Benchmarking spin-state chemistry in starless core models

0.97 MB·English

by  O. Sipilä

Astronomy&Astrophysicsmanuscriptno.spinstate˙benchmark (cid:13)c ESO2015
January21,2015
Benchmarking spin-state chemistry in starless core models
O.Sipila¨1,2,P.Caselli1,andJ.Harju2,1
1 Max-Planck-InstituteforExtraterrestrialPhysics(MPE),Giessenbachstr.1,D-85748Garching,Germany
e-mail:[email protected]
2 DepartmentofPhysics,POBox64,00014UniversityofHelsinki,Finland
Received/Accepted
5 ABSTRACT
1
0 Aims.Weaimtopresent simulatedchemical abundance profilesfor avarietyof important species, withspecial attention givento
2 spin-statechemistry,inordertoprovidereferenceresultsagainstwhichpresentandfuturemodelscanbecompared.
Methods.Weemploy gas-phaseandgas-grainmodelstoinvestigatechemical abundances inphysical conditions corresponding to
n
starlesscores.Tothisend,wehavedevelopednewchemicalreactionsetsforbothgas-phaseandgrain-surfacechemistry,including
a
J the deuterated forms of species with up to six atoms and the spin-state chemistry of light ions and of the species involved in the
ammonia andwater formationnetworks. Thephysical model iskept simpleinorder tofacilitatestraightforwardbenchmarking of
0
othermodelsagainsttheresultsofthispaper.
2
Results.Wefindthattheortho/pararatiosofammoniaandwateraresimilarinbothgas-phaseandgas-grainmodels,atlatetimesin

particular,implyingthattheratiosaredeterminedbygas-phaseprocesses.Furthermore,theratiosdonotexhibitstrongdependence
]
A oncoredensity.Wederivelate-timeortho/pararatiosof∼0.5and∼1.6forammoniaandwater,respectively.Wefindthatincluding
orexcludingdeuteriuminthecalculationshaslittleeffectontheabundancesofnon-deuteratedspeciesandontheortho/pararatios
G
of ammonia and water,especially ingas-phase modelswhere deuteration isnaturally hindered owing tothepresence of abundant
. heavyelements.Althoughwestudyarathernarrowtemperaturerange(10−20K),wefindstrongtemperaturedependencein,e.g.,
h
deuterationandnitrogenchemistry.Forexample,thedepletiontimescaleofammoniaissignificantlyreducedwhenthetemperature
p
isincreasedfrom10to20K;thisisbecausetheincreaseintemperaturetranslatesintoincreasedaccretionrates,whiletheveryhigh
-
o bindingenergyofammoniapreventsitfrombeingdesorbedat20K.
r
Keywords.ISM:abundances–ISM:clouds–ISM:molecules–astrochemistry
t
s
a
[
1. Introduction Owingtoitsimportance,spin-statechemistryisnowwidely
1
adopted in numerical chemical models, and has been ap-
v Theortho-to-pararatioofmolecularhydrogen,H ,playsalarge
2 plied to all the stages in the star formation process, i.e., dif-
5 roleinthedevelopmentofdeuteriumchemistryatthehighden-
fuse clouds (Albertssonetal. 2014a), starless/prestellar cores
2 sityandlowtemperatureattributedtostarlesscores.Thedeuter-
(Walmsleyetal. 2004; Floweretal. 2004; Paganietal. 2009;
8 ationsequencebeginswiththeexothermicreactionbetweenH+
4 3 Sipila¨ etal. 2010, 2013; hereafter S13) and protostellar sys-
andHD:
0 tems (Taquetetal. 2013; Taquetetal. 2014). However, spin-
1. H+3 +HD←→H2D++H2+232K. (1) sptraotbelecmhesmaidsotrpytinisguvseuraylldyiffdeirsecnutsspehdysiincatlhme ocdoenltse,xatnodfcsopmecpiafirc-
0
The H D+ ion can then donate its deuteron to other abundant ison between the results of different works can be difficult. In
5 2
1 species, such as CO and N2, yielding DCO+ and N2D+, re- thispaper,weaimtoremedythisbypresentingrelativelyeasily
: spectively. However, spin-state effects complicate the reaction reproduciblereferenceresultspertainingtospin-statechemistry,
v
scheme. Chemical species with multiple protons, or deuterons, inphysicalconditionsappropriatetostarlesscores.Tothisend,
i
X can exist in different spin configurations– for example H has we have developeda state-of-the-artspin-state chemicalmodel
2
two distinct spin states where the nuclear spin wavefunction thatincludesthespinstatesoflighthydrogen-containingspecies
r
a is either symmetric (ortho-H ; hereafter oH ) or antisymmet- (H , H+...),and the spin states of the speciestaking partin the
2 2 2 3
ric (para-H ; hereafter pH ). The difference in energy between formationanddestructionnetworksofammoniaandwater.Our
2 2
thegroundstatesofthesetwospinstates, ∼ 170K(Hugoetal. modelalso includesthe deuteratedformsof species with up to
2009),canbeaveryimportantenergyreservoiratthelowtem- sixatoms.Toextendtheusabilityofourresults,wepresentre-
peraturesofstarlesscores.Indeed,reaction(1)canproceedrel- sultsforbothgas-phaseandgas-grainmodels.
ativelyeasilyinthebackwarddirectionwhentheorthoformsof
bothH D+andH areinvolved.Consequently,theortho-to-para
2 2
(hereaftero/p)ratioofH isanimportantparametercontrolling
2
deuteriumchemistry(Floweretal.2006b).Inadditiontodeuter- Thepaperisorganizedasfollows.Sect.2describesourphys-
ation,spin-stateeffectsplayalargeroleinotherareasofstarless icalandchemicalmodelsindetail.InSect.3,wepresentthere-
corechemistryaswell.Forexample,theformationchainofam- sultsofourcalculations.InSect.4,wediscussourresultsandin
moniadependscriticallyontheN++H reaction,whichrequires Sect.5 we presentour conclusions.AppendicesA to E include
2
the presence of oH to proceed efficiently at low temperatures complementarydiscussiononourmainresults,andalsopresent
2
(Dislaireetal.2012). additionalmodelingresults.
1
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
Table1.Adoptedvaluesofthevariousphysicalparameters(see However,therearesomeexceptions.Forphotodissociationreac-
textfordefinitionsoftheparameters). tions,theratecoefficientisdefinedas
k =αexp(−γ A ) , (3)
Parameter Value photo 1 V
T =T 10K
gas dust where A is the visual extinction. For cosmic-ray-induceddis-
ζ 1.3×10−17s−1 V
sociation,theratecoefficientisdefinedas
A 10mag
V
a 0.1µm
ρg 3.0gcm−3 kCR =γ2ζ, (4)
g
n 1.5×1015cm−2
s whereζ isthecosmicrayionizationrate.InEqs.(3)and(4),γ
E /E 0.77 1
d b andγ areefficiencyfactors.
R 0.01 2
d
Theabundanceofdustgrainsiscalculatedas
Table2.Bindingenergies(correspondingtoawatericesurface) X = ng =R µmolmH , (5)
ofselectedspecies. g nH d43πa3gρg
Species Bindingenergy[K] whereµ isthemeanmolecularweightperHatom(1.4);ρ is
mol g
H 450 the grainmaterialdensity;R is the dust-to-gasmassratio.For
d
H2 500 gas-phase chemicalreactions involvinga grain and another re-
C 800 actantwithdifferentelectriccharge,theratecoefficientismulti-
N 800
pliedbythe“J-factor”takingintoaccountincreasedreactionef-
N 1000
2 ficiencyduetopolarization(Draine&Sutin 1987;Paganietal.
O 1000
2 2009;Sipila¨etal.2010).
CO 1150
Gas-phasechemistryis linkedwith grain-surfacechemistry
O 1390
NH 2378 through adsorption and desorption processes. The adsorption
OH 2850 ratecoefficientofspeciesiisgivenby
NH 3956
2
NH 5534 kads =υ Sσ, (6)
3 i i
H O 5700
2
whereυ = 8k T /πm isthethermalspeedofspeciesi(k
i p B gas i B
istheBoltzmannconstantandm isthemassofspeciesi);S is
i
2. Model the sticking coefficient, set to unity for all species; σ = πa2 is
g
thegraincrosssectionassumingsphericalgrainswithradiusa .
g
2.1.Physicalparameters
Theadopteddesorptionmechanismis cosmic-rayinduceddes-
orption,withratecoefficientgivenby
Inordertofacilitatestraightforwardcomparisonoffuturemod-
elingworksagainstthe resultspresentedin this paper,we con-
kdes = f kTD(70K)= f ν exp −E /70K , (7)
siderhomogeneousmodels.Thatis,wefixthevaluesofallphys- i 70 i 70 0,i (cid:2) b,i (cid:3)
ical parameters but the density of the medium. The model pa-
where f = 3.16 × 10−19 is an efficiency factor; ν =
rameters(introducedbelow)alongwiththeirassumedvaluesare 70 0,i
2n k E /π2m is the characteristic vibration frequency of
presentedinTable1.Inallcalculations,wesetthegastempera- p s B b,i i
species i (Hasegawaetal. 1992; Hasegawa&Herbst 1993). In
tureT equaltothedusttemperatureT .Althoughwerestrict
gas dust
the above, n and E stand for the density of binding sites on
thetemperaturetoT = 10Kinthemaintext,wepresentrefer- s b,i
thegrainsurfaceandthebindingenergyofspeciesionthegrain
ence results also for T = 15K and T = 20K in AppendixC
surface, respectively. For simplicity, we consider only cosmic-
(theseresultsarebrieflydiscussedinSect.4.5).
rayinduceddesorptioninthiswork,andneglectalternativedes-
The binding energies of the variousspecies, corresponding
orptionmechanismssuchasphotodesorptionorreactivedesorp-
to a water ice surface, are mainly taken from Garrod& Herbst
tion.
(2006;see alsoSipila¨ 2012). Table2presentsthe bindingener-
The rate coefficient for a grain-surface reaction between
giesofselectedspecies.Weassumethatthebindingenergyofa
speciesiand jisgivenby
deuteratedspeciesisequaltothatofthecorrespondingundeuter-
atedspecies.Thisapproachhasbeenpreviouslyadoptedby,e.g.,
Cazauxetal.(2010),Taquetetal.(2013)andS13.Tocovertyp- kij =ακij(cid:16)Rdiiff +Rdjiff(cid:17)/ng (8)
icaldensityvaluesassociatedwithstarlesscores,wepresentre-
whereαisthebranchingratioofthereaction;theefficiencyfac-
sultsatfourdifferentdensitiesrangingfrom103to106cm−3.
torκ = exp(−E /T )orunityforexothermicreactionswith
ij a dust
orwithoutactivationenergy(E ),respectively;n isthenumber
a g
2.2.Chemicalcode density of dustgrains(see below).The (thermal)diffusionrate
Rdiff isgivenby
We use the gas-grain chemical code discussed in Sipila¨ etal.
(2010),Sipila¨ (2012)andS13,whichusestherateequationap- Rdiff = νi exp(−E /T ), (9)
proachto calculate chemicalevolutionin the gasphase and on i N d,i dust
s
grainsurfaces.Thereactionratecoefficientis,forthemajorityof
gas-phasereactions,definedwiththemodifiedArrheniusequa- where Ns = ns4πa2g isthenumberofbindingsitesonthegrain
tionas andEd,iisthediffusionenergyofspeciesi.Thediffusionenergy
isdeterminedbyassumingaconstantvalueforthediffusion-to-
k=α(T/300K)βexp(−γ/T) . (2) binding-energyratioE /E .
d b
2
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
Table3.Initialchemicalabundanceswithrespectton ,andthe with rate coefficient k, separates into three reactions when the
H
adoptedinitialH o/pratio. spinstatesofthespeciescontainingmultipleprotonsareconsid-
2
eredexplicitly:
Species Initialabundance
H 0.5 H+(o) + O−→k OH++H (o)
2 3 2
He 9.00×10−2
HD 1.60×10−5 H+(p) + O−21→k OH++H (o) (11)
O 2.56×10−4 3 2
C+ 1.20×10−4 H+(p) + O−12→k OH++H (p).
N 7.60×10−5 3 2
S+ 8.00×10−8 In S13, the branchingratio matrices for some reactingsystems
Si+ 8.00×10−9 werederivedbyhandandappliedintheo/pseparationroutine.
Na+ 2.00×10−9 However, for more complicated reactions involving many pro-
Mg+ 7.00×10−9 tonsand/ormultipleproducts,customseparationruleswereap-
Fe+ 3.00×10−9
plied(seeAppendixAinS13).Themotivationfordoingsowas
P+ 2.00×10−10
threefold.Firstly,Oka’smethodmaynotbeapplicablewhenthe
Cl+ 1.00×10−9
exothermicityofagivenreactionisverylow.Secondly,wedid
H (o/p) 1.00×10−3
2 ini not want to follow the spin states of species heavier than H+
3
(with the exceptionof its deuterated forms),so in any reaction
Weassumethatthegasisinitiallyatomicwiththeexception wheresuchspecies(e.g.,H2S)werepresent,weassumedthatthe
ofhydrogenanddeuteriumwhicharelockedinH andHD,re- speciesisinitsparaform.Thirdly,thebranchingratiomatrices
2
spectively (Table 3). We used the same assumptions about the were deduced by hand, which quickly becomes tedious when
initial abundances as Semenovetal. (2010) except for HD for multiple protons and product species are present, even though
whichweadoptedn(HD)/n(H) = 1.6×10−5 basedontheD/H theseparationmethoditselfisstraightforward.
ratiomeasuredinthelocalISM(Linskyetal.1995).Theinitial Forthispaper,wehavedevelopedanewversionofthesepa-
H ortho/pararatiois(arbitrarily)setto1×10−3. rationroutine.Inthenewversion,thebranchingratiosarecalcu-
2
Finally we notethatwe do notconsiderquantumtunneling latedautomaticallyusingOka’smethodsothatweeasilyobtain
on grain surfacesin the main bodyof the text. However,refer- thebranchingratiomatrixofanyreaction.Consequently,every
ence results including tunneling are presented in Appendix E, specieswithmultipleprotonsisseparatedintoitsorthoandpara
wherewealsodiscussthemodificationstothegas-grainmodel (andmetawhenapplicable)states.However,inordertomaintain
requiredwhentunnelingisincluded. relativesimplicityofthereactionnetwork,weonlykeepthespin
statesofthelighthydrogen-bearingspecies,andofthosespecies
includedin theformationnetworksofwater andammonia(see
2.3.Gas-phaseandgrain-surfacereactionsets Sect.2.3.2).
When spin species other than those mentioned above are
Thechemicalreactionsetsforgas-phaseandgrain-surfacereac-
presentin a reaction,we recombinethereactionsoverthe “un-
tions used in this work are reworked versions of the networks
wanted”spinspecies.Forexample,considerthereaction
presented in S13; the present gas-phase network is based on
osu 01 20091 insteadofthemodifiedversionofosu 03 2008
(Semenovetal.2010)adoptedinS13.Inthepresentmodel,the H+3 +CH2−k→1 CH+3 +H2. (12)
spin-state chemistry description of S13 is expanded by adding
When separated using spin selection rules, reaction (12)
thespinstatesofthespeciesinvolvedintheformationofwater
branchesintothefollowingsetofreactions:
andammonia.Also,thepresentmodelcontainsdeuteratedforms
toafnstpsepceiceisewssituhchupastow6ataetro,mams,minocnluiadianngdombseethrvaantoiol.nWalleydimiscpuosrs- oH+3 +oCH2 −3670→k1 oCH+3 +oH2
thevariousupdatesandadditionsindetailinthefollowing. −650→k1 oCH++pH
3 2
2.3.1. Thespin-stateseparationroutine −1640→k1 pCH++oH
3 2
IanraSte13an,yarreoauctitnioenwinavsodlevvineglolpigedhttohyadurtoogmeant-ibceaallryinsgpisnp-esctaietes(sHep2-, −640→k1 pCH+3 +pH2
oHn+2parned-dHe+3te)r.mIninperdacbtircaen,cthhiengroruattiinoes.crIenatSe1s3n,ewtherebarcatniocnhsinbgasread- oH+3 +pCH2 −41→k1 oCH+3 +oH2
t(i2o0s0f4o)r, minowsthriecahcrteiopnresswenetraetidoendsuocfedtheusninugcltehaer smpeinthwodavoeffuOnkca- −41→k1 oCH+3 +pH2
trieoancstivoeftchoellvisairoionus.sTspheecrieessualtrienugsberdantochdienrgivreatsieolsecctoiorrnesrpuolensdfotor −42→k1 pCH+3 +oH2
tphuerenunculcelieaarrespcionmsptaletitsetliycaml iwxeeidghintsthuendreeracthtieona,ssaunmdpthtiuosntthheayt pH+3 +oCH2 −1640→k1 oCH+3 +oH2
a(Oreklaik2e0l0y4t)o.Fboermexoasmt applep,litchaebrleeatcotiohnighly exothermicreactions −1600→k1 oCH+3 +pH2
H+3 +O−→k OH++H2, (10) −2680→k1 pCH+3 +oH2
1 Seehttp://www.physics.ohio-state.edu/∼eric/ −680→k1 pCH+3 +pH2
3
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
pH++pCH −51→k1 oCH++oH adopted here (Semenovetal. 2010), the non-additionreactions
3 2 3 2 thatcreateH∗ (theasteriskdenotesasurfacespecies),forexam-
2
−52→k1 pCH++oH pleH∗+H2CO∗ −→HCO∗+H∗2,alreadypresenthighactivation
3 2 barriers.Ofcourse,oH∗canbecreatedby(cr-induced)photodis-
2
−52→k1 pCH++pH . sociations;weassumethattheseeventsaresufficientlyenergetic
3 2 sothatoH∗ andpH∗ areproducedinthestatisticalratio3:1.
2 2
TodeterminethebranchingratiosoftheoH++CH −→CH++ We notethattheconservationofnuclearspin maynothold
3 2 3
(o/p)H system,i.e.,neglectingthespinstatesofCH andCH+, for grain-surface reactions as there is experimental evidence
2 2 3
wesumovertheoH andpH productionpathwaysandaverage to the contrary(Fushitani&Momose2002; Hama&Watanabe
2 2
theratecoefficientsonthenumberofspinmodificationsofCH 2013).WediscussthisissuebrieflyinSect.4.4.
2
(two).AsimilartreatmentofthepH++CH −→CH++(o/p)H
3 2 3 2
systemfinallyresultsinfourreactions:
2.3.2. Spin-statechemistryofammoniaandwater
oH++CH −45→k1 CH++oH (13) In this work, we have included the spin-state chemistry
3 2 3 2 of nitrogen-containing species involved in the ammonia for-
−15→k1 CH++pH (14) mation chain, recently studied using the Oka method by
3 2 LeGaletal. (2014; see also Floweretal. 2006a; Dislaireetal.
pH++CH −2103→k1 CH++oH (15) 2012;Faureetal.2013;Ristetal.2013).Wehavecheckedthat
3 2 3 2 ouro/pseparationroutineproducesthesamebranchingratiosas
−270→k1 CH++pH . (16) given in Tables B.1. and B.2. in LeGaletal. (2014) (see also
3 2 Sect.4.2.)
ThebranchingratiosinEqs.(13)to(16)arebasedontheas- Because of the high exothermicities of the hydrogen addi-
sumptionthattheorthoandparaformsofCH areequallyabun- tionreactionsongrainsurfacescreatingNH∗andNH∗(∼4.2eV
2 2 3
dant. Using the statistical ortho/para CH ratio (3:1), the four and 4.7eV, respectively, as calculated from Eqs.(3) and (4) in
2
branchingratiosare33/40,7/40,27/40and13/40,respectively, Allen&Robinson1977andusingdatapresentedinAppendixC
while assuming that CH is completely in the para state yields ofDuetal.2012),weassumethatthehigh-temperaturestatisti-
2
thebranchingratios3/4,1/4,3/5and2/5.Ifweassumethatthe calbranchingratiosfortheformationreactions,
reactionproceedsthroughaprotonhopprocessinsteadofcom-
pletescrambling,weobtainthebranchingratios1,0,1/2and1/2 NH∗+H∗ −3→/4 oNH∗
2
(Oka2004,Table8b).Evidently,therearedifferencesintheout-
comedependingonthe assumedortho/pararatioofCH orthe −1→/4 pNH∗
2 2
assumed reaction mechanism (which is not known for the vast
oNH∗+H∗ −2→/3 oNH∗
majorityofreactions).Wenote,however,thatheaviermolecules 2 3
havea negligibleeffectonthe H2 ortho/pararatioforexample, −1→/3 pNH∗
andourassumptionsseemjustifiedinthepresentcasewherewe 3
onlyconsiderexplicitlythespinstatesofalimitedsetofspecies. pNH∗+H∗ −→1 pNH∗,
2 3
It should be noted that the Oka method allows the forma-
tion of oH from pH , simply because this is statistically pos- arevalid.Thesebranchingratiosare,ofcourse,givendirectlyby
2 2
sible.However,theformationofoH shouldbeunlikelyatlow theOkamethod.
2
temperatureswherethecollisionalenergiesaresmallcompared Wehavealsoincludedthespin-statechemistryofthespecies
with the energy difference ∆E/k = 170K between the ground involved in the water formation network. The branching ratios
statesofoH andpH ,unlessthereactionissufficientlyexother- for the most important reactions in the water network are pre-
2 2
mic.In S13,we assumedthatthe requiredexothermicityisnot sented in AppendixB. Similarly to the nitrogen chemistry, we
reached in general, and hence the network favored pH forma- adoptstatisticalbranchingforwaterformationongrainsurfaces:
2
tion.Inthispaper,weslightlyrelaxtheassumptionsofS13,and
apply the separation routine to all reactions other than charge- OH∗+H∗ −3→/4 oH O∗
2
transfer reactions, where we assume that spin states are con-
served. However, we add an activation energy of 170K to the −1→/4 pH2O∗. (17)
γ coefficient in those reactions where oH is created by reac-
2
tantswhosespinstatesarenotexplicitlyconsidered(forexam-
2.3.3. Deuteration
ple,CH++CH −→C H++H ;seealsoAlbertssonetal.2014a).
3 2 2 3 2
ThenewapproachmodifiestheresultsofS13onlyveryslightly; In S13, a deuterationroutine was applied to the OSU network,
see Sect.3.1. With these changes, the resultant network should andspecieswithuptofouratomsweredeuterated.Inthepresent
be better applicable at higher temperatures (Albertssonetal. work,thedeuterationroutineisextendedtohandlespecieswith
2014b;seealsoAlbertssonetal.2014a).Thecombinationofnu- uptosixatoms,sothatthedeuteratedformsofimportantspecies
clearspinstatisticalweightsandactivationenergiesforprobably such as methanol and ammonia (whose formation depends on
endoergicreactionsapproximatesthemethodHugoetal.(2009) NH+) can be included. The deuteration routine is based on
4
used to calculate the thermal rate coefficients for the H+ +H thatpresentedbyRodgers&Millar (1996),in whichdeuterons
3 2
isotopicsystem,butwenotethatadetailedstate-to-stateanaly- are substituted in place of protons in the various reactions and
sis such as that performed by Hugoetal. (2009) is required to branching ratios are calculated assuming complete scrambling
studyendothermicreactionsconsistently. (seealsoS13).
We apply the same spin-state separation routine to grain- Thecalculationofthenuclearspin-statebranchingratiosfor
surfacereactions.Noratecoefficientcorrectionshavebeenmade multiply-deuterated species is more complicated than for un-
tothesurfacereactionsbecauseinthebasesurfacereactionset deuterated species. For species with three or more deuterium
4
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
nuclei Oka’s method, based on angular momentum algebra, is D++CH 29k2ex−p(→−170/T) CD++oH
insufficient because there is no one-to-one correspondencebe- 2 2
tween angular momentum and symmetry representations. The −19→k2 CD++pH
statistical branching ratios between the nuclear spin states of 2
species with up to five hydrogen or deuterium nuclei can be −96→k2 CH++HD
obtained from Tables III and IV of Hugoetal. (2009). In the
present paper, the spin-state chemistry in reactions between D++CHD −29→k2 CH++oD
2
species containing H and/or D only is included using these
rules,andtheyaremostlyavailableintheliterature.Specifically, 91k2ex−p→(−86/T) CH++pD
2
we include the spin-state chemistry of the H+ + H react-
ing system from Hugoetal. (2009), complem3ented 2by data −69→k2 CD++HD
fboerarointhgerspreeaccietison(sH+3c,onHce2rDn+in,gHlDighetthc.y)drforogmen-Wanadl-mdesluetyereiutmal-. D++CD2 −32→k2 CD++oD2
(c2ia0t0iv4e)raencdomFlboiwnaetrioetnabl.et(w20e0en4)H.T+haendraittescdoeeuffitecriaetnedtsffoorrmdsisasnod- 31k2ex−p→(−86/T) CD++pD2.
3
electronsaretakenfromPaganietal.(2009).
Reactions yielding pH or oD are assumed to have no activa-
Thenuclearspinchemistryofmultiply-deuteratedmolecules 2 2
tionenergies,whereasthoseproducingpD areassumedtohave
containing heavy elements is not considered in the present 2
anactivationenergyof86K,correspondingtotheenergysepa-
model,with the exceptionthat it is necessaryto predictthe ra-
ration between the ground states of pD and oD (Hugoetal.
tioofoD andpD releasedinreactionsinvolvingheavyspecies 2 2
2 2 2009). As noted above, the branching ratios for the reactions
toachieveaproperlyclosedreactionnetwork.Furthermore,oD
2 producing D are correct under the implicit assumption that
andpD producedbythesereactionscanberelevanttothechem- 2
2 [oCD ] : [pCD ] = 2:1. However, as in the case of H , reac-
istry of light molecules containing only H and/or D which are 2 2 2
tionsinvolvingheavyspecieshaveanegligibleeffectontheD
treatedusingtheappropriatespinselectionrules(seebelow). 2
o/pratio.Note thatfortheH+ +CHD andD+ +CH reactions
Thedeuterationprocedureusedheredirectlypropagatesthe 2
above,one would expectH formationin the o/p ratio 3:1, but
hydrogenspin-statechemistryintothedeuteriumchemistry,for 2
in the example the ratio is instead 2:1 because the deuterated
molecules with up to two deuterium nuclei. For hydrogenated
reactionsadoptthebranchingratiosfromtheundeuteratedpar-
species like CH , we assumed that the ortho and para forms
2 entreactions,inthiscasereactions(19),wherethethree-proton
of CH are equally abundant(see Sect. 2.3.1).However,copy-
2 systemleadstoanH o/pratioof2:1.
ingthereactionschemefromhydrogenatedtodoublydeuterated 2
We haveverifiedthroughtesting thatthe spin separationof
moleculesisequivalenttofollowingthecorrectnuclearspinse-
doubly-deuterated(heavy)speciesisoflittleconsequencetothe
lectionrulesforspin1systemswiththeassumptionthatoD and
2 resultspresentedlaterinthispaper,andthereforetheseparation
pD areinsteadpresentintheratio2:1(i.e.,thestatisticalvalue)
2 method used here seems reasonable for the present work. We
incomplexeswithheavynuclei,e.g.,CD .
2 willdiscussthespinseparationofmultiply-deuteratedmolecules
As an example of the spin-state separation of doubly-
indepthinafuturededicatedpaper.
deuteratedspecies,considerthereaction
H++CH −k→2 CH++H . (18) 2.3.4. OtherupdateswithrespecttoS13
2 2
In addition to the updates to the o/p separation and deutera-
Sinceourprogramperformsthespin-stateseparationofhydro-
tion routines described above, the rate coefficients of several
gen species prior to deuteration, the above reaction is first di-
reactions have been updated. First of all, we now adopt the
videdintothefollowingtwobranches:
osu 01 2009 reaction set instead of (modified) osu 03 2008,
so any updates of the base reaction set, including anion chem-
2
H++CH −→ CH++oH , k= k exp(−170/T), istry, are included in our new model. The modifications made
2 2 2
3
to osu 03 2008 by Semenovetal. (2010), already included in
1
−→ CH++pH , k= k . (19) S13,havebeenincorporatedtothenewmodelaswell.
2 2
3 Wehavealsoincludednewratecoefficientdatafromthelit-
erature. We adopt the rate coefficients given in Tables 12 and
Thebranchingratio(2/3oH ,1/3pH )followsfromthenuclear
2 2 13 in Albertssonetal. (2013) – except for reactions involving
spinstatisticsundertheimplicitassumptionthatpCH andoCH
2 2 hydrogen and/or deuterium onlyfor which we use other data
haveequalabundances,i.e.[pCH ]= [oCH ].Deuteratingboth
2 2 as detailed above. We have also included selected data from
branchesleadsinourroutinetothefollowingreactions:
LeGaletal.(2014),whichwesummarizeinTableB.2.We re-
ferthereadertoAlbertssonetal.(2013)andLeGaletal.(2014)
H++CHD 92k2ex−p(→−170/T) CD++oH fortheoriginaldatareferences.
2
−91→k2 CD++pH2 SectT.h3e.1.impact of the rate coefficient updates is analyzed in
−96→k2 CH++HD
H++CD −29→k2 CH++oD 3. Results
2 2
In this section, we present benchmarking results for spin-state
19k2ex−p→(−86/T) CH++pD chemistry for different values of density, using gas-phase and
2
gas-grainmodels.Alloftheresultspresentedbelowcorrespond
−96→k2 CD++HD toT =10K.ResultsforT =15KandT =20Karepresentedin
5
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
10-3 10-4 10-3
10-4 CO oH 10-5 H2O∗
2 HD
10-5 10-6 10-4
nH 1100--76 H2O NH3 10-7 D NH3∗
/ 10-8 10-5
nX 1100--98 10-9 e− HDO∗
1100--1110 N2H+ HCO+ 1100--1110 oH2D+ N DD+CO+ 10-6 NH2D∗
10-12 10-12 2 10-7
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
t [yr] t [yr] t [yr]
10-3 10-4 10-3
10-4 CO oH 10-5 H2O∗
2 HD
10-5 10-6 10-4
nH 1100--76 H2O NH3 10-7 D NH3∗
/ 10-8 10-5
nX 1100--98 10-9 e− HDO∗
1100--1110 N2H+ HCO+ 1100--1110 oH2D+ N DD+CO+ 10-6 NH2D∗
10-12 10-12 2 10-7
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
t [yr] t [yr] t [yr]
10-3 10-4 10-3
10-4 CO oH 10-5 H2O∗
2 HD
10-5 10-6 10-4
nH 1100--76 H2O NH3 10-7 D NH3∗
/ 10-8 10-5
nX 1100--98 10-9 e− HDO∗
1100--1110 HCO+ N2H+ 1100--1110 oH2D+ NDDC+O+ 10-6 NH2D∗
10-12 10-12 2 10-7
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
t [yr] t [yr] t [yr]
Fig.1.Upperpanels:abundancesofselectednon-deuterated(left),deuterated(middle)andgrain-surface(bothnon-deuteratedand
deuterated,right)speciesasfunctionsoftime,ascalculatedwithmodelT1(solidlines)ormodelT2(dashedlines).Middlepanels:
as the upper row, but comparingmodels T1 (solid lines) and T3 (dashed lines).Lowerpanels:as the other rows, but comparing
modelsT1(solidlines)andF1(dashedlines).Inallcalculations,thedensityofthemediumissetton =105cm−3.Theabundances
H
ofH O,NH andNH Drepresentsumsovertheirrespectiveorthoandparastates.
2 3 2
AppendixC,whileresultswithoutdeuteriumandincludingtun- impactonthe overallchemistry.In thefollowing,we studythe
neling are presented in AppendicesD and E, respectively.The effect of the various updates, by successively introducing new
data for the variousfigures presented below are available from updates into the S13 chemical model. The models introduced
theauthorsuponrequest. belowarealsodescribedinTable4.
First,weconstructedatestreactionsetbyspin-stateseparat-
ingthe S13 base reactionset (modifiedosu 03 2008)with the
3.1.ComparisonofthenewmodelagainstS13
new routine presented here, but using the old S13 deuteration
In our new model, there are two main sources of updates: 1) routine and including no new rate coefficient data (model T2).
our new spin-state separation and deuteration routines and 2) TheupperrowinFig.1plotstheabundancesofselectedspecies
the rate coefficient updates for various species from the litera- as functions of time calculated using model T2 (dashed lines)
tureandfromthetransitionfromosu 03 2008toosu 01 2009. andusingtheoldmodelofS13(solidlines;modelT1).Inthese
Qualitatively, the new spin-state separation routine may affect calculations,thedensityofthemediumissetton = 105cm−3,
H
somewhattheabundancesofthevariousspeciesbecauseofthe andtheotherphysicalparameterscorrespondtothevaluesgiven
increasedemphasisonoH inthenewseparationroutine(albeit inTable1.Intherightpanel,theabundancesoftherespectiveor-
2
with a 170K barrier in most cases). However,the extensionof thoandparastatesofH O∗,NH∗andNH D∗havebeensummed
2 3 2
deuterationfromfourtosixatomsisnotexpectedtohavealarge over. It is observed that the new spin-state separation routine
6
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
oH oH+ oH D+ pD H+
10-2 2 10-8 3 10-9 2 10-10 2
110034 10-9 10-10 10-11
nH 105 10-11 10-12
/ 10-3 106 10-10 10-13
nX 10-12 10-14
10-11 10-13 10-15
10-4 10-12 10-14 10-16
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
N H+ N D+ oNH pNH
10-8 2 10-10 2 10-7 3 10-7 3
10-9
10-11 10-8 10-8
H10-10
n
/ 10-11 10-12 10-9 10-9
X
n 10-12
10-13 10-10 10-10
10-13
10-14 10-14 10-11 10-11
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
oH O pH O HCO+ DCO+
10-5 2 10-5 2 10-8 10-9
10-6 10-6 10-9 10-10
nH 10-11
/ 10-7 10-7 10-10
nX 10-12
10-8 10-8 10-11 10-13
10-9 10-9 10-12 10-14
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
10-3 CO 10-5 D 10-4 HD 10-6 e−
10-7
H10-4 10-6
n
/ 10-5 10-8
X
n 10-5 10-7
10-9
10-6 10-8 10-6 10-10
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
t [yr] t [yr] t [yr] t [yr]
Fig.2. Abundances of selected species calculated with model F2 (i.e., surface reactions and adsorption/desorption excluded) as
functionsoftimeatdifferentdensities,labeledintheupperleftpanel.Thelabelsindicatedensitiesofthemedium;forexample,103
standsforn =103cm−3.
H
modifiesonlyslightlytheabundancesofnon-deuteratedspecies modelatlongtimescalesbecauseoflessefficientHDdepletion.
atearlytimesbothinthegasphaseandongrainsurfaces,while Inspectionofthereactionratesrevealsthatthiseffectiscaused
the abundances of deuterated species are virtually identical in bythedissociationofHDO∗,the maingrain-surfacedeuterium
both cases. Hence the new oH -creating reactions with 170K carrierinourmodel,whosedissociationproducedonlyOD∗+H∗
2
barriers included here (as opposed to S13) are of little conse- in S13 owing to a bug in the deuterationroutine, but here pro-
quence to the chemistry as a whole (althoughat high tempera- ducesalsoOH∗+D∗.Consequently,moreD∗isavailabletoform
turesthesituationmightbedifferent). HD∗,replenishingthegas-phaseHDabundance.
The middle row in Fig.1 plots the abundances of selected InthebottomrowofFig.1,weplotagaintheabundancesof
species calculated with a test reaction set constructed by ap- selectedspecies,nowcalculatedwiththefullmodelpresentedin
plying the new spin-state separation and deuteration routines this paper, i.e., including the rate coefficient updates discussed
to the modified osu 03 2008 reaction set; as before, no new inSect.2.3.4(modelF1).Evidently,theratecoefficientupdates
ratecoefficientdatais included(modelT3).Itisobservedthat, leadtosignificantdifferenceswithrespecttothepreviouscases,
overall,theextensionofthedeuterationschemehaslittleeffect bothinthegasphaseandongrainsurfaces.Forexample,theCO
on the chemistry.However,deuterationis enhancedin the new formationtimescaleismuchshorterwiththeupdatedratecoef-
7
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
oH oH+ oH D+ pD H+
10-2 2 10-8 3 10-9 2 10-10 2
10-3 10-9 10-10 10-11
nH 10-12
/ 10-4 103 10-10 10-11
nX 104 10-13
10-5 110056 10-11 10-12 10-14
10-6 10-12 10-13 10-15
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
N H+ N D+ oNH pNH
10-8 2 10-10 2 10-7 3 10-7 3
10-9
10-11 10-8 10-8
H10-10
n
/ 10-11 10-12 10-9 10-9
X
n 10-12
10-13 10-10 10-10
10-13
10-14 10-14 10-11 10-11
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
oH O pH O HCO+ DCO+
10-5 2 10-5 2 10-8 10-9
10-6 10-6 10-9 10-10
nH 10-7 10-7 10-11
/ 10-8 10-8 10-10
nX 10-9 10-9 10-12
10-10 10-10 10-11 10-13
10-11 10-11 10-12 10-14
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
10-3 CO 10-5 D 10-4 HD 10-6 e−
10-4 10-7
H 10-6 10-5
n
/ 10-5 10-8
X
n 10-7 10-6
10-6 10-9
10-7 10-8 10-7 10-10
103 104 105 106 107 103 104 105 106 107 103 104 105 106 107 103 104 105 106 107
t [yr] t [yr] t [yr] t [yr]
Fig.3.AsFig.2,butcalculatedwithmodelF1.NotethattheabundancescalesareinsomecasesdifferentthaninFig.2.
Table4.Themodelsdiscussedinthiswork. initially very rapidly in the new model. From an observational
point of view, the most striking difference between the models
Model Description istheabundanceofN H+,whichisoveranorderofmagnitude
2
T1 theSipila¨etal.(2013)model loweratlate timesin thenewmodel,resultingmainlyfromin-
T2 osu 03 2008+newspin-stateseparationroutine; creased(factor2-3)electronDRratecoefficientsandalsofrom
olddeuterationroutine;noratecoefficientupdates
changes in neutral-neutral chemistry, with respect to the OSU
T3 osu 03 2008+newspin-stateseparationroutine+ values.Thechangesis N H+ andHCO+ abundancespropagate
newdeuterationroutine;noratecoefficientupdates 2
totheirdeuteratedcounterpartionsN D+ andDCO+.Also,the
F1 osu 03 2008+newspin-stateseparationroutine+ 2
abundanceofammoniadecreasesbyafactorof2-3atlatetimes
newdeuterationroutine+ratecoefficientupdates
(fullmodel) inthenewmodelwithrespecttoS13.
F2 modelF1withoutgas-graininteraction(i.e.,no
adsorption/desorptionorsurfacereactions); Surfacechemistryisalsoaffectedbytheratecoefficientup-
H formationfromKongetal.(2013) dates.Inthenewmodel,atomichydrogenisatearlytimespro-
2
ducedmainlybyneutral-neutralreactionsbetweenlighthydro-
carbonsinsteadofelectronDRreactionsofvariousions(owing
ficients, which is mainly due to numerous changes in electron todecreasedelectronabundance),andthereismoreatomichy-
DRratecoefficients.Accordingly,theelectronabundancedrops drogenavailableinthegasphase.Thehydrogenisthenadsorbed
8
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
ontograinsurfaces,leadingtoefficientproductionof,e.g.,water
1.0
and ammonia which form mainly by hydrogenation.We stress
0.9 ggggaaaassss pppphhhhaaaasssseeee ggggaaaassss ggggrrrraaaaiiiinnnn
thattheseeffectsarecausedbychangesinthegas-phasechem- −−−− −−−−
0.8
istry, as none of the surface reaction rates have been updated. o
These results emphasize the importanceof constrainingthe re- ati 0.7
r
actionratecoefficients,particularlyforkeyreactions. p 0.6
/
Our chemical model predicts gas-phase and grain-surface o 0.5
3
abundances in physical conditions attributed to starless cores, H 0.4
N
and our model results could in principle be used to interpret 0.3
ice observations. However, direct observations of grain-mantle 0.2
species toward starless cores are extremely hard owing to the 0.1
verylargeextinctions.Thus,wewouldneedtorelyon,e.g.,ob- 103
servationstowardembeddedClass0sources,assumingthatthe 2.6 104
icefeatureoriginatesinthesourceenvelope.Adetailedinvesti- atio 2.4 110056
gationofmodelediceabundancesversusobservationsisleftfor r
2.2
p
futurework,andwefocusourattentionongas-phasespeciesin /
thepresentpaper. Oo 2.0
In what follows, all results have been produced with the H21.8
newortho/paraseparationanddeuterationroutines,andinclude
1.6
the rate coefficient updates from the literature as described in
Sect.2.3.4. 1.1403 104 105 106 103 104 105 106 107
t [yr] t [yr]
3.2.Gas-phasechemistry
Fig.4.o/pratiosofNH (upperpanels)andH O(lowerpanels)
3 2
Figure 2 present the results of gas-phase modeling at different as functions of time at different densities, labeled in the upper
densities. Here, we have notconsidered adsorptionand/ordes- left panel. The left panels correspond to the gas-phase model
orptionofanyspecies,andtheformationofH2,HDandD2 on (F2), while the right panels correspond to the gas-grain model
grainsurfacesisincludedin theformofgas-phasereactionsas (F1).
inthemodelofKongetal.(2013).
Ion abundances decrease significantly with increasing den-
lar) nitrogen is relatively low (Table 2), so nitrogen chemistry
sity,whichisaconsequenceoftheincreasedelectronDRratesat
can still occur efficiently after other heavy elements have been
highdensity,andofthehighabundancesofheavyneutralspecies
depletedontograinsurfaces.Consequently,anappreciableabun-
owingtotheabsenceofdepletion.Theabundancesofheavyions
follow largely that of H+ which is primarily destroyed by re- danceofN2,theprecursormoleculeofbothNH3andN2H+(see,
3 e.g.,Fontanietal.2012),canbepresentinthegasatlatetimes.
actions between abundantneutral species like CO and N , and
electrons.OneexampleofthistendencyisHCO+, which2isthe This is demonstrated by two effects. Firstly, the abundance of
NH isless thanan orderofmagnitudelowerinthe fullmodel
most important reaction partner of free electrons at late times 3
thaninthegas-phasemodelathighdensity,eventhoughdeple-
bothatlowandhighdensities.Thisionis formedina reaction
between H+ and CO and destroyed mainly in electron recom- tion tends to decrease its abundance. Secondly, the abundance
3 ofN H+, dependentonH+, isordersofmagnitudehigherwith
binationwhichreturnsCO.Athighdensities,theenhancedpro- 2 3
respecttothegas-phasemodelevenathighdensity(weassume
ductionoffreeelectronsbythecosmicrayionizationofH leads
2
thationsdonotdepleteontograinsurfaces,butcanrecombine
toanincreaseintheelectronDRrates(atconstanttemperature),
andtheHCO+abundancedecreasesaccordingly.N H+islocked withnegativelychargedgrains).
2
inasimilarcycle(H++N −→N H+;N H++e− −→N +H), Deuterationincreasesstronglywhengas-graininteractionis
dependenton the ab3undan2ce of H2+. Also2the N H+ abun2dance taken into account.However,a localpeak in deuterationis ob-
3 2 servedaroundthetimethatHDstartsdeplete,inlinewiththere-
decreasesclearlywhenthedensityincreases.
sultsofS13.HDdepletionissomewhatlesssevereinthepresent
Deuteration is also suppressed in the absence of depletion,
modelthaninS13becausewedonotconsiderquantumtunnel-
becauseH+reactspreferentiallywiththeabundantheavyspecies
3 ing.Inagreementwithpreviousresultsintheliterature,ourre-
ratherthanwithHD.
sultsclearlyshowthatdepletionisneededtoproduceobservable
amountsof,e.g.,oH D+ andN H+ athighdensity.
2 2
3.3.Gas-grainchemistry Figures2and3indicatethattheo/pratiosofammoniaand
waterdependonlyslightlyondensity,bothinthegas-phaseand
Figure 3 presents the results of gas-grain modeling at differ- gas-grainmodels.Wediscussthisissuefurtherbelow.
ent densities, adopting the full model (F1) described above.
Evidently,theinclusionofdepletionsignificantlydecreasesthe
abundances of carbon and oxygen-containing species with re- 4. Discussion
specttothegas-phasemodel.TheH+abundanceismuchhigher
3 4.1.Theo/pratiosofwaterandammonia
atlatetimesinthefullmodelwithrespecttothegas-phasemodel
because of the depletion of its main reaction partners (e.g., Figure4plotstheo/pratiosofNH andH Oatdifferentdensi-
3 2
CO) onto grain surfaces. The chemistry of nitrogen-containing tiesaccordingtogas-phaseandgas-grainmodels.Theo/pratio
speciesisdifferentthanthatof,e.g.,carbonandoxygenbecause ofammoniaisverysimilarinbothmodelsupton =105cm−3.
H
nitrogen chemistry depends on slow neutral-neutral reactions. Theratioislargerat∼ 104−105 yearsatn = 106cm−3 inthe
H
On the other hand, the binding energy of (atomic and molecu- gas-phasemodel,inwhichoneofthemainproductionpathways
9
O.Sipila¨,P.Caselli,andJ.Harju:Benchmarkingspin-statechemistryinstarlesscoremodels
forNH+att∼105yristheH O++NH −→NH++H Osystem Table5.Abundancesandabundanceratiospredictedbyourgas-
4 3 3 4 2
whichformsallthreespinvariantsofNH+.However,mNH+for phasemodel(F2)andthatofLeGaletal.(2014).
4 4
example only dissociates to oNH (see Table 2 in LeGaletal.
3
2014). The detailed behaviorof the spin-state chemistry is dif- Parameter Ourmodel LeGaletal.(2014)
ferentinthegas-grainmodel,wherethereactionpathwayswith [NH] 5.9×10−9 1.1×10−8
H O+ are practically absentat t & 105yr because of water de- [NH ] 9.5×10−10 3.5×10−9
3 2
pletion.Neverthelessourresultsindicatethat,atlatetimes,o/p- [NH ] 3.2×10−8 1.4×10−8
3
NH3is∼0.4−0.5regardlessoftheconsideredmodelorassumed [NH2]/[NH] 0.16 0.3
density. [NH3]/[NH] 5.4 1.3
The o/p ratio of H2O behaves similarly to that of NH3 in [[ooNNHH2]]//(cid:2)ppNNHH2(cid:3) 01..48 02..65
thesensethatthelargestdifferencesbetweenthegas-phaseand 3 (cid:2) 3(cid:3)
gas-grainmodelsare observedat n = 106cm−3. Theo/pratio
H
ofH OistiedtothatofH O+,whichevolvesdifferentlyinthe
gas-g2rainmodelowingtom3 ultiplespin-statedetails(H O+ and and[S] = 8×10−8).LeGaletal.(2014)donotexplicitlystate
3
H2O are connectedmainlythroughH2O+ +H2 −→ H3O+ +H theinitialH2o/pratio;weassumedavalueof3.
andtheH++H O−→H O++H system).Theo/p-H Oratiosat Table5summarizestheresultsofthesetests.Inourmodel,
differentd3ensit2iesandin3differe2ntmodelsare,again,2veryclose therearemanycosmic-ray-inducedandphotodissociationreac-
toeachotheratlatetimeswherewederiveo/p-H O∼1.5−1.7. tionswithlongtimescales,whichpreventthesystemfromreach-
2
Unlike the o/p ratio of H which is strongly influenced by ingatruesteady-state;thevaluesgiveninthetable correspond
2
grain-surfacechemistry,theo/pratiosofH O andNH arede- to late-time chemical evolution (t = 2.0×107yr), after which
2 3
terminednearly completelyby gas-phasechemistrybecause of temporal changes in chemical abundances are generally small.
theirhighbindingenergies(seeTable2).Thefactthattheo/pra- The Le Gal et al. steady-state values have been read off their
tiosoftherespectivespeciesareverysimilarinbothgas-phase Figs. 4 and 5. Evidently, our model gives lower NH and NH2
and gas-grain models supports this interpretation (Fig.4). The abundancesandahigherNH3 abundancethantheLeGaletal.
late-timevaluesoftheo/pratioscanbejustifiedbyaratecoeffi- model,buttheortho/pararatiosofbothNH2andNH3aresimilar
cientanalysisofthemainformationanddestructionpathsofam- inbothmodels.
moniaandwater;suchananalysisispresentedinAppendixA. Wealsotestedaninitial[C]/[O]ratioof0.3,andfoundthat
We note that the late-time H2O o/p ratios derived here inthiscasethelate-timeNHandNH2 abundancesarelowerby
are much lower than those typically observed in the ISM one and two orders of magnitude, respectively, than those pre-
(vanDishoecketal. 2013;see also the discussion in Ketoetal. dictedbyLeGaletal.(2014).However,theNH3abundanceand
2014).Thedisagreementisprobablyduetothefactthatobser- theNH2andNH3o/pratiosareagainsimilartotheLeGaletal.
vationstowarddarkcloudswithintermediatetohighdensityare (2014)model.
missing. To investigatethis issue, we ran test calculationswith Our test results indicate that there are minor differences
ourgas-grainmodelatconditionssimulatingtranslucentclouds in fractional abundances between our model and that of
(n = 102cm−3 andT = 10K)with two valuesof A , 10mag LeGaletal. (2014). The two models predict similar o/p ratios
H V
and1mag.We foundthatat AV = 10mag,theH2Oo/pratiois for NH2 and NH3, which is expected since we adopt the same
∼ 1.6,butat A = 1magtheratiois ∼ 3,suggestingthatpho- spin-statechemicaldescriptionforthesespeciesasLeGaletal.
V
tochemistryplaysalargeroleindeterminingtheo/pratioinre- (2014).
gionswithlowvisualextinction.Thisresultunderlinestheneed
foraccuratephysicalmodelswheninterpretingobservations.
4.3.H formationingas-phasemodels
Ammonia is a useful probe of the gas temperature in dark 2
clouds (Tafallaetal. 2004; Juvelaetal. 2012), and simulated In the gas-phase results presented above, the formation of H
2
NH line emission profiles can be used to constrain the ki- (anditsisotopologsHDandD )isincludedintheformofgas-
3 2
netic temperature. However, a proper comparison of simulated phasereactions(seeKongetal.2013).FromFig.2itisevident
line emission against a detection of, e.g., pNH requires an thatthisapproachleadsto, e.g.,an increase ofthe H o/pratio
3 2
estimate of the NH o/p ratio. Given that the NH o/p ratio at late times. Another approach to including the formation of
3 3
changes very little with density in our models, we deduce that H anditsisotopologsin a gas-phasemodelisto invokegrain-
2
o/p-NH ∼ 0.4−0.5 is a goodconservativeestimate ofthe ra- surfaceformationprocesses,butlettingonlyatomicHandDto
3
tioindarkclouds.Thisresultisconsistentwithobservationsby beadsorbedontothegrainsurfaces.
Perssonetal.(2012)andthemodelsofLeGaletal.(2014)(see WehaveruntestcalculationsatT =10Kcomparingthetwo
alsoSect.4.2). approaches. The results of these calculations are presented in
Finally, we stress that we have not carried out a complete Fig.5,wheretheabundancesofselectedspeciesasfunctionsof
parameter-spacestudyoftheammoniaandwatero/pratios,and timeareplottedatdifferentdensities,usingdifferentapproaches
thatsuchastudyshouldbetakenoninthefuture. to H formation. Evidently, the Kongetal. (2013) approach is
2
practically equivalent to the grain-surface formation approach
when “normal”bindingenergies(450K for H and D) are used
4.2.ComparisonagainstLeGaletal.(2014)
(thedottedanddash-dottedlinesarepracticallysuperimposed).
Recently,LeGaletal.(2014)presentedgas-phasemodelingre- Inthegas-grainmodelwithverylowHbindingenergy(100K),
sults of nitrogen chemistry in dark clouds. They included in H desorbsveryfast,leadingtoinefficientH productiononthe
2
their modelthe spin-state chemistrypertainingto the ammonia grain surfaces regardlessof the density. Increasing the binding
formation network, as we do here. We have run some test cal- energyincreasestheaveragetimespentbyHatomsonthegrains
culations to compare our results against those of LeGaletal. andthusleadstomoreefficientH production.
2
(2014),adoptingthesamephysicalconditionsandinitialchem- The choice of the H formation efficiency has little effect
2
icalabundancesforHe,C,NandFe(wechoose[C]/[O] = 0.8 ontheabundanceofH D+ becausedeuteriumchemistryissup-
2
10