Pulsating sdB Stars A New Approach to Probing their Interior(7)

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

InteriorsofsdBstars7

modelshowssomemixed–charactermodesfor =2whichcanhavesigni cantamplitudeinthecore(Charpinetetal.,2002).

Figure3liststhecomputedsplittingsaCaseBsdBmodel.Thesurfacerotationvelocity,ifrepresentativeoftheentirestar,wouldproduceasplittingoflessthan0.01µHzforallmodes(surfacerota-tionvelocityofonly6m/s),yettherapidinternalrotationresultsinsplittingsrangingfrom1µHz( =1,n=1)to80µHz( =2,n=0).

Inallcases,therotationalsplittingismuchlargerthanexpectedfromthesurfacerotationrate.Also,thesplittingchanges(sometimesdramatically)fromonemodetothenextinasequenceofthesame butdi erentn.Thekernels(seeFigure3)sweepingacrossthesteepdropin producethese uctuations.Modetrappingbythecompositiontransitionzonesproducessomestrongcorelocalizationofthekernelsforcertainmodes,andthesealsoshowlargerrotationalsplitting.

4.Conclusions

ThesdBstarsmayretainrapidlyrotatingcoresasarelicoftheirevolutionontheRGB.Suchrapidrotationcouldserveasareservoirofangularmomentumwhich,whentapped,canproduceanomalouslyfastrotationatthesurfaceontheHB.

Nonradialpulsationscanrevealtherapidlyrotatingcoresviaro-tationalsplittingofnonradialmodes.Therotationalsplittingwillbemuchlargerthanexpectedfromthesurfacerotationvelocity.ThismaybehappeninginPG1605+072;therotatonalsplittingidenti edinthatstarbyKawaler(1998)isabout3timeslargerthanthevsinimeasuredviaspectroscopy(Heberetal.,1999).Also,thesplittingsseeninFeige48(Reedetal.,2003)aresigni cantlylargerthanexpectedfromtheupperlimitstovsinibyHeberetal.(1999).

Thefactthatthesplittingscanbequitelarge,coupledwiththelargedi erencesinexpectedsplittingsfrommodetomode,canmakeobservationalidenti cationofrotationalsplittingquitedi cult.Gen-erally,onelooksforasequenceofequally–spacedtripletsinaFouriertransform,andidenti esthemas =1forexample.Evenifallmembersofsuchtripletsarenotseen, ndingseveralpairsofmodessplitbythesameamountwouldsuggestrotationalsplitting.ForsdBVstars,withsigni cantmode–to–modedi erencesinsplittingsexpected,aseriesofrotationallysplitfrequencieswouldbeindistinguishablefrommodesofdi erent andn.Withoutconsideringdi erentialrotation,sucharichmodespectrumwouldrequireappealingtoothermechanisms.

Finally,wenotethattheperiodsseeninthePG1716+426(“Betsy”)starsareaboutthesameperiodsthatweexpectfortherotationrates