Time-dependent H2 formation and protonation

0.24 MB·

by  H. S. Liszt

Astronomy&Astrophysicsmanuscriptno.ms5070 c ESO2009
(cid:13)
January27,2009
Time-dependent H formation and protonation in diffuse clouds
2
H.S.Liszt1
NationalRadioAstronomyObservatory,520EdgemontRoad,Charlottesville,VA,USA22903-2475
9 receivedJanuary27,2009
0
0 ABSTRACT
2
n Aims.Todemonstratethetime-approachtoequilibriumofH2-formationandprotonationinmodelsofdiffuseorHIinterstellargas
a cloudspreviouslypublishedbytheauthor.
J Methods.ThemicroscopicequationsofH2-formationandprotonationareintegratednumericallyovertimeinsuchamannerthatthe
overallstructuresevolveself-consistentlyunderbenignconditions.
8
Results.TheequilibriumH formationtimescaleinanHIcloudwithN(H) 4 1020 cm 2is1 3 107yr,nearlyindependentof
theassumeddensityorH fo2rmationrateongrains,etc.Attemptstospeedup≈the×evolution−oftheH− -f×ractionwouldrequiredensities
] 2 2
A wellbeyondtherangeusuallyconsideredtypicalofdiffusegas.Thecalculationssuggestthat,underbenign,quiescentconditions,H2
inthediffuseISMformationofH isfavoredinlargerregionshavingmoderatedensity,consistentwiththeratherhighmeankinetic
G 2
temperaturesmeasuredinH ,70-80K.
2
. FormationofH +isessentiallycompletewhenH -formationequilibratesbutthefinalabundanceofH + appearsmorenearlyatthe
h 3 2 3
verylastinstant.Chemistryinaweakly-moleculargashasparticularpropertiessothattheabundancepatternschangeappreciablyas
p
gasbecomesmorefullymolecular, eitherinmodel sequences orwithtimeinasinglemodel.Onemanifestationofthisisthatthe
-
o predictedabundanceofH3+ismuchmoreweaklydependentonthecosmic-rayionizationratewhenn(H2)/n(H)< 0.05.Ingeneral,
r high abundances of H3+ do not enhance the abundances of other species (e.g. HCO+) but late-time OH format∼ion proceeds most
t vigourously in more diffuse regions having modest density, extinction and H fraction and somewhat higher fractional ionization,
s 2
a suggestingthatatypicallyhighOH/H2abundanceratiosmightbefoundopticallyindiffusecloudshavingmodestextinction.
[
Keywords. interstellarmedium–molecules

1
v
1 1. Introduction. equilibriumisactuallyattainedintheinterstellarmedium,which
4
isthesubjectofthiswork.
1 The fact that individual H I/diffuse clouds have a substantial Hereweshowtheapproachtoequilibriuminthemodelsdis-
1
componentofmolecularhydrogenhasbeenrecognizedobserva- cussedbyLiszt&Lucas(2000),Liszt(2002)andLiszt(2003):
.
1 tionallysincetheoriginalCopernicusobservations(Jura,1974; we present calculations of time-dependentH and H + forma-
2 3
0 Spitzer, 1978) and a quite high fraction of hydrogen in the tioninsmall,mostly-staticgasparcelsmeanttorepresenttypical
9 nearby diffuse interstellar medium (ISM) overall is in molecu- diffuse “clouds”,like, for instance,the “standard”H I cloudof
0
lar form (Savageetal., 1977; Liszt&Lucas, 2002). More sur- Spitzer (1978). As we discuss, the distinguishingcharacteristic
:
v prising perhaps is the recent discovery that this molecular ofthechemistryinsuchcloudsisthattheH formationprocess
2
i component hosts a rich polyatomic chemistry with relatively isunsaturated(n(H )<n(H)/2).Forthisreasontheequilibrium
X 2
large amounts of H3+ (McCalletal., 2002) and a dozen other timescales for H2 formation cannot be calculated from simple
r speciesincludingsuchionsasHCO+ (Lucas&Liszt,1996)and scalingargumentsbasedonthelocalmicroscopicH formation
a 2
HOC+ (Lisztetal., 2004) and molecules as complex as 3¸h2 rate, noraretheyshortenedbyself-shielding,or in manycases
(Coxetal., 1988; Lucas&Liszt, 2000), H2CO (Liszt&Lucas, by assuming higher density or even a higher rate constant for
1995; Moore&Marscher, 1995; Lisztetal., 2002) and NH3 H2 formationongrains,etc.FurthermoretheabundanceofH3+
(Nash,1990;Lisztetal.,2002). does not always vary as might be expected from consideration
The presence of copious H and relatively large amounts ofitsequilbriumchemistryinmorefullymoleculargas.
2
of H + in H I clouds is supported theoretically when self- Section 2 gives details of the methods used in the calcula-
3
shielding (Leeetal., 1996) is included in equilibrium mod- tions,resultsofwhicharepresentedanddiscussedinSect.3and
els of diffuse gas (Liszt&Lucas, 2000; Liszt, 2003) using 4.
empirically-determinedH formationrates(Jura,1974;Spitzer,
2
1978; Gryetal., 2002); observed HD/H ratios are also ex-
2 2. Detailsofthecalculationsandmicrophysics
plained as long as the cosmic-ray ionization rate is taken large
enoughtosupporttheinferredprotondensityinthepresenceof 2.1.Frameworkandinitialconditions
atomic-ion neutralization on small grains. However, formation
The calculations presented here build on a framework which
of H is a notoriously slow and supposedly rather fragile pro-
2
wasestablishedintheworkofWolfireetal.(1995).Specifically,
cess. Moreover, it remains to be determined whether any such
the two-phase model of heating and cooling developed by
Wolfireetal. (1995) (see also Wolfireetal. (2003)) was ap-
Sendoffprintrequeststo:H.S.Liszt pliedtosmall,uniformlyilluminatedsphericalgasclotsofcon-
Correspondenceto:[email protected] stantdensity,intendedtorepresentdiffuse’clouds’;ourmodel,
2 H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds
2
however,uses the gas-phaseabundancesof Savage&Sembach effectinvolvingassumptionsaboutcloudgeometry,ISMtopol-
(1996)whichmakesthemabithotter.Assumptionofageometry ogy,andsoforth.Thepurposeofthisworkistounderstandthe
isrequiredbecausetheaccumulationofH andCOdependson macroscopicaspectsof theaccumulationof H inthe ISM and
2 2
shieldingbydustandothermoleculesandis,therefore,strongly we employ only the most standard, empirical, microscopic de-
non-linear.WeusedtheshieldingfactorscalculatedbyLeeetal. scriptionofitsformation.
(1996).Typicaldensitiesandcolumndensitiesconsideredhere,
n(H)= 32cm−3,N(H)= 4×1020cm−2 correspondtoaSpitzer That is, the volume formation rate of H2 is expressed as
“standardcloud”(Spitzer,1978)havingadimensionofafewpc dn(H )/dt=n(H)n(HI)R <v >= 3 10 18cm3 s 1 n(H)n(H
2 G T − −
andmedianreddening0.05magoverthefaceofthecloud.The I) √T (Spitzer, 1978) wherethefact×orn(H)(the totaldensity
K
centralcolumndensityinsuchanH I cloudcorrespondsto the of H-nuclei) representsa constantnumberof large H -forming
2
regimewheretheappearanceofhighH2-fractionsisfirstnoted grainsperH-nucleusinthegas;n(HI)is thedensityofatomic
intheISM. hydrogen(afterprotons,H ions,andH ,etc.arereckoned)and
− 2
Ingeneral,thehydrogendensitiesinourmodels(numberor thethermalvelocityand/orkinetictemperaturetermscorrespond
column)areassumedvalues.Thetemperatureandthermalpres- to the speed at which H-atoms move throughthe gas, possibly
sure follow from the details of the calculation, chiefly through encountering large grains. The rate constant R nominally in-
G
the assumed gas-phase abundances of the dominant coolants cludesastickingcoefficient.
carbon and oxygen, and the influence of the radiation field in
heating the gas via the photoelectric effect on the same small
The inferred rate in the diffuse ISM has been remark-
grains which are so largely responsible for the overall charge
ably steady over the last 25 years (Jura, 1974; Spitzer, 1978;
balance. As shown in Fig. 9 of Liszt&Lucas (2000), a given
Gryetal., 2002) and use of this simple formulation, com-
value of the scaling factor (G ) for the overall radiation field
0 bined with the modern shielding coefficients, accounts ex-
produces a roughly constant thermal pressure in the outer re-
tremelywellforthe observationsofH indiffuselinesofsight
2
gionsofourmodels,increasingsomewhatwithassumeddensity
(Liszt&Lucas,2000).AsdiscussedinSect.3(seeFig.4)vary-
anddecreasingslightly goinginwardfromthe cloudedge.The
ingtheassumedvalueofR byfactorsofafewhasappreciable
generally-acceptedvalueforthethermalpressureoftheISM,p/k G
effectupontheamountofH whichisproducedbuttheequilib-
2 3 103cm 3K(Jenkins,2002;Jenkins&Tripp,2001)in- 2
− riumtimescalechangeslittle.Asanasidewenotethatthegas-
≈ − ×
deedappliestoourtypicalmodeloftheSpitzer“standardcloud”
phaseformationofH viaH ,whichcouldaccountforsomeof
2 −
and the very densest models considered here have pressures a
theverylowmolecularfractionsseenalonglinesofsighthaving
factor2-3timeshigher,asseemsobservationallytobethecase
low extinction(Liszt, 2002), is includedin the presentcalcula-
aswell.
tionsaswellbutwithoutmucheffect.
The initial condition here is simply the equilibrium diffuse
cloud model which would be calculated in the absence of any
molecular chemistry, as is more typical in discussions of the
overallstructure of the diffuse ISM (Wolfireetal., 2003). That 2.3.SolvingtheH-accumulationproblem
2
is, the initial modelis equilibratedand self-consistent in terms
of thermal and ionization equilibrium, but no molecule forma-
tionhasoccurred.Ourmodelsincludetherudimentsofmolec- TheequilibriumsolutionsfortheradialdistributionsofCO,H2
ularchemistryasdiscussedinseveralrecentpapersconcerning and H3+ describedin our earlier paperswere achievedthrough
questionsofequilibriumCO,H ,HDandH + formationindif- what is essentially a relaxation method. An initially atomic
2 3
fusegas(Liszt&Lucas,2000;Liszt,2002,2003).Incorporation sphere is divided into a substantial number (typically 100) of
ofthechemistryshouldnotnormallyupsetthebasicmicrophys- thin radial shells and the molecular densities are calculated
icalbalance(ionization,thermodynamic,etc.)indiffusegasbe- for each, working inward, self-consistently accounting for the
causesuchsmallfractionsofoxygenandcarbonaresequestered, shielding which accrues from each configuration. Each time a
althoughinclusionofOHandH formationcanaffectsomeas- quasi-equilibriumstateisreachedfortheentirestructure(thatis,
2
pectsofthedistributionofchargeamongspecies. whenthecalculationhassuccessivelyconvergedineachshell),
Another effect mitigating the influence of H2 formation in the calculation starts anew at the outermost shell (whose H2-
diffuse gas is the dominance of atomic-ion neutralization by abundancewas,afterall,calculatedinatleastpartialignorance
small grains, substantially lowering the H+ and electron den- oftheconditionsinteriortoit)andtheprocessisrepeateduntil
sitywhichwouldotherwiseobtaininthepresenceofcosmic-ray the whole structure varies sufficiently little between iterations.
ionization of hydrogen(Wolfireetal., 1995; Liszt, 2003). This The processis notparticularlydifficultorunstable andconver-
effect is of the utmost importance in understanding the inter- genceisrapid,typicallyrequiringonlyafewsecondsonarecent
play between the cosmic ray ionization rate ζ (here taken as laptopcomputer.Notethatthethermalandchargebalance,etc.
H
therateperfreeH-nucleus)andabundanceofH + (Liszt,2003) arecontinuallyupdatedduringthecalculation.
3
.Detailedcalculationincludinggraincharging(Draine&Sutin,
1987; Weingartner&Draine, 2001) is required if the heating The time-dependent calculations basically just wrap the
rate is to be properly calculated according to the prescription equilibriumsolverinanouterloopwhichallowstheentirestruc-
ofBakes&Tielens(1994). tureto evolveself-consistentlyovershorttimes. Thetime step,
which initially cannot be as large as even 1000 years in most
cases, is examinedandlengthenedbya factorof √2 whenever
2.2.FormationofH
2 the structurechangessufficientlylittle betweentime steps. The
InthisworkwedistinguishbetweentheformationofH ,which full time-dependent calculation is somewhat tedious, typically
2
weconsidertobeamicroscopicphysicaleffectoccuringonindi- requiring several hours per model and much exercising of the
viduallargegrainsandinvolvingindividualorpairedH-atoms, tiny(butassertive)fanontheauthor’slaptopcomputerincases
andtheaccumulationofH intheISM,whichisamacroscopic ofhighH -fraction.
2 2
H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds 3
2
2.4.Elementaryanalyticconsiderationsofthe 2.6.Thecosmic-rayionizationrateζ
H
time-dependentsolutionsforH
2
The evolution of the H fraction is largely independent of the
Althoughthe real solution to the time-dependentaccumulation 2
assumedvalueofζ inourmodelsbutthestandardcosmic-ray
problemisstronglynon-linearandcanonlybeachievedglobally H
ionizationrateassumedinthemodelsinthisworkisζ =10 16
over an entire geometrical construct, several important aspects H −
s 1(thecosmic-raydestructionrateperH isslightlymorethan
of the problem may be understood with reference to a simple − 2
2ζ ).Thisisapproximatelyoneorderofmagnitudelargerthan
parametrictreatmentofpurelylocalbehaviour. H
whatisoftenusedincalculationsofcosmic-rayionizationofthe
Accordingly,thelocalrateofaccumulationofmolecularhy-
ISM(Wolfireetal.,1995)especiallyfordensedarkcloudchem-
drogenmaybewritten
istry and is about that which is needed to explain the overall
abundance of H + (see Sect. 4). The equilibrium H + concen-
3 3
trationis nearlyproportionalto ζ in ourmodelshavinglarger
H
dn(H2)/dt=−n(H2)ΓH2 +RGn(H)n(HI)pTK (1) H2fractions(seeFig.5)owingtotheinterventionofsmall-grain
neutralization of protons: the formation can be pushed harder
where Γ is the rate of H destruction (mostly by cosmic without unduly increasing the electron density and recombina-
H 2
rays and ultra2-violet photons, although interaction of He+ and tionrateforH3+.However,forreasonsdiscussedinSect.4,the
concentrationofH +ismoreweaklydependentonζ inregions
H is included in the numerical calculation), T is the kinetic 3 H
2 K
temperature(calculatedinthemodels)andR = 3 10 18 cm3 ofsmallH2-fractionorwhenζH isverylarge.
G −
s 1 (seeSect.2.2).Afterrewritingn(HI)=n(H)-×2n(H )(for
− 2
thepresentpurposes;allformsofhydrogenareconsideredinthe
numericalmodels)thesolutionis 2.7. HeatingbycosmicraysandH2-formation
n(H ) =b/a+(n(H ) b/a)e at (2) The current assumption is that the diffuse ISM is heated by
2 t 2 t=0 −
| | − thephotoelectriceffectonsmallgrainsin boththewarmphase
wherea=Γ +2R n(H)√T ,b=R n(H)2√T . (where x-raysmake a larger contribution)and cool phase. The
H G K G K
2 heating rate as a function of density in partly-shielded gas is
The time constant in the problem is 1/a, where a is a lin-
shown in Fig. 3 of Wolfireetal. (1995) based on the work of
ear combination of the per-particle formation and destruction
Bakes&Tielens (1994). As may be seen from that Figure, the
rates, observing the conservation of H-nuclei, and is therefore
cosmicrayheatingrateisroughly1.2dexbelowthatofthepho-
relatively short in weakly-shielded gas. The rate of accumula-
toelectric effect in diffuse gas and 2-2.5dex lower in coolgas,
tionofH takesonitshighestvaluedn(H )/dt=battime0and
2 2 for ζ = 10 17s 1. Thus the higher cosmic-ray ionization rates
the equilibriumsolution n(H ) = b/a may be thoughtof as H − −
2 t consideredheremayimplyasubstantialcontributiontotheheat-
the result of accumulation at t|h→e∞maximum rate over a period
ingofthewarmgasbycosmicrays,harkeningbacktothevery
oftime1/a.Thus,self-shielding(loweringΓ )cannotincrease
H2 earliestdiscussionsoftwo-phaseequilibrium,beforetheroleof
therateatwhichH formsorspeeduptheaccumulationofH ,
2 2 diffuseX-rayheatingwasincorporated(Goldsmithetal.,1969).
it only increases the final amount of H by allowing the accu-
2 The highest cosmic-ray rates considered here still do not pro-
mulationprocesstoworklonger.Bylengtheningthetime-scale,
ducedominantheatingeffectsinthecoolneutralgas,butmuch
self-shieldingmay also providea bufferagainstsuddenchange higherionizationrates ζ > 10 15s 1 were recentlysuggested
H − −
onceequilibriumisattained. byLePetitetal.(2004)for∼thelineofsighttoζ Persei.
Increasing the microscopic formation rate constant or den-
sity will hasten the pace at which H accumulatesbut even so, In our modelsthere is a modest contributionto the heating
2
globalequilibriaarenotgenerallyachievedmorerapidlyincases duetoH formation,comparabletothatarisingfromheatingby
2
wheretheH fractionwouldotherwisebesmall,asdiscussedin cosmic-ray ionization of H I. The volume heating rate due to
2
Sect.3(seeFig.4);itonlyhappensthatmoreH ismade(which the latter is ζ n(H I) E where E 8eV is the energy
2 H h cri h cri ≈
requiressomewhatmoretime).Maintenanceofhighequilibrium availableforheatingaftertheprimaryionization.Theequivalent
Heq2u-fivraacletinotntsorreeqduuicriensgΓthHe2ph<∼otoRdGens(trHu)ct√ioTnKr,awteh(iocfhoirsderrou1g0h−l1y0 rraetperefsoernHts2t-hfoartmfraatciotinonisoRfGthne(Hhe)nat(HofI)fo√rTmKahtEioHn2oifwHh2erwehhiEcHh2isi
s 1infreespace)toinsignificancei.e.Γ ζ . availabletoheatthegas.Theheatingratesforthetwoprocesses
− H H
2 ≈ areverynearlyequalundertypicalconditions,ζ = 10 16 s 1,
H − −
T =80K,n(H)=32cm 3and E =1.5eV.
K − H
h 2i
2.5.Weakvs.slowprocesses
Indeed, the situations which equilibrate most rapidly are those
for which the H2 abundanceis smallest, which exemplifiesthe 2.8.TherecombinationrateofH3+andotherchemical
fact that even processes like H formation or cosmic-ray ion- reactions
2
ization – which seem weak becausethey have low rates – may
equilibrate quicklywhen notcalled upon to do very much;the The chemical rate constants used in our models have been
timeconstantisthendeterminedbytheoveralldestructionrate, taken from the UMIST database (LeTeuffetal., 2000) (see
whichmaybehigh.ItisforthisreasonthatformationofH +–a http://www.rate99.co.uk) including,for consistencywith the re-
3
muchhigher-orderprocesswhichafterallrequiresformationof sultsofLiszt(2003),therateconstantfore+H +recombination
3
H , cosmic ray ionization of H and further interaction of H + α(T ) = 4 10 6/√T cm3 s 1. This rate has been measured
2 2 2 K − K −
×
and H (see Sect. 4.2) – is essentially complete as soon as H many times, including, most recently and probably accurately,
2 2
accumulationequilibrates:oneneednotwaitforafurtherperiod byMcCalletal.(2003).Theirmeasuredvalues,at23Kand300
1/ζ . K,are70%ofthoseusedinourwork.
H
4 H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds
2
10 1886 -6 4 88816
4 8 10 4
4 2 4
2
4
2
2 -7 1 2
10 1
1 2
1
1
-8
10
1
]
] 3
3 -
-m 1 m -9 0.5
c [c 10
) [ 0.1 0.5 +)
2 3
H H
n( n( 10-10
0.5
-11
0.5 10
0.01
-12
10 0.5
0.5
nH=32 cm-3 ζH=10-16 s-1
10-3 10-13
4 5 6 7 8 4 5 6 7 8
10 10 10 10 10 10 10 10 10 10
time [yr] time [yr]
Fig.1. Density of molecular hydrogenn(H ) (left) and H + (right) as functions of time within spherical, uniformly illuminated,
2 3
initially atomic gas spheres of constant density of H-nuclei n(H) = 32 cm 3, threaded by a cosmic ray flux yielding a primary
−
ionizationrateperH-atomζ =10 16s 1.Threecurvescorrespondingtoshellsatfractionalradii0,1/3and2/3fromthecenterare
H − −
shownforeachofaseriesofmodelswithdifferingcentralcolumndensityofhydrogen0.5 1020cm 2 N(H) 16 1020cm 2.
− −
Thephysicalsizeofthemodelsinpcandtheircentral(edge-to-edge)columndensityinuni×tsof1020 cm≤2aree≤quala×ndshownat
−
therightofeachcurve.
3. Time-dependentH accumulationindiffuse appreciable (easily detectable) amounts of H form in as little
2 2
clouds as 104 yr demonstrates why it is so hard to find lines of sight
havingmeasurablereddeningwhicharedevoidofH .ForN(H)
2
3.1.Evolutionaryeffectofvaryingcolumndensity aslargeas16 1020cm 2 theH accumulationprocessisthor-
− 2
×
oughlysaturated(n(H ) n(H)/2)whenequilibriumisreached
Figure 1 shows the evolution of the H2 and H3+ densities in a at very large times ap2pr→oaching 108 yr. Models in which the
seriesofmodels,eachhavingthesameuniformtotaldensityof
equilibrium H -distribution is more uniform also evolve more
hydrogenn(H)= 32cm 3 threadedbyacosmicrayfluxyield- 2
− uniformly,asillustratedinFig.2whichshows(attop)thetime-
ing ζ = 10 16 s 1. The central column density of hydrogen
H − − dependentevolutionoftheradialvariationofn(H )inthemodel
2
acrossthecloudsN(H)(fromedgetoedge)variesfrom0.5to16
resembling a “standard” H I cloud. The H -density is remark-
1020cm 2,asindicatedattherighthandsideofeachcurve.The 2
− ablyconstantforfractionalradiiof90%ormoreformostofthe
×
physical size of the models (diameter) in pc is, coincidentally, first1 3 106yr,afterwhichamoremolecularcoredevelops,
equal to the column density as labelled in units of 1020 cm 2. − ×
− aswellasaverythin(actually,unresolved)transitionlayerinto
Three curves are shown for each model, corresponding to the
amorenearlyatomicenvelope.
shells centered at fractional radii 0, 1/3 and 2/3 from the cen-
ter. These curves separate at larger times when the outermost Clearly, self-shielding is important only at somewhat later
regionshavereachedequililbrium.Forasphere,themedianline times.Insomemodelswithmoderatedensity,n(H )behavesas
2
of sight occurs at a fractional impact parameter of 2/3 where a single power-law from center to edge, as illustrated in Fig. 2
the column density traversed is 3/4 that at the center. The me- at bottom which shows the equilibrium solutions for n(H ) =
2
dianlineofsightthroughthemodelwithcentralcolumndensity 32 cm 3 correspondingto the models used in Fig. 1. However
−
4 1020cm−2,3 1020cm−2correspondsexactlytothestandard thisisnotageneralfeatureoftheequilibriumsolutions.Figure
× ×
HIcloudofSpitzer(1978). 2 also illustrates the effect of finite resolution on the structure
For the optically-thinnestmodel there is a large radial gra- oftheatomicenvelope,whichfractionallyissubstantiallylarger
dientin the H density and a wide disparity between the times with higherresolution.Theresultsin Fig. 1arenotaffectedby
2
requiredtoreachequilibrium(104 106 yr).Thefactthatsuch theillustrateddoublingofthenumberofradialshells.
−
H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds 5
2
10 3.2.Evolutionaryeffectofvaryingnumberdensity
30561
nH=32 cm-3 NH=4.0E20 cm-2 10157 Itseemsnaturaltoinquireinwhatwaystheevolutionmightbe
5832
hastened.ShowninFig.3areresultsforseriesofmodelsofdif-
3356
2328 ferentnumberdensity8cm−3 n(H) 128cm−3atcolumnden-
1612 sitiesN(H)=2 16 1020cm≤ 2.At≤leastformoderatecolumn
1 1114 − × −
densities, as shown at the left in Fig. 3, increasing the number
772
534 densitywithintherangeexpectedfordiffusegashassurprisingly
370 littleeffectonthetimerequiredforthemodelstoreachequilib-
308
] 213 rium:theincreasedrateofaccumulationiscompensatedbythe
3
- 147 tendencytoproducemoreH ,makingtheequilibriumtimescale
m 0.1 101 2
c aboutconstantoverawiderangeofdensityforthestandardHI
) [ 4780 cloudcolumndensity.
2
H 33 OnlywhenveryhighH2fractionsareattainedatagivenden-
n( 22 sitydoesincreasingthedensityshortentheequilibriumtime(i.e.
15 Fig.3atright,orforthetwoveryhighestdensitiesatleft).With
0.01 810 reference to Fig. 3, note that, although the local accumulation
6 rateinitiallyvariesasn(H)2√T n(H)3/2 inthermalpressure
5 K
4 equilibrium,thetotalamountofH∝producedwithinamodelat
3 2
any time is much less dependent on density because the more
2
tenuous models are larger, varying as 1/n(H). Obviously, all
10-3 1 modelsinwhichtheH2 accumulationsaturatesathighmolecu-
larfractionsproducethesameN(H )iftheyhavethesameN(H),
2
solessdensemodelshavingthesameN(H )thenmakemoreH
2 2
10 0.01 0.1 116 moleculesoverallbecausetheyarelarger.
-3 8
nH=32 cm 4
2
3.3.Doessizematter?
1
1
N(H) PhysicallylargercloudstendtoproducemoreH inbothseries
2
ofmodelsjustdiscussed.ThoseinFig.1withlargercolumnden-
sityN(H)arephysicallylargerandhavehigherinternalmolecu-
larnumberdensity,so,atfixednumberdensity,physicallylarger
0.1
regions of higher column density are responsible for the very
greatbulkoftheaccumulationofH .InFig.3,molecularnum-
2
berdensitiesarehigherincloudsofhighern(H),butusuallynot
0.01 by such largeamountsas to compensatefor the very large dif-
ferencesinvolume.Thatis,themodelvolumesvarybyafactor
192 zones (128/8)3 4000whereasn(H2)variesbyfactorsof100-500for
96 zones themodel≈swithN(H)=4 16 1020 cm 2.Overasubstantial
−
10-3 rangeinN(H),itisexpecte−dtha×tthebulkofthemoleculeswill
0.01 0.1 1 formin(again)physicallylargerregions,butoflowerdensity.
fractional distance inside SoisthebulkoftheinterstellarH reallyformedinlargeten-
2
uousregions,orinmorecompact,denserones?Observationally,
Fig.2.Radialandsecularvariationofmolecularhydrogenden-
themeancolumndensity-weightedkinetictemperatureinferred
sity within models illustrated in Fig. 1. Top: Time evolution for H -forming diffuse gas is 70–80 K (Savageetal., 1977;
of n(H ) for n(H) = 32 cm 3, N(H) = 4 1020 cm 2. Labels 2
2 − − Shulletal., 2004), which, for typical interstellar thermal pres-
×
at right give the elapsed time in units of 1000 yr. Bottom: sures, implies densities like those of the standard H I cloud 1.
Radial variation in equilibrium for n(H) = 32 cm 3 and N(H)
− Attempts to form the observed H more rapidly in regions of
= 1,2,4,8,16 1020 cm 2,forcalculationsemploying96and 2
− high density must account for these high kinetic temperatures;
×
192radialzones.
perhapsitisrelevantthatJenkins&Tripp(2001)foundasmall
but pervasive fraction of material at much higher than normal
thermal pressure in typical diffuse clouds probed in the fine-
structureexcitationofCI.Thishigh-pressurecomponentisgen-
erallyignoredincalculationofthemeanthermalpressureinthe
ISM,butwouldapproximatelydoubleit.
As shown in Fig. 1, even a standard H I cloud model has
a very substantial fraction of molecular hydrogen in its inte-
3.4.Changesinformationanddissociationrateconstants
rior.Thisofcourseisborneoutobservationally(Jura,1974)as
molecular fractions of 25%-45% are derived for even the dif- The empirically-inferredmicroscopic formation rate of molec-
fuseISMobservedinuv/opticalabsorptionlinesofH2 andCH ular hydrogen formation has changed remarkably little since
(Savageetal., 1977; Liszt&Lucas, 2002). Less obvious,how- H was first observed in the ISM (Jura, 1974; Spitzer, 1978;
2
ever,isthattheconditionssofavourabletoH mayactuallywork
2
foraslongasthecalculationsrequiretoreachequilibriuminFig. 1 Notethatthesurveysfromwhichthesemeantemperaturesarede-
1,i.e.fortimesaslongas108yr. rivedhavesomewhatlowsamplemeanH -fractions,0.17-0.18.
2
6 H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds
2
10
2
2
2
1
]
3
-
m 0.1 2
c
[ 2
)
2
H n n
( H H
n0.01 128 128
64 64
10-3 32 2 32
16
16
10-4 8 NNHH==42xx11002200 ccmm--22 8 NH=16x1020 cm-2
3 4 5 6 7 8 3 4 5 6 7 8
10 10 10 10 10 10 10 10 10 10 10 10
time [year]
Fig.3. Density of molecular hydrogen n(H ) as a function of time within spherical, uniformly illuminated, initially atomic gas
2
spheresofdifferingdensityofH-nuclein(H)=8 128 cm 3(asshownattheleftofeachfamilyofcurves),threadedbyacosmic
−
ray flux yielding a primary ionization rate per H−-atom ζ = 10 16 s 1. At right, all models have a central column density N(H)
H − −
= 16 1020 cm 2 (from edge to edge); at left, results are interspersed for N(H) = 2 (dashed; red in appropriate media) and 4
−
1020×cm 2. Asin Fig. 1,threecurvesare shownforeachmodel,correspondingtofractionalradii0, 1/3and2/3fromthe cloud
−
×
center.
Gryetal.,2002).Figure4showstheeffectsofchangingtheas- Figure5atrightshowstheeffectofvaryingtheprimarycos-
sumedH formationrateconstantR insomeofthemodelsil- mic ray ionization rate by factors of three about the standard
2 G
lustratedin Fig.1.AlthoughtheH columnandnumberdensi- value ζ = 10 16 s 1. Such variations have little effect on the
2 H − −
tiesincreasefasterthanlinearlywithchangesinR atlatetimes, equilbriumH densities in standard H I clouds as long as they
G 2
thetimescalemayonlybeshortenedafterthemolecularfraction arenotsolargeastoupsetthethermalbalance(whichcanoccur
approachesitsmaximumpossiblevalue. for ζ > 10 15 pc). The more complicated behaviour of H + is
H − 3
AsnotedinSect.2.4,highmolecularfractionsmayonlyac- discuss∼edinSect.4.
crueincaseswherethe free-spacephotodissociationrateofH
2
is attenuated (by dust and self-shielding) to the point where it
is no more than competitive with cosmic-ray induced destruc- 4. H3+ andothertracespecies
tionrates.Itfollowsthatnaturalvariationsintheambientinter- 4.1.Evolutionofn(H+)
stellar radiation field (ISRF) may encourage or discourage H 3
2
accumulation, but only modestly and at late times when equi- In the ISM there is a general increase in N(H +) with redden-
3
librium is approached.Shown in Fig. 5 at left are results for a ing correspondingto N(H +) = 8 1014 cm 2 over 6 magni-
3 −
lower-densitymodel(n(H)= 8cm 3)atN(H)= 4 1020cm 2, tudes, or to N(H +)/N(H) 2.3 ×10 8 for the standard gas-
− − 3 −
with the ISRF lowered by factors of 2 and 4. Cl×early the H reddeningratioN(H)/E ≈= 5.8 ×1021 cm 2 mag 1 (seeFig.
2 B V − −
accumulationprocessmaybeenhancedbymakingthematerial 14ofMcCalletal.(2002−)). ×
sufficientlydark,butonlyattheexpenseofincurringverylong Asdiscussedpreviously(Liszt,2003)orasshowninthefig-
equilibriumtimes.Notethatthedarkermodelsactuallyformand ures here, n(H +) concentrations comparable to those required
3
accumulatesomewhatlessH atsmallertimesbecausetheyare canbeproducedinequilibriummodelsofdiffusecloudsofmod-
2
substantiallycooler;lowerphotoelecticheatingratesaccompany eratenumberandcolumndensityforcosmicrayionizationrates
lowerphotoionizationratesformolecules.Cloudsinverylocally ζ at or somewhat above 10 16 s 1 (see Fig. 5 at right). Such
H − −
darkerregionswouldhavetobeoverpressuredinordertocom- models of H + in diffuse gas have the added virtue that the
3
pensateforthissluggishness,butintheISMatendencytohigher HD/H ratiosobservedindiffuseclouds–whichareverysensi-
2
thermalpressureathigherdensityseemsarealeffect. tivetotheactualprotondensity–arealsoreproduced.
H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds 7
2
As showninthe figures,theH + fractionis sensitiveto the
3
sameeffectswhichincreasetheconcentrationofH2,andinsome H2++H2 H3++H, (4c)
circumstances to the cosmic ray ionization rate as well (Fig. 5 →
here).Therearesomemoresubtleeffectswhicharelessobvious
in the figures: in models which achieve large H -fractions, the H ++e 3H, etc (4d)
2 3
→
electrondensityislower bya factorof (typically)abouttwo at
late times because the gas cannotsustain high proton densities So, whenever the recombination described in reaction 4b
whenmostofthehydrogenismolecular. dominatesovertheprotonationinreaction4c,theabundanceof
samAelfithnoaulgthimtehsecaHle3+asfrtahcattioonfeHq2u,iltihberaptersobolnemveorfytimmuecshcatlhees nH(2H+2+w)i/lnl(bee)∝inζvHer/sne(ley)2p.rCoaplocrutliaotninalgttohen(ioe)niaznadtionn(Hb3a+la)n∝ceni(nHa2n)
issomewhatmorecriticalforH + becauseitstimederivativeis atomicgasaccordingtotheprescriptioninSpitzer(1978)indeed
3
muchsteeper;thefinalconcentrationoccursmorenearlyatonly yieldsn(e) √ζH forζH 10−17s−1underconditionstypicalof
∝ ≥
the final momentsof the calculation.Conversely,the H + frac- HIclouds.
3
tionwoulddeterioratemorerapidlyshouldconditionssuddenly For the model of a typical H I cloud shown at right in
becomelesshospitable.Ofcoursethiseffectismitigatedslightly Fig. 5, such considerations are apparently sufficient to remove
whenthe H3+ fractionis calculatedwith respectto H2 (instead much of the dependence on ζH from the H3+ density at early
ofn(H))butinmostcasesthelinesofsightwithknownN(H +) times. To ascertain the conditions under which this effect is
3
arenotaccessibletodirectmeasurementofN(H2)orevenN(H important, note that the recombination coefficient of H2+ is
tIh).eNeoffteectthiastrHea3+llyissatrlsoongmoonrelyceinntmraolldyeclsonwciethnitnrawtehditchhanthHer2e,baruet αrate=c4on×sta1n0t−k6/=√T2K.08cm31s0−−19acnmd3rse−a1ctiinonthe4cUpMroIcSeTeddsatwabitahsea,
×
largerradialgradientsinn(H ). see LeTeuffetal. (2000) or http://www.rate99.co.uk. Thus for
2
T =100Kandtakingn(e)asasmallmultiple(2 )ofthegas-
K
phaseabundanceofcarbon,n(C+) 1.4 10 4n(×H),itfollows
−
4.2.EffectofchangingζH thatrecombinationdominatesandt≈hefun×ctionaldependenceof
The presenceof highcosmic ray ionizationratesin diffuse gas n(H3+)uponζH isweakenedforn(H2)/n(H)<0.05,withhigher
has been inferred from very elementary analysis of the H + H2concentrationsrequiredforhighern(e)an∼d/orζH.InFig.5at
3 right,thisiscaseforthefirst1 2 106yr.
abundance which treats it like an atomic ion (McCalletal.,
− ×
2002).Assuming–asistrueofdark,densemoleculargas–that
everyprimaryionizationofH2leadstoanH3+ ionandthatH3+ 4.3.InfluenceofH+onothertracemoleculeabundances
3
ions are destroyed by electron recombination with a rate con-
stant α , there followsa simple, formalexpressionfor the H + IngeneralthesurprisinglyhighabundanceofH + indiffusegas
e 3 3
density: shouldnotaltersignificantlythepatternsofabundanceofother
tracespeciesunderthequiescentconditionsdiscussedhere,and
n(H +) 2ζ n(H )/(α n(e)) (3) itwillcertainlynotbyitselfexplainsuchoutstandingmysteries
3 H 2 e
≈ asthehighabundancesofCH+,NH,HCO+,etc.Fortheformer,
The discrepancy between observation and the values of thereactionC+H + CH+ +H isexothermicbutnotpartic-
n(H3+)whichresultfromputtingtypicalvaluesforζH,n(e),etc. ularlyfastandthef3ra→ctionofgas-2phasecarbonwhichisneutral
in this expressionis sufficientto suggestthat ζ >> 10 17 s 1.
H − − isverysmallindiffusegas,typicallybelow1%:thisformsonly
Nonetheless,Eq. 3 is only a formal,veryapproximatesolution minisculeamountsofCH+ (moreCH+ mightbeformedbythe
for n(H3+) because of the implicit dependencesof n(e) and αe reactionof C with H +). ForNH (Crawford&Williams, 1997;
uponthephysicaleffectsofionizationandheating(respectively) Meyer&Roth,1991)2,thereactionofNandH +isendothermic.
denotedby ζH, and because of other,less obviousassumptions ForHCO+,whichindarkcloudsisformedvia3thereactionH +
made aboutthe molecularchemistry.Furthermore,the obvious +CO HCO+ +H ,theamountsofbothH + andCOareto3o
changesintheH3+/H2 ratiowithtimeshowthatsuchconsider- small i→n diffuse clou2dsto sustain HCO+ agai3nstits recombina-
ations mightat best applyonly at very late times (e.g Fig. 5 at
tion to CO, HCO+ + e CO + H . CO canformfromHCO+
right). → 2
inquiescentdiffusegas(Liszt&Lucas,2000),butnottheother
Figure5atrightexhibitsthefurthersurprisingresultthatthe
wayaround.
H + abundanceislargelyindependentofthecosmicrayioniza-
3 OnespeciesforwhichH + mightmakea differenceis OH,
tion rate at early times when the H abundance is small. This 3
2 becauseboththereactionsO+H + OH++H (rateconstant
occurs because formation of H3+ is a multistep process with a k = 8 10 10 cm 3 s 1) andO+3+→H OH+2+ H (rate con-
resultantinversedependenceontheelectrondensitywhichmay st1antk ×= 1.−7 10 9 c−m3 s 1)areexo2th→ermic.Figure6shows
be much faster than linear (as suggested by Eq. 3), combined thetim2eevolut×iono−fthevolu−meformationrateofOH+through
withthetendency(suppressedbutnoteliminatedbyneutraliza-
bothroutes(shownarek n(O)n(H +)andk n(O+)n(H ))inthree
tionofatomicionsonsmallgrains)fortheionizationfractionto 1 3 2 2
modelsthreadedbyahighcosmicrayflux,ζ = 3 10 16 s 1,
increasewithζH. at three densities n(H) = 32 cm 3, 64 cmH3 and×128−cm−3.
Inasomewhatsimplifiedformneglectingchemicalreactions − − −
TheclouddiameterisheldfixedsothatN(H)=4 1020 cm 2,
of H2+ and H3+ with neutral atoms etc. (appropriatein diffuse 8 1020 cm 2and16 1020 cm 2,respectively,pu×rposelydr−iv-
gas),andthecomplexitiesofgrainneutralization,themainsteps in×g the high−est densit×y gas to v−ery high H fractions and H +
involved in forming and destroying H + and its immediate an- 2 3
3 abundancesatlatetimes.
tecedentH + are:
2 As shown in Fig. 6, the reaction of O and H + is never a
3
dominant source of OH+. The figure does show, however, the
cosmicray+H H ++e, (4a)
2 → 2 effect of ionizationbalance on the OH formationrate (see also
Sect.2.3ofLiszt(2003)):atlatertimesthefirststeptowardOH
H ++e 2H, (4b) formation occurs more vigorouslyin the more tenuous models
2
→
8 H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds
2
x2
10 x2
-6
10 1
1
]
-3] /2 -3m10-7 /2
m 1
c
c [
[
+
)2 )3
H H10-8
n( n(
0.1
-9
10
5 6 7 5 6 7
10 10 10 10 10 10
time [yr] time [yr]
Fig.4. Similar to Fig. 1, for models having n(H) = 32 cm 3, N(H) = 4 1020 cm 2 and primary cosmic ray ionization rate ζ
− − H
=10 16s 1,withtherateconstantforH formationscaledbyfactorsof2×aboutthestandardvalue.
− − 2
G
0
1 //44 10-5
/2 /4 ζ
/2 H
//11 /2 x3
0.1 /1 -6
10
/3
/4
/4
0.01 /2 /4 H 10-7
/2 2 n
3] //11 /2 (H
-
m -3 -83
10 /1 10 +
c
)
) [ H2 [c
2
m
H -4 -9
n(10 10 -3
]
-5 -10
10 10
+
10-6 H3 10-11
-7 + -12
10 H3 nH=8 cm-3 NH=4E20 cm-2 nH=32 cm-3 NH=4E20 cm-2 10
4 5 6 7 8 44 55 66 77
10 10 10 10 10 1100 1100 1100 1100
time [yr] time [yr]
Fig.5.H andH +densitiescalculatedforvaryingstrengthsoftheinterstellarradiationfield(left)andcosmicrayprimaryionization
2 3
rate ζ (right):the scale for n(H ) is given at far left, that for n(H +) at far right. In the panelat left the scaling parameter G is
H 2 3 0
takenas1,1/2and1/4;atrightζ variesbyfactorsof3,1 and1/3aboutthestandardmodelvalueζ = 10 16 s 1. Asin Fig.1,
H H − −
three curves are shown for each model, at fractional radii 0, 1/3, and 2/3 from the center. The models in both panels have N(H)
=4 1020cm 2butthemodelatlefthaslowernumberdensityn(H)=8cm 3.Notethatn(H +)isrelativelyinsensitivetochanges
− − 3
×
inζ atearlytimeswhenn(H )issmall,asdiscussedinSect.4ofthetext.
H 2
H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds 9
2
5. Summaryanddiscussion
-15 H2 5.1. Summary
10
Weshowedtheapproachtoequilibriumunderbenignconditions
forsomerecently-publishedmodels(Liszt&Lucas,2000;Liszt,
-1s]10-16 nH H3+ 2ti0o0n2i,n2p0c0-3si)z,ec,aolcthuelartwinisgethlaergtiemlye-sdtaetpicengdaesnptaHrc2ealsndmHea3n+tftoorrmepa--
-3m 10-17 1623482 rseeslfe-nsthiteylpdiicnagldqoueisesncoetnhtadsitffeunstehe“cfloorumdast”i.onWoerpaoccinutmeduloautitonthoaft
c
[ H ,althoughitmayfostertheproductionofmoreH overlonger
e 2 2
at times.BecausetheH2formationprocessindiffusegasisincom-
n r10-18 plete,timescalescaningeneralnotbededucedfromsimplescal-
o ingargumentsbasedonthelocalH2formationrate.Theequilib-
ati rium H2 formation timescale in an H I cloud having a column
m -19 density N(H) 4 1020 cm 2 is 1 3 107 yr, nearly inde-
or10 pendentofthe≈assu×meddensit−yorH−for×mationrateongrains,
f 2
+ etc.Underthebenignconditionsdescribedhere,thebulkofthe
OH10-20 128 H2 formation in the diffuse ISM actually occurs under diffuse
conditionsinphysicallylargerregionsofmoderatedensity;that
is, there is little apparentadvantagein hypothesizinga process
10-21 64 whichformsH2 indenserclumps,ifthedensityremainswithin
therangeinferredforquiescentdiffusegas.
Other species reach equilibrium essentially as soon as H
32 2
does, even when they involve higher-order and/or very “slow”
104 105 106 107 processes (like cosmic ray ionization of H2) but their equilib-
time [yr] riumabundancesappearmorenearlyatjustthelastminute;itis
morecriticalforexplainingH +thatconditionsequilibratethan,
Fig.6.OH+ volumeformationratesduetoreactionofO+ +H 3
2 say,forH itself.Thisisalsorelevantbecausethechemistryof
(upperfamilyofcurves)andO+H +(lowerfamily)inthepres- 2
3 aweakly-moleculargas–whichcouldbeeitheramodeloflow
enceofahighprimarycosmicrayionizationrateζ =3 10 16
H − densityoroneofhigherdensityatearlytime –behavesinvar-
s 1. Results areshown atthe usualthreefractionalradii×within
− ious particular ways. For instance, the predicted abundance of
modelsof diameter4.05pc having n(H)= 32 cm−3, 64 cm−3 H + islessstronglydependentonthecosmic-rayionizationrate
and128 cm−3 ,sothatN(H)= 4 1020 cm−2,8 1020 cm−2 w3henn(H )/n(H)<0.05.
and16×1020 cm−2,respectively).× × Attem2ptstofo∼rmincreasedamountsofH3+maybethwarted
at very high assumed values of ζ both because the fractional
H
ionization increases and because the H -fraction declines as
2
cosmic-ray ionization overtakes photodissociation as the main
because their higherionizationlevels(both overalland in oxy-
H -destructionmechanism.Assumingζ >> 10 16s 1 will also
gen)morethancompensateforlowerH fractions.Inthemod- 2 H − −
2 change the thermal balance in the diffuse ISM as a whole as
els with larger H fractions, the proton density declines at late
2
cosmic-ray ionization becomes the dominant heating process
timesbecauseamorenearlymoleculargascannotsustainahigh
protondensityandtheO+/Oratioalsodeclines,duepartlytoits in both warm and cold neutral diffuse gas. Although observa-
tions of both HD and H + seem to indicate an enhanced low-
rapidchargeexchangereactionwithhydrogenandbecauseofits 3
level source of hydrogen ionization, it is important to ascer-
rapidreactionwithH .Thecosmic-rayionizationalone,evenat
2
tain whether it is indeed a cosmic-ray related process which
thehighratesassumedhere,cannotsupporthighionizationfrac-
is responsible (or some other form of very hard radiation) and
tionsinatomichydrogenoroxygeninthepresenceofPAHand
whetheranyrelatedeffectsoccurinotherphasesoftheinterstel-
highH concentrations.
2
larmedium,eitherinthewarmordarkgas.
The next (necessary) step toward OH formation, OH+ +
H OH + + H willdominateoverrecombinationoftheOH+ ThepresenceofrelativelyhighH3+abundancesperseprob-
2→ 2 ablydoesnothavestrongeffectsonthechemistryofothertrace
ionforH -fractionsassmallas2%atdiffusecloudtemperatures.
2 specieswhoseabundancesarepuzzling(CH+,NH,HCO+ etc.)
Thus, the thinner models will actually form OH more rapidly
(not just OH+), as the H accumulation process equilibrates 2. oronthoseofspecieslikeOHwhicharegenerallyconsideredto
2
be better understood. However, in considering competition be-
Chemical effects like those shown in Fig. 6 undoubtedly con-
tweenOHformationpathsthroughH andH +,weshowedthat
tributetotheappearanceofradiofrequencyOHemissioninthe 2 3
late-timeOHformationproceedsmostvigourouslyinmoredif-
envelopesofdarkcloudswelloutsidethemoststronglymolecu-
fuse regions having modest density, extinction and H fraction
larregions(seeWannieretal.(1993)andFig.6ofLiszt&Lucas 2
andsomewhathigherfractionalionization,suggestingthathigh
(1996)).Inthecurrentcontextweexpect/predictthatregionsof
OHabundancesmightbefoundopticallyindiffusecloudshav-
higherthannormalOHabundanceshouldbefoundopticallyin
ingmodestextinction.
diffusecloudshavingmodestextinctionandH fractions.
2
2 At early times, the formation of OH in less dense clouds will be 5.2. LifetimesofdiffusecloudsandtheirH
2
seriouslyimpededbytheirlargere/H ratiosandthedensermodelsmay
2
makemoreOH.AswithH +itself,highOHabundancesonlyappearat In this work we modelled the formation and accumulation of
3
theconclusionoftheH accumulationprocess H underconditionslikethosewhichareinferredfromobserva-
2 2
10 H.S.Liszt:Time-dependentH formationandprotonationindiffuseclouds
2
tionsoftheH2 andrelatedneutralgasspeciesthemselves;tem- Jura,M.1974,ApJ,191,375
peratures from H (Savageetal., 1977; Shulletal., 2004) and LePetit,F.,Roueff,E.,&Herbst,E.2004,A&A,417,993
2
mean thermal pressures (densities) from C I (Jenkins&Tripp, LeTeuff,Y.H.,Millar,T.J.,&Markwick,A.J.2000,aas,146,157
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that molecule-free sightlines are relatively rare, the observed Liszt,H.2002,A&A,389,393
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H aside, timescales for thermal, ionization, chemical
2 Liszt,H.S.&Lucas,R.1995,A&A,299,847
etc. equilibrium are short (Spitzer, 1978; Wolfireetal., 2003; —.1996,A&A,314,917
Rawlingsetal., 2002) and diffuse gas is not normally thought —.2000,A&A,355,333
of as having much longevity in any particular form. The H I Lucas,R.&Liszt,H.S.1996,A&A,307,237
—.2000,A&A,358,1069
cloudspectrumevolvesunderthecontinualinfluencesofcloud-
McCall,B.J.,Hinkle,K.H.,Geballe,T.R.,Moriarty-Schieven, G.H.,Evans,
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2
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is observedto exist at very high pressure within diffuse clouds
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derstoodinsuchterms.
Acknowledgements. TheNationalRadioAstronomyObservatoryisoperatedby
AssociatedUniversites,Inc.underacooperativeagreementwiththeUSNational
Science Foundation. The calculations described here were mostly completed
whiletheauthorwasenjoyingthehospitalityofBel’EsperanceandLaClemence
inGenevaandtheHoteldelaPaixinLausanne.Theauthorisgratefultotheref-
ereeandtheeditorforseveralstimulatingcomments.
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