1978ApJ. . .226. .2313 The AstrophysicalJournal,226:231-239,1978November15 © 1978.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. constant mass.Theobservationalfeaturesthathave retical computationsinwhichastarevolveswith diagram hasnotbeencompletelyexplainedbytheo- unbroken distributionofstarsbetweenspectraltypes been mostdifficulttoexplainare(1)anapparently rapid thinningoutofthedistributionforspectral O andearlyA,forlog(L/L)>4.5;(2)arelatively the constructionofmodelsluminousstars, a “gap”atspectraltypeMforlog(L/L©)>5.3. subtypes laterthanB3,iflog(L/L©)>5.3;and(3) choice ofradiativeopacitieshasturnedouttobethe most important.IfthefamiliaropacitiesofCoxand tween thebluemain-sequencestarsburningcore Stewart (1965,1970)areadopted,thenasignificant hydrogen andthebluesupergiantsburningcore “gap” ispredictedtoexistontheH-Rdiagrambe- feature 1mentionedabove;nor,asitturnsout,can helium. Inthiscase,itimpossibletoaccountfor features 2and3besimultaneouslyexplainedwiththe 0 provement atveryhighmassesisobtained.Onthe models basedonCox-Stewartopacities,someim- same setofphysicalassumptions(StothersandChin features 2and3canbeexplained(ChiosiNasi lost duringtheearlypartofmain-sequencephase, assumption thatasubstantialfractionofthemassis feature 1isonlylessened,notremoved. Sreenivasan 1978).Butthedifficultypresentedby Sreenivasan andWilson1978;Chiosi,Nasi, explained withouttheassumption ofanymasslossat 1976). However,whenmasslossisintroducedintothe opacities areadopted,features 1and2arepartially principal reasonforthisdifference inresultsisthat all (StothersandChin1977a, hereafterPaperV).The the newopacitiesareverylarge intheCNOionization 1974; deLoore,DeGrève,andLamers1977; The observedpatternofstarsatthetopH-R Among thebasicphysicalassumptionsthatgointo On theotherhand,whennewCarson(1976) © American Astronomical Society • Provided by theNASA Astrophysics Data System investigated forstellarmodelsinwhichCarson’sopacitieshavebeenemployed.Severalcases blue andredsupergiantscanaccountwellfortherelevantobservationsofOBNstars,WN adequately forthepropertiesofBsupergiantslowestluminosity.Acriticalcomparison of masslosshavebeenconsidered.Itisfoundthattheassumptionheavyfromboth is madebetweenthepresentresultsandsomeearlierbasedonadoptionofCox- stars, andveryluminoussupergiantsofallspectraltypes.Butnoamountmasslosscanaccount Stewart opacities. Subject headings:stars:evolution—interiorsmasslosssupergiants The effectofastellarwindontheevolutionstarsinmassrange7-60M©hasbeen STELLAR WINDSANDTHEEVOLUTIONOFLUMINOUSSTARS NASA GoddardInstituteforSpaceStudies,FlightCenter,NewYork I. INTRODUCTION stars: winds Richard StothersandChao-wenChin Received 1978May1;accepted26 ABSTRACT 231 zone underconditionsoflowdensity;consequently, the radiiofstarswithveryhighmassescanbecome the phaseofcoreheliumburning.Butthesetheoretical hydrogen burningandthereafterremainsoduring enormously extendedevenduringthephaseofcore to investigatewhethertheadoptionofmasslossin high masses.Itisourintentioninthepresentpaper models stilldonotaccountverywellfortheblue tion forthesetwoparticularobservationalproblems. form ofastellarwindintheoreticalmodelsbasedon at allfortheabsenceofredsupergiantswithvery supergiants withlowmasses,andtheydonotaccount loss fromstarsofhighluminosityaresummarized. Carson’s opacitiescanprovideanadequateexplana- presented in§§IVandV.Comparisonwiththe models arenotedin§III,andthemodelresults relevant observationsismadein§VI.Finally,VII Special assumptionsneededtocalculatethestellar contains asummaryofourmainconclusions. most likelymechanismofmasslossfromearly-type been madetotheoreticalestimates.Atpresent,the stars areveryuncertain;therefore,recoursehasoften Abbott, andKlein1975).Alternatively,iftheobserved loss couldbeanywherefrominsignificant(Lucyand stars isaradiation-drivenstellarwind.Butdepending are importantinabsorbingradiation,therateofmass line broadeninginearly-typesupergiantsisdueto on thedegreetowhichsubordinatespectrallines could alsoexpelmassatalarge rate(Hearn1975).In macroturbulence, thentheimpliedacousticflux Solomon 1970;Lucy1975)toquitelarge(Castor, either case,theoryandobservation indicatethatthe with luminosityandradius (fortheobservations, rate ofmasslossfromearly-type starsincreasesboth see, e.g.,Hutchings1976). In §II,theknownmechanismsandratesofmass Observed ratesofmasslossfromhighlyluminous II. MASS-LOSSRATES 1978ApJ. . .226. .2313 1 1 -1 2-1 the ratecouldbeashigh~0.5M©yr“(Bisnovatyi- unidentified butisprobablyrelatedtothepowerful to alocaldensityinversion(Peterson1971;Bisnovatyi- may developdynamicallyunstableatmospheresdue these stars.Observationsindicatethattherateof convection andpulsationintheouterenvelopesof mass, asaresultofsomemechanismthatisstill major consequenceoftheinstability(Wentzel1970; mild outbreakofconvectionmaywellbetheonly radius (GehrzandWoolf1971;Sanner1976;Bernat Bisnovatyi-Kogan 1973). Kogan andNadezhin1972;Schmid-BurgkScholz mediate spectraltypeandofveryhighluminosity L, R,andMareexpressedinsolarunits.)Anadopted considered fourcasesforillustration. to usbelittlepointinattemptingdoanything types ofluminousstarsaresouncertain,thereseems outflow increasesbothwithluminosityand Kogan andNadezhin1972).Ontheotherhand,a tion ofthemass-lossrate.Accordingly,wehave 232 more sophisticatedthantoadoptasimplerepresenta- tionally forbothearly-typeandlate-typesupergiants. value ofk=1x10"producesratesthatarevery 1975). Ifthisinstabilityleadstoanoutflowofmatter, type supergiants.Inthiscase,equation(1)isapplied form ofequation(1)orthevaluekshouldbe close totheupperlimitofthosededucedobserva- (The constantA:isexpressibleinunitsofAfoyrif of theH-Rdiagramatarategivenby(McCrea1962) 1977; Reimers1977). rate istakentobezero. whenever logT<3.85,i.e.,anextensive same forallclassesofsupergiants. the modelswithoutmasslossevolverapidly(on effective temperaturethatliesintherangeofyellow However, thereisnoreasontoexpectthateitherthe perature. Theinitialmassesofstarsthataresubject although anyothervalueintherange4.0>logT (Bisnovatyi-Kogan andNadezhin1972;Schmid- determined tobegreaterthanorequal20M to thisinstabilityintheiratmosphereshavebeen a criticaleffectivetemperatureoflogT=3.70, outer convectionzoneexists.Otherwise,themass-loss equal tozero. within thelimitationsof ourcomputerprogram loss rateisheresetequalto the highestrateobtainable envelope Kelvintime)inthisrangeofeffectivetem- 3.6 wouldprobablyleadtoverysimilarresultsbecause of Bisnovatyi-KoganandNadezhin(1972),weadopt supergiants ofveryhighluminosity.Fromthework Burgk andScholz1975).If logT«,<3.70,themass- ( —ä10"Myr); otherwise,therateisset e e 0 e q Theory furthersuggeststhatsupergiantsofinter- Finally, redsupergiantsareobservedtobelosing Since themeasuredratesofmasslossfromdifferent Case A.—Nomasslossoccursatall. Case B.—Masslossoccurscontinuouslyinallparts Case C.—Masslossisimportantonlyamonglate- Case D.—Suddenmasslossoccursatsomecritical © American Astronomical Society • Provided by theNASA Astrophysics Data System -dM/dt =kLR/M.(1) STOTHERS ANDCHIN the outerlayersbuthaveadoptedPaczyñski’s(1967) the deepinterior.Therefore,wehavenotfollowed they areusedtoformasimpleboundaryconditionfor rate ofmasslossishigh,thegravitationalterm is donebyastraightforwardcomputationalprocedure, approximation, envelope andshouldnotbesetequaltozerothere, described byKippenhahnandWeigert(1967).Ifthe which requiresnoknowledgeoftheproperties Kippenhahn andWeigertinneglecting—TdS/dt as isnormallydonefortheselayersofthestarsince has workedwellforourcasesBandCofmassloss. outer layersoftheprecedingmodel.Thisprescription However, inourcaseD,thedecreaseofmassturned out tobesorapidthatlargeentropychangesthrough- fore, wewerefinallyobligedtoignoretheterm matching theenvelopeandinteriorsolutions;there- out theenvelopecreatednumericalproblemsin loss isactuallyinprogress. nificantly affectedbythesurfacemasslosswhile the deepinteriorstructureisfoundtobenotsig- infinitesimal fractionofthestellarlifetimeandsince time duringwhichmasslossoccursincaseDisan the CNOelementsatatemperatureofaboutmillion have alargebumpduetotheultimateionizationof log T>3.85.Itshouldbenotedthattheseopacities (1976) radiativeopacitieshavebeenadoptedfor equal tothepressurescaleheight(a=1).Carson’s envelope, theconvectivemixinglengthhasbeenset instability, althoughthedifferencebetween face isnonadiabatic,thestellarradiiaresomewhat the moremassivestellarmodelspossessextensive this bumpincreaseswithdecreasingdensity.Therefore, actually unimportantherebecauseheavymassloss adopted theSchwarzschildcriterionforconvective stellar modelsarethesameasinPaperY.Wehave convection zonesintheirenvelopesevenonthezero- degrees whenthedensityissufficientlylowandthat of meanmolecularweight.Intheouterconvective suppresses convectioninthelayerswithagradient on thederivedevolutionarytracks,sincetotal Such anomissionprobablyhasnosignificanteffect age mainsequence;sinceconvectionsonearthesur- Schwarzschild criterionandtheLedouxis — rdS/diwillnolongerbenegligibleintheouter sensitive tothevalueofaadopted(Stothers1976). core hydrogenburninghas beenfollowedforcases (Z, Z)=(0.71,0.04).Evolution duringthephaseof adopted forazero-agechemical compositionof B, C,andDofmassloss.Case Awasinvestigatedin P — TdS/dtintheouterenvelopeforthisparticularcase. P e Removal oflayersmassfromthestellarmodels Our otherproceduresusedincalculatingthepresent Initial stellarmassesof15,30, and60M©havebeen III. COMPUTATIONALPROCEDURES IV. EVOLUTIONATHIGHMASSES ds ^dM dt~ dtdM(r)’ t Vol. 226 (2) 1978ApJ. . .226. .2313 No. 1,1978 have beenextendedintothephaseofcorehelium Paper V.Threeofthenewevolutionarysequences burning (seeTable1). clusively intheregionofbluegiantsonH-R burning, incontrasttotheresultsbasedonCox- evolutionary sequencesextendedacrossthewhole diagram. However,aboveacertainstellarmass,the of 15Mwerefoundtoburncorehydrogenex- very farduringthered-supergiantphaseformasses prevented usfromexplicitlyfollowingtheevolution higher than20M©ifZ=0.04. mass waslessthan—6MifZ=0.04(or subsequent phaseofcoreheliumburningtookplace Stewart opacities.Thiscriticalstellarmasswas H-R diagramduringthephaseofcorehydrogen only intheregionofredsupergiants,unlessstellar from acomparisonofevolutionarytrackscomputed hydrogen burning.Forthepurposesofdiscussion, with andwithoutmasslossduringthephaseofcore having thesamecentralhydrogenabundanceXçin ception occursinthecaseofanextremelyheavymass case theeffectivetemperatureislowered).Anex- tion issignificantlyreduced(inourcasesentirely loss andwillbediscussedbelow.Third,semiconvec- remains nearlyunchangedunlessZ<0.1(inwhich mass isreduced.Second,theeffectivetemperature mass. Themostimportantinferencesareasfollows. leads tothewholestar’sbeing overluminousforits fraction containedintheconvective coreisincreased, sequences thatarecharacterizedbythesameinitial our comparisonwillbeconfinedtostellarmodels First, thesurfaceluminosityislowerwhentotal even thoughthetotalcoremass itselfissmaller.This -20 MqifZ=0.04(or-30M0.02).The 0 suppressed) bythelossof mass.Fourth,themass mass, sinceagreaterfraction ofthestarishelium- e 0e — 8M©ifZ=0.02).However,numericaldifficulties c e0€ e We recallthemainresultsofPaperV.Themodels Certain generalinferencescanusefullybedrawn © American Astronomical Society • Provided by theNASA Astrophysics Data System in theH-Rdiagram;(Z,Z)=(0.71,0.04). 60. log T(tip)representsthehottesteffectivetemperatureachievedbystarduringitsleftwardmotion 30. 15. e e 111 * A:=1x10Myr(casesBandC);rreferstotheamountoftimespentatlogT>3.70; 0be Initial M/M 0 Evolutionary SequenceswithMassLossforStarsof15,30,and60M©Initially* a) CaseA b) CaseB Case B B D D B A C C (10^yr) 13.255 12.704 12.704 4.123 3.814 5.728 5.780 3.918 Core HydrogenBurning 0.989 0.960 0.981 1.000 1.000 1.000 1.000 1.000 Tö/t h STELLAR WINDS iogr e 4.33 4.18 4.34 4.23 4.09 4.23 4.14 (tip) 3.95 TABLE 1 M/M 76_1 0 8 -1 54 Final 25.1 26.5 16.9 12.5 12.7 15.0 15.0 rich andahighermeanmolecularweightimplies with comparablemass-lossrates(Tanaka1966a; been obtainedpreviouslywithdifferentopacitiesbut higher luminosity. we wouldhavefoundthatevolutionintheH-R had weadoptedasignificantlygreatermass-lossrate, and Wilson1978;Chiosi,Nasi,Sreenivasan de Loore,DeGrève,andLamers1977;Sreenivasan 4 x10",and210“Moyrforinitialmasses high asobservationsseemtopermit.Ourzero-age diagram neverdepartsveryfarfromthezero-age Chiosi andNasi1974;DearbornEggleton1977; main-sequence modelslosemassatratesof7x10“, main sequence(cf.Tanaka19666;Hartwick1967; tracks intheH-RdiagramisshownFigure1. very highstellarmasses.Atthesemassesthenew such alargerateofmasslossontheevolutionary of 15,30,and60M©,respectively.Theinfluence Simon andStothers1970;ChiosiNasi1974). central hydrogenexhaustion(astheydidincaseA). models attainared-supergiantconfigurationbefore earlier workbasedonCox-Stewartopacitiesreferto noteworthy thatmostoftheevolutiontimeisspent hydrogen abundance,asshowninFigure2.Itis yr forinitialstellarmassesof30and60M©, extremely high,reaching6x10“and1M© in aplotofeffectivetemperatureversuscentral respectively. Whenabout25%oftheinitialmasshas Consequently, themass-lossrateseventuallybecome 1978). Suchagreatsimilarityleadsustobelievethat, back intotheregionofbluesupergiants. posed atthestellarsurface,starbeginsashift been ejectedandhydrogen-processedlayersareex- this phaseandthesurface appearsmoreand and ofthesurfacehydrogenabundanceareshownin at logT>4.1.Thehistoriesofthetotalstellarmass hydrogen-poor. Atthestage ofcentralhydrogen giant, significantamountsof massarelostevenduring mass ratioatthetimewhen thestarisabluesuper- Figures 3and4.Becauseof thehighluminosity-to- e 9.4 These resultsareverysimilartothathave As itis,ouradoptedmass-lossratesareaboutas The majordifferencesthatwehavefoundfrom The brevityofthered-supergiantphasecanbeseen thg/th t^/tho(tip)M/M 0.101 0.091 0.ÍÓ7 0.098 0 Core HeliumBurning 0.000 0.473 l’.ÓÓO 1.600 log TFinal e 4.50 4.64 4.63 3.50 23.3 15.0 ’3.6 ‘s.b 233 234 STOTHERS AND CHIN Vol. 226
Fig. 3.—Total mass, in units of initial mass, versus central hydrogen abundance for case B.
c) Case C Although numerical difficulties of a nature similar to that of case A developed in the present case for an Fig. 1H-R diagram showing the evolutionary tracks up initial stellar mass of 30 M©, they did not develop for to the stage of core helium ignition for case A (dashed lines) 60 Mq. Therefore, the phase of core hydrogen burning and for case B (solid lines). Except for case A with starting could be completed for the 60 M© sequence and is masses of 30 and 60 M0, the tracks terminate when log TÍ = 8.1. Masses are indicated in solar units. shown in Figure 5. Apart from a very brief excursion into the region of red supergiants (similar to case B), the evolutionary history resembles rather closely that exhaustion, the star finally attains its highest effective of case D, which is discussed below. temperature since leaving the region of red super- The situation is very different for a star of 15 Af©, giants. But very quickly thereafter, the residual hydro- which completes core hydrogen burning as a blue giant gen envelope reexpands. The star becomes red for a and hence before the loss of any mass. The evolution second time. In analogy with the somewhat similar in the H-R diagram for this case is shown in Figure 6. final results obtained for case D, we expect that Unlike the mass-conserving star, which remained in further evolution would lead to the loss of most of the the red-supergiant configuration throughout the phase remaining hydrogen envelope, so that the star would of core helium burning, the mass-losing star executes end up being very blue and lying near the helium main a long blue loop, beginning when the star’s mass sequence on the H-R diagram.
Fig. 2.—Effective temperature versus central hydrogen Fig. 4.—Surface hydrogen abundance versus central abundance for case B. hydrogen abundance for case B.
© American Astronomical Society • Provided by the NASA Astrophysics Data System No. 1,1978 content hasreachedY=0.40.Althoughextensive has droppedbyabout75%anditscentralhelium envelope convectionatthetopofred-supergiant branch hasalreadypenetratedintothehydrogen- abundance forcaseC. the directexposureofhydrogen-processedlayers processed layersandhastransportedtothesurfacea small amountofhelium-enrichedmaterial,itisonly c is shownforreference.Masses are indicatedinsolarunits. case C(dottedlines),andD (solidlines).ExceptforcaseAwithstartingmassesof30and 60M©,thetracksterminatewhen
Y =0.1.Evolutionaryloopsfor caseDintheunstableborderarea(3.77 © American Astronomical Society • Provided by the NASA Astrophysics Data System 1978ApJ. . .226. .2313 No. 1,1978 the theoreticallowerlimitforstarsburningcore core heliumina“blueloop”phase.Quantitatively, blue supergiantshaveluminositiesthatfallbelow Z =0.02-0.04.Ifoneisunwillingtoaccept>0.04, the modelsburningcorehydrogenwereallbrighter the observedlowerlimitislog(L/Lq)ä4.5,while hydrogen andabovetheupperlimitforstarsburning helium ina“blueloop”phasewereallfainterthan than log(L/Lq)=4.8andthemodelsburningcore log (L/Lq)=3.8,foramixedpopulationofstarswith then thetheoreticallowerlimitcannotbelowered 0.02, thenthetheoreticalupperlimitisalsofirm.A any further(unlessa<1);andifonedeniesZ possible resolutionofthisimpasseistheintroduction hydrogen. ItispossibleincaseBforastartohavean luminosity bluesupergiantscouldbeburningcore of massloss. average underluminosityof8log(L/L)=0.4with e if ithadevolvedwithoutmassloss.ForcaseD(and respect totheluminositythatstarwouldhavehad log (L/L)=0.3canbeachieved.Theseunder- probably alsoforcaseC),anunderluminosityof8 luminosities wouldhavebeenaboutlog(L/L)=4.8, luminosities, ifappliedtostarswhoseundisturbed are sufficienttoaccountforthefaintestluminosities hydrogen thatarethisfaint,ahighinitialmetals Pe order toobtainmodelsofsupergiantsburningcore observed amongthebluesupergiants.However,in abundance (Z=0.04)isrequired.Thismaybe blue supergiantsthenumberofis acceptable, butinyoungstarclusterscontainingfaint is directlycontrarytoourmodelpredictions.More- approximately equaltothenumberofredones.This 0 where calculationswereperformed,aremuchtoo peratures forthebluesupergiants,atallluminosities 0 over, incasesDandC,thepredictedeffectivetem- 0 low ascomparedwiththeobservedvaluesoflog luminosity bluesupergiantsistoassumethatthey T =4.0-4.2. are ina“blueloop”phaseduringcorehelium can beinducedonlybyveryheavymasslossinthe e preceding evolutionarystages.Aserioustheoretical burning. However,aswehaveseen,the“blueloop” though therelativenumbersofblueandredsuper- nants whichareburningcoreheliumturnouttobe consequence ofthisisthatthecomputedstellarrem- much bluerthantheobservedbluesupergiants(even compact blue-giantconfiguration). giants canbeadequatelyexplainedifthepriorphase blue supergiants(and,ofcourse, somehigh-luminosity theoretical modelspredict thatalllow-luminosity of corehydrogenburninghastakenplaceonlyinthe e by afactorof2or3.Unfortunately, theobservational ones) shouldbeundermassive fortheirluminosities It wasnotedinPaperVthatthefaintestobserved We shallfirstreconsiderwhethertheobservedlow- A secondwayofpossiblyexplainingthelow- In thecaseofbothalternative explanations,the © American Astronomical Society • Provided by theNASA Astrophysics Data System VI. COMPARISONWITHOBSERVATIONSOF a) BlueSupergiants MASSIVE STARS STELLAR WINDS evidence bearingonthispointisinconclusive(Stothers are exposedthatwereatonetimeinthehydrogen- more, sinceinteriorregionsofthetheoreticalmodels burning core,heliumenrichmentandnitrogenen- richment (withcarbonandoxygendepletion)atthe in anysuchexamination. would, ofcourse,alsohavetobetakenintoaccount stellar surfacearealsopredicted.Theknownblue of massloss;theinfluenceanybinarycompanions supergiants areworthexaminingforpossibleeffects 1972; deLoore,DeGrève,andLamers1977).Further- than log(LILq)ä5.3.Theonlyobvioussolutionto is theobservedabsenceofredsupergiantsbrighter this problemistheintroductionofmassloss.How- ever, suddenanddevastatingmasslossfromayellow highest ratesobservedforlessluminoussupergiants red-supergiant masslossatratesextrapolatedfromthe supergiant (caseD)isnotnecessary;ordinary (case C)seemstobeadequate.Thisresultsupersedes the observedratesofmasslosswereprobablyinade- our earlierconclusion(StothersandChin1970)that for nearlyalltheveryluminoussupergiantsinstead quate; ournewresultsarebasedontheassumption core carbonburning)thatwehadenvisagedearlier. of averylonglifetime(thatcorehydrogenburning) red. However,theratesthatwehaveadoptedforcase they arebluecouldpreventthemfromeverbecoming mass lossfromthemostluminoussupergiantswhen of theshortlifetime(thatcoreheliumburningand the stellarmodelsinthiscasedonotavoidred region. B areaboutequaltothemaximumratesobserved,and our casesisfoundtoproducewithinthemain- and nitrogen-rich.Intheyounggalacticpopulation, sequence bandanumberofstellarremnantsthat properties thatmeettherequirementsofourmost certain heliumstars,OBNandWNstarshave should beobservedasundermassive,helium-rich, massive modelsevolvingwithmassloss(caseB) very differentinthisrespectfrompreviousresults results, whicharebasedonCarson’sopacities,not during thephaseofcorehydrogenburning.Sinceour the readertoearlierpapersforamoredetailed based ontheCox-Stewartopacities,wesimplyrefer discussion (seethereferencesin§IVè). hydrogen attheirsurfacesandhavehighereffective temperatures. Theseobjectscorrespondveryclosely to ourmodelsthatareinthephaseofcorehelium burning, forallourcasesof veryheavymassloss.A helium starswithouthydrogen envelopes,hasalready more detailedcomparison, basedonmodelsof been published(Stothers 1976; StothersandChin 1977è) andthereforewillnot berepeatedhere. A seriousproblemthatwasunresolvedinPaperV It isevenpossiblethatanextremelyhighrateof The assumptionofaheavystellarwindinall Other WNstars,ontheotherhand,showless c) OBNandWNStars b) RedSupergiants 237 1978ApJ. . .226. .2313 238 in themassrange7-60M©hasbeeninvestigatedfor giants. catastrophic masslossfromluminousyellowsuper- loss fromredsupergiantsalone;andD,sudden employed. Fourcasesofmasslosshavebeendistin- from bothblueandredsupergiants;C,heavymass guished: A,nomasslossatall;B,heavy stellar modelsinwhichCarson’sopacitieshavebeen entirely satisfactorytheoreticalpredictions,regardless some masslossfromstarsinitiallymoremassivethan been carriedthroughfortheCox-Stewartopacities, adopted. CasesCandD,althoughtheyhavenotyet also yieldpartiallyunsuccessfulpredictionsifCarson’s of whethertheCarsonorCox-Stewartopacitiesare WN starsinthemain-sequencebandH-R case BcanaccountwellforthepresenceofOBNand opacities areused.Forbothsetsofopacities,however, diagram andfortheabsenceofveryluminousM explanation ofeitherthegreatwidthmain- the Cox-Stewartopacitiesreallyleadtoasatisfactory supergiants. Nevertheless,thereisnocaseforwhich very luminousbluesupergiantswithspectraltypes require aperhapsunrealisticallyhighrateofmain- that maybetoocool(seeStothers1976)andfailto effective temperaturesforthezero-agemainsequence while solvingthoseproblems,neverthelessleadto later thanB3.Ontheotherhand,Carson’sopacities, sequence bandathighluminositiesortheproperties (induced bythelargevaluesofCNOopacityin account satisfactorilyfortheobservationsofblue sequence masslossinordertoexplainthepaucityof of WNstarswithlargehydrogendeficiencies,andthey based ontheCox-Stewartopacities,opacity configuration possible.Incontrasttothesequences abundances ofthemetalsareadopted). supergiants oflowestluminosity(atleastifstandard ^20 M.Asdiscussedin§I,caseAleadstonot sequences basedonCarson’sopacitiesisthetendency .1970,Ap.J.Suppl.,19, 243. Bisnovatyi-Kogan, G.S.1973,Ap.SpaceSei.,22,307. stellar envelope)forthestartoexpandintolargest Chiosi, C.,Nasi,E.,andSreenivasan,S.R.1978,Astr.Ap., Chiosi, C.,andNasi,E.1974,Astr.Ap.,34,355. Castor, J.I.,Abbott,D.C.,andKlein,R.I.1975,Ap.J., Carson, T.R.1976,Ann.Rev.Astr.Ap.,14,95. Bisnovatyi-Kogan, G.S.,andNadezhin,D.K.1972,Ap. Bernat, A.P.1977,Ap.213,756. overwhelms allothercompetingphysicalfactors, Dearborn, D.S.P.,andEggleton, P.1977,Ap.J.,213,448. Carson, T.R.,andStothers,R.1976,Ap./.,204,461. Cox, A.N.,andStewart,J.N.1965, Ap.J.Suppl.,11,22. de Loore,C.,DeGrève,J.P., and Lamers,H.J.G.L.M. Forbes, J.E.1968,Ap.J.,153, 495. 0 The effectofastellarwindontheevolutionstars Observational evidenceseemstorequireatleast The mostoutstandingfeatureoftheevolutionary 63, 103. Space Sei.,15,353. 195, 157. 1977, Astr.Ap.,61,251. © American Astronomical Society • Provided by theNASA Astrophysics Data System vn. CONCLUSIONS STOTHERS ANDCHIN REFERENCES eliminated doestheenvelopecontractsignificantly. homogeneity ofthestarhasbeenalmosttotally including massloss.Onlywhenthechemicalin- their existencemightbeexplainedbythesupposition not havebinarycompanionswithwhichthey parameters couldmakeaconsiderabledifference.For Therefore, ourresultsarenotexpectedtobegreatly they couldbeina“blueloop”phaseduringcore that theyhavestartedwithZ<0.02,inwhichcase interacted soastoavoidbecomingredsupergiants, rate ofmassloss.However,largechangesinthese dependent onourparticularchoicesofZandthe wide rangeofZamongtheyoungstarsgreater helium burning,orbythesuppositionthattheyhave example, ifthebluesupergiantsoflowluminositydo be burningcorehydrogen.Perhapstheoccurrenceofa values ofZrequired,wehavecalculatedafew started withZ>0.04,inwhichcasetheycouldstill servational possibility. 0.04 and0