Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics

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Applications of Atomic and Molecular Physics to Astrophysics 82.7 Shocked Gas 1243

infrared region. CO, SiO and possibly H

have been

identiﬁed. In the absence of grains, molecules must

be formed through either three-body or radiative pro-

cesses. In the supernova ejecta, the densities are too low

for three-body processes to be effective and molecules

are formed through radiative association reactions. The

molecules are removed by reactions with He

and the

molecular abundances put a constraint on how much he-

lium can be mixed back into the region with carbon and

oxygen [82.37].

82.7 Shocked Gas

Shock waves occur in compressible ﬂuids when the pres-

sure gradients are large enough to generate supersonic

motion, or when a disturbance is propagating through

the ﬂuid at supersonic velocities. Because information

about the disturbance cannot propagate upstream in the

ﬂuid faster than the speed of sound, the ﬂuid cannot re-

spond dynamically until the shock arrives. The shock

then compresses, heats, and accelerates the ﬂuid. The

boundary separating the hot compressed gas and the up-

stream gas is the shock front in which the energy of

directed motion of the shock is converted to random

thermal energy.

Shocks are ubiquitous in the interstellar medium

where they are driven by the ionization fronts of ex-

panding Hii regions or nebulae, by outﬂowing gas

accompanying stellar birth and evolution, and by super-

nova explosions. If the shock velocity is above 50 km/s,

the shock gas is excited, dissociated, and ionized. The

subsequent recombination and cooling radiation pro-

duces photons that may ionize and dissociate the gas

components ahead of and behind the shock. This pre-

cursor radiation modiﬁes the effects of the shock and

inﬂuences its dynamical and thermal evolution. Fast

shocks destroy all molecules by dissociating H

by col-

lisions with H, H

and He and with electrons. Exchange

reactions with H atoms destroy the other molecular

species. At low densities, radiative stabilization occurs

and dissociation is less efﬁcient. Molecules reform in

the cooling postshock gas. Slower shocks do not cause

ionization or dissociation, but the chemical composition

and the ion composition are modiﬁed by reactions taking

place in the warm gas. The response of the interstellar

gas to slow shocks is signiﬁcantly affected by the pres-

ence of a magnetic ﬁeld. In some ionization conditions,

a magnetic precursor may occur in which a magne-

tosonic wave carries information about the shock, and

the ionized and neutral components of the gas react dif-

ferenly to the shock. Many different kinds of shock have

been identiﬁed [82.38].

A very fast shock with a velocity of hundreds of

km/s such as are driven by supernova explosions, cre-

ates a hot dilute cavity in the interstellar medium with

a temperature of millions of degrees. The density is low

and the gas cools and recombines slowly. Overlapping

supernova-induced cavities may be responsible for the

hot gas that occupies a considerable volume of the in-

terstellar medium in the Galaxy and in some external

galaxies. The conditions are far from coronal equilib-

rium as the gas cools more rapidly than it recombines.

The cooling radiation appears as soft X-rays and UV

emission lines with a characteristic spectrum.

As the gas cools below 10 000 K, molecular for-

mation occurs. Molecular hydrogen is formed on the

surfaces of grains as in molecular clouds and by the neg-

ative ion sequence that is effective in the early Universe

Sect. 82.8. With the formation of H

in a still warm gas,

the chemistry is driven by exothermic and endothermic

reactions with H

. Thus OH is produced by the reac-

tion of O atoms, and H

O by the further reaction of

OH with H

. Enhanced abundances of other neutral and

ionic molecules are the products of subsequent reactions

with OH. The reactions of S

and S with OH lead to

and SO, and their simultaneous presence may be

an indicator of a dissociative shock. There are in addi-

tion physical indicators of shocks, such as asymmetric

line proﬁles indicating high velocities.

In a nondissociative shock in a molecular gas, reac-

tions with warm H

dominate the chemistry as it does in

the cooling zone of a dissociative shock. The composi-

tion is controlled by the post shock temperature and the

H/H

ratio. The warm H

changes the ionic composition

by converting C

into CH

. Evidence for a nondissocia-

tive shock is the infrared emission from H

.Thethermal

emission from collisionally excited vibrational levels in

shock-heated gas is readily distinguished from that dis-

cussed in Sect. 82.3 arising from UV pumping in a PDR.

Emission from H

has been detected in numerous ob-

jects in the Galaxy and in many distant external galaxies.

In external galaxies, X-rays may contribute to the H

in-

frared sprectrum through heating the gas and through

excitation by photoelectron pumping to excited states

followed by a downward cascade [82.39,40].

Part G 82.7

1244 Part G Applications

82.8 The Early Universe

Molecules appeared ﬁrst in the Universe after the adi-

abatic expansion had reduced the matter and radiation

temperature to a few thousand degrees and recombi-

nation occurred, creating a nearly neutral Universe. The

small fractional ionization that remained was essential to

the formation of molecules. Molecular hydrogen formed

through the sequences

+ H → H

+ hν (82.25)

+ H → H

+ H

(82.26)

and

H+ e

−

→ H

−

+ hν (82.27)

−

+ H → H

+ e

−

, (82.28)

the protons and electrons acting as catalysts. Many other

atomic and molecularprocesses occurred Fig. 82.3,some

involving excited hydrogen atoms. Thus

∗

+ H

→ H

+ e

−

(82.29)

was a source of H

–

H(n = 2)

Fig. 82.3 Diagram showing the important reactions in the

production of hydrogen molecules in the early Universe

The Universe contained trace amounts of deuterium

and

Li nuclei with which heteronuclear molecules

could be made. Molecules with dipole moments may

leave an imprint on the cosmic blackbody background

radiation that occupies the Universe. The deuterated

molecules HD form from

+ H

→ HD+ H

, (82.30)

and H

from

D+ H

→ H

+ H , (82.31)

+ H

→ H

+ H , (82.32)

and

HD+ H

→ H

+ H . (82.33)

Lithium hydride is formed through

Li + H → LiH + hν

(82.34)

Li+ H

−

→ LiH+ e

−

(82.35)

−

+ H → LiH+ e

−

. (82.36)

There are many destruction processes, of which

LiH+ H → Li + H

(82.37)

may be the most severe, though its rate coefﬁcient

is uncertain. The chemistry of the early Universe is

summarized in [82.41].

The formation of molecules was a crucial step in

the fragmentation of the ﬁrst gravitationally collapsing

objects which separated out of the cosmic ﬂow. Three-

body recombination

H+ H + H → H

+ H (82.38)

Li+ H + H → LiH + H (82.39)

may be a major source of molecules as the density

increases.

82.9 Recent Developments

While the core atomic and molecular process outlined

are still unchanged, our understanding of the astro-

physical environment has been greatly enhanced by

a number of recent satellites. The Wilkinson Microwave

Anisotropy Probe (WMAP) has given us the best map

of the universe at the time of recombination and given

us general conﬁrmation of the Big Bang model. Per-

haps the most surprising result is that stars seem to have

formed much sooner than would have been expected,

about 180 million years after the big bang [82.42]. This

makes it even more difﬁcult to understand how the uni-

verse goes from the relative uniformity at the time of

recombination to the collapse and formation of the ﬁrst

objects so quickly, a problem which is certainly con-

trolled by atomic and molecular processes. The relevant

atomic and molecular processes have been recently re-

Part G 82.9

Applications of Atomic and Molecular Physics to Astrophysics References 1245

viewed by Lepp, Stancil and Dalgarno [82.43]. Two

recent X-ray satellites, Chandra and XMM-Newton,

both launched in 1999, have greatly increased our ability

to detect hot ionized gas in stars, supernova remnants,

active galaxies and other regions [82.44]. In particular,

Chandra has allowed us for the ﬁrst time to directly ob-

serve the hot gas between galaxies [82.45]. The Infrared

Space Observatory (ISO) has provided a tremendous

amount of data on cold regions in our own galaxy and

allowed us to directly observe the icy mantles of dust

grains [82.46].

Since the detection of molecules in SN 1987A, there

have been many more observations of CO molecules in

Type II supernova and theymay even occur in every Type

II [82.47]. CO has also been observed in a Type Ic super-

nova [82.48]. It remains a puzzle as to why the molecules

are not rapidly removed by helium ions. A recent calcu-

lation of the O+ He

system [82.49] ﬁnds that radiative

charge transfer is much faster then direct charge transfer

for temperatures below 10

K, but still too slow to sig-

niﬁcantly reduce the helium ion abundance in supernova

ejecta. The most likely explanation remains that mixing

is not complete in supernova ejecta, and the molecules

survive in regions of relatively low helium abundance.

The state of modeling photoionized clouds has been

recently reviewed by Ferland [82.50]. He also highlights

the great need for atomic and molecular data for analyz-

ing these clouds. New satellite data along with continued

ground observations continually raise new astrophysi-

cal puzzles, puzzles which are controlled and probed by

atomic and molecular processes. The astrophysical com-

munity owes a great debt to both atomic and molecular

laboratory measurements and theoretical models of en-

ergy levels, reaction rates, and transition probabilities.

In order to continue to progress in our understanding of

the universe we will need to continue to fund the under-

standing of the atomic and molecular processes which

control it.

82.10 Other Reading

Astronomy is one of the oldest sciences and one

of the fastest evolving. Advances in technology are

rapidly increasing the sensitivity and resolution of

our instruments and so new observations and more

sophisticated models lead to an ever greater under-

standing of the Universe. This means that books

will often be somewhat dated when they appear.

However, the series Annual Review of Astronomy

and Astrophysics is a good source of recent review

articles.

In addition, good introductions or overviews of

a particular ﬁeld are given in [82.1, 51–56]. Many

sources of atomic and molecular data are listed and dis-

cussed in [82.7]. For details on atomic spectroscopy,

see [82.57, 58]. For details on molecular spectroscopy,

see [82.59,60].

References

82.1 D. E. Osterbrock: Astrophysics of Gaseous Nebulae

and Active Galactic Nuclei (Univ. Science Books, Mill

Valley 1989)

82.2 P. F. Winkler, G. W. Clark, T. H. Markert, K. Kalata,

H. W. Schnopper, C. R. Canizares: Astrophys. J. Lett.

246,27L(1981)

82.3 R. F. Reilman, S. T. Manson: Astrophys. J. Suppl. Ser.

40, 815 (1979)

82.4 B. L. Henke, P. Lee, T. J. Tanaka, R. L. Shimabukoro,

B. K. Fujikawa: Atom. Nucl. Data Tables 27, 1 (1982)

82.5 M. Balucinska-Church, D. McCammon: 400,699

(1992)

82.6 D. A. Verner, D. G. Yakovlav, J. M. Band, A. B. Trzhas-

kavskaya: Atom. Nucl. Data Tables 55, 233 (1993)

82.7 Special issue of Revista Mexicana de Astronomia

y Astroﬁsica, March 23 (1992)

82.8 H. Nussbaumer, P. J. Storey: Astron. Astrophys. 178,

324 (1978)

82.9 H. R. Ramadan, Y. Hahn: Phys. Rev. A 39, 3350

(1989)

82.10 N. R. Badnell: Phys. Scr. T 28, 33 (1989)

82.11 M. C. Bacchus-Montabonel, K. Amezian: Z. Phys. D

25, 323 (1993)

82.12 P. Honvault, M. C. Bacchus-Montabonel, R. McCar-

roll: J. Phys. B 27, 3115 (1994)

82.13 B. Herrero, I. L. Cooper, A. S. Dickinson, D. R. Flower:

J. Phys. B 28, 711 (1995)

82.14 C. Mendoza: Planetary Nebulae IAU Symp. 103,ed.

by D. R. Flower (Reidel, Dordrecht 1983) p. 143

82.15 M. Brocklehurst, M. Salem: Comp. Phys. Commun.

13, 39 (1977)

82.16 M. Salem, M. Brocklehurst: Astrophys. J. Suppl. Ser.

39, 633 (1979)

82.17 P. G. Martin: Astrophys. J. Suppl. Ser. 66, 125 (1988)

82.18 P. J. Storey, D. G. Hummer: Mon. Not. R. Astron. Soc.

272, 41 (1995)

Part G 82

1246 Part G Applications

82.19 M. Arnaud, R. Rothenﬂug: Astron. Astrophys.

Suppl. 60,425(1985)

82.20 T. J. Gaetz, E. E. Salpeter: Astrophys. J. Suppl. Ser.

52,155(1983)

82.21 E. van Dishoeck, J. Black: Astrophys. J. Suppl. Ser.

62, 109 (1987)

82.22 W. G. Roberge, D. Jones, S. Lepp, A. Dalgarno: As-

trophys. J. Suppl. Ser. 77, 287 (1991)

82.23 A. Sternberg, A. Dalgarno: Astrophys. J. Suppl. Ser.

99, 565 (1995)

82.24 R. Gredel, S. Lepp, A. Dalgarno, E. Herbst: Astro-

phys. J. 347, 289 (1989)

82.25 T. J. Millar, A. Bennett, J. M. C. Rawlings, P. D. Brown,

S. B. Charnley: Astron. Astrophys. Suppl. 87,585

(1991)

82.26 P. R. A. Farquhar, T. J. Millar: CCP7 Newsletter 18,6

(1993)

82.27 R. L. Kurucz: Astrophys. J. Suppl. Ser. 40, 1 (1979)

82.28 M. J. Seaton: J. Phys. B 20, 6363 (1987)

82.29 A. E. Lynas-Gray, M. J. Seaton, P. J. Storey: J. Phys.

B 28, 2817 (1995)

82.30 M. J. Seaton, Y. Yan, B. Mihalas, A. K. Pradhan:

Mon. Not. R. Astron. Soc. 266, 805 (1994)

82.31 C. A. Iglesias, F. J. Rogers: Astrophys. J. 443,460

(1995)

82.32 A. Omont: Circumstellar Chemistry. In: Chemistry in

Space, ed. by J. M. Greenberg, V. Pirronello (Kluwer

Academic, Dordrecht 1991) p. 171

82.33 G. A. Mamon, A. E. Glassgold, A. Omont: Astrophys.

J. 323, 306 (1987)

82.34 L. A. M. Nejad, T. J. Millar: Astron. Astrophys. 183,

279 (1987)

82.35 T. J. Millar, E. Herbst: Astron. Astrophys. 288, 561

(1994)

82.36 R. McCray: Ann. Rev. Astron. Astrophys. 31,175

(1993)

82.37 W. Liu, S. Lepp, A. Dalgarno: Astrophys. J. 396,679

(1992)

82.38 B. T. Draine, C. F. McKee: Ann. Rev. Astron. Astro-

phys. 31, 373 (1993)

82.39 S. Lepp, R. McCray: Astrophys. J. 269, 560 (1983)

82.40 R. Gredel, A. Dalgarno: Astrophys. J. 446,852

(1995)

82.41 A. Dalgarno, J. Fox: Ion Chemistry in Atmospheric

and Astrophysical Plasmas. In: Unimolecular and

Bimolecular Reaction Dynamics, ed. by C.-Y. Ng,

T. Baer, I. Powis (Wiley, New York 1994)

82.42 C. L. Bennett et al.: Astrophys. J. Suppl. 148, 1 (2003)

82.43 S. Lepp, P. Stancil, A. Dalgarno: J. Phys. B 35,R57

(2002)

82.44 F. Paerels, S. Kahn: Ann. Rev. Ast. Appl. 41,291

(2003)

82.45 F. Nicasto et al.: Nature 433, 495 (2005)

82.46 C. Cesarsky, A. Salama: ISO Science Legacy: A Com-

pact Review of ISO Major Achievements (Springer,

2005)

82.47 J. Spyrimilo, B. Leibundgut, R. Gilmozzi: Ast. Ap.

376, 188 (2001)

82.48 C. Gerardy et al.: PASJ 54, 905 (2002)

82.49 L. B. Zhao et al.: Astrophys. J. 615, 1063 (2004)

82.50 G. Ferland: Ann. Rev. Ast. Appl. 41, 517 (2003)

82.51 C. W. Allen: Astrophysical Quantities (Athlone, Lon-

don 1973)

82.52 K. R. Lang: Astrophysical Formula (Springer, Berlin,

Heidelberg 1980)

82.53 W. W. Duley, D. A. Williams: Interstellar Chemistry

(Academic, London 1984)

82.54 L. Spitzer: Physical Processes in the Interstellar

Medium (Wiley, New York 1978)

82.55 A. Dalgarno, D. R. Layzer: Spectroscopy of Astro-

physical Plasmas (Cambridge Univ. Press, Cam-

bridge 1987)

82.56 T. Hartquist: Molecular Astrophysics (Cambridge

Univ. Press, Cambridge 1990)

82.57 R. D. Cowan: The Theory of Atomic Structure and

Spectra (Univ. California Press, Berkeley 1981)

82.58 I. I. Sobelman: Atomic Spectra and Radiative Tran-

sitions (Springer, Berlin, Heidelberg 1979)

82.59 G. Herzberg: Molecular Spectra and Molecular

Structure (Prentice-Hall, New York 1939)

82.60 P. F. Bernath: Spectra of Atoms and Molecules (Ox-

ford Univ. Press, Oxford 1995)

Part G 82

1247

Comets

83. Comets

With the exception of the in situ measurements

made by the Giotto and Vega spacecraft at

comet 1P/Halley (the P/ signiﬁes a periodic comet)

during March 1986, all determinations of the

volatile composition of the coma are derived

from spectroscopic analyses. Detailed modeling

is then used to infer the volatile composition

of the cometary nucleus. This chapter focuses

on the principal atomic and molecular processes

that lead to the observed spectrum as well as

the needs for basic atomic and molecular data in

the interpretation of these spectra. The largely

collisionless and low density coma, with no

gravity or magnetic ﬁeld, is a unique spectroscopic

laboratory, as evidenced by the discovery

of C

before its identiﬁcation in terrestrial

laboratories [83.1]. Many key discrepancies remain

to be resolved concerning the basic molecular

composition and the elemental abundances of

both the volatile and refractory components of the

cometary nucleus, as well as the comet-to-comet

variation (particularly between “new” and evolved

periodic comets) of these quantities. These issues

(and many others) are discussed in the recent

83.1 Observations .......................................1247

83.2 Excitation Mechanisms.........................1250

83.2.1 Basic Phenomenology................1250

83.2.2 Fluorescence Equilibrium ...........1250

83.2.3 Swings and Greenstein Effects ....1251

83.2.4 Bowen Fluorescence ..................1252

83.2.5 Electron Impact Excitation ..........1253

83.2.6 Prompt Emission .......................1253

83.2.7 OH Level Inversion.....................1254

83.3 Cometary Models .................................1254

83.3.1 Photolytic Processes ..................1254

83.3.2 Density Models .........................1255

83.3.3 Radiative Transfer Effects ...........1256

83.4 Summary ............................................1256

References ..................................................1257

analytical review of Festou et al. [83.2, 3]orin

the compendia of Halley results [83.4]. The former

also contains a comprehensive bibliography. Other

sources concentrating largely on the physics and

chemistry of comets include the volumes edited

by Wilkening [83.5]andHuebner [83.6]andthe

pre-Halley review of Mendis et al. [83.7].

Comets are small bodies of the solar system believed

to be remnants of the primordial solar disk. Formed

near the orbits of Uranus and Neptune and subsequently

ejected into an “Oort cloud” of some 40 000 AU in ex-

tent, these objects likely preserve a record of the volatile

composition of the early outer solar system, and so are

of great interest for the physical and chemical mod-

eling of solar system formation. The comets arrive in

the inner solar system as a result of galactic pertur-

bations. The cometary volatiles are vaporized as their

orbits bring them closer to the sun and it is solar ra-

diation that initiates all of the processes that lead to

the extended coma. Gas vaporization also leads to the

release of dust into the coma, and the scattering of sun-

light by dust is the major source of the visible coma

and dust tail of comets. Somewhat fainter, and much

more extended, is the plasma tail, resulting from pho-

toionization by solar extreme UV radiation of the neutral

volatiles and their subsequent interaction with the solar

wind.

83.1 Observations

In a review in 1965, Arpigny [83.8] summa-

rized the known molecular and atomic emis-

sions detected in the visible region of the spec-

trum (here deﬁned as 3000 to 11 000 Å) as

follows:

radicals: OH, NH, CN, CH, C

,andNH

ions: OH

,CH

,CO

,andN

;

metals: Na, Fe .

Part G 83

1248 Part G Applications

The only known atomic feature was the O i forbid-

den red doublet at 6300 and 6364 Å. From the radicals

and ions one could infer the presence of their progen-

itor “parent” molecules such as H

O, NH

,HCN,CO

and CO

, directly vaporizing from the comet’s nucleus.

The metals, seen only in comets passing close to the

sun, were assumed to come from the vaporization of

refractory grains. The inventory of metals was soon

expanded to include K, Ca

, Ca, V, Cr, Mn, Ni and

Cu, from observations of the sun-grazing comet Ikeya-

Seki (C/1965 S1) [83.9,10]andH

was identiﬁed in

comet Kohoutek (C/1973 E1). This latter comet was also

the ﬁrst to be extensively studied at wavelengths both

shortward and longward of the visible spectral range.

The ﬁrst parent molecule to be directly identiﬁed

was CO, which ﬂuoresces in the Fourth Positive system



− X



in the VUV [83.11], although the in

situ neutral mass spectrometer measurements made of

Halley disclosed the presence of an extended, domi-

nant source of CO [83.12] whose origin is still being

debated [83.13]. Ideally, the molecular species should

be detectable through their radio and sub-mm rotational

transitions or through the detection of vibrational bands

or individual ro-vibrational lines in the near IR. Water

was ﬁrst directly detected through ro-vibrational lines

near 2.7 µmincometHalleyandagainincometWilson

(C/1986 P1) [83.14, 15]. However, due to the low col-

umn densities of the other expected species, typically ≈1

or less than that of H

O, the direct detection of species

such as H

CO, H

SandCH

OH has only recently been

made possible by the development of more sensitive

instrumental techniques together with the fortuitous ap-

paritions of two bright comets, C/1996 B2 (Hyakutake)

and C/1995 O1 (Hale-Bopp) in 1996 and 1997. To date,

more than two dozen parent molecules have been iden-

tiﬁed [83.16]. Isotope ratios, particularly the D/H ratio,

in molecules such as HDO have been determined from

sub-millimeter observations [83.17].

The ultimate result of solar photolysis (and to a lesser

degree, the interaction with the solar wind) is the re-

duction of all of the cometary volatiles to their atomic

constituents. The atomic inventory is somewhat easier

to derive as the resonance transitions of the cosmically

abundant elements H, O, C, N and S all lie in the VUV

and, in principle, the total content of these species in the

coma can be determined by an instrument with a suitably

large ﬁeld of view. Of course, a fraction of the atomic

species of each element will be produced directly in ionic

form, and will not be counted using this approach. In ad-

dition, another fraction exists in the coma in the solid

grains, and this component will also not be included,

except for a small amount volatilized by evaporation

or sputtering by energetic particles. The composition of

the grains, though not the absolute abundance, has been

determined from in situ measurements made by the Hal-

ley encounter spacecraft [83.18], and can be inferred,

though not unambiguously, from reﬂection spectroscopy

of cometary dust in the 3–5 µm range.

The advent of space-borne platforms for obser-

vations in the VUV has produced a wealth of new

information about the volatile constituents of the coma.

The A

− X

Π(0, 0) band of the OH radical at

≈ 3085 Å was well known from ground-based spectro-

scopic observations, but as this wavelength lies very

close to the edge of the atmospheric transparency win-

dow, the strength of this feature (relative to that of

other species) was not appreciated until 1970 when

comet Bennett (C/1969 Y1) was observed from space by

the Orbiting Astronomical Observatory (OAO-2). The

OAO-2 spectrum also showed a very strong, broadened

H i Ly-α emission from H, the other principal dissocia-

tion product of H

O. The broad shape of Ly-α seen in

the OAO-2 spectrum is due to the large spatial extent

of the atomic H envelope, the result of a high velocity

acquired in the photodissociation process and a long life-

time against ionization. Later, at the apparition of comet

Kohoutek (C/1973 E1), atomic O and C were identiﬁed

in the spectra and direct UV images of the H coma, as

well as of the O i and C i emissions, were obtained from

sounding rocket experiments. These experiments were

repeated for comet West (C/1975 V1) and led to the ﬁrst

detection of CO [83.11].

Between 1978 and 1996, over 50 comets were

observed spectroscopically over the wavelength range

1200–3400 Å by the International Ultraviolet Explorer

(IUE) satellite observatory [83.19, 20]. Most of the

spectra were obtained at moderate resolution (∆λ =

6–10 Å), although high dispersion echelle spectra (∆λ

=0.2–0.3 Å) are useful for some studies, particu-

larly those of ﬂuorescence equilibrium (Sect. 83.2.2).

For Halley alone, over 200 UV spectra were obtained

from September 1985 to July 1986. The launch of the

Hubble Space Telescope (HST) in 1990, together with

subsequent enhancements to the spectroscopic instru-

mentation that were made on-orbit, marked another

advance in sensitivity as well as the ability to observe

in a small ﬁeld-of-view very close to the nucleus. This

yielded the ﬁrst detection of CO Cameron band emis-

sion, a direct measure of CO

being vaporized from

the nucleus [83.21]. For an overview of a cometary

spectrum, a composite spectrum of 103P/Hartley 2 span-

ning the region from H i Ly-α to 7000 Å taken with

Part G 83.1

Comets 83.1 Observations 1249

the Faint Object Spectrograph of HST, using ﬁve sep-

arate gratings, is shown in Fig. 83.1. The launch of the

Far Ultraviolet Spectroscopic Explorer (FUSE) in 1999

provides access to the spectral region between 900 and

1200 Å at very high spectral resolution, and has led to

the detection of H

(Sect. 83.2.4), upper limits on Ar

and N

, and some three dozen unidentiﬁed emission

lines [83.22,23].

Several other satellite observatories have contributed

unique cometary observations in the UV and sub-mm

spectral windows. The Solar and Heliospheric Ob-

servatory (SOHO) has two valuable instruments: The

SWAN (Solar Wind Anisotropies) instrument provides

skymapsinHi Ly-α at 1

◦

resolution and has ob-

served over 20 comets since 1996 [83.25]. The UVCS

(Ultraviolet Coronograph Spectrometer) provides far-

uv spectra and images of comets close to the Sun,

where HST and FUSE are prohibited from observing,

and has recently detected C

in the tail of comet

C/2002 X5 (Kudo-Fujikawa) [83.26]. The direct de-

tection of H

O in the fundamental rotational line at

557 GHz in several comets was made by the Submil-

limeter Wave Astronomy Satellite (SWAS) [83.27]and

the Odin satellite [83.28]. This line cannot be ob-

served from ground-based telescopes because of the

10 000.00

1000.00

100.00

10.00

1.00

0.10

0.01

1100 2000 3000 5000 8000

Wavelength (Å)

Brightness (Rayleighs/Å)

Cameron

Sun

Fig. 83.1 Composite FOS spectrum of comet 103P/Hartley 2. After [83.24]

strong absorption by water vapor in the terrestrial

atmosphere.

Prior to 1996, X-rayshad not been detected in comets

and the conventional wisdom wasthat they were unlikely

to be produced in the cold, rather thin cometary atmo-

sphere. The discovery of soft X-rayemission (E <2keV)

from comet Hyakutake (C/1996 B2) by the Röntgen

Satellite (ROSAT) thus came as a surprise [83.29].

Since then, X-ray emission has been detected from over

a dozen comets using ROSAT and four other space

observatories, the Extreme Ultraviolet Explorer, Bep-

poSAX,theChandra X-ray Observatory (CXO), and

Newton-XMM [83.30]. The earliest observations were

at very low spectral resolution, making it difﬁcult to se-

lect amongst the possible excitation mechanisms: charge

exchange, scattering of solar photons by attogram dust

particles, energetic electron impact and bremsstrahlung,

collisions between cometary and interplanetary dust, and

solar X-ray scattering and ﬂuorescence. The more re-

cent CXO observations, at higher spectral resolution,

favor the charge exchange of energetic minor solar wind

ions such as O

, and others, with

cometary gas, principally H

O, CO, and CO

, as the pri-

mary mechanism. This mechanism would explain why

the X-ray intensity appears to be independent of the gas

Part G 83.1

1250 Part G Applications

production rate of the comet, and that the peak emis-

sion is offset from the location of the comet’s nucleus.

This conclusion is also supported by recent laboratory

work on the charge transfer of highly ionized species

with cometary molecules [83.31] and by theoretical cal-

culations of state speciﬁc cascades [83.32]. The X-ray

emission thus tells us more about the solar wind than

about the gaseous composition of comets.

83.2 Excitation Mechanisms

83.2.1 Basic Phenomenology

Coma abundances may be derived from spectropho-

tometric measurements of either the total ﬂux or the

surface brightness in a given spectral feature. The un-

certainty in the derived abundances includes not only

the measurement uncertainty, but also uncertainties in

the atomic and molecular parameters and, in the case

of surface brightness measurements, uncertainties in the

model parameters used. Thus relative abundances, de-

rived from observations of different comets with the

same instrument and under similar geometrical condi-

tions, are often more reliable.

Atoms and ions in the cometary coma emit radiation

primarily by means of resonance re-radiation of solar

photons. For the cosmically abundant elements H, C, N,

O, and S, their strongest resonance transitions are in the

VUV. The few exceptions are noted below. Assume that

the coma is optically thin in these transitions. The total

number of species i in the coma is

= Q

(r), (83.1)

where Q

is the production rate (atoms or molecules s

−1

)

of species i and τ

(r) is its lifetime at heliocentric dis-

tance r, τ

(r) = τ

(1 AU)r

.Ther dependence arises

from photolytic destruction processes induced by solar

UV radiation, and to a lesser degree by the solar wind,

as described in Sect. 83.3.1.

The luminosity, in photons s

−1

, in a given transition

at wavelength λ,isthen

iλ

= M

iλ

(r), (83.2)

where the ﬂuorescence efﬁciency, or “g-factor”, g

iλ

(r) =

iλ

(1 AU)r

−2

,is

iλ

(1 AU) =

πe

πF



photons s

−1

atom

−1

, (83.3)

where f

is the absorption oscillator strength, πF



the solar ﬂux per unit wavelength interval at 1 AU and

is the albedo for single scattering, deﬁned for a line in

an atomic multiplet as

ω =



, (83.4)

where A

is the decay rate. If a given multiplet is not

resolved, then

ω = 1. For diatomic molecules, ﬂuores-

cence to other vibrational levels becomes important and

the evaluation of

ω depends on the physical conditions in

the coma, as discussed in Sect. 83.2.2. Thus, for a comet

at a geocentric distance ∆, the total ﬂux from the coma

for the transition is

iλ

4π∆

iλ

(r)τ

(r)

4π∆

, (83.5)

and the product g

iλ

(r)τ

(r) is independent of r.

Unfortunately, the scale lengths (the product of life-

time and outﬂow velocity) of almost all of the species of

interest in the UV are ≈10

–10

km at 1 AU. Thus, total

ﬂux measurements require ﬁelds of view ranging from

several arc-minutes to a few degrees. This has been done

only in the case of a few isolated sounding rocket exper-

iments. Most information about the UV spectra comes

from observations made by orbiting satellite observa-

tories whose spectrographs have small apertures (e.g.,



×20



for IUE) and thus sample only a very small

part of the total coma. In this case, again assuming an

optically thin coma, the measured ﬂux F



iλ

in the aper-

ture can be converted to an average surface brightness

iλ

(in units of Rayleighs):

iλ

= 4π10

−6



iλ

Ω

−1

, (83.6)

where Ω is the solid angle subtended by the aperture.

The brightness, in turn, is related to

, the average

column density of species i within the ﬁeld of view by

iλ

= 10

−6

iλ

(r)N

. (83.7)

The evaluation of Q

from N

requires the use of a model

of the density distribution of the species i (Sect. 83.3.2).

A similar treatment can be applied to the excitation

of the near infrared vibrational transitions of cometary

parent molecules since the direct pumping by solar IRra-

diation far exceeds the indirect pumping of ground state

vibrational levels through electronic transitions excited

by the solar UV ﬂux [83.16]. However, this does not ap-

ply to the rotational transitions which are controlled by

collisional excitation, primarily collisions with H

O. In

this case, the observed rotational temperature may be re-

garded as a reliable measure of the kinetic temperature

of the coma gas.

Part G 83.2

Comets 83.2 Excitation Mechanisms 1251

83.2.2 Fluorescence Equilibrium

In the case of low resolution spectroscopy, where an

atomic multiplet or molecular band is unresolved, the

evaluation of the g-factor (83.3) does not require knowl-

edge of the population of either atomic ﬁne structure

levels or molecular rotational levels in the ground state

of the transition. Furthermore, the assumption that the

solar ﬂux does not vary over the multiplet or band allows

us to use the total transition oscillator strength. This as-

sumption is more often than not invalid because of the

Fraunhofer structure of the solar spectrum in the near

uv and visible region and the emission line nature of

the spectrum below 2000 Å. For high resolution spectra,

the g-factors for each individual line must be calculated

separately and the relative populations of the ground

state levels must be included. There are three cases to be

considered:

1. The g-factor, or probability of absorption of a solar

photon, is less than the probability that the species

will be dissociated or ionized, i. e., g

iλ

<(τ

)

−1

In this case, the ground state population is not af-

fected by ﬂuorescence and a Boltzmann distribution

at a suitable temperature (typically ≈200 K at 1 AU)

corresponding to the production of the species may

be used. This is often the case in the far UV,where

the solar ﬂux is low, such as for the Fourth Posi-

tive band system of CO. For atomic transitions from

triplet ground states, such as is found with O, C

and S, downward ﬁne structure transitions are fast

enough to effectively depopulate all but the lowest

ﬁne structure level.

2. The species undergoes many photon absorption and

emission cycles in its lifetime, and the ground state

population is determined (usually after 5 or 6 cycles)

by the ﬂuorescence branching ratios. This is the con-

dition of ﬂuorescence equilibrium, which applies for

almost all radicals observed in the visible and near

UV regions. The general procedure is to solve a set

of coupled equations of the form

=−n



b=1



b=1

, (83.8)

where n

is the relative population of level a and p

and p

are transition rates out of and into this level,

respectively. The n

are normalized to unity. The

steady state, obtained after many cycles, is given

by dn

/dt = 0. Since the downward transition rates

are determined only by quantum mechanics, while

the absorption rates depend on the magnitude of the

solar ﬂux, the steady state population varies with

distance from the sun with higher rotational levels

(as for the case of CN [83.8]) populated closer to the

sun. In some cases, where only a few cycles occur,

the equations are integrated numerically. As the g-

factor varies with time, it also effectively varies with

the position of a species in the coma. Care must also

be taken when spectra taken with small apertures are

analyzed as the transit time for an atom or molecule

to cross the aperture may be

 g

iλ

(r)

−1

. In practice,

these considerations are often not important.

3. The same as 2. except that the density is sufﬁciently

high that collisional transitions must be included in

addition to the radiative transitions between lev-

els. However, as the collisional rates are poorly

known, in practice a “collision sphere” is deﬁned

such that a molecule traveling radially outward from

this sphere suffers only one collision with other

molecules or atoms. Outside this sphere, ﬂuores-

cence equilibrium is assumed to hold, while inside

a thermal distribution of ground state levels is used.

A rough estimate of the radius R

of the colli-

sion sphere, based on the radial outﬂow model of

Sect. 83.3.2 is given by [83.2,3]

= 10

km , (83.9)

where Q isthe total production rate in molecules s

−1

83.2.3 Swings and Greenstein Effects

Swings [83.33] ﬁrst pointed out that because of the

Fraunhofer absorption lines in the visible region of the

solar spectrum, the absorption of solar photons in a mo-

lecular band would vary with the comet’s heliocentric

velocity

r, leading to differences in the structure of

a band at different values of

r when observed at high

resolution. In (83.8), this corresponds to evaluating the

= p

(

r). For typical comets observed near 1 AU,

r can range from –30 to +30 km/s, while in certain

cases of comets with small perihelia the range can be

twice as large. This effect of the Doppler shift between

the sun and the comet is commonly referred to as the

Swings effect. Even for observations at low resolution,

the Swings effect must be taken into account in the cal-

culation of the total band g-factor, and this has been

done for a number of important species such as OH, CN

and NH. A particularly important case, that of the OH

− X

Π (0,0) band at ≈ 3085 Å, which is often

used to derive the water production rate of a comet,

Part G 83.2

1252 Part G Applications

is illustrated in Fig. 83.2, which also shows the de-

pendence of ﬂuorescence equilibrium on heliocentric

distance [83.34].

While this effect was ﬁrst recognized in the spectra

of radicals in the visible range, a similar phenomenon

occurs in the excitation of atomic multiplets below

2000 Å, where the solar spectrum makes a transition to

1.00 AU; unquenched

1.00 AU; quenched

0.25 AU; unquenched

0.25 AU; quenched

–60 –40 –20 0 20 40 60

Heliocentric velocity (km/s)

L/N × r

(10

–15

erg/s × molecule)

Fig. 83.2 OH (0,0) band g-factor as a function of heliocen-

tric velocity. After [83.34]

–0.3 –0.2 –0.1 0 0.1 0.2 0.3

(km/s)

80 40 0 –40 –80

g(× 10

–6

/s × atom)

Solar

flux

(×10

photons/

× s

× Å)

∆λ(Å)

λ 1302.2 Å

g(Lyβ)

× 10

Fig. 83.3 Solar ﬂux and ﬂuorescence efﬁciency for O i λ1302 as

a function of heliocentric velocity. After [83.35]

an emission line spectrum. For example, the three lines

of O i λ1302 have widths of ≈ 0.1 Å, corresponding to

a velocity of ≈25 km/s, so that knowledge of exact so-

lar line shapes is essential for a reliable evaluation of

the g-factor for this transition [83.35], as illustrated in

Fig. 83.3.

A differential Swings effect occurs in the coma since

atoms and molecules on the sunward side of the coma,

ﬂowing outward towards the sun, have a net velocity that

is different from those on the tailward side, and so, if

the absorption of solar photons takes place on the edge

of a line, the g-factors will be different in the two direc-

tions. Differences of this type appear in long-slit spectra

in which the slit is placed along the sun-comet line (the

Greenstein effect [83.36]). Again, an analogue in the far

UV has been observed in the case of O i λ1302 [83.37],

as can be seen in Fig. 83.3. Although it is also possible

to explain the observation by nonuniform outgassing,

this was considered unlikely as all of the other observed

emissions had symmetric spatial distributions. The mea-

surement of the Greenstein effect leads immediately to

a determination of the mean outﬂow velocity of the given

species.

83.2.4 Bowen Fluorescence

Figure 83.3 also demonstrates that for heliocentric ve-

locities > 30 km/s, the Doppler shift reduces the solar

ﬂux at the center of the absorption line to a very small

value, so that the O i λ1302 line is expected to appear

weakly, if at all, in the observed spectrum. Thus, it was

a surprise that this line appeared fairly strongly in two

comets, Kohoutek (C/1973 E1) and West (C/1975 V1),

whose values of

r were both > 45 km/s at the times of

observation. The explanation invoked the accidental co-

incidence of the solar H i Ly-β line at 1025.72 Å with the

O i

D −

P transition at 1025.76 Å, cascading through

the intermediate

P state as shown in the simpliﬁed en-

ergy level diagram of Fig. 83.4 [83.35]. This mechanism,

well known in the study of planetary nebulae, is referred

to as Bowen ﬂuorescence [83.38]. The g-factor due to

Ly-β pumping is an order of magnitude smaller than

that for resonance scattering, as shown in Fig. 83.3,but

sufﬁcient to explain the observations and to conﬁrm that

O is the dominant source of the observed oxygen in

the coma.

Ly-β is also coincident with the P1 line of the (6,0)

band of the H

Lyman system



− X



lead-

ing to ﬂuorescence in the same line of several (6,v



)

bands, the strongest being that of the (6,13) band at

1608 Å [83.39]. This line is, however, difﬁcult to ob-

Part G 83.2