2 O O 2MNRAS.333. .1213 2 12 1 With nonuclearreserves,theirevolutionwillbedominatedby binary isapairofwhitedwarfswithmasses~0.6Mqorbelow. This paperaddressesthequestion ofwhathappenswhenapair increasingly commonasthestellar populationofagalaxyages. the mergeroftwowhitedwarfs; aprocessthatshouldbecome magnetic-wind braking.Itisreasonabletosupposethata Increasing numbersofsuchbinariesarenowbeingdiscovered. The likelyoutcomeoftheevolutiontwostarsinadetached Accepted 2002January31.Received14;inoriginalform2001February23 Armagh Observatory,CollegeHill,BT619DG Mon. Not.R.Astron.Soc.333,121-132(2002) ^E-mail: csj@star.arm.ac.uk companion startstoaccretematerial. Inlooseterms,thisdescribes companion. Tidalforceswilltakeoveranddisruptthelessmassive connects thetwostars(Rochelobe)andspilloverontoits will thenfillthecommongravitationalpotentialsurfacethatjust completely withinaHubbletime.Thelessmassivewhitedwarf orbital decayasaconsequenceofgravitationalradiationor star, causingittoformadiscfromwhichthemoremassive substantial fractionoftheorbitssuchbinarieswilldecay Hideyuki SaioandC.SimonJeffery* white dwarfsandtheprogenyofextremeheliumstars Merged binarywhitedwarfevolution:rapidlyaccretingcarbon-oxygen © 2002RAS 1 INTRODUCTION AstronomicalInstitute,SchoolofScience,TohokuUniversity,Sendai980-8578,Japan © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem rates forCO+Hewhitedwarfpairs,theevolutionarytime-scalesareroughlyconsistentwith We haveexaminedtheevolutionofmergedlow-massdoublewhitedwarfsthatbecome merger asthebest,ifnotonly,viablemodelforcreationofextremeheliumstarsand,by helium zoneoftheinitialCOwhitedwarfs.Theseresultsestablish+Hedwarf helium shellduringapreviousasymptoticgiantbranchphaseareassumedtoexistinthe the observednumbersofextremeheliumstars.Predictedsurfacecarbonandoxygen The theoreticalmodelsforthemergerofaO.b-M©COwhitedwarfwith0.3-MqHe mass isaccumulated,aheliumshellflashoccurs,theradiusandluminosityincrease matter, consistingmostlyofhelium,ontoacarbon-oxygen(CO)whitedwarf.Aftercertain ABSTRACT Key words:binaries:close-stars:chemicallypeculiarevolutionwhitedwarfs. luminosities andmassesobtainedfromtheirpulsations.Togetherwithpredictedmerger logTeff-logg diagram,withtheirobservedratesofbluewardevolution,and dwarf agreeverywellwiththeobservedlocationsofextremeheliumstarsin enough, thestarevolvesbluewardalmosthorizontallyinHertzsprung-Russelldiagram. luminous heliumstars.Wehaveapproximatedthemergingprocessbyrapidaccretionof association, themajorityofRCoronaeBorealisstars. abundances canbeconsistentwiththeobservedvaluesifcarbonandoxygenproducedin a pre-determinedvalue.Whenthemassabovehelium-burningshellbecomessmall star becomesayellowgiant.Massaccretionisstoppedartificiallywhenthetotalmassreaches by enhancementsofCNO-processed,5a-and«-captureproducts is whethertheyaretheproducts ofsingle-starorbinary-star luminosities (Asplundetal.2000); thelatterwillalsobe Hill &Heber1999).EHesareoftenconsideredtoberelatedthe A fewhavesignificantlylowerL!Mratiosanddonotshow3a- hydrogen (Jeffery1996).Inmostcasestheyarealsocharacterized luminous starswithhighlyprocessedsurfaces. helium core,coalesce.Itsmotivationisanattempttoexplainthe evolution. Thetaskhasbeendifficult fromtheoutsetbecause,in considered inthispaper. cooler RCrBstarsbecauseoftheir similarsurfacecompositionand gravities), whereluminosity,L,andthemass,M,areinsolarunits. evolutionary originofextremeheliumstars(EHes),arareclass white dwarfs,onewithacarbon-oxygencoreandtheother and themajorityhavelogL/M>4(asindicatedbytheirsurface and A-typegiantstarswithextremelylowsurfaceabundancesof acquired theirunusualcharacteristics.Typically,theyarerareB- «-capture productsintheiratmospheres(e.g.V652Her,Jeffery, The majorquestionconcerningthe evolutionaryoriginofEHes The taskofstellarevolutiontheoryistoexplainhowthesestars 2 O O 2MNRAS.333. .1213 1 been developedbyconsideringevolutionarymodelsforaccreting binary systems(Jeffery,Drilling&Heber1987),forcingthe reasons, namely:(i)adegenerateCOcorewithhelium-burning been causedbytheabsenceofdetailednumericalMBWDmodels. WD tocoolgiantobservedinV605Aql(Pollaccoetal.1992), by thelargedegreeoffreedomallowedinreproducingawiderange post-AGB sequence. become awhitedwarf,alsoforcingthestartoexpandrapidly. rich surface.Twoprincipalhypothesesemergedduringthe1980s. ignition ofaheliumshellintheaccretedenvelope,whichforces Tutukov 1984;Webbink1984)consideredtheaccretionofawhite the normalevolutionofsinglestarsfrommainsequenceto necessary toexaminetheirdetailed propertiesalongsideanumber have beenconsidered(Saio&Nomoto 1998;Iben1990),itis the generalpropertiesofsuchmodelsforbothCOandHeWDs higher thanobservedinEHes(Herwigetal.1999).Pandey In particular,theLTPmodelfailstoaccountforallEHestwo Benetti 1996),allofwhicharehydrogen-deficienttosomeextent. FGSge (Herbig&Boyarchuk1968)andY4334Sgr(Duerbeck LTP modelhasalsobeensupportedbytherapidevolutionfrom Heber &Hunger1991;Leuenhagen,HamannJeffery1996).The high CandOconcentrationsinPG1159[WC]stars(Werner, Again, thesubsequentevolutionwouldresemblecanonical mass thatafinalthermalpulsewouldoccurafterthestarhad near thesurfaceofastaratendAGBevolutionwassuch merger, orcontractiontotheheliummainsequence-possibly dwarf (WD)secondaryontoawhiteprimary,resultinginthe white dwarfphase,itseemedimpossibletoremovethehydrogen- of observationalconstraints.The first constraintisthedistribution white dwarfs(Saio&Nomoto1998;SaioJeffery2000).Whilst companions. of abinarysystem.Anyputativesingle-staroriginimpliesthat conclusion thattheirevolutionmusthaveincludedthedestruction 2000). IthasalsobeenestablishedthatnoEHesaremembersof one low-L/MEHewithremarkableprecision(Saio&Jeffery extreme heliumstarsonthebasisofthisargument. 2000) and(ii)correctlycomputedLTPmodelspredictsurface of surfacecompositions,froms-processelementsinsomeRCrB deficient stars.PartofthesuccessLTPmodelshasbeencaused et al.1999)andusedtodiscusstheoriginsofvarioushydrogen- considered whatwouldhappenwhentheheliumlayerremaining giving asubdwarfBstar-inthecaseofHe+WDmerger contraction tothewhitedwarftrack,incaseofaCO+HeWD would followthecanonicalpost-asymptoticgiantbranch(AGB) abundances ofcarbonandoxygenthatareanordermagnitude (Iben 1990). star toexpandbecomeacoolgiant.Thesubsequentevolution some fractionwouldcontinuetohaveobservablebinary successfully thephysicaldimensionsandpulsationpropertiesof (2001) haveemphaticallyrejectedtheLTPmodelfororiginof shell cannotaccountforthelow-luminosityEHes(Saio&Jeffery stars (Bond,Luck&Newman1979;LambertRao1994)tovery (Iben &MacDonald1995;BlockerSchönberner1997;Herwig TheMBWDandLTPmodelsarealso referredtointheliteratureas ‘double-degenerate’ (DD)and‘final-flash’ (FF)models,respectively. 122 H.SaioandC.S.Jeffery 1 Methods tostudytheconsequencesofMBWDsystemshave In contrast,themergeroftwoheliumwhitedwarfshasdescribed However, anotherpartofthesuccessLTPmodelmayhave The LTPmodelhasbeenstudiedextensivelyinrecentyears The ‘latethermalpulse’model(LTP:Ibenetal.1983) The ‘mergedbinarywhitedwarfmodel’(MBWD:Iben& © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 8 -51 Mi =0.6Mand0.9.Thecomputationalmethodisthe M =0.9,0.8and0.7for0.6,0.8, rapidly accretinghelium-richmaterial(T=0.98,Z0.02).In We havecalculatedevolutionarymodelsstartingwithwhitedwarfs properties, willbecomparedwiththeobservationalconstraints range 0.6-0.9M©.Thesemodels,includingtheirpulsation recently beenmeasured(Jefferyetal.2001a).Finally,pulsational ratio. ThesecondisthesurfacecompositionofEHescompared range impliesawidefortheassumedefficiencyof 2.1 Assumptionsandinitialmodels 2 EVOLUTIONMODELS measurements usingBaade’smethod(Jefferyetal.2001a)ora the firstinstance,massestimatesbasedonpulsationperiod instability isubiquitousamongstEHesandRGBs.Thisprovides,in the evolutionarymodels.Athirdisprovidedbyseculartime- for theearlyaccretionphaseofevolution. that theresultsareinsensitiveto choiceoftheinitialTexcept ignition (whenpresent).Theycorrespondtoevolvedwhitedwarfs the accretionphaseshouldbelowenoughtoavoidhydrogen values forTwereoriginallychosensothattheshelltemperaturein temperature arelogL/L=-3.03and-2.64logr6.774 model hasM=O.46M.Theluminosityandthecentral model hasadegenerateC-0coreof0.58M,whiletheO.5-M helium starsof0.6and0.5Mfromthezero-agemain merger process. mass isbetween0.1and0.4Mgreaterthantheinitialmass.This merger hasamassintherange0.3-0.4M.Thechoiceoffinal in theformM(Mi).Thus0.9(0.6)meansmodelhaving helium starsintheliterature,wehaveadoptedfinalmassesof Eddington limitaccretionrateforwhitedwarfs.Initialmasses hydrogen {X=0.001).Fortheinitialaccretionphase,whichis accreting carbon-oxygenwhitedwarfswithfinalmassesinthe comparison withnon-linearhydrodynamicmodels. alone (Saio&Jeffery1988)and,ultimately,directmass with thatgivenasaconsequenceofnucleosynthesisandmixingby of EHesintheeffectivetemperature(r)versussurfacegravity dwarf havinglogT=7.072(logL/L =—2.39).Wehavefound computed additionalmodelsequence startingwithaO.6-Mwhite with agesof6-9X10yr. and 6.999forthe0.6-O.5-Mmodels,respectively.These 0.6 Mo,forMi=0.5M.Modelswilloccasionallybereferredto final mass.Consideringtherangeofmassesreportedforextreme was stoppedwhenthetotalmassincreasedtoapre-determined double whitedwarfsystem,wehaveadoptedanaccretionrateof considered asaroughapproximationofthemergingprocess considered accretionofmattercontainingasmallfraction order toseetheeffectofatraceamounthydrogen,wehavealso summarized above. scales which,inthecaseofsomerapidlyevolvingEHes,have (log g)plane.Thelatterisaproxyfortheluminosity-to-mass(L/M) sequence tothewhitedwarfsequence.TheO.6-M (2000). same asthatusedinSaio&Nomoto(1998)andJeffery (Mi) ofwhitedwarfsconsideredare0.6and0.5M.Theaccretion 1 X10Moyr,whichisapproximatelyone-halfofthe 0f f0 c c 0c co0 0 0 0 0 f0 eff c 0 0 0 0 0 0 It isthepurposeofthispapertopresentevolutionmodelsfor To seethedependenceofresults ontheinitialr,wehave Initial whitedwarfmodelshavebeenobtainedbyevolving Our modelsassumethattheheliumwhitedwarfdestroyedin c © 2002RAS,MNRAS 333,121-132 2 O O 2MNRAS.333. .1213 represents evolutionstartingwitha0.5-MCOwhitedwarfaccreting represents theevolutionstartingwitha0.6-MoCOwhitedwarfaccreting measured as0.94±0.68and0.790.46 M,respectively. The tracksaftertheterminationofaccretion areshownasthicklines.The model sequencethataccretesmatterwithhydrogenisnotshowntoavoid for a0.5-MoCOwhitedwarfaccretingmostlyhelium(dashedline).(The Figure 2.ExpandedsectionofFig.1withadditionalmodels.Initialmodels mass became0.7M. mostly heliumandnohydrogen.Theaccretionwasstoppedwhenthetotal mostly heliumandnohydrogen(Y=0.98,Z0.02).Theaccretionwas Figure 1.EvolutionarytracksstartingwithCOwhitedwarfs.Thesolidline are shownforcomparison.Themasses ofPVTelandV2244Ophwere dimensions oftwoextremeheliumstars takenfromJefferyetal.(2001a) 0.9 MforMi=0.6Mq,and0.6,0.7, 0.8and0.9MforMi=0.5Mq. confusion.) Evolutionwasstoppedwhen thetotalmassbecame0.7,0.8and are fora0.6-MqCOwhitedwarfaccretingmostlyhelium(solidline),and containing asmallfractionofhydrogen(X=0.001).Thedashedline each track.Thedottedlineisforthesamemodelbutaccretinggas stopped whenthetotalmassbecame0.7Mnearlyatcoolestpartof © 2002RAS,MNRAS 333,121-132 o 0 0 0 0 0 © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem loT g df Merged binary(CO+He)whitedwarfevolution123 repeating verymildflashesandtheluminosityincreasesupto burning shell;thereafteritfollowsthe helium-burningshell. logL/L© —3.5onatracknearlyparalleltotheoriginalwhite After thefirstflash,helium-burningshellmovesinward in radius)thenthestarexpandsalittle;Alog/?—0.8 log L/Lq—0alongawhitedwarfsequence(i.e.withlittleincrease logL/L© ——2.6beforeaheliumshellflashisignitedatM= is forthecasestartingwithsamewhitedwarfmodelbut matter withouthydrogen(F=0.98,Z0.02)andthedottedline lines areforcasesstartingwiththe0.6-Mwhitedwarfaccreting Figs 1and2showevolutionarytracksafterstartingaccretion.Solid 2.2 Evolutiontoayellowgiant He-shell flash.InitiallytheHe-shell/CO-core boundary(wherethehelium Figure 3.EvolutionofthemodelwithMi—0.6M©showingbehaviour than theabove0.6Mcase.Theearlierignitionisprobablycaused ignition shellislocatedatM—0.5003M©when0.013 the luminosityincreasesalongwhitedwarfsequence.Thefirst white dwarftoayellowgianttakes~200yr(Fig.3). dwarf sequence.ThenitturnsrightontheHertzsprung-Russell 0.604 Mq(Fig.3).Atignitionamassof0.029Mhasbeen with the0.5-Mqwhitedwarfaccretingmatterwithouthydrogen. abundance iszero)locatedatthepoint ofdeepestingressthehelium- of time.Notetherapidexpansion(< 100 yr)tolowrfollowingthefirst the positionofhelium-burningshell andconvectivezonesasafunction of thenuclearluminosity(L),total L,effectivetemperatureT, accumulated. Afterignition,theluminosityincreasesinitiallyupto and 2).Withthestartofaccretionluminosityincreasesto accreting mostlyheliumwithouthydrogen(solidlinesinFigs1 accreting mattercontainingasmallfractionofhydrogen accreted (Fig.4).Themassbeforetheignitionissmaller (HR) diagramtobecomeayellowgiant.Thetransitionfrom (AlogTeff ——0.2).Withthisexpansionthefirstshellflashends. (X =0.001).Dashedlinesrepresentevolutionarytracksstarting shell flashoccurswhenlogL/L©—3.5andlogoff~5.2.The shown bydashedlinesinFigs1and2.Withthestartofaccretion r o 0 r0 0 eff n QÍÍ First, wediscussthecasestartingwith0.6-Mwhitedwarf Evolution sequencesstartingwiththe0.5-Mwhitedwarfare o o 3 45 log t(yr) 2 O O 2MNRAS.333. .1213 Mi -0.6M. panels. burning shellmovesinwardrepeatingverymildflashesandthe by thefactthatinitialcoretemperatureof0.5-Mmodelis luminosity dropstologL/L©—2.84.Thereafter,thehelium- higher thanthatofthe0.6-Momodel.Followingshellignition, luminosity andeffectivetemperature (K)areshownintheupperthree Figure 5.Thelocationofthehelium (solidline)andhydrogen-burning following helium-shellignitionissignificantlyslowerthanfor Figure 4.AsinFig.3forthemodelwithMi=0.5Mq.Theexpansionrate envelope expandstobecomeayellowgiant. and mass(M).Theconcurrentvalues ofnuclearluminosity,surface (broken line)shellsandconvectivezones areshownasafunctionoftime 0 o 124 H.SaioandC.S.Jeffery 0 A jumpinthelocationofhelium-burningshellappearsto 2 3456 © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem log t(yr) log t(yr) 4 _51 but averysmallheliumabundanceandtheouterpeakhasslightly by whetherthemassabovehelium-burning shellissmallerthan reaches apre-determinedvalue,notionally representingtheamount base oftheconvectionzone. role indredging-upnewlyprocessedmaterialtothestellarsurface than thecasewithouthydrogen,evolutionarypathtoyellow luminosity beginstoincrease.Followingtheheliumshellflash, After arapiddecreaseinluminosity,whichlastsonly~20yr, transformed toastructuresupportedbythehelium-burningshell. logL/L© —3.7,consumingmostoftheaccretedhydrogen.After luminosity increasesalongthewhitedwarfsequenceupto fraction ofhydrogen(thedottedlineinFig.1),ashell that oftheinnerpeak. lower temperaturebutalargerheliumabundance.Theinnerpeak two peakswithintheshell;innerpeakhasahighertemperature This arisesbecausethedistributionofenergygenerationhas the carbonabundanceinconvection zonedecreaseswith inflated andthestarremainsayellowgiantaslongaccretion 2.3 Bluewardevolutionfromayellowgiant helium-rich layerssothattheveryweakhydrogen-burningshellis up to—0.1and—2.5X10,respectively.However,these material mildlyenhancedincarbon.Thisisdredgeduptothe helium flash.Thehelium-burningshellhasmovedinwards,leaving the yellowgiantareimportantbecausetheycanplayan hydrogen abundanceistoosmalltomodifytheopacity the helium-burningshellbecomesfullyestablished(Fig.5).The helium-burning shellgovernstheenvelopestructure,even for agivenmass(0.7-M©trackisshowninFig.1),becausethe giant regionisbluerandmoreluminous.However,theevolution expansion oftheenvelopeextinguisheshydrogen-burning evolution governedbythehelium-burningshellbeginsand 0.600 M)when0.002hasbeenaccreted(Fig.5).The flash occursclosetotheoriginalwhitedwarfsurface(M= occurs whentheenergygenerationrateofouterpeakexceeds weakens astheheliumabundancedecreaseswithtime.Thejump occur afterthegiantphaseiswellestablished(cf.Figs3and4). available fromthemergerprocess. Furtherevolutionisdetermined accretion. caused byadecreaseintheenvelopeopacity,whichoccursbecause each trackincreasesslightlyinthelatephaseofaccretion.Thisis continues. AscanbeseenfromFig.2,theeffectivetemperatureof Since theaccretionrate10Myrishigh,envelopestays abundances aredilutedconsiderablyasmassaccretionproceeds. convection zoneextendsinwardstobelowthepositionoffirst and —0.0002,respectively.Asthestarbecomesagiant,surface oxygen abundanceintheconvectiveshellatthatphaseare—0.1 zone thatreachesjusttothesurfaceofstar.Thecarbonand considering theweaknuclear-burningshellthatisre-ignitedafter after theyellowgiantphaseisverysimilartothatwithouthydrogen shell. SincethevalueofMathelium-burningshellislarger surface luminositybeginstodecreaserapidlyandtheenvelopeis shifted inwardstoalayerbetweenthehelium-burningshelland surface toincreasethecarbonandoxygenabundancesby (Fig. 5).Thefirsthelium-shellflashisassociatedwithaconvection significantly. ~600yr theheliumshellburningignitesatM—0.602M©, 0 r Q r r For the0.6-Mowhitedwarfaccretingmattercontainingasmall The massaccretionisstoppedartificially whenthetotalmass In themodelwithhydrogen,protonsarecarrieddownwardsinto The locationandextentofconvectionzonesintheenvelope © 2002RAS,MNRAS 333,121-132 2 O O 2MNRAS.333. .1213 2 8 2 required tosustainagiveneffectivetemperature.Therefore,for relation. Inturn,thelowerluminosityincreasesenvelopemass relative importanceofthermalpressure.Alargerradiusat relation betweentheradiusandmassofC-0core.Because blueward nearlyhorizontallyontheHRdiagram. Recallthat,forshell-burningstarsin equilibrium,theshellluminosityis LSS 3184isconsiderablyabovethe dottedcurve,butthesurface high-luminosity extremeheliumstarsseemtobeconsistentwith to —4.46for0.9(0.5)M©(dashedlines).Theobservedpositionsof to —4.47for0.9(0.6)M©(solidlines)and—3.770.6(0.5)M© higher-mass modelsrangingfromlogL/M~4.22for0.7(0.6)M© mass modelsforagivenMi. lines (Mi=0.5M©).Theuppercorrespondtothehigher- Table 1.Solidanddashedlinesindicateevolutiontracksformodels Fig. 6showsevolutiontracksduringthecontractionphaseand 3 L/MRATIOS temperature zoneislessimportant. total massbecausetheratioofthermaltodegeneratepressuresis model from=0.6M©.Thedifferenceissmallerforalarger mass isassociatedwithadifferentcore-massshell-luminosity lower gravitythere)andhencealuminosity,thuseachinitial the helium-burningshellyieldsalowertemperature(becauseof in themodelfrom=0.5M©than high-temperature (sayT>10K)zoneintheC-0coreisthicker mass butwith=0.5and0.6Mqarisesfromadifferenceinthe luminosity increasesasthemassofCOcoreowingto the equilibriumvaluecorrespondingtocoremassatcurrent core massandtheenvelope(cf. Saio 1988;Iben&Tutukov1989). governed bythecoremassandeffective temperatureisgovernedbythe gravity maynotbeaccurate(Woolf &Jeffery2000). Saio &Jeffery(2000).Thelow-luminosityextremeheliumstar our COwhitedwarfmergermodelshavingtotalmassesofbetween during thecontractionevolution.ThevaluesofL/Marehigherfor dwarfs, respectively.Thetotalmassesare0.7,0.8and0.9M©for obtained inthispaperstartingwith0.6-and0.5-M©COwhite diagram. Theobservationaldataandtheirsourcesaregivenin observed positionsofextremeheliumstarsinthelogg-logrff 0.5 M©hasalargerenvelopemassandislessluminousthanthe given totalmassandeffectivetemperaturethemodelfromMi= 0.6 M©foragivencoremass,theradiusathelium-burning above thehelium-burningshellbecomessufficientlysmall, an outwardprogressofthehelium-burningshell.Whenmass accretion, thestarevolvesslowlyasayellowgiantforwhile.The evolution occursforthecaseof0.6(0.5)Mq. diagram) correspondingtotheenvelopeandcoremasses.Such evolution immediatelytowardtheequilibriumposition(onHR effective temperature.Ifthisisthecase,starstartsablueward sequence obtainedstartingwitha0.4-M©heliumwhitedwarfby (Fig. 2),theluminosity-to-massratio,L/M,isnearlyconstant solid lines(M[=0.6M©)and0.6,0.7,0.80.9M©fordashed smaller inthelargerC-0coreandhencethicknessofhigh- shell inthemodelfromM)=0.5M©islargerbecauseof surface temperaturebeginstoincreaseandthestarevolves © 2002RAS,MNRAS 333,121-132 — 0.7and1M©. 144941 areclosetothedottedline,whichisanevolutionary e Low-luminosity extremeheliumstarssuchasV652HerandHD The causeforthedifferencebetweenmodelswithsame If theenvelopemassissufficientlyhighatterminationof Since theevolutiononHRdiagramisroughlyhorizontal © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Merged binary(CO+He)whitedwarfevolution125 radius ofthehelium-burningshellislargerandhence respectively. Theupperlinescorrespond tohighertotalmasses.Themasses from equilibriummodels,whichconsistofanisothermal in theenvelopehardlyaffectscontractionrate. indicates clearlythattheexistenceofasmallamounthydrogen luminosity islower. the modelfromM[=0.5—M©whitedwarf,because Numbers inparenthesesindicatetheinitialwhitedwarfmass(Mi). Fig. 7showsratesoftheeffectivetemperaturechangecausedby 4 CONTRACTIONRATES luminosity extremeheliumstars,andseemtobeconsistentwiththe line for0.6(0.5)M©areBD+10°2179andHD124448.These with a0.4-Moheliumwhitedwarf.Open squaresshowobservedpositions models obtainedstartingfrom0.6-and0.5-MCOwhitedwarfs, Figure 6.Evolutionarytracksforthebluewardevolutionfromyellow for 0.8M©obtainedfromequilibriummodelsisshownbyadash- contraction. Foragiventotalmassthecontractionrateisslowerfor consumption ofheliuminmoremassivemodelsyieldsafaster outward progressionofthehelium-burningshellsothatfaster contraction againsttheeffectivetemperatureforvariousmodels. dwarf. evolution modelof—0.6M©startedwitha0.5-M©C-0white of someextremeheliumstars(seeTable 1). extreme heliumstarscomputedinSaio &Jeffery(2000),whichwasstarted dashed lines.Thedottedlinedenotes a0.7-Mtrackforlow-luminosity are 0.7,0.8and0.9M©forsolidlines and0.6,0.7,0.80.9Mfor giant phaseonthelogg-logLffplane.Solidanddashedlinesarefor dotted line. obtained withMi=0.6M©.Forcomparisonthecontractionrate envelope. Theseratesaresimilartothoseofourevolutionmodels degenerate C-0core,helium-burningshell,andahelium-rich stars haveL/Mvaluesintermediatebetweenthoseofhigh-andlow- o o 0 e The contractionratesinmostmodelsaregovernedbythe Two starswithlogLff~4.2andg—2.5alongthedashed Another modelproposedtoproduceluminousheliumstarsisa Comparing dottedandsolidlinesfor0.7(0.6)M©inFig.7 Saio (1988)estimatedcontractionratesofextremeheliumstars e log T ef( 2 O O 2MNRAS.333. .1213 region ontheHRdiagramcontracting fromitsborn-againAGB much fasterthanthoseforourmodels havingsimilarmasses.The late (orfinal)thermalpulsemodel, whichpassestheheliumstar Figure 7.Ratesoftheeffectivetemperaturechangecausedbycontraction. observed byJefferyetal.(2001a). curve representstheheatingratesfor0.8Mfromequilibriummodelsby 0.5-Mo whitedwarf.NumbersinparenthesesindicateThedash-dotted originated fromthe0.6-Mwhitedwarf,anddashedcurves and 0.836-Momodels,respectively. Thesecontractionratesare Saio (1988).Opensquaresareheatingratesforextremeheliumstars Solid curves(andadottedcurvefor0.7M©withhydrogen)aremodels (1997) wecanestimatethelog[dT ff/dt]s as1.6and3.3for0.625- stage. Fromevolutionarytracksshown inBlocker&Schönberner 126 H.SaioandC.S.Jeffery 0 Q e © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem 0 0 24 Lyn84, Lynas-Grayetal.(1984);Lyn87,(1987)(basedonrandL);PanOl,Pandey Jeffery (1998);Jef98b,etal.Jef99,(1999);JefOl,(2001a); V652 Her4.3903.68 LSS 3184(—BXCir)4.3663.35 DYCen 4.2902.15 LSS 994.1851.90 LSS 43574.2072.00 LSIV-14°109 3.9770.90 LSIV— 1°2(—V2244Oph)4.1061.35 LSIV+62 4.5024.05 BD- 9°4395(=V2205Oph)4.362.55 BD—1°3438 (=NOSer)4.072.30 BD+1°4381 (=FQAqr)3.940.75 BD+10°2179 4.232.55 HD225642 (=V1920Cyg=LSII+33°5)4.2092.00 HD 168476(=PVTel)4.141.35 HD 160641(=V2076Oph)4.502.73 HD 1449414.3653.9 HD 1244484.1922.52 Table 1.Measuredsurfacepropertiesofextremeheliumstars. et al.(2001);Sch74,Schönberner&Wolf(1974);Wal81,Walker(1981);WooOO,Woolf CoD—461775 (=LSE78)4.262.00 (1983); Jef92,Jeffery&Heber(1992);Jef93,(1993);Jef93b,Jef98a, Star & Jeffery(2000)((/f*>(r). References: Dri98,Drilling,Jeffery&Heber(1998);Har97,Harrison(1997);Heb83, eff rff l0T g e„ logoff logglogL/Lo birth rates,Iben,Tutukov&Yungelson(1996)arrivedatasimilar between 0.8(0.6)and0.9M©.Wenote,however,thatthepositions plotted inFig.7asopensquares.Itisremarkablethatthreeofthe poor surfaceshaveeffectivelysimilarcontractionrates(Blocker Jeffery 1988),thisgiveswhat hasbeenreferredtoasa luminosity-to-mass ratio.When combined withanappropriate used forestimatingthestellarmass. Oneisthestellarsurface In previousstudiesofextremehelium stars,twoproxieshavebeen is thecorrectmodel. Arguing fromthestandpointofobservednumbersandpredicted luminosity extremeheliumstarmodelsinFig.6. in thisfigurearenotalwaysconsistentwiththepositions four starsarelocatedalongthetracksfor0.9-Mqmodels.The BD-9°4395 andBD-1°3438(seeTable1).Theirresultsare variations oftheextremeheliumstarsHD160641,168476, in thelatethermalpulsemodelismuchsmallerthanthatof hydrogen-rich atmospheres.Morerecentmodelswithhydrogen- models ofBlocker&Schönberner(1997)stillhavesubstantially core-mass shell-luminosity(M- L) relation(e.g.Saio1988; gravity, whichprovidesadirect measurementofthestellar 5 RADIALPULSATIONS of extremeheliumstarsarethereforeessentialtodeterminewhich conclusion. Accurateestimatesofthemassesandluminosities consistent withthelatethermalpulsemodelifmasswere close tothelinefor0.9MinFig.7buttracklow- log Tff—loggplane(Fig.6).Inparticular,BD-1°3438islocated exception (HD168476)isconsistentwiththerateforamodel equilibrium valueforagiveneffectivetemperaturerangingfrom 2001). Thisdifferencecomesfromthefactthatenvelopemass — 0.6M©,whileourmergermodelrequires—0.8-0.9M. -10000 to-40000K. c s 0 e 0 The observedcontractionrates(Jefferyetal.2001a)wouldbe Jeffery etal.(2001a)measuredtheratesoftemperature 4.28 4.40 3.03 3.15 1 (Kyi-) dr/dr eff 120 95 20 33 Dri98,Woo00 Wal81,Jef01 Lyn84,Jef99 Lyn87,Jef01 PanOl, JefOl PanOlJefOl Jef92,Jef01 Reference © 2002RAS,MNRAS 333,121-132 Jef93b Jef98b Jef98b Heb 83 Jef98b PanOl PanOl Har97 Sch74 Jef98 Jef93 2 O O 2MNRAS.333. .1213 by avarietyofprocesses.Thehydrogendeficiencyextreme record ofpreviousevolution,dredgedtoordepositedonthesurface radius andcontractionrates,asecondwindowontothehistoryof remarkable coincidencewiththecorrespondingmassmeasure- Woolf &Foliáceo2001b;Jeffery2000).Theseare resolve themass.Incaseoftwoshort-periodpulsators physics inthemodelatmospheres.Therefore,itisimportantto range 0.77-0.95M©.Usingmorerecentspectroscopicanalyses, provides anindependentmeasureoftheluminosity-to-massratio the stellarmetallicity;(ii)a high carbonabundanceand Pandey etal.2001).Principalamong theseare:(i)anitrogen helium starsistheprimaryindicatoroftheirextremelyprocessed highly evolvedstarsisprovidedbytheirsurfacecomposition.The In additiontothegrossstellardimensionsofmass,luminosity, these observationsarethestrongestevidenceyetavailablethat models. Whilemorecouldbedonetoimprovethemeasurements, measurement thatfitthemodelsof0.9(0.6,0.5)M©mergedbinary ments (0.79and0.94M©). for 0.8(0.6)and0.9(0.6,0.5)-M©modelsinFig.2 4.40 ±0.06,respectively. LS IV-1°2=V2244OphandHD168476PVTel,respectively. measured massesof0.79±0.46and0.940.68M©for Fig. 6. measure extremeheliumstarluminositiesdirectly.Thiscanbe frequently measuredtoanaccuracyof±0.3dex,andissensitive Jeffery etal.(2001a)showedMtolieintherange0.5-1.0M©(14 the massesMforfivepulsatingextremeheliumstarsliein helium starsthatpulsate,bythepulsationperiodwhich,together oxygen abundancesinanyprogenitor asestimatedfromproxiesfor abundance equivalenttothecombined carbon,nitrogenand general abundancepatternsatlength (Heber1986;Jeffery1996; atmospheres. Previousauthorshave reviewedanddiscussedthe chemicals exposedatthestellarsurfaceeffectivelyprovideafossil 6.1 Predictedabundances 6 SURFACECOMPOSITIONS dwarf. and notofevolutionfollowingalatethermalpulseinsinglewhite extreme heliumstarsaretheresultofbinarywhitedwarfmergers as 31±3and344R©logL/L©=4.280.06 corresponding radiiandluminositiesaremorepreciselymeasured are primarilycausedbythemeasurementerrorinlogg.The gravity estimateofJefferyetal.(2001a).]Thelargeerrorsinmass consistent withthelowmassesinferredfromtheirpositionsin 0.4 M©havebeenmeasured(Lynas-Grayetal.1984;Jeffery, achieved forpulsatingstarsusingBaade’smethodtomeasurethe assuming astandardM-Lrelationforshell-helium-burningstars, with atheoreticalrelationderivedfromlinearpulsationtheory, (CO +He)whitedwarfevolutionandcontradictlatethermalpulse (V652Her andLSS3184=BXCir),massesof0.5-0.7 stellar radiusandluminosity.Again,surfacegravityisrequiredto (Saio &Jeffery1988).Again,asuitableM-Lrelationprovides © 2002RAS,MNRAS 333,121-132 stars), witheightstarshavingM>0.7M©. [We haveadoptedthevalueforLSIV—1°2basedonlower ‘pulsation’ mass(M).Saio&Jeffery(1988)showedthat, ‘spectroscopic’ mass(M).Thesecondisprovided,forthose s p cs cs p s HD 168476hasbothadirectmassandcontractionrate The luminositydataplacethesetwostarsdirectlyonthetracks For themoreluminousheliumstars,Jefferyetal.(2001a)have The weaklinkintheseargumentsisthesurfacegravity,which © Royal Astronomical Society •Provided bytheNASA Astrophysics DataSystem Merged binary(CO+He)whitedwarfevolution127 -4 3 5 -5 -4 -3 _4 been adoptedfortheremainingheavyelements.Insomemodelsa predominantly ofheliumwithamasslessthan0.4M©.Onits respectively. ForthecaseofMi=0.5M©,corresponding through theCNOcycle.Fromtheseconsiderationswehave helium whitedwarf.Thedonorisassumedtoconsist is thattheaccretedgasfullymixedremnantofadonor model withhydrogen.Thesurface carbonandoxygenabundances the convectiveenvelopebecomesdeeperanddredgesupmatter the weakerheliumflash. The smallerextentoftheshellconvectionzoneand increased upto0.12and2.5X10,respectively,beforetheflash mass fractionsofcarbonandoxygenintheconvectiveshell involved intheshellconvectionzonewas~0.025M©,and the firstheliumflash.Duringflash,shellconvectionzone helium zone.Somecarbonandlittleoxygenwereproducedduring include somecarbonandoxygen. has aheliumzonewithoutcarbonandoxygen.Inordertoseethe AGB (e.g.Herwig2000).However,ourinitialwhitedwarfmodel helium layertherewouldexistconsiderableamountsofcarbonand neglected athinhydrogenlayerwithmassofsome~0.0001M©, of ~0.5-0.6M©;wehaveshownhowmassaffectsthesubsequent gas. CNO abundances.ThesolarabundancescaledtoZ=0.02has oxygen inthedonorwouldhavebeenconvertedtonitrogen qualitatively consistentwiththeobservations.Thefirstassumption of assumptions,sowecanonlydemonstratethattheyare extreme heliumstarsmustbeabletoreproducetheseobservables. downwards intothestar.Asuccessfulmodelforevolutionof occasionally ahighoxygenabundanceindicativeofmixingfrom of thismodelare5.1X10“and 1.9 X10“inmass,respectively. considerably bythematteraccreted afterwards. carbon abundanceisashigh —0.1,butitwillbediluted carbon andoxygenabundancesforMi=0.5M©,areattributedto quantities were—0.01M©,—0.03and—2X10,respectively. oxygen abundancesintheshellwere—0.06and2xl0, convection zonewas~0.006M©andthemaximumcarbon diminished. Forthecasewithhydrogen,massinshell zone. Forthecaseof=0.6M©withouthydrogen,mass extended throughalmostalloftheenvelopeaboveignition with aheliumzone,thecompositionofwhichismodifiedto effect ofcarbonandoxygenintheheliumzone,wehavecalculated oxygen createdduringthermalpulseswhenthestarwason which wouldhavesurroundedthehelium-richlayer.Within evolution. ExteriortotheCOcorethereexitsahelium-richlayer accreting COwhitedwarf.Thecoreisassumedtohaveamass abundances. Thenitrogenabundanceisthesumoforiginal adopted Y=0.98andX0.011fortheheliumnitrogen a zoneaffectedbyheliumburningintothestellarenvelope;and and oxygentothesurface.At deepestpenetrationthesurface affected bytheheliumburningasseeninFig.5,bringingcarbon small fractionofhydrogen{X=0.001)isincludedintheaccreted surface wouldhavebeenahydrogenlayerofmass~10- (iii) tracesofhydrogen,representingarelicouterlayermixed started withawhitedwarfmodelhavingnocarbon/oxygeninthe some modelsequencesstartingwithinitialwhitedwarfmodels (CNO-processed) withaofmass~0.02-0.04M©.Wehave 10M© (Driebeetal.1998).Alloftheoriginalcarbonand N The secondsetofassumptionsconcernsthestructure The theoreticalmodelspresentedinthispapercontainanumber Fig. 8showsthedistributionofelements withinthe0.7(0.6)-M© The envelopeexpandsaftertheheliumflashandbottomof First wediscusschemicalcompositionsofevolutionmodels 2 O O 2MNRAS.333. .1213 12 is receding(Figs3-5).Forthesame reasonthesurfaceabundance Table 2,respectively.Thecarbonandoxygenabundancesare the smallamountofhydrogen. the convectionenvelopeandmixedwithaccretedmatter.Fig.8 The surfacehydrogen,heliumandnitrogenabundancesarevery Figure 8.Thedistributionofelementswithintheoutermostlayers oxygen abundances,whichisattributed toweakerheliumburning. does notchangeaftertheaccretion wasterminated.Foragiven explained byadilutioneffect becauseappreciablemass given (bymassfraction)inthesecondandthirdcolumnsof 0.675