1991ApJ. . .377. .541C © 1991.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. The AstrophysicalJournal,377:541-552,1991August20 liams 1981;Léger&Puget1984;Aflamándola,Tielens, infrared bandsandthediffuseinterstellar(Duley&Wil- been suggestedascarriersoftheinterstellar“unidentified” Tielens, &Barker1989;Puget &Léger1989).Theradiation contribute totheaccelerationofstellarwind,commonly ments (Keller1987;Frenklach&Feigelson1989). Nevertheless, thereexistonlytwostudiesonPAHproduction d’Hendecourt 1985).ItislikelythatPAHsarekeyinterme- pressure actingonPAHswas then computed. force actingonPAHsrequiresknowledgeoftheiroptical envelope (Lucy1976).Estimationoftheradiationpressure resemble theonesoccurringinsootingflames(Tielens1990). diates inthecarbonstardustformationprocesses,which Barker 1985;vanderZwet&AflamándolaLéger (Mathis &Whiffen1989)thatPAHshavethesameoptical ecules, itisusuallyassumedininterstellargrainmodels constants orrefractiveindicesofaromatichydrocarbonmol- properties. Intheabsenceofexperimentaldataondielectric ascribed toradiationpressureactingonthedustpresentin the and itsrelationtoC-sootformationincircumstellarenviron- carbon atomspermolecule) and large(~400carbonatoms) were computedbasedonpolarizabilityestimatesforseveral resulting radiationpressureareestimated.Refractiveindices properties asamorphouscarbon(AC). radiation pressurecrosssection wascalculatedforsmall(<25 thought tobepresentintheinterstellar medium(Aflamándola, small PAHs.FollowingGilman(1974),thePlanckmeanof the PAH molecules,sincethese twosizegroupsofPAHsare Polycyclic aromatichydrocarbon(PAH)moleculeshave Our resultsshowthatsmall andlargePAHmolecules If PAHsareformedintheoutflowofcarbonstars,theymay In thepresentwork,PAHopticalpropertiesand cene, andcoronene)aredeterminedfromtheirmeasuredlaboratoryabsorptionspectra.ThePlanckmeanof present incarbon-richstellaroutflows,theradiationpressureforcesactingonthemarecalculatedandcom- the radiationpressurecrosssectioniscomputedforeachmoleculeandamorphouscarbon(AC)grains, properties fromACgrains.SmallPAHsmayexperiencean“inversegreenhouse”effectintheinnerpartof pared withtheradiationforcesonACparticles.TheresultsshowthatPAHspossessverydifferentoptical and semiempiricallyestimatedforlargePAHmoleculesupto400carbonatoms.AssumingthatPAHsare dynamics oftheoutflow. always muchlessthantheforceatworkonACgrains,andPAHmoleculesdonotaffectsignificantly the envelope,astheydecouplefromgasclosetophotosphere.TheradiationpressureforceonPAHsis Subject headings:interstellar:molecules—stars:circumstellarshells The opticalconstantsoffourpolycyclicaromatichydrocarbon(PAH)molecules(benzene,pyrene,penta- POLYCYCLIC AROMATICHYDROCARBONOPTICALPROPERTIESANDCONTRIBUTION © American Astronomical Society • Provided by the NASA Astrophysics Data System Department ofAtmospheric,Oceanic,andSpaceSciences,PhysicsResearchLaboratory,TheUniversityMichigan, 1. INTRODUCTION Space ScienceDivision,NASA-AmesResearchCenter,Mailstop245-3,MoffettField,CA94035 TO THEACCELERATIONOFSTELLAROUTFLOWS Isabelle CherchneffandJohnR.Barker Received 1990November9;accepted1991February22 Alexander G.M.Tielens Ann Arbor,MI48109-2143 ABSTRACT AND 541 from theabsorptionspectra,anddielectricconstants and putations. Foreachmolecule,thepolarizabilitywascalculated possess opticalpropertiesverydifferentfromthoseofamor- refractive indexeswerethenestimated. and isdefinedby very smallparticlesofthesamechemicalcomposition.Inaddi- envelope. Finally,acomparisonoftheradiativeforcesacting tion, an“inversegreenhouseeffect”mayoccur,allowingsmall that opticalpropertiesofthebulkmaterialarenotvalidfor phous carbon,inagreementwithHuffman(1989),whoshows molecules, ifpresentincircumstellaroutflows,areunlikelyto growth toformlargeraromaticsgreaterdistancesinthe play animportantroleinthedynamicsofenvelope. and discussedin§4. tional methodisdescribedin§3,andtheresultsarepresented on ACgrainsandPAHsleadstotheconclusionthatPAH PAHs toexistclosethephotosphere,andshiftingtheir (solid orgas)maybedescribed asacollectionofclassical where Pisthepolarization vector, Ntheconcentrationof by itsthreemaincomponents a,and.Thematerial & Wolf1975).Ingeneral,ais adiagonaltensorcharacterized dipoles perunitvolume,and E theeffectiveelectricfield(Born dielectric responseisthesame, andthepolarizabilityis harmonic oscillators,orasaquantum system.Inbothcases,its l523 The polarizabilityaisanintrinsicpropertyofthematerial, PAH opticalpropertieswerebaseduponpolarizabilitycom- The theoreticalframeworkisoutlinedin§2,thecomputa- 2.1. PolarizabilityandRefractiveIndex 2. THEORETICALBACKGROUND P =NolE,(1) 1991ApJ. . .377. .541C 2 2 21/ fj andadampingcoefficientyj.The(Djarethefrequencies 542 where aistheparticle(molecule)radius. where eistheelectroncharge,mmass,andco elliptical disksthanbyspheres.Foranellipsoid,thepolariza- and imaginary partawith=+ia,where frequency. Thesumisoveralltheatomicormolecularexcited bility isanisotropic,andtheconnectionformulabetweena and characteristic ofthetransitions.Thepolarizabilityisacomplex states eachofwhichischaracterizedbyanoscillatorstrength quantity andmaybeseparatedintoarealpartan expressed as(Axe1973) the refractiveindexmis(vandeHulst1981) e =m,whereistheindexofrefraction,andn+ik, line, andisrelatedtothedampingcoefficienty,-byTj=yJin. a =a),therefractiveindexmisrelatedtobyLorentz- where nandkaretherealimaginarypartsoffh.The The totalpolarizabilityisdefinedasthemodulus|a|of Here v=a>/2n,v,cojín,Tjisthenaturalwidthfor7th Lorenz formula(Born&Wolf1975), part eandimaginary€,aredefinedaswellforthedielec- (5) isthenrewrittenforasphericalvolumeas tric constant,andareequalton—kInk,respectively. (a +a?). the complexpolarizability(Born&Wolf1975),with|a|= one dipolepervolumeoftheparticle,andNisthusequalto For aparticle(ormolecule),itmaybeassumedthatthereis Furthermore, ifthemeanpolarizabilityisisotropic(R*is ext (Gilman 1974) mean oftheradiationpressureefficiency,whichisdefinedas where B(T*)isthePlanckfunction. prext where y=hv/kT*(histhePlanckconstantandk the where hydrocarbons: benzene(CH),pyrenepentacene data fortheUV,visible,andIRdomainsarenecessary. a =v/cexpressedincm)requirestheknowledgeoftheir is thecomplexpolarizability,and/(£,L)expressedas where eisthedielectricconstantofmedium(solvent),a}(v) solvent effectwasextractedusingthefollowingequation possess p-bands(inthenear-UVforsmallerPAHs)thatmay and compactPAHs(suchasbenzene,pyrene,orcoronene).On The solventusedinpyreneandcoronenespectrawascyclo- solution spectrawerefromKarcheretal.(1985,1988),andthe Bolo vinos(1978).Forpyrene,pentacene,andcoronene,the shift totheredasmolecularsizeincreases,leading benzene (e=1.5). hexane, withe=1.42,whereasforpentacenethesolventwas ments foreachmolecule,but theIRlinestrengthsareknown and coronenehavebeenestimated fromthefrequencyassign- for otherPAHs.Thisfar-UVfeatureisduetothe<7<7*tran- only forbenzene.Thevibrational assignmentandtheIRline hydrogenated amorphouscarbon(HAC)(Robertson1986). cene, andcoronene,theoscillatorstrengthofband was benzene strengthwasthenrescaledto3e.Forpyrene,penta- as deducedfromexperimentalspectraofgraphite,AC,and sition, andcorrespondstothreeeffectiveelectronsperCatom, the benzenespectrum(£antosetal.1978)wasauoconsidered scaled tothenumberofcarbonatomsineachmolecule. Since thetentativeoscillatorstrengthforthisbandgiven by 214 insignificant errorsinthepolarizability calculations(<2%of line width,andpeakabsorptioncoefficient),whichwereused in spectra havebeensimulatedbyasumofGaussianlineprofiles. Pantos etal.isequivalenttoonlytwoeffectiveelectrons, the 610 not shown).Theminorimperfectionsinthesimulationslead to pyrene arecomparedinFigure1(thefar-UVcontribution is Each profilewasspecifiedbythreeparameters(peakfrequency, y m the a-values). the computationofpolarizabilitiesandarepresentedinTable m m 1. Theexperimentalandsimulatedabsorptionspectra for -1 The computationofthepolarizabilityforpolycyclicaro- The calculationhasbeencarriedoutforfouraromatic The verystrongfar-UVbandat~140000cmpresentin The IRabsorptionfeaturesfor benzene,pyrene,pentacene, For computationalpurposes,thePAHUVabsorption © American Astronomical Society • Provided by the NASA Astrophysics Data System 3. COMPUTATIONPROCEDURE Wv) ocImLjjap),(14) € m j 3.1. Data PAH PROPERTIESANDEFFECTONSTELLAROUTFLOWS 1 -1 -1 pyrene, theIRassignmentwasfromBreeetal.(1971),and (1979), andthevibrationalassignmentforcoronenewasfrom Cyvin etal.(1982). Cyvin etal.(1979).PentacenedataweretakenfromOhno strengths forbenzenewerefromBishop&Cheung(1982).For frequency range,takingallowedtransitionsandlinedegener- modes ineachmolecule(Léger&d’Hendecourt1987).The have beenassumedequaltothebenzenestrengthsinsame simulated. plane bendingmodeshavebeenassumedequaltothecorre- coronene, whicharenotpresentinbenzene,correspondto far-IR vibrationalbandspresentinpyrene,pentacene,and following, itshouldbeborneinmindthattheIR-extinction acy intoaccount,andscalingtothenumberofC-HC-C envelope. FortheIRandUVdomains,naturalwidthswere sponding ratioforPAHssuspendedinKBrpellets.Inthe ton. Thestrengthratioofthefar-IRbandsandC-Hout-of- out-of-plane bendingmotionsofthemolecularcarbonskele- They werearbitrarilyspaced, foreachGaussianbandprofile, resented. Instead,“surrogate” transitionswereconsidered. tional limitations,noteveryrovibronic transitioncouldberep- levels ofthemolecule.Thenaturallinewidthsaremuch The assignmentsandassumedlinestrengthsaresummarized able gas-phaseIRabsorptionintensitiesforthesemolecules. properties ofPAHsareuncertain,owingtothelackavail- at 1cm"intervalsintheIRrange, andat10cmintervalsin strengths (Bransden&Joachain 1983).Becauseofcomputa- smaller thantheassumedwidthofabsorption-band hand, therefractiveindexresultsinIRdomaindepend on pressure forcearenotsensitivetothesechoices.Ontheother al envelopes;Herzberg1968).ThePlanckmeanoftheradi- above, respectively(thesevaluesaretypicalofIRlinerotation- obtained fromtheEinsteincoefficients derivedfromtheline allowed transitionsbetweenthevibrationalandrotational series ofverynarrowlinescorrespondingtothevarious on equations(3)and(4).Anabsorptionbandconsistsof a ation pressurecrosssectionandtheresultingradiation cm forlinepositionslessthan3000andor in Table2.TheIRbandwidthswereassumedtobe10and30 the IRbandwidthconsidered. The IRlinestrengthsofgas-phasePAHsotherthanbenzene Fig. 1.—Absorptionspectraofpyreneincyclohexane:(a)experimental;(b) The methodusedtoestimatePAHpolarizabilitiesisbased Wavelength (Â) 3.2. Method 543 1991ApJ. . .377. .541C each narrowline,andthecontributionssummedovertotal grated bandstrength.Thepolarizabilitywasthenestimated for of theGaussianenvelopeatsamespectralposition,and the tion ofeachlinewasproportionaltotheabsorptioncoefficient the UVregion.Theabsorptioncoefficientatcentralposi- domain ofabsorption. sum oftheintensitiessurrogatelinesequaledinte- 544 example, apolarizabilityiscalculated foreachbandenvelope by Gilman(1974).Histreatment doesnottakeintoaccountthe vibrational structureoftheabsorption bands.Forolivine,for This methodisslightlydifferent fromtheprocedurefollowed 49200 181762.0 27620 2672.4 26880 2521.0 28010 2742.5 55880 103079.6 55430 2015518.6 38600 3434.2 41490 378446.4 29810 222364.4 28450 2833.9 44640 697156.0 43100 557380.0 42020 441510.0 36630 402350.4 33900 58030.8 32680 42784.1 38020.... 506159.1 31250 390210.2 30120 272140.1 39530 46866.6 21090 15610.5 25010 1887.0 24270 2063.5 22470 1778.4 30430 27817.5 29560 175420.4 29000 50484.1 27600 2291.1 34390 4139182.2 33010 382777.8 17330 10521.0 30100 272122.6 18760 12314.0 31550 149137.4 30940 191168.2 32030 308161.8 48500 823519.3 46620 761401.5 43820 57650.5 35880 386144.4 34460 174483.5 33120 2741822.0 39650 47128.7 2 Line ParametersforGas-PhasePAHSimulated A1 Position Half-WidthKx10 © American Astronomical Society • Provided by the NASA Astrophysics Data System abs (cm "^~)(litersmol“cm Absorption SpectraintheUV Pentacene (CH.) Coronene (CH) 214 241 Pyrene (CH) Benzene (CH) 160 6 TABLE 1 CHERCHNEFF, BARKER,&TIELENS for pyrene,estimatedwiththe threemethods.Theagreement function, andthesummationthenincludesallabsorption agreement isverygood.The firstmethodwaschosenforthe at moderatetemperatures(visible domain),butthegeneral results differslightlyathightemperatures (far-UVregion),and given bytheabsorptionspectraofmolecule].Figure 2 method assumedthattherewasnoscattering,andß = explicitly considered.Atestwascarriedouttocompare the between thefirstandthird methodsisexcellent.Gilman’s shows thePlanckmeanofradiationpressurecrosssection both methods,andtheresultsweretestedagainstathird bands, butthevibrationaltransitionswithineachbandare not simple treatment,whichgavealowerlimittoß(<7).Thethird two methods:a(v)andQ(T)werecomputedforpyreneusing Gabs =^IbsAgeo[wherek'(G)wastheabsorptioncrosssection pr pr abs a d c b Bishop&Cheung1982. Cyvinetal.1982. Ohno1979. Breeetal.1971;Cyvin1979. 3080 1530.5 3050 15250.4 1490 56.5 1040 54.4 1610 534.9 1420 587.3 1180 536.7 1000 522.0 3040 15122.0 3060 15490.8 1320 552.4 1310 596.8 1150 541.2 1610 526.2 1460 526.2 1140 5176.0 1580 572.1 1450 596.1 440 548.0 710 5147.0 650 5147.0 670 588.2 744 5294.0 820 5147.0 945 552.0 610 5205.8 560 5205.8 300 593.1 840 5205.8 760 5616.0 850 5176.4 780 5352.8 550 5176.4 380 526.0 5 -1 PAH IRVibrationalAssignmentsand Position Half-WidthStrengthx10 (cm) mol Absorption-Line Parameters c d Pentacene (CH) b Coronene (CH) 214 a 241 Pyrene (CH) 160 Benzene (CH) 6 TABLE 2 Vol. 377 1991ApJ. . .377. .541C 3 No. 2,1991 ing totheestimatedfar-UVbandenvelopewasincluded.The visible, andIRdomains,apolarizabilitytermcorrespond- the vibronicabsorptionspectraofPAHmolecules. present calculations,becauseofitsmorecompletetreatment computed usingequation(7),andtherealcomplex real andimaginarypartsofthedielectricconstantwerethen pyrene, estimatedfromthreedifferentmethods(seetext). volumes ofbenzene(127Â),pentacene(383andcoronene refractive indexeswerecalculatedusingequation(8).The 2 The polarizabilitiesaanda¿werecomputedintheUV, Fig. 2.—Planckmeanoftheradiationpressurecrosssection(incm)for r © American Astronomical Society • Provided by the NASA Astrophysics Data System 4. RESULTSANDDISCUSSION n 1.5 2.5 0.5 4.1. IndexofRefraction ? 2 30000 3500040000450005000055000600006500024 6 81012141618 0 3 2 1 PAH PROPERTIESANDEFFECTONSTELLAROUTFLOWS 1 Fig. 3.—Realpart(n)andcomplex {k)oftherefractiveindexforbenzene Wavenumber (cm)Wavelength (urn) 3 3 (Rérat &Rérat1981;Campbell,MonteathRobertson, (358 Â)moleculeswerederivedfromcrystallographicdata Trotter 1962;Donnay&Ondik1972).Forpyrene(264Â)the volume wasdeducedfromthesolidstatedensity(Weast1986). length. Thiscontrastingbehaviorillustratesthedifficultyof featureless overlargespectraldomains,leadingtoasmooth grains. Indeed,absorptionbandsofsolidmaterialsareoften in Figure7.ForAC,thepolarizabilitieswerecomputedfrom were calculatedusingequation(12).Theresultsaredisplayed extending theopticalpropertiesofbulkamorphouscarbonto variation oftherealandcomplexrefractiveindexeswithwave- tured absorptionspectraoffreemoleculescomparedwithsolid far-UV contributiondescribedin§3.1waschoseninsteadof benzene, pyrene,pentacene,coronene,andamorphouscarbon which are1.76and1.88,respectively.Ontheotherhand, gave betteragreementwithexperimentalrefractiveindexesin index valuesforthefourmoleculesarelistedinTable3.The the dielectricconstantdatagivenbyMathis&Whiffen(1989), small PAHs. values arelow,andmayreflecttheinadequacyofflat-disk values forbenzenearesomewhatoverestimated.Pentacene the visibleforpyreneandcoronene(Davis&Gottlieb1963), taking theresultsderivedbyPantosetal.(1978),becauseit shown inFigures3,4,5,and6,respectively,therefractive Planck meanoftheradiationpressurecrosssectionsfor an oblatespheroid. approximation forthemolecule,whichmorecloselyresembles The detailedshapesofthecurvesreflecthighlystruc- The crosssectionswereestimatedfromequation(9),andthe The resultsforbenzene,pyrene,pentacene,andcoroneneare 0 5 5 1 2 4681012 14 1618 4.2. PlanckMeanoftheRadiationPressureEfficiency _r 1 i -lí. i.I.t,A■/ A,I Benzene UV Wavelength (^m) 545 1991ApJ. . .377. .541C n © American Astronomical Society • Provided by the NASA Astrophysics Data System 1 Fig. 5.—Realpart(n)andcomplex (k)oftherefractiveindexforpentacene 1 -1 Fig. 4.—Realpart(n)andcomplex(k)fortherefractiveindexpyrene Wavenumber (cm*) Wavenumber (cnrr) Wavenumber (cm) 1991ApJ. . .377. .541C (this correspondstoa~420carbonatomparticle).Theradi- using equation(6).Theparticleradiuswasassumedtobe10Â ation pressurecrosssections,estimatedintheRayleighlimit, constant values,althoughbothledtoK(T)curves(notshown The twodatasetsshowedsomedifferencesinthedielectric phous carbon(HAC)wasalsoconsidered.Theopticaldata, not beappropriate(Huffman1989),andthepresentresultsfor applied toparticleswithradiussmallerthan160Â.Forsuch K(T) maybeaffectedbythisproperty.Hydrogenatedamor- small grains,thedielectricconstantsofbulkmaterialmay in Fig.7)consistentwiththeACresults(theHACcurvewas log K(T)=-13.24+m, T-exp[-2.7(log2.33)]. obtained frommeasurementsonHACfilms(a-C:H),were slightly lowerthantheACcurve,atlowtemperatures). McKenzie, McPhedran,&Savvides(1983)andSmith(1984). contributions, onefromtheIRdomain(lowtemperature) and empirically, basedontheresultsforsmallPAHs.Each functions : the otherfromUVregion(hightemperature).TheIR and UV partsofthecurvewerefittedwithfollowingempirical PAHs largerthancoronenehavebeenestimatedsemi- PAH curveinFigure7wasconsideredtobethesumof two The Planckmeanoftheradiationpressurecrosssectionsfor In theUV: In theIR: 2B log K(T)=—8.59[(logT- m)/llA7y°- .(16) 2 © American Astronomical Society • Provided by the NASA Astrophysics Data System 25000 30000350004000045000500005500027121722273237 PAH PROPERTIESANDEFFECTONSTELLAROUTFLOWS Fig. 6.—Realpart(n)andcomplex(k)oftherefractiveindexforcoronene 1 -1 Wavenumber (cm*)Wavelength(^im) Wavelength (cm) (15) where Nisthenumberofcarbonatomspermolecule.Since The parametersmanddependuponthemolecularsize, ecules madeupof40,96,294,and420carbonatoms.The tive shapeforlargemolecules. absorption spectraforlargePAHsarenotavailable,thiscrude and wereexpressedempiricallyasfollows: approach givesestimatesoftheK(T)curvesandtheirrespec- (7) 294Catoms,(8)420(9)amorphous carbon. benzene, (2)coronene,(3)pyrene,(4) pentacene, (5)40Catoms,(6)96 c 12 2 2.5 0.5 1.5 2.5 0.5 This methodwasappliedforfour“fictitious”PAHmol- 1.5 Fig. 7.—Planckmeanoftheradiation pressurecrosssection(incm):(1) 2 3 0 1 2 0 1 2 7121722273237 01396 m =-2.7Nc,3.2SN¿-(17) 12 Wavelength (^m) Temperature (K) 547 1991ApJ. . .377. .541C 2 (294) carbonatommoleculehasaK-valueequalto3(6),and (coronene, amemberofthisseries,correspondstoK=1).A96 growth lawN=6{K+l),whereKisageneratingindex dust grains,accordingtothePAHhypothesis(Allamandola et series ofhexagonallysymmetricmolecules(Stein&Brown third “fictitious”moleculesbelongtothefirsthomologous explains thepronouncedminimumofK(T)around2000-4000 follows: smallPAHs,asalreadymentioned,donotpossess the computation,andallowsdirectcomparisoninFigure7. al. 1989;Puget&Léger1989).The420Catommolecule has sentative oflargePAHsthatcouldbethebuildingblocks of an approximateradiusof10(18)Â.Thesemoleculesarerepre- tion featuresinthenearUVandvisible.Thiseffect absorption featuresinthevisibleregionofspectrum. This the samenumberofcarbonatomsasACgrainchosen in pressure crosssectionofthe solid phasematerialisquitedis- curves inFigure7showsthat thePlanckmeanofradiation produces ashiftoftheminimumtowardlowertemperatures, K. However,thelargermolecule,strongerabsorp- similar tothatoffreemolecules. Thisdifferenceisdueinpart and tendsto“fillin”theminimum. (Allamandola etal.1989).Thismoleculeisintermediateinsize 1987), whichstartswithbenzene,andisdescribedbythe formed inacarboncircumstellarenvironment,accordingto to coroneneandcircumcoronene(54Catoms).Thesecond similar insizetothatdeducedfromtheinterstellarIRbands the chemicalmodelofFrenklach&Feigelson(1989),andis smallest moleculecorrespondstotheaverage-sizedPAH c 548 The shapeoftheK(T)curvesforPAHsmaybeexplained as Comparison betweentheAC andthe420CatomPAH 900 .. 670 .. 3070. 680 .. 38600. 38000. 3200. 3110. 3100. 3090. 3080. 3060. 3050. 2100. 660 .. 38400. 36000. 570 .. 1040. 1030. 1500. 1490. 1480. 1200. 1050. (cm *) Real andComplexPartsoftheRefractiveIndexfor © American Astronomical Society • Provided by the NASA Astrophysics Data System Benzene, Pyrene,Pentacene,andCoroneneat 0.542 2.432 2.5 1.759 1.598 1.576 1.566 1.572 1.604 1.636 1.641 1.593 1.552 1.589 1.622 1.575 1.763 1.754 1.724 1.613 1.602 1.562 1.6 1.634 1.698 Selected Wavenumbers 0.021 0.013 0 0 0.004 0.019 0.049 0.067 0.048 0.019 0 0.005 0.086 0.005 0 0.079 0.001 0.004 0 0.005 0.089 0.005 0.115 0 1.88 A. Benzene TABLE 3 48100. 49800. 49300. 49100. 48800. 48600. 48400. 47000. 42000. 62000. 60000. 55500. 55000. 54500. 53900. 53000. 51100. 39400. 58000. 57000. 56500. 56000. 50200. 50000. 39000. 38800. 38700. -1 (cm) a CHERCHNEFF, BARKER,&TIELENS 0.705 0.365 0.215 0.256 2.026 2.313 2.509 2.617 2.654 2.567 2.159 2.059 2.059 2.064 2.068 2.070 2.038 2.048 2.040 2.044 2.050 1.0545 1.813 1.756 1.747 1.751 1.755 n 0 0.163 0.197 0.050 0.171 0.865 0.481 0.198 0.223 0.222 0.213 0.202 0.189 0.167 0.077 0 0.001 0.013 0.148 0.182 0.210 0.021 0.022 1.691 1.913 1.439 1.172 stellar radii(Draine1981;McCabe 1982).Thesameeffect star envelopes,wherethegrains decouplefromthegasatafew particles toexperiencethe“inverse greenhouseeffect”inC carbide (SiC)presentedinFigure 3ofGilman(1974).Thelack of strongabsorptioninthe visible andnear-IRcausesSiC found intheinnerpartofCstarenvelopes(1000-4000K). to thelargeopacityofamorphouscarboninUV,visible, and IRdomains,isgreatestinthetemperaturerange Figure 7maybecomparedtotheQ(T)curveforsilicon 430 .. 450 .. 440 .. 29700. 29100. 28500. 990 .. 900 .. 660 .. 650 .. 640 .. 340 .. 27200. 27000. 26800. 24800. 830 .. 710 .. 700 .. 820 .. 810 .. 760 .. 750 .. 740 .. 730 .. 720 .. 550 .. 2400. 1000. 3070. 3060. 3050. 3040. 1180. 1170. 1100. 1010. 3100. 3030. 3010. 1190. 1420. 1410. 1300. 1610. 1600. 1500. 1430. 1620. -1 (cm) a 4.3.1. “InverseGreenhouseEffect” 4.3. AstrophysicalImplications 2.644 0.779 0.255 2.117 2.050 2.038 2.145 2.136 2.002 2.506 3.309 1.860 1.918 1.799 1.498 1.789 1.775 1.343 1.957 1.886 1.825 1.638 1.556 1.595 1.904 1.894 1.589 1.680 1.752 1.707 1.803 1.689 1.558 1.586 1.717 1.830 1.699 1.570 1.649 1.844 1.603 1.767 1.675 1.448 1.762 1.915 1.776 1.705 1.695 TABLE 3—Continued 0.453 0 0.010 0.012 0.189 0.012 0 0.885 0.052 0 0.132 0.002 0 0 0.011 0.011 0.009 0.159 0.069 0.003 0.002 0.013 0.200 0.012 0.173 0.011 0.003 0.106 0.172 0.279 0.017 0 0 0.076 0.190 0.245 0.068 0.544 0.032 0 0.018 0.002 0 0.012 0.196 0.011 0 0.038 1.249 B. Pyrene 30000. 31800. 31600. 31400. 30700. 30300. 36800. 36600. 36300. 35400. 34300. 34000. 33200. 32900. 32800. 32700. 32500. 32200. 31200. 31000. 48500. 46500. 45300. 42200. 42000. 41800. 41600. 41300. 40600. 37500. 37200. 37000. 33700. 44700. 42900. 42600. 42400. 37800. 44600. 44300. 43700. 43300. 43000. 38600. 38000. 39800. 39600. 39500. 39100. 38400. 38200. (cm 2.092 2.164 2.291 2.013 1.706 0.960 2.346 2.516 1.901 1.715 1.706 1.683 1.592 1.635 1.668 1.699 1.726 1.629 1.383 1.460 1.910 1.959 1.726 1.392 2.068 1.622 1.426 1.556 1.881 1.752 1.634 1.723 1.747 1.755 1.758 1.687 1.517 1.544 1.468 1.328 1.143 1.203 1.251 1.316 1.511 1.771 1.210 1.176 1.221 1.344 1.337 Vol. 377 0.255 0.245 0.096 0.300 0.550 0.644 0.535 0.334 0.145 0.666 0.452 0.746 0.840 0.701 0.325 0.002 0.071 0.087 0.083 0.156 0.248 0.185 0.307 0.223 0.097 0.238 0.350 0.409 0.386 1.127 0.828 0.015 0.144 0.158 0.152 0 0.003 0.183 0.294 0.271 0.542 0.792 0.738 0.717 0.543 0.291 1.029 1.182 1.248 1.209 1.024 1991ApJ. . .377. .541C -3 -1 1 heating rateequalstheircoolingrate.Closetothephoto- which possesssimilarabsorptioncharacteristics. could operatewithbenzene,pyrene,pentacene,andcoronene, where nisthegasconcentration,5R*). (McCabe, Smith&Clegg1979). 0.8 (Keady,Hall,&Ridgway 1988),andtheratioofacetylene PAHs tomuchlargersizes(~200Catoms)andtheirsub- to molecularhydrogenmayrange from2x10“to410~ 3000 K(Gustafsson1989),^/-coefficients mayvaryfrom0.3to total forceactingonthe numberofgrainsormolecules 2 2 eff Fig. 8.—RadiativetemperaturesforselectedPAHsanda10ÂradiusAC The resultsarepresentedinFigure8,alongwiththeradi- There existonlytwostudiesonPAHformationprocessesin A “radiationpressureforcedensity” canbedefinedasthe © American Astronomical Society • Provided by the NASA Astrophysics Data System 4.3.2. RadiativeAcceleration CHERCHNEFF, BARKER,&HELENS 13 4 nuclei lossrateratioof(5.2±1.7)x10".Arevisedvalue the Cstarenvelopesthangraphitegrains,accordingto pressure ongrains,asalowlimitingcase. given byJura(1986)ishigherafactorof~2,buttheresults predicted bythe“standardmodel,”waschosentorepresentall where theaveragesizeof40carbonatomsperPAHmolecule, purposes, andthePAHabundanceiswritten “standard yield”of1.3%.Thisvaluewasadoptedforpresent equal toorlargerthannaphthalene(CH).Theyfounda initially presentinCHthataccumulatesPAHmolecules molecules), relativetoH.Frenklach&Feigelson(1989)define spectral indexvalueofthegrainemissivitydeducedfrom the PAHformationyieldYasfractionofcarbonatoms (Y variesasthecubeof[CH]/[Hratio).Computations was initiallyintheformofPAHs. models (Rowan-Robinson&Harris1983). in thecomputation.TheonsetofACgraincondensationwas radius of0.1/mi.Forsuchlargeparticles,Mietheorywasused ation pressureefficiencywascalculatedforatypicalgrain of Knappwerechosenforthecomputationradiative observations byKnapp(1985),whofoundadustlossratetoH PAHs intheenvelope. AC grains[curvelabeled(c)].Frenklach&Feigelsondescribe the curvelabeled(a).TheradiationpressureactingonPAHsis perature andassumingthatallthecarboncontentofACgrains temperature; and(3)the“standardmodel”withhighertem- the “standardmodel”parametersfromFrenklach&Feigel- observations (Whittet1989).ThePlanckmeanoftheACradi- (carbon starsoftenhaveeffectivetemperaturesgreaterthan were thencarriedoutinthepresentworkforahighacetylene their PAHyieldashighlysensitivetotheacetyleneabundance about threeordersofmagnitudelessthantheforceatworkon son (1989);(2)the“standardmodel”withahighereffective assumed tooccurat1000K,atemperatureoftenspecifiedin much less,andtheTeff radiusdependenceofthetem- consequence ofincreasingthephotospherictemperature was little effectonthecomputedPAHyield.Inthiswork, only abundance derivedfromthermodynamicequilibriumcalcu- perature profiletendtoincrease thespatialseparationbetween temperature tolargerradii.In theseregions,thegasdensityis lations byCherchneff&Barker(1991)(fortypicalC star to shiftthePAHformation zone andtheACcondensation Feigelson foundthatthesurfacetemperatureofstar has iting situation,theradiationpressureforce[labeled(b)in Fig. consistent withobservations;McCabeetal.1979).Inthis lim- parameters, theratiowasfoundequalto~3x10“,which is radiation forceactingonACparticles. (a), butisstillabouttwoordersofmagnitudesmallerthan the 9] actingonaromaticmoleculesis~30timeslargerthancurve abundance ofeachtypeparticle(ACgrainsorPAH where Pisgivenbyequations(11)and(13)Xthe per cubiccentimeter.Itisexpressedas the PAHproductiontemperature windowandtheACconden- 1500 K;Tusuallyrangesfrom2000to3500K).Frenklach & 108 2 2 2 par e{{ The dustabundancehasbeendeducedfromseveralstellar Amorphous carbonparticlesaremorelikelytobepresentin Radiation pressureforceswerecomputedforthreecases:(1) Case 1.—Resultsfromcase1arerepresentedinFigure9by Case 2.—Ahighersurfacetemperaturewasconsidered = ^par(R) =PjR)Xn,(21) pH2 ^pah 2YXJ40,(22) C2ii Vol. 377 1991ApJ. . .377. .541C -6 _ 4 .1989,ApJS,71,733 No. 2,1991 Axe, J.D.1973,inSolidStateChemistry andPhysics,Vol.1,ed.P.Weller Allamandola, L.J.,Tielens,A.G.M., &Barker,J.R.1985,ApJ,290,L25 Bohren, C,&Huffman, D.1983,AbsorptionandScattering ofLightbySmall Bishop, D.M,&Cheung,L.M.1982, J.Phys.Chem.Ref.Data,11,119 Birks, J.B.1970,OrganicMolecular Photophysics (London:Wiley) increase of^efffavorsPAHsoverACgrainsforeffectivetem- variation withtemperatureforACgrainsislargerthan40 radiation pressureonPAHs.ForT<3000K,theK(T) the inverseofsquareradius.Alltheseeffectsfavor sation temperature.Theradiationpressureforcevariesalsoas peratures largerthan3000K,althoughtheresultsprovedthat C molecules,andovercomestheeffectsjustmentioned.The dominant. the radiationforceactingonamorphouscarbonwasstill model, withtheassumptionthatwholecarboncontentof close tothestellarphotospheredoesnotsignificantlyaffect were thesameasincases1and2,PAHsurrogatewas with thebroadandfeaturelesssolidphaseabsorptionspectra. molecules formedatthesametemperatureaspreviously,and the observedACgrainabundancewasinitiallyinformof dynamics oftheenvelope.Inessence,thismerelyreflects the tured natureoffreemolecularabsorptionbandscompared amorphous carbonparticles.Thisisduetothehighlystruc- emit mostoftheirenergy. low PAHopacityinthe0.5-3jamspectralregionwhereCstars poor couplingofPAHstothestellarradiationfield,due the acting onACparticles. ation pressureforceatworkonPAHsisonly20%ofthe for T=1500K.Themaximumvalueattainedbytheradi- were convertedtodustattheACcondensationtemperature sponded toamaximumPAHabundanceof5.4x10.The again amoleculeof40carbonatoms.Thislimitingcasecorre- PAHs somewhereclosetothephotosphere.Theparameters specified incases1and2.TheresultsaredisplayedFigure10 c{{ 3 x10,(c)ACgrains. eff (New York:Dekker),411 Particles (NewYork :Wiley) These resultsindicatethatthepresenceofPAHmolecules PAH moleculespossessopticalpropertiesverydissimilarto Case 3.—ThiscasewasbasedontheFrenklach&Feigelson Fig. 9.—Case1:T=1500K;(a)standardmodel,(b)CH/H eff2 © American Astronomical Society • Provided by the NASA Astrophysics Data System 5. 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