Feraudy and Schreiber 1995) pointed to sources that are located aboveauroral heights at altitudes between ∼2,000 and 4,000 km with the intensityof radiation decreasing as the inverse square of distance from Earth. Whenlooked at from far away, the source of the auroral kilometric radiation andthus the location of the electron–cyclotron maser is therefore about point-


like. This region is known as the ‘auroral cavity’ (Calvert 1981b; Hilgers 1992)because of its very low plasma density. This has also been confirmed by theabove-mentioned polarization measurements (Gurnett and Green 1978) whichfound the auroral kilometric radiation being strictly correlated with ratiosωce/ωpe,r � 1.

The existence of the auroral cavity poses a problem in itself as it is by nomeans obvious that the plasma density on auroral field-lines must be as lowas it is observationally found. For a long time the relevance of this fact for theemission process and the dynamics of the auroral plasma has been grossly under-estimated. On the other hand, the auroral cavity is not a permanent, invariablefeature. Rather the auroral plasma consists of many wider or narrower cavitieswith varying latitudinal extension and generally much larger extensions in lon-gitude. Each of them can be looked at as a two-dimensional depletion of theauroral plasma content which, in most cases, is confined latitudinally by denseplasma walls.

3.2 The auroral plasma cavity: plasma and its field properties

Figure 3 shows a representative collection of the plasma and field measurementsduring a crossing of the auroral plasma cavity by FAST at ∼ 4,000 km altitude.One of the main properties of this region is that it contains comparably strongfield-aligned electric currents. These currents couple the conducting part of theupper Earth’s atmosphere, the ionosphere, to the electrical currents flowing inthe outer magnetosphere and being generated by the solar–wind interaction asshown schematically in Fig. 4. The magnetic field Bz of these field-aligned cur-rents is transverse to the strong ambient magnetic field and is shown in panela. Positive (negative) gradients in Bz indicate downward (upward) currentscorresponding to upward (downward) ionospheric electron fluxes.

These relations are shown in panels e and f where the electron energy flux andelectron pitch angles (i.e., the angle of individual particle velocity with respectto the ambient magnetic field) are given. The electron flow direction can betaken from panel f, where the broad region of upward current and downwardelectron fluxes concentrates at angles of 0◦ and 360◦ but, in addition, exhibitsa broader distribution in pitch angle with practically no upward electrons at180◦. Moreover, the energy flux (panel e) shows the strong downward fluxesconcentrated at an energy near 10 keV and absence of low-energy electrons.

Panels g and h show the corresponding ion energy fluxes and pitch angles,respectively. In the upward current region, all ions flow upward at 180◦ pitchangle covering a narrow energy band with energy varying between a few keVand 10 keV. Obviously these ions have been accelerated in the upward direc-tion. Such behavior in ions and electrons is typical for the presence of an electricfield pointing upward along the ambient magnetic field, accelerating the ionsupward and electrons downward. In fact, electrons with an energy of ∼10 keVmoving downward along the magnetic field carry this current. This electric fieldis responsible for the very low cold plasma density in the auroral cavity; it createsthe auroral cavity. The temporal width of the auroral cavity in the present case is

248 R. A. Treumann

a

b

c

d

e

f

g

h

Fig. 3 Overview of plasma characteristics observed by instruments on board of the FAST spacecraftat altitudes in and above the source region of the auroral kilometric-radiation electron–cyclotronmaser source. Crossing of the cavity boundary occurs at 18 s. a Magnetic field of field-alignedcurrent; b electric wave form <16 kHz; c Fast Fourier transform (FFT) of wave form showing theelectric wave spectrum for frequencies < 16 kHz; d: wave spectrum <500 kHz (black line near360 kHz in panel d is the local fce); e parallel electron energy flux; f electron pitch angle; g parallelion energy flux; h ion pitch angle. For further description see text (after Pottelette and Treumann(2006))

∼30 s which at spacecraft velocity of 5 km s−1 corresponds to a latitudinal exten-sion of just 150 km. Much narrower cavities have been detected as well (Fig. 5).

In the narrow downward current region upward electron fluxes concentrateat pitch angles 180◦ while their energies cover the whole range from 0 keV up to∼10 keV. The ions are found here at two intermediate pitch-angles sparing out


Auroral ZoneSubauroral

Latitude

Polar

Cap

Fast

Orbit

ionospheric

density

E

-j

E

||-j ||

j||

j||

j||

⊥ ⊥

Fig. 4 The auroral cavity-current and electric-field system as explored by the FAST spacecraft.The auroral cavities are the broad regions of upward directed current flow (−j‖, in blue) parallelto the (vertical) magnetic field-lines (light red). They close the perpendicular ionospheric Pedersencurrents (indicated by the converging horizontal red arrows) which flow in the direction of theconverging perpendicular electric fields E⊥ (yellow vectors). The upward −j‖ currents correspondto downflow of keV auroral electrons which precipitate into the ionosphere and cause the enhancedionospheric ionization. The negative potential in the upward current region (shown as dotted greenlines) confines the auroral electrons to low altitudes. The enhanced ionospheric electron density isshown in dotted red. In the narrow regions between the two upward currents downward currentsj‖ (light red) flow along the magnetic field from the magnetosphere into the ionosphere. Theycorrespond to positive potentials (shown in solid green) and upward electron fluxes. The ray bar atthe bottom is the surface of the Earth (after Elphic et al. 1998 with permission by the AmericanGeophysical Union)

upward pitch angles. This region is of lesser interest for the electron–cyclotronmaser.

3.3 Wave fields and radiation

For the AKR, we refer panel d of Fig. 3 which is the dynamic spectrum ofwave activity observed during the present pass of the spacecraft. The horizon-tal black line in this panel at ∼360 kHz indicates the local (non-relativistic)electron–cyclotron frequency fce.

Strong auroral kilometric radiation, the broad dark emission band at fre-quency above fce has been observed during the entire passage of the auroralzone on this day. This band is modulated at spacecraft spin period as seen in itshigher frequency part. The modulation identifies the radiation as being in theRX mode perpendicular to the ambient magnetic field.

250 R. A. Treumann

v ⊥

⊥

(10

km/s

)4

-10-10 - 5 5 10

- 5

5

10

v || (10 km/s)4

-12.0

-13.4

-14.9

-16.3

-17.8

log

[#/c

m-(

km

/s)

]3

3

losscone

Parallel velocity v||

Per

pend

icul

ar v

eloc

ity v

losscone

0

0

v T

> 0 f

beam

plateau

acceleratedbeam

initial ∂∂

Fig. 5 Left: A typical auroral electron-velocity phase-space distribution function as measured bythe FAST satellite at about 4,000 km altitude in the auroral region during auroral activity (afterDelory et al. (1998), Pritchett et al. (1999) with permission by the American Geophysical Union).This distribution exhibits a loss-cone, a central isotropic cold plasma component around zerovelocity which is most likely due to photoelectrons produced by the satellite itself and thus is notconsidered real, an energetic incomplete ring-shell (horseshoe) distribution with ∂f/∂v⊥ > 0, arudimentary beam component, and a broad nearly flat plateau. Note the nearly circular shape ofthe horseshoe part. Right: A schematic of such a measured distribution as used in calculations andsimulations

When the spacecraft enters the auroral cavity at about 10 s the AKR bandsuddenly shifts below the local electron–cyclotron frequency. At this time thespacecraft has entered the radiation source region where it stays for a shortwhile. Moreover, spin-modulated lower frequency emissions can be seen tooccur at this time as well as fading out to low frequencies. These are non-escaping Z-mode (slow mode) emissions of the same polarization as the RXmode.

At frequencies below 30 Hz in this panel, separated by a wide gap infrequency from the radiation, one finds low-frequency waves with sharp up-per frequency cutoff. This is the local plasma frequency fpe. These emissionsin the VLF band are of immense importance for the dynamics of the plasma.Outside the auroral cavity the emissions extend to higher frequencies, as theplasma is much denser there, and hence the plasma frequency is higher. How-ever, in the auroral cavity with near absence of cold plasma, the VLF is morestrongly confined.

Panel c of Fig. 3 shows the lowest 15 Hz of the dynamic VLF spectrum, andpanel b its wave form. The latter, in this low resolution, exhibits occasional spikybehavior with peak amplitudes of a few mV m−1 in the cavity and larger ampli-tudes outside it in the downward current region. The VLF spectrum shows thatin the cavity the whole VLF consists of spiky broadband bursts of emissions oftwo distinct types: one modulated in the same way as the radiation being roughlyperpendicular to the magnetic field; the other being much more narrowband,strictly bound in frequency by the plasma frequency and about parallel to themagnetic field, such that these emissions are slightly out of phase.


In summary, the AKR source region, i.e. the source region of the electron–cyclotron maser has the following main global properties:

• intense field-aligned currents (in the Earth’s case directed upward),• very dilute plasma density with ωpe � ωce; in the present case this ratio is

0.1,• field-aligned energetic electron fluxes (in the Earth’s case downward and of

∼10 keV mean energy),• strong upward parallel stationary electric fields diluting the plasma (in the

Earth’s case of field strength ∼1 Vm−1),• ring-shell electron-velocity distributions in addition to the downward elec-

tron beam,• upward collimated ion-beam distribution of same energy as downward elec-

tron beam,• intense electromagnetic radiation in the source region at emission frequency

ω < ωce,• 100% circularly polarized radiation in the RX mode (fast electromagnetic

mode),• radiation at ωce is directed strictly perpendicular to the ambient magnetic

field,• at frequencies ω ≤ ωce there is weak radiation in Z-mode polarization (slow

electromagnetic mode),• low-frequency waves are confined to frequencies ω < ωpe,• two types of VLF waves are present: intense broadband bursts with highest

frequencies exceeding ωpe, and weak modulated VLF emissions confinedbelow ωpe,

• the electric wave form at VLF modes exhibits spiky pulses in relation to thebroadband bursts.

3.4 Fine structure of auroral kilometric radiation

One of the most pronounced properties of the AKR is its fine structure. Ithas been reported first by Gurnett and Anderson (1981). Figure 6 shows theexample of a recent measurement of the auroral kilometric spectrum with thewideband instrumentation on the Cluster spacecraft SC1.

This observation which had been anticipated already much earlier by theHawkeye (Gurnett and Anderson 1981) and again later at progressively lowerdistance from Earth by the Viking and FAST spacecraft suggests that the instan-taneous AKR covers by no means a broad emission band. Rather it is emittedin narrow banded rays of bandwidth <1 kHz within sources which move at com-parably high speeds along the magnetic field-lines up and down depending onthe conditions prevalent in the source region. In the present case the velocityis ∼ 300 km s−1, roughly comparable to the ion acoustic speed. Upward driftin space is reflected by downward drifts in the frequency-time diagram sinceemission at the electron–cyclotron frequency as suggested by the electron–cyclotron maser mechanism implies that an upward moving source region in

252 R. A. Treumann

12511 13 1591 3 75

130

135

140Cluster SC1 t =1614:20 UT 08-31-20020

f(k

Hz)

Time (s)

Fig. 6 A 15-s snapshot of wideband observations made by the Cluster mission, depicting auroralkilometric fine structure. This dynamic spectrum representation shows a smooth radiation back-ground with many fast-drifting narrow-band emissions superimposed. The white line around 130kHz is the local electron–cyclotron frequency at the orbital position of Cluster at the time whenthese measurements were taken at about 4 Earth radii distance away from Earth. The structuresdrift from high to low frequencies. This implies an upward drift of the radiation source away fromEarth, i.e., towards lower magnetic field and thus lower electron–cyclotron frequency. Note thatnone of the structures are moving towards higher frequencies, i.e., downward in real space. Thisindicates that all the structures were generated below the Cluster spacecraft. The elementary radia-tors detected by Cluster have thus escaped from their generator at low altitudes along the magneticfield up to the altitude of Cluster

the vicinity of Earth passes from high to low magnetic dipole field strengths.Since the emissions cross the local electron–cyclotron frequency, one would alsoconclude that the radiation sources pass through the altitude of the spacecraft.

Figure 7 shows an observation with very high-time and frequency resolu-tion by the FAST spacecraft of auroral kilometric radiation that was detectedat a much lower altitude of only about 4,000 km above Earth’s surface. Thefrequency of the detected emission fine structure is above the local cyclotronfrequency, and thus the radiation source region is below spacecraft. This record-ing extending over only 2 s exhibits a wealth of fine structuring in the emissionwhich is important as it provides information about the very radiation sources.

The first lesson learned from Fig. 7 is that obviously the entire AKR is com-ing from very fast moving ‘elementary radiation sources,’ the nature of whichhas to be identified. Below we will argue that these are all so-called electronholes which are produced under particular conditions in the plasma. The speedof these elementary radiation sources (or electron holes) as inferred from thedrift of these elements across the dynamic spectrum of the AKR in the figureis of the order of a few 103 km s−1. This value lies close to the electron thermalvelocity of ∼1 keV electrons which are known to be present in multitude in theAKR source region. In most cases it is faster than the time resolution.

The second lesson learned is that these elementary radiation sources some-times arrange themselves in groups which drift as an ensemble through spaceand thus their emitted radiation drifts as an intense line in frequency space. Theinstantaneous width of such a line is of the order of 1 kHz which at the altitudesof the source near-Earth corresponds to roughly 1 km along the nearly verti-cal magnetic-dipole field lines. The arrangement of the elementary radiationsources in a line frequently resembles trapping like it is seen in Fig. 7 wherethe radiators seem to turn around and stay for some time until being reflected.Moreover, two such lines may interact (see the figure) without merging and


FAST ORBIT 1761t = 0645:1.002 UT0

4250.0 0.5 1.0 1.5 2.0

430

435

440

Time (s)

Fre

quen

cy (

kHz)

Fig. 7 A two-second snapshot taken with very high time- and frequency-resolution of a dynamicspectrum of auroral kilometric radiation above the radiation source region. The spectrum exhibitstwo narrow-band structures of radiation that move across the spectrum. The local bandwidth of thetwo structures is of the order of <1 kHz. Both structures are identified as the superposition of evennarrower emission events which reach maximum intensity inside the structure, some of them evenchanging the direction of motion. Also note that the entire auroral kilometric-radiation emissionseems to consist of such ‘elementary radiation events’ of very narrow bandwidth and high spectralvelocity, ∂ω/∂t. The instrumental resolution reaches a bandwidth of ∼ 0.1 kHz (after Potteletteet al. 1999 with permission by the American Geophysical Union)

after interaction moving together (in the case of the figure they move down-ward) as if two regions of similar potential reject each other, the region with thestronger momentum pushing the weaker one ahead. Similar effects have beenfound in numerical simulations (see below in the section on electron holes).

Finally, the last lesson from Fig. 7 is that the local bandwidth of the modu-lations of the AKR in one elementary radiation source can be as low as theresolution, viz. �f 0.1 kHz corresponding to a field-aligned extension of theelementary radiation source of the order of 100 m or even less. Such a smallbandwidth implies that the elementary radiation sources of the AKR, i.e. theelectron–cyclotron maser radiators are very small-scale structures, not largerthan of the order of the Debye length.15 Their observation requires in situmeasurements in the source region. However, they can be inferred by a remoteobserver by their properties and the excitation conditions of the electron–cyclo-tron maser.

15 The Debye-length (or Debye radius) λD = √2mekBTe/ωpe, with Te the electron temperature,

defines the scale above that the plasma can be treated as an electrically quasi-neutral ‘fluid’, i.e.,for lengths L > λD the densities of electrons ne and ions ni can be taken to be approximately thesame, ni ≈ ne. On scales L < λD the electric fields of the single charges of the plasma constituentscannot be neglected anymore. Here single-particle effects come into play and thermal fluctuationsbecome important.

254 R. A. Treumann

One of the characteristic features of the AKR also seen in the above figures isits pronounced fine structure (Gurnett and Anderson 1981). In high-resolutiondynamical power spectra, the auroral kilometric radiation is observed to consistof many components that are closely spaced in frequency and have very nar-row-band components that display a high degree of variability with time. Thebandwidths span the range from few kHz (Gurnett and Anderson 1981) downto widths of the order of ∼10 Hz. Such widths have been indirectly inferred firstby Baumback and Calvert (1987) but can be recognized also in the high reso-lution spectra of Fig. 7. It is not yet clear what their nature is as they could beinterferences, propagation effects, absorption effects, and also the direct signa-ture of very small-scale structures — even smaller than what we have describedas the elementary radiation events which seem to build up the entire spectrumof AKR. In the next section we are going to describe the contemporary state ofthe art of our knowledge of the electron–cyclotron maser radiation mechanism.Since AKR is the only paradigm on which this mechanism can be, and has beentested, we will always refer to it as the ultimate confirmation of whether or notthe mechanism can be taken as a valid explanation for the direct generation offree space radiation.

4 Elementary physics of the cyclotron maser

Keeping in mind that the electron–cyclotron maser is a classical maser withno involvement of quantum correlation effects, we provide in this section sim-ple physical though quantitative arguments for the operation of the cyclotronmaser under the two conditions of mono-energetic and hot non-thermal distri-butions, the former related to electron-phase-space bunching, the latter relatedto phase-space distributions not in thermal equilibrium. It emphasizes in whichway, classically, correlation and coherence can be achieved since this is one ofthe main properties of the electron–cyclotron maser. In this respect the veryemission mechanism is of lesser interest.

4.1 Phase space bunching mechanism

Relativistic phase bunching in the gyrational motion of electron in strong mag-netic fields had first been realized by Twiss (1958). The bunching is due tothe relativistic mass dependence of the electrons at energies above a few keVtransverse energy. Bunching at a particular gyrophase angel replaces quantumcoherency in ordinary masers providing sufficiently strong correlation such thatthe electrons gyrate coherently and thus radiate coherently. This radiation isstimulated radiation because it is stimulated by an electromagnetic wave whichthe electrons are in phase with satisfying the resonance condition (1).

Such resonant electrons moving along a strong external magnetic field B0at speed v‖ and together with right-hand polarized electromagnetic wave andgyrate at velocity v⊥ feel the constant transverse electric wave field E⊥ whichcan either decelerate or accelerate the electron perpendicular to the ambient


magnetic field, depending on whether the respective electrons rotate faster orslower than the wave. Faster electron will thus become retarded and slowerelectrons will be pushed until both have same phase angle as the wave. Mono-energetic electron beams will in this way bunch at one particular phase angle.The evolution of the kinetic energy of the electrons W = (γ − 1)mec2 is thengiven by

dWdt

= −ev⊥ · E⊥ = −eE0v⊥ cos(ωt − k‖z − φ), (9)

if φ is the angle between v⊥ and E⊥, and E0 the wave amplitude. The angle φ

evolves in time asφ ωce/γ . (10)

On using the resonance condition (which now becomes a synchronism condi-tion) one can easily show that the effective cyclotron angle φeff ≡ k‖z + φ ofthe electrons advances as

φeff k‖z + ωce/γ ≡ ωce,eff. (11)

Synchronism is thus reached when ω ωce,eff. This is illustrated in Fig. 8which shows that the electrons tend to bunch in gyration phase angle alongthe wave magnetic field perpendicular to the wave electric field in order tominimize the change in energy. Bunching happens simply because electronsgaining energy on the left become heavier and rotate at a reduced cyclotron

B0

v T

TE

TB

..

.

.

eff

eff

eff

bunchingcenter

v T. TE < 0

v T. TE > 0

∇

φ ∇

φ

φ

Fig. 8 Qualitative representation of the bunching process in velocity space. The circle indicatesthe rotation of the perpendicular velocity component with angle φeff against the wave electricfield E⊥ in phase space during gyration. Particles in the left (right) half space have v⊥ · E⊥ < 0(v⊥ · E⊥ > 0) and thus, according to Eq. (9), gain (loose) energy with the consequence that theireffective phase angle moves toward the direction of the wave magnetic field. On both sides thechanges in effective phase angle �φeff point upward, since the relativistic mass of particles gainingenergy increases while for particles loosing energy it decreases. This causes the bunching of theparticles perpendicular to the wave electric field along the wave magnetic field in order to minimizethe energy change. Electrons arrange at a phase where the transverse wave electric field in theirframe of reference vanishes, i.e. at v⊥ × B⊥ = 0, as they always do in collisionless plasmas

256 R. A. Treumann

frequency ωce/γ , while electrons which loose energy on the right increase theirmasses and rotate faster. Since all the particles attain the same phase angle,they bunch and moving together like a single macro-particle. One should notethat the bunching at constant magnetic field does not contribute to radiationsince the emission and absorption on both sides in Fig. 8 cancel. However,when the magnetic field is detuned the correlated motion of the bunch leads tocoherent emission, an effect exploited in the laboratory ‘gyrotron emission’. Inaddition to this bunching in the cyclotron motion there is also bunching due tothe motion parallel to the magnetic field which acts in a similar way through theterm k‖v‖ in the resonance condition which as well changes the effective phaseangle. Both bunching mechanisms compete, and partially cancel (Chu 2004).

The above arguments for bunching involve only the very simple and basicphysics of single particle motion in an electromagnetic wave in a strong mag-netic field. It neglects the very complicated (chaotic) phase space dynamics ofelectrons in a strong electromagnetic wave to which the wave piles up in maseremission. Thus they hold only for the initial linear state. Direct application isthus restricted only |δ|t ≡ |ω − k‖v0z − ωce/γ0|t � 1, where the index 0 refersto the initial values of particle velocity and energy. In addition, application isrestricted to a cold mono-energetic particle distribution only. Extensions havebeen given to loss-cone distributions by Lau and Chu (1983) and to spiralingmagnetic-field aligned electron beams by Kho and Lin (1988).

4.2 Radiation and absorption in bunching

In the bunching process radiation can either be emitted or absorbed dependingon whether ωce,eff < ω or ωce,eff > ω, respectively. This is easily seen if forinstance detuning the ambient magnetic field initially according to the first ofthese conditions. In this case the electrons in order to escape the v⊥×B⊥-electricfield rotate as a whole in the clockwise sense during bunching with the bunchcenter slipping into the right half-plane in Fig. 8 resulting in a net transfer ofenergy to the wave resulting in coherent radiation. In the opposite case energythe motion is anti-clockwise and energy is transferred to the particles. Thus,depending on their initial phase φ0 the electrons may radiate or absorb. Theaverage rate of change in their energy γ − 1 is given by

〈γ 〉 =2π∫

0

γ dφ0

2π. (12)

On the basis of this expression, the kinetic energy transfer efficiency at time t isdefined through

ηγ (t) ≡ − 1γ0 − 1

t∫0

〈γ 〉dt (13)


which when expanded with respect to time gives the linear efficiency at |δ|t � 1in the form

ηγ ,lin(t) ≈ e2E20/2m2

ec2

γ0(γ0 − 1)

[v2⊥0|δ|12ω

(ω2 − k2zc2)t4 −

(1 − v2⊥0

2c2

)t2

]. (14)

This expression shows that the emission on the short time scale is ∝ (|δ|t)4,while absorption is ∝ (|δ|t)2. Thus initially absorption dominates until emissiontakes over. Synchronism is maintained until |δ|t ∼ π . This yields the followingratio for the emitted to absorbed energies:

Wem

Wabs∼ (v⊥0/c)2

1 − (v⊥0/c)2 , |δ|t ∼ π . (15)

So, as expected, emission efficiency decreases with decreasing perpendicularelectron energy. These expressions remain valid for a cold particle distribu-tion fv⊥ ∝ δ(v⊥ − v⊥0)/v⊥ where v⊥0 is the bulk perpendicular speed of theparticles. For warm distributions with finite velocity spread one would have tointegrate all these expressions over the distribution function in order to obtainthe emission and absorption coefficients. However, the above expressions forthe cold component indicates that emission is nothing else but the generationof a negative absorption coefficient, and this makes up the similarity to a maser.

The above emissivities and absorptivities which are valid for one single elec-tron (or a bunch of non-interacting zero temperature relativistic electrons)could be generalized to other distributions simply by integrating over the dis-tribution weighted expressions. It is, however, more straightforward to deter-mine them in a plasma stability approach. Emission of radiation can then, in aplasma physical picture, be interpreted as a simple (fluid-like) plasma instabilitypumping a free space electromagnetic mode (Chu and Hirshfield 1978; Winglee1983). To this end one solves the linearized relativistic Vlasov equation for theelectron-distribution function

∂tf1 + v · ∇f1 − e v × B0 · ∂pf1 = e (E + v × B) · ∂pf0, (16)

for the disturbed distribution f1(t, x, p) in the presence of the uniform back-ground magnetic field and the undisturbed distribution function f0(p), wherep = γ v is the relativistic momentum. Taking the undisturbed distribution asone of the cold though relativistic plasma f0 = δ(p‖)δ(p⊥ − p⊥0)/2πp⊥ andusing conventional methods to solve the linearized Vlasov equation (16) andMaxwell’s equations for plane waves of frequency ω and wave number k yieldsthe linear dispersion relation

ω2 − k2‖c2 = ω2pe

γ0

[ω

ω − ωce/γ0+ k2⊥v2⊥0(1 − ω2/k2‖c2)

2(ω − ωce/γ0)2

]. (17)

258 R. A. Treumann

The real k, complex ω = ωr + i� solution to this expression is shown in Fig. 9(Chu and Hirshfield 1978) (this was the paper which led Wu and Lee (1979)to start considering the relativistic correction in the development of their suc-cessful theory of terrestrial kilometric radio emission from the aurora). Onerealizes that under certain conditions which coincide with the bunching processthe two possible free space electromagnetic modes (the ‘fast’ RX and ‘slow’ Zcircularly polarized waves) propagating in the plasma can be directly amplifiedby the plasma. The important conditions are that the plasma must be relativisticeven if weak, and that it must be extremely dilute with ω2

ce/ω2pe � 1 as already

mentioned in the introduction to this paper. Note that it is easy to derive theabove phase bunching conditions also in this plasma case by inspecting the evo-lution of �ωce,eff = k‖�v‖ − �γωce/γ

2 under the evolution of particle energy[see, e.g., Chu (2004), his Eq. (73)].

Instability under these conditions for both modes occurs close to theelectron–cyclotron frequency. Whether the amplified slow wave can escapefrom the plasma is a different one and - is difficult to answer. Analytical andnumerical calculations have been presented by Kho and Lin (1988) for the slowwave in a field-aligned beam plasma system and γ0 = 2, ωce = 2ωpe findinga strong instability. It seems that the slow wave can be more easily be madeunstable when a beam along the magnetic field is present in the plasma. An-other extension of the above theory has been given by Lau and Chu (1983)to a loss-cone plasma which applies to magnetically confined plasmas of thekind present in confinement devices and in many natural systems. This will bediscussed briefly in the next subsection.

fast fast

slow

slow

ω /

ωr

pe

Γ /ω

pe

a b

00 5 10 15 20 0 5 10 15 20 25

5

10

15

20

25

0

5

10

15

20

25

k c/|| ωpe k c/|| ωpe

10-3

Fig. 9 Dispersion relations ωr(k‖) of the two electromagnetic free-space modes, the ‘fast’ and‘slow’ waves, in a cold relativistic plasma and their growth rates �(k⊥) (after Chu and Hirshfield1978). Note that the scale on the growth rate is the same as on the frequency except that thegrowth rate is multiplied by a factor of 10−3. Hence, the growth rates are only 0.1% of the fre-quency for the chosen parameter range of a weakly relativistic γ0 = 1.02 underdense plasmawith ωce/(γ0ωpe) = 10. With this normalization the unstable ‘fast’-mode branch is amplified at afrequency very close to the electron–cyclotron frequency (ωr ≈ 10ωpe ≈ ωce. The slow wave isamplified at a slightly lower frequency


5 Electron–cyclotron maser theory

In the following we go into greater detail of the electron–cyclotron maser mech-anism. We start with a review of the loss-cone maser even though it has becomehighly improbable that it is of the importance which had been originally attrib-uted to it. We then come to the mechanism of the ring-shell maser and, finallyto the question of how the magnetic field-aligned electric potential drops canbe generated which will become the subject of the next section.

5.1 Review of the loss-cone maser

Lau and Chu (1983) following Chu and Hirshfield (1978) considered thefollowing problem: Let a right-handed polarized electromagnetic wave withwave frequency close to the electron–cyclotron frequency propagating along astrong ambient magnetic field interact with a warm weakly relativistic loss-conedistribution of electrons

f0(p⊥, p‖) = A(p⊥)2j exp

[ −p2

(�p)2

]. (18)

An example of a loss-cone distribution as observed in the Earth’s auroral regionis shown schematically in Fig. 12. Such distributions imply that there the prob-ability to find a particle at small pitch angles is zero, describing totally emptiedloss cones in a mirror magnetic field geometry and had been investigated previ-ously by Dory et al. (1965) in the context of electrostatic loss-cone instabilitiesin hot non-relativistic plasmas. A is a normalization constant, and j > 0 is theloss-cone index. The above distribution is a relativistic distribution if properlynormalized as

∫d3pf0 = 1. For j = 0 the distribution becomes the famous

Boltzmann–Jüttner distribution. �p is a measure of the electron temperaturekBT = mec2[1 + (�p)2/m2

ec2] 12 − mec2. The distribution peaks at

√j�p. Hence

for j �= 0 there is a ‘population inversion’ in p⊥ indicating ‘excitation’ of elec-trons as necessary in masers.

Linear Vlasov-Maxwell theory of the same kind as given in the previoussubsection becomes slightly more involved due to the presence of the loss-conefactor. The dispersion relation (2) replacing (17) now becomes

ω2 − k2‖c2 = 2πω2pe

∞∫0

∞∫−∞

dp‖f0

γ

[ω − k‖p‖/m − eγ

ω − k‖p‖/meγ − ωce/γ

− p2⊥(ω2 − k2‖c2)

2γ 2m2ec2(ω − k‖p‖/meγ − ωce/γ )2

], (19)

an expression which has to be solved numerically. Solutions are shown in Fig. 10and 11.

260 R. A. Treumann

0.02

0.00

0.04

0.06

0.08

0.00.0

0.4

0.8

1.2

1.6

0.2 0.4 0.6 0.8 1.0

Γω

Γ/ω

ω /ω

ω /ω = 0.5

/ω

ce

ce

ce

r

r

pe ce

k||c

kBT=50 keV

j = 1

j = 2

j = 1

Fig. 10 Growth rate �/ωce and frequency ωr(k‖)/ωce of the parallel propagating unstable electro-magnetic mode excited in the presence of an energetic electron loss-cone distribution. The loss-coneparameters chosen are j = 1, 2. The electron temperature is kBTe = 50 keV, and the plasma-to-cyclotron frequency ratio is ωpe/ωce = 0.5 (after Lau and Chu 1983). The frequency (dotted line)changes very little over the unstable domain in k‖. The small wave numbers of the fast mode aredriven unstable at a substantial growth rate of several percent of the electron–cyclotron frequency

0.02

0.00

0.04

0.06

0.08

Γ/ω ce

40 80 120 160 2000kBT(keV)

Γωr

ω /ω = 0.5pe ce

k||= 0

j = 2 j = 2

j = 2

j = 1 j = 1

j = 1

ω /ω pe ce

ω /ω

r

ce0.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

0.4

0.8

1.2

1.6

k T= 30 keVB

Γ

ω r

Fig. 11 Left: The growth rate and frequency of the loss-cone driven maser emission as functionof electron temperature. For instability the electron temperature must exceed a certain thresholdvalue which decreases with increasing loss-cone parameter j. Increased ‘emptiness’ of the loss-conefavors the emission and thus the maser action. Right: Dependence of growth rate and frequencyof the loss-cone driven maser emission as function of the ratio between plasma frequency andelectron–cyclotron frequency at electron energy kBTe = 30 keV. The important information thatcan be taken from this figure is that the maser instability occurs only in underdense (ωpe < ωce)plasmas and in a narrow range of ratios between plasma frequency and cyclotron frequency (afterLau and Chu 1983)

What is hidden in the above expression is the location where the free energyin the distribution function is located. This free energy is necessarily a sourceof radiation in the electron–cyclotron maser. It can, however, be identified byinspecting (16) more closely. The above dispersion relation has resulted froman integration over the right-hand side of (16) along the unperturbed particleorbits. This integration yields an expression for the dielectric function ε whichwe write down here for the RX-mode only:


εRX(ω, k) = 1 + A − N2‖ −iA N‖N⊥

iA 1 + A − N2 0N‖N⊥ 0 1 − N2⊥

. (20)

N‖,⊥ = k‖,⊥c/ω are the parallel and perpendicular indices of refraction, respec-tively, of the wave under consideration, in this case the RX-mode, and thequantity A which follows from (4–5) is given by

A = π

2

ω2pe

ω2

∞∫−∞

du‖∞∫

0

u2⊥du⊥(γω − k‖u‖ − ωce)−1

×[ω

∂

∂u⊥+ k‖

γ

(u⊥

∂

∂u⊥− u‖

∂

∂u⊥

)]f0. (21)

For simplicity the massless components of the electron momentum u‖ = p‖/me,u⊥ = p⊥/me have been introduced here. This expression shows that the paral-lel momentum component and its derivatives are compensated by the resonantdenominator (γω − k‖u‖ − ωce)

−1 ≈ iπδ(γω − k‖u‖ − ωce). The only depen-dence which remains is the partial derivative with respect to the perpendicularmomentum ∂f0/∂u⊥ which determines the sign of the maser growth rate �. Thegrowth rate is positive only for positive perpendicular velocity gradients in f0.Population inversion, required for maser emission, thus implies that the par-ticle distribution does not decay monotonically with increasing perpendicularmomentum u⊥ like it is found in thermal equilibrium distributions. Instead itis required that ∂f0/∂u⊥ > 0. Figure 12 shows such a behavior in the region ofthe loss-cone along the right-hand part of the elliptic line. The relevance of thisline is discussed below.

Figures 10 and 11 do in principle already contain all the information about theeffect of the loss-cone maser. Its efficiency increases the wider the loss-cone is,i.e. the larger j, and the higher the electron energy is. The electron temperaturemust exceed a certain threshold for the maser to overcome absorption. How-ever, in this calculation-here is no assumption of the effect of a possible plasmabackground which should usually be expected to be present under naturalconditions where the loss-cone particle distribution represents, however, adilute energetic tail distribution of magnetically mirroring particles on a muchdenser background. Hence the question arises as to how a maser could workin presence of dense background plasmas? It turns out that this is the keyquestion to the whole maser project under natural conditions. Intuitively, onewould suggest that a less energetic and isotropic background plasma will inhibitmaser action by imposing a high absorbing power. This is basically true as allinvestigations have shown, leading to the result that it is instrumental for theelectron–cyclotron maser to have either no background at all or at least a verydilute one in order to minimize background absorption. Before proceeding wewill have to more closely analyze the resonance condition (1) and afterwardsreturn to the most efficient particle distributions in maser action.

262 R. A. Treumann

Fig. 12 Sketch of an auroral electron-distribution function in the Earth’s auroral region includingthe loss cone (after Ergun et al. 1993). The loss cone is the triangular shape on the left of thedistribution function in velocity space, where one finds a lack of electrons. These electrons are, inthe case of the auroral region, lost to the atmosphere since their velocities are mostly parallel tothe magnetic field. Particles at velocities with such angles with respect to the magnetic field are notreflected by the magnetic field and thus do not return into the plasma. They are lost. The ellipsedrawn inside the loss-cone shows the position of the resonance ellipse for loss-cone maser radiation(see text)

5.2 Analysis of the resonance condition

The main contribution to the cyclotron maser instability comes from parti-cles satisfying the resonance condition (1). This resonance condition is thedenominator under the integral sign which appears for instance in (24), (21)or generally in the explicit form of the electromagnetic dispersion relation (2).This dispersion relation requires explicit knowledge of the relativistic dielec-tric function ε(ω, k) as has been given in (2). The maximum contribution to theintegral in (3) is provided by those particles satisfying the condition of vanishingdenominator. In non-relativistic plasmas, these are just those particles whichmove along the magnetic field with parallel phase velocity of the wave shifted bythe cyclotron frequency. Resonant particles experience the stationary electricwave field and are thus either accelerated or retarded. In the relativistic case thecyclotron frequency is modified by the relativistic factor ωce/γ , and hence theresonant frame depends on particle energy and differs for all particles. Settingthe relativistic resonance condition (1) to zero, the resonance condition can berewritten in terms of the electron velocity components v‖, v⊥ in the form of theequation of an ellipse

(β‖ − β‖0)2

a2 + β2⊥b2 = 1, (22)


where β‖,⊥ = v‖,⊥/c. The center of this ellipse is shifted out of origin along thev‖-axis by

β‖0 = N‖N2‖ + l2ω2

ce/ω2

. (23)

The half axes of the ellipse are given by

a2 ≡ b2

1 + (N‖ω/lωce)2

b2 ≡ 1 + (N2‖ − 1)(ω/lωce)2 (24)

There is a set of resonant ellipses, one for each value of l. Figure 13 showss schematic of the resonance curves in the velocity space for a non-relativisticcase (curve a), when the resonance line is a straight line, and the relativistic case(b) when it is an ellipse, as in Fig. 12 shifted to the position of the loss-cone ina loss-cone plasma including a thermal (cold) electron component. It is easy tosee that these ellipses in velocity space are all confined entirely to the interior ofthe circle with radius v = c. Since the ellipses are the geometric locations of theresonances in velocity space, integration in (19 (or any other equivalent equa-tion) has to be performed along these ellipses. Moreover, one observes that forfinite parallel wave numbers k‖ �= 0, i.e. for oblique propagation to the ambientmagnetic field there will always exist a displaced resonance ellipse for givenharmonic l which has to be positioned in such a way that for a given harmonicwave ω = ω(k‖, k⊥) it collects all the contributions from the particles whichcarry the free energy in order to maximize wave excitation. (One such ellipse isshown in Fig. 12 superimposed on a measured though still schematic loss-conedistribution.) Thus for small parallel phase velocities, the ellipse becomes highlyelongated with parallel phase velocity small against the velocity of light, while

v T/c

v ||/c

loss-cone

thermal electrons

non-thermalelectrons

a

b

Fig. 13 Resonance lines for the non-relativistic case a and the relativistic case b in the velocityspace of a loss-cone distribution of hot non-thermal particles and a thermal cold electron compo-nent. The non-relativistic resonance line is a straight line, while the relativistic resonance line isellipse (as already shown on the data displayed in Fig. 12). This ellipse has been shifted into theloss-cone

264 R. A. Treumann

in the opposite case when the parallel phase velocity is large against the velocityof light, the ellipse becomes nearly circular.

The observation that the unstable frequency in the relativistic electron–cyclo-tron maser falls below the electron–cyclotron frequency is somewhat disturbingsince the RX-mode has a low-frequency cutoff which is given by (8) which isclearly above ωce. For ωce � ωpe this expression simplifies to ωx ≈ ωce(1 +ω2

pe/ω2ce) > ωce, slightly above the electron–cyclotron frequency. The unstable

RX-maser wave to be able to propagate this expression has to be examined forthe relativistic case, which has been done by Pritchett (1984a,b), (Le Quéau etal. 1984a,b). Pritchett (1984b) found that the RX cutoff for a weakly relativisticMaxwellian distribution depends on the electron energy through the parameterµ = mec2/kBTe. This is illustrated for the particular case of k = 0 in Fig. 14.The frequency ω of the RX mode crosses the electron–cyclotron frequencyfrom above to below at µ ≤ 3

2 (ω2ce/ω

2pe) and for a certain range below this value

stays below ωce. For ωce/ωpe = 10 the transition occurs for electron energieslarger than 150 eV. Hence the electron–cyclotron maser unstable RX mode canindeed propagate below ωce in a limited electron energy range.

Let us briefly discuss the relevance of the resonance ellipse for the loss-conemaser as illustrated schematically in Fig. 12. The resonance ellipse with its right-hand shoulder passes along the loss cone where ∂f0/∂u⊥ > 0. Here the wavethat satisfies the resonance condition along the ellipse becomes amplified. Theleft-hand shoulder of the ellipse on the other hand encounters a negative gradi-ent in the velocity distribution and thus causes absorption and damping on thesame wave. However, the number of absorbing particles is very small in com-parison to the number of emitting particles such that along the resonance ellipseemission dominates. Any other resonant ellipse put into the distribution wouldbelong to different resonant waves and would cover only absorbing particles.Hence, the only wave which will become amplified is the one which generatesthe resonance ellipse along the boundary of the loss cone. Clearly, the numberof particles with positive perpendicular velocity space gradient in the case ofthe loss-cone is small, and the loss-cone maser will therefore be rather weak.

This poses the question for a more efficient particle distribution than theloss-cone distribution. The first observation is that any resonant ellipse willalways cover only a small amount of resonant particles unless the distributionfunction is exotic. For instance, if the resonant ellipse degenerates to a circleand the distribution is ringlike, the number of particles with positive perpen-dicular velocity gradient will become large and, hence, the emission becomesmuch stronger. The resonance condition degenerates into a circle for N‖ = 0which implies strictly perpendicular propagation which is possible only for theRX-mode in magnetoionic theory (Fig. 1). From Eq. (22)–(24) one learns thatin this case β‖0 = 0. The resonance line is centered at the origin. Moreover,

a = b and the resonance line is a circle of radius (1 −ω2/l2ω2ce)

12 . For the funda-

mental l = 1 this implies that ω < ωce. Instability and emission will thus be at afrequency which is slightly below the non-relativistic cyclotron frequency. Thusa particularly promising distribution function for intense electron–cyclotron


Fig. 14 The relativistic RX-mode cutoff, ωx, versus the inverse particle temperature µ, and forωce/ωpe = 10 and the marginal case of wave number k = 0 at which the wave degenerates and isreflected. For orientation also shown is the k = 0 perpendicular electrostatic first-harmonic Bern-stein mode. This mode is strictly perpendicular and separates from ωx at large µ (after Pritchett1984a)

maser emission is a hot ring distribution, which poses the question of whetheror not such ring distributions can exist under natural conditions.

Before investigating this question let us turn to the generation of emission.This is in the RX mode as previously argued. Setting the determinant of (21)to zero, one obtains the dispersion relation for the RX mode Le Quéau et al.(1984a)

1 − N2 + (2 − N2⊥)A = 0. (25)

For k = 0, one obtains A = − 12 . In this limit the imaginary part of A vanishes:

Ai = 0. On the other hand, for k‖ = 0 and k⊥c/ωce → 1 and assuming thatemission is close to the fundamental, |ω − ωce| � ωce, which is satisfied in viewof the above discussion, the real part of A is small. To first order one has that

� = − 12ωceAi. (26)

Then in the semi-relativistic approximation where γ is expanded for small u2/c2

and 1/γ ≈ 1 − u2/2c2 the expression for A becomes

A = π

2

ω2pe

ω

∞∫−∞

du‖∞∫

0

du⊥ u2⊥∂f0(u⊥, u‖)/∂u⊥

ω − ωce + ωceu2/2c2 , (27)

where u2 = u2⊥ + u2‖. Since the growth rate will be small such that � � ωce canbe safely assumed, and defining u2

0 = 2c2(1 − ω/ωce the resonant denominator

266 R. A. Treumann

can be replaced by a delta-function yielding

Ai = −π2c2

2

ω2pe

ωωce

∞∫−∞

du‖∞∫

0

du2⊥ u⊥∂f0

∂u⊥δ(u2 − u2

0). (28)

One concludes that for strictly perpendicular radiation ω < ωce, permittingperpendicular maser instability and emission only at frequencies below theelectron–cyclotron frequency are permitted.

Applying these expressions to the loss-cone distribution (18) one definesx2

0 ≡ meu20/(�p)2 and evaluates the above integrals to obtain an analytic expres-

sion for the growth rate in perpendicular emission

� = √π

2j+1

(2j + 1)!!ω2

pe

ωωce

mec2

�p2 x2j+10 ex2

0

(j − 2(j + 1)

2j + 3x2

0

)(29)

from which it is clear that � vanishes for vanishing last bracket in this expres-sion. At larger x2

0 absorption dominates. Hence the range of applicability ofthe resonance circle in this case to the loss-cone distribution is rather restrictedas discussed above. We will thus have to turn to another distribution func-tion which is more promising for generating intense maser emission, the ringdistribution.

Pritchett (1986a) has performed numerical simulations of the weakly relativ-istic loss-cone maser instability. Figure 15 shows his results for the total emitted

Fig. 15 Numerical simulations of the loss-cone maser instability in strictly perpendicular directionfor loss-cone parameter j = 2 and various ratios ωpe/ωce (left), and for several oblique angles atωpe/ωce = 0.05 (right). The normalized total emitted electromagnetic energy in the radiation isshown as a function of time that has been normalized to the electron–cyclotron period. Normaliza-tion is to the initial perpendicular kinetic plasma energy. Note that the exponential increase duringlinear instability which is followed by saturation. The larger the ratio ωpe/ωce, the weaker is themaser radiation. Similarly, the smaller the emission angle against the magnetic field the weaker isthe radiation (after Pritchett 1986a)


electromagnetic energy density. Several remarkable results can be read fromthis figure. First, the emitted wave energy in all cases passes through an initialexponential rise phase which shows that the maser instability initially can bedescribed by linear theory. After a certain time it reaches saturation. the levelof which depends on the plasma to cyclotron frequency ratio. The smaller thisratio the higher is the saturation amplitude. Also, the rise time (growth rate) isa function of this ratio. It is longer for smaller ratio simply because less particlesparticipate in radiation. However, the more particles are involved the strongeris the self-limitation by self-absorption of the radiation. In addition, the morethe angle of radiation emission turns away from the perpendicular directionthe weaker is the emission, and at an angle of ∼ 70◦ it drops to backgroundnoise level, implying that emission takes place in a narrow cone perpendicularto the magnetic field. Finally, the emptier the loss-cone which means the steeperthe perpendicular gradient in velocity space, the more intense is the radiation.However, altogether these simulations show that the loss-cone maser is ratherinefficient since only very few particles are actively involved into the emission,and other distribution functions have to be investigated.

5.3 The ring-shell maser

The observation that in ring distributions the emission at k‖ ≈ 0 is about per-pendicular to the magnetic field and that the fundamental emission is beneaththe electron–cyclotron frequency restricts the emission at the first place to theRX mode. Figure 16 (top) shows the different strictly perpendicular wave dis-persion branches for the first three harmonics l = 1, 2, 3 in a plasma dominatedby such a cold ring-shell distribution

f0(p⊥, p‖) = 12πp⊥

δ(p⊥ − pR)δ(p‖). (30)

In such a distribution thermal effects are neglected, and it is assumed that thethermal background is much weaker such that it plays only a minor role. HerepR is the ring momentum which in Fig. 16 is taken as pR = 0.4c, and ωce/ω−pe =7.5. These branches are indicated by the numbers at each of the curves. The topof the figure shows the coupling between the various branches: RX and purelyelectrostatic perpendicular Bernstein modes. The coupling regions are respon-sible for the maser instability. Excitation of the RX-mode is not in a directway. The perpendicular gradient in velocity space drives relativistic Bernsteinmodes which at the electron–cyclotron harmonics couple to the RX-mode. Inthe non-relativistic case such coupling can occur only for extreme temperatureanisotropies. In the lower part of the figure the electron–cyclotron maser growthrate �(k⊥) is given as function of the perpendicular wave number for all threeharmonics shown. The growth rate is non-zero just below the harmonic wavenumbers k⊥c/ωce = l and for ω < ωce and decreases rapidly with increasing l,and at small k⊥ increases as kl⊥. Largest �s are found at l = 1, the fundamen-

268 R. A. Treumann

00 1 2 3

10.02

0.04

2

3

0.000 1 2 3

/ce

ω ω

k c / ce ωTk c / ce ωT

v /ce

ω Γ

Fig. 16 Weakly relativistic dispersion curves for the RX-modes in the electron ring-shelldistribution for perpendicular propagation k‖ = 0, k⊥ �= 0 and the first three lowest harmon-ics l = 1, 2, 3 (after Pritchett 1984b with permission by the American Geophysical Union). Left:Real frequency dispersion curves showing the coupling between the RX- and Bernstein modes atthe harmonics, numbered from 1 to 6. Right: Growth rates � for the three harmonics. Instabilitycoincides with coupling ranges below the lth harmonics where they maximize. However, the unsta-ble ranges are quite broad as expected for relativistic effects. Moreover, note that � �= 0 also belowl = 1 (labeled 1,2) indicating coupling to the Z-mode, i.e., the slow branch of the RX-mode whichcannot escape the plasma

tal. It is expected that in the relativistic or ultra-relativistic regimes the growthrates will overlap over a much broader range leading to a broad synchrotron-like emission spectrum. Possibly, due to propagation effects the fundamentalcould be reabsorbed in the plasma allowing only the higher harmonics to escapeand causing a cut-off on the observed spectra. Note that � �= 0 also below l = 1(labeled 1,2) indicating coupling to the Z-mode, the slow branch of the RX-mode which cannot escape the plasma.

When adding a small cold background component, the growth rate is sup-pressed gradually with increasing cold fraction due to the increased waveabsorption. This absorption is strongest at the fundamental and is of lessimportance at higher electron–cyclotron harmonics implying that the funda-mental harmonic in the presence of a cold background is suppressed strongestand what remains are higher though weaker harmonics. Moreover, for increas-ing emission angles (not shown here) the maser-growth rate decreases steeplysimilar to the case of the loss-cone distribution. The reason for this decrease isthat the resonance circle becomes an ellipse which does not cover anymore thepositive derivative range on the full ring-shell distribution.

In order to obtain a simple analytical expression for the condition when themaser instability of the ring-shell maser will set on, we consider the dispersionrelation (2) with the above undisturbed distribution (30) for k‖ = k⊥ = 0 andωpe/ωce � 1 and fundamental wave frequency close to the electron–cyclotronfrequency, ω ≈ ωce. Then the dielectric tensor components ε13 = ε23 = 0, andthe RX-mode dispersion relation reduces to a cubic equation


ω(γRω − ω2ce)

2 = ω2pe

2γ

[(γ 2

R + 1)ω − 2γRωce

](31)

which in the non-relativistic case γR = (1 + p2R/m2

ec2)1/2 → 1 just reproducesthe Bernstein and RX-modes ω = ωce and ω = ωx. In the relativistic case forfinite γR − 1, one has ω/ωce = 1 + δ and

δ = ω2pe

2ω2ce

− (γR − 1) ± 12

ω2pe

ω2ce

[1 − 4(γR − 1)

ω2ce

ω2pe

]1/2

. (32)

This expression becomes complex and thus unstable for a resonant electronkinetic energy

γR − 1 >14

ω2pe

ω2ce

(33)

exceeding a threshold which is determined by the small ratio of the plasma tocyclotron frequencies. At unstable frequency ωr < ωce the growth rate of themaser is γR → (pR/

√2c)ωpe.

A simple extension of this approach is to a complete three-dimensional shellwhich has distribution function

f0(p⊥, p‖) = 12πpS

δ(

p2⊥ + p2‖ − p2S

). (34)

In the complete shell case the dispersion relation (32) is replaced by

δ = ω2pe

2ω2ce

− (γS − 1) ± 12

ω2pe

ω2ce

[1 − 8

3(γS − 1)

ω2ce

ω2pe

]1/2

, (35)

where γS = (1 + p2S/m2

ec2)1/2, and the condition for electron–cyclotron maserinstability indicates that instability will still occur but now at higher shell mo-menta and shell-kinetic energy

γS − 1 >38

ω2pe

ω2ce

(36)

also leading to smaller than ring-shell growth rates. This decrease is simply dueto the increased homogeneity of the pure shell distribution in the third dimen-sion. The observation of electron–cyclotron shell-maser emission from a remoteobject should thus provide an estimate of either the available free shell-energyor the plasma-to-cyclotron frequency ratio in the source region.

The simulations of the evolution of the cyclotron-maser emission by ring-shell and shell distributions are shown in Figs. 17 and 18. In such simulationsthe ring distribution has an unavoidable finite spread and for small or interme-diate relativistic momenta is thus more realistic than the extremely cold shell

270 R. A. Treumann

ap

/mc e

||p /m ce

T

p /m ce||

-0.8-0.8 -0.4 0.0 0.4 -0.8 -0.4 0.0 0.4 0.8

-0.4

0.0

0.4

0.8b

Fig. 17 The ring-shell distribution at times ωpet = 0 (left) and ωpet = 30 (right) used in the one-dimensional simulation of the ring-shell maser for pR = 0.4mec and ωce = 7.5ωpe (after Pritchett1984b with permission by the American Geophysical Union). Since the radiation cannot escapefrom the simulation box the initial ring-shell is smeared out non-linearly with time leading to thefinal, completely filled velocity space inside the initial ring in the right part of the figure

0.02

0.00

0.04

0.06

(ε Ε

2 /2)/

k.e.

0

70˚

0 25 50 75 100

0.01

0.00

0.02

0.03

petω

90˚

80˚

70˚

90˚

0 25 50 75 100

petω

Ring Distribution Shell Distribution

Fig. 18 Top: Time evolution of the total transverse electric energy in radiation with pS = 0.4mecand ωce/ωpe = 7.5 at the two emission angles 90◦ and 70◦ for the ring-shell maser Bottom Thesame evolution for the shell maser at the three emission angles 90◦, 80◦, and 70◦ versus time ωpet(after Pritchett 1984b with permission by the American Geophysical Union). The radiation energyhas been normalized to the initial kinetic energy. After a short exponential growth phase of theemission the power in the ring maser saturates for perpendicular emission at about 6%. At thesmaller angle the radiation is spiky and after having reached a temporary maximum at ωpet = 25, itdecays away probably due to the strong non-linear effect imposed by the perpendicular component.The behavior of the energy for the shell maser is similar except that the total intensities reachedare lower and the growth is retarded

distribution. These simulations show that ring-shell and complete shell distri-butions indeed lead to an exponential growth phase of the emitted radiationwith the intensity of the emission and growth rate being larger for the ring-shell than for the complete shell distribution. The reason is that the completeshell distribution has a higher symmetry and thus is less unstable than the


ring-shell distribution. The main result in both simulation cases is that forsufficiently large perpendicular electron momenta in the ring or shell distri-bution maser instability sets on since the distribution provides something likean inverted population in energy space and thus fakes the quantum effect ofcorrelated electrons.

In the simulations the radiation saturates at later time. This is a nonlin-ear effect, which we will briefly discuss here, as it suggests that in nature themaser would really saturate within a couple of electron plasma periods, forthe parameters of the simulations shown here in a few tens of ω−1

pe . The elec-trons loose energy to the radiation as can be seen from the positive growthrate. This energy loss will in principle diminish the transverse momentum spacegradient in a purely classical way scattering electrons away out of the positivegradient to lower momenta. This effect though very weak causes the observedsaturation. However, this saturation is an artifact of the simulation since thesimulation does not allow the radiation to escape. This would be correct forany plasma mode which is trapped in the plasma and thus cannot leave. Butradiation above the cut-off can practically freely leave the plasma being lost,and then the small energy loss of the particles is practically not appreciated ifonly the distribution rebuilds itself by external forces. Here, in the simulationsthis is inhibited. The radiation stays in the simulation box, being in resonancewith the energetic electron component and has plenty of time to react on thedistribution until the latter has become depleted. Then the final level of the radi-ation is reached where it stays until the simulation ends. For natural applicationto emitted radiation saturation plays a role only if it is confined in the totalradiating volume. Otherwise it will immediately leave, encounter other plasmaswhere it can be absorbed or leave to free space. In this sense a quasi-lineartreatment of the maser emission as one can find it in many of the publishedpapers is of little relevance to natural application. These considerations holdfor weakly relativistic ring-shell plasmas. If the plasma becomes highly relativ-istic, two effects will modify the conclusions. One is the beaming effect on theradiation which narrows the emission angle. The other is the gradual overlapof the various cyclotron harmonics which will lead to a broader more synchro-tron emission-like but more intense than incoherent radiation spectrum whilethe low frequency cutoff of the emitted spectrum will remain at a frequencyclose to though below the electron–cyclotron frequency. Such conditions can beexpected in many highly relativistic astrophysical objects like binaries, pulsarmagnetospheres and AGNs. Closeness to ωce, however, depends on the avail-able bulk γS. For large γS the cutoff could be substantially below ωce and ifincorrectly interpreted could cause an underestimate of the magnetic field inthe maser source region. Louarn et al. (1986) has given an attempt to accountfor such a relativistic effect. The main result is that even though the growthrate of the maser mechanism increases with γS, the relativistic overlap of theharmonics and the resulting spreading of the spectrum decreases the emissiv-ity at the single harmonics since the energy is spread over a wide range infrequencies.

272 R. A. Treumann

5.4 Ring-beam maser

For completeness we note that the ring-shell maser has been extended to includethe propagation of the ring-shell distribution along the magnetic field (Freundet al. 1983) though so far only for the case of a dense background plasma withonly a thin suprathermal propagating beam. This case is of practical interest forsystems containing dense background plasmas traversed by relativistic beams.In this case the distribution becomes a ‘hollow beam’ distribution

fhb(u⊥, u‖) = exp(−ζ 20 )

π�u2⊥√

π�u2‖[1 + ζ0Z(ζ0)]

× exp

(− (u‖ − u‖0)

2

�u2‖− (u⊥ − u⊥0)

2

�u2⊥

), (37)

where as before u‖ = p‖/me, u⊥ = p⊥/me, �u‖, �u⊥ are the thermal spreadsof the distribution in parallel and perpendicular direction, respectively, ζ0 =−iu⊥0/�u⊥, Z(ζ0) the plasma dispersion function, u‖0 is the beam velocityalong the ambient magnetic field, and u⊥0 is the ‘population inversion’ of thevelocity distribution in perpendicular direction. This distribution is to someextent a generalization of the ring-shell distribution to the inclusion of a beam.Such distributions might be of interest in astrophysical application like jetswhere fast plasma beams are the rule. If such beams, in addition, exhibit apopulation inversion caused for instance by a field-aligned electric potentialdrop (parallel electric field), the above distribution offers a model of such a‘hollow beam’. Maser instability of such a hollow beam has been investigatedin the presence of a cold background plasma by Freund et al. (1983). The mostimportant result of the linear treatment of the hollow beam is summarized inFig. 19. From this figure it is obvious that the RX-mode is excited strongest atthe second harmonic l = 2, while the LO-mode has maximum excitation at thefundamental l = 1.

5.5 Inhomogeneous medium

So far we have dealt with only a homogeneous medium. The electron–cyclotronmaser radiation source plasma as paradigmatically represented by the AKRsource which is located inside the auroral cavity is known to be violently inho-mogeneous on all scales. On the macroscopic scale which we have identifiedearlier to be of the order of 100 km in latitudinal extension and possibly a few1,000 km in longitudinal extension it is bounded by dense plasma walls whichinhibit propagation out of the source region. This inhomogeneity is even morerestrictive for the ring-shell distribution since the electron–cyclotron maser actsmost effectively in perpendicular direction. It is thus unclear whether or notthe radiation once excited can ever leave the radiation source. Similar argu-ments will apply to any other system than the Earth’s or planetary auroral


∆u|| =∆u T=0.11c

u T

0u||0

= 0.244c= 0.140c

75˚

90˚

60˚

60˚

90˚

75˚

∆u|| =∆u T=0.11c

u T

0u||0

= 0.244c= 0.140c

0.05

0.05

0.00 0.00

0.10

1.95

2.05

2.15

90˚75˚

60˚ 60˚

75˚90˚

ωpe/ωce0.6 0.8 0.6 0.8

RX-mode LO-mode

rce

ωω

/ce

ωΓ

/(

) max

Fig. 19 The maximum growth rates for the RX-mode (left) and LO-mode (right) in hollow-beammaser emission (after Freund et al. 1983) vs. ωpe/ωce and for different propagation angles. Notethat the RX-mode is excited only at the second harmonic l = 2, while the LO-mode has maximumgrowth rate for the fundamental

regions depending on the relative geometries of the magnetic field and plasmadensity. It is then tempting to assume that only obliquely emitted radiationcan ultimately escape. However, the efficiency of the maser drops steeply withincreasing emission angle, and extraordinarily high radiation temperatures can-not be expected for oblique propagation.

Figure 20 shows two cases where radiation from an embedded localized elec-tron–cyclotron maser source emitted about perpendicular might leave the cav-ity. On the left the RX rays encounter the RX mode cutoff which is mostprobably along the inclined magnetic field-lines in the mirror geometry. Herethe rays become reflected thereby increasing their angle. This increase in thepropagation angle will necessarily let them leak out of any further resonantamplification. Further gradual increase of the angle transforms them continu-ously into the completely circularly polarized R-mode and let them escape tofree space parallel to the magnetic field. Other smaller scale inhomogeneitiesrelated to the presence of density fluctuations, electron and ion holes will scatterradiation as well. However, the most serious restriction is actually given by thecavity.

The mechanism on the right is different (Le Quéau et al. 1984b; Le Quéau1988; Louarn and Le Quéau 1996a,b; Louarn 2006). In this case the RX modecutoff is incomplete, and the RX-mode reaching the boundary of the plasmacavity can couple to the LO mode which propagates in the external dense plasmaregion and can freely escape to space. This is what happens in an non-ideal wave

274 R. A. Treumann

Source

up

war

dp

rop

agat

ion

X-mode X-mode

O-mode

Plasma density

Production ofO-mode

Plasma cavity

RX-cutoff

B-field

RX-mode

ray pat

h

ec-maser source

RX-mode ray path

Dense Atmosphere

PlasmaCavity

PlasmaPlasma RX-cutoff

Fig. 20 Schematic of an auroral cavity which traps the electron–cyclotron maser radiation. Left:Complete trapping. The RX-mode cutoff does not allow the radiation to pass into the plasma, butthe RX-mode rays emitted from the electron–cyclotron-maser source perpendicular to the localfield are reflected at the cutoff in the inclined fields and can after several reflections escape to freespace. Right: Incomplete trapping (after Louarn 2006). Radiation hitting the RX-mode cutoff at theboundaries of the plasma cavity is allowed to couple to the external LO-mode like in an incompletewave-guide. Rays making it up to the region above cutoff can freely escape in the RX mode, as onthe left of the figure

guide and may explain the occasional observation (Louarn 2006) of relativelyintense LO mode radiation from the auroral plasma cavity. Since direct ampli-fication of the LO mode in the plasma cavity in the electron–cyclotron maserprocess is by far less efficient than RX mode excitation such, a RX to LO wavetransformation mechanism provides a reasonable explanation of the LO modeobservation.

Pritchett 1986 (Pritchett and Strangeway 2002) performed full particle sim-ulations of the cyclotron maser radiation in localized sources in an inhomoge-neous plasma cavity. In the first of these papers he allowed for the presenceof several narrow irregularly distributed density irregularities elongated alongthe magnetic field in order to investigate their effect on the propagation ofthe RX mode and to check the waveguide feedback model of amplification ofCalvert 1981a,b, 1982, 1987, 1995. These simulation led to the conclusion thatthe feedback mechanism did not work efficiently. Instead, narrow inhomoge-neities were easily crossed by the ω < ωce perpendicular radiation via couplingto the slow RZ mode inside the inhomogeneity and recoupling to the RX modein the cavity at exit from the inhomogeneity with very little attenuation. Inter-estingly enough, it was found that the radiations occur in intense bursts whichform wave packets traveling at group speeds (0.1–0.2)c, typical for being closeto RX mode cutoff. Reflection at the cavity edges turned out to be quite weak,


with only 0.1% of the incident energy being reflected which supports the modelof a bad waveguide and coupling to the RZ mode instead of the LO mode.This result to some extent also contradicts the analytical calculations of Louarnand Le Quéau (1996a,b) and Louarn (2006), which favor coupling to or ratherexcitation of the LO mode at the cavity boundary. Such a contradiction is intel-ligible as the RX and RZ mode are of same polarization while the LO modehas opposite polarization. One thus intuitively expects that a wave transfor-mation at the boundary should be easier between waves of equal polarizationthan between waves of opposite sense of polarization. Excitation in the lattercase should be much weaker and thus less efficient and in addition should notproceed via transformation from one wave into the other. Rather it should pro-ceed via absorption of one wave of one sense of polarization and re-emission ofthe wave with the other polarization. The simulations suggest that this processmight be possible but is favored less than the direct transformation.

Using a complete shell distribution as suggested by FAST observations, two-dimensional simulations (Pritchett et al. 2002) have basically confirmed theseconclusions. In this case the magnetic field was allowed to have a mirror geom-etry. Again generation of bursts of radiation of 0.5 ms length were observed,and the coupling of the perpendicular RX mode to the Z mode at the boundarywas reproduced though in the two-dimensional case stronger attenuation wasfound than in one dimension, and that the part of the wave propagating in the Rmode parallel to the magnetic field was stronger amplified. However, the mostimportant observation in view of trapping of the radiation and amplificationwas that no standing wave structure was ever observed and thus waveguideamplification is irrelevant for reaching the high emissivities in the shell elec-tron–cyclotron maser. Inhomogeneity determines the propagation properties,attenuation, and coupling to the Z-mode of the originally excited ω < ωceradiation in the RX mode, and the high intensities reached are entirely due tothe direct linear excitation properties of the shell maser mechanism with nofurther macroscopic waveguide amplification necessary.

In addition, it is very interesting to find excessively bursty emission in allthese simulations which could not be explained in a simple way. This burstyradiation points on something which is hidden in the radiation mechanism itselfand which we believe is related to the generation of microscopic structuring ofthe plasma in the presence of strong field-aligned electric fields. In the followingwe therefore review the reasons for the occurrence of magnetic field-alignedpotentials and their effect on the structure of the plasma in the plasma cavityregion.

6 Electric double layers

The key to the maser mechanism is found in the presence of field-aligned elec-tric potential drops which act to accelerate electrons in one and ions into theopposite direction along the magnetic field. The possibility of such localizedpotential drops causing parallel electric fields in collisionless plasmas has been

276 R. A. Treumann

proposed half a century ago (Block 1972, 1977) and has been provisionallythough not definitely been confirmed in laboratory (Saeki et al. 1979; Leunget al. 1980) and space plasmas (Temerin et al. 1982; Boström et al. 1998; Ergunet al. 2001a; Pottelette et al. 2003).

Theoretically, the maintenance of electric double layers along the magneticfield in collisionless plasmas encounters severe and still not completely resolveddifficulties. Clearly, double layers are related to the presence of sufficientlystrong electric currents along the magnetic field. When these currents exceeda critical value they undergo instability and generate electrostatic waves. Forstrong currents the localized electric fields of these waves cannot be compen-sated fast enough, and localized potentials occur which survive for times longenough to affect the dynamics of the plasma.

Simple global relations have been derived by several authors between theparallel current strength and the potential drops which can be achieved underdifferent assumptions like Maxwellian and non-Maxwellian distribution func-tions. These relations are all oversimplified as the real electron-distributionfunctions deviate strongly from those models in the presence of electric wavefields. They actually develop into incomplete ring-shell (‘horseshoe’) distribu-tions, the presence of which we have identified as the necessary condition forthe electron–cyclotron maser.

6.1 Generation of incomplete ring-shell (‘horseshoe’) distributions

Chiu and Schulz (1978) investigated the adiabatic motion of electrons along amirror magnetic field geometry like the one realized in the vicinity of magne-tized planets, in many places in the solar atmosphere, the atmospheres of activemagnetized stars in general and in other places. They found that in the presenceof a field-aligned electric field component the concerted action of the electricacceleration of the electrons and the mirror effect of the magnetic field, whichtends to increase the pitch angle of the electrons, should produce a deformationof the initial electron-distribution function.

In addition to the prevalent loss cone in the distribution function, low-energyelectrons were excluded from the distribution, and the more energetic beamelectrons were found to be diverted to larger pitch angles. Both these effectsleading to the formation of an incomplete ring or to ring-shell distributionsof the kind discussed in previous sections and now known to be responsiblefor the electron–cyclotron maser emission in the Earth’s auroral region — andprobably at many other places as well. Without a parallel electric field thedistribution function would simply remain a loss-cone distribution. Thus it isthe electric field which — in analogy to molecular masers — excites the parti-cles and lifts them into a non-thermal higher energy level. The particles drawtheir excess energy from the presence of the electric field. Schematically this isshown in Fig. 21. This requires the generation of electric fields which are directedparallel to the magnetic field and must be directed away from the object (Earth)so that they accelerate electrons towards the object and empty the plasma cavity


Fig. 21 Left: Schematic of the formation of a ‘horseshoe’: a parallel electric field accelerates theelectrons towards the mirror, while the mirror effect of the converging magnetic field-lines shufflesthe excess energy which the electrons gained in the electric field from parallel into perpendicularenergy. The magnetic moment of the electrons is conserved thereby and the pitch-angle of the elec-trons is increased. This results in the horseshoe-like shape of the electron distribution with respectto pitch-angle and the two velocity components v‖ and v⊥. On the right part of the figure we haveindicated two relativistic resonance lines. Red is the horseshoe-resonance circle of the RX-modefor perpendicular radiation, green is the loss-cone resonance line. The latter one is necessarily foroblique propagation since it is an ellipse that is shifted out of the origin. Right: An incompletering-shell (‘horseshoe’) phase-space distribution occurs, given the mirror effect in a convergingmagnetic field and a parallel electric field. The ‘horseshoe’ is an incomplete ring-shell since theparticles inside the loss-cone are missing

by evaporating its low-energy plasma component along the magnetic field intospace.

6.2 Generation of double layers

Figure 22 shows the schematic of a double layer in a mirror magnetic field con-figuration. In ideally conducting collisionless stationary plasma the magneticfield-lines become electric iso-potentials with electric field having only compo-nents perpendicular to the magnetic field. The plasma under such conditionsperforms a current-free drift motion ve = E⊥ × B0/B2

0 perpendicular to boththe magnetic and electric fields. However, when by some process two regions ofoppositely directed sheared drift motions come into contact, the electric fieldseither converge or diverge. In this case the transition region between the shear

278 R. A. Treumann

Fig. 22 Schematic of theconditions inside an electricdouble layer with the electricpotentials deviating from theiroriginal direction parallel tothe magnetic field-lines. Inthis case the electric field isdirected upward acceleratingelectrons downward and ionsupward. An ion beam isgenerated in this way whilethe plasma below the doublelayer is evaporated. Theenergetic electrons becomedeformed into a ring-shelldistribution as has beendescribed earlier. Theiso-potentials shown areassumed to be 3 kV apart,adding up to a total potentialdrop of 10 kV

B

E E

Ion Beam

Electron Beam

-j

+j

Iso-Potentials

10 kV

Atmosphere of object~ 100 km

SpacecraftOrbit

motions acts like a charged layer. Of interest here is only a negative chargelayer corresponding to converging electric fields.

Such a layer requires that the electric iso-potentials start deviating frombeing parallel to the magnetic field-lines as shown in Fig. 22. Numerical simula-tions of Singh et al. (2006) of such shear flows (Fig. 23) have demonstrated thatbeneath the shear flows a region evolves where negative potentials accumulate,the initially straight stretched iso-potentials turn into U-shaped and S-shapedpotentials, and a field-aligned electric field (which is upward directed under theconditions at Earth) evolves in a limited spatial domain, and thus evaporatesall the plasma in the region below the shear flows.

This is nicely shown in the Fig. 23 as a dark U-shaped hole in the plasmadensity forming at 1,000 plasma times with the dark equipotential line becom-ing S-shaped. In this way the plasma cavity is generated, and at the same time aregion of parallel electric fields appears which lasts as long as the shear flows aremaintained atop the layer. Internal non-linearities of this structure let it becomeunstable for longer simulation times with the bottom of the cavity becomingerased, developing filamentary density structures and moving upward as anion-acoustic disturbance in order to erase the shear flows. One thus concludesthat the process of double-layer formation is non-stationary: it lasts for limitedtimes only and causes pulsed parallel electric fields to appear and to disappear.Since, however, ωpe � ωce these times are much longer than those requiredfor the generation of the ring-shell or horseshoe distributions and emittingelectron–cyclotron maser radiation.

A rare direct in situ measurement by a FAST-spacecraft crossing an electricdouble-layer is shown in the lower part of Fig. 24 where the two componentsparallel and perpendicular to the magnetic field have been plotted as a functionof time. The double layer appears as a short unipolar excursion of the paral-


V(x)

Lz

Lx0

0

z/

λ de

x / λD

V(x)

Φ /

Φ0

Hot Plasma

Cold Plasma

Φ(0) = Φ(L )x

B

T

T

z/1

28

x

1

2

3

4

01 3 1 3

0

/ 2560 2 40 2 4

1000 1500 2000 2500t =40

-40

0

λ D

λD

ωpe

0

Fig. 23 Top: A shear-flow model, as it is used to simulate the evolution of a double layer in a mag-netic-mirror geometry. Shown is the simulation box with the smooth shear flow profile on top. Thesimulation is periodic in x, which requires that the electric potentials at x = 0 and x = Lx are thesame. Bottom: Sequence of the two-dimensional evolution of the plasma cavity (gray-scale codedplasma density in box) and of one individual vertical double-layer potential-line at four differenttimes (measured in inverse plasma times ω−1

pe ). The distances in the vertical (i.e., parallel to themagnetic field) and horizontal (i.e., in the perpendicular direction) are measured in multiples ofDebye lengths λD. The deviation of the density from its initial value is given on the gray scale barin arbitrary units (after Singh et al. 2006, with permission by the European Geophysical Society).A deep plasma cavity evolves at time tω−1

pe = 103. After another 103 time steps it has moved up thefield lines and has developed a distinct substructure. The smooth shape of the originally S-shapediso-potential line is distorted, and short-scale alternating parallel electric fields have evolved belowthe cavity along the magnetic field. Such fields correspond to local charges and thus representphase-space holes

lel electric field. Interestingly, the generation region of the electron–cyclotronmaser radiation in this crossing, which is located on the left-hand side, corre-sponds to the low potential side of the layer in agreement with the presenceof a negative space charge (electron beam) in the center of the cavity andconverging perpendicular electric fields as expected in a shear flow layer. Thebehavior of the perpendicular electric field also shows that the double layer is

280 R. A. Treumann

Fig. 24 Top: The dynamic spectrum in the source region of auroral kilometric radiation obtainedwith very high time resolution. The emission is partially local, namely at frequencies below thelocal electron–cyclotron frequency (black line). The very narrow-band fine structure suggests thatit consists of many small-scale elementary radiators which, however, here in the source region areless well separated than in Fig. 7 where the spacecraft is at larger distance from the radiation source.Therefore, their emissions overlap and produce a nearly continuous spectrum. Nevertheless, onecan distinguish some fast drifting vertical structures, narrow-band emissions and some narrow-bandabsorptions. These indicate radiation from electron holes as explained below (see Fig. 30). Bottom:DC electric field measurement during the same time interval in parallel (green) and perpendicular(red) directions. The parallel field exhibits a unipolar anti-Earthward signature typical for a dou-ble-layer potential ramp (after Pottelette and Treumann 2005 with permission by the AmericanGeophysical Union)

crossed at a position above its dip (cf. the detached line indicating the space-craft orbit in Fig. 22). At dip position the perpendicular electric field shouldvanish whereas here it does not. Possibly, the double layer is a three-dimen-sional structure with the two-dimensional assumption which is being a crudeapproximation only. Observations of this kind identify electric double-layers


as a reality in collisionless high-temperature plasmas when imposed on strongconverging magnetic fields in mirror geometries.

We should also note that the position of the double layer is the site of directelectron and ion acceleration. In fact, Fig. 3 shows that, at the boundary crossingsof the plasma cavity, ions become steeply accelerated into a fast cold upwardbeam. Closer inspection of the high time- and energy-resolution data of theelectron distribution (Pottelette et al. 2004) reveals a very similar effect on theelectrons. The electrons become effectively accelerated when entering the dou-ble layer just by the amount of the measured potential difference which addsto their already quite high initial energy which they received when leaving asa warm weakly relativistic beam from the distant source. In the case of Earth’sauroral plasma cavity this is the magnetic reconnection site which is found acouple of Earth radii away from the Earth in the tail of the magnetosphere.

Figure 24 in its upper part gives the highest time and frequency resolutionthat is currently available in the radiation spectrum during a double-layer cross-ing. We should remember that, while crossing the boundary, the spacecraft isnot yet deep enough inside the plasma cavity, i.e., such that the optimum condi-tions for the electron–cyclotron maser are not yet reached. The plasma here isstill relatively dense and the maximum emission efficiency should therefore notbe attained yet. Moreover, it is expected that the emissivity will not be highestbelow the local electron–cyclotron frequency in this case and that the emissionwill be slightly oblique. This is reflected in the spectrum shown. Highest intensi-ties are reached just at or just above the local cyclotron frequency. Nevertheless,strong emission is already observed also from beneath ωce (which is the blackline in the figure). Finally, the outstanding phenomenon revealed by this figureis the enormously fine structuring of the emission in frequency. This suggeststhat almost all the radiation in the source region is generated by very small‘elementary radiation sources’.

6.3 Phase space holes

These in situ observations raise the interesting but tantalizing question of thenature of the ‘elementary radiators’ identified in the radiation spectra of Figs. 7and 24. This question is not an academic one: only when one is able to answer it,can one expect to understand the nature of the radiation and, on the other hand,extract information from the radiation received from a more remote object. Wenote that this becomes possible even though one will probably never be in aposition to resolve any distant source as well as is the case for the near-Earthradiation sources of the AKR. In order to proceed, we consider two questions:

• What is the physical nature of the elementary radiators, i.e. what is thephysical nature of the elementary sources of the electron–cyclotron maseremission?

• What is the mechanism that turns a small-scale entity like a phase-space holeinto an ‘elementary radiation source’, i.e. how does the electron–cyclotronmaser mechanism work within a small-scale source?

282 R. A. Treumann

In the present subsection we attempt to deal with the first question onlyremembering that the interior of the cavity (and therefore the macroscopicelectron–cyclotron radiation source region) contains a strong field-aligned cur-rent that is passing through a very dilute plasma. Such currents excite kineticplasma instabilities of the family of the two-stream instability, which is excitedin the interaction of the counter-streaming electron and ion beams. When thecurrent drift speed v = v‖i − v‖e (which is the difference of the average ion andelectron drift velocities) exceeds the electron thermal velocity ve,th, this insta-bility growth very fast. It readily traps electrons in the wave-electric potentialand thus generates localized structures on the electron-distribution function,which are known as ‘electron phase space holes’. These holes correspond to asplitting of the electron-distribution function into trapped (consisting of elec-trons with energies less than the potential of the wave on the wave frame ofreference) and untrapped (consisting of electrons with energies larger thanthe wave potential) distributions (Schamel 1979, 1986). At lower current driftvelocities, the instability is on the ion-acoustic branch and may excite similarlocalized structures on the ion distribution function. Such entities are known asBGK (Bernstein–Green–Kruskal) modes and contain localized electric fieldsthat can be detected with high-resolution instrumentation.

Figure 25 gives a recent example of the wave form and spectrum of a sequenceof such localized structures as detected by the FAST spacecraft in situ in theauroral plasma cavity Pottelette and Treumann (2005). The representation isonly 200 ms long showing seven electric field signatures of localized structures.It takes the spacecraft less than < 10 ms to pass through a structure of typical

100 0.1 1.0 10.0- 600

- 200

0

200

400

- 400

0 200

E(m

V/

m)

||

Electric Waveform Electric Power Spectrum

FAST Orbit 18341997-02-07 20 UT

fpe

f

~f

ci

-2

Time (ms) Frequency (kHz)

Earthward

anti-Earthward

tripolar

Fig. 25 Left: A 200-ms excerpt of parallel electric VLF wave form that shows a chain of seven nearlyequally spaced tripolar electric-field structures that are embedded into a fluctuating background ofelectric waves. One distinguishes the large-amplitude anti-Earthward field signatures which typi-cally last for a few milliseconds. They are flanked by two weaker Earthward field excursions. Suchanti-Earthward fields accelerate electrons Earthward along the magnetic field. Right: The VLFspectrum for the same time period maximizes below the ion cyclotron frequency and exhibits thepower law shape towards higher frequencies that is typical for broadband noise. A second weakmaximum occurs at the plasma frequency, indicating the presence of electron-plasma waves thatare excited by the accelerated electron beam in the ‘horseshoe’ distribution (after Pottelette andTreumann 2005 with permission by the American Geophysical Union)


length, and this probably corresponds to only a few electron Debye lengths. Theelectric amplitudes reach values of 0.5 Vm−1 inside a structure, a very strongelectric field, indeed. Such fields can be maintained in a collisionless plasmaonly if particles with an energy less than a few 100 eV are trapped inside thelocalized electric wave fields. The electric power spectrum of the phase-spacehole is broad and featureless as is typical for a localized structure of this kind.Such a spectrum is shown in the figure.

In Fig. 26 we present a simple model of an electron phase-space hole whichhas been produced by Muschietti et al. (1999, 2002). This model is a BGKstructure based on the theory of Schamel (1986). From left to right the figureshows the electric potential, the electric field, and the phase-space density. Thedip on the ambient distribution function is obvious from this figure. The exactlysymmetric potential and electric fields are however, an artifact of the numericalmodel and need not actually occur in nature. Rather a finite potential differ-ence across the hole may be retained there. In the presence of many holes,these potential differences add up to a large-scale potential drop that can make

Fig. 26 A numerical model of a Bernstein-Green-Kruskal (BGK) electron-hole in a collisionlessplasma (after Muschietti et al. 2002. Left: Potential φ, normalized density ne (in arbitrary units),and electric field components E‖, E⊥ at the hole position. The density depletion in the interiorof the hole is well recognized. Lengths are given in units of the Debye-length λD, potentials aremeasured in units of kBTe/e; the unit of the electric field is kBTe/eλD. The solid curves representvalues along the ambient magnetic field, the dashed curves hold for the direction perpendicularto the magnetic field. The parallel and perpendicular cuts through, respectively, the potential andthe perpendicular field have the form of hats, while the parallel electric field has a clear bipolarstructure, as is measured in many cases. The perpendicular electric field is unipolar instead. Thesymmetry of the hole is intrinsic to the model and will not necessarily be reproduced in naturewhen a residual potential difference and, hence, an electric field in the parallel direction may bemeasured across the hole. Right: Pseudo-three-dimensional representation of the electron-distri-bution function showing the hole as a dip in the total (external) distribution with a small numberof electrons trapped and sharp boundaries of externally attached electrons

284 R. A. Treumann

up for the entire potential drop along the magnetic field in the plasma cavity.For instance, in Fig. 25 electron-holes occur at a rate of one hole every 20 msyielding 500 holes per 10 s. The small potential difference of 10 mV m−1 in thesequence shown then corresponds to a 5 Vm−1 electric field along the field-line.Stretched over a length of ∼1 km effective length (depending on the velocityof the electric structures), this yields a ∼5 kV potential difference or, applied toparticles, an electron acceleration up to 5 keV which is in pretty good agreementwith observation.

On the one hand, these phase-space holes result from the existing parallel-potential drop, on the other hand they contribute themselves to the existingparallel electric field. This ambivalence has not yet been resolved.

The physics of formation of phase-space holes is highly non-linear and thus isnot accessible to a perturbational approach. The only way of investigating theirevolution is by numerical simulation. Such simulations have been performedby several authors (Newman et al. 2001, 2004; Goldman et al. 1999, 2003).They have either been based on the assumption of approximate equations orperforming numerical particle-in-cell simulations, in one and more dimensionsand with large numbers of particles involved. Recently such simulations haveproduced important results as given in Figs. 27–28.

Figure 27 shows the space-time evolution in one dimension of the energy ofthe parallel electric-field (normalized to thermal energy) in a plasma carryingan electric double-layer. The double-layer is modeled by a dip in the plasmadensity (indicated here as quasi-stable ramp). As suggested by the discussionin the former sections, a field-aligned electric potential-drop (parallel electricfield) evaporates the plasma from the spatially limited region (interval 300–330on x-axis in the figure) where the electric field is present. The double-layer inthese simulations is the dark-shaded region near x = 300 λD. It is artificiallykept alive by regenerating it permanently. (In nature it may be regenerated bythe external maintenance of the shear flow.) The important results to be readfrom this simulation are the following:

• Immediately after initiating the simulation, the double-layer starts releasingnarrow electron-holes of small amplitude which move at high velocity to theright away from the ramp. Their velocity is comparable to the electron-ther-mal velocity;

• These electron holes are of bipolar electric-field signature like the onesmodeled in Fig. 26;

• After roughly 1,000 plasma times, the double-layer releases ion-holes whichmove comparably slowly to the left. These ion-holes are dips on the ionphase-space distribution and represent local ion-density decreases in realspace;

• Being of larger spatial extension, these holes are themselves ramps on theelectron scale. They reflect electrons and generate secondary electron-holes;

• The electron holes on the left try to escape to the right, but remain capturedbetween the ion holes and the double-layer ramp for a relatively long time;


2500

2000

1500

1000

500

0100 300 500

Tim

e(

t)pe

ω

Distance λ(x / D)

E ||

k BT e

/eλ D

/()

Fig. 27 One-dimensional numerical full particle simulation of the evolution of a localized doublelayer in a high-temperature plasma (after Goldman et al. 2003 with permission by the EuropeanGeophysical Society). The shading, as given on the right, signifies the strength of the parallel electricfield E‖, which is normalized to kBTe/eλD. The double layer (shadow) is represented as a local,steep density-decrease causing an electric potential ramp in space. It continuously releases small-amplitude electron holes which escape at high velocity to the right. At a later time large-amplitudeion holes form which move slowly to the left thereby attracting electron holes which grow until theyare large enough to break through the ramp and escape at high speed to the right. During breakingthey briefly erode the ramp

Electron distribution Ion distribution280

-280

0

-5 5 100 -5 -10 -105 0 010 5 50 -5 -5

60

-60

-40

-20

20

40

0

v/viv/viv/vev/ve

δx

δx δx

60

-60

-40

-20

20

40

0

Fig. 28 Phase-space history of the (one-dimensional) electron (center left) and ion (center right)distribution functions during the evolution of a double-layer with phase-space hole formation (afterGoldman et al. 2003 with permission by the European Geophysical Society). The vertical axis is thespace coordinate along the magnetic field, and the horizontal axis is the velocity along the magneticfield. The double-layer ramp is in the center near δx = 0. A chain of electron-holes evolves on theelectron distribution function for positive δx > 0, while for δx < 0 one single ion-hole developson the ion distribution function. This ion-hole generates a reverse ion beam. In the velocity theelectron-holes are characterized by a cold-electron beam, a hole gap, and by a broad hot-electrondistribution. The figures at far left and far right show the small central sections of the electron andion phase spaces, as indicated, in high resolution

286 R. A. Treumann

• During this time, while the electron holes move slowly to the left togetherwith the ion-holes, they grow and reach large amplitudes;

• The electron-holes which are trapped between the ion-hole and the ramp,interfere with other newly created electron- and ion-holes;

• When having reached large enough amplitudes, the electron holes attainenough momentum to break through the initial double-layer ramp to theright from where they escape at high speeds;

• In this process the double layer ramp becomes periodically eroded butrebuilds permanently;

• After long simulation times > 3,000 plasma times the production of ion-holes slows down, and the system settles into a quasi-steady state (not shownhere) when strong ion-electron hole pairs are generated on the left and thebreak-through occurs on a longer timescale.

The sequence of electron- and ion-hole generation shown above indicates thedynamical coupling between electron- and ion-holes in the presence of a strongdouble-layer. This coupling is important for the application to the electron–cyclotron maser mechanism. It explains a number of observations which so farhave been left open, even though the simulations have been performed on aMaxwellian background plasma. They neglect the formation of the ring-shell orhorseshoe distribution which in the presence of a magnetic field-aligned electricfield is unavoidable. Therefore the simulations do not contain any signature ofthe radiation. Inclusion of a ring-shell distribution would considerably changethe dynamics of the holes in phase space and also in real space, as we will discussbelow. It also leads to energy loss and thus attenuation of the electron-holeswhich on the basis of this simulation we can identify as the elementary radiationsources.

The large number of small-amplitude electron-holes escaping at high speedfrom the double layer to the right forms the elementary background-radiationsources (Fig. 7) of the emitted radiation. On the other hand, the smaller numberof large-amplitude holes that are trapped on the left side of the ramp betweenthe ion-holes and the double-layer ramp and move along with the double layerproduce the intense narrow-band signatures of the fine-structure of the elec-tron–cyclotron maser emission referred to in Figs. 6 and 7. One should note, ofcourse, that the ion-holes themselves do not contribute to radiation. The gener-ation of radiation can only be done by the electrons. However, the simulationsshow that the occurrence of the intense fine-structure emission-bands can beexplained only when ion-holes and secondary electron-holes are produced atthe double-layer ramp and the electron holes are trapped between the ion-holesand the ramp. This is in fact possible since ion-holes are the result of a paral-lel current instability of the kind of the ion-acoustic instability. Ion-holes arenothing else but localized depletions of the ion-plasma density. They representnegative charges which are localized on the plasma background and reflect elec-trons of less energy than the ion-hole potential. These reflected electrons formcold electron-beamlets that are attached to the ion-hole and are themselves


capable of producing the electron-holes which, in the simulation, occur on theleft of the potential ramp.

Figure 28 shows the evolution of the electron and ion distribution functions inthe presence of the double-layer ramp at different locations in phase space. Thelarge ion-hole is visible in the ion distribution function on the right, where theion-hole appears as a kink with missing low-energy ions in the ion distribution.At the location of the ion-hole the ion distribution splits into the two parts: theordinary ion distribution and a return-ion beam, which both are needed in theformation of the ion-hole.

Instead, the electron distribution on the left of Fig. 28 shows the formationof many electron holes which form a long and wavy chain on the electron dis-tribution. These holes cause the electron distribution to split into a thin coldbeam and a broad hot distribution function of considerably larger width thanthe original distribution. The position of the electron holes in velocity space isidentified as the lack of electrons between the narrow beam and the hot broaddistribution. It is very interesting to note that the formation of electron-holesis accompanied by two effects on the electron distribution: these are the strongheating of the electron plasma and at the same time the cooling of the initialbeam.

6.4 Radiation from electron holes

In regard to the second of the above question, one asks as to the presence ofan electron hole can contribute to radiation. This is a delicate question, since aselectron holes, even those trapped at the ramp of the double-layer, constitutesmall-scale structures with a size of only a few electron Debye-lengths. Nev-ertheless, radiation is generated in the presence of these small-scale entitiesbecause of two reasons. First, as we will show below, each of the holes producesa very steep phase-space gradient at its boundary, much steeper than any othergradient in the distribution function. Such gradients are required for intensemaser-action and generation of the high observed radiation temperatures foundin the auroral kilometric radiation (and the radiation from other magnetizedplanets like Jupiter and Saturn). Second, under the conditions described aboveelectron-holes appear in very large numbers and thus their individual contribu-tions to the radiation add up to produce high radiation intensities.

In order to contribute to the generation of radiation via the electron–cyclo-tron maser mechanism, an electron-hole must be able to modify the originaldistribution function by imposing a steep perpendicular velocity-gradient onthe electron-distribution function. How this can be achieved is schematicallydemonstrated in Fig. 29. On the right in this figure an electron hole is imposedon the horseshoe distribution which is known to be present in the auroral cav-ity-radiation region of the electron–cyclotron maser. The hole is essentially anentity in the direction of the parallel velocity. The hole forms a narrow stripin velocity space that initially, for all perpendicular velocities v⊥, is located atinitial velocity v‖,h. Since it lacks electrons, this hole is a positive charge on

288 R. A. Treumann

v

,v =const)fe(v

t0

t1

t2 t0< t1< t2

||

||

T

fe

center of ring

V (1000km/s)||

V(1

000k

m/s

)T

-5

-5

0

5

0 5

incompletering distribution

coldplasma

e-hole(t=0)

e-hole(final)

Fig. 29 Schematic evolution of an electron-hole when interacting with an incomplete ring-shelldistribution. Left: Growth of the electron-hole due to parallel momentum exchange with the elec-tron distribution. The hole, being a positive charge on the electron background, is attracted by themain distribution. When it moves into the bulk of the distribution, its relative depth increases. Thiscorresponds to growth of the hole amplitude. Right: In phase space the hole can ‘move’ only inparallel velocity v‖ at fixed v⊥. Moving (at each fixed v⊥) into the bulk of the distribution, the initialhole at t = 0 (shown in blue) is deformed. Thereby the hole becomes nearly circular (shown in red).The final state is reached when momentum balance is achieved. The deformation of the hole inmomentum space creates a gradient in perpendicular velocity along the hole. The bulk velocity ofthe hole along the ambient magnetic field varies during this process. The bulk velocity is obtainedby performing the integral 2π

∫hole v⊥dv⊥dv‖fhole(v‖, v⊥) along the deformed shape of the hole

in phase-space. Here fhole is the velocity distribution of the hole

the electron background and therefore experiences an attraction by the bulkof the negative electron-distribution function. This attraction acts only in thedirection parallel to the magnetic field.

Consider a small part of the electron-hole located at constant perpendicularvelocity. The attractive force that is exerted on the electron-hole by the bulkof the horseshoe-distribution results in momentum exchange between the holeand the horseshoe distribution and causes this particular part of the hole tomove into the direction of the maximum of the bulk electron-distribution. Thiscontinues until this part of the electron-hole settles at a parallel velocity v‖,where momentum balance is achieved. Note that for a completely symmetricring the attraction to the left and right would partially cancel and the holewould move slowly to that part of the ring-shell distribution that is closer to theelectron-hole. An electron-hole that is initially situated at v‖,h = 0 experiencessymmetric drags to the left and to the right and will thus remain in position.However, for a non-symmetric distribution like the horseshoe-distribution, thedifferent parts of the hole at different v⊥ = const will move different distances inparallel-velocity direction, and the hole will become deformed and will assumea bent structure. This is shown schematically on the right in the figure. Therethe hole has become deformed into a nearly circular section located close tothe maximum of the horseshoe-distribution function.


The left-hand side of Fig. 29 shows what happens to the hole when it movesinto the bulk of the distribution. As long as it can resist inflow of electrons fromthe outside into the hole, i.e., as long as there are no particles of low energy suchthat they become trapped inside the electron-hole, the number of particles inthe interior of the hole remains constant. The local environment of the hole invelocity space attains higher and higher density as the hole moves into the bulkof the distribution, and the hole effectively grows to large amplitude. Since thispotential increase when the hole moves into the bulk distribution, electrons areeffectively expelled from the hole. This is quite realistic as the whole traps onlythose particles which have smaller energy than the local potential in the holeframe. Thus, the number of trapped electrons inside the electron-hole remainsconstant as long as the walls of the hole do not become erased by instabilities.Ultimately, this will of course happen and will destroy the hole. The hole willbecome oblate in velocity space when this occurs. However, before it happens,the velocity gradients on the distribution function at the boundaries of the elec-tron-hole increase steeply in both directions — parallel and perpendicular to themagnetic field — when the hole deforms and enters the horseshoe distribution.

In this way deformed electron-holes produce steep perpendicular gradients∂f/∂v ⊥ in the velocity distribution at the hole boundaries. This effect turnsthe distorted electron-hole into an efficient emitter of radiation, an ‘elemen-tary radiation source’. Emission occurs at the upward edge of the electron-holewhere ∂f/∂v⊥ > 0, while at its downward edge, where ∂f/∂v⊥ < 0 and which isat smaller v⊥, the hole absorbs radiation. Radiation and absorption are due tothe different signs of the perpendicular velocity gradients at the two boundariesof the hole, as shown in Fig. 30. Fortunately, due to the different positions of the

> 0∂f /∂ v

< 0∂f /∂v

Emission

Absorption

T

T

T

Center of Horseshoe

f (v T ||; v = const )

f (v )T

v

Fig. 30 The mechanism of electron–cyclotron maser radiation emitted from an electron hole.Shown is the cross section of the horseshoe distribution for a given constant parallel velocity v‖showing the signatures of deformed electron holes. These have positive and a negative gradient inthe perpendicular velocity. The positive gradient generates maser radiation, the negative gradientabsorbs radiation. Since both are separated by the hole-width �, they belong to different resonancecircles. Hence, emission and absorption occur at different frequencies separated by �f . This impliesthat the hole emission consists of a combination of an emission and an absorption line. From theresonance condition (1), one concludes that for perpendicular direction of radiation the absorptionis at the high-frequency side of the emission

290 R. A. Treumann

perpendicular velocity gradients in the hole and the finite width � of the holein velocity space, the emissions and absorptions take place at slightly differentfrequencies. The resonant circles passing through the upward and downwardedges of the hole have radii which differ by the velocity spacing �. From theresonance condition (1) for strictly perpendicular radiation, one concludes thatfor constant v‖ the absorption at the location of smaller v⊥ implies absorption ata slightly higher frequency than emission. And a hole which has passed throughthe maximum of the distribution would have this order reversed. This lattercase should, however, be less probable. The frequency spacing is small. Fromthe resonance condition for perpendicular radiation and for a velocity spread �

of the hole one estimates the frequency gap between emission and absorptionto be

�ffce

∼ �

cvh

c, (38)

where vh is the resonance velocity at the location of the hole in velocity spacewhere it forms a dip in the horseshoe-distribution. In deriving the above expres-sion, it is assumed that the shape of the hole in the velocity space can beapproximated by a resonance circle. For the AKR the spacing between emis-sion and absorption is of the order of 10−5 < �f/f < 10−4. This correspondsto a frequency gap which is of the order of ∼100 Hz. We note that the relativ-istic broadening of the emission emerging from a highly relativistic plasma willreadily smear out the gap.

The occurrence of a sequence of emissions and absorptions in weakly rela-tivistic plasmas is a very interesting effect. It should permit the identificationof hole radiation from the sequence of closely spaced absorption and emissionbands. It also should allow us to then determine the widths of the electron holes.Altogether one finds that the phase-space dynamics of electron holes providesthe key to an understanding of the intense emission obtained from horseshoe-distributions when electron-holes are generated in the current-carrying plasma.Some signatures of narrow emission and absorption lines during a crossing ofthe auroral kilometric radiation-source region can actually be recognized in thedynamic spectrum in the upper part of Fig. 24.

6.5 Stability of phase-space holes

Phase-space holes are unstable they loose energy by emitting radiation. How-ever, this loss is minuscule and can be neglected. Moreover, since radiationwill not become trapped by the hole, non-linear wave-particle interactions andquasilinear reaction of the radiation on the electron-hole distribution func-tion can be neglected as well. The instability of an electron-hole is never-theless an important characteristic property which limits the emission fromthem.

The instability of electron-holes results mainly from waves that are excitedinside the hole by the bouncing trapped-electron distribution, and from waves


that are excited at the steep boundaries of the hole. Various types of plasmawaves, namely electrostatic oscillations and very low frequency electromagneticwaves, can be excited in these ways. Both these types of waves can exit from thehole but remain to be trapped inside the plasma. They deplete the electrostaticenergy that is stored in the holes and erode the electron-distribution functionas reviewed by LaBelle and Treumann (2002).

These secondary effects caused by wave excitation in the electron-holes havebeen investigated in numerical simulations by various authors (Oppenheim etal. 1999, 2001; Muschietti et al. 2000). Their most important prediction wasthat electron-holes should generate whistler waves. This has been confirmeddramatically by in situ observations of FAST (Ergun et al. 2001b). Ergun et al.(2001b) found very intense emissions of whistler waves when the FAST space-craft was crossing the environment of electron–cyclotron maser-source regions.These whistlers propagated upward along the magnetic field at the whistlerresonance-cone boundary. Emissions of this kind were called ‘saucer emissions’because of their saucer-like images in the dynamic wave spectrum.

When following the path of these saucers, Ergun et al. (2001b) could iden-tify almost every saucer source with a very localized region in space whichitself turned out to be an electric-field structure having the properties of anelectron- or ion-hole. These saucers are the result of the instability of thetrapped hole-electron population. Propagating away at the local Alfvén speed,the saucer-whistlers transport away a substantial part of the hole energy intothe ambient plasma and thereby heat it. This heating by secondary instabil-ities and saucers is an important effect. In the wave-field of the saucers theparticles in the gradient of the horseshoe-distribution experience quasilineardiffusion in pitch-angle and energy; this depletes the general perpendicular gra-dient of the horseshoe-distribution and produces the plateau at lower electronenergies that has been continuously found in the measurements of the elec-tron distribution function. Thereby, it weakens the effect of the contribution ofthe general gradient in the perpendicular velocity to the maser-emission fromthe horseshoe-distribution. The main contribution to radiation thus comes fromthe deformed electron-holes. Finally, we note that the heating of the plasma ismost efficient at the boundaries of the plasma cavity. There a substantial amountof plasma is still present in order to absorb the whistler energy.

6.6 Reconnection

Jaroschek et al. (2004b) suggested that a large volume filled with manyreconnection sites, which evolve when the plasma is turbulent, will generatedetectable incoherent synchrotron-emission. An interesting question is whethersuch reconnection, one of the most important processes in collisionless plasmas,can map itself into electron–cyclotron maser emission that would be of muchhigher intensity than incoherent synchrotron radiation.

Reconnection is the process where anti-parallel magnetic fields, which aredriven by plasma flow towards each other until they come into contact, merge

292 R. A. Treumann

B

C

C

B

D

D

A

A

t = t1

t = t2

B

CD

A t = t3

y

zz

xx

t

t0

Ey

Ey

1

v

v

in

out

Fig. 31 The physics of reconnection of magnetic field-lines in a schematic representation. Left,from top to bottom: Three phases of the reconnection process between two field-lines of oppositedirection approaching each other with velocity vin, merging and rearranging at contact, and sepa-rating with larger velocity vout determined by the relaxation of magnetic curvature tensions. Right,from bottom to top: The (xz)-plane in the bottom part of the figure is the same plane as the planes ofthe three figures on the left. The (xy)-plane in the top part of the figure is the plane perpendicular tothe figure on the left. Both parts show the color-coded electric field Ey in the central reconnectionregion during merging and rearranging in two sections. Bottom: Same plane section as in left part offigure. Shown is just the X-point region. The magnetic geometry is about the same as in the bottomgraph on the left. Dark blue-to-green and yellow-to-red colors indicate opposite polarities of theelectric field Ey. Ey points either in or out of the simulation plane. The white line shows a numberof one electron’s gyrations in projection and then the path taken between start and end time of thesimulation and shows the violent acceleration of the electron in the electric field before it escapesalong the magnetic field (in the x-direction) becoming a field-aligned electron beam-particle. Top:Same in the perpendicular plane showing the finite extension of the electric field and reconnectionregion and the wavy structure of the field (right part after Jaroschek et al. 2004a). In this section Eyis in the plane. Blue-to-green fields point downward, yellow-to-red fields point upward. All lengthsare in terms of the electron inertial length c/ωpe. Times are measured in inverse electron plasma

frequencies ω−1pe . Electric fields are normalized to cB0, the product of the velocity of light and the

magnetic field outside the current sheet

and annihilate. In this process the initially anti-parallel magnetic fields restruc-ture, and the initially strictly separated plasmas mix and become accelerated tohigh bulk velocities (cf. Fig. 31).


Reconnection in vacuum can proceed without any problem since magneticfields can reorder there as they like.16 In a plasma, however, and in particularin a collisionless plasma, simple reordering of the magnetic fields is inhibitedby the frozen-in character of the magnetic field. Locally the particles gyratearound the magnetic field on circular orbits at cyclotron frequency ωce withgyroradius rce = v⊥/ωce. Conservation of the magnetic flux, � = πr2

ceB = const,that cuts through the surface of the cyclotron orbit implies that the plasma par-ticles cannot get away from the magnetic field-lines to which they are tied.This is expressed by the Lorentz transformation law for the electric field inmoving plasmas which requires that the electric field transforms according toE′ = E+v×B = 0. Hence, in the laboratory system E = −v×B. Reconnectionis thus possible only if some diffusion process works which breaks the frozen-incondition.

Numerical simulations of the reconnection process have shown that the diffu-sion process results in the generation of localized electric fields transverse andparallel to the magnetic field. When plasma is not supplied on a very fast scale tothe reconnection site — which happens only in a strongly driven reconnectionscenario — reconnection depletes the plasma density around the reconnectionsite. The plasma leaves from there in two forms: First, the tension forces exertedon the plasma by the strongly bent magnetic field lines accelerate the bulk ofthe plasma into low-velocity jets perpendicular to the magnetic field, as seenon the left in Fig. 31. The velocity of these jets is a fraction of the Alfvén veloc-ity. Second, the reconnection electric field ∇ × E = −∂B/∂t near the X-pointaccelerates a substantial fraction of the more energetic tail electrons to highenergies. These electrons attain an increase in their gyroradii. When their gy-roradius exceeds the width of the reconnection site, they escape and form ahigh-energy beam along the stretched magnetic field lines.

Because of the fast plasma outflow, the reconnection site itself retains verylow plasma densities such that locally ωpe < ωce becomes possible. In thepresence of strong guide-magnetic fields that point out of the reconnectionplane this condition can even more easily be satisfied. In this case reconnec-tion sites might act as electron–cyclotron maser sources. Similarly, the electronbeams ejected from the reconnection site leave along the magnetic field lineswhich pass through the X-point in reconnection, the two separatrices. Along theseparatrices the plasma density is lower than in the surroundings. Here again theabove condition can be satisfied. Together, with the passing electron beam thattransports the Hall-current, and the increasing magnetic field strength with dis-tance from the X-point — which is similar to a mirror geometry — the separatrixregion are also candidates for a working electron–cyclotron maser. The physicsof this process has, however, not yet been explored. The geometries are consid-erably more complicated than in the case of the auroral regions where the mag-netic fields possess clear mirror symmetries. Near a reconnection site, the mirror

16 In fact, in terms of the reconnection picture, the vacuum velocity of light, c, can be interpretedas having the property of a velocity of diffusion of the electromagnetic field across empty space.Such an interpretation is based on the vacuum resistance (µ0/ε0)1/2.

294 R. A. Treumann

symmetry is different from the auroral region and thus the maser-mechanismwill also be different. Hollow-beam masers will probably be more importanthere than ring-shell masers, and the emission will possibly be at higher harmon-ics of the local electron–cyclotron frequency, in which case it will be weak.

In this context it should be noted that chains of phase space holes haverecently been observed (Cattell et al. 2005) in a region where magnetic recon-nection was going on in the collisionless plasma sheet of the Earth’s mag-netotail at roughly 15 Earth radii anti-Sunward distance behind the Earth. Atwo-dimensional simulation supporting these observations is shown in Fig. 32.The simulation assumes the presence of a strong magnetic guide-field which

00

0 30 60

0.0

1.0

-1.0

3015

5

10

15

z

x

path

electric field along path

path length

E||

0.6

-0.6

0.0 E||

X-point

X-point

Fig. 32 Chains of electron holes in a simulation of magnetic reconnection including a strong guidefield which points out of the plane (after Cattell et al. 2005, with permission by the AmericanGeophysical Union). Shown is the (xz)-plane of reconnection as defined in Fig. 31. Lengths are interms of the ion-inertial length c/ωpi (where c is the velocity of light, and ωpi = ωpe

√me/mi is the

ion plasma frequency). The gray-scale code of the electric field E is given on the right vertical barin non-physical computer units. E points out of the simulation plane. Because of technical reasonsthe simulation is performed in a box containing two vertically (along z) well-separated anti-parallelcurrent sheets (the current in the lower sheet flows out of the plane in +y-direction, the current inthe upper sheet flows into the plane in −y-direction). This causes the development of X-points inboth current sheets. Top: The upper part shows the simulation plane with the final magnetic-X-pointconfiguration. Superimposed is the electric field. Along the black about closed magnetic field line(labeled ‘path’) that connects to the main X-point, the electric field exhibits a chain of localized,small-scale structures. Below: The lower part is the amplitude (wave form) of the parallel electricfield taken along the ‘path’-black magnetic field line. The formation of bipolar and tripolar electronholes is clearly seen


points out of the plane. The upper part of the figure shows the formation ofthe X-line which is typical for reconnection, and the egg-like structure of thefinal reconnected magnetic fields. Along the magnetic-field boundary the elec-tric field is highly structured. Its representation in the lower part of the figureexhibits the characteristic structure of bipolar and tripolar electron holes whichare generated by the instability of the current flowing along the magnetic field.

Inspection of the density (not shown here) reveals moreover that the plasmaalong this path is less dense than in the surroundings by up to a factor of ten. Thisis the result of the presence of a field-aligned component of the electric fieldwhich evaporates the plasma locally. Hence, the conditions for the electron–cyclotron maser to work seem to be satisfied. It is, however, not clear whether ornot enough energy is available under these conditions in the deformation of theelectron-distribution function to feed an electron–cyclotron maser efficientlyenough.

Thus, one may conclude that electron–cyclotron maser emission could, inprinciple, occur at or in the surroundings of a reconnection site. One expects,however, only weak intensities. The main reason for only a weak-intensityemission is that one does not expect horseshoe distributions to be generatedin the modest mirror geometry of reconnection. Therefore, reconnection willprobably manifest itself in direct electron–cyclotron-maser emission only in anaverage way when a very large number of reconnection sites — X-points — areembedded into the volume and all the contributions of the single X-points andseparatrices add up to the emission.

7 Outlook toward astrophysical applications

The weakly relativistic electron–cyclotron maser emits narrow-band radiationjust below the local non-relativistic electron–cyclotron frequency fce. The highlyrelativistic electron–cyclotron maser emits relativistically broadened radiationwith maximum intensity around fce. Hence, their observation is a measure ofthe local magnetic field, B. Its strength is approximately given by

B (gauss) = 3.57 × 102fGHz. (39)

From the working condition f 2pe/f 2

ce � 1 of the electron–cyclotron maser oneis then in the position to set an upper limit on the local plasma density in theradiation source region as

ne (cm−3) < 1.24 × 1010f 2GHz. (40)

Moreover, as we have argued, the source regions of the radiation are small. Theradiation, on the other hand, moves at high velocity across the dilute plasmasuch that the non-linear response of the plasma is negligible. The linear growthof the radiation is limited simply by convection out of the plasma-cavity sourceregion. With L the extension of the source, the transition time of the radiation

296 R. A. Treumann

is approximately ttrans ≈ L/c. The wave intensity Wwave grows exponentiallylike Wwave = WS exp (2〈�〉ttrans), where 〈�〉 is the average electron–cyclotronmaser growth rate in the cavity, which is approximately

〈�〉 ≈ π3√

2

(mec2

kBTe

) 32 f 2

pe

fQ. (41)

Here Q is a (dimensionless) measure of the steepness of the phase-space gra-dient on the distribution function. It can be taken to be at most in the range ofone to two orders of magnitude, Q ∼ 10 to 100. f ≈ fce is the emitted frequency.The wave intensity is proportional to the wave power, Wwave ∼ P, such thatthe above expression for the growth of intensity can be written in terms of thepower. WS ∼ PS is the initial wave intensity respectively the initial wave power.Resolving for the transition time provides an estimate for the spatial extensionL of the plasma cavity region as

L ≈ c2〈�〉 ln

PPS

∼ c√2π3

fce

f 2pe

(kBTe

mec2

) 32

Q−1 lnTB

TS. (42)

The radiation grows out of the available background radiation. This backgroundcan be taken as the (initial) incoherent gyro-synchrotron-emission power PSlevel at the estimated magnetic-field strength. Then, the logarithm is sim-ply the enhancement factor ln(P/PS) = ln(TB/TS) of the coherently emittedpower over the incoherent gyro-synchrotron radiation power, which is also theenhancement factor of the coherent brightness temperature over the incoher-ent gyro-synchrotron brightness temperature, TS. This factor is typically of theorder of a few times 10. Since the density, ne, and magnetic field strength, B,are already known, the above expression (42) allows to estimate the spatialextension, L, of the plasma cavity, i.e. the electron–cyclotron maser-radiationsource. In the most fortunate case when intensity variations are observed, theextension L is also known from light-travel arguments. Then, the expression(42) provides an estimate of either the plasma temperature in the source or theaverage steepness parameter, Q, which is a characteristic average property ofthe elementary radiators.

Having reviewed the relevant physics of the electron–cyclotron maser, wenow focus on the principal goal of this investigation: the possible relevance ofthe new physics involved in the electron–cyclotron maser for astrophysics. Asusual, such an investigation will have the character of an outlook only, as it isimpossible to provide in situ observations of any remote astrophysically inter-esting systems, exceptions being the nearest planets in our own solar systemand some occasional measurements at the outskirts of the heliosphere.

Even the Sun, the nearest star, is not accessible to in situ observations. TheSun hides its secrets on most of the interesting physics which underlies theemission of radio waves under the skirt of its high optical and X-ray radiationpower. Nevertheless, astrophysics in this case, like in many others, may use our


knowledge about the relevant physical processes and mechanisms that can beaccessed directly on Earth and in the Earth’s environment, and look towardapplying this knowledge in the investigation of exotic objects in distant space. Itis one of the beauties of scientific progress that we can expand the bounds of ourknowledge by ever more precise measurements in our accessible environment,thereby providing ever better evidence for the reality of such astrophysicalprocesses.

7.1 Other planets: Jupiter, Saturn

The paradigm of the electron–cyclotron maser emission is the auroral kilomet-ric radiation of Earth. It is tempting to extrapolate from Earth to the otherstrongly magnetized planets of the solar system and to search for auroral radi-ation from these planets. Radio emissions from Jupiter and Saturn, the nearestouter strongly magnetized planets in the solar system, have been known (Zarkaet al. 1986, 2004; Zarka 1992a,b, 1998, 2004) for a long time from ground-basedobservations. Jovian radio emission in S bursts (see Fig. 33) reaches brightnesstemperatures of 1018 K at 30 m wavelength strongly suggesting a nonthermalemission mechanism.

The five families of Jovian radio emissions, listed in Table 1, are believed tobe generated by the electron–cyclotron maser mechanism. Some of the emis-sions are clearly related to the presence of the active Jupiter satellite Io whichcarries with it a magnetic flux tube around Jupiter and is thus strongly coupledto Jupiter. Io exchanges plasma and currents with the planetary atmosphere ofJupiter, and these currents give rise to intense radio emissions whose strengthand spectrum vary strongly with time. However, it is not clear whether or notthese radio emissions are actually generated by the electron–cyclotron masermechanism as the plasma configuration and the actual shape of the electron-distribution function are not really known.

Table 1 Electron-cyclotron maser radio emission of Jupiter

Type Frequency Source Power (W) Mechanism

I Non-Io <40 MHz Auroral 1010–1011 Ring-shellDAM field-lines Horseshoe

II Io DAM Io torus < 1011 Ring-shell(L & S bursts) Io field-line Ring-beam

III HOM 200 kHz Auroral 108–109 Hollow→ few MHz ∼ 70◦ beam

IV bKOM 10–300 kHz Auroral 108–109 Horseshoe?V QP bursts, < 700 kHz Auroral ∼108 ?

nth-cont MP ?

DAM decametric, HOM hectometric, bKOM broadband kilometric, nKOM narrow band kilomet-ric, L long (minutes), S S-shaped short (few tens of ms) bursts, nth-cont non-thermal continuum,MP magnetopause

298 R. A. Treumann

Fig. 33 Comparison of thespectral intensities of thevarious radio emissions fromthe outer planets and Earth(after Zarka 1998 withpermission by the AmericanGeophysical Union). Jovianspectra, including thoseoriginating from the Io torus,are shown as bold lines. (Themeaning of the abbreviationsis HOM = hectometric, DAM= decametric, bKOM =broadband kilometric, nKOM= narrow-band kilometric, QP= quasi-periodic pulses, Sbursts = S-shaped short radiobursts, DIM = decimetric)

Flu

x de

nsity

at ~

4AU

(Jy

)102

104

106

10-2 100 102 104

Frequency (MHz)

bKOM

nKOM

HOM S bursts

Io DAM

non-IoDAM

QP

Saturn

Earth (AKR)

UranusNeptune Thermal

DIM

Provided that intense electric fields evolve in the Io flux tube, the plasmamay become sufficiently diluted so that favorable conditions are created for theelectron–cyclotron maser close to the Jupiter surface. The magnetic field wouldindeed be strong enough, and one believes that the magnetic-field-aligned cur-rents that flow along the Io flux tube and couple the satellite to the planetare so strong that they undergo current instability. In this case they excitewaves, generate Bernstein-Green-Kruskal (BGK) modes, and support large-scale field-aligned electric-potential drops — or double layers — in the Io fluxtube. Moreover, strong shear flows could generate a double layer as well as isthe case in the Earth’s auroral plasma cavity, where external reconnection isthe driver of the shear flow. Such shear flows may, for example, arise when Io’sflux tube moves across the ambient plasma together with the satellite aroundJupiter and causes vortices in the plasma flow.

Spectacular aurorae have been observed on Jupiter in the ultraviolet spectraldomains by the Hubble Space Telescope, and similar emissions have been seenon Saturn. Figure 34 shows such an observation centered around Jupiter’s northpole. The bright spot on the left indicates the magnetic foot point of the Io fluxtube in the Jupiter atmosphere. The bright emission coming from there resultsfrom the Io plasma which collides with the constituents of the Jovian atmo-spheric constituents. The extended bright emissions forming the Jovian auroraloval are caused by the same processes as aurorae on Earth, resulting fromreconnection at Jupiter’s magnetopause and from reconnection in the Jovianmagnetotail. Similar auroral rings are observed around the poles of Saturn.They are shown in the right-hand panel of Figure 34.

The deformation of the auroral oval seen particularly on the night side of Jupi-ter — and to some extent also on Saturn — are caused by shear flows in Jupiter’stailward plasma content in the wake of ongoing reconnection. From this one canconclude that reconnection-generated shear motions will be strong enough to


Fig. 34 Hubble Space Telescope views of planetary aurorae. Left: Aurora around the pole in thenorthern hemisphere of Jupiter. Similar to aurora on Earth, auroral activity occurs in a circle that isapproximately centered at the magnetic pole, the so-called auroral oval. Seen from space the auroraoccurs in several irregular bands which indicates the dynamics of the auroral oval, ongoing Jupitersubstorm activity and the immense dynamics of Jupiter’s plasma-magnetic-field environment. Alsoseen on the dayside is the intense emission from the footpoint of Io’s magnetic flux tube on thesurface of Jupiter; Right: Ongoing aurora in both polar caps of Saturn. On both giant planets of oursolar system, the aurora appears bright and irregularly structured. In all cases its location encirclesthe magnetic poles of the planets which it shares with Earth’s aurora. This circle is formed by thefootpoints of the magnetic field lines which connect the planet to the regions of reconnection atthe magnetopauses and in the magnetic tails of the planets. Substorm activity on these planets isrelated to the ongoing magnetic reconnection in their nightside magnetotails, generation of mag-netic-field-aligned currents and the existence of an energetic plasma component in the planetarytails. The latter stems from solar-wind plasma entering the magnetosphere by reconnection at themagnetopauses, and from plasma of the planetary atmospheres, from their rings, and from theirsatellites, like Io in the case of Jupiter

generate the required auroral currents and cause field-aligned potential dropsto develop, even though in situ measurements confirming such a conjecturehave not yet been made. But the similarity to the Earth’s auroral motions andflux-tube deformations is so tempting that the analogy must be invoked! Withmagnetic-field-aligned electric fields present, all the constraints on the elec-tron–cyclotron maser would be fulfilled in Jupiter’s — and as well in Saturn’s— auroral zones. Therefore, the assumption that auroral radio emissions inthe hectometric (HOM) and kilometric (KOM) bands and the short and fastdrifting S-burst radio emissions, which are believed to be related to the Io fluxtube, are caused by the electron–cyclotron maser in the ring-shell mechanismare reasonable.

The loss-cone maser might also contribute to emission, but the experiencewith the dominance of the ring-shell maser and emission in the nearly perpen-dicular RX-mode are strong enough to support the assumption that the fastmoving striations in Jupiter’s radio emissions, like those of the S-bursts, arecaused by chains of microscopic electron-holes and ion-holes that move acrossthe plasma in the auroral cavities on Jupiter in connection with the doublelayers.

Recently, Zarka et al. (2005) argued that S-bursts are the result of loss-conemaser activity inside the Io flux tube. They find consistency with a loss-conemaser model in frequency drift and source-electron energy of ∼4 keV inside the

300 R. A. Treumann

flux tube. In addition, however, they find evidence for a magnetic-field-alignedelectric potential drop of 1–3 keV which coexists with the emissions. They attri-bute this electric field to Alfvén waves along the Io flux tube. Moreover, theyadvocate the validity of adiabatic theory for the motion of energetic electrons.

In the light of the arguments in the present review, such large potential dropstogether with adiabatic motion of electrons along the converging Io flux-tubewould rather indicate a deformation of the electron-distribution function intoa ring-shell distribution and the action of the much stronger ring-shell maser.One could easily argue that such parallel potential drops inside the Io flux-tubecould be generated by the motion of the flux-tube across Jupiter’s magneto-sphere. This necessarily causes circulation around the flux tube and thus shearmotion of the plasma at its boundary. And, following our previous arguments,this will lead to field-aligned potentials drops and plasma evaporation on asmaller scale. Both these consequences argue in favor of the ring-shell maser.No doubt, Alfvén waves and in particular kinetic or shear Alfvén waves willbe involved in the transport of information along the magnetic field since theyare the main mode for exchanging information along the magnetic field in aplasma. But in order to account for high potential drops, these modes mustbecome highly non-linear so that it is not reasonable anymore to speak aboutsingle Alfvén modes as the ultimate energy source of the radiation.

Recently, the Cassini mission has provided first high time and frequency res-olution results of auroral radio emissions from Saturn (Kurth et al. 2005a,b).These observations indicate that Saturnian auroral radio emissions are strik-ingly similar to those in the Earth’s auroral plasma cavity, exhibiting the samekind of drifting narrow band structure (Pottelette et al. 2001) observed here.It is therefore highly probable that the mechanism generating the Saturnianauroral radio emissions is the same as that on Jupiter and Earth, of which wetoday believe that they are caused by the ring-shell maser mechanism. All theseradio emission similarities among the magnetized planets in the solar systemsuggest that the electron–cyclotron ring-shell maser mechanism is the most effi-cient radiation mechanism even though loss-cone maser contributions cannotbe excluded.

No generally agreed upon mechanism of generation of the electron–cyclotronmaser fine structure emission does yet exist (Pritchett et al. 2002). However thearguments for the involvement of double layer electric fields, electron and ionholes have now become overwhelming, even though the very fine structureof the Saturnian or Jovian auroral radio emissions cannot yet be resolvedas well as that of the Earth’s kilometric radiation. The more, however, thesestructures can be resolved the more will a model develop which confirms theelectron–cyclotron maser emission mechanisms as resulting from the genera-tion of steep perpendicular gradients in the electron velocity distribution bydeformed electron holes on the smallest scales. And the radio emission willbe seen as the superposition of the radiation from many such microscopicelementary radiation sources.

This conclusion is far reaching. It provides a universal mechanism for applica-tion to other remote, strongly magnetized systems, planets, stars, brown dwarfs,


etc., allowing from observation of highly non-thermal radio emission from suchobjects to draw conclusions about the structure and parameters of their magne-tized plasma environments and their dynamics. It has been concluded (Mitchellet al. 2005) that Saturn exhibits similar magnetic substorms as the Earth. Sub-storms are generated by reconnection as noted above and provide the ultimateenergy source of the auroral electron–cyclotron maser emission. The obser-vation of substorms in remote objects together with coherent radio emissionconfirms the identification of reconnection as a widely realized universal mech-anism of redistribution of energy in collisionless magnetized plasmas.

7.2 Exoplanets

The discovery of extrasolar planets has immediately stimulated the idea thatin analogy to the strongly magnetized planets in the solar system, exoplanetscould also radiate in the radio band, possibly emitting maser radiation (Farrellet al. 1999; Bastian et al. 2000; Zarka et al. 2001b; Winterhalter et al. 2005).Farrell et al. (1999) suggested that detection of exoplanets in such an emissionwould be most favorable in the meter and decameter bands. From the knowl-edge of the emissivities of Earth and Jupiter under solar-wind conditions, onemay scale emissivities up to exoplanets of the family of ‘hot Jupiters’ close totheir mother stars (Zarka et al. 2001b). One expects intensities that are higherby factors 103 to 105 than those of Jupiter’s decameter radiation. Radiation ofsuch high intensities may become detectable with the largest radio-telescopesthat already exist or are under construction. Searches have been going on at theVery Large Array (VLA) in New Mexico (Bastian et al. 2000) and a comparablearray UTR-2 in Kharkov (Ukraine) (Zarka et al. 2001b).

High-resolution observations have already been performed with the VLAby Bastian et al. (2000) who looked at a number of extrasolar planets at 333and 1,400 MHz. In addition they observed 47 Ursa Major at 74 MHz, but didnot find any signature on any of these objects, so far. The Kharkov observa-tions were also not able to detect radio emission from their exoplanet candi-dates. This negative result might be a consequence of either observing in thewrong frequency band, insufficient sensitivity and insufficient frequency reso-lution, incorrect assumptions on the expected magnetic field strengths of exo-planets, or incorrect assumptions about the magnetic interaction between themother star and the exoplanet. The latter might not be of the same kind as theinteraction between Io and Jupiter.

In fact, the exoplanets which have been taken as candidates are those whichbelong to the class of planets which had not been expected to exist. They arevery large and very close to their mother stars. Their interaction with the motherstar is probably very intense. If the planets are magnetized it is possible thattheir magnetic field is tied to the star or that it at least interacts very stronglywith the stellar magnetic field. This has stimulated the idea that reconnectionmight dominate the interaction. One would not, however, be able to observethe reconnection site in radiation. Nevertheless, one then expects that strong

302 R. A. Treumann

currents flow along the field-lines up and down to the planet and generateviolent phenomena which should be similar to the phenomena in the auroralplasma cavity. If this held, then the planet should emit electron–cyclotron maserradiation. It is, however, not yet clear in which frequency band this emissionwould occur.

Another serious argument why radio emission from the electron–cyclotronmaser might not be detectable from exoplanets is strong self-absorption of theradiation at the fundamental. This argument has been put forward by Melrose(1999) in the context of solar radio spikes. In fact, in the case of solar radiospikes the argument might be less strict than it sounds (see below). The knownexoplanets have, however, been found very close to their mother stars andare thus probably in very dense plasma environments. Even though in such anenvironment plasma cavities will exist close to the planetary surface, it is notunreasonable to assume that the optical depth for the radiation becomes toolarge outside the source region, so that the radiation will be fully absorbed overthe pathlength it has to travel in order to escape from the planet. This situationis different from that of the planets in the solar system where the radiation caneither tunnel through the walls of the narrow plasma cavity, or it can escape byperforming wave transformation; it is, however, not unreasonable to assume thatstrong self-absorption occurs in the exo-planetary environment. Any escapingradiation must then be at higher harmonics of the electron–cyclotron frequencywhere the excitation is much weaker.

Far higher instrumental sensitivities in the frequency range from 10 to240 MHz have been announced (Farrell et al. 2004) to be expected from thenew Low Frequency Array (LOFAR) which is currently under construction.Its more precise observations may confirm that exoplanets are, in fact, radioemitters.

7.3 The quest for solar and stellar radio-maser emission

Solar radio emissions have not only been the first candidates of electron–cyclotron maser action, with Earth and planets they continue to be a potentialhost of electron–cyclotron masers. In spite of its proximity, the Sun — like othermore remote astrophysical objects — does not allow the investigation in situof the various potential source regions of the expected maser emissions. Thisimpossibility has not inhibited and should not inhibit attempts to apply masertheory to solar phenomena. Actually, there is a long tradition: the first ideasof the possibility of a direct amplification of the free-space modes appeared insolar physics. Coronal electron-temperature anisotropies were identified as theenergy source of the maser emission. This assumption was based on analogieswith radiation-belt electron trapping at Earth, but turned out to be ineffec-tive. Subsequently, following the work of Wu and Lee (1979) on the weaklyrelativistic electron–cyclotron maser, the assumption of loss-cone distributionssurvived until very recently as the basis for almost all solar application of themaser mechanism.


Since the structure of the solar magnetic field close to the photosphere, i.e.,in the regions where the electron–cyclotron maser may be assumed to work,is extremely complicated there are very many such source regions that canbe distributed all over the solar surface at various distances, and resolutionof them will still for a long time be inhibited by their small scales and shortsurvival times. Experience with the Earth’s AKR indicates that the size of aterrestrial plasma cavity, which is determined by the presence of shear flowsabove the source region, is restricted to merely several 10 km to 100 km. Thismay be larger on the Sun because of the larger dimensions of the solar activeregions, but shear flows at the base of the corona will probably not exceed scalesof say 103 km to 105 km, and shear flows caused by turbulence might occur oneven smaller scales. Since large-scale magnetic-field-aligned electric fields can-not be maintained over very long times, externally driven shear flows will bethe most important in generating magnetic field-aligned electric-potential dropsand parallel electric fields.

Numerical simulations have suggested that plasma cavities are highly time-variable. Such cavities will therefore decay into even smaller structures. Theiroverall size is determined by the size of the reconnection and accelerationregion of which we know today that they are not larger than a few ion-iner-tial lengths in the transverse dimension. Located at coronal altitudes — say atplasma densities of 109 cm−3 — their diameter will not be larger than a fewtimes ∼100 m at best. In mirror-magnetic-field geometries, this distance mapsdown at the foot-points of the magnetic field to even narrower regions of whicha multitude fit into the environment of one solar active region. One henceexpects that plasma cavities of the size of some 10 m will be created, and willbe elongated both in the azimuthal direction and in the vertical direction alongthe magnetic field. Such regions are the generator regions of electron–cyclotronmaser emission. Field-aligned electric fields will evolve in them and generatering-shell and horseshoe distribution functions on the electrons and cause theions to escape along the magnetic field in the form of cold fast ion beams. Theemitters themselves, being identified as BGK modes, are structures of the sizeof a few electron Debye lengths only, i.e. of the size of a few centimeters, inwhich case myriads of them will make up the radiation, and none of them willever be resolved by observation.

From the observational side, extremely high brightness temperatures havebeen reported from the Sun for the solar radio spikes (Melrose and Dulk1982; White et al. 1983; Willson 1985; Benz 1986). Similarly high brightnesstemperatures in the radio emission have been found for flare stars (Kuijpers1985; Benz et al. 1998; Stepanov et al. 2001), dwarf M stars (Lang et al. 1983;Lang 1994), and recently in the bursty radiation of T Tauri stars (Smith et al.2003). In addition, the fine structure of solar type IV radio bursts has oftenbeen attributed to maser action [cf., for instance, the reviews by (Aschwanden1990a,b; Bastian et al. 1998; Fleishman et al. 2003; Fleishman 2006)]. This mightor might not be the case. The models developed so far require confinement ofthe radiation and are thus not entirely convincing. We will, therefore, not enterinto a discussion of them.

304 R. A. Treumann

Solar microwave spikes are short radio bursts of brightness temperatureTB ∼ 1012K. They are observed at frequencies from ∼100 MHz to 5 GHz andhave a duration of <100 ms during solar flares. Their circular polarization is∼100% and their bandwidth is narrow, namely only of a few percent of the band-width of the background emission. These radio emissions are clearly expectedto be generated by a coherent process like the one which is found in the elec-tron–cyclotron maser mechanism. This conclusion is backed by the very highdegree of circular polarization of these emissions, which identifies them as beingradiated in the RX-mode close to the local electron–cyclotron frequency ωce. Ifthis is true, the emission maps the strength of the magnetic field in the emissionregion and identifies the source as a plasma cavity with ωpe/ωce � 1. Some ofthese emissions do practically not drift across the spectrum, and therefore othermechanisms like electron-beam excited coherent radiation (which occurs in thecase of solar type-III bursts) are inappropriate as a generation mechanism.

Melrose (1999) has criticized the application of the electron–cyclotron maserto all these emissions by pointing out that the emission suffers from high self-absorption of the radiation near the fundamental when trying to escape fromthe plasma. He shows the inefficiency of several mechanisms to help overcom-ing self-absorption, among them tunneling. However, while tunneling might beno way for the radiation to escape, it has been shown above that radiation canescape from inhomogeneous media in several ways, namely by being channeledalong the inhomogeneity, or by being transformed to the Z-mode and then, atthe outer boundary of the plasma, being re-transformed into the RX-mode. Inrare cases the RX-mode radiation may even be transformed into the LO-modeas it happens in incomplete wave-guides. The LO-mode will then freely escapesince its frequency is above the plasma frequency — its low-frequency cutoff.In all these cases the radiation would be able to escape, at least in part. Hence,self-absorption might not provide a really serious argument against the elec-tron–cyclotron maser mechanism, in particular not when the radiation is veryintense, so that it is sufficient to convert only a percentage of it into escapingradiation.

As the loss-cone maser is highly improbable as source of solar radio spikes,the shell maser provides an effective alternative. Here the emission is belowthe electron–cyclotron frequency and the electrons are weakly relativistic, sothat the effective temperature of the electrons satisfies the approximate con-dition kBTe/2mec2 > γ 2f 2

pe/f 2ce. The density in the source region is very small

such as fpe/f ∼ 0.01. Hence, self-absorption in such a dilute plasma and forperpendicular propagation is negligible. What is left unclear is only the prob-lem of radiation escape.

Flare stars are similar candidates. The radio image of one of them, UVCeti – a nearby flare star –, has recently been obtained with the VLBI at3.6 cm wavelength by Benz et al. (1998) exhibiting a brightness temperature ofTB > 1.2 × 1012 K. The image showed two emission components separated by4.4 stellar radii. The alignment of the components is similar to the most likelyaxis of rotation and magnetic field for the star — that is, the two componentsare apparently located above the polar regions. The authors interpreted the two


components as being caused by huge magnetic flux tubes, whereby the magneticfield was estimated, based on the gyro-synchrotron mechanism, to be between15 and 130 gauss and the electron density was between 106 cm−3 and 108 cm−3,respectively. All the radio flares were entirely right-hand polarized. Stepanovet al. (2001) have presented similar observations of the dMe-star AD Leo at4.85 GHz with a bandwidth of 480 MHz and found brightness temperaturesTB > 3 × 1013 K in strictly right-hand polarization. Assuming electron–cyclo-tron maser emission they estimate magnetic field strengths B ∼800 gauss andelectron densities ne ∼ 2 × 1017 m−3.

Such observations are in clear agreement with the electron–cyclotron maseremission mechanism of coherently generated radiation. Bingham et al. (2001)have successfully applied the shell-maser mechanism to the case reported in(Benz et al. 1998). Given a plasma frequency for the above estimated densi-ties of only ∼100 MHz, and taking the observed frequency of ∼8 GHz as theapproximate cyclotron frequency, we are clearly in the range of a dilute plasmaembedded in a strong magnetic field of order of 300 gauss. The dilution on theother hand points to the presence of a substantial field-aligned electric fieldthat is present in the source region. Such a field, in the converging magnetic-field geometry of UV Ceti must generate a shell-horseshoe distribution and willtherefore satisfy all the conditions of a RX-maser in perpendicular propaga-tion. This is also in agreement with the completely circular polarization of theradiation in the RX-mode.

Recent VLBI observations of T Tauri South (T Tauri Sb) (Smith et al. 2003)also indicate very high brightness temperatures of ∼106 K during the burstphases of the emission, which comes from very compact sources, and exhibits100% circular polarization. These observations are again typical for electron–cyclotron maser action, and have been used to estimate the magnetic field ofthe star to be of the order of 1.5–3 kilogauss.

Coming, finally, to the dwarf M stars, radio spikes at 20 cm wavelength (i.e.,1.5 GHz) with a duration of less than 100 ms and with ∼100% circular polar-ization have been reported. The emission amplitude is in excess of 100 mJy(Lang et al. 1983). Since the bursts are very impulsive, the source region mustbe small — based on light travel-time arguments, much smaller than the stel-lar diameter. This implies brightness temperatures of the order of TB >1015 K,clearly indicating a coherent process (Lang 1994). It is reasonable to assume thatthe electron–cyclotron maser would be responsible for the observed emissions.However, from the available information it cannot be decided whether or notthe loss-cone or the shell maser is at work in these objects. This would requirehigher time- and frequency-resolution that could reveal fast moving structures.It also would require an indication of the plasma density in these objects. Assum-ing that the emission is at the fundamental, the magnetic field in these objectsshould be of the order of 60 gauss. In order to satisfy the cavity condition theplasma density in this case must be not larger than a few times 109 cm−3. Suchdensities correspond to the plasma density in the solar corona.

306 R. A. Treumann

7.4 Emission from pulsars

The generation of radio emission from pulsars is much less and in fact insuffi-ciently understood. The emission is intrinsically very bright, with brightnesstemperature reaching values up to TB > 1025 K which suggest a coherent mech-anism probably involving some cyclotron instability.

The plasma in the pulsar magnetosphere close to — and probably also inside— the source region of the radiation is highly relativistic. The mechanisms thathave been proposed to explain the generation of intense radiation belong to thedirect and indirect emission mechanisms and range from curvature radiation,to linear acceleration of electrons and positrons to the free-electron-maseremission, or to relativistic plasma emissions, which are indirect. Magneticfields in pulsars are superstrong with estimated strengths of B ∼ 1011 gaussto 1013 gauss. Millisecond pulsars have magnetic fields four to five orders ofmagnitude weaker. The plasma in pulsar magnetospheres can freely escapefrom the polar region, but is trapped in the closed-field regions around theequator.

In current models it is assumed that very large electric potential drops formalong the field-lines in the polar cap and lead to the spontaneous creation ofelectron-positron pairs which form an electron-positron plasma. In the lowestLandau levels the radiation emitted is gyromagnetic emission. Estimates of thecharge density can be given, but are quite uncertain.

In any case, for the objects with strong magnetic fields one expects thatfce � fpe which, together with the strong electric fields and the mirror geome-try of the magnetic field, seems to be in favor of the electron–cyclotron maseremission mechanism.

To provide an estimate we consider the typical parameters of a pulsar mag-netosphere. The surface magnetic-field strength in the pulsar magnetospherecan be expressed through the pulsar rotation period P and its time drivative P(Manchester and Taylor 1977) as

B0 (gauss) = 3.2 × 1019(PP)12 . (43)

Similarly, the plasma frequency is given by (Manchester and Taylor 1977)

ωpe =(

8eγ�B0

mec

) 12(

Rr

) 32

, (44)

where r is the radial distance, R the pulsar radius, � its rotation frequency, andγ the relativistic factor of the accelerated electron-positron plasma inside thepulsar magnetosphere. The ratio of plasma to cyclotron frequency of streaming— with gamma factor γs — particles in a dipolar is then given by

ωpe(r)

ωce(r)= 1.7 × 10−9

(γ γ 2

s

PB0, 12

) 12

r32 (45)


where B0,12 is the surface magnetic field measured in 1012 gauss. Therefore,closer to the pulsar surface the ratio of plasma-to-cyclotron frequency is verysmall, and very large gamma factors would be required to reduce this ratio tounity. However, under the special conditions in the pulsar magnetospheres di-rect electron–cyclotron maser emission seems to work only for the non-escapingmodes via the anomalous Doppler resonance (Machabeli and Usov 1979). Emis-sion near the light cylinder has also been proposed by Machabeli and Usov(1989) and Kaabegi et al. (1991). Thus, the theoretical emission height is muchfarther out than has been inferred from observation (Hoensbroech and Xilouris1997).

Thus, all mechanisms including the electron–cyclotron maser process encoun-ter serious difficulties in an electron-positron plasma. Recently a hollow-beamcyclotron-maser mechanism has been proposed by Ma et al. (1998) that shouldwork, however, for streaming positrons and for the LO-mode only. Whether thisresult can be maintained is uncertain. It is also not clear whether an analogycan be drawn between ordinary magnetized planets with their auroral emis-sions and pulsar emissions. This leaves open the problem of how pulsars canso intensely radiate, and what role could be played by the highly relativistic(ring-shell) electron- and positron-cyclotron maser under the conditions closeto the pulsar.

7.5 Coherent radiation from Blazar jets

The most recent and most speculative attempt of application of the electron–cyclotron maser by Begelman et al. (2005) concerns the time-varying emissionfrom Blazar jets.

Blazar jets are strongly magnetized, relativistic low-density plasma jetsejected from a central machine which is believed to be an accreting massiverotating black hole. Blazar jets are visible at radio frequencies, where theyexhibit rapid intra-day variability at GHz frequencies. By using light-travelarguments one can infer angular sizes of these sources and thus some of thesesources arrives at brightness temperatures TB ∼ 1021 K, exceeding the synchro-tron self-absorption upper limit of ∼ 1011 K by a very large factor. This can bereduced only by invoking a relativistic boost of the temperature by a factor of γ

and an increase in solid angle by an additional factor of γ 2. Relativistic factorsof γ ∼ 103 would thus be able to reduce the observed brightness temperatureto the above limit. However, as Begelman et al. (1994) argued, synchrotronefficiencies in high-γ jets are rather low. This would require unreasonably largeenergy fluxes in the jet to explain the observed radiation intensities. Thus amechanism that creates very high brightness temperatures in a natural wayoffers a practical way out of the dilemma.

Such a mechanism can, under several, not entirely unreasonable assumptions,be provided by the electron–cyclotron maser and thus replace the incoherentsynchrotron mechanism. It should be noted that other coherent radiation mech-anisms based on the non-linear evolution of various plasma waves in the jet

308 R. A. Treumann

plasma have been proposed as well. These mechanisms do, however, requirelarge plasma densities and most important, given plasma frequencies fpe > fceincreasing the emission frequency. This is the opposite limit to the more rea-sonable one of the electron–cyclotron maser which is expected to exist in thejet in the strong magnetic fields that are generally assumed. Such high plasmadensities must still be justified.

The plasma in the jets moves at a velocity that is practically the velocity oflight. Since the magnetic guide-fields of the jet are believed to be very strong,the maser condition fce � fpe is readily satisfied. The second condition, theinversion of the electron (and possibly also the positron) population, requiresthe presence of a mirror magnetic field. Its existence is crucial for either the ring-shell cyclotron-maser or the loss-cone maser mechanisms to work. There areclearly no direct observations of such populations. Since the magnetic fields arevery strong and may be too stiff for a susceptible convergence, one must assumethat mirror geometries are generated locally by some mechanism like magneto-hydrodynamic instabilities, turbulence, and shock waves. Either of these mech-anisms might locally force the magnetic field on a large enough scale into amirror geometry along the current-carrying jet flux-tube. Proposals of this kindare now known in the literature. For instance, Bingham et al. (2003) proposedthat turbulence in strong shocks may locally produce sufficient mirror-magneticfield-structure.

Another possibility is the Weibel instability (Jaroschek et al. 2004c, 2005)which occurs when the jet is pulsed irregularly by its central machine. The Wei-bel instability generates transverse magnetic fields that may locally bend thejet magnetic field thereby causing mirror geometries. Once this happens thedeveloping field-aligned electric field will accelerate the particles in order toproduce ring-shell or horseshoe distributions. This then sets the framework forthe cyclotron maser in the jet.

Assume that local mirror magnetic-field geometries are generated by tur-bulence, shocks, or Weibel instabilities inside a jet. Also assume that parallelelectric potential drops arise as a consequence of the turbulent shear motionsthat apply to the magnetic field — or otherwise are generated by currentinstabilities which are driven by the field-aligned current inside the jet. Wethen have arrived at the scenario in which a ring-shell distribution function canlocally be created on the scale of the turbulence. Each of the small mirrors con-tributes to the emission of radiation, and the radiation from all these turbulentmirrors adds up to intensities that are high enough to match the high observedbrightness temperatures of TB ∼ 1015 K which have been estimated for Blazars.

Such a scenario has recently been presented by Begelman et al. (2005). Inthis theory the distance r of electron–cyclotron maser emission at frequencyf from the central engine of the jet depends on the (average) mirror ratioρ = B(r)/Bm of the small turbulent mirrors and the jet power L. Here Bm is themirror-magnetic field-strength emission for ρ ∼ 5 occurs at a typical distanceof 103 gravitational radii for a central-engine mass of 108 M�, where M� is thesolar mass. In order to reproduce the observed luminosity (i.e., the brightnesstemperature) of the Blazar radiation, Begelman et al. (2005) need only a very


small fraction of surface coverage in the sky by cyclotron-maser sources — ofthe order of 10−5 to 10−4. The volume filling factor is then only ∼ 10−15, and thetotal number of sites required in one jet amount to N ∼ 3×1015 which is verysmall considering their small size. The total broadband maser power measuredat the distance r = robs of observation can then be estimated as

P(r = robs) ∼ 9 × 1025ρ2TB15L38fGHzγ−4 W, (46)

where TB15 is the brightness temperature measured in units of 1015 K, L38 isthe total jet power measured in 1038 W, and fGHz is the frequency measuredin gigahertz. Thus the broadband isotropic power is boosted by the Lorentzfactor to fourth order. The volume-averaged emissivity of the maser radiationin this case at distance robs is only a fraction ∼ 2.5×10−10ρ2TB15γ

−2 of thecomoving energy density passing through the observation point r per unit oftime. These low volume efficiencies are both surprising and encouraging asthey show that only very little kinetic or magnetic energy is needed to beconverted into radiation in order to produced extraordinarily high brightnesstemperatures.

Whether the maser-radiation can escape from the jet is a different problemthat has been discussed extensively by Begelman et al. (2005). They came to theconclusion that for all but the most extreme parameters the jet plasma wouldbe optically thick to the radiation. Radiation will probably be observed onlyfrom a narrow, optically thin boundary layer of the jet and will produce highbrightness temperatures without excessive demands on the model parameters.The required electron energy densities remain far below equipartition ener-gies. Hence, only little magnetic energy is dissipated in the maser process. Inconclusion, then, the electron–cyclotron maser model seems to provide a veryinteresting and very successful model of emission from Blazar jets.

8 Concluding remarks

The electron–cyclotron maser is capable of generating intense and coherentradio emission under some very peculiar – but not unlikely — conditions. It has,therefore, already become a powerful diagnostic tool for such conditions. Itstheory has been developed up to quite a mature level. Once the electron–cyclo-tron maser can be identified as generator mechanism in some remote object,it permits us to infer the magnetic field strength and the density in the radiosource. It also allows us to infer some qualitative properties of the source:the presence of an electric field along the magnetic field-lines, the presence oflarge-scale plasma cavities and the degree of density depletion and, finally, theenergy of the resonant electrons. Moreover, the measured degree of polari-zation tells us whether the radiation can escape directly from the source inthe RX-mode or is partly transformed into the LO-mode when passing acrossregions of higher density.

We have presented two versions of the cyclotron maser: the bunching maserand the genuine electron–cyclotron maser. Theoretically both are two sides

310 R. A. Treumann

of the same coin. However, under natural conditions the electron–cyclotronversion of the maser is probably more frequently realized since the plasma dis-tributions found in the source are in the overwhelming majority of cases hot, andthe mono-energetic approximation ceases to be valid. In ultra-relativistic plas-mas, however, the situation might be reversed. Such plasmas probably radiatevia the mechanism of particle bunching; their spectrum should become relativ-istically broadened resembling a synchrotron spectrum of very high brightnesstemperature. Applications of the bunching maser have not yet been attemptedto ultra-relativistic objects.

The canonical paradigm of the electron–cyclotron maser emission is theEarth’s AKR. Here, its properties have been extensively reviewed. The AKRhas been identified as a narrow-band radiation emitted beneath the local(non-relativistic) electron–cyclotron frequency f < fce. It possesses a verynarrow bandwidth, sometimes of the order of �f/fce ∼10−4 to 10−3. The driftsof these narrow emission bands across a frequency-time diagram reflect theenormous dynamics of the radiation process and its elementary sources ofemission. We have identified these sources as electron-holes in phase spacewhich are of the spatial size of just a few Debye-lengths. They can thus be re-solved only by investigating the sources in situ. This is possible near the Earthbut is impossible for any remote object. Such elementary radiators occur in thepresence of magnetic-field-aligned currents and strong magnetic-field-alignedelectric fields in a magnetic-mirror geometry.

The first candidates for conditions in favor of the electron–cyclotron maseremission mechanism are the magnetized planets, extrasolar planets, magneticstars, flare stars, pulsars, and active galactic nuclei or Blazars. Radio emissionfrom some of those objects has been interpreted more or less successfully interms of the electron–cyclotron maser mechanism. Probably one of the mostinteresting results of these applications has been that the loss-cone maser mech-anism plays an insignificant role only. In the objects discussed in this review thering-shell maser is by far the more efficient and more interesting emission pro-cess. In addition it is the only one that allows for quantitative estimates. Suchestimates for the different objects that have been considered here yield volumeemission efficiencies — in terms of the plasma kinetic energy density — rangingfrom several percent in the magnetized planets of our solar system to 10−10 inBlazar jets.

Somewhat surprisingly, no radio emission has so far been identified from thenewly discovered hot Jupiters. This may suggest that they are very different intheir magnetic behavior from the planets known in the solar system.

The range spanned by the emissivities is very wide, indeed. Even though theemitted radiation is coherent and very intense in absolute terms, it representsonly a fraction of the energy losses in the medium. The radiation itself does,therefore, not play an important role in the dynamics of most systems underconsideration — with the exception of the auroral processes in magnetizedplanets where it provides a direct and not insignificant loss of energy of theaurora to free space. In the other objects this loss is much smaller. For instance,in Blazar jets the main loss process is related to the jet itself. The radiation


emitted in radio waves appears as a by-product of the dynamic processes insidethe jet which can be used with success to diagnose the state of the plasma inthe emitting region. Any back-reaction on the plasma can be safely ignored.This applies also to the more intense emitters like the Earth’s aurora. Here theelectron–cyclotron maser is not responsible for the depletion of the distributionfunction nor is it responsible for degrading the electric potential.

The potential is degraded, because electrons are accelerated in the electricpotential drop and the depletion of the distribution function is the work ofvery low frequency waves that are excited in the dilute plasma backgroundby the same positive gradient in velocity space that is the source of the elec-tron–cyclotron maser radiation. That the radiation is ineffective in distortingthe distribution function is a result of its nature which causes it to disappear atsignal speed from the source region. In contrast, the low-frequency plasmawaves propagate at much slower velocity and stay in resonance with the ener-getic electrons for long enough time to be capable of affecting the electrondistribution by quasi-linear diffusion. The proof of this conjecture can be foundin the observations which show that a broad plateau is generated by the low-frequency waves on the horseshoe distribution function which maintains onlya modest phase-space gradient that is just sufficient to keep the electron–cyclo-tron maser working.

We therefore conclude that the electron–cyclotron maser mechanism pro-vides modest energy losses only for the magnetized planets and negligible en-ergy losses for more violent objects. On the other hand, it not only explains thecoherent, highly polarized, highly time- and frequency-variable radio emissionsfrom many sources, but also serves as a valuable diagnostic tool for the physicalproperties in those sources.

The most interesting of these properties is that in the presence of the elec-tron–cyclotron maser mechanism we are dealing with plasmas that are capableof generating strong magnetic field-aligned electric-potential drops. Such elec-tric potential drops cause strong magnetic-field-aligned electric fields whichaccelerate electrically charged particles — electrons, positrons, and ions — tothe energies corresponding to the full electric potential drop along the mag-netic field-line. Such objects are of considerable interest as sources of ener-getic charged particles released to their environment. They can be identifiedthrough the coherent radio-emission generated by the electron–cyclotron masermechanism.

Acknowledgments The author thanks M.C.E. Huber for suggesting this research, for many dis-cussions, and in particular for his indispensable help in editing the paper. He also thanks M. André(IRF Uppsala, Sweden), R. Ergun (Boulder, CO, USA), C. Jaroschek (Tokyo University, Tokyo,Japan), J. LaBelle and K. Lynch (Dartmouth College, Hanover, NH, USA), H. Lesch (MunichUniversity, Munich, Germany), S. Matsukiyo (Tohoku University, Kyushu, USA), and R. Pottelette(CETP/CNRS St. Maur des Fossés, France) for discussions on the present subject. Preparationof this review has been part of a Senior Visiting Scientist programme at the International SpaceScience Institute, Bern. The support of the ISSI staff and the ISSI directors, R.-M. Bonnet, R. vonSteiger, and A. Balogh, is thankfully acknowledged. This work has benefitted from a Gay-Lussac-Humboldt Prize awarded by the French Government, Direction des Relations Internationales etde la Coopération, Paris. Awarding this prize is gratefully acknowledged.

312 R. A. Treumann

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