Pulsating sdB Stars A New Approach to Probing their Interior(2)

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