Table Of Content

MNRAS000,1–18(2016) Preprint19January2017 CompiledusingMNRASLATEXstylefilev3.0 Effects of dust evolution on the abundances of CO and H 2 Hiroyuki Hirashita1⋆ and Nanase Harada1 1Institute of Astronomy and Astrophysics, Academia Sinica, PO Box 23-141, Taipei 10617, Taiwan AcceptedXXX.ReceivedYYY;inoriginalformZZZ 7 1 0 ABSTRACT 2 The CO-to-H conversionfactor (X ) is known to correlate with the metallicity (Z). 2 CO n Thedustabundance,whichisrelatedtothemetallicity,isresponsibleforthiscorrela- a tionthroughdustshieldingofdissociatingphotonsandH formationondustsurfaces. 2 J In this paper, we investigate how the relation between dust-to-gas ratio and metal- 8 licity (D–Z relation) affects the H and CO abundances (and X ) of a ‘molecular’ 2 CO 1 cloud.For the D–Z relation,we adopt a dust evolutionmodel developedin our previ- ous work, which treats the evolution of not only dust abundance but also grain sizes ] A in a galaxy. Shielding of dissociating photons and H2 formation on dust are solved consistently with the dust abundance and grain sizes. As a consequence, our models G predictconsistentmetallicitydependence ofX with observationaldata.Amongvar- CO h. iousprocessesdrivingdustevolution,graingrowthbyaccretionhasthelargestimpact p on the XCO–Z relation. The other processes also have some impacts on the XCO–Z re- - lation,buttheir effects areminorcomparedwiththe scatterofthe observationaldata o at the metallicity range (Z>0.1 Z ) where CO could be detected. We also find that tr dust condensation in stella∼r ejecta⊙has a dramatic impact on the H2 abundance at s lowmetallicities(<0.1Z ),relevantfordampedLymana systemsandnearbydwarf a [ galaxies,and that∼the gra⊙in size dependence of H formation rate is also important. 2 1 Key words: methods:analytical—molecularprocesses—dust,extinction—galax- v ies: evolution — galaxies: ISM — radio lines: galaxies 7 3 9 4 0 1 INTRODUCTION UV radiation by their own absorption (Draine& Bertoldi . 1996)(i.e.self-shielding).Sinceself-shieldingofCOisweaker 1 Galaxies evolve through star formation. Since molecular 0 (Leeet al.1996),COformsinmoreembeddedregionsthan cloudsarethebirthplaceofstars,understandinghowmolec- 7 H2.Dustextinctionalsoplaysanimportantroleinshielding ularcloudsevolveprovidesuswithanimportantkeytohow 1 dissociating radiation.AlthoughCO emission isempirically stars form in galaxies. The main chemical constituent of v: molecular clouds is molecular hydrogen (H2). Since emis- knnotowonbvtiooutsratcheatHt2hiisnissoglaern-emraetllayllitcriutye feonrvigraolnamxieensts(,i)itbeis- Xi sion from H2 is weak in cold molecular environments (H2 causethesespecieshavedifferentformationmechanismsand emission is more easily observed in regions with shock or r theformationrateshavedifferentdependenceonmetallicity ultraviolet excitation; e.g. Naslim et al. 2015 for a recent a (Maloney & Black1988),and(ii)becauseUVintensityand observation), emission from carbon monoxide (CO) is often dustabundancevaryindifferentstagesof galaxyevolution. used as a tracer of molecular clouds. Thus, understanding theformation and evolution of H2 and CO and therelation For the purpose of deriving the H2 abundancefrom an betweenthesetwospeciesisimportanttoclarifytowhatex- observed CO intensity, one assumes a CO-to-H2 conversion tent CO can really trace molecular clouds at various stages of galaxy evolution. factor,XCO≡NH2/WCO,whereNH2 istheH2 columndensity, andWCOistheintensityoftheCOJ=1 0emissionlinein- InthepresentUniverse,H2formspredominantlyonthe tegratedforthefrequency(thefrequenc→yisoftenconverted surfaceofdustgrains(Gould & Salpeter1963).Ontheother to the velocity shift in units of km s 1). Another expres- − hand,COformsinthegasphaseviavariousreactions.Both sion for the conversion factor, a CO, is based on the column species favour ‘shielded’ environments with a high column massdensity(orsurfacemassdensity)ofthemoleculargas, draednisaittyionof.Agatshsiignhcecotlhuemynardeednissistoiecsi,aHte2dmbyoleuclturlaevsicoalents(hUieVld) tS hmeolc=on1t.r3ib6umtHio(2nNoHf2h),elwiuhmereto1t.h36etiostaalfmacatsosr.tIno tahcicsoeuxnptrfeosr- sion, theconversion factor isdefinedas a CO S mol/WCO.In ≡ this paper, we represent theCO-to-H2 conversion factor by ⋆ E-mail:[email protected] XCO. (cid:13)c 2016TheAuthors 2 H. Hirashita and N. Harada DerivingareasonableCO-to-H2conversionfactorisnot the full details of grain formation and processing mecha- easy.ToobservationallyderivetheCO-to-H2conversionfac- nisms,therearestillsomeuncertainfreeparametersregard- tor, we need to know the H2 content, which is not directly ing, especially, the time-scales of individual processes. The observed by its emission. The H2 content (or the total col- time-scales (or efficiencies) of accretion, shattering, and co- umn density or mass of a molecular cloud) is usually es- agulation are strongly affected by the density structures in timated indirectly through an estimate of the virial mass the ISM (Bekki 2015; McKinnon et al. 2016; Aoyama et al. or a conversion from the dust far-infrared intensity to the 2016), since accretion and coagulation take place only in total gas column density (see Bolatto et al. 2013, for a re- the dense and cold ISM while shattering occurs predom- view).WithsuchmethodsofobtainingtheH2 content,XCO inantly in the diffuse ISM (Yan et al. 2004; Asano et al. has been derived for various galaxies, mainly nearby ones. 2013). Therefore, to complement those detailed models, a In particular, it has been found that XCO depends on the parametersurveystudyisdesirable;thatis,weneedtosur- metallicity (Wilson 1995; Arimoto et al. 1996; Israel 1997; veyallthereasonablerangesofthetime-scales,forthepur- Bolatto et al. 2008; Leroy et al. 2011; Huntet al. 2015) as pose of examining how sensitive the evolution of grain size well as the density and temperature (Feldmannet al. 2012, distributionistotheassumedtime-scalesorforthepurpose hereafter FGK12; Narayanan et al. 2012). of finding the ranges of the time-scales that reproduce suc- As mentioned above, dust has an influenceon both H2 cessfully the observed extinction curves (Bekkiet al. 2015; and CO abundances through shielding of UV dissociating Hou et al.2016).However,afulltreatmentofgrainsizedis- photonsandH2 formation ondustsurfaces. Themetallicity tribution requires a lot of computational time, and is not dependenceofXCOmentionedabovemayreflectdustenrich- suitable for such a parameter surveystudy. ment, which occurs simultaneously with metal enrichment To make a parameter survey possible in a reasonable (Lisenfeld & Ferrara 1998; Dwek 1998). Dust enrichment is computationaltime,weadoptasimplifiedmodeldeveloped oneofthemostimportantaspectsforunderstandingtheevo- by H15 to calculate the evolution of grain size distribution: lutionofgalaxies.Dustabsorbsandscattersthestellarlight H15adopteda‘two-size approximation’ approach,inwhich andemit itin thefarinfrared, therebyshapingthespectral thegrain sizesarerepresentedbytwosizes(largeandsmall energy distribution (e.g. Yajima et al. 2014; Schaereret al. grains)separatedaroundaradiusof0.03 m m.Thisapproxi- 2015,for recent modelling). Asmentioned above,grain sur- matedmodelstillincludesalltheaboveprocessesconsidered faces provide a condition suitable for efficient formation of by Asano et al. (2013) but simply treats the production of molecular hydrogen, which is an important coolant in low- ormassexchangebetweenthesmallandlargegrainpopula- metallicity clouds (e.g. Cazaux & Tielens 2004). Dust it- tionsfortheevolutionofgrainsizedistribution.H15showed self is also an important coolant in star formation, induc- thatthistwo-size approximation traces thesame evolution- ingthefinalfragmentation thatdeterminesthestellar mass arybehavioursofgrainsizedistributionandextinctioncurve (Omukaiet al. 2005;Schneideret al. 2006). as presented in Asano et al. (2013, 2014). Therefore, H15 Not only the dust abundance, but also the grain size confirmed that the two-size approximation can be used as distribution is important in various aspects. In particular, a simplified (or computationally cheap) version of the full shielding of dissociating photons and H2 formation on dust treatment of grain size distribution. Bekkiet al. (2015) ap- surfaces depend on the grain size distribution through the pliedthetwo-sizeapproximationincombinationwithextinc- dependenceofthesurfaceareaonthegrainsize.Asano et al. tioncurvecalculations,findingthatthevarietyofextinction (2013)formulated theevolutionof grainsize distributionin curvesamongtheMilkyWayandtheLargeandSmallMag- a consistent manner with galaxy evolution. In their calcu- ellanic Clouds can be explained by different transportation lation, dust condensed in stellar ejecta [supernovae (SNe) efficiencies of small grains out of the galaxies. Indeed, they andasymptoticgiantbranchstarwinds],dominatethegrain took advantage of the quickness of two-size approximation sizedistributionattheearlystageofgalactic evolution(see calculationstofindoptimumparametersthatreproducethe also Valianteet al. 2009). These stellar sources form large observed extinction curves(see also Hou et al. 2016). ( 0.1 m m) grains, based on theoretical and observational Inthispaper,utilizingthedustmodelsmentionedabove ∼ evidence (see section 2.1 of Hirashita 2015, hereafter H15, (specifically the two-size approximation in H15), we exam- fordetailedreferences);thus,thedustisdominatedbylarge ine the effect of dust evolution on the abundances of H2 grains at the early stage of galaxy evolution. As the sys- and CO molecules. This enables us to examine the effect tem is enriched with dust, shattering as a result of grain– of dust evolution on the H2 and CO abundances. In par- graincollisionbecomesefficientenoughtoincreasetheabun- ticular, we will focus on how the dust evolution, including danceofsmallgrains.Theincreaseofsmallgrainsdrastically the evolution of grain sizes, affects the metallicity depen- boosts the total grain surface area; as a consequence, grain dence of XCO. The dependence of H2 formation rate on the growth by the accretion of gas-phase metals becomes the evolutionof grain sizedistribution hasnot beenfully inves- most important process for dust enrichment. Afterwards, tigated: Yamasawa et al. (2011) incorporated the effect of the abundant small grains coagulate to form large grains. grainsizedistributiononH2formationinagalaxyevolution Nozawa et al. (2015) used the same model with a modifi- model, but they only focused on the early stage of galaxy cation of incorporating the molecular cloud phase, which evolution. Since there have already been analytic models hosts strong accretion and coagulation, in addition to the forH2formation(Hirashita & Ferrara2005;Krumholzet al. originally included warm and cold phases. They explained 2008,2009;McKee & Krumholz2010),wefocusontheeffect not only the Milky Way extinction curve but also the ex- of grain size, which has not been included in those mod- tinction curve observed in a high-redshift quasar taken by els. The grain size distribution also affects the CO abun- Maiolino et al. (2004) (see also Gallerani et al. 2010). dance through shielding of dissociating photons. Through Although the above recent models took into account this work, we not only understand or quantify the effect MNRAS000,1–18(2016) Dust and molecules in galaxies 3 of dust evolution on XCO but also estimate how much the where Z is the metallicity, fin is the dust condensation effi- observational scatter in theXCO–metallicity relation can be ciencyofmetalsinthestellarejecta,R isthereturnedfrac- explainedbythevariationofdustevolutionamonggalaxies. tionofgas from stars,YZ isthemassfraction ofnewly pro- Sincethereareseveralprocesses drivingthedustevolution, ducedmetalsbystars,andb SN,b sh,b coandb accindicatethe using amethod suitable for aparameter survey such as the efficiencies(explainedbelow)ofSNshockdestruction,shat- two-size approximation is crucial for thepresent work. tering, coagulation and accretion, respectively. Note that This paper is organized as follows. In Section 2, we these efficiencies (referred to as b s) depend on Ds or Dl model the dust evolution, the abundances of H2 and CO, except b SN (H15). The right-hand size of equation (1) rep- and the CO-to-H2 conversion factor. In Section 3, we show resents the stellar dust production [fin(RZ+YZ); note that the results for the basic predictions of our models. In Sec- dust grains supplied by stars are assumed to be large; see tion 4, we further discuss the dependence on some physical H15 and references therein], the increase by coagulation of components that cause major influences on the H2 and CO small grains (b coDs), the decreases by SN destruction and abundances.InSection5,wecommentonsomeimplications shattering(b SNDl and b shDl,respectively),andthedilution forvariousgalaxypopulations.Finallywegiveconclusionsin ofdust-to-gasratiobyreturnedgasfromstars(RDl).Equa- Section6.Throughoutthispaper,weadoptthetypicalcon- tion (2) shows the increase of small grains: the shattering versionfactorfortheMilkyWayasXCO=2 1020cm−2K−1 andcoagulationtermsinequation(2)havetheoppositesign km−1s,whichcorrespondstoa CO=4.3M ×K−1km−1spc2 tothoseinequation(1),sinceshatteringissourceandcoag- (Bolatto et al. 2013), and Z = 0.02 for t⊙he solar metallic- ulation is sink for small grains. The increase of dust abun- ityusedforthemetallicity n⊙ormalization in themodels(we dance by accretion (b accDs) only appears in equation (2) adopt thesame value as in H15). basedontheargumentthataccretionismuchmoreefficient for small grains than for large grains because small grains havemuch larger surface-to-volume ratio (Hirashita& Kuo 2011; Asanoet al. 2013). 2 MODEL The efficiencies denoted as b s are defined as b SN tSF/tSN,b sh tSF/tsh andb co tSF/tco,wheretSF Mgas/≡y We first calculate how the dust content evolves as a func- (Mgas is the≡total gas mass in≡the galaxy and y is≡the star tionofmetallicitytoobtaintherelationbetweendust-to-gas formation rate) is the star formation time-scale, and the ratio and metallicity (D–Z relation). In this calculation, we shattering and coagulation time-scales are proportional to also trace the evolution of grain sizes by adopting the two- the dust-to-gas ratios, since shattering and coagulation are sizeapproximationdescribedbelow.UsingthecomputedD– collisional processes: Z relation,wecalculatethemolecularabundanceofasingle tgyivpeiscahlocwlouthdeinmotlheecuglaarlaxaby.unAdsanacecsoninseqaucelnocued, tisheaffmecotdeedl tsh=tsh,0 DDl −1, (3) bythe D–Z relation. (cid:18) MW,l(cid:19) D 1 tco=tco,0 D s − , (4) (cid:18) MW,s(cid:19) 2.1 Dust evolution wherethetime-scalesarenormalizedtotsh,0andtco,0,which are the values at the MW dust-to-gas ratio, DMW,l=0.007 We use the two-size dust enrichment model developed by andDMW,s=0.003(H15).Theaccretionefficiencyb accisreg- H15. In this model, to avoid heavy computation, the en- ulated by the lifetime of dense clouds (tcl) and the metal- tlairregesigzerarinasng(erooufghdluystdgivriadiends iastraep∼re0s.e0n3temdmb,ywshmearlel aanids nliceietdy.tAheccarevteiroangeisdmvaolrueeseffiocfieanℓt(fℓo=r l1o,ng2e,ratncdl. F3)or(sbeaecc,Awpe- the grain radius), considering that various grain processing pendix A) because accretion is a surface process in which mechanismsworkdifferentlybetweenthesetwograin popu- the grain size, surface and volume play an important role. lations. The model takes into account dust condensation in Thecalculation of b acc is explained in AppendixB. stellar ejecta, dust destruction in SN shocks, grain growth Bysolvingequations(1)and(2),weobtaintherelation byaccretion andcoagulation, andgrain disruptionbyshat- between dust-to-gas ratio and metallicity (D–Z relation). tering. Below, we consider a cloud whose column density is typical H15consideredtheevolutionoftheabundancesofsmall of Galactic molecular clouds, and calculate the H2 and CO andlargegrains,andcalculatedthetotalmassofsmall/large abundancesinthecloudbasedonthedustabundancegiven grains divided by the total gas mass, referred to as the as a function of metallicity bytheabove D–Z relation. small/large-grain dust-to-gas ratio. We denote the small- andlarge-graindust-to-gasratiosasDs andDl,respectively. The total dust-to-gas ratio is the sum of these two compo- 2.2 H abundance 2 nents as D =Ds+Dl. After applying the instantaneous re- cycling approximation (Tinsley 1980), the evolutions of Ds We consider a cloud with a hydrogen column density of andDlaredescribedintermsofmetallicityevolutionas(see NH∼1022 cm−2 (typicalofGalacticmolecularclouds)under H15 for thederivation) agivenmetallicity.Weassumethatthiscloudhassmall-and large-graindust-to-gasratiosDs(Z)andDl(Z)calculatedby YZddDZl = fin(RZ+YZ)+b coDs−(b SN+b sh+R)Dl, (1) tbheedmetoedremliinnedSebcytiotnhe2.b1a.lTanhceeHb2etawbeuenndfaonrcmeaitsioanssuamndedditso- YZddDZs =b shDl−(b SN+b co+R−b acc)Ds, (2) seoncdiaotfiotnhi(sthsiusbeseqcutiiloibnr)i.umThaessHu2mfpotrimonatiisondirsactuessiesdparotptohre- MNRAS000,1–18(2016) 4 H. Hirashita and N. Harada tional to the local density represented by the number den- where the rate coefficient Rdiss is given by sityofhydrogennucleinH.Fordissociation,thecolumnden- (Hirashita & Ferrara 2005) scityisoifmhpyodrrtoagnetnfnourcslehiieNldHinags wofeldliasssotchieatUinVg rpahdoiatotinosn[fic elids Rdiss=4.4×10−11c Sshield,H2Sshield,dust, (9) theUVradiationfieldintensityattheLyman-Werner(LW) with Sshield,H2 and Sshield,dust being the correction factors band normalized to the solar neighbourhood value derived for H2 self-shielding and dust extinction, respectively. We by Habing 1968, 3.2 10−20 erg s−1 cm−2 Hz−1 sr−1; see adoptthefollowingformforSshield (Draine& Bertoldi1996; × alsoHirashita & Ferrara2005].ExpressingtheUVradiation Hirashita & Ferrara 2005): field with a single parameter c means that we neglect the dliceipteyn.dAesncsehoowfnstelalltaerr,UtVhespveacrtiarutimon(oorf hUaVrdrnaedssia)toionnmheatsala- Sshield,H2 =min1, 10211f4Hc2NmH−2!−0.75, (10) largeinfluenceonthemolecularabundancesatlowmetallic-   ity,wherewearenotmuchinterestedintheCO abundance and sinceitis toolowtobedetected.TheH2 abundanceatlow metallicity could be affected by the variation of UV spec- Sshield,dust=exp (cid:229) tLW,i , (11) trum. However, according to Schaerer (2002), with a fixed − i ! star formation rate, the H2 dissociation rate only differs by where tLW,i is the optical depth of dust component i at the a factor of 1.5 between low ( 1/50 Z ) and solar metal- LW band.This optical depthis estimated as licities, while we will vary c b∼y orders ⊙of magnitude in this t D (pUapVeri.ntTenhsuist,y)waensdimnpeglylecctonthceenvtararitaetioonn othfehavradrniaetsiso.n of c tLW,i=(cid:18) NLHW(cid:19)0.01,i(cid:18)0.0i1(cid:19)NH, (12) Under a given set of (nH,NH,c ), we calculate the H2 where(tLW/NH)0.01,i istheopticaldepthofdustcomponent fraction, fH2 achievedasaresultoftheequilibriumbetween i (again, i=s or l for small and large grains, respectively) theformationondustandthedissociationbyUV(LWband) for Di =0.01 at the LW band, normalized to the hydro- radiation. The H2 fraction is defined in such a way that gen column density. H15 showed that, with Ds=0.003 and fH2NH/2givesthecolumndensityofH2.Theratesofforma- Dl=0.007, which are appropriate for the Milky Way, the tion and dissociation are given in what follows. MilkyWayextinctioncurveisreproducedwithamassratio The increasing rate of fH2 by H2 formation on dust is of silicate-to-carbonaceous dust of 0.54 : 0.46. We fix this described as silicate-to-carbonaceousdustratioincalculatingtheextinc- (cid:20)ddfHt2(cid:21)form=2(cid:229) i (1−fH2)RiH2,dustnH, (5) ft8oi.o2rntfho1er0−sLi2mW1pclmbica2itnyad.nIdafsw(et1L0aW0d0/oNp˚AHt),t0h.w0e1er,le=pobre2ts.a3einnta1(tt0iL−vWe21/wNcaHmv)e02l..e0n1F,gsitx=h- where the rate coefficient RiH2,dust (superscript i indicates ing×the silicate-to-carbonaceous dust abu×ndance ratio does small or large grains; i.e. i=s or i=l) is introduced. The not affect our results significantly. Grain composition is in- rate coefficient, which depends on the dust-to-gas ratio, is deed suggested to be different in different galaxies: studies determined by(Yamasawa et al. 2011) on extinction curves indicate that the dust composition in 3Dm m S v¯ a2 theSmallMagellanic Cloud (SMC)isdominatedbysilicate Ri = i H H h ii, (6) with little contribution from carbonaceous dust (Pei 1992; H2,dust 8sha3ii Weingartner& Draine2001).Underthesamegrainsizedis- where s is the material density of dust, mH is the atomic tribution, the extinction curve composed purely of silicate mass of hydrogen, v¯ is the mean thermal speed, SH is the hasanenhancementbyafactorof 1.4around1000˚Acom- ∼ probability of a hydrogen atom reacting with another hy- paredwiththesilicate-graphitemixturethatreproducesthe drogen atom on the dust surface to form H2, and a2 i and MilkyWayextinctioncurve(Pei1992).Asweseelater,dust a3 i are the second and third moments with suhbsciript i extinction is important for CO formation, but considering h i indicating small or large grains (Appendix A). We adopt the sensitive dependence of CO abundance on dust-to-gas s=3.3 g cm−3 (Draine& Lee 1984) and m =1.4. Adopting ratio, difference in tLW only by a factor of 1.4 does not af- insteads 2gcm−3appropriateforcarbonaceousdustdoes fectourdiscussionsandconclusionsinthispaper.Although ∼ not affect our conclusions below. We also fix SH=0.3: such the above extinction curve studies cannot exclude a possi- a high value is reasonable to adopt since we are particu- bility of other dust species than silicate and carbonaceous larly interested in H2 formation in cold and shielded envi- dust (note that Tchernyshyovet al. 2015 suggest that dust ronments (Hollenbach & McKee 1979). The thermal speed containing no silicon atom should exist in some regions in is estimated as (Spitzer1978) the SMC based on their study of elemental depletion), we concentrate on the change of dust abundance Di by fixing v¯= 8kBTgas, (7) thecoefficient (tLW/NH)0.01,i in thispaper. s p mH In the above, we assumed the equilibrium between H2 formation anddestruction.Thus,weimplicitly assumethat where kB is the Boltzmann constant, and Tgas is the kinetic temperatureof thegas. thecloud hasalonger lifetime thantheH2 formation time- The changing rate of fH2 by photodissociation is esti- scale. TheH2 formation time-scale, tH2, is estimated as mated as f (cid:20)ddfHt2(cid:21)diss=−RdissfH2, (8) ItfH2w=e[dapfHp2r/oHdx2ti]mforamte. the reaction rate in equation (6)(1b3y) MNRAS000,1–18(2016) Dust and molecules in galaxies 5 using an intermediate value of ha3ii/ha2ii ∼0.01 m m be- waysadoptNH/nH=NH′/n′H tomakethefollowingequations tween large and small grains (Table A1) and by re- solvable (following FGK12). placing Di with D, we obtain (omitting superscript The CO abundance xCO is defined as the numberratio ic)mR3H2s,−du1s,t ∼wh3.i7ch×1le0a−d1s7(Dto/0.t0H12)(∼T/f1H02/K(R)H1/22,d(unsHtn/H1)03∼c8m.7−3×) oFfGCKO12m, tohleactutlehsetCoOhyadbruongdeannncuecilseid.eWteermaisnsuedmbe,yftohlleowdiunsgt t1i0m5efH-s2c(aDle/0c.a0n1)b−e1(cTom/1p0arKed)−w1i/t2h(ntHh/e1f0r3ee-cfmal−lt3i)m−1eeystri.mTatheids ethxutisn,cwtieonwraintedtthheeCraOdiaabtiuonndfiaenlcdeuansdxeCrOa=gixvCeOn(AmVe,tca,llZic)i.ty; astff∼1.4×106(nH/103 cm−3)−1/2 yr.WefindthattH2<tff Nowlet usformulatetheestimation methodof theCO is satisfied if thedust-to-gasratio is neartotheMilky Way abundance. We utilize the calculation results in GM11 to value. Thus, if we consider a typical molecular cloud, the estimate xCO. GM11 provideCO fraction x′CO at c ′=1.7.1 equilibriumassumption ontheH2 abundanceisreasonable, Following FGK12, we start with the equilibrium be- since the time-scale of gravitational evolution occurs on a tween dissociation and formation of CO in the two systems longertime-scalethanthereactiontime-scale(althoughthe that realize CO abundancesof xCO and x′CO (recall that the reaction may be non-equilibrium for small-scale structures; quantitieswithaprimemeanthoseobtainedinGM11’ssim- Gibson et al. 2015). However,if thedust-to-gasratio is sig- ulation): nasifisucmanpttlyionlowsheorutlhdabnetchoensMidielkreydWcaaryefuvalllyu,es,intcheeteHq2ubileibcormiuems xCOc Sdust(AV,eff)SH2(NH2)SCO(NCO)=nH(cid:229)i,jRi,jxixj, (14) longinproportiontoD 1 (seealsoHu et al.2016).Theas- − sumptionofequilibriumisyetjustifiedifthemolecularcloud and nisifisucastnatilnyesdmaaglaleinrstthtahneufrneietyf.aFlloorreixfatmheplree,suiflttihnegmfHo2leiscusliagr- 1.7x′COSdust(AV′ )SH2(NH′2)SCO(NC′O)=n′H(cid:229) Ri,jx′ix′j, (15) i,j cloud is sustained for a few free-fall times as indicated for nearby molecular clouds (e.g. Ward-Thompsonet al. 2007, whereRi,jisthereactionratesofCOformationfromspecies although this is still debated), the equilibrium assumption i and j, the abundances of which are denoted as xi and xj forH2formationisreasonabledowntoD∼0.001.Intermsof (or x′i and x′j), respectively. As mentioned in FGK12, it is tinheobcojemctpsarwisiothnDwi>th0.o0b0s1e,rvfoartiwonhsi,chweCaOrecomualdinlbyeindteetreecstteedd. epxlapuescitbltehtahtatthxei∼lefxt′i-haannddxsji∼dex′jofuneqdueratxiCoOn=(1x4′C)Od.iTvihduesd,wbye Nevertheless,wesh∼ouldkeepinmindthatourresultsaround nH is equal to the left-hand side of equation (15) divided Dpre∼te0d.0c0a1r,efruolulyg,hlayndcotrhreastpcoanldcuinlagtitoonsZt∼ak0i.n1gZi⊙ntoaraeccinotuenrt- bxCyOn=′H.x′CROe,cwalelinogbttahinat we adopt nH/n′H=NH/NH′ and using non-equilibriumH2formationisdesirableforafuturestudy. c Sdust(AV,eff)SH2(NH2)SCO(NCO)/NH =1.7Sdust(AV′ )SH2(NH′2)SCO(NC′O)/NH′, (16) 2.3 CO abundance where Sdust(AV), SH2(NH2), and SCO(NCO) are the shielding The CO abundance is determined by a complicated chem- factors of CO-dissociating photons (1 S is the fraction of − ical network that includes a lot of reactions. For exam- shieldedCO-dissociatingradiationbyeachspecies)bydust, ple, Glover et al. (2010) treated a chemical network com- H2, and CO, respectively, and AV,eff=A1000 /4.7 is the ef- posed of 200 reactions. Since calculations of such a large fective V-band extinction. The shielding functions S’s are ∼ chemical network are generally time-consuming, perform- taken from Lee et al. (1996). To obtain AV,eff, we first ob- ing full chemical calculations for the CO abundance with tain A1000 1.086(cid:229) itLW,i using equation (12). We convert ≃ alarge numberof cases fordustevolution at variousmetal- this to AV,eff with the above relation, where the factor 4.7 licities is not realistic. Therefore, we utilize CO abun- comes from theMilky Way extinction curve(Pei 1992). dance data already calculated for various physical condi- Equation (16) is the one we solve to obtain the CO tions by Glover & Mac Low (2011, hereafter GM11) (see abundance. Note that all the quantities on the left-hand also Shettyet al. 2011). They calculated spatially resolved sidein equation (16) are given byoursimulation exceptfor H2 and CO abundances over a region of 5–20 pc using dy- NCO=xCONH=x′CONH whilethoseontheright-handsideare namical simulations of magnetized turbulencecoupled with given as a function of AV′ as we see below. Because x′CO is achemical network for H2 and CO and atreatment ofpho- a function of AV′ as we see below (thus, with the assump- todissociation. We follow the method used by FGK12, who tion of xCO=x′CO, xCO is also a function of AV′ ), equation adopted the calculation results in GM11. Below we explain (16) isanequationfor AV′ .Onceweobtain AV′ ,wecalculate thecalculation method of CO abundance. xCO=x′CO(AV′ ). Before we explain our formulation, we need to relate Now we explain how NH′2 and NC′O are expressed as a the column density with the local density, since the reac- function of A . Based on GM11’s result, we adopt the fol- V′ tion rate is determined by the local density. In the origi- lowing fittingformulae: nal formulation in FGK12, the dependences on nH and NH are both absorbed in AV by imposing AV (cid:181) nH(cid:181) NH. In this fH′2=1−exp(−0.45AV′ ), (17) paper, the proportionality constant between AV and NH is givenconsistentlywithourmodel,whileweusetherelation given in FGK12 for AV′ and NH′ (see below), where we put 1 TheMilkyWayinterstellarradiationfieldadoptedbyGM11is aprimetothequantitiescalculated inGM11 todistinguish basedonDraine(1978)’sestimate,whichcorrespondsto c =1.7. them from the quantities calculated in our model. We al- Asshownlater,wecanpracticallyregardx′CO asafunctionofAV′. MNRAS000,1–18(2016) 6 H. Hirashita and N. Harada and Table 1.Parameterrangessurveyedfordustevolution. logx′CO=−7.64+3.89logAV′ , (18) wheretheH2fraction fH′2 isrelatedtoNH′2 asNH′2=fH′2NH′/2, Parameter Process Minimum Maximum Fiducial and fin stellarejecta 0.01 0.1 0.1 NH′ = 5.348 10 2A2V′(Z/Z ) cm2 (19) btcSlN aScNcrdeetisotnruction 1046.8yr 10189yr 190.76y5r × − ′ ⊙ tsh,0 shattering 107 yr 109 yr 108 yr inGM11’sformulation(weadoptZ′=Z).Notethatthesere- tco,0 coagulation 106 yr 108 yr 107 yr lations(equation17–19)donotholdamong fH2,xCO,NHand tSF starformation 0.5Gyr 50Gyr 5Gyr AV because physical conditions such as dust properties and radiationfieldaredifferentbetweenourmodelsandGM11’s calculations. We also use NH2 = fH2NH/2 and NCO=xCONH, wrehdesrheiftTCoMfBt=he2.g7a3l(a1x+yzc)oinsstidheereCdM; Bweteamdpopertatzu=re0(zinistthhies and use fH2 calculated in Section 2.2. As mentioned above, paper).For thevelocity width,we simply adopt thetypical we are looking for a solution that satisfies xCO=x′CO.Thus, valueadoptedinFGK12,D v=3kms 1,partlybecauseour equation (16) is rewritten as − models are based on their model, partly because a direct c Sdust(AV,e=ff)1S.H72S(dfuHst2(NAHV′/)2S)HS2C(OfH′(x2N′COH′N/2H))S/CNOH(x′CONH′)/NH′, (20) c‘ccooamlluibpmranartisdeodenn’sbwiytiytthhcetaihlrceumirlaomtdeoedld)e.inlUiSssiepncgotsieosqinbul2ae.t2(io,i.new.(eo2u2fi)rnaamnlloyddtoehlbsetaaHrine2 where fH′2,x′CO,andNH′ areallfunctionsofAV′ throughequa- theCO-to-H2 conversion factor, XCO,by equation (21). tions (17), (18), and (19), respectively. Note that NH is a givenparameter,andthatAV,effand fH2 arecalculatedbythe 2.5 Choice of parameter values model. Thus, we solve equation (20) to obtain A , which is V′ translated intotheCO abundancex′CO=xCO throughequa- For the dust evolution model, we adopt R=0.25 and YZ= tion (18). 0.013(Hirashita & Kuo2011).Fortheparametersgoverning WeimposeanupperlimitxC=1.41 10−4Z/Z (carbon thedustevolution,weadopt thesamerangesasadoptedin abundance)forxCO;thatis,iftheobtain×edxCOisla⊙rgerthan H15as listed in Table 1. thecarbonabundance,weadoptxCO=xC.Thisonlyoccurs As assumed in Section 2.3, we give c and NH for the at super-solar metallicities in ourmodels. physical condition of the cloud at a given Z. Although nH is not essential to our formulation for the CO abundance, it is necessary in calculating the H2 abundance. Whenever 2.4 CO-to-H2 conversion factor necessary, we adopt nH =103 cm−2, which is appropriate for the molecular clouds in the Milky Way (but not nec- Using the quantities calculated above, we finally calculate essarily ‘molecular’ in galaxies with higher c or lower Z theCO-to-H2 conversion factor: than in the Milky Way) (Hirashita & Kuo 2011). For the XCO=NH2/WCO. (21) column density, we investigate a range of NH =1021–1023 cm 2,correspondingtosurfacedensitiesof10–103M pc 2. WecomputeWCO using thefollowing expression (GM11): Th−is covers the range of surface densities of giant m⊙olec−u- t WCO=TrD v 102b (t )dt , (22) larcloudsinvariousenvironments(e.g.Bolatto et al.2013). Z0 FortheUVintensitynormalizedtotheHabing(1968)value, Hirashita & Ferrara (2005) derived the relation between c lwahteerreinTreiqsutahteioonb2se5r)v,eDdvraisditahteionvetloemcitpyerwatidutrhe (ocfaltchuelaCteOd andthesurfacedensityofSFR(S SFR)byassumingthatthe line,t10 istheopticaldepthof theCOJ=1 0transition, UVluminosity traces thecurrent star formation rate as and b (t ) is the photon escape probability a→s a function of S SFR=1.7 10−3c M yr−1 kpc−2. (26) the optical depth. The escape probability is estimated as × ⊙ We survey a range of c = 1.7–170 (1–100 times the (Tielens 2005) Galactic value), corresponding to S SFR = 2.9 10−3–0.29 b (t )=(1[1/−(4etx[lpn((−t /2√.34pt))]1]//2()4.68t ) iiff tt ≤>77.; (23) SMdtis⊙acrbyugr−arsl1atxkigpeacsl−a2x(,KiewsehninhciahcvuertotuS gS1hF9Rl9y81)c0o–v(1esr0ese0thtaielmsoreasnSghe×ecigtoihofenrneS5a.rS2bF)Ry. Theopticaldeptht10isestimatedas(Tielens2005;FGK12) (Kennicutt 1998), thus c . We consider such extreme values of c later in Section 5.3. In Table 2, we list the ranges t10=1.4×10−16(1−e−5.5/Tgas) 3 kmD vs 1 −1 cNmCO2 . and fiducialvalues of NH and c . (cid:18) − (cid:19) (cid:18) − (cid:19) (24) The radiation temperature of the CO J=1 0 transition 3 RESULTS → with the subtraction of the cosmic microwave background 3.1 Basic properties (CMB) taken into account is calculated by Here we investigate the general evolution of H2 and CO 1 1 Tr=5.5 e5.5/Tgas 1−e5.5/TCMB 1 K, (25) acibaulnvdaalunecsesfourntdheer pvaarraiomuestecrosndoiftidounsst. eWvoeluatdioonptanthdecfiloduud- (cid:18) − − (cid:19) MNRAS000,1–18(2016) Dust and molecules in galaxies 7 ratio increases. A fully molecular condition is realized at Table 2.Parameterrangesforthephysicalcondition ofclouds. Z>0.1Z .Thus,acloudwithatypicaldensityandcolumn de∼nsity o⊙f Milky Way ‘molecular’ clouds is not fully molecular below metallicity 0.1 Z . The CO fraction, xCO, also Parameter Minimum Maximum Fiducial increases associated with th⊙e increase of dust-to-gas ratio. NH 1021 cm−2 1023 cm−3 1022 cm−3 TounderstandwhatdrivestheincreaseofxCO,wealsoshow c 1.7 170 1.7 thecaseswithouteitherdustshielding,H2 shielding,orCO self-shielding in the third window in Fig. 1. The prediction without H2 shielding underproduces the CO abundance at low metallicity <0.2 Z , which indicates that H2 shielding is important for∼CO fo⊙rmation. This is associated with the metallicity at which the cloud becomes fully molecular. At Z>0.2 Z , the main shielding component changes to dust: If∼we do⊙not include dust shielding, the CO abundance re- mains as low as 10 6–10 5. Dust shielding becomes im- − − ∼ portant after the dust abundanceis increased by accretion. Self-shieldingof CO hasan influenceon theCO abundance only around solar metallicity, but its contribution is minor. The CO abundance, xCO cannot be larger than the carbon abundance (xC); thus, at Z>2 Z , xCO is limited by the carbon abundance. ∼ ⊙ The CO-to-H2 conversion factor, XCO is sensitive to metallicity. This is particularly because there is a metallicity range where the cloud is rich in H2 but is not rich in CO at Z>0.1 Z . Around solar metallicity, XCO is near to the value∼observ⊙ed in the Milky Way ( 2 1020 cm 2 K 1 − − km−1 s;Bolatto et al.2013).Abovesol∼arm×etallicity,XCO is notsensitivetometallicity becausetheCO J=1 0lineis → optically thick.We also show themetallicity dependenceof the CO-to-H2 conversion factor without one of the shielding mechanisms. H2 shielding has an influence on the slope of the XCO–Z relation, since it has a larger impact on the CO abundance at low metallicity as discussed above. Dust Figure1.Quantitiesofinterestasafunctionofmetallicity.Pan- elsfromuppertolowershowthedust-to-gasratio(D),H2fraction tsuhdieeldhinigghherasthaadnratmheatMicilikmypwacaty:vXaClOueisattwsooloarrdemrsetoafllmicaitgynii-f (fH2), CO fraction (xCO) and CO-to-H2 conversion factor (XCO). wedonotincludedustshielding.COself-shieldinghaslittle For the dust-to-gas ratio, the small and large grain components are shown by the dotted and dashed lines, respectively, and the influenceon XCO. total dust-to-gas ratio is shown by the solid line. For xCO and XCO, the cases without either dust shielding(dotted), H2 shielding (dashed), or CO self-shielding (dot-dashed) are also shown. 3.2 Dependence on the cloud parameters XCO isshownonlywhenxCO>10−10. We investigate the dependence on the cloud parameters listedinTable2(i.e.NH andc ).InFig.2,weshowthevari- properties(Tables1and2).InFig.1,weshowthemetallic- ationofthequantitiesofinterestasafunctionofmetallicity. ity dependence of the quantities investigated in this paper, Notethat theD–Z relation is not affected bythe changeof namely, the dust-to-gas ratio (D), H2 fraction (fH2), CO thoseparameters. fraction (xCO) and CO-to-H2 conversion factor (XCO). XCO InFig.2a,weshowthedependenceonthecolumnden- is only shown where xCO>10−10, below which detection of sity(NH).Becauseofstrongerself-shielding, fH2 islargerfor CO is impossible in any case. a larger NH (fH2 (cid:181) NH3 for the self-shielded regime as long H15 already investigated and discussed the D–Z rela- as fH2≪1; Hirashita & Ferrara 2005).The increase of dust tion,whichisbrieflydescribedinwhatfollows. Dustissup- abundance around Z 0.1 Z is important to raise the H2 pliedbystarsatlowmetallicities,andisdominatedbylarge fractionforNH=1021∼cm−2;t⊙hus,theincreaseofdustabun- grains. Small grains gradually increase because of shatter- dancebyaccretionisimportanttomakethecloudmolecule- ing of large grains. At a certain point, the increase of small richatlowcolumndensities.TheCOabundanceisverysen- grainsisacceleratedbecauseofaccretion,whichinducesthe sitivetoNH;atZ<0.1Z ,theCOabundanceisgovernedby increase of large grains as well through coagulation. As a H2 shielding,whi∼leathi⊙ghermetallicities, itisregulatedby consequence, the total dust abundance steeply increases as dust shielding (Section 3.1). In the case of NH=1023 cm−2, seen around Z 0.1–0.2 Z . After that, the dust-to-gas ra- therapidchangeofxCOaroundZ 0.1Z isduetotherapid tio gradually in∼creases bec⊙ause of the metal enrichment; at increase of dust abundance(or d∼ust shi⊙elding). The CO-to- thisstage,thedust-to-gasratioisdeterminedbythebalance H2 conversion factor, XCO, drops to 1021 cm−2 K−1 km−1 between accretion and SNdestruction. s even at Z 0.2 Z in the case of NH=1023 cm−2, while The H2 fraction, fH2 also increases as the dust-to-gas it does not d∼rop fur⊙ther because of high CO optical depth. MNRAS000,1–18(2016) 8 H. Hirashita and N. Harada Figure2.SameasFig.1butwiththefollowingparameterschanged:(a)NH=1021,1022,and1023 cm−2forthedotted,solid,anddashed lines, respectively, with c =1.7. (The solid linealways shows the fiducial case in all the figures in this paper.) (b) c =1.7, 17, and 170 for the solid, dotted, and dashed lines, respectively, with NH=1022 cm−2. We fix the values of the parameters other than the changed parameter atthefiducial valueslistedinTable2.Weadopt thedustevolution modelcharacterized bythefiducialparameters inTable 1. In contrast, XCO for NH=1021 cm−2 is much higher than 3.3 Effects of the dust evolution parameters theGalacticvalue( 2 1020 cm 2 K 1 km 1 s)becauseof − − − ∼ × We investigate the dependenceon the parameters that reg- low dust shielding. Around solar metallicity, the case with NH=1022 cm−2 has the smallest XCO among the three col- ulate the dust evolution (Table 1). The resulting variation ofthequantitiesofinterestbythechangeoftheparameters umndensities.Thisisconsistentwiththetheoreticalexpec- is shown in Fig. 3. tationbyFGK12(seetheirfigure3):asmentionedabove,at NH<1022 cm−2,XCO is dominatedby dustshieldingso that We show the effect of the dust condensation efficiency XCO∼islower at higherNH, while at NH>1022 cm−2, theCO sintelsltaerllsaorurecjeecstoaf,dfuinstindoFmigin.a3tae.thAesdeuxsptl-atoin-gedasirnatHio1a5t, ltohwe emission is saturated by its large optic∼al depth so that XCO metallicity before grain growth by accretion becomes effi- crmiosoleusstmfeonffirdhceiiegnnhstietryinNoHCf.OmInoelmoetcihusselairorwncolproedursd,Hst,2hNemHcol∼oleuc1du0s2le2wacitrmhou−an2,dtyisspoitclhaaerl aacitnednZtx<∼.CTO0.h2aupsZp,⊙etah.reAadtsifflaoewrceonmnceseetaqinlulieDcnitcbye,e,twtwhheeeerneeffvtehacretiosCuOosfafifbninuanpodnpaenafHcres2 metallicity. is too low for detection. Thus, the effect of fin on xCO and XCOisdifficulttobeconfirmedobservationally.Ontheother hand, the effect of fin on fH2 could be examined if we ob- serveobjects with Z<0.2Z .A directdetermination of H2 In Fig. 2b, we present the dependence on the UV ra- abundanceispossibl∼eforda⊙mpedLymana objects(DLAs) diation field intensity (c ). In the most intense radiation usingH2 LW absorption lines (e.g. Ledouxet al. 2003). (c =170), the H2 fraction is strongly suppressed at a level InFig.3b,weshowthedependenceonb SN,whichregu- wNHhe=re10s2e2lfc-smh−ie2l)diantgZi<s0n.0o7tZimp;oartthanigthe(rfHm2e<ta2lli×cit1i0e−s,8seflofr- laasttersotnhgeere/ffiwceiaeknecrydoufsdtudsetsdtreusctrtuiocntidoencbreyaSseNs/ei.nAcrseeaxsepsecbtoetdh, shielding coupled wit∼h the d⊙rastic increase of dust abun- fH2 and xCO because of less/more shielding of dissociating dance makes the sharp transition toward the fully molec- photons. Around solar metallicity, since the CO abundance ular phase in a narrow metallicity range of 0.007–0.2 Z . is governed by dust shielding, xCO is almost inversely pro- The CO fraction is sensitive to c at low metallicities whe⊙re portional to b SN. However, XCO does not vary as expected H2 shielding is important, while it is less sensitive to c at from thechangeof xCO atsolar metallicity, becausetheCO Z>0.3 Z , where dust shielding is important. This is be- emission is optically thick. ca∼use dus⊙t shielding, which has an exponential dependence InFig.3c,wepresentthedependenceontcl,whichgov- on the dust-to-gas ratio, sufficiently suppresses the dissoci- ernstheefficiencyofdustgrowthbyaccretion.Thisparam- ating photons at high metallicity. Accordingly, the slope of eter determines the metallicity at which accretion signifi- XCO asafunctionofZ changesindifferentc .Wewillrevisit cantly raise the dust-to-gas ratio (Hirashita & Kuo 2011). thisdependenceon c in Section 5.3. Accretion affects the H2 abundance only if it occurs at low MNRAS000,1–18(2016) Dust and molecules in galaxies 9 Figure 3.SameasFig.1butwiththefollowingparameterschanged: (a) fin=0.01,0.1,and0.5forthedotted, solid,anddashedlines, respectively. (b)bSN=4.8, 9.65,and19forthedotted, solid,anddashedlines,respectively. (c)tcl=106,107,and108 yrforthedotted, solid,anddashedlines,respectively.(d)tsh,0=107,108,and109 yrforthedotted,solid,anddashedlines,respectively.Inthetopwindow in this panel, we show the total dust-to-gas ratio (thick lines) and the small grain dust-to-gas ratio Ds (thin lines), since the effect of shattering is clearly seen in the small-to-large grain abundance ratio. (e) tco,0=106, 107, and 108 yr for the dotted, solid, and dashed lines,respectively.Inthetopwindowofthispanel,weshowthetotaldust-to-gasratio(thicklines)andthesmallgraindust-to-gasratio Ds (thin lines), since the effect of coagulation is clear in the small-to-large grain abundance ratio. (f) tSF=0.5, 5, and 50 Gyr for the dotted, solid, and dashed lines, respectively. In the top window of this panel, we show the total dust-to-gas ratio (thick lines) and the smallgraindust-to-gas ratioDs (thinlines).We fixthe values ofthe parameters other than the variedparameter atthe fiducial values listedinTable1.WeadoptthefiducialvaluesfortheparametersofthecloudinTable2. MNRAS000,1–18(2016) 10 H. Hirashita and N. Harada metallicity such as in the case of tcl =108 yr. Since the Ds occursinanarrowmetallicityrangeforashorttSF.This increase of CO abundance is associated with the increase produces a drastic change of xCO and XCO around Z 0.2– of D, accretion largely affects xCO and XCO. In particular, 0.3Z .Therefore,thestarformationtime-scalealsoa∼ffects our results predict that the XCO–Z relation is sensitive to them⊙etallicity dependenceof CO abundancein such a way the metallicity level at which accretion dominates the in- thatmildstarformationactivitieswithlongtSFtendtopro- crease of dust abundance. In the case of tcl=106 yr (the duce smooth increase (decrease) in xCO (XCO) as a function leastefficientaccretion),theeffectofaccretiononlyappears of metallicity. at super-solarmetallicity;accordingly,xCO remainslow and XCO is much higher than the Milky Way value ( 2 1020 cm 2 K 1 km 1 s) even at solar metallicity. In t≃he c×ase of − − − tcl=108 yr(themostefficientaccretion),incontrast,ahigh 4 DISCUSSION value of xCO at low metallicity leads to a shallower slope in 4.1 Metallicity dependence of CO-to-H theXCO–Z relationthanintheothercases.Thus,theXCO–Z 2 conversion factor relation dependslargely on theefficiency of dust growth by accretion. The main purpose of this work is to clarify how the metal- InFig.3d,weshowthedependenceontsh,0,whichreg- licity dependence of the H2 and CO abundances is affected ulates the efficiency of shattering (i.e. production of small by the dust enrichment and evolution in galaxies. In par- grainsfromlargegrains).Smallgrainsproducedbyshatter- ticular, the CO-to-H2 conversion factor has been measured ingeventuallygrowbyaccretion.Thus,theincreaseofdust for various types of galaxies with different metallicities. In- abundancebyaccretionappearsatthelowestmetallicityfor deed,ithasbeenknownobservationallythattheconversion theshortesttsh,0.InthetopwindowofFig.3d,wealsoshow factordependsstronglyonmetallicity.Asshown above,the the contribution from small grains to the dust-to-gas ratio: evolution of dust content, which regulates the abundances there is a clear difference in the small grain dust-to-gas ra- ofH2 and CO,is also drivenbymetallicity.Forcomparison tioatallmetallicities.BecausesmallgrainshavealargerH2 with observations, we examine therelation between CO-to- formationrateanddustextinctionperdustmassthanlarge H2 conversion factor and metallicity. grains,alargerfractionofsmallgrains(orahigherefficiency We adopt the following data sets compiled in of shattering) leads to a higher molecular abundance. Nev- Bolatto et al.(2013).Leroy et al.(2011)estimatedtheCO- ertheless,theeffectofshatteringonXCO isminorcompared to-H2 conversion factor in five Local Group galaxies us- with that of accretion. ing dust as a tracer of gas with a variation of dust-to- In Fig. 3e, we show the dependence on the coagu- gas ratio among the galaxies taken into account. For their lation time-scale, tco,0. The effect of coagulation becomes metallicity data given in the form of 12+log(O/H), we put prominentaftertheabundanceofsmallgrainshasincreased an uncertainty of 0.2, and assume that the solar metallic- by shattering and accretion; thus, the variation of coagu- ity corresponds to 8.7 following Bolatto et al. (2013) (we lation time-scale affects the quantities of interest only at use the same oxygen abundance for the solar metallicity Z>0.1 Z . Because the cloud becomes fully molecular at unless otherwise stated). For M31, M33, and the Small th∼is meta⊙llicity, coagulation does not have any appreciable Magellanic Cloud, we adopt their spatially resolved data. impact ontheH2 abundance.Sincestrongcoagulation sup- Bolatto et al. (2008) derived the CO-to-H2 conversion fac- pressestheabundanceofsmallgrains,italsosuppressesac- tor in nearby galaxies based on virial mass estimates of cretion (recall that the role of accretion is to increase the giant molecular clouds. We assume the same metallicity small grain abundance; Section 2.1). As a result, the total uncertainty (0.2) as assumed in the above sample. Israel dust abundance is the smallest in the case of the most ef- (1997) estimated the CO-to-H2 conversion factor in the ficient coagulation (tco,0=106 yr) around Z 0.2–0.3 Z . Magellanic Clouds and nearby irregular galaxies. We also Moreover, coagulation also suppresses the r∼elative abu⊙n- adopted their metallicity data. Sandstrom et al. (2013) an- danceofsmallgrains,whichleadstoadecreaseofshielding alyzed spatially resolved CO, dust, and H i maps on kpc ∼ effect(recallthatsmallgrainshavelargerdustopticaldepth scales of nearby star-forming galaxies, and derived the spa- per mass). As a consequence, the CO abundance is lower, tially resolved CO-to-H2 conversion factor. We adopt their and the CO-to-H2 conversion factor is higher for a shorter mean CO-to-H2 conversion factor for each galaxy. We take tco,0. the metallicity data of their sample from Moustakas et al. In Fig. 3f, we examine the dependence on the star for- (2010): among their metallicity calibrations, we adopt the mation time-scale of the galaxy, tSF. The star formation one by Pilyugin & Thuan (2005) and assume, following time-scaleregulatesthetime-scaleofmetal/dustenrichment Bolatto et al. (2013), that thesolar metallicity corresponds bystellarsources.Aquickmetalenrichmentleadstoaquick to12+log(O/H)=8.5.Besides,wenewlyaddthedatataken increaseinthelarge-grainabundance,whilethetime-scaleof fromCormier et al.(2014)fornearbylow-metallicity galax- shatteringisfixedsotheproductionefficiencyofsmallgrains ies.TheyobtainedXCO,assumingdusttotracethemolecular does not increase. Thus, the abundance of small grains rel- gas with a variation dust-to-gasratio among galaxies taken ative to that of large grains is suppressed if tSF is short. intoaccount. Since small grains have larger shielding and H2 formation There are two remarks on the observationally derived ratepermass,theH2 fraction islarger foralonger tSF.Be- CO-to-H2 conversionfactors. Thedust-basedXCO estimates cause the shattering efficiency is higher if the abundanceof (i.e.otherthanBolatto et al.2008above)commonlyassume largegrainsishigher,shattering,ifitstartsatahighmetal- that the dust-to-gas ratio in molecular clouds is the same licity(i.e.largeDl)suchasinthecaseoftSF=0.5Gyr,hasa as that in diffuse gas. In reality, we expect that the dust- dramaticimpactontheincreaseinDs.Thus,theincreaseof to-gas ratio in molecular clouds is higher because of dust MNRAS000,1–18(2016)