Pulsating sdB Stars A New Approach to Probing their Interior(4)

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

4

2S.Kawaler&S.Hostler

1

2

-11.5

-2

-3

0.050.110

0.050.1

Figure1.Rotationpro lesforEHBmodels.Left:CaseBevolution.Right:CaseDevolution.Modelsatthreestagesofevolutionareshown;verticallinesatthebottomcorrespondingtothetransitionfrompureheliumtothehelium–depletedcore.Thepro lesshowverysubtlechangesintheouterlayerswithevolution.

theangularvelocitypro le.OntheRGBthedominantfeatureoftheinternalrotationpro leisthechangeinangularvelocitythatoccursnear0.27M⊙fromthecenterofthemodel.Therotationpro ledropsprecipitouslybeyondastheresultofdrainingofangularmomentumfromthecorebytheconvectiveenvelope.

HorizontalbranchstarsevolvedfromCaseBRGBmodelsshowmuchsmallersurfacerotationvelocitiesthanthosewithCaseDprecur-sors.Allmodelspreservearapidlyrotatingcorewithroughlyconstantangularvelocityouttoabout0.3M⊙.Therotationpro lesofmodelsdescendedfromCaseDRGBevolutioncontainrelicsofthehighspeci cangularmomentumofmaterialintheouterlayersoftheRGBprogen-itor.Theangularvelocitypro lechangeslittleduringEHBevolution-thecoredoesspindownabitastheangularmomentumismixed,buttheinnercorecontinuestospinaboutafactorof5slowerthanthefastestmaterial.Theangularvelocitydropsfromthemaximumbyafactorofabout10orsotothesurface.

Theinternalrotationpro leremainnearly xedthroughthestageofcoreheliumburning.AsshowninFigure1,therotationpro le(withradius)showsthesamegeneralfeaturesatthestartandendofHBevolution.Furtherevolutionresultsinlittleadditionalangularvelocitychangewithradius.Thisrelativelysmallchangeinangularvelocitypro leontheEHBcouldallowe cientparameterizationforstudiesoftheirseismicin uence.