Astronomy&Astrophysicsmanuscriptno.11683˙v2 c ESO2011 (cid:13) January12,2011 Polycyclic aromatic hydrocarbon processing in a hot gas E.R.Micelotta1,2,A.P.Jones2,A.G.G.M.Tielens1,3 1 SterrewachtLeiden,LeidenUniversity,P.O.Box9513,2300RALeiden,TheNetherlands e-mail:micelot@strw.leidenuniv.nl 2 Institutd’AstrophysiqueSpatiale,Universite´ParisSudandCNRS(UMR8617),91405Orsay,France 3 NASAAmesResearchCenter,MS245-3,MoffettField,CA94035,USA Received20January2009;accepted16October2009 1 1 ABSTRACT 0 2 Context.PAHsarethoughttobeaubiquitousandimportantdustcomponentoftheinterstellarmedium.However,theeffectsoftheir n immersioninahot(post-shock)gashaveneverbeforebeenfullyinvestigated. a Aims.WestudytheeffectsofenergeticionandelectroncollisionsonPAHsinthehotpost-shockgasbehindinterstellarshockwaves. J Methods.Wecalculatetheion-PAHandelectron-PAHnuclearandelectronicinteractions,abovethecarbonatomlossthreshold,in 0 Hiiregionsandinthehotpost-shockgasfortemperaturesrangingfrom103 108K. 1 Results.PAH destruction isdominated by Hecollisions at low temperature−s (T <3 104 K), and by electron collisionsat higher temperatures.SmallerPAHsaredestroyedfasterforT <106K,butthedestructionrate×sareroughlythesameforallPAHsathigher A] fteomunpdertaotubreesa.bTouhtetPhAouHsalnifdetyimeaersi,noardteernsuoofusmhaogtngitausde(nsHho≈rt0e.r0t1hacnmt−h3e,tTyp≈ic1a0l7lifKe)ti,mtyepoicfasluocfhtohbejceocrtso.nalgasingalacticoutflows,is G Conclusions.Inahotgas,PAHsareprincipallydestroyedbyelectroncollisionsandnotbytheabsorptionofX-rayphotonsfromthe hotgas.TheresultingerosionofPAHsoccursviaC lossfromtheperipheryofthemolecule,thuspreservingthearomaticstructure. 2 h. TheobservationofPAHemissionfromamilliondegree,ormore,gasisonlypossibleiftheemittingPAHsareablatedfromdense, p entrainedclumpsthathavenotyetbeenexposedtothefulleffectofthehotgas. - o Keywords.shockwaves–dust,extinction–ISM:jetsandoutflows r t s a 1. Introduction in the lifecycle of such species (Dweketal. 1996; Jonesetal. [ 1996). Themid-infraredspectralenergydistributionofthe generalin- 2 Observationally, there is little direct evidence for PAH v terstellarmediumofgalaxiesisdominatedbystrongandbroad emission unequivocally connected to the hot gas in super- 5 emission features at 3.3, 6.2, 7.7 and 11.3 µm. These fea- nova remnants. Reachetal. (2006) have identified four super- 9 tures are now univocally attributed to vibrational fluorescence nova remnants with IR colors that may indicate PAH emis- 5 of UV pumped, large ( 50 C-atoms) Polycyclic Aromatic 1 Hydrocarbon(PAHs)mol≃ecules.Theselargemoleculesarevery sion. Tappeetal. (2006) have detected spectral structure in the 2. abundant(3 10−7 bynumberrelativetoH-nuclei)andubiqui- emissioncharacteristicsofthesupernovaremnantN132Dinthe × Large Magellanic Cloud that they attribute to spectral features 1 tousintheISM(forarecentreviewseeTielens2008).Besides of PAHs with sizes of 4000 C-atoms. Bright 8 µm emission 9 largePAH molecules,thespectraalso revealevidenceforclus- ≃ has been observed by IRAC/Spitzer associated with the X-ray 0 tersofPAHs–containingsomehundredsofcarbonatoms–and : verysmallgrains( 30Å).Indeed,PAHsseemtorepresentthe emission from the stellar winds of the ionizing stars in the M v ≃ 17Hii region(Povichetal.2007).Likely,thisemissionisdue i extensionoftheinterstellardustsizedistributionintothemolec- X to PAHs – probably,in entrainedgasablated fromthe molecu- ulardomain(e.g.De´sertetal.1990;Draine&Li2001). lar clouds to the North and West of the stellar cluster. Finally, ar PAHmoleculesareanimportantcomponentoftheISM,for brightPAH emission hasbeen detectedassociated with the hot example,dominatingthephotoelectricheatingofneutralatomic gas of the galactic wind driven by the starburst in the nucleus gasand the ionizationbalance of molecularclouds. Small dust of the nearby irregular galaxy, M 82 (Engelbrachtetal. 2006; grainsand PAHs can also be importantagentsin cooling a hot Beiraõetal.2008;Gallianoetal.2008). gas,at temperaturesabove 106 K (e.g.Dwek1987), through their interactions with therm∼al electrons and ions. The energy Electronandioninteractionswithdustandtheimplications transferredinelectronandioncollisionswiththedustisradiated of those interactions for the dust evolution and emission have asinfraredphotons.Theevolutionofdustinsuchhotgas(T > already been discussed in the literature (e.g. Draine&Salpeter 106K),e.g.,withinsupernovaremnantsandgalacticoutflows,i∼s 1979; Dwek 1987; Jonesetal. 1994; Dweketal. 1996; criticalindeterminingthedustemissionfromtheseregionsand Jonesetal.1996).Inthisworkweextendthisearlierworktothe thereforethecoolingofthehotgas.ThedestructionofPAHsand caseforPAHs,usingourstudyofPAHevolutionduetoionand smalldustgrainsinahotgasmayalsobeanimportantprocess electroninteractionsinshockwavesintheISM(Micelottaetal. 2009, hereafter MJT). Here we consider the fate of PAHs in thehotgasbehindfastnon-radiativeshocksandina hotgasin Sendoffprintrequeststo:E.R.Micelotta general. 2 E.R.Micelottaetal.:PAHprocessinginahotgas The aim of this paper is to study the PAH stability against ϑ electronandioncollisions(H,HeandC)inathermalgaswith α temperatureT intherange103–108K. The paper is organized as follows: Sect. 2 and Sect. 3 de- scribethetreatmentofionandelectroninteractionswithPAHs, R Sect.4illustratestheapplicationtoPAHprocessinginahotgas andSect.5presentsourresultsonPAHdestructionandlifetime. Theastrophysicalimplicationsarediscussedin Sect. 6 andour d conclusionssummarizedinSect.7. 2. IoninteractionwithPAHs 2.1.Electronicinteraction The ion – PAH collision can be described in terms of two simultaneous processes which can be treated separately (Lindhardetal. 1963): nuclear stopping or elastic energy loss Fig.1. The coordinate system adopted to calculate the energy andelectronicstoppingorinelasticenergyloss. transferredto a PAH via electronic excitation by ion collisions Thenuclearstoppingconsistsofa binarycollisionbetween andbyimpactingelectrons.Themoleculeismodeledasa disk theincomingion(projectile)andasingleatominthetargetma- with radius R and thickness d. The trajectory of the incoming terial.Acertainamountofenergywillbetransferreddirectlyto particle is identified by the angle ϑ, while the angle α corre- the targetatom, which will be ejected if the energytransferred spondstothediagonalofthedisk. is sufficient to overcome the threshold for atom removal. The physicsofthenuclearinteractionforaPAHtargetwaspresented inthecompanionpaper(MJT).Asummaryofthetheoryispro- is assumedto be thesphericallysymmetricjelliumshell calcu- videdinSect.2.2andweherepresenttheresultsofourcalcula- latedbyPuska&Nieminen(1993),whichcanbeapproximated tion. bythefollowingexpression(Hadjaretal.2001): In this paper we focuse on the electronic stopping, which consists of the interaction between the projectile and the elec- n =0.15 exp[ (r 6.6)2/2.7] (3) tronsofthetargetPAH,withasubsequentenergytransfertothe 0 − − wholemolecule.Theresultingelectronicexcitationenergywill wherer(inatomicunits,a.u.1)isthedistancefromthefullerene betransferredtothemolecularvibrationsofthePAHthroughra- center.Theelectrondensitydecaysoutsidetheshellandtoward diationlessprocesses(eg.,interconversion& intramolecularvi- thecenterinsuchawaythatthemajorcontributioncomesfrom brationalredistribution).Thevibrationallyexcitedmoleculewill theregionwith4 10eV)overapathlength 8 Fit of 10 20 Å. Or to phrase it diff∼erently, at low energies a ev / Å) 67 Carbon: S(E) mPAuH≃chs)lairng−eorrdpearthtolentrgatnhsfhearsstuoffibceietrnatveenrseerdgy(tthoancaiussreelfervaagnmtefonr- er ( 5 tation. Then, since we know E0, we can calculate F(E0), and w F(E ) isthengivenby F(E ) l(ϑ).We alsocalculated E asa g po 4 func1tion of F(E). We can t0he−n determine E1 from F(E1) and, pin 3 finally,TelecfromEq.11. p o 2 St 1 4. PAHdestruction 0 0.01 0.1 1 10 4.1.Dissociationprobability Electron energy (keV) Ion or electronic collisions (or UV photon absorption) can 90 leavethemoleculeinternally(electronically)excitedwithanen- ergyT .Internalconversiontransfersthisenergytovibrational 80 F(E) = integral of dE/S(E) E modes,andthemoleculecanthenrelaxthroughdissociationor 70 IRemission.Thesetwo processesarein competitionwitheach 60 other. To quantifythe PAH destructiondue to ion and electron Å) 50 collisions we need to determine the probability of dissociation F(E) ( 40 rathIenrtthhaenmIiRcreomcaisnsoinoinc.aldescriptionofaPAH,theinternalen- 30 ergy,T ,is(approximately)relatedtotheeffectivetemperature E ofthesystem,T ,bythefollowingequation 20 eff 10 T (eV) 0.4 E (eV) T 2000 e 1 0.2 0 (12) 0 eff ≃ N ! − T (eV)! 0 50 100 150 200 C e where E isthebindingenergyofthefragment(Tielens2005). Electron energy (eV) 0 This effective temperature includes a correction for the finite Fig.2.Toppanel-ExperimentalmeasurementofdE/dxinsolid size of the heat bath in the PAH. The temperature T is de- eff carbonforelectronswithenergybetween10eVand2keV,from finedthroughtheunimoleculardissociationrate,k ,writtenin diss Joy (1995), overlaid with the fitting function S(E) (solid line). Arrheniusform Bottom panel- Integral F calculated numericallyas a function oftheenergyoftheincidentelectron,E. k =k (T ) exp[ E /kT ] (13) diss 0 eff 0 eff − where k = 8.617 10 5 eV/K is the Boltzmann’s constant (cf. − incoming electron is defined by its impact angle ϑ and by the × Tielens2005). geometryofthemolecule. Considerthecompetitionbetweenphotonemissionatarate BecausethethicknessofthePAHisnon-negligiblewithre- k (photons s 1) and dissociation at a rate of k (fragments IR − diss specttoitsradius,thestoppingpowerisnotconstantalongthe s 1). For simplicity, we will assume that all photons have the − electron path. To calculate the energy loss we thus follow the same energy, ∆ε. The probability that the PAH will fragment proceduredescribedbelow.WehavedE/dx= S(E),then betweenthenthand(n+1)thphotonemissionisgivenby − dE dx= = F(E) (10) n Z −Z S(E) ϕ = p (1 p) (14) n n+1 i − Thus, x x = [F(E ) F(E )] where x x = l(ϑ) is Yi=0 1 0 1 0 1 o − − − − the maximumpathlengththroughthe PAH. Frominspectionof The (un-normalized) probability per step p is given by p = i i Fig. 1, one can see that, if tan(ϑ) < tan(α), l(ϑ) = d/ cosϑ, k (E)/k (E)andE =(T i ∆ε),withT theinitialinternal | | | | diss i IR i i E E otherwise l(ϑ) = 2R/ sinϑ. E is the initial energy of the im- − × 0 energy,coincidentwiththeenergytransferredintothePAH.The | | pactingelectron,E istheelectronenergyafterhavingtravelled 1 totaldissociationprobabilityisthengivenby the distance l(ϑ), which needs to be calculated so we can then determinetheenergytransferredtothePAH nmax P(n )= ϕ (15) max n T (ϑ)= E E (11) elec 0− 1 Xn=0 The integral F, calculated numerically as a function of E, is If we ignore the dependence of k on E, the temperatures IR i showninthebottompanelofFig.2.Werecognizethatforlow (Eq.12)dropapproximatelybyT/T = (1 0.4∆ε/T ).The i i 1 E energies, F rises sharply, reflecting the small energy stopping probabilityratioisapproximately: − − powerinthisenergyrange(cf.,toppanelinFig.2).Forhigher energies,F(E)risesslowly(andlinearly)withincreasingenergy p E ∆ε i =exp 0 0.4 (16) overthe relevantenergyrange. We note that the initialrise de- p " kT ! ε # i 1 i 1 pendsstronglyonthe (uncertain)details ofthe stoppingpower − − at low energies.However,it is of no consequencein ourdeter- These equationsbecome very difficult to solve in closed form. mination of the amount of energy deposited since we are only However, let us just assume that p does not vary and is given i E.R.Micelottaetal.:PAHprocessinginahotgas 5 by p .Thenwehavethetotalun-normalizeddissociationprob- av ability k exp[ E /kT ] P(n )=(n +1)p = 0 − 0 av (17) max max av k /(n +1) IR max whereweadoptk =100photonss 1(Jochimsetal.1994),and IR − theaveragetemperatureischosenasthegeometricmean T = T T (18) av 0× nmax p whereT andT aretheeffectivetemperaturescorresponding 0 nmax toT (initialinternalenergyequaltotheenergytransferred)and E (T n ∆ε)(internalenergyaftertheemissionofn pho- E max max − × tons).FortheenergyoftheemittedIRphotonweadoptthevalue ∆ε=0.16eV,correspondingtoatypicalCCmode. If the p’s were truly constant, then n would be n = i max max (T E )/∆ε.However,theydodecrease.So,ratherwetakeit E 0 − tobewhentheprobabilityperstephasdroppedbyafactor10. Adirectcomparisonbetweenthefullevaluationandthissimple Fig.3.TheappearanceenergyasafunctionofthenumberofC- approximationyieldsnmax=10,20and40forNC=50,100and atomsinthePAH.Theredlineprovidesafittotheexperimental 200respectively.The quantitynmax scales with NC because for data using Eq. 13 for an assumed pre-exponential factor k0 = a constant temperature (eg., required to get the dissociation to 1.4 1016 and a (fitted) Arrhenius energy, E = 3.65 eV. The 0 occur),theinternalenergyhastoscalewithNC.Asaresult,the data×pointsaretheexperimentalresultsofJochimsetal.(1994). numberofphotonstobeemittedalsohastoscalewithNC. ThebluelineistheappearanceenergyforISMconditions(eg., The choice of the values to adopt for k0 and E0 is a deli- atarateof1s−1). cate matter. In the laboratory the dissociation of highly vibra- tionallyexcitedPAHsistypicallymeasuredontimescalesof1- 100µsbecauseeitherthemoleculesarecollisionallyde-excited apparent.Indeed,thiskineticshiftcanamounttotensofeVfor byambientgasorthemoleculeshaveleftthemeasurementzone relevantPAHs. of the apparatus. In contrast, in the ISM, the competing relax- The derived Arrhenius energy of 3.65 eV is small com- ation channelis throughIR emission and occurstypicallyon a paredtothebindingenergyofaC H groupinaPAH (4.2eV, timescaleof1s.Asisalwaysthecaseforreactionscharacterized 2 2 Ling&Lifshitz 1998). This is a well known problem in statis- byanArrheniuslaw,alongertimescaleimpliesthattheinternal tical unimolecular dissociation theories (cf. Tielens 2008). We excitationenergycan be lower. This kinetic shiftis well estab- emphasizethattheseresultsshowthatatypicalinterstellarPAH lished experimentally and can amount to many eV. Moreover, with a size of 50 C-atoms would have a dissociation probabil- only small PAHs (up to 24 C-atoms) have been measured in ity of 1/2afterabsorptionofanFUV photonof 12eV(cf. the laboratory and the derived rates have to be extrapolated to ∼ ∼ Fig.3).Hence,PAHswouldberapidlylostintheISMthrough muchlarger( 50C-atoms)PAHsthatareastrophysicallyrele- ∼ photolysis. It seems that the experiments on small PAHs can- vant.Inan astrophysicalcontext,theunimoleculardissociation not be readily extrapolated to larger, astrophysically relevant ofhighlyvibrationallyexcitedPAHs–pumpedbyFUVphotons PAHs. Possibly, this is because experimentally C H loss has –hasbeenstudiedexperimentallybyJochimsetal.(1994)and 2 2 only been observedfor verysmall catacondensedPAHs with a furtheranalyzedbyLePageetal.(2001).Here,wewillmodify very open carbon skeleton (e.g., naphthalene, anthracene, and theanalysisofTielens(2005)forH-lossbyUVpumpedPAHsto phenanthrene) which are likely much more prone to dissocia- determinetheparametersforcarbonloss.Thedissociationrate– tionthantheastrophysicallymorerelevantpericondensedPAHs. givenbyEq.13–isgovernedbytwofactors,thepre-exponential Indeed, the small pericondensed PAHs, pyrene and coronene factork andtheenergyE .Thepre-exponentialfactorisgiven 0 0 did not show any dissociation on the experimental timescales by (Jochimsetal.1994;Ling&Lifshitz1998). kT ∆S Turningtheproblemaround,wecandeterminetheArrhenius k = eff exp 1 + (19) 0 energy,E ,asafunctionofthedissociationprobabilitybyadopt- h " R # 0 ingan IRrelaxationrate of1 s 1 andaninternalexcitationen- − where ∆S is the entropy change which we set equal to 10 cal ergyequaltoatypicalFUVphotonenergy(12eV).Theresults mole 1 (Ling&Lifshitz 1998). We will ignore the weak tem- fora50C-atomPAHareshowninFig4.Ifweadoptalifetime, − peraturedependenceofk inthefollowingandadopt1.4 1016 τ , of 100millionyears,a PAH in thediffuseISM will have 0 PAH s 1. The parameter E can now be determinedfroma fit×to the typicallysurvivedsomeσ N τ = 2 106N UVphoton − 0 uv uv PAH C experimentsbyJochimsetal.(1994)onsmallPAHs.Theseex- absorptions(withσ =7 10 18cm2,N ×=108photonscm 2 uv − uv − perimentsmeasuredtheappearanceenergyE –theinternalen- s 1inaHabingfield).Henc×e,ifthelifetimeofthesmallestPAHs ap − ergy at which noticable dissociation of the PAH first occurred. intheISM(eg.,with N 50C-atom)issetbyphotodissocia- C The rate at which this happened was assumed to be 104 s 1. tionoftheC-skeleton,the≃probabilityfordissociationhastobe − Adopting this value, the appearance energy can be estimated 5 10 7 correspondingto an Arrheniusenergyof 4.6eV (Fig. − fromEq.13.TheresultsofouranalysisareshowninFig.3.The 4)×.We notethatinaPDRthephotonfluxishigher(G 105) 0 internalenergyrequiredtodissociateaPAHdependsstronglyon whilethelifetime (ofthePDR) issmaller (τ 3 1∼04 yr), PDR thePAHsize.Likewisethekineticshiftassociatedwiththerel- resultingin6 107UVphotonsabsorbedoverthe≃PDR×lifetime. × evanttimescaleatwhichtheexperimentwasperformedisquite SurvivalofPAHsinaPDRenvironmentwouldthereforerequire 6 E.R.Micelottaetal.:PAHprocessinginahotgas both target and projectiles are charged, and thus the collision crosssectioncouldbeenhancedordiminisheddependingonthe chargesign. The electron coulombianfactor is always equalto 1 (to within 1%) because electrons have low mass. For a fixed temperaturetheyreachhighervelocities,withrespecttotheions, andarethuslesssensitivetotheeffectsoftheCoulombianfield. ThequantityϑistheanglebetweentheverticalaxesofthePAH andthedirectionoftheprojectile.Thetermσ isthegeometrical g crosssectionseenbyanincidentparticlewithdirectiondefined by ϑ. The PAH is modelled as a thick disk with radius R and thicknessd.Thecrosssectionisthengivenby σ =πR2 cosϑ + 2Rd sinϑ (22) g which reduces to σ = πR2 for ϑ = 0 (face-on impact) and to g σ = 2Rd forϑ = π/2(edge-onimpact).Theterm P(v,ϑ)rep- g resentsthetotalprobabilityfordissociationuponelectroncolli- sionsandelectronicexcitation,foraparticlewithvelocityv PAH and incoming direction ϑ. It was calculated from Eq. 17 using Fig.4.Theprobabilityfordissociationofa50C-atomPAHex- the appropriatedvalue of the energytransferred:T for elec- citedby10eVasafunctionoftheArrheniusenergy,E . elec 0 trons(Eq.11)andT forelectronicexcitation(Eq.7) e Weareconsideringahotgasandthereforeweareinterested inthethermalcollisionrate,givenby asomewhatlargerE (oralternatively,onlyslightlylargerPAHs 0 couldsurviveinsuchanenvironment). We note that the binding energy of a C2H2 group to small Re,T = ∞Re(v) f(v,T)dv (23) Z PAHsisestimatedtobe4.2eVandisprobablysomewhatlarger v0,e for a 50 C-atom condensed PAH. Loss of pure carbon, on the wherev istheelectron/ionvelocitycorrespondingtotheelec- 0,e other hand, requires an energy of 7.5 eV, close to the bind- tronicdissociationenergyE .ThetemperatureT isthesamefor 0 ing energy of C to graphite. Loss of C2 from fullerenes has a both ions and electrons, but these latter will reach much larger measuredE0 of9.5 0.1eV(Tomitaetal.2001).Theselatter velocities. From Eq. 21 we then expect to find a significantly ± twounimoleculardissociationchannelsareforallpracticalpur- highercollisionratewithrespecttotheioncase. posesclosedunderinterstellarconditions.Finally,likely,H-loss will be the dominant destruction loss channel for large PAHs (E = 3.3 eV), leading to rapid loss of all H’s (LePageetal. 5. Results 0 2001; Tielens 2005). The resulting pure C-skeleton may then 5.1.PAHdestructioninahotgas isomerize to much more stable carbon clusters, in particular fullerenes,andthismaybethedominant‘loss’channelforinter- To describe the destructive effects on PAHs of collisions with stellarPAHs(cf.Tielens2008, andreferencestherein).Itisclear ionsi(i= H,He, C) andelectronsin a thermalgaswe haveto that there are many uncertainties in the chemical destruction evaluatetherateconstantforcarbonatomloss. routesofinterstellarPAHsandthatthesecanonlybeaddressed For all processes the rate constant J is defined by the ratio by dedicated experimental studies. For now, in our analysis of J = R /n , where R is the thermal collision rate appropriate T H T the unimoleculardissociationof PAHs –excitedbyelectronor fornuclearandelectronicexcitationandelectroncollisions(cf. ioncollisions–wewilladoptE0 = 4.6eVasastandardvalue. Eq. 8 and 23), and nH is the density of hydrogen nuclei. For WewillhoweveralsoexaminetheeffectsofadoptingE0 =3.65 electronicandelectroninteractionstheratemustbemultiplyied eV(eg., p=1/2)andE0 =5.6eV(eg., p=3 10−12). byafactorof2,totakeintoaccountthefactthateachcollision × leadstothelossoftwocarbonatoms. Theelectron,nuclearandelectronicrateconstantsforthree 4.2.Collisionrate PAH sizes (Nc = 50, 100 and 200 C-atom) are shown in Fig. Once the dissociation probability is determined, we can calcu- 5 as a function of the gas temperature. We assume for the nu- late the destructionratethroughelectronicexcitationfollowing clearthresholdenergyT thevalueof7.5eV(MJT),andforthe 0 electron or ion collision. Adopting the configuration shown in electronicdissociationenergythevalue4.58eV(Sect.4.1). Fig.1,thedestructionrateisgivenby Forthenuclearinteraction,thethresholdenergyT isinde- 0 pendentfromthePAHsize,sothethreecurvesstartatthesame 1 R =vχn F dΩσ (ϑ)P(v,ϑ) (20) temperature (not shown in the plot). The small separation be- e H C 2πZ g tweenthecurvesisduetothefactthatthePAH‘surfacearea’– andhencetherateconstant–scaleslinearlywith N , therefore with Ω = sinϑdϑdϕ, ϕ running from 0 to 2π and ϑ from 0 to C J ishigherforbiggerPAHs. π/2.Eq.20canbere-writtenas For nuclear (and electronic) interactions, the rate constants π/2 decrease from hydrogen to carbon because of the lower abun- R =vχn F σ (ϑ)P(v,ϑ) sinϑdϑ (21) danceoftheheavierprojectileswithrespecttohydrogen(H:He e H C g Zϑ=0 :C=1:0.1:10 4).Ontheotherhand,thenuclearcurvesshift − The term v is the velocity of the incident particle, χ is the toward lower temperatures from lighter to heavier projectiles. ion/electron relative abundance in the gas, and F is the This is the reflection of the fact that the critical energy of the C Coulombian correction factor, taking into account the fact that particle,requiredtotransferthethresholdenergyT0,decreases E.R.Micelottaetal.:PAHprocessinginahotgas 7 10−2 10−4 Nc = 50 Electronic ) Nc = 100 −1s 10−6 NNcc == 2 0500 Nuclear 3m 10−8 Nc = 100 Nc = 200 c Nc = 50 ( 10−10 Nc = 100 nt Nc = 200 a 10−12 st ELECTRONS on 10−14 C e 10−16 Electrons −−> PAH t a R 10−18 Hydrogen −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) 10−2 10−4 Nc = 50 Electronic ) Nc = 100 −1s 10−6 NNcc == 2 0500 Nuclear 3m 10−8 NNcc == 120000 c Nc = 50 ( 10−10 Nc = 100 nt Nc = 200 a 10−12 st ELECTRONS on 10−14 C e 10−16 Electrons −−> PAH t a R 10−18 Helium −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) 10−2 10−4 Nc = 50 Electronic ) Nc = 100 −1s 10−6 NNcc == 2 0500 Nuclear 3m 10−8 NNcc == 120000 c Nc = 50 ( 10−10 Nc = 100 nt Nc = 200 a 10−12 st ELECTRONS on 10−14 C e 10−16 Electrons −−> PAH t a R 10−18 Carbon −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) Fig.5.Nuclear(dashedlines),electronic(solidlines)andelectron(dashed-dottedlines)rateconstantforPAHcarbonatomlossdue to collisions with H, He, C andelectronsin a thermalgas. The rate constantsare calculated as a functionof the gastemperature forthreePAHsizesN =50,100,200C-atoms,assumingthenuclearthresholdenergyT =7.5eVandtheelectronicdissociation C 0 energyE =4.58eV. 0 8 E.R.Micelottaetal.:PAHprocessinginahotgas 10−2 10−4 Nc = 50 Ionic ) Nc = 100 −1 10−6 Nc = 200 s Nc = 50 ELECTRONS 3m 10−8 Nc = 100 Nc = 200 c ( 10−10 t n a 10−12 t s on 10−14 C e 10−16 Electrons −−> PAH t a R 10−18 Hydrogen −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) 10−2 10−4 Nc = 50 Ionic ) Nc = 100 −1 10−6 Nc = 200 s Nc = 50 ELECTRONS 3m 10−8 NNcc == 120000 c ( 10−10 t n a 10−12 t s on 10−14 C e 10−16 Electrons −−> PAH t a R 10−18 Helium −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) 10−2 10−4 Nc = 50 Ionic ) Nc = 100 −1 10−6 Nc = 200 s Nc = 50 ELECTRONS 3m 10−8 NNcc == 120000 c ( 10−10 t n a 10−12 t s on 10−14 C e 10−16 Electrons −−> PAH t a R 10−18 Carbon −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) Fig.6. Analytical fits to the calculated rate constants shown in Fig. 5. The ‘Ionic’ curve is the fit to the sum of the nuclear and electronicrateconstants,thusrepresentsthetotalcontributionfromioncollisionstoPAHdestruction. E.R.Micelottaetal.:PAHprocessinginahotgas 9 withincreasingmassoftheprojectileitself.Then,acarbonatom thefittingparametersarereportedinTable2.Toprovideanex- withatemperatureof 4 103Kishotenoughtotransfertheen- ampleoftheaccuracyofourfittingprocedure,Fig.7showsthe ∼ × ergyrequiredforatomremovalvianuclearinteraction,whereas comparisonbetweenthe calculatedrate constantandthecorre- for hydrogena temperatureof at least 104 K is necessary. The spondinganalyticalfit,forelectronsandheliumimpactingona almost-constantbehaviouraftertheinitialrisereflectsthelarge 50 C-atom PAH. The He fit is overthe sum of the nuclear and maximum observed in the nuclear cross section (cf. Fig. 2 in electronicrateconstants.Theaveragefittingdiscrepancyis 15 ∼ MJT). %andthefitsarethereforewellwithinanyuncertaintiesinthe ThedissociationprobabilityP(n )(Eq.17)dependsonthe method. max bindingenergyofthefragmentE ,onthePAHsize N andon Fig. 8 shows the comparison between the carbon loss rate 0 C theenergytransferred(throughT ),whichinturnsdependson constants for a very big PAH, N = 1000, and a 50 C-atom av C theinitialenergy(velocity)ofthe projectile.Forathermaldis- molecule.WeassumeT =7.5eVandE =4.6eV.Becauseof 0 0 tribution,thislatterwillbedeterminedbythegastemperatureT. the decrease of the dissociationprobabilitywhen the PAH size The electronic rate constant curves for the different PAH increases,asexpected,theelectronandelectronicrateconstants sizesarewellseparatedatthelowesttemperatures.Thisreflects arestronglysuppressed,andbothcurvesshifttowardhighertem- the fact that, for a fixed value of the transferred energy and of peratures.Indeed,forsuchabigPAH,amuchhigherinternalen- theelectronicdissociationenergyE ,thedissociationprobabil- ergyisrequiredtoreachtheinternaltemperaturewheredissocia- 0 ity decreases for increasing N because either more energy is tionsetsin.Ontheotherhand,thenuclearrateconstantincreases C requiredinthebondthathastobebrokenorbecausetheenergy linearlywiththePAHsize.Asaresult,fora1000carbonatoms is spread over more vibrational modes and hence the internal PAH, the nuclearinteractionisthe dominant(andefficient)de- excitationtemperatureislower.Ontheotherhand,themoreen- struction mechanism up to T 2 107 K. In conclusion, elec- ∼ × ergythatisdepositedintothePAH,thehigheristhedissociation trons are responsible for the destruction of small/medium size probability.Theenergytransferredviaelectronicexcitation(and PAH,whileforbigmoleculesthisroleistakenbyions. thenT )increaseswiththeenergyoftheprojectileuptoamax- AsmentionedattheendofSect.4.1,weexaminedtheeffects av imumvalue,correspondingtoanincidentenergyof 100keVfor ofadoptingdifferentvaluesfortheArrheniusenergy,E =3.65 0 H(andhigherformoremassiveparticles),anddecreasesbeyond and 5.6 eV, lower and higher, respectively, than our canonical thatforhigherenergies.Theenergycontentofathermalgasat value 4.6 eV. The results are shown in Fig. 9. The dissociation T =108 Kis 9keV,thus,inthetemperaturerangeconsidered probabilitydecreasesforincreasingE ,becausemoreenergyis 0 ∼ in this study,the energytransferredincreaseswith temperature requiredinthebondthathastobebroken.Hence,asexpected, (energy)andhencethedissociationprobabilityincreasesaswell. both the electron and electronic rate constants decrease in ab- Thisisthebasisforthemonotonicriseoftheelectronicratecon- solutevalueandshifttowardhighesttemperatures.Inparticular stant.Aftertheinitialseparation,thethreecurvesconverge,be- the electronicthermalshiftis verypronounced,indicatinghow causetheriseinthetransferredenergycompensatestheeffectof sensitivethisprocessiswithrespecttotheassumedE .Avaria- 0 increasingN . tionintheadoptedelectronicexcitationenergytranslatesintoa C AsdiscussedinSect.3,theenergytransferredbyimpacting significantvariationoftherateconstant,reemphasizingtheim- electronsrisessharplyforenergiesinexcessof10eV,peaksat portanceofexperimentalstudiesofthiscriticalenergy. ∼ 100eVanddecreasesmoreslowlydownto10keV.Thisresults inadissociationprobabilityshapedasastepfunction:for10eV < v < 4 keV, P(n ) jumpsfromvaluesclose to zero up to 1. 5.2.PAHlifetime max ∼Thes∼elimitingenergiesapplytoa50C-atomPAH;forNC=200 Underthe effectof electronand ion collisionsin a hotgas, the thewidthofthestepissmaller(100eV PAH t a R 10−18 Helium −−> PAH 10−20 103 104 105 106 107 108 Temperature (K) Fig.7.Calculatedrateconstantsforelectronsandheliumimpactingona50C-atomPAH,overlaidarethecorrespondinganalytical fits.TheHefitisforthesumofthenuclearandelectronicrateconstants.Theaveragediscrepancyis 15%. ∼ Table2.AnalyticalfitparametersforthePAHcarbonatomlossrateconstant,calculatedforelectronandioncollisions. Fittingfunction f(T)=a+bT +cT2+dT3+eT4+ fT5 a b c d e f Electrons 2136.83 1632.17 -499.822 76.4347 -5.82964 0.177174 H -1896.69 1480.8 -462.733 71.8957 -5.54719 0.169996 N =50 He -971.448 770.259 -245.561 38.8995 -3.05787 0.0954303 C C -704.392 551.313 -175.063 27.6506 -2.16871 0.0675643 Electrons -2255.38 1681.45 -503.451 75.4339 -5.64956 0.168959 H -1645.64 1257.06 -384.309 58.4103 -4.41007 0.132356 N =100 He -945.901 747.921 -237.984 37.6808 -2.96613 0.0928852 C C -711.244 558.48 -177.983 28.2547 -2.23145 0.0701374 Electrons -2234.37 1597.71 -459.647 66.332 -4.79841 0.139019 H -1473.64 1109.01 -334.292 50.1417 -3.74133 0.111164 N =200 He -963.188 765.639 -245.054 39.0745 -3.10123 0.0980047 C C -738.791 584.928 -187.884 30.0819 -2.39748 0.0760639 molecule.Thisoccursafterthetimeτ (Eq.27)whichweadopt InM82,PAHsarecompletelydestroyedbyelectrons,even 0 asthePAH lifetimeagainstelectronandionbombardmentina for the largerPAH, before electronic and nuclear contributions gaswithgivendensityandtemperature. starttoberelevant.Theelectronandelectronicfractionallosses Table 3 summarizesrelevantdata andPAH lifetime, τ , for decrease with PAH size, thus bigger molecules can survive 0 fourobjectscharacterizedbywarm-to-hotgas,X-rayemission, longer,whilethenuclearlossisindependentofNC.Thedestruc- and(bright)IRemission features.The lifetime hasbeen calcu- tiontimescale isveryshort:afteronethousandyearsthe PAHs latedforPAHswithN =200.τ (ref)hasbeenevaluatedadopt- shouldhavecompletelydisappeared. C 0 ingourreferencevaluesfortheinteractionparameters,E =4.6 In Orion the situation is reversed. At the temperature con- 0 eVandT =7.5eV,τ (min)correspondstotheminimumvalues sideredforthisobject,electronsandelectronicexcitationdonot 0 0 E = 3.65 eV and T = 4.6 eV, and τ (max) to the maximum contributetoPAHerosion(cf.Fig.5).Thedamageiscausedby 0 0 0 valuesE =5.6eVandT =15eV.τ isthelifetimeofthe nuclearinteractionduetoHecollisions,withamarginalcontri- 0 0 object object. butionfromcarbonbecauseoflowabundance,andthetimescale Clearly, PAHs or relatedlargerspeciescan survivein these ismuchlarger:onlyafter10millionyearsthePAHdestruction environments.Fig. 10 showsthe fractionalC-atom loss, due to becomesrelevant.Ofcourse,wehavenotevaluatedthedestruc- electronandion(H+He+C)collisions,fortwowidelydiffer- tion of PAHs by H-ionizing photons in the Orion Hii region, entobjects:the OrionNebula (M 42)andthe M 82 galaxy(cf. whichisexpectedtobeveryimportant. Table 3). The famousOrion Nebula is an Hii region with high The young ( 2500 yr) supernova remnant, N132D, in density(n =104cm 3)andlowtemperature(T =7000K)gas, the Large Magel≃lanic Clouds has been studied in detail at H − whileM82isastarburstgalaxy,whichshowsoutsidethegalac- IR, optical, UV, and X-ray wavelengths (Morseetal. 1995; tic plane, a spectacular bipolar outflow of hot and tenuous gas Tappeetal.2006).ASpitzer/IRSspectrumoftheSouthernrim (n =0.013cm 3,T =5.8 106K). shows evidence for the 15-20 µm plateau – often attributed H − ×

Polycyclic aromatic hydrocarbon processing in a hot gas

Similar Polycyclic aromatic hydrocarbon processing in a hot gas