1984ApJ. . .284. .223L (1972) withlinesofthefundamentalvibration-rotation(V-R) discarded. Spectrainthe3-4gmwindowprovidedBeeret al. with CNredsystembands(WingandSpinrad1970) the factor of15.Then,thefeaturesassignedtoH0wereidentified N/O =2whereasæ0.1fortheSun).TheOabundance enhanced (i.e.,O/C=1.05,where=1.6fortheSun) and model atmospheres.TheCabundancewasreportedto be model atmospheres(Auman 1969). Beeretal.suggestedthat original identificationsofHwererejectedbyLambert, reduced theCOcolumndensity(Spinradetal.1970)by a was foundtobenearlysolar.However,newinfraredspectra accompanied byastrongerenhancementofN(i.e.,N/C æ by SpinradandVardya(1966).Werestrictdiscussiontotheir literature. TheinitialattemptataCNOanalysiswasreported C, N,andOfortheMsupergiantBetelgeuse(aOri)tryto surface. Inthispaper,wediscusstheelementalabundancesof by nuclearreactionsintheinteriorandmixedoutto pared withpredictions(Goon andAuman1970)obtainedfrom bands ofOH.TheOHcolumn densitywasderivedandcom- Brooke, andBarnes(1973).Clearly,thisinitialanalysismust be CO andanalyzedthemolecularcolumndensitieswithcrude results foraOri.TheyobservedbandsofH,0CN,and trace theoriginofprocessedmaterialinatmosphere. The AstrophysicalJournal,284:223-237,1984September1 © 1984.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. Astronomy, Inc.,under contractwiththeNationalScience Foundation. 2 2 2 2 1 The atmosphereofaredgiantcontainsmaterialprocessed Abundance analysesfortheMsupergiantsarerarein KPNOisoperatedbytheAssociation UniversitiesforResearchin JohnSimonGuggenheimMemorial Fellow,1980-1981. 13 1213 1214 ment. ThisanalysisdoesnotconfirmrecentreportsthatCisseverelyunderabundant. exception oftheobservedhighCabundances,andpredictedabundancesareingoodagree- CN-cycle processedmaterialhasbeenmixedtothesurfaceasaresultoffirstdredge-upphase.With These abundancesandespeciallythelowC/Nratio([C/N]=—0.9)withC/suggestthat sphere withT=3800Kandlogg0.0isadopted.Resultsare: the MsupergiantBetelgeuse(aOrionis)areanalyzedtoobtainC,N,andOabundances.Amodelatmo- Subject headings:nucleosynthesis—stars:abundancesindividualinteriors star isdeficientinC,andricherN: If aOriisassumedtobemetalrichbyabout0.1dex,theatmospherecomparedwiththatofanunevolved eff © American Astronomical Society • Provided by the NASA Astrophysics Data System Vibration-rotation bandsofCO,NH,andOHinfraredlinestheCNredsysteminspectrum I. INTRODUCTION CARBON, NITROGEN,ANDOXYGENABUNDANCESINBETELGEUSE stars: supergiants log 6(C)=8.4,e(N)8.6ande(O)8.8. [C] =-0.4,[N]+0.6and[O]-0.2. 1 David L.LambertandJefferyA.Brown Received 1983April14;accepted1984March12 Department ofAstronomy,UniversityTexas Astronomy Department,IndianaUniversity 2 Kitt PeakNationalObservatory Kenneth H.Hinkle Hollis R.Johnson ABSTRACT AND 223 NH fundamentalV-R1-0and 2-1bandsbetween3and4gm, dances; theprimarysources are thefollowingmoleculartran- carbon wasnotstronglydepletedintheatmosphere(Lambert (1981), whomodeledtheKi7699Âfluorescentemission and portions ofthe5gmfundamentalV-RbandsCOwere are strongsothatthecolumndensityissensitiveto dances. Unfortunately,theOHandCOlinesusedbyBeeretal. the OHfundamentalV-Rbands alsonear3gmandlines sitions: theCOsecondovertone V-Rbandsnear1.6gm,the supergiants. WeconsiderseveralindicatorsoftheCNOabun- abundances usesline-blanketedmodelatmospheresfor M to resolvetheseconflictingreports.OurattackontheCNO led toaseveredepletionofC,anenhancementNand recent modelatmosphereanalysisofCO,OH,andCNlines ratio wasaboutafactorof12smallerthanthesolarratio.A analyzed byGeballeetal.(1977)whoconcludedthattheC/H assumed microturbulence.High-resolutionobservationsof both C(heretheCOcolumndensitywasused)andOwere the CNredsystemlinesat8000 Â. 2 gmoftheCNredsystem.We alsodiscussthe[Oi]linesand showed that,incontrasttoamajorityoftheearlieranalyses, nary analysisofweakCOsecond-overtoneV-Rlineswhich sphere wasdeficientbyafactorofabout25. suggested thatCintheshelland,hence,stellarphoto- the COrotationallineemissionfromcircumstellarshell, near-solar abundanceofO(Tsuji1979).JuraandMorris underabundant byaboutafactorof10relativetosolarabun- 1974). Anewcomprehensiveanalysiswasbeguninanattempt Our analysiswasstimulated,inpart,byanearlierprelimi- Our modelatmospheres andthedefining parametersare 1984ApJ. . .284 . .223L -1 -4 (§ V)withadiscussionoftheabundancesandpredictions (§ III),wepresenttheabundanceanalysisin§IVandconclude discussed in§II.Afterabriefdiscussionoftheobservations of nucleosynthesisandmixinginredsupergiants. 224 Tsuji 1976a;Johnson,Bernat,andKrupp1980,hereafterJBK). refer fordetailstotheoriginalpapers(Gustafssonetal.1975; for thisproject.Theinputdefiningparametersaretheeffective stars arenowavailableinquantity.Interestedreadersshould giant modelsorwerecomputedfromthesamecodespecifically equations isquitestandardandhasalreadybeenrepeatedly include theequationofhydrostaticequilibrium,constancy ciples oftheoreticalstellaratmospheres.Theseprinciples composition. Themodelsaresubjecttotheconventionalprin- temperature (T),thesurfacegravity(g),andchemical but turbulentpressurewasneglectedexceptfortwomodels hydrostatic equilibriumincludesgasandradiationpressure, neous geometry.Thepressuretermintheequationof dynamic equilibriuminaplane-parallel,horizontallyhomoge- total energyflux(radiativeandconvective)localthermo- length topressurescaleheightistakenasunity.Thesetof later. Convectionistreatedwiththestandardmixing-length with 2and3kms.Theassumptionofaplane-parallelatmo- (Kurucz 1970),whichisalsowellknown,thoroughlydescribed, discussed intheliterature.Theequationsoutlinedaboveare theory (see,forexample,Kurucz1970),andtheratioofmixing sphere forasupergiantsuchasBetelgeusewillbediscussed solved bythemodelstellaratmosphereprogramATLAS5 paper containsinformationrelatingtoionizationenergies,dis- and oftenused. tional modelshaveenhancedmetalabundances.TheJBK included asdescribedbyKurucz(1970). The standardhydrogenandheliumopacityofATLAS5are the moleculesCO,CN,C,TiO,NH,MgH,OH,andH0. accounts forthelineopacityofmanyatomsaswelllines sociation energies,andlinebandstrengths.Thecode Johnson andKrupp(1976)hasbeenusedincalculations of frequencies. TheopacityofH0istreatedasastraightmean. model ofbetterthan50K.Inourcalculationsweuse 1010 frequency pointsaresufficientforanaccuracyinthe final tremann (1974),Sneden,Johnson,andKrupp and concerned aboutthepossible effectsofsphericity.Intheplane- model atmosphereswerecomputedunderthestandard the opacitiesareaccuratelycomputedatafewfrequenciesscat- no averagingorsmoothingoftheopacitiesisemployed;rather, a widevarietyofstellaratmosphericmodels.Inthistechnique, opacity samplingtechnique,whichhasbeendescribedbyPey- eff g =0)hasanatmosphericextent (betweent=1and10) cally. Amodelrepresentative ofaOri(T=3800K,log parallel approximation,theassumption ismadethattheextent approximation ofplane-parallelgeometry,Betelgeuse is a tered overtheentirespectrum.Testshaveshownthat500-600 of theatmosphereissmallcompared totheradiusofstar.A supergiant starwithaverylarge atmosphere,andonemustbe simple testcanthereforebemade ofthisassumptionnumeri- 2 2 eff Realistic modelatmospheresforcoolgiantandsupergiant Our modelatmospheresaretakenfromtheJBKgridofred Most ofourmodelshavesolarcompositionbutafewaddi- All oftheselinesexceptthoseH0weretreatedbythe A problemofsomeconcernisthefactthat,whileall 2 © American Astronomical Society • Provided by the NASA Astrophysics Data System a) DescriptionoftheModels II. MODELATMOSPHERES LAMBERT ETAL. 7 4 extent, andsuchasmallvalueproducesverychangesin models. Amorerigoroustesthasbeenprovidedbythestudyof this alonewouldleadustobelievethattheplane-parallel icity leadstoanincreaseinatmosphericextent,almostno investigate theeffectsofsphericity.Briefly,theyfindthatspher- approximation willnotintroducesignificanterrorsinour see §lib),theratioofatmosphericheighttoradiusis0.03,and of 1.2x10km.Basedontheradiusforstar(R=650R, lar bandsasTiOandH0duetothecoolingresultingfrom difference incolor,aslightdecreaseabsolutevisualmagni- nongray staticLTEmodelatmospheresinfivedifferentsetsto Kodaira (1978,1979).Theyhaveconstructedspherical, the sphericityeffectsoflate-typestarsbyWatanabeand are predictedtobequitespectacular.However,wenotethat extended atmospheresasinlong-periodvariables,theeffects tude, andstrengtheninginsuchtemperature-sensitivemolecu- model B1ofWatanabeandKodaira,whichhasparameters the divergenceofradiativefluxinouterlayers spherical atmosphere.Insomecases,especiallyforsuch been choseninourstudy,areformedfairlydeeptheatmo- r¡ =3%,whererjistheirparametermeasuringatmospheric quite representativeofthoseBetelgeuse,hasavalue atmospheric structure.Finally,themolecularlines,whichhave enced bythecoolingwhichwouldresultfromourtakinginto sphere ;consequentlytheyarenotexpectedtobegreatlyinflu- parallel geometry. duced byouruseofmodelatmospheresbasedonplane- appear toindicatethatnosignificanterrorsarebeingintro- account theeffectsofsphericity.Alltheseconsiderations e 2 gravity, thechemicalcomposition,etc.),andinterstellar and circumstellarreddening.Severalmethodshavebeenpro- stellar atmosphere(thetemperaturedistribution,surface monochromatic fluxprovidesarelationbetweenthesurface line densityisquitelowsothatameasurementofthecontin- infrared, outsidethemajormolecularbands,absorption- posed forextractingTfromthecontinuousspectrum.In The totalintegratedfluxemittedbythestarprovidesasecond perature andwhichiscomputedusingamodelatmosphere). depends—approximately linearly—ontheeffectivetem- the emergentinfraredfluxperunitarea(aquantitywhich area (proportionaltothesquareofangulardiameter)and uum fluxispossibleviaphotometry.Theintrinsicinfrared flux distributionspredictedbymodelatmospheres(Tsuji (T inthiscase).Thus,thecombinationofobservedinfra- relation betweenthesurfaceareaandeffectivetemperature the angulardiameterandT—see,forexample,Blackwell, red andtotalfluxeswithanestimateofthereddeningprovides dix Aforadiscussionoftheextinction(T).Theuncertainty A =0.8magandT3740Kif0.3mag—seeAppen- blanketed atmospheresledTsuji toconcludethatT=3900 posite energydistributionand thepredictionsofhisline and multicolorphotometry. A comparisonbetweenthecom- phase. obtained fromtheinfraredflux methoddoesnotchangewith apart fromthatcontributedbyAis±50K.TheTeff as Petford, andShallis(1980).Augasonetal.(1979;also 1980) reportnewspectrophotometrywhichtheycombine with eC{ 1976a; FaÿandJohnson1973)toobtainT:=3850 K if eff eff y veff eff v eff The fluxdistributionofthecontinuousspectrumissetby Tsuji (1976h)collatedpublished infraredspectrophotometry b) TheDefiningParameters i) TheEffectiveTemperature Vol. 284 1984ApJ. . .284 . .223L n No. 1,1984 with mostoftheaboveresults. Weassignhighweighttothe depends slightlyontheadoptedsurfacegravity:AT= ±50 containing high-andlow-excitationlines.Thederived T ing and/orathoroughspectrumsynthesisofselectedregions infrared fluxmethodobtains T=3800±40K.Thereferee result providedbyAugasonet al(1980).ThisTffoverlapsthe K forAlogg=±0.5.Thisresultisquiteconsistentwith the probably bereducedbyadetailedconsiderationoflineblend- estimate theuncertaintytobe±250K.Thecould model atmosphereshownotrendwithexcitationpotential. We The CO1.6/milinesconfirmthatTä3800Kbecausethe C problem istoobservetheweaklow-excitationOHlineswhich temperature ofaM2IIIstar forwhichTsuji(1981)withthe abundances providedbytheindividuallinesandouradopted temperature. TherangeinXexcabout2eVatallWlevels. neutral atomscrowdthe1.6jamwindowandlimitnumber tion inaWversusXcxcpl°t-Iaddition,CO,CN,andthe atmosphere. TheAi;=2OHlinesprovideasimilardistribu- opportunity todeterminetheexcitationorrotation-vibration of measureableweakOHlines. are largelyinaspectrumintervalobliteratedbytheEarth’s photometric measurementsofthespectraltype. larger thantherange(±60K)indicatedbynarrow-band effective temperaturemightbeobtainable.Thekeytothe excellent thermometer(HinkleandLambert1975).Wecon- lines willbedifficulttocollectbecausemolecularobliter- potential thermometers.Thenecessaryobservationsforatomic that Tmustvaryby±300K,but,asWhitenotes,thisis vary morethanafewpercent(Dyck,Lockwood,andCapps diameter) overthe5.8yearperiod.Sincetotalfluxdoesnot measurements leadsWhite(1980)toproposeT=3680K.He with it.Anindependentanalysisofpublishedangulardiameter also fixestheshapeofcurve,wereknownaccurately, the pointsaboutameancurve.Ifmicroturbulence,which temperature) fixestheshapeofcurvebutnotscatter growth, theadoptedeffectivetemperature(hence,rotation width oftheWversus%plotisjust0.8eVforanarrow excitation potentialofthelowerlevelOCexc)-Themaximum provides aninsufficientnumberoflines. rotation bandfromaboundelectronicstateshouldbean ately tightcorrelationbetweenequivalentwidth(WJandthe the rotationalandvibrationaltemperaturesarenotobtainable. sidered theCOandOHbandsaspotentialthermometers;NH ate largeportionsofthespectrum.Inprinciple,avibration- hint ata±8milli-arcsecvariation(+18%changeinangular suggests thatthepublishedangulardiametermeasurements flux andtheangulardiameter.Tsuji(1976h,1978,1979)argues the OHlinesareoffweak-lineportionofcurve range and~0.4eVovermostoftheplot.Sincemajority Examination oftheOHlinelistshowsthatthereisamoder- K—Dyck, Lockwood,andCapps1974)sometimesassociated of about3800Kratherthanthelowervalues(e.g.,T=3250 that thismethodistooconsistentwithaneffectivetemperature spectrum usesthesinglerelationbetweentotalintegrated Kodaira etal(1979)toproposeT=3800±100K. T estimatesbaseduponthe continuous spectrum. eff eff 1974; Augason1980),theangulardiametervariationimplies eff e eff 0 a eff eff aexc eff eff eff ± 150K.Analysisoftheirphotometry(1.3-2.2jum)led We adoptT=3800±100 K.Thisestimateisconsistent The COAv=3bandsnear1.6/miprovidethebest The atomsandmoleculesinthestellaratmospherearealso Although theOHAi;=1V-Rbandsarewellrepresented, An alternativemethodforderivingfromthecontinuous eff © American Astronomical Society • Provided by the NASA Astrophysics Data System C, N,ANDOABUNDANCESINBETELGEUSE 3 method. Weselectedsomeunblendedweakandmoderately strong linesofneutralatoms (Nai,SiTiFeNii)from surface gravityofalate-typestar.Weadoptedvariant this yield thesameabundanceiscommonlyusedtodetermine the the redgiantbranch.Wèadoptaprobablerange10 < the H-Rdiagramincludecompositionandmasslossbefore Additional factorscomprisingtheidentificationofmass via luminosity increasecorrespondstoamassfrom 15 model towardtheredgiantbranch.Onnewtheory, red (1980) adoptanewtheoryofconvectionandevolve15M Reticon spectrawith2>10000 Â(seeTable1).Thisregionis M/Mq <30or—0.2logg0.3forR/R=650. M toabout21accordingtracksgivenbyLambet al. supergiant isbrighterbyabout0.14dexinlogL/L. This and Chin1979)giveM^30.CloutmanWhitaker other differences(StothersandChin1977;seealsoStothers Other trackscomputedwithhigheropacitiesandapparently stellar evolutioncalculation.Evolutionarytrackscomputedby ciple, obtainablebyaninspectionofatheoreticalH-R Lamb, Iben,andHoward(1976)suggestM^15foraOri. diagram. Unfortunately,theevolutionarytracksofmassive ( =0"041forA0.7)derivedbyAugasonetal.(1979) (1980) recommendsameanangulardiameter(totallimb- (1978)’s measurementoftheclusterdistancemodulus(M= firming MestimateisderivedfromWilson’s(1959)’sobserva- stars likeaOriaremostsensitivetotheinputphysicsof two estimates:R/Rq=650. radius R/R=680.Weshalladoptastraightaverageofour the infraredfluxmethod.Weadopt=0"041toobtaina circumstellar dust)of0=0'.'043.Thisisclosetotheresult darkening assumedandanempiricalcorrectionfortheeffectof cussion ofavailableangulardiametermeasurements,White ing themeanapparentmagntitudem=0.8,A0.1,and bolometric correctionBC=—1.55(Lee1970)toobtain tion thataOriandHD14270,supergiantinthehx line widthandtherevisedHyadesdistancemodulus.Acon- gives theabsolutevisualmagnitudeM=—5.9fromaCanK observed angulardiameteranddistanceestimates.Bycombin- Mboi =-7.4and,thenR/Rq620forT3800K. radius, TandthebolometricmagnitudeM.Wilson(1976) 1971; WhiteandWing1978)a CN-index versusMrelation.Heobtains M =—5.85,weobtainadistanced155pc.Afterdis- Persei cluster,haveequalKlinewidths,andHumphreys stellar radiusandmass.Astandardexpressionrelatesthe decreased from3800Kto3600K. how thederivedabundancesarechangedwhenTeffis to beexcludedbytheinfraredfluxmethod,weshalldiscuss according toTsuji’sTscaleforMgiantsshouldbe= band strengths,supergiantsshouldbeatleast100Kcooler at thetimeofourobservationswasM2.8(see§III), than agiantofthesametype.Then,ifspectraltypeOri suggests thatbecausespectralclassificationsarebasedonTiO 3570 K,not3800K.Althoughthislowertemperatureappears = 96pcandameanradiusR/R460 for=0"043. 0 0 q0 0 0 0 v v v Q v — 5.8forHD14270).ForaOri,weadoptM=—5.85and v eff effbol v v effefi Q v 3 The requirementthatneutralandionizedlinesofanelement When MandTffareknown,thestellarmassis,inprin- WhiteestimatesMfromthemeasured narrow-bandCNindex(Wing A secondestimateoftheradiusisprovidedfrom The surfacegravitymaybecalculatedfromestimatesofthe bole v ii) TheSurfaceGravity 225 1984ApJ. . .284 . .223L -1 -1 226 not marredbyTiOlines,andintervalsexistwhereCNlinesare also unimportantcontributors.Thespectrahadbeentakenfor purpose. Weobtained¿/-valuesfromsolarequivalentwidths a varietyofdifferentprojectsbutwerewellsuitedtoour (Na) andhigh(Si,Fe)ionizationpotentialspeciesasasurface (for afixedlogg\theSi(andFe)andNalocihavequite from theweakestlines.Inaplotofabundanceagainst Abundances wereobtainedforagridofOrimodels. and theHolweger-Müller(1974)modelsolaratmosphere. enriched inHe,weexpectthemetalabundancetofallbetween gravity monitor(foragiveneffectivetemperature). abundances inthesunandaOriallowsustocombinelow different slopeandtheirintersectiongivesaloggsolution. atmosphere: the=3800Kandlogg0modelgives abundance. Theresultdependsonlyslightlyonthemodel the weakandstronglinesofSiiFeprovidesame Our assumptionthatSi,Fe,andNahavethesamerelative mates aretemperaturedependent;theformerestimate and theyellowlbsupergiants(Luck1977,1979);i.e., younger Hyadescluster(Branch,Lambert,andTomkin1980) the solarvalueandslightlyhigherexhibitedby Ç —3kms.TheNa,Si,andFeabundanceswereobtained lic linesprovideroughconfirmationofourearlierestimate becomes loggf^0forTeff=3900K.Weseethatthesemetal- the surfacegravity.OuradoptionofLTEisaprobablesource latter qualification,wefindthatthemetalliclinesjustconfirm gravity forafixedTmaybeanunderestimate.With this Woodrow 1975),and,hence,thepresentestimateofsurface the atmosphere,and,hence,LTEmaybeareasonableassump- of systematicerror.Theweak6eVSiilineisformeddeep in reflector withthenewFourier transformspectrometer(Hallet windows from1.4to5.3/un, were acquiredattheKPNO4m adopt asurfacegravityloggf=0.0±0.3. the surfacegravityderivedfrommassandradiusestimates. We tion. NamaybeoverionizedrelativetoLTE(Auman and [Fe/H] -0.0-0.2,where[X]=logX. al. 1978).Theresolutionwas Act>0.07cmafterapo- tively providealmostcompletecoverageoftheatmospheric source oflines.Theseveralspectra(seeTable2),whichcollec- Tf =3800Kand[Fe/H]«0.2atloggf—1.Theseesti- almost theentirespectrum. Some spectrawerecorrectedfor dization. Thesignal-to-noise ratio(S/N)exceeded100over the telluricabsorptionlinesby ratioingtheaOrispectrumto eff a0 ef The microturbulentvelocityissetbytherequirementthat Unless theatmosphereisnowseverelydepletedinHand The Na,SiandFelocishowaverycloseapproachfor High-resolution infraredspectraofaOriareourprimary Nai ...... 10746.453.1979-1.48 Til 10066.552.16191-1.79 Si i10301.446.1022-1.97 Nil 10193.254.05186-0.73 Cn 9900.952.99173-1.93 Fe i10007.323.0291-4.72 eVm Species ¿(Â)X()^)loggf © American Astronomical Society • Provided by the NASA Astrophysics Data System 10694.25 5.96142-0.41 10265.23 2.22199-4.57 III. OBSERVATIONS The AtomicLineList 9889.05 5.03198-0.30 TABLE 1 LAMBERT ETAL. IRC +10216ortheplanetMercury. the nearlycontinuousspectrumofembeddedcarbonstar absorption lines.Theideathattheinfraredisasourceof lines thespectrumcontainsfewstellarlines.Thisregioncon- spectra, afterratioingtoareferencestarremovethetelluric unblended linesislargelyamythforcoolstarslikeOri. coudé spectrometeratthe2.7mreflector(Vogt,Tull,and trates thecleannessof3-4gmspectra. tributes theimportantOHandNHV-Rlines.Figure1illus- Fortunately, mythandfactaresynonymousforthe3-4gm at theMcDonaldObservatoryusingReticon-equipped a similarairmass. ric lineswereaseverecontaminant,hotstarwasobservedat Kelton 1978).Resolutionsof0.1-0.2Âwereused.Whentellu- spectra spanninganumberofyears;theearlierwere 2 gmlinesvarybylessthanabout10%-15%ontheseveral weaker OHAi;=1linesforwhichcoverageislesscomplete transform spectrometer(Beer,Norton,andSeaman1971).The obtained attheMcDonaldObservatorywithJPLFourier valent widthsofCOAv=2linesnear1.6gmandtheCN The molecularlinesdonotvarybylargeamounts.equi- The CNredsystemnear8000Ahasalsobeenobservedatthe also shownosignificantchangefromspectrumtospectrum. mean setofatmosphericparameters.Ourlineselectionis might havebeencoolerthannormal. weighted infavoroflinesobtainedfromthe1980February be combinedandanalyzedwithamodelatmospherefor slight. Weassumethatobservationsfromdifferentepochsmay spectra whènaOriwasnearminimumlight(spectraltype McDonald Observatory;equivalentwidthchangesareagain equivalent widthversuscentraldepthrelation.Then, the width computedfromthecalibration.Thisuseofpartly central depthofCOlineswasmeasuredandtheirequivalent a selectionofwell-resolvedlinesallspeciestocalibrate the resolved fromneighboringlines.Inthiswindow,wemeasured the finallinelists.VeryfewofCO1.6gmlinesarecleanly and onlythelineswithawell-definedprofilewereincluded in M2.8 lbaccordingtoWhite1980)sothatthephotosphere employed intheselectionof the NH,OH,andCNlines.The have beenachievedwithastrictadherencetothecriteria blended linesprovidedalargersampleofthanwould For NH,OH,andCNlines,allavailablelineswereinspected (location ofcontinuum,undetected blends,andmeasurement identical abundance.Thestandard deviationsoftheabun- dances aredeterminedpartly byequivalentwidtherrors selected linesofasetappear, asexpected,toyieldverynearly uncertainties duetonoise)and by(small)systematicerrorsin the/-values. Thestandarddeviations are+0.14(CO,48lines), spectra apodizedwithNortonandBeer1976function12. Long stretchesoftheinfraredspectrumarecrowdedwith Selected intervalsintheredandnear-infraredwereobserved a Oriissemiregularvariablewithperiodof5.8years. Our analysisisbasedonequivalentwidthmeasurements. 4000-5100,5550-6600 1980Aug260.036280 4000-5100,5550-6600 1980Feb50.070130 2830-3100 1980Feb50.070230 2390-2800 1977Oct210.060250 a 3a 1977Oct21unapodized,observedwithprototypeFTS.Other Wavenumber RegionDateResolutionS/N Infrared Spectra TABLE 2 Vol. 284 1984ApJ. . .284 . .223L 1 1216 1216- lines aredisplacedfromthetheoretical curveofgrowthfittedtothe4-3and3-2lines.Thesolidis a theoreticalcurveofgrowthforlinelowerstate photosphere. Thefundamental(At;=1)COlinesarevery monitors ofthevelocityfieldandstructureupper were alsoexamined.Thestrongerfirst-overtone(At;=2) potential x=1.14eVandfrequency c =2935cm"\forthecasewheremicroturbulenceisaconstant3km s"throughouttheatmosphere. Table 3listslineswithlogWJa<—5.1butstronger systematic error(seebelow). tainties issmallrelativetoothersourcesofuncertaintyand lines). Themeanerrorattributabletoequivalentwidthuncer- out thetelluricfeatures.Thelowerspectrumisstellarwithlinesremoved. spectrum istheobservedshowingseveraltelluriclines.ThemiddleIRC+10216,whichfeaturelessinthisregionandhasbeen usedtodivide No. 1,1984 C0 linesofferacheckontheAt;=3butareprimarily C0 linesinthe5600-6700cmatmosphericwindow. ±0.10 (NH,13lines),±0.05(OH,62lines)and±0.11(CN,10 1 Fig. 2.—Acompositecurveofgrowth forOHfundamentallines.TheabscissaislogX=gf-OiWJx- is theexcitationtemperature.Notethat5-4 Fig. 1TheBetelgeusespectrumfrom2602to2617cm"showingtwoNHtripletsandOHquartets.Notethegreaterwidthoflines. Theupper Our abundanceanalysisusestheweakovertone(At;=3) © American Astronomical Society • Provided by the NASA Astrophysics Data System IV. THEABUNDANCEANALYSIS a) COandOH 38400 383503830038250 C, N,ANDOABUNDANCESINBETELGEUSE Angstroms (SIP) -1 2 1316 km s.TheCOlinessuggestaslightlyhighervalue.Our growth inFigure2iscomputedforamicroturbulenceof^=3 overtone OHlines(seeTable4).Thetheoreticalcurveof We commentintheAppendixonourselectionoffirst- provide equivalentwidthsoffundamental(At;=1,3-4fim) OH lines.AcompositecurveofgrowthisshowninFigure2. vibration-rotation transitionswerediscoveredinthe Betelgeuse spectrumbyBeeretal(1972).Thenewspectra transitions oftheXHgroundstate.Thefundamental not discussthelinesofC0andotherisotopicallysub- stituted molecules. sphere. WepostponeadiscussionoftheAt;=1lines.do tion, offeratestofthethermalstructureupperphoto- strong; thelinecores,whichprovidelittleabundanceinforma- The OHradicalisdetectablethroughthevibration-rotation 227 1984ApJ. . .284 . .223L 1 228 ly ofanassumptionabouttheOabundance.Thenearindepen- ence (O—C)and,therefore, analysis oftheOHlinesprovides dence fromtheOabundanceoccursbecauseCis fully sphere. Thepartialpressureof Oissetbytheabundancediffer- associated intoCOthroughoutthegreaterpartofatmo- locus fromtheCOlineanalysis definestheCandOabun- constant. Theintersectionof this locuswiththecorresponding plane alongwhichthe(O—C) abundancedifferenceisnearly not theOabundancebutalocus intheOversusCabundance must beincludedwhenfittinglineprofiles. dances areinsensitivetothemicroturbulencewithachange lines. Sinceourlineselectionincludesweaklines,theabun- this valuethetheoreticalcurvewillalsofitweaker2-1 OH abundance analysisisbasedon¿=4kms”;notethat with dances. WederivedtheCO and OHlociforagridofatmo- 4-1. 3-0. 5-2. 6-3. 7-4. 9-6. 8-5. 10-7. 11-8. The COlinesprovidetheCabundancealmostindependent- _1 = 2kmsleadingtoAloge(X)~0.04.Macroturbulence Band CO Second-OvertoneVibration-RotationLines © American Astronomical Society • Provided by the NASA Astrophysics Data System Line R69 P60 P49 P51 P65 P1A P5 P47 P81 P79 P76 P58 P61 P73 PI P88 P84 Rll P0 P56 R96 P56 P78 RIO R63 P89 R19 P4 P56 P31 R63 R9 P84 P13 P16 P25 R55 P12 Rll R7 P2 P24 P13 P14 R39 R37 R52 R49 R9 cm XloeV a (cmT()gX” 6058.7 6041.4 6023.7 6380.9 6330.2 5823.3 5811.8 6350.3 6267.4 5881.4 5852.1 5715.4 6130.8 6141.4 6156.3 5650.0 6117.0 6032.3 6069.9 5746.5 6008.3 6019.3 5669.8 5872.4 5939.7 5966.4 5751.9 5807.5 5756.2 5838.6 5897.1 5902.3 5827.6 5822.8 5908.7 5870.8 5740.3 5788.2 5886.0 5830.0 5830.4 5747.2 5777.1 5761.3 5757.0 5778.8 5757.6 5763.9 5777.5 TABLE 3 0.040 0.041 0.028 0.038 0.040 0.046 0.020 0.037 0.028 0.023 0.015 0.017 0.045 0.034 0.026 0.032 0.031 0.024 0.037 0.014 0.028 0.010 0.034 0.024 0.032 0.045 0.040 0.045 0.041 0.010 0.018 0.015 0.043 0.044 0.031 0.036 0.022 0.008 0.028 0.024 0.023 0.027 0.036 0.030 0.030 0.028 0.034 0.032 0.031 -8.59 -7.80 -7.79 -7.78 -7.10 -7.08 -7.05 -7.02 -7.13 -8.64 -7.11 -6.69 -6.62 -5.87 -5.90 -6.36 -5.85 -5.50 -5.58 -7.89 -5.45 -5.11 -7.04 -6.08 -5.08 -5.09 -5.18 -5.27 -5.98 -6.14 -6.06 -5.90 -4.97 -6.91 -6.17 -4.84 -5.08 -6.16 -5.98 -5.94 -5.93 -5.01 -5.36 -5.66 -5.74 -5.08 -5.11 -4.90 -4.94 LAMBERT ETAL. 0.534 0.579 0.627 Ö.862 0.007 0.266 0.787 2.049 2.153 1.265 2.557 2.404 1.770 1.148 1.553 1.134 1.065 1.872 1.267 2.201 3.117 1.520 1.977 2.704 2.669 2.408 3.070 2.442 1.048 1.769 2.047 2.472 3.116 1.614 2.075 2.064 1.607 1.691 2.377 2.344 2.167 1.547 1.581 1.586 2.638 2.571 1.566 1.838 1.812 1213213 f (Tf =3800Kandlog0.0)are lines at6300and6363Â.Toourdismay,theCOabun- where weadoptC/=6topresentthetotal(+) Ori. Theabundancescorrespondingtotheadoptedparameters spheres centeredontheadoptedatmosphericparametersfora line %200mÂ)farexceedtheobservations45mÂ). dances providedbytheCOandOHlinesdidnotpredict to Mstars,weobtainedReticonechellespectraofthe[Oi] giants andsupergiants.Withtheintentofextendingtheirrole abundance. TheuncertaintiesattributabletoTandlogg The B2IIIstaryOriwasalsoobserved.Onthecomposite with asingleexposurecovering100Âatresolutionof0.2Â. depresses the6300-6363Âregion.Weobtainedaseriesof Warren 1973)showsthattheTiOy'systemAi>=0sequence observed VL/softhe[Oi]lines.Thepredictionsfor6300Â uncertainties aresummarizedlater. red-degraded y0-0headandtheregionaround6500Â.This the continuumbetweeninterval6100-6160Âbeyond spectrum showingthefluxratioaOri/yOri,weinterpolated overlapping Reticonexposuresovertheinterval6100-6500Â bution near6300Âcomesfromhighrotationallines(Phillips continuum clearlyshowsthatthelocaladoptedin depressed belowtheinterpolatedcontinuum(Fig.3). the measurementof[Oi]linesoffechellespectraisseverely sion. Weestimatethattherearebetween10and20TiOlines this andthe2-2bandtocontributecontinuumdepres- Gerry, andMerer1979)donotextendto6300Â.Weexpect 1973). Laboratoryobservationsofthe1-1band(Hocking, ef eff interpolated continuumisdefinedusing the6100-6500Áinterval. The localcontinuumissetfromthe interval ±10Áaboutthe[Oi]line.The The [Oi]linesareusefulabundanceindicatorsforGandK Inspection ofaspectrophotometricscan(Faÿ,Stein,and The y'systemlinelistsareincomplete.0-0bandcontri- Fig. 3.—Aportionofanechellespectrum aroundthe[Oi]6300.3Âline. log e(C)=8.41ande(O)8.77, 1984ApJ. . .284 . .223L 1-0. 2-1. a 3-2. Theg/’-valuesarecomputedfromMies’s 1974 T-values.Seethetextforvaluesusedinabundanceanalysis. Band P +8.5 P -9.5 P+ 8.5 P- 8.5 © American Astronomical Society • Provided by the NASA Astrophysics Data System P +10.5 1 t P- 9.5 2 P+ 8.5 P -11.5 2 P, +8.5 : x 2 2 Line 22.5 21.5 20.5 22.5 21.5 20.5 15.5 12.5 11.5 10.5 19.5 16.5 21.5 20.5 17.5 16.5 14.5 13.5 12.5 18.5 11.5 16.5 14.5 13.5 21.5 20.5 19.5 17.5 14.5 12.5 11.5 18.5 16.5 15.5 13.5 19.5 15.5 14.5 13.5 12.5 19.5 16.5 10.5 17.5 17.5 16.5 15.5 14.5 18.5 13.5 12.5 11.5 10.5 12.5 17.5 16.5 15.5 14.5 14.5 13.5 18.5 16.5 15.5 11.5 9.5 9.5 9.5 9.5 9.5 l a (cm)Wloggf*f(eV) a 2890.0 2565.5 2672.9 2675.9 2839.0 3044.4 3092.6 3142.1 3188.5 3235.6 2785.9 2837.4 2941.9 2994.3 3189.4 2511.5 2567.5 2620.9 2730.3 3043.2 2509.6 2892.4 2945.6 3143.2 3193.7 2624.0 2733.5 2786.1 3047.5 2512.6 2566.6 2944.5 2996.9 3145.5 3194.3 2787.5 2839.6 2893.5 3046.6 2991.3 2510.9 2568.6 2622.5 2679.0 2846.8 2896.7 2798.7 2539.1 2697.6 2747.0 2990.3 2644.2 2696.0 2748.5 2797.3 3037.0 2947.4 2995.5 2592.0 2645.9 2699.5 2749.5 2801.1 2849.9 2899.9 3041.5 2850.9 2899.0 2595.2 2646.4 2647.6 2698.3 2750.6 2800.1 2542.2 2885.4 2929.5 2795.6 0.140 0.150 0.051 0.054 0.062 0.094 0.102 0.131 0.140 0.140 0.112 0.123 0.137 0.150 0.042 0.070 0.082 0.077 0.045 0.047 0.049 0.130 0.140 0.160 0.097 0.108 0.039 0.050 0.074 0.082 0.140 0.150 0.040 0.084 0.087 0.095 0.122 0.121 0.132 0.078 0.034 0.045 0.050 0.061 0.057 0.056 0.074 0.081 0.037 0.047 0.055 0.053 0.054 0.070 0.090 0.038 0.044 0.060 0.063 0.077 0.080 0.043 0.044 0.056 0.056 0.074 0.074 0.053 0.064 0.066 0.035 0.044 0.052 0.040 0.035 0.039 0.036 0.036 OH FundamentalVibration-RotationLines -4.21 -4.27 -4.34 -4.42 -3.80 -3.83 -3.95 -4.00 -4.20 -3.95 -4.04 -4.09 -4.15 -4.34 -3.74 -3.77 -3.80 -3.87 -3.91 -4.39 -3.74 -3.77 -4.07 -4.18 -4.32 -3.89 -3.93 -4.02 -3.75 -3.79 -3.82 -4.13 -4.18 -4.32 -4.39 -3.93 -3.98 -4.02 -4.07 -3.96 -4.09 -3.75 -3.79 -3.82 -3.85 -3.75 -3.80 -3.85 -3.90 -4.16 -3.63 -3.71 -3.80 -3.85 -4.09 -4.13 -4.21 -3.70 -3.71 -3.76 -4.06 -3.93 -4.00 -3.72 -3.78 -3.83 -3.88 -3.78 -3.83 -3.88 -3.93 -4.00 -3.70 -3.66 -3.72 -3.98 -4.13 -4.22 0.299 0.250 0.205 0.164 0.926 0.841 0.609 0.539 0.353 0.682 0.609 0.473 0.411 0.353 0.205 0.926 0.760 0.357 0.255 0.210 0.685 0.542 0.477 0.928 0.763 0.415 0.357 0.255 0.210 1.105 1.014 0.844 0.612 0.542 0.477 0.683 0.928 0.685 1.105 1.014 0.960 0.897 0.838 0.782 0.639 0.960 0.897 0.683 1.108 1.017 0.735 0.688 0.645 1.108 1.017 0.964 0.901 0.842 0.786 1.028 0.964 0.901 0.842 0.786 1.251 1.098 1.173 1.098 1.028 1.031 1.176 1.102 1.254 1.102 1.031 1.141 1.054 1.016 TABLE 4 4-3. 5-4. Band P, -4.5 P- 5.5 P+ 9.5 P -4.5 P, +2.5 P+ 5.5 P- 5.5 P+ 5.5 P,- 5.5 P, +5.5 P- 5.5 2 2 t 2 2 2 2 Line 13.5 15.5 13.5 12.5 11.5 10.5 16.5 15.5 14.5 13.5 12.5 11.5 17.5 16.5 14.5 12.5 12.5 11.5 16.5 15.5 14.5 16.5 14.5 13.5 11.5 10.5 14.5 13.5 12.5 15.5 10.5 13.5 12.5 11.5 10.5 13.5 12.5 11.5 10.5 11.5 10.5 10.5 11.5 10.5 9.5 6.5 9.5 4.5 7.5 9.5 9.5 9.5 8.5 6.5 9.5 8.5 5.5 5.5 9.5 6.5 8.5 7.5 7.5 8.5 7.5 8.5 7.5 xa a (cm^W)loggff(eV) a 2799.7 2864.3 2555.6 2606.5 2654.0 2749.3 2796.6 2886.3 2971.6 2505.3 2557.1 2605.1 2655.3 2702.0 2750.4 2752.9 2845.7 2507.4 2559.0 2607.7 2657.8 2705.2 2753.7 2703.3 3089.8 2608.8 2656.8 2706.1 2935.2 3021.3 2933.1 2508.6 2557.9 2741.1 2867.4 2558.8 2603.5 2649.4 2692.4 2736.2 2896.4 2932.8 2512.2 2557.6 2604.5 2648.4 2693.3 2735.4 2778.1 2895.9 3001.8 2740.7 2544.4 2585.2 2626.4 2665.2 2740.3 2607.1 2653.3 2697.3 2867.2 2514.8 2560.9 2607.9 2652.6 2632.5 2673.5 2713.0 2590.9 2632.9 2673.2 2713.2 2501.8 2543.5 2665.8 2505.8 2548.5 2591.4 <0.004 <0.004 <0.003 0.026 0.028 0.032 0.027 0.026 0.029 0.034 0.028 0.029 0.030 0.033 0.035 0.033 0.039 0.027 0.024 0.031 0.030 0.033 0.030 0.036 0.035 0.032 0.027 0.028 0.026 0.027 0.033 0.022 0.025 0.014 0.008 0.017 0.009 0.027 0.029 0.013 0.014 0.014 0.011 0.012 0.017 0.016 0.015 0.010 0.015 0.014 0.015 0.015 0.017 0.017 0.007 0.008 0.006 0.006 0.004 0.010 0.008 0.006 0.008 0.009 0.011 0.008 0.009 0.003 0.013 0.013 0.016 0.010 0.012 0.014 0.011 0.009 0.005 0.010 -4.11 -3.71 -3.75 -3.81 -3.86 -3.92 -3.98 -4.13 -4.32 -4.71 -3.69 -3.71 -3.76 -3.81 -3.86 -3.92 -4.28 -4.50 -3.69 -3.74 -3.78 -3.84 -3.86 -3.96 -4.02 -3.78 -3.84 -3.89 -3.96 -4.11 -4.67 -4.84 -5.09 -3.69 -3.74 -4.01 -4.09 -4.61 -3.91 -3.98 -4.05 -4.12 -4.21 -4.67 -4.84 -3.86 -3.91 -3.98 -4.05 -4.12 -4.21 -4.30 -4.86 -4.36 -4.57 -4.71 -4.86 -4.21 -4.30 -4.63 -4.74 -4.30 -4.40 -4.59 -4.63 -4.74 -4.01 -4.09 -4.17 -4.61 -3.89 -3.95 -4.26 -4.36 -4.57 -4.70 -4.26 -4.35 0.982 0.905 0.960 1.100 1.426 1.362 1.301 1.244 1.191 1.141 1.054 1.494 1.426 1.362 1.301 1.244 1.191 1.498 1.430 1.305 1.248 1.195 1.146 1.366 1.305 1.248 1.195 1.100 1.022 1.366 1.488 1.275 1.430 1.689 1.634 1.584 1.536 1.453 1.358 1.630 1.579 1.532 1.478 1.326 1.305 1.685 1.630 1.579 1.532 1.488 1.478 1.412 1.326 1.305 1.498 1.827 1.793 1.763 1.736 1.902 1.861 1.756 1.861 1.822 1.787 1.756 1.705 1.584 1.536 1.493 1.358 1.827 1.793 1.763 1.736 1.707 1.907 1.865 1984ApJ. . .284 . .223L -1 230 cross thewindowprovidingNHandOHlines.Fortu- identified additionallinesonaKPNOspectrum—seeTable5 were firstidentifiedbyLambertandBeer(1972).Wehave calculations andtocompleteanabundanceanalysis;Luck and Figures14.TheAv=—3bandsoftheGNredsystem doublet. must befacedinanalysesofallabsorptionlinesthisregion. from ouroriginalsetofatomicandmolecularlines.Thisfact Lambert (1982)discusssuchananalysisoftheLii6707Â tistical approximation,theoverlyingTiOlinesinopacity near-infrared spectrumremovesausefulabundanceindicator TiO lines. continuous opacity.Thisexplainswhythe[Oi]linesappear Ä near6300Â.Atthisdensity,TiOprovidesaquasi- Several lines(unresolvedtriplets)ofthe1-0and2-1V-Rbands Eventually, itshouldbepossibletoinclude,atleastinasta- uum levelacrosslargestretches(perhaps,all)ofthevisibleand atomic linesappearwithoutobviousperturbationbyintruding anomalously weakontheechellespectrainwhichexpected underlined symbolsdenotetheuncertain measurements.Thepredictedvaria- tions oftheequivalentwidthinP- andR-branchesisshown. The NHlinesprovideoneestimateoftheNabundance. The realizationthattheTiOmoleculesetslocalcontin- Fig. 4.—NHvibration-rotationlines intheBetelgeusespectrum.The © American Astronomical Society • Provided by the NASA Astrophysics Data System b) NHandCN 2-1. Band 1-0. 1 Line a(cm“)^(cm“P l P6 P3 12 10 15 13 12 10 9 7 9 8 5 NH FundamentalVibration-RotationLines 2685.5 2724.8 2763.0 2522.7 2614.9 2519.1 2604.0 2645.2 2659.9 2747.4 2789.9 2950.1 3023.8 LAMBERT ETAL. TABLE 5 0.018 0.022 0.019 0.023 0.007 0.017 0.013 0.018 0.017 0.025 0.029 0.030 0.025 1/2 1 NH V-Rlines.ThedemotionofCNiswelcomedbecausethe by NmoleculeformationwiththeresultthatNHdensity does notexceedabout10%.ThepartialpressureoffreeNisset weak; weestimatethattheCNcontributiontoanNHline locus shiftswiththeadoptedOabundancesuchthat log €(N)-log£(C)plane—seeFigure5.IfCNisconsideredto plagued bytheuncertaindissociationenergy.With CN densityiscontrolledbytheC,N,andOabundances lines mayplayasupportingrolethankstothepresenceof effective temperature. scales approximatelyase(N).TheNabundancefor nately, theseCNlinesarepredictedandobservedtobevery neities (seebelow)arelikelytointroducesystematicerrors in decreasing temperature.Therefore,atmosphericinhomoge- CN linesincontrasttoCO,NH,andOHweaken with Alog 6(0)»Alog6(C).Forafixedchemicalcomposition, the CN-NH intersectionis0.25dexlessthanthatprovidedbythe be aCabundancemonitor,theprovidedby OH lines,theCNlines(Table6)providealocusin adopted modelandtheOabundanceprovidedbyCO role oftheNabundanceindicator.Inthisanalysis,CN this differenceof0.25dexisjustacceptable.Wenotethatthe CO lines. to theadoptedsurfacegravitybutmoderatelysensitive In thistemperaturerange,anNHline’sintensityisinsensitive 3800 K,logg=0.0,and£4kmsis 2 xe 0- 2. PA* 4609.60.024-2.160.956 2- 4 Q^O4508.90.032 -1.63 1.203 Band Linea(cm)Wloggfx"(V) 1- 3 P304623.70.027 -2.06 0.961 a 2 The CNlinesinspectraofGandKgiantsoftenassumethe If theseveralsourcesoferrorpeculiartoCNareassessed, 4.57-5 4.57- 5 4.53-5 4.44-5 4.32-5 4.11-5 1.29-5 1.40-5 1.45-5 1.54-5 1.57- 5 1.38-5 1.06-5 log gf 4.27-5 4.21-5 4.15-5 4.04-5 9.20- 6 3.89-5 3.66-5 1.22- 5 1.31-5 1.35-5 1.42-5 1.44-5 1.21- 5 032 4504.40.029 -1.62 1.231 Ri 295022.10.035 -2.27 0.702 058 4555.00.028-1.721.281 (L48 4703.80.036-1.791.040 g45 4553.80.037 -1.55 1.218 q44 4567.10.036 -1.56 1.198 P32 4598.00.028 -2.03 0.990 2 2 2 2 2 4.97-6 2.91-5 9.06-6 3.45-5 3.22-5 3.87-5 3.73-5 3.61-5 1.13-5 1.20-5 1.23-5 1.25- 5 1.26- 5 2 MicronCNRedSystemLines log €(N)=8.62. X" (eV) 0.527 0.496 0.469 0.474 0.686 0.599 0.561 0.362 0.311 0.221 0.181 0.061 0.024 TABLE 6 Vol. 284 1984ApJ. . .284 . .223L 0 No. 1,1984 together withtheCabundancederivedfromCOlines. further thatourlinelistiscomposedlargelyofmeasurements provided bytheCOlines.IfsolarCNlineswithindepen- light. Ontheotherhand,ouradopteddissociationenergy, dently determinedCandNabundancesareusedtoestablish experiments, theCabundancewouldbe0.8dexlessthanthat D° =7.9eVwereadopted,avaluesuggestedbyrecent D° =7.52eV,isatthelowendofrangesuggestedby our analysisbetweenCNandtheotherthreemolecules.Note may besubjecttoNLTEeffects(HinkleandLambert1975). 0.2 dexofthatfromCOforallreasonableD°values. the CNoscillatorstrengthsforagivenD°analyzingC abundance derivedfromtheCNlinesinaOriiswithinabout recent measurements.TheCNlocusinFigure5istranslated of the1980FeburaryspectrawhenaOriwasatminimum lation oftheCNlocusinFigure5.Inshort,linesare to linesoftheCNredsystemshowthaterrorsincurredbyour assumption thattheatmosphereisnotseverelyopticallythick shocktube experiment(seeAppendixB)andseveralearlier along theloge(C)axisbyAä—1.4AD(eV);if NH, andOHlines,butareexaminationoftheissuewillbe in theconstructionofthisfigure differslightlyfromthefinal Note thattheselectionsoflines andbasicmoleculardataused ciencies intheassumptionsbehindconstructionof the called foriffutureexperimentsputthedissociationenergy presently consistentwiththeabundancesprovidedbyCO, use ofLTEshouldnotamounttomorethana0.1dextrans- However, ourtestcalculationsbasedonthesimplifying choices sothatFigure6does notprovidetheabundances model atmosphere. higher thanD°=7.65eV. immaterial whenFigure6is usedtoobtainthetemperature quoted earlierforthestandard model,butsuchdifferencesare surface gravityontheabundancesaresummarizedinFigure 6. and logg),wecommentonpossibleinconsistencies defi- quences ofincorrectchoicesforthedefiningparameters (T discuss thisthirdfactor.Inadditiontosummarizingtheconse- spectra, and(iii)themodelatmosphere.Inthissection, we abundances :(i)thebasicmoleculardata,(ii)qualityof the and gravitydependencesof theabundances.Ourestimates AT =±100 K andAlog#=±0.3correspond toAloge= 0 0 0 0 0 0 eff eff Fig. 5.—AbundancesolutionsforNHandCNtheadoptedmodel As thesoleelectronictransitioninanalysis,CNlines Three principalfactorsdeterminetheaccuracyoffinal The effectsofalternativechoiceseffectivetemperatureand © American Astronomical Society • Provided by the NASA Astrophysics Data System c) TheAtmosphere C, N,ANDOABUNDANCESINBETELGEUSE -1 defining parameters,e.g.,theN/Oratiochangesbylessthan improved forTeff=3600K.ThedifferenceintheCabun- information fromCNandtheothermoleculesismarginally abundances by0.25dex.Theconsistencyoftheabundance 0.05 dexoverthesamerangeofATandAlogg.AtT= dances fromCOandCN(seeFig.5)of0.20dexatT=3800 abundance isreducedby0.12dex,theN(fromNH)andO current abinitiocalculationsofdemonstrablyhighaccuracy nate thesurfaceoradoptedOHoscillatorstrengthsaretoo essential ingredientcausingON-cycledmaterialtocontami- tionary calculations(see§V)predictmuchsmallerreductions sun by0.4dexifT=3600Kandlogg0.0.Stellarevolu- oscillator strengths,oxygenisunderabundantrelativetothe K iscutto0.12dexatT=3600K.WiththeselectedOH 3600 K,analternativeconsideredatthereferee’srequest,C would precludethissimpleexplanation—seeAppendixB.In large byafactorof3.Althoughrecentexperiment(Podolske of thesurfaceoxygenabundance.Then,aselection^ff— iterate ontheabundancesinordertoachieveagreement short, theoxygenabundancetendstoconfirmselectionof and Johnston1983)isconsistentwiththelattersuggestion, 3600 Kwouldrequirethateitherthesecalculationslackan discussion ofsuchaniterationshowsthatthecorrectionsare small fortheabundancedifferencesreportedhere.Hisfirstset between theadoptedandderivedabundances.Tsuji’s(1979) and molecularlineblanketing,itis,inprinciple,necessaryto of abundancesdifferedfromtheassumedvaluesby—1.17, ing theturbulentpressure.ModelsatT=3800Kand km s)giveabundancesfromCO,OH,andNHdifferingby log g=0.0withandwithouttheturbulentpressure(^3 consistent atthe±0.05dexlevelwithinputabundancesof 0.10 dexforC,N,andO,respectively.Ourfinalresultsare from thefirst(andinconsistent)setbyjust—0.03,—0.05,and tainty. Amajorityofourcalculationsusedmodelsnotinclud- the model.Turbulentpressureisanadditionalsourceofuncer- Tf =3800Kratherthanatemperatureof3600orbelow. only 0.02(C),0.00(N),and0.03(O)dex. sion oftheiterativeprocedure,finalabundancesdiffered ±0.15 dexorless.Abundanceratiosarelesssensitivetothe effe{{ eff eff eff + 0.88,and—0.01forC,N,O,respectively.Attheconclu- eff mic ef solid linesshowtheresultsfromCO, NH,andOH.Thebrokenlinesshowthe C abundancederivedfromCNlines and theONabundancesprovidedby the othermolecules. Since theatmosphericstructureisinfluencedbyatomic Fig. 6.—TheC,N,andOabundances asafunctionofTiffandlogg.The 231 1984ApJ. . .284 . .223L 4 -1 232 mental resultsareneededforvibrationalexcitationby H incomplete. Inparticular,additionaltheoreticaland/orexperi- from LTEintheV-RtransitionsofCOandOHcannotyet be atoms. ThefactthattheOHandCOcurvesofgrowth are provided becausethedataoncollisioncrosssections are (blue) wing;theemissionhasanequivalentwidthabout10% (and withtime,ifthenumberofgranulesisverysmall).On collisional dampingconstantisafactor ofabout1000largerthanexpectedfor and Lambert1975).Adefinitivecalculationofthedepartures ground statesshouldbeclosetoLTE(Thompson1973;Hinkle from thepredictedatmosphericstructure.Additionalobserva- is present.Itunlikelythattheweaklinesemployedinour models ;e.g.,granulationorawarmexpandingchromosphere lines areaccompaniedbyweakemissioninthehigh-frequency curve ofgrowthforOHlines.Possiblecausesthefailure (Piccirillo, Bernat,andJohnson1981). model atmospherequitesimilartoourspredictssatisfactorily ponents willaccountfortheempirical curveofgrowth. also showsthatneithertheexistence ofhyperfinesplittingnorsatellitecom- OH moleculesinthelowpressureatmosphere ofBetelgeuse.Aquickcheck Although thecurvemaybereproduced byatheoreticalcurve,therequired interest. dence thattherealatmosphereismorecomplexthanour that oftheabsorptioncomponent.Thisemissionisclearevi- exhibit adifferentweightingacrossthegranuledistribution (more generally,avelocityfieldwithrelativeflowsofatleast This providesapartialcheckonthemodelatmosphere.In the observedfluxdistributionfromvisibletoinfrared. tion overlapsthatofthecontinuum.Tsuji(1979)showsa Goldberg etal.(1982)fromspeckleinterferometrythrougha20 tions tomonitortheOH(andother)profileswouldbeof abundance analysisareseriouslyaffectedbythisdeparture Clearly, differentpropertiesoftheemergentspectrumwill giant mightbecomposedofasmallnumberlargegranules. boundary temperature. widths totheobservedvalue.Thecentralintensityofcores photosphere; thepresenceofsupergranules(Schwarzschild steep gradientofthemicroturbulenceinupperphotosphere the modeltopredictobservedcurveofgrowthinclude:a understood surfacedwhenweexaminedthestrongerCOand and theempiricalrelation(Ridgwayetal.1980)agreeverywell the Wingsystemandeffectivetemperaturefrommodels addition, thepredictedrelationbetweencolortemperatureon decay ofactiveregionsandtheirrotationacrossthedisk are uting about0.08magtotheintegratedbrightness.Growth and Á bandpassat6500Â.Theirpreliminaryreportdiscussesa of thestrongestCOlinesat2.3and5.0/unsetalimiton ably notbereducedsufficientlytoincreasetheequivalent atmosphere (see§IIforadiscussionofatmospheric OH lines—see,forexample,Figure2showingacomposite ation atvisiblewavelengths(Hayes1980). suggested bytheobservationsofchangesinlinearpolariz- single observationinwhichtheyfoundabrightspotcontrib- sphericity). Theupperphotospherictemperaturescanprob- 1980 February5spectrum,thestrongAv=1OHabsorption 1975); departuresfromLTEand/orplane-parallelismofthe 1-3 kms);asteepertemperaturegradientintheupper 4 Theempiricalcurveofgrowthissuggestive ofalargedampingconstant. Our analysisisbasedonweaklineswhoseregionofforma- The vibrational(androtational)levelsoftheelectronic Direct evidenceforsurfaceinhomogeneitieswasprovidedby Evidence thattheformationofstrongerlinesisnotfully Schwarzschild suggestedthatthesurfaceofacoolsuper- © American Astronomical Society • Provided by the NASA Astrophysics Data System LAMBERT ETAL. 13 -1 -1 (1979) modelatmosphereanalysis consideredCO,OH,and certain earlieranalysesweregivenin§I.Here,wereferto the confirm theseveralearlierreportsofalargeCdeficiencyin the from thesolarabundanceisnotreallysignificantinlight of may alsohaveamoremundaneexplanation—thedifference papers byTsuji(1979)and Jura andMorris(1981).Tsuji’s the abundanceuncertainties. ciency, [O]=—0.15,mayreflecttheoperationofslower the atmospherewithCN-processedmaterial.TheslightO defi- currently loge(C)=8.4,e(N)8.6,ande(O)8.8. atmosphere. Briefexplanatorycommentsoninadequacies of ON-cycles (orevenhighertemperaturenuclearprocessing) but total C,N,andOabundancepointstothecontamination of strong Nenrichmenttogetherwiththeconservationof the The C/Nratioisdistinctlynonsolar,[N/C]=+0.9. This have beenconserved. uncertainties arerecognized,itappearsthattheCNOnuclei compare thetotal(includingC)CNOabundance:wefind position changes,conserveCNOnuclei,itisofinterestto changes. Ourresultsgive[C/O]=—0.18and[N/C] Hence, theabundanceratiosC/N/Oarelessaffectedbysuch log 6(C)=8.41,€(N)8.62,ande(O)8.77.The cules, and(iii)theCNmoleculewithadifferenttemperature variation ofthemolecularabundanceswithtemperatureand weak linesareusedfortheabundanceanalysis,(ii)(LTE) line formation.Thisasertionismadeonthreegrounds:(i) sphere parametersareofthesamesignforthreeelements. abundances arisingfromadjustmentstothethree-modelatmo- tributed byourinadequaterepresentationoftheatmosphere log öf,andequivalentwidthuncertaintiesareabout enhancement [Fe/H]where^4-0.1islikely.The pressure changesaremoderatelysimilarforthesethreemole- arising fromourinadequatemodelingoftheatmosphereand chromosphere. could beviewedastheheatingmechanismunderlying were takenfromtheliterature: Spinradetal.(1970)forCOand and deficienciesinthemoleculardata.Correctionsto abundance uncertaintiesarisingfromin star’s initialcompositionmustbedecreasedbythemetal is metalrich,thedifferences[X]abundancerelativeto abundances relativetothesun(Lambert1978)are[C]= OH analysis. sensitivity generallyconfirmstheresultsofCO,NH,and abundance indicatorsshouldminimizethesystematicerrors the observedonesisimproved.Theincreaseinturbulence the photosphere,fitofpredictedequivalentwidthsto problem. provided theCNequivalent widths.Amodelatmosphere [CNO] =—0.04relativetothesun;i.e.,whenabundance similar maybeevidencethatNLTEisnotattherootof Beer etal.(1972)forOH.Photographic 8Âmmplates CN lines.Equivalentwidths of CO2-0andOHAi;=1lines 3800 K,logg=0.0,£4kms)providetheabundances 4-0.96. SincetheCNOcycles,aprobablesourceofcom- — 0.26,[N]=+0.63and[O]—0.15.If,asexpected,aOri + 0.15dex.Systematicandill-defineduncertaintiesarecon- -1 Comment issurelyrequiredonthefactthatwedidnot In summary,thecompositionofBetelgeuse’satmosphereis The CO,NH,andOHlineswiththeadoptedmodel(T= Our selectionofCO,NH,andOHlinesastheprimary If themicroturbulenceincreasesto10kmsattopof eff v. DISCUSSION Vol. 284 1984ApJ. . .284 . .223L 124 124 12 124 1462 1462 146 1 _1 146 162 extrapolated resultsfora15Mstar.Theseobserved and favorably withthepredictions:[C/N]=—0.81to—0.96, predicted ratiosareingoodagreementconsideringtheremain- with thesolarratiosofC,N,andO.Theseresultscompare (have) suffer(ed)thesmallincrementalchangeinCNOabun- from sphericallysymmetricand/ortheCatomsinshellare are considered.Theobservedchanges[C/N]=—0.96, sphere ontheabundancesisreducedwhenabundanceratios dredge-up, BeckerandIben(1979)predict[C]=—0.19, dredge upprocessedmaterial(seeLamb,Iben,andHoward vective envelopeofaredgiantorsupergiantispredictedto deserve scrutiny. factor of3lessthanourphotosphericabundance.Juraand (1984) toahigherCabundanceanddeficiencyof6 assumed tobeslightlymetalrichrelativetheSun[Fe/H]= star ofmass15M,oneobtains[C]^—0.22,N] their predictionsfor7,9,and11Mstarsareextrapolatedtoa their Table6D),themostmassivestarconsideredbythem.If dances resultingfromtheseconddredge-up.Forfirst dredge-up at8-10M©and,therefore,aOriisunlikelyto and Becker(1978)puttheuppermasslimitforasecond the redgiantbranchfollowingHecoreexhaustion.Kaler,Iben, up ispredictedforintermediatemassstarsontheirreturnto CN-cycle processedmaterialintheatmosphere.Thedeepcon- not associatedintoCOmolecules.Theseandotherfactorsnow sources oferrorintheiranalysis:theexpandingshellisfar solar Cabundance(Lambert1974)dididentifytwopossible for example,Tsuji(19766)adopted A=0.68mag.Two(B—V) brightness ofthecircumstellarKiemissionledMauronetal deficient byafactorof25.Newobservationsthesurface from observationsofthecircumstellarCOradioemissionand mag (Johnston 1967)and0.18mag(Lee1970) whichwitha measurements andassumedintrinsic colorsgaveE_=0.22 [N/0] =+0.56to+0.79,andC/-0.15 to [N/0] =+0.78,andC/-0.08ifaOribegan Morris notingourearlierandpreliminaryreportofanear- the Ki7699Âfluorescentemission.Carbonwasreportedtobe model atmosphereandspectrumanalysisprogramsarenotthe within 0.1dexofourresult.Thisagreementshowsthatthe No. 1,1984 [N] =+0.53,and0]—0.04fora11Mstar(see log g=0.0,and£3kms"modeltoobtainaCabundance line portionofourcurvesgrowth.Dr.Tsujiverykindly lines ofCO,OH,andCN.Nonetheareonweak- analyzed oneofourCOlineswithhisT=3800K, turbulence assumedbyTsuji(£=9kms)inanalyzingthe result. TheNandOabundancesarewithin0.2dexofour underabundance byafactorof20,i.e.,10belowour origin ofthediscrepantCabundances. values. Thediscrepancyis,inlargepart,duetothehighmicro- analysis withT=3900±150Kandlogg0.0ledtoaC 1976 fordiscussionofa15Msupergiant).Aseconddredge- 0 — 0.12,wherethesecondentryforeachquantityrefersto the -0.43, [N]=+0.53,and0]-0.25ifaOriis + 0.1.Asdiscussedabove,theinfluenceofmodelatmo- 0 0 + 0.69,and[0]æ—0.10.TheobservedvaluesareC= v BV 0 eff eff 0 13 The highNandCabundancespointtothepresenceof The totalextinctionforaOri isoftensetnearA«0.7mag; Jura andMorris(1981)derivethephotosphericC/Hratio v © American Astronomical Society • Provided by the NASA Astrophysics Data System INTERSTELLAR ANDCIRCUMSTELLAR EXTINCTION C, N,ANDOABUNDANCESINBETELGEUSE APPENDIX A 121314 121313 1213 16178 1213 1213 1213 Houston, Texas. this researchhasbeensupportedinpartbytheNational Gustafsson fortheirhospitality.AttheUniversityofTexas, perature. ApartofthepaperwaswrittenwhileD.L. on lar, forthesuggestionthatweconsideralowereffective tem- enthusiastic assistancewiththecalculations.Wethank the sabbatical leave.HethanksProfessorP.ErmanandDr. B. anonymous refereeforconstructivecommentsand,inparticu- Science Foundation(grantsAST79-22014,79-13109, 81- trell forassistanceatthetelescope,andDr.J.F.Dominyhis V-R transitions.WealsothankDrs.J.TomkinandP.L.Cot- discussions onthe/-valuesfortheCNredsystem,andMr.D. B. SlavskyforcomputinglinestrengthstheOHandNH helpful correspondence,Dr.B.Gustafssonforacriticalreview of theCO/-values,Dr.M.Larssonforextensiveandlively of adraftthepaper,Dr.R.H.Tippingforprovidinglisting third (uncertain)estimateof E_=0.16mag(Eggen1973) provided ameanE_=0.19 magandAJE_=3.6(Lee 17485, and82-05800)theRobertA.WelchFoundation of means. tasks maybetackledandsolvedwithcurrentlyavailable range intheCNOabundances.Aconsiderablenumberofthese propose thatexistingcalculationsunderestimatethesizeof of redsupergiantsshouldbeanalyzedinordertodeterminethe star withanonstandardinitialcomposition.Finally,sample supergiant aresimplytheresultofstandardevolutiona the possibilitythatunexpectedCNOabundancesinared ing spectraobtainedatdifferenttimes.Carefulstudiesofthe lines andtheCNdissociationenergy;(iii)athoroughstudyof more precise.Thiswillrequire:(i)accuratemeasurementsof dance ratio.WenotethatCloutmanandWhitaker(1980) without amajorperturbationofthepredictedC/N/Oabun- cessing ofCtoandNcanbeaccomplished CNO abundancesinOBstarsareneededordertoeliminate the atmosphericstructure;(iv)reobservationandanalysisat the strongmolecularlinesinordertogleaninformationabout rate determinationoftheband/-valuesCNredsystem identifying severalkeytasks.TheCNOanalysiscouldbemade relative tothepredictionisuncertain,butadditionalpro- predicted C/(~20)values.Theoriginoftheexcess ing uncertainties.TheC/ratiopointstoadeficiencyin several differentphasestoeliminateerrorsincurredbycombin- the V-RtransitionprobabilitiesforOHandNH;(ii)anaccu- tion isreached,additionalworkessential.Weconcludeby discuss the0/ratios. the calculations.TheobservedC/ratio(6)isbelow and lowerC/ratios—seeHarrisLambert(1984)who development oftheconvectiveenvelopewillalsoproduceC/N calculations throughtothedredge-up.Masslossprior 1970) gave=0.68mag. the redgiantbranch.Unfortunately,theydidnotfollowtheir result inlowerC/NandC/ratiosafterthedredge-upon convective core.Alargercoreandasmallerenvelopeshould BV BV BV We thankDrs.T.Tsuji,G.C.Augason,andW.J.Stevensfor Intrinsic colors ofMsupergiantswerechecked byJohnson Before acompleteunderstandingofOri’ssurfacecomposi- 233 1984ApJ. . .284 . .223L -1 1216 1216 samples ofearly-typestarsandMsupergiantsintheh% and Mendoza(1966)whoobtainedthesameE_from 234 colors. ObservationsofthesouthernMsupergiantHD90586 valid checkontheMstars’intrinsiccolorsbecauseneither within asubclassofOri.HD90586hasnearbybluecom- measurements ofaTiOindexshowthatthissupergiantis stellar samplehadbeenusedtoestablishtheadoptedintrinsic Per seicluster,andthenremarkedthatthisobservationwasa also offeracheckonthesecolors.WhiteandWing’s(1978) panion withE_=0.45mag(Humphreys,Strecker,andNey we deducethatE^=0.26magforaOri,anestimateslightly larger thanTsuji’sadoptedvalue. vations ofareddening-independentTiOindexandnear- infrared color.ObservationsofbrightMgiants,whichare color calibration.Whiteassumesthatthiscalibrationisapplic- assumed tobeunreddened,providetheTiOindex-intrinsic weaker insupergiantsunlessthemicroturbulenceislargerthan BV able toMsupergiants.However,TiObandsarepredictedbe 1972). Ontheassumptionthatpairformaphysicalsystem, in giants(Johnson,Mould,andBernat1982;Johnson lines inthe5600-6700cmatmosphericwindow. a coolstar.OurabundanceanalysisusestheC0At;=3 state ofCOareprominentfeaturestheinfraredspectrum Steinman-Cameron 1982).Aroughestimateis»0.5mag BV lines frommolecularconstants.Weadoptoscillatorstrengths been measured.Wecomputedthefrequenciesforadditional BV employ adipolemomentfunctionwhichisderivedfrommea- provided byChackerianandTipping(1983).Theircalculations These newresultsdonotdiffersubstantiallyfromanearlier leading bandsofthesequences;e.g.,1-0,2-0,3-0,and4-0. surements oftheline(orband)absorptioncoefficientsfor Av =3C0linesislessthan0.1dex.Theoscillator recipe (Tipping1976).Themeandifferenceoverthesampleof energy asthetransitionmatrixelementdependsmoreheavily expected toincreasewithincreasingvibrationalandrotational in theabundanceanalysis.Asystematicerrorcould be bands intheAv=3sequenceor±20%forlinesemployed strengths shouldbeaccurate(±10%)foratleasttheleading calculations byKirby-DockenandLiu(1978).Thetheoretical surements ofcoolorcoldCOgas. outside therangecoveredadequatelybylaboratorymea- on thedipolemomentfunctionatinternuclearseparations for thestellarlinesinourlist. Thedifferenceislargerforthe results fortheAv=2sequenceareabout10%to15%smaller which havebeenthesubjectof severallaboratoryexperiments, difference increasestoabout 70%forhighmembersofthe smaller forlowrotationallines intheP-andR-branches.The Av =3sequencelines.Thetheoretical resultsareabout40% v appearance ofthesedifferences forthelow-excitationlines, P-branch anddecreasestonear 20%fortheP-branch.The 1+ White (1980)reportedA=0.71magforaOrifromobser- The vibration-rotationtransitionswithintheZground Precise frequenciesformanyvibration-rotationlineshave v We havecomparedtheoscillatorstrengthswiththeoretical © American Astronomical Society • Provided by the NASA Astrophysics Data System a) CarbonMonoxide BASIC DATAFORMOLECULARLINES LAMBERT ETAL. APPENDIX B 3 1 3- Note thatthisestimateincludesthenongraycontributionof pending adirectcalibrationoftheTiOindexinsupergiants. from acolorindexincludecircumstellarcontributiononlyto circumstellar grains,whereasstandardAestimatesderived lar grainsissmallunlessthegrainalbedoremarkablyhigh. excess infraredemissionrepresentsasmallfractionofthetotal circumstellar contributiontoAisprobablysmall.Sincethe the extentthatdustshellaroundaOridiffersfromtypical Orion stars.However,interstellarextinctionispatchy.The appropriate becauseaOriisprobablylessdistantthanthe A ä0.2-0.3mag(Lee1970).limit<0.3seems shell ofthesampleusedtoderiveintrinsiccolor. mined, buttherange0.3mag<0.8islikelyto stellar luminosity,theextinctionintroducedbycircumstel- encompass thetruevalue. by theinterstellargrains. strongly at11fim,couldsupplementtheextinctionprovided away fromthestar.Suchcoldgrains,whichwouldnotemit Mass lossoveranextendedperiodmayhavedrivengrainsfar v v v adopted oscillatorstrengths. suggests thatthetheoreticalresultsarenotasaccurate initio calculationoftheX2TstatewasreportedbyDas, ignored untilrecentlybylaboratoryspectroscopists.Fre- method ofOptimizedValenceConfigurations,whichisdis- Wahl, andStevens(1974;seealso1973)whopredicted quencies forlinesofthe1-0bandfromP(4)toP(5).Anab quency predictionswerediscussedbyLambertandBeer. markedly strongerthantheirP-branchcounterparts. Our cussed indetailbyWahlandDas(1970),wasalsoappliedto the bandoscillatorstrengthsforV-Rtransitions.Their Bernath andAmano(1982)havesinceprovidedaccuratefre- ed andobservedvariationofalongtheP-P-branches combined thedipolemomentfunctionprovidedbyDas,Wahl, responsible forthiseffectwasconfirmedbyacalculation. We OH (seebelow). comprising atripletwastakenintoaccountinthepredictions. and StevenswiththeRKR-potentialenergycurvefor X suspicion thatthevibration-rotationinteraction was The accuracyoftheg/valuesislikelytobecomparable the are comparedinFigure5;thesplittingofcomponents members. Thegreaterpartof thisdifferenceoriginateswiththe branch areapproximatelytwice asstrongtheP-branch tainty of±25%.Itisseenthat thestrongestlinesinP- similar predictionsforOHwhichweestimateanuncer- X statetoobtainthegf-valuesgiveninTable5.Thepredict- P-branch islargelyresponsible fortheunusualvariationofW V-R interaction.Thechange inthetripletsplittingalong with N". a 3- Betelgeuse isnearthe“OrionNorthwest”regionwhere In summary,theextinctionforaOriisnotyetwelldeter- The V-RtransitionswithintheEstateofNHhavebeen Inspection ofFigure5showsthattheP-branchtripletsare b) TheImidylRadical Vol. 284 1984ApJ. . .284 . .223L 2 No. 1,1984 parison forthefirst-overtonebandsgives/(OVC)//(CI)» 1.3, near theequilibriuminternuclearseparation.Asimilarcom- tent withthedifferentslopesofdipolemomentfunctions is approximately1.6,1.8,2.0,and2.3forthebands1-0, 2-1, line list:theratio/(OVC)//(CI)forarepresentativestellar line dipole momentfunctionpredictsloweroscillatorstrengths for change inthedipolemomentfunction.Wefindthat Cl figuration calculationisslightlysuperior.Ourcalculations are molecular propertiessuggeststhattheoptimizedvalencecon- (configuration interactionorCl)calculation(Chu,Yoshimine, forming ourowncalculationswithtwodipolemomentfunc- (1974) foradiscussionoftheirabinitiomethodOptimized fi =1.660±0.010D.ThereaderisreferredtoStevensetal. example: thedissociationenergyD=4.53eVfitsobserved mentally determinedpropertiesoftheOHgroundstate;for molecular potential.Thetheoreticalcalculation(Stevensetal. from Mies(1974)whomadeadetailedcalculationofOHtran- (Carlone andDalby1969). value D=4.63,andthecomputeddipolemomentfor tric dipolemomentfunctionandacompositeRKR-theoretical is welldeterminedfromspectroscopy:D°=4.391±0.002eV for Ai;=1and2linesareprovidedbyMaillard,Chauville, (Graham andLew1978;Zetzsch1978). moment function;forexample, Murphy(1971)measureda fundamental transitionsoffers atestoftheoreticaldipole tively. Theratiooftheoscillator strengthsforfirst-overtoneto the P-branchfundamentallineswhichcompriseBetelgeuse spin-uncoupling, theresultsareindicativeofeffect of a based uponanRKRpotentialandnumericalevaluationof the provide reliableabsoluteoscillatorstrengths. necessary test.Fortunately,Miesnotedthatrelativeoscillator interest. Availablemeasurementsofabsoluteoscillator the predictedandobservedOHproperties. Valence Configurations(OVC)andadetailedcomparisonof ground staten=1.680Disclosetotheexperimentalvalue sition probabilitiesbycombiningatheoreticallyderivedelec- for initialmembersoftheQ-branch. Miesnotesthathiscalcu- 3-2, and4-3,respectively.Thesenseoftheratioisquiteconsis- transition matrixelements.Althoughwedonotinclude the and Liu1974).Acomparisonofthepredictedobserved tions: theStevensetal.functionandasecondabinitio scale ofthedipolemomentfunction.Hiscalculationsshould shows howtheavailablemeasurementsconfirmshapeand several bandshavebeenmeasured.Mies(1974,pp.170-171) tion. Relativeoscillatorstrengthsforfundamentalandfirst- strengths provideanexcellenttestofthedipolemomentfunc- Cerny 1973)arenotofsufficientaccuracytoprovidethe strengths (seeMiesforreferences;alsoRoux,dTncan,and theoretical andexperimentaloscillatorstrengthswouldbeof OH oscillatorstrengths,adirectconfrontationbetweenthe transitions oftheXHgroundstate.Accuratelinepositions transition probabilityratio a =A(2,0)/A(2,1)0.44±0.03 overtone linesandthestrongvibration-rotationinteractionin Mantz (1976)andBeer(1975).ThedissociationenergyofOH 1.3, 1.4,and1.5forthe2-0, 3-1, 4-2,and5-3bands,respec- 1974) predictstoasatisfyingprecisionvarietyoftheexperi- e e 0 We attemptanassessmentoftheoscillatorstrengthsbyper- Although theircomparisonencouragesconfidenceinthe Oscillator strengthsfortheOHlineswereoriginallytaken The OHradicalisdetectablethroughthevibration-rotation The NHdissociationenergyissetatD°=3.46±0.03eV 0 © American Astronomical Society • Provided by the NASA Astrophysics Data System c) TheHydroxylRadical C, N,ANDOABUNDANCESINBETELGEUSE -201 -192 -201 /-values willplaceallOH lines onthepredictedcurveof 4-3 and3-2bandsdefinea curveclosetotheshapeof celation. The4-3bandisimportantbecauseitprovidesmany dance analysis.Itappearsunlikely thatuseofWernereta/.’s predicted curveofgrowth,the 4-3/-valuesareprobablynot dently ofassumptionsaboutthemicroturbulence.Since the bands toalesserextent)mayalsobeaffectedbythe can- curve fromthe1-0to4-3bands.Theband(andother cessful; theupperlimitsonequivalentwidthdonotallow growth. seriously inerror.The5-4band isnotincludedintheabun- of theweaklineswhichyieldanabundancealmostindepen- us todetermineifthebandfallsonextensionofsmooth atomic wavefunctions.Asearchforthe6-5bandwasunsuc- note thatthissensitivityarisesfromthemolecular(vibrational) The astronomermorefamiliarwithatomicspectroscopy may ities forthe5^4andadjacent4-36-5bands were ment andtheMCSCF-SCEPpredictionwouldseemtofall analog ofseverecancelationtheradialintegralinvolving sensitive tothepreciseshapeofdipolemomentfunction. his Fig.2andaccompanyingtext)thatthetransitionprobabil- by thelinesfrombands1-0throughto4-3.Miesnotes(see band displacedbyabout0.5dexfromthesmoothcurvedefined values. Acurveofgrowth(Fig.2)showsthelinesfrom5-4 from Mies’scalculations(seeGillisandGoldman1981) measured anintegratedabsorptioncoefficientof Johnston (1983)usingatunablediodelasertosenseOH sequence confirmedonelimitationofMies’stheoretical/- outside therangepermittedbyabinitiocalculations. 5 ^7.1x10cmmolfromWerner,Rosmus,and sition. ThiscompareswithS=1.06xlOcmmol The adoptedoscillatorstrengthsareprobablyaccurateto This compromiseisnotexpectedtoresultinasignificanterror. is basedonacombinationofMies’sresultsforthe4-3band Reinsch (1983).Thefactorof2discrepancybetweenexperi- S =(3.3±1.5)x10cmmolfortheP!-^^)tran- normalized totherotationlessA-valuelistedbyWerneretal. dipole momentfunctionissuperiortotheOVCprediction used byMies(Sauvaietal.1984).Ourfinalabundanceanalysis v" =0,1,and2levelsalsosuggeststhatWernereta/.’selectric ed byreactionswithknownrateconstants(H+N0andH who measuredtheinfraredemissionfromOHradicalsproduc- noted thattheirpredictedA-valuesagreedtowithinabout the bands1-0,2-1,3-2,and4-3,respectively.Werneretal. the OVCresults:/(OVC)//(SCEP)=1.5,1.4,1.3,and1.1for lower rotationlessEinsteinA-valuesthanMiespredictedfrom calculation appearstobesuperior.Theratio/(OVC)//(CI) MCSCF-SCEP wavefunctions.Theircalculationsprovide Rosmus, andReinsch(1983)publishedcalculationsbasedon surely indicatesthemaximumerror. experimental ratioh=1.15±0.05isnotquitesowellmatched b =7.4-2.6forlowPlines.Onthebasisofthesetests,OVC by Mies’scalculations;hisaverageisb=1.62witharangeof 10% withestimatesbyArgawalla,Manocha,andSetser(1981) substantially larger.Theratiob=A(3,1)/A(3,0)withamean the Cldipolemomentfunctiongivesavalueofwhichis lations reproducedthisratioora=0.46±0.06.Wefindthat ±25%. 2 + C10).Analysisofsolarpurerotationtransitionsfromthe 1.34—2.44. WefindthattheCldipolemomentfunctiongives 2 Our analysisofthestellarequivalentwidthsforÀf=1 A discordantnotemustbeacknowledged.Podolskeand As ourabundanceanalysiswasbeingcompleted,Werner, 235 1984ApJ. . .284 . .223L 236 dipole momentfunction,and,therefore,theselineswould line portionofthecurvegrowth.Thehighdensityin Unfortunately, oursearchdidnotlocateOHlinesontheweak appear tobesuperiorabundanceindicatorstheAi;=1lines. the weakOHlinesfallinregionsoflowatmospherictransmis- Av =1lines. C abundance)consistentwiththeresultprovidedby sion. TheweakestOHlinesprovideanOabundance(atafixed providing observablelinesfromtheredtonear-infrared. weak blanketofunresolvablelines.TheAv=—2sequence Initially, weselectedlinesfromtheAv=+2sequencearound (Table 6)oflinesfromthe0-2,1-3,and2-4bandsisbuta near 2fimdominatestheabsorptionlinesthere.Ourselection initio calculation(Larsson,Siegbahn,andÀgren1983).These the Av=—2sequenceisunavailable—seeSnedenand small representativesampleoftheavailablelines. 8000 ÂbutrejectedthemwhenwerealizedthatTiOprovidesa 1.6 fimwindowisoneresponsiblefactor.Inaddition,manyof published byCartwrightandHay(1982—seealsoSneden predictions aresimilartobutmoreaccuratethanthose results. Fortunately,accurate/-valuesareprovidedbyanab Lambert (1982)whosummarizetheavailableexperimental Augason, G.C.1980,privatecommunication. Argawalla, B.S.,Manocha,A.andSetser,D.W.1981,J.Phys.Chem.,85, Auman, J.R.,andWoodrow,E.1975,Ap.J.,197,163. Auman, J.R.1969,Ap.J.,157,799. 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Goldberg, L.,Hege,E.K.,Hubbard,N.,Strittmatter,P.A.,andCocke, W. Gillis, J.R.,andGoldman,A.1981,Quant.Spectrosc.Rad.Transf.,26,23. Engleman, R.,andRouse,P.E.1975,J.Quant.Spectrosc.Rad.Transf.,15, 831. Eggen, O.J.1973,Pub.A.S.P.,85,289. Faÿ, T.D.,Stein,W.L.,andWarren,H.Í973,inProc.Conf.RedGiant Faÿ, T.D.,andJohnson,H.R.1973,Ap.J.,181,851. Hall, D.N.B.,Ridgway,S.T.,Bell,R., andYarborough,J.M.1978,Proc.Soc. Gustafsson, B.,Bell,R.A.,Eriksson, K.,andNordlund,A.1975,Astr.Ap.,42, Graham, W.R.W.,andLew,H.1978, CanadianJ.Phys.,56,85. Goon, G.,andAuman,J.R.1970,Ap.J.,161,533. Hayes, D.P.1980,Ap.J.(Letters),241, L65. Harris, M.J.,andLambert,D.L.1984, Ap.J.,281,739. Hinkle, K.H.,Lambert,D.L.,andSnell, R.L.1976,Ap.J.,210,684. Hinkle, K.H.,andLambert,D.L.1975, M.N.R.A.S.,170,447. 2+ The/-values oftheAv=2linesarenotsosensitiveto 2873. AAS, 11,645. The CNredsystem(AIl-X£)isanelectronictransition 89, 840. 172,89. J. 1982,inSecondCambridgeWorkshoponCoolStars,StellarSystems,and Stars (Indiana:AstronomyDepartment),p.147. 407. Rept., No.392),Vol.1,p.131. the Sun,ed.M.S.GiampapaandL.Golub(SmithsonianAp.Obs.Spec. A directandaccuratemeasurementoftheband/-valuesfor Photo-Opt. Instrum.Eng.,172,121. © American Astronomical Society d) TheCNRadical LAMBERT ETAL. REFERENCES Provided bythe NASA Astrophysics Data System lations andascalingfactorobtainedfromtheirpredicted reproduce thelimitedavailableexpetimentalresultsonred impossible toquantify;Larssonetal.write“onecanprobably system andtherelative//^valuesderivedbySneden Lambert 1982).Larssonetal.notethattheircalculations from Larssonetal.andtheCNabundanceseither the adopted/-valuestobeaccurateabout±15%. Lambert (1982)fromthesolarspectrum.Inshort,weexpect choice ofamodelsolaratmosphere;thisderivationisbasedon lines giveD°=7.51±0.05eValmostindependentlyofthe also beusedtoestimateD°;forexample,the0-0lineswith/ safely statethat7.4