Pulsating sdB Stars A New Approach to Probing their Interior

Horizontal branch stars should show significant differential rotation with depth. Models that assume systematic angular momentum exchange in the convective envelope and local conservation of angular momentum in the core produce HB models that preserve a ra

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aPulsatingsdBStars:ANewApproachtoProbingtheirInteriorsStevenD.KawalerandShelbiR.HostlerDept.ofPhysicsandAstronomy,IowaStateUniversity,Ames,IA50011USAAbstract.Horizontalbranchstarsshouldshowsigni cantdi erentialrotationwithdepth.Modelsthatassumesystematicangularmomentumexchangeintheconvectiveen-velopeandlocalconservationofangularmomentuminthecoreproduceHBmodelsthatpreservearapidlyrotatingcore.Adirectprobeofcorerotationisavailable.ThenonradialpulsationsoftheEC14026starsfrequentlyshowrichpulsationspectra.Thustheirpulsationsprobetheinternalrotationofthesestars,andshouldshowthee http://doc.guandang.netingmodelsofsdBstarsthatincludeangularmomentumevolution,weexplorethispossibilityandshowthatsomeofthesdBpulsatorsmayindeedhaverapidlyrotatingcores.1.IntroductionFirststudiedindetailbyR.Petersoninthemid1980s(Peterson1983,1985a,b),therapidrotationofsomehorizontalbranchstarsremainsanenigmaticfeatureofthisphaseofevolution.ObservationsbyBehretal.(2000a,b)showagapinthehorizontalbranchofM15andM13,withtwodistinctrotationratesoneitherside.Coolerthanabout11000K,HBstarsfrequentlyshowrapidrotation(vsini≈40km/s)whilenorotationratesabove10km/sappearinthehotterstars.Oneclassof eldstarsisclearlyrelatedtohorizontalbranchstars.ThesubdwarfB(sdB)starsareveryhot(Te 25,000K),andshowhighgravity(logg≈5.3 6.1).Modelsproposedtoexplaintheiroriginincludecommonenvelopebinaryevolution(eg.Sandquistetal.,2000,Mengeletal.,1976),variationsofmasslosse ciencyontheRGB(D’Cruzetal.,1996),andevenmassstrippingbyplanetarycompanions

(Soker&Harpaz,2000).Someproposedoriginscenariosmakeclearpredictionsabouttheirrotationalproperties;forexample,thosethatinvolvebinarymergersorcommonenvelopeevolutionshouldspinupthesdBproduct.ExtrapolationoftheresultsforPop.IIstarssuggeststhatsdBstarsshouldbeslowrotators,withvsini 10km/s.TheworkbyHeberetal.(1999)hasshownthatatleastonestar,PG1605+072,isamorerapidrotator–asexpectedbasedonanasteroseismicanalysisofthepulsationsbyKawaler(1998).

Sills&Pinsonneault(2000)(hereafterSP2K)exploredHBrotationandsingle-starevolutionwithdi erentassumptionsaboutinternalan- c2008KluwerAcademicPublishers.PrintedintheNetherlands.

Horizontal branch stars should show significant differential rotation with depth. Models that assume systematic angular momentum exchange in the convective envelope and local conservation of angular momentum in the core produce HB models that preserve a ra

2S.Kawaler&S.Hostler

gularmomentumtransport.Startingwithmodelsthatarerotatingassolidbodiesatthedeparturefromthemainsequence,SP2Kfollowedevolutionofthemodelsthroughthehelium ashandontotheHB.Theystudiedseverallimitingcasesofangularmomentumtransport,twoofwhichwefollowuponinourstudyofPop.IhotHBstars.Bothconservespeci cangularmomentum(angularmomentumperunitmass,j)inconvectivelystableregions.Inconvectiveregions,convectivemixingisassumedtoproduceeitherconstantangularvelocityintheconvectionzone(CaseB)orconstantj(CaseD);inbothcases,theangularmomentumcontainedwithintheconvectionzoneispreserved.

SP2Kconcludedthatthebest ttoobservationsofPop.IIHBrotationcamefromprecursorswithrapidlyrotatingcoresandconstantspeci cangularmomentuminconvectionzones(i.e.CaseD).ThesemodelscouldrotateattheratesseeninthecoolHBstars.TheslowrotationinthehotterHBstarsrequireschokingofangularmomentumtransportbychemicalcompositiongradientsproducedbydi usion-suche ectsareseeninHBstars(andmodels)attemperaturesabove11,000K(SP2K).AllrotatingmodelsofHBstarsshowrapidlyrotatingcores.Similarly,sdBstarsthatoriginatethroughbinarymergersorcommonenvelopeevolutionshouldshowpathologicalrotation.

AsubsetofsdBstarsaremultiperiodicpulsatingstars.Thepulsat-ingsdBVstars,iftheyrepresent“typical”sdBstarsand,byextension,typicalHBstars,shouldallowasteroseismologytoaddressthestateofinternalrotationofHBstars.Infact,onesdBVstar,PG1605+072,wasfoundtohaverapidrotationbasedontheasteroseismicanalysisbyKawaler(1998)–thiswaslaterpartiallyveri edbyHeberetal.(1999)throughmeasurementofrotationalbroadeningofspectrallines.Basedonthisinitialsuccess,itislikelythatasteroseismologycanbeausefultooltoexploreimportantquestionsofthesecondparameterprobleminglobularclustersandtheoriginsof eldsdBstars.

ThesdBstarsprobablyoriginatefromhighermassprogenitorsthanPopIIHBstars.StarsthatarenowsdBstarscouldhavehadmuchhigherinitialangularmomenta(Kawaler,1987).Therefore,wehavecomputedmodelsofrotatingRGBandsdBstarsusingPopulationIprogenitorswhichsamplethevariousstructuresthatmightberelevantforthepulsators.Welookattheasteroseismicconsequencesoftheserotationpro lesontheobservedsdBstarspulsations.

2.EvolutionaryModelCalculations

TheevolutionofourstellarmodelswascomputedusingISUEVO,astandardstellarevolutioncodethatisoptimizedforproducingmodels

Horizontal branch stars should show significant differential rotation with depth. Models that assume systematic angular momentum exchange in the convective envelope and local conservation of angular momentum in the core produce HB models that preserve a ra

InteriorsofsdBstars3

foruseinasteroseismologystudies.ISUEVOcomputesmodelsrangingfromtheZAMSthroughtheRGBandAGBandbeyondthathavebeenusedforstudiesofHBstars(Stobieetal.,1997;vanHoolstetal.,1999;Kawaler,1998;Kilkennyetal.,1999;Reedetal.,2003).

AswearemodelingPopulationIstars,weassumeametallicityZ=0.02andaninitialmixturethatissolar.Modelsequenceswerecom-putedwithinitialmassesof1.0,1.5,and1.8M⊙,andevolvedfromtheZAMSuntiltheheliumcore ash.Thecorema …… 此处隐藏：16153字，全部文档内容请下载后查看。喜欢就下载吧 ……