Session 3E:STARS Oscillationsand stellarmodels Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Theimpactofasteroseismology on the theoryofstellarevolution

C. S. Jeffery

ArmaghObservatory,College Hill, Armagh BT619DG,N.Ireland, UK

Abstract

We summarizethe theory of stellarevolution,highlighting keyphysics to be resolved at variousstages in astellarlifetime.The rˆoleofasteroseismology in testing theoryisillustrated by discussion of pulsationsinhighlyevolved stars.

IndividualObjects: oCet, δ Cep,BPM 37093, FG Sge, GW Vir, XTE J1814–338

Introduction:Pulsating Stars

Thefirst star recorded to be properly variable (rather thaneruptively variable)was discovered by David Fabriciusin1596 (Wolff1877).In1639, JanFokkens Holwarda showed it to have aperiodofsomeelevenmonths.Johannes Hevelius(1662)was so impressedbythis star,which varies by nearly7magnitudes in visiblelight, thathecalled it Mira,meaning “wonderful, astonishing”, foritacted likenootherknown star (Hoffleit 1997).Thisisstill true.Alsoknown as oCeti,itwas the third star (after the Sunand Betelgeuse)tohaveits surfaceresolved, showingacurious prominence (Karovskaetal. 1997),and wasdiscovered to be shedding atail some 8.105 astronomical units in length long (Martinetal. 2007).Mirais an asymptoticgiantbranch star –ofwhich more later –which meansthatfromtimetotime it undergoes athermal pulse whichradicallyaltersthe structureofits outer layers. Mira’s period varies slightlyfromcycle-to-cycle, but other Mira variablesshowsystematic changes in period whichmustbeassociated with changes in internalstructure(Templetonetal. 2005). Suchobservationsenabledirect tests of the stellarevolution theory.

δ Cephei

Stellarpulsation science came into itsown with the discoveryofpulsationsinδCephei (Goodricke1785) andthe subsequent discoveryofthe Cepheidperiod-luminosity relationship (Leavitt 1908).Providing aruler with whichtomeasure the universe,Goodricke’sdiscovery ultimatelychanged the global human perspective.Yet understanding whyLeavitt’srelation should work,whatthe interiorofaCepheidvariable should look like, andhow pulsations aredrivenwould lead to aserious discrepancy between the masses inferredfrompulsation andevolution theoryrespectively (Cox 1980).Thisdiscrepancy wouldnot be resolved until the physics,i.e.the opacity, of stellarmaterial wassufficientlyunderstood (Simon 1982, Moskaliketal. 1992).Now,withconfidence thatpulsationshavemuch to tellusabout physics andcosmology,and new instruments to observeindividualstars over long periods of time,the science of asteroseismology hasmatured andbeenappliedinahugerange of contexts. C. S. Jeffery 241

Figure1:Schematic Hertzsprung-Russelldiagram showing thelocus of majorclassesofpulsatingvari- able star.The zero-agemain sequenceshown as aheavy solidlineand evolution tracks from themain sequencethroughhelium-burning shownasdottedlines arecomputations by theauthor. Thezero-age horizontal branch is shown as aheavy dot-dashline. Coolingtracksfor He andand CO whitedwarfs arealso shown (dotted).Diagonally-shadedregions correspond to opacity-driven p- andg-modepulsating variables. Horizontally-shaded regions show acoustically-driven (solar-like) variables. Vertically-shadedre- gions correspond to highly non-adiabatic pulsations,possiblystrange modesofvarious types. Thefigure conceptfollows one by J. Christensen-Dalsgaard.

Asteroseismology This paperreviews the impact of asteroseismology on the theoryofstellarevolution.Strictly, asteroseismology is the science that“studies the internalstructureofpulsating starsbythe interpretation of theirfrequency spectra” (according to Wikipedia).Again strictly, stars whichpulsate with onemodeonlygiveinformationabout theirmeandensity, andnot about their internalstructure. Even in thiscase, additional information maybeavailable to infer something abouttheirstructure. Conversely,toinfer the complete core-to-surfacedensity distribution of astarfromafrequency inversion requiresapulsation spectrum so rich that it mayonlyeverbeobtained forthe Sunand afew bright stars. However, studies with a resolution intermediatebetween theseextremescan tellusmuch aboutthe structureand local physics withinastar.Whether thiscan be translated to information abouttheirevolution (asdistinctfromstructureorphysics)isnot alwaysapparent. Consequently, thisreviewconsidershow the study of stellaroscillations of all typeshas madeanimpactonour understanding of stellarevolution (Fig.1). Theemphasisleans towardscases wheremultipleperiods have enabled some resolution of structureinthe radial direction. Thefirst half of the paperprovides abrief reminder of the stellarevolution theory, including asummary of the open questionsimportant at different stages in the lifeofa star andthe typesofpulsating starsavailable to testthe theory.The second half reviews specific examplesofwhereasteroseismology hashelpedtoresolvekey questions.Reflecting the author’sinterest, thisisbiased toward starsintheirlater stages of evolution. 242 Theimpactofasteroseismology on thetheoryofstellarevolution

TheStellarEvolutionTheory

Aprimary object of the stellarevolution theoryistoexplain the widelydiverse properties andthe overall distribution of starsrepresented in the Hertzsprung-Russell (HR) diagram. Another is to understandhow starschangeboththeirphysicaland chemical structureas theydeplete theiravailable energy reserves.The extent of the task canbeillustrated by noting thatstars exhibitoscillations with periodsranging from ∼ 10−3 s(neutron stars) to ∼ 108 s(Mira variables),and by recallingthatthe fundamentalpulsation period varies inversely as the root mean density, i.e. the mean densitiesfound in starsspansome22orders magnitude. Asimplifiedpictureofthe theory of stellarevolution showingthe evolution of representative starswithmasses1and5M⊙through the HR diagrammay be found at www.maths.monash.edu.au/∼johnl/StellarEvolnV1/.

Main Sequence Stars

On the mainsequence, wherestars spend over 90%oftheirlives,hydrogen is converted to heliuminthe stellarcorevia the pp-chainsand the CN(O)cycles. Most of the major questions abouthow these starsevolverevolve around the micro-physics.Thus κ,the radiativeopacity, ∇,the physics of convection, ω,rotation, B,magneticfields,and diffusion all influence the rate of energy transport, chemical transportand consequently the overall structureofthe star.Onthe upper mainsequence, stellarwinds andmasslossfeed into thissystem andall feed back to affect the overall luminosityand mainsequence lifetime. Pulsatingstars associated with thisphase of evolution include the Sunand solar-type, δ Sct, γ Dor, SX Phe(variable blue stragglers),ro-Ap,53Per (slowly-pulsating Bstars),and β Cepvariables.

Giant-Branch Stars

As hydrogen in the core is depleted, the core contracts andhydrogen-burning shifts to a shell, the outer layers expand andthe star becomes ared giant. Convectively-drivenmixing between the unprocessedsurface andprocessedcorematerial, andmass-loss due to adust- driven wind, dominate the long-termevolution.Bothprocessesare strongly mediated by the localopacity.Rotationalsoplays an important role;the contracting core attempts to spin up, while the expandingenvelopeslows down,potentiallyleading to strong shearforces andcomplex magneticstructures.Acoustically driven oscillations have been identifiedin sub-giants (e.g. ξ Hya),providing apossibleasteroseismicprobe of the convective layers.

HeliumStars

Once the heliumcorereaches acriticalmass, core helium-burningthrough the 3α and 12C(α, γ)16Oreactions provides arelativelylong-lived phase of evolution. Intermediate-mass starswill evolve as yellowgiants andpassthrough the classical (δ)Cepheidinstabilitystrip. Thereare severalwaystoconsider the massesand ages of stars. For the Cepheids,it is possibletomeasure radii, luminosities andmassesdirectlyusing Baade’smethodorsome variant. Massescan alsobeestimated by matching the luminosity andradiuswithevolution modelsfor helium-burning starsthatpassthrough the instabilitystrip,and by matching the observedluminosityand pulsation period usingstellarpulsation theory. As discussed already, the mismatch between Cepheidmassespredicted by thesemethods wasone of the longest-standing failuresoftheory untilitwas proven to be due to missingopacity.Metal- poor counterpartstothe classicalCepheids appear as WVir (longperiod) andBLHer (short period)variables. C. S. Jeffery 243

Low-mass core-heliumburning starsformaclumpnearthe base of the redgiantbranch (clumpgiants), unless theyare either metal-poor or have very thinhydrogen envelopes. In thiscasethey appear as horizontal-branch stars, some of whichfall in the RR Lyraeinstabil- itystrip.The bluesthorizontal-branch stars(or subdwarf Bstars) lie in the EC14026 and PG1716 instabilitystrips. Therˆo le of opacityand the 12Cα reaction cross-section dominate uncertainties in the evolution through thisphase. For massivestars, helium-core burning mayoccur while the star is still hotand blue and, beingassociated with high luminosity,pulsationsare likelytobeassociated with strange-mode instability.

AsymptoticGiant-Branch Stars With core-heliumexhaustion, the focus of nuclear-burning in low- andintermediate-mass starsshiftstoadouble-shellstructure. Becauseofanimbalance between the burning rates of the hydrogen andheliumshells,aninstabilityknown as thermal-pulsing is established. Thethermal pulse is oneofthe most importantprocessesincosmology.The faster-burning hydrogen-burning shellproduces an accumulationofhelium-rich material abovethe boundary with the degeneratecarbon-oxygen core.When sufficientlymassive,the helium-shellignites mildly,the intershellregion is forced to expand andhydrogen-burning is extinguished. A nuclear-driven convection zone penetrates upwardsand through the helium-hydrogen bound- ary, mixing processedmaterial upwardsand bringing protons down into hothelium-richlayers. Theseprotons seed the nucleosynthesisofexoticelements.The helium-shellcannotsustain itself once the inter-shellmassdrops belowacritical value. Helium-burning reactionssubside, the inter-shellcontracts,the hydrogen-shellisreignitedand opacity-drivenenvelopeconvec- tion dredges freshlyprocessedmaterial up to the stellarsurface, whence it escapestoenrich the interstellarmedium. As aconsequence of the intensity of the hydrogen-burning shell, the star becomes very luminous andverylarge. Theouter layers areincreasingly unstable,exhibited first as opacity- driven pulsationsofverylong-period (e.g. oCet),and then as strong stellarwinds creating an extended optically thick envelope.While the evolution driver is the nuclearphysics of the shells,the stellarstructureisgoverned by opacity, dust-formation andthe wind.

Planetary NebulaFormationand WhiteDwarf Cooling Ultimately, the expansionresults in adynamical instabilitywhich causes the expulsion of the outer layers as aplanetary nebula. Unabletosustain nuclearreactions,the remnantenvelope starts to contractonathermaltimescale.When it hascooledsufficiently(the surfaceactually heats,but the totalentropyfalls),the star approaches the whitedwarf coolingtrack.The significantphysics in thisphase arethe chemical structureofthe coolingenvelopeand the very high overall luminosity. As the star reaches the whitedwarf coolingtrack with effective temperatures > 100 000 K, even the envelopebecomes electron-degenerate. Opacity-driveng-modepulsationscan man- ifestwhen the internalchemical structureisright (GWVir variables). As the star descends the coolingtrack,ionizationzones in thewhite dwarfatmosphere becomeconvective.Duringsubsequent cooling, the star passes throughthe DBV and DAV=ZZ Cetinstabilitydomains. Again,g-modes areexcited,offering apossibilitytoexplore the chemical structureofthe deep interior, as well as the physicsofsurface convection and the whitedwarf equation of state.

Binary Stars Theabove description appliestothose starswhich evolve as single starsorasmembers of wide binary systemswhich do notinteract. It is increasingly clearthatalargefraction of starsare 244 Theimpactofasteroseismology on thetheoryofstellarevolution born in binary systemsinwhich the components exchange material at some pointduringtheir evolution.Masstransfermay be slow andconservative(stable Roche Lobeoverflow), rapid (dynamicalmergers),ornon-conservative(common-envelopeejection). Theresulting stars (e.g. blue stragglers, early-R stars, subdwarf Bstars, RCrB stars) have structures entirely different from those predicted by single-startheory.Avitaltaskofasteroseismology is to probethe current structureofthesestars andexplain the physicsofthe priorinteraction.

TheImpactofAsteroseismology

In reviewingthe impact of asteroseismology on the theoryofstellarevolution,wehavealready touched on one major probleminstellarpulsation –the Cepheidmassdiscrepancy.Another wasthe drivingmechanism forthe β Cepheidvariables(Moskalik&Dziembowski1992).In both casesthe solution wasopacity –specifically the contribution of iron-group elements to opacityattemperatures around 105K. It will be seen thatthe rˆoleofopacity is arecurring themeinasteroseismology. Time andspace do notpermitdiscussion of the recent impact of studies of the Sunand solar-likeoscillations, δ Sctand γ Dorvariables, ro-Apstars andslowly-pulsating Bstars, nottomention RR Lyr, BL Her, andWVirvariables, bumpCepheids andmanyothers. The authorhas chosen to focus on familiarterritory,i.e.asteroseismology in the latestages of stellarevolution.

ExtremeHorizontalBranch Stars Extremehorizontal-branch (EHB) starswerefirst discovered as faintbluestars in the Galac- tichalo,wherethey became more commonlyknown as subluminousB(orsdB)stars (Greenstein&Sargent 1974). Theircosmicimportanceisestablished by the contribution they maketothe ultravioletlight of giantellipticalgalaxiesand certain galacticglobular clusters (Yi&Demarque 1998, Brown et al. 2000).Straightforward studiesoflow-massstellarstruc- tureand evolution demonstrates thatsdB stars(a) must be helium-core burning starswith amassof∼0.5M⊙andanegligible hydrogen envelope and(b) cannotbeproduced by conventionalsingle-star evolution. Fortunately, it is clearthatthereare at leastfourbinary- star evolution channelsthatwill result in the production of an EHBstar, as well as at least four typesofstellarsystem containingansdB star.The question is whether we cancompare natureand theory.Stellarpopulationsynthesiscan be used to estimatethe mass distribution of the EHBstars expected from each of the binary evolution channels(e.g. Hanetal. 2003). While aspecific mass distribution depends on certain simulation parameters(metallicity, crit- ical mass ratio forstablemasstransfer, mass transfer efficiency,etc.)itisclear that, for example,heliumwhite dwarfmergerswill result in amuch broader sdBmassdistribution thancommon-envelopeevolution,orstableRoche lobe overflow. It is possibletoidentify whichsdB star came from whichevolution channel from itsbinaryproperties, but notusually to measure itsmassprecisely.Fortunately, the discoveryofpulsationsinsdB stars(EC 14026 stars: Kilkenny et al. 1997, PG 1716 stars: Green et al. 2003) hasmadeitpossibletocarry outasteroseismology (e.g. Charpinet et al. 2008) andhence determine the mass distribu- tion of different classesofsdB star (e.g. Randall et al. 2008). More systemswill have to be solved by asteroseismology before thistechnique yields an unequivocaltestofthe theory –but current signsare promising. Asecond consequence of the pulsation discoverieswas evidence of chemical stratification–iron-group elements have to be enriched in the driving zones by radiatively-drivendiffusionifthey aretopulsate at all (Charpinet et al. 1997).

Post-AGB Stars Beyond the horizontaland asymptotic-giantbranches,low-massstars contracttowards afully degenerateconfigurationonthe white-dwarfcoolingsequence. Theirinteriorpropertiesare C. S. Jeffery 245 governed by chemical stratification, arecord of previous evolution frozen in by the hard equa- tion of state. Alongthe coolingsequence, whitedwarfstraverse aseriesofinstabilitystrips where, if the compositionofthe drivinglayersisright, excited g-modes makeitpossibleto explorethisdeep interior. Recent progressisreviewedamply elsewhere(Fontaine2008).It suffices heretorecall the poster child BPM 37093 (= Lucy:Metcalfeetal. 2004).Asteroseis- mology usingdatacollected by the WholeEarth Telescopeconcluded thatthisstarwas 90% crytallized carbon –agiantdiamondinthe sky–andplaced strong constraints on the masses of the outer hydrogen andheliumlayers(−4.2 > log MH > −5.6, 2 > log MHe > −2.6). While the details arenot entirely uncontested (Brassard &Fontaine2005),itissignificant thattwentyyears ago, there wasconsiderable debate over the valueofMHat the endofAGB evolution. Strong limitsonMHand MHe from asteroseismology nowdirectlyconstrain stellar evolution theory.

Post-Post-AGBStars Also in the lasttwo decades,substantial evidence hasaccumulated thatcontraction to become awhite dwarfisnot the final journey in the lifeofverylow-massstar. In some stars, it appears thatre-ignition of the helium-burning shellasthe star is contracting (a latethermal pulse)or even after it hasreached the coolingtrack (a very-latethermal pulse)causesthe star to expand vigorously to becomeayellowsuper-giant. Whilstcooland luminous,anincreasing pulsation period maygivedirect evidence of expansion(cf.FGSge, vanGenderen &Gautschy1995). Thechallengefor stellarevolution theoryistounderstandthe physics of theselatethermal pulses. For example,following alatethermal pulse,modelssuggestthatflash-driven convec- tion mixesfresh nuclearmaterial up through the inter-shellregion, but theseare notdredged to the surfaceuntilthe star hasbecomeagiantand hasdeveloped adeep opacity-driven surfaceconvection zone, whereupon the surfacebecomes rich in heliumand carbon.Inthe case of avery-latethermal pulse,modelssuggestthatflash-driven convection is sufficiently energetictopenetratethe nowmuch lowerentropybarrier at the base of the hydrogen enve- lope andtoreach all the waytothe stellarsurface (Sch¨onberner 1979, Herwig et al. 1999). Promptmixingofthe entire outer layers will result,including ingestion of protonsinto hot helium- andcarbon-rich inter-shellmaterial with the likelyproduction of additional s-process elements. As the energy of afinalflashisdissipated, the envelopecools andthe star contracts for asecond time to the white-dwarfcoolingtrack,asanhydrogen-deficient star.While the times-scales of contraction (and expansion) depend on when the final-flashoccurred(lateor very late), both channelsproduce very hot(DO)white dwarfs.Several starsatthe transition between contraction andcoolingshowmulti-periodicg-modepulsations. Asteroseismology of these GW Virvariableshas provided very strong constraints on the global properties (mass, radius,effective temperature) of these stars, as well as internal properties such as the thickness of the heliumenvelope(Corsico et al. 2007a,b,Althaus et al.2008).One challengeisthat the best modelsofthe best-observedstar(GW Vir) predict an increasing period,whilstthe observations show adecreasing period.The question is whether thisisaproblemwiththe heliumenvelopethicknessorsomeotheraspect of the internalstructure.

Post-White-DwarfEvolution –IsThereLifeAfter Death? TheGWVir variablesand other PG 1159–035 starsand DO whitedwarfsformthe hotend of asequence of “post-post-AGB” starswithhydrogen-deficientand very carbon-richsurfaces (∼ 10%bynumber).Another hydrogen-deficient sequence, with ratherlower carbon abun- dance (∼ 1% by number) is suggested by the RCrB variables, extremeheliumstars (EHe) andotherhydrogen-deficient hot subdwarfs(cf.www.arm.ac.uk/∼csj/research/ehe links/ andJeffery2008a). Thelatethermal pulse fails to account formanyofthe properties of thissequence; astronger model is provided by the idea thatbinarysystemscontainingtwo 246 Theimpactofasteroseismology on thetheoryofstellarevolution whitedwarfsmay merge. Theignitionofheliummaterial accreted onto the CO whitedwarf surfaceforces the star to becomeayellowsuper-giant, andsubsequentlytocontractalong thissequence (Saio &Jeffery2002, Claytonetal. 2007).The most massive of these stars have luminosity-to-mass ratiosthatare so high thatthey arepulsationallyunstablebothwhile theyare in the classicalCepheidinstabilitystrip (theRCrBstars) andasthey evolve to higher effective temperature(Saio &Jeffery1988, Jeffery2008b). Therehavebeen suggestionsthat the hottestEHesexhibit multi-periodic pulsations, andclear evidence of strong line-profile variations,but with periods ∼ 1day andlonger,and the likelihood of extremenon-adiabacity, adirect applicationofasteroseismology to testthe whitedwarf merger model forthesestars remainsacherished dream.

ReallyDeadStars

Most exoticofall, arethe oscillations thatmight be exhibited by neutron stars. Theclock- likeradio signatures of pulsars arewell-known, thoughpossiblylesswell-understood.Some authors have examined the potential forgeneratingsurface Rayleigh wavesinthe solid crust (e.g. Yoshida&Lee 2001, 2002),while Piro &Bildsten (2004, 2005a,b) have looked at oscillations in the fluid layers abovethe solid crust. Thequestioniswhether anyofthese oscillations,ifexcited, wouldmanifesttoadistantobserver. X-rayobservationspoint to millisecond oscillations in anumberofneutron stars(Kaaretetal. 2007, Casella et al. 2008, Strohmayeretal. 2003).XTE J1814-338 hassuggested an asteroseismologicalapplication thatleads to the mass-radiusratio andhence to astrongconstraintonastiff equation of statefor the neutron-starinterior(Bhattacharyyaetal. 2005,Leahy et al. 2008).

Conclusion

Theopening slideofthe talk on whichthispaper is basedshowedaphotograph of an asteroseismologist andageologist (theauthorand daughter) sailingasmall boat on Belfast Lough. Thereisevidence of adriving mechanism –windacting on the sails of the boat.The motion of the boat demonstrates oscillations of the water surface; since gravity(or buoyancy) is the restoringforce –thesemustbegravity waves. Sprayfromthe dinghy’s bowshows evidence of damping, at leasttothe crew.Following closer inspection of the supporting fluid (bycomplete immersion) –the expedition concluded thatfurther study of such waveswould tellthem alot aboutfluiddynamics, andperhaps aboutthe surfacegravity of the Earth, but relativelylittleabout itsglobalstructureorevolution.The lessonisthatstellaroscillations invariably inform aboutthe physics of astellarenvelope; theextensiontoinformationabout stellarevolution is notalwaysobvious. Ourintroduction emphasizedcaution;much of the recent impact of asteroseismology has been to reveal the structureofapulsating star,and therebytoexplore the underlying physics, such as convection, rotation,opacity anddiffusion. Thereisnodoubt thatthe study of stellarpulsation as awhole hashad aprofound impact on all of these,aswellasradically reforming ourtheories of stellarevolution and, indeed, cosmology.Asteroseismology perseis comingofage as more sensitiveexperiments andmorenumerous targets becomeavailable. It is becomingpossibletotestthe evolution theorybyobserving stellarstructureatmany points between the stellarnursery andthe stellargraveyard.Inthisbrief r´esum´e ,wehave discussedevidence thatasteroseismology hasmadeamajor impact on:understanding the physics of mainsequence stars, resolvingthe theory of stellarevolution through He-burning phases, testing newaspects of evolution theory andphysics for“exotic” stars, resolvingthe C/He/H structureofwhite dwarfs,providing tests of nuclearprocessesand mixing in prior phasesofevolution,and, viamassesand rates of period change,testing modelsfor stars evolving on thermaland/or nucleartimescales. C. S. Jeffery 247

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DISCUSSION

Noels: Idonot understand whyyou completely rejectthe singlestarscenario to explain sdB stars. Are youconfident enough about mass loss ratesduringmass loss ratesduringred giantphase andhelium flashes to rule out such ascenario? Jeffery: So farIhave not seen anyresultthatwouldleadmetobelieve that asingleRGB star canlose itsenvelopeearly.Heliumflash models do not predictenhanced mass loss. Normalred giantwinds do not suggest removalofthe entire H-envelope. Otherwise,Iwouldexpecttosee many more sdBstars than we do –especiallyinglobular clusters.Havingsaid that,the sdBstars in globularand old-red-dead galaxiesmusthaveasignificantlydifferentprogenitorpopulationtothoseinthe disk of theGalaxy. It is conceivablethatRGB winds behave differently in theseenvironments. However Ithink it more likelythat ashift in thebalance between theclose-binaryformation channels (merger versuscommon-envelope, for example)isresponsible forthe different sdBstatistics. Lampens: Coulditbethatthe problem with g-mode instabilitystrip is due to thefactthatmanysdB starsare closebinariesand that g-modesare not intrinsically excited? Jeffery: Sinceonlyafraction of g-mode sdBs areinclose binaries,intrinsic excitation must operateinthe remainderand therefore, most likely,inall. Nowthatweunderstand theopacities better(Jeffery,C.S., &Saio,H., 2006, MNRAS, 372, L48),Ido not believe thereisany problem with thefundamental physics of theg-modeinstabilitystrip,thoughthe details must stillberefined.

Audience paying attention to atalk Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Examples of seismicmodelling

A. A. Pamyatnykh1,2,3

1 N. Copernicus Astronomical Center, ul.Bartycka18, 00-716 Warsaw,Poland 2 Institut f¨ur Astronomie,T¨u rkenschanzstrasse 17, A-1180Vienna,Austria 3 InstituteofAstronomy, Pyatnitskaya Str.48, 109017 Moscow, Russia

Abstract

Findings of afew recent asteroseismicstudiesofthe mainsequence pulsating stars, as per- formedinWojciechDziembowski’sgroup in Warsawand in Michel Breger’s groupinVienna, arebrieflypresented anddiscussed. Theselected objects arethree hybrid pulsators ν Eridani, 12 Lacertaeand γ Pegasi,which show both β Cephei andSPB type modes,and the δ Scuti type star 44 Tauri.

IndividualObjects: ν Eri,12Lac, γ Peg, 44 Tau

Introduction Main sequence stars(including the Sun) seem to be idealobjects forthe seismicmodelling, i.e. forconstruction -orrather refinement -ofthe modelsofindividualstars usingdataon their multiperiodicoscillations.The structureofthe MS starshas been understood qualita- tively quite well but some details of the structureand some physicalprocessesstill need to be explained. Theseproblemshavebeen specifiedand discussedinavery compact andinfor- mativeformbyMarc-AntoineDupret(2008) in hisintroductory talk (theseProceedings). By fitting stellarmodelstoobservational data on oscillations, we canobtain detailedconstraints on stellarparametersand on physicalprocessesininteriors. Most of the results, presented in thiscontribution,havebeen discussedmorethoroughlyby Dziembowski&Pamyatnykh (2008) andbyLenz et al. (2008).However, newestobservational data (inparticular, for44Tau)may change some conclusions of those papers.

Hybrid stars ν Eri, 12 Lac and γ Peg Hybrid starsare main sequence pulsating variableswhich show twodifferent typesof oscillations:(i) low-order acoustic andgravity modes of β Cephei type with periods of about3−6hours,and (ii) high-order gravitymodes of the SPBtypewithperi- odsofabout 1.5 − 3days. Theoretically,such abehaviourwas predicted for ℓ>5by Dziembowski&Pamyatnykh (1993, seeFigs. 5and 6there) andlater,when usingnewer opacity data,alsofor the low-degreeoscillations (Pamyatnykh 1999).Inthe HR diagram, the overlappedregion of the β Cepand SPBtypepulsationsisverysensitivetothe opacitydata (see Figs.3and4in Pamyatnykh 1999),thereforethe modelling of hybrid star pulsationswill allowtotestthe opacityofthe stellarmatter -for example,tochoosebetween twoindepen- dent sets of the OPAL andOPdata(Iglesias &Rogers1996 andSeaton2005, respectively). Theoretical β Cepand SPBinstabilitydomainsand position of three confirmed hybrid stars areshown in Fig. 1. Allthree starsare very closetothe region wherehybridpulsationsare expected when usingthe OP opacities. 250 Examples of seismicmodelling

Figure 1: Pulsationalinstabilitydomainsinthe upper part of themain sequence. In theoverlapped region of the β Cep type andSPB type oscillations thehybridpulsations areexpected. OP opacity data for Z =0.015 andfor newsolar proportions in theheavy elementabundances were used (mixtureA04, Asplund et al. 2005).The positions of observed starswereobtainedusingcatalogs of Stankov &Handler (2005, β Cep)and De Cat(2007, SPB).Three hybrid starsare marked explicitly.

Fig. 2shows the observationalfrequencyspectraofνEriand 12 Lac. High-frequency modes of the β Ceptypeare well resolved, andtheirdegree, ℓ,and in some casesalso azimuthalorder, m,are determined from photometryand spectroscopy. For very slowrotating star ν Eri, oneradial mode, two ℓ =1triplets (modes g1 andp1)and onemoremode (ℓ =1,p2, ν =7.89c/d)are identified. For 12 Lac, oneradial mode, twocomponents of a ℓ =1tripletand 5other ℓ =1and/or ℓ =2modes areidentified. TheseismicmodelsofνEriwhich fit radial andtwo ℓ =1,m=0frequencies were con- structed fordifferent opacities (OPand OPAL)and different assumptionsabout the efficiency of the overshooting from the stellarconvective core.Ausseloos et al. (2004) constructed seis- micmodelsofthisstarwhich fit onemoremode, ℓ =1,p2 at ν =7.89c/d,but it was necessary to assume rather unrealisticchemical composition parameters(Xand/or Z )and a quite effective overshooting.Moreover,they didnot consider the low-frequency modes of the SPBtypepulsations. We argued thatthe overshooting from the convective core is ineffective in ν Eri(seismicmodelswithovershooting arelocated outsidethe observationalerrorbox in the HR diagram)but thisresultcritically depends on the Teff determination. A. A. Pamyatnykh 251

Figure 2: Observationalfrequencyspectra of ν Eri and12Lac basedonJerzykiewiczetal. (2005) and Handler et al. (2006) data,respectively. Thenumbers abovefrequencybarsmarkmodedegreevalues, ℓ, as inferredfrommulticolour photometry (accordingtoDziembowski&Pamyatnykh2008).

Fig. 3illustrates the effectofthe opacitychoicebetween the OPAL andOPdataon the instabilityofℓ=1and ℓ =2modes of ν Eriseismicmodel.The OPAL model was discussedbyPamyatnykh et al. (2004).Using the OP data leadstowider frequency insta- bilityrange, as it hasbeen demonstrated very clearlyfor whole β Cepand SPBdomainsby Miglio et al. (2007).They also showed that the effectofthe choice between oldand new solar proportionsinthe heavy element abundances-respectively,GN93(Grevesse &Noels 1993) andA04 (Asplund et al. 2005) -issignificantlysmallerthanthatofthe opacitychoice. Only the model constructedwiththe OP data is unstableinlow-frequency modes (high-order g modes of ℓ =2)and canfitthe measuredfrequencyat0.61c/d.The local η maximum for ℓ =1nearlycoincides with another measuredlow frequency at 0.43 c/d,but no instability wasfound there. Thereisalsoaproblemofexcitationand fitting of theobservedpeaks at 7.89 c/d,one of them wasidentifiedfromphotometryasanℓ=1mode (itmustbe ℓ=1,p2 mode).Zdravkov&Pamyatnykh (2008) demonstrated thatanadditional opacity enhancement by approximately50% around the iron bumpatits slightlydeeper location mayleadtothe instabilityofbothhigh-order gmodes and ℓ =1,p2 mode at the observed frequencies. Thetwo ℓ =1triplets in the ν Erifrequencyspectrum allow to constrain internalrotation rate. In Fig. 4, the rotational splitting kernels(weighting functionsinthe integral over the localrotationalvelocityinsidethe star)for twodipolemodes of theseismic ν Erimodel are shown. Thesekernelsdetermine the sensitivityofdifferent layers to the rotational splitting of the oscillationfrequencies, thereforefromthe measuredspacingsbetween components of different multiplets we canobtain informationabout internalrotation. We showed that in ν Erithe convective core rotates approximately5timesfasterthanthe envelope. 252 Examples of seismicmodelling

Figure 3: Thenormalizedgrowthrate, η,asafunction of mode frequencyfor ν Eri seismic modelcon- structed both with OPAL andOPopacities (η>0for unstablemodes). Both models fit theobservational errorbox (log L,log Teff )inthe HR diagram. Thefrequenciesofradial fundamental andtwo dipole modes (ℓ =1,modes g1 andp1)fitthe observed values at 5.763, 5.637 and6.244 c/d, respectively. Theob- served frequenciesare shownbyverticallines,withtheir lengths proportionaltothe mode amplitudesina logarithmicscale.Notethatinthe OP case thereare unstablelow-frequencyquadrupole (ℓ =2)modes, whereasinthe OPAL case all low-frequencymodes arestable.

Figure 4: Therotationalsplitting kernels, K,for thetwo dipole (ℓ =1)modes in theseismic modelof νEri.The correspondingpartofthe frequencyspectrumisshown in thesmall box. Theinnermaxima extendover thechemically nonuniform zone abovethe convectivecore. A. A. Pamyatnykh 253

Figure 5: Thenormalizedgrowthrates, η,ofℓ=1and ℓ =2modesasafunction of mode frequencyin seismic modelof12Lac computed with theOPopacities for Z =0.015 andheavy elementmixture A04. Vertical lines mark theobserved frequencies, with amplitudes given in alogarithmicscale.

In Fig. 5, the observed frequency spectrum of 12 Laciscomparedwithresults foraseismic model whichwas constructed to fit four dominant peaksat5.0-5.5 c/d: theradial fundamental mode, twocomponents of ℓ =1tripletand onecomponent of the ℓ =2quintuplet. Most of remaining peaksalsohavetheircounterpartsamong theoreticalfrequencies. The η(ν) dependence is similartothatfor the ν Erimodel in Fig. 3. Thetheoreticalfrequencyrange of unstable β Ceptypemodes fitsthe observed peaksverywell. However, the high-order g modes of ℓ =1and ℓ =2arestable, in contrasttothe ℓ =2case of ν Eri. Again,the solution of the problemmay require an opacityenhancement in the drivingzones in deep envelope. From the frequencies of twocomponents of rotationally splitted ℓ =1triplet(and taking into account anecessity to fit the observed ℓ =2peak at 4.2c/d)weestimated that the convective core rotates approximately4.6 timesfaster thanthe envelope, thisresultis similartothatfor ν Eri. Thecalculated surfaceequatorial velocity of 47 km/s agrees very well with the spectroscopicestimationofabout 50 km/s. γ Pegisalsoahybrid star (Chapellieretal. 2006 andprivate communication by G. Handler) with twooscillationfrequenciesofthe β Ceptype(6.01 and6.59c/d), andtwo -ofthe SPB type (0.686 and0.866 c/d). Fig. 6illustrates preliminaryresults of themodelling. Themodels were constructed by fitting the frequency of theradial fundamentalmodetothe observed frequency at 6.59 c/d.Asitiseasytosee from Fig. 6, the frequency of dipole mode ℓ =1,g1 canfitthe observed value6.01c/d in amodel with Z valueinbetween 0.015and 0.02. Twoobservedlow-frequency modes arewellinsidethe frequency rangeofunstablehigh- order gravitymodes of ℓ =2.The identificationofthe mode degreefor observed peaks will allowtocheckthesepreliminaryassessments.Now,anintensivecampaignofground- basedand satelliteobservations(with the MOST satellite) is on the way(G. Handler,private communication).

44 Tau

The δ Scttypevariable 44 Tauisanextremely slowly rotating star in which15oscillation frequencies have been measured(Antoci et al. 2007, Breger &Lenz 2008). Twoofthem are identifiedasradial modes.Moreover,7other modes have been identifiedasℓ=1and ℓ =2 oscillations.The log g valueasdetermined from photometryand spectroscopydoesnot allow to choosebetween themain sequenceand post-MS model forthisstar. Lenz et al. (2008) gave asteroseismicarguments in favorofthe post-MS model.Inparticular,onlypost-MS model canfitbothobservational errorbox in the HR diagram andfrequenciesoftwo radial modes.InFig.7 the observed andtheoreticalfrequencyranges arecomparedfor two44Tau 254 Examples of seismicmodelling

Figure 6: Thenormalizedgrowthrates of ℓ =1and2modes in two γ Pegmodelsconstructedwiththe OP opacities forthe heavyelement mixtureA04. Both models have mass of 8.7 M⊙ butdiffer in the heavyelement mass fraction, Z.Two larger points closetothe ν4 mark mode ℓ =1,g1.

Figure 7: Thenormalizedgrowthrates of ℓ =0−2modes in themain sequenceand post-MSmodels of 44 Tau. Vertical lines mark theobserved frequencies, with longerlines fortwo identifiedradial modes. Both models fit theseradial frequencies. star models. In contrasttoasimilarplotgiven by Lenz et al. (2008),thisfigure also includes thepreviouslyunknown lowest frequency mode at 5.30 c/d whichhas been detected very recently (Breger &Lenz 2008). This finding maybeanargument against the post-MS modelsfor 44 Tauwhich have no unstablemodes at theselow frequencies. A. A. Pamyatnykh 255

Acknowledgments. Apartial financial supportfromthe PolishMNSiW grantNo. 1P03D 021 28 andfromthe HELASproject is acknowledged. Iamgrateful to Tomasz Zdravkov for Figs.1 and6,and to PatrickLenz forFig.7 andusefulcomments. References Antoci,V., Breger,M., Rodler,F., et al. 2007, A&A, 463, 225 Ausseloos,M., Scuflaire, R.,Thoul, A., &Aerts,C.2004, MNRAS, 355, 352 Asplund, N.,Grevesse,N., &Sauval, A. J. 2005, ASPC, 336, 25 Breger,M., &Lenz, P. 2008, A&A, 488, 643 Chapellier, E.,LeContel,D., Le Contel,J.M., et al. 2006, A&A, 448, 697 De Cat, P.,Briquet, M.,Aerts,C., et al. 2007, A&A, 463, 243 Dupret,M.-A. 2008, CoAst, 157, 16 Dziembowski, W. A., &Pamyatnykh, A. A. 1993, MNRAS, 262, 204 Dziembowski, W. A., &Pamyatnykh, A. A. 2008, MNRAS, 385, 2061 Grevesse,N., &Noels, A. 1993, in Origin and Evolutionofthe Elements,eds.PratzoN., Vangioni-Flam E.,Casse M.,Cambridge Univ.Press.,p.15 Handler,G., Jerzykiewicz,M., Rodriguez,E., et al. 2006, MNRAS,365, 327 Iglesias, C. A., &Rogers,F.J.1996, ApJ, 464, 943 Jerzykiewicz,M., Handler,G., Shobbrook,R.R., et al. 2005,MNRAS,360, 619 Lenz, P.,Pamyatnykh, A. A., Breger,M., &Antoci, V. 2008, A&A, 478, 855 Miglio,A., Montalb´a n, J., &Dupret, M.-A.2007, MNRAS, 375,L21 Pamyatnykh,A.A.1999, AcA, 49, 119 Pamyatnykh,A.A., Handler,G., &Dziembowski, W. A. 2004, MNRAS, 350, 1022 Seaton, M. J. 2005, MNRAS, 362, L1 Stankov,A., &Handler,G.2005, ApJS, 158, 193 Zdravkov &Pamyatnykh2008, CoAst, 157, 385

DISCUSSION

Noels: Ifully agree with youthatthere probablyisamissingopacity not only in β Cep starsbut all along the MS.Iamhowever surprisedbyyour resultsfor ν Eri on thecomparisonbetween OP andOPALopacities. The”best”modelsyou obtain areverydifferentwhich meansthatthe change is not only due to changes in theironbumpbut also to changesinthe wholestar. Do youagree with that?Thisisverydifferent from an increase of opacity limited to theironbumpwhich will onlyaffect theexcitation of themodes. Pamyatnykh: Youare correct in that our best seismic models computed with theOPALand OP data differinasome extentnot onlyinthe iron bump region butalso in thewhole star.The most important differencebetween theOPand OPAL opacities is that in theOPcase theironbumpislocated slightly deeper in thestar(at slightly highertemperatures) compared with theOPALcase.Our seismic models of ν Eri fit theobserved frequenciesofthe radial fundamental mode andtwo dipole modes(g1and −3 p1)verynicely, with an accuracy betterthan10 .The opacity changesaround theironbumpeven by about 20 percent(whichisasystematic differencebetween OP andOPALatfixed temperaturein this region) lead to achange of thestellarstructure andconsequently to achange of theoscillation frequencyspectrum, so to fit theobserved frequencieswemust adjust globalstellarparameters-such as mass, heavyelement abundanceand effectivetemperature.Therefore,the structureofthe seismic modelconstructedwiththe OP data will differinsomeextentfromthatofthe modelconstructedwith OPAL.Again,anadditionalsimilaropacity change aroundthe iron bump will alsoaffect theoscillation frequencies(not only themodeexcitation) andthereby thecorrespondingseismic model. Such atest with artificially enhanced opacity in avicinityofthe iron bump (more exactly,slightly deeper than the iron bump!) hasbeen performedbyT.Zdravkovand myself (these Proceedings). Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Asteroseismology of pre-main sequencestars

K. Zwintz1,D.Guenther2 andT.Kallinger1 1 Institut f¨ur Astronomie,T¨u rkenschanzstrasse 17, A-1180Vienna,Austria 2 Department of Astronomyand Physics, St. Mary’s University, Halifax,NSB3H 3C3, Canada

Abstract

More than30years agothe first pulsating pre-mainsequence (PMS)stars have been discov- ered.Since then, pulsationsin18HerbigAestars and18members of young open clusters were detected anddetailedasteroseismicinvestigationswereconducted forsomeofthem. We describeour latestresults in thisfield. Usingground-basedobservationsofNGC 6530 278, it waspossible forthe first time to show thatthe star’s observed frequency spectrum canonlybeexplained by aPMS model. Observations obtained with the MOST spacetelescopeallowedtostudythe pulsationsofthe enigmatic Herbig Ae star HD 142666, whichisalsosurrounded by adensecircumstellardisk. In addition,4new pulsating PMSstars were discovered in the young open cluster NGC2264 basedontime-series photometrywiththe MOST satellite.

IndividualObjects: HD 142666, NGC6530, NGC2264

Introduction

Pre-main sequence (PMS)stars areontheirway from the birthlinetothe zero-age main sequence (ZAMS) in the Hertzsprung-Russell (HR) diagram. They derivemostoftheirenergy, half of whichheats the star andhalf of whichradiates away,fromthe releaseofgravitational potential energy as the star collapses. As hydrogen hasnot ignited in their cores, their interiors aremostlychemically homogeneousand lackregionsofalready processednuclear material, whichisthe maindifference to their(post-)mainsequence counterparts. Onecan distinguishbetween twogroups of young stars: (i)the low-mass (M ≤ 1M⊙)TTauristars with spectral typesfromlateFtoMwhichare notthe maincandidatestosearchfor pulsation; (ii) the intermediate-mass (1M⊙ ≤ M⋆ ≤ 10M⊙)HerbigAe/Bestars with spectral types Btoearly Fthatcan becomepulsationallyunstable. Butthe evolutionarystages of these stars areambiguous:stars with masseshigher than ∼ 6M⊙ do nothaveavisiblePMS phase as their birthlineintersects with the ZAMS(Palla &Stahler 1993),while starsbelow ∼ 6M⊙ have an observable PMSphase.Furthermore,the evolutionarytracksofpre-and post-main sequence starsofsame mass, effective temperatureand luminosity intersect severaltimes closetothe ZAMS(Breger &Pamyatnykh 1998) prohibitingacleardetermination of the evolutionary phase of afieldstar. Thereasonisthatyoung starsand theirmoreevolved counterparts show similarenvelopepropertiesand only differintheirinteriors (Marconi &Palla1998). As the coresofpost-mainsequence starsare much denser thanthose of PMSobjects, the small frequency spacings aredifferent in the twoevolutionaryphases(Suranetal. 2001). If the observed oscillationspectrum of astariscomplete enough,itshouldbepossibleto determine the ageofapulsating star from asteroseismology.Totestthishypothesis pulsating PMSstars forwhich the evolutionaryphase is knownfromanindependent source need to be investigated. K. Zwintz,D.Guenther, andT.Kallinger 257

Pulsating PMSstars

The36known PMSpulsators (Zwintz 2008) areeither Herbig Ae field stars(with masses ≤ 4M⊙)ormembers of young open clusters. Thelatter have to be younger than 10 MyrtoensurethattheirAandFtypemembers areintheirPMS phase.These36stars pulsate likethe classical δ Scuti starswithperiods between 20 minutes and6hoursand with amplitudes at the millimagnitude level. Theirpulsation is alsodrivenbythe κ and γ mechanisms in the Hand He ionization zones (Marconi &Palla1998).

NGC6530 2781 For starsinthe young open cluster NGC6530, CCD time-seriesphotometrywas obtained using the CTIO 0.9m telescope andJohnson V & B filters. 6PMS cluster memberswerediscov- ered to pulsate (Zwintz &Weiss 2006);among thoseisNGC 6530 278 (V =12.16 mag) whichhas amembership probabilityof68% (van Altena&Jones 1972). Theidentified 9pulsation frequencies of NGC6530 278 were subject of an asteroseismicanalysisusing a denseand extensivegridofmodel spectratofind the best match to the observed frequency spectrum.Thismethodwas originally developed by Guenther &Brown (2004) formod- ellingstars in advanced evolutionarystages.All frequencies-except one -could be fit as l =0,1and2modes providingclear evidence of the existence of nonradial pulsationsinPMS stars(Guenther et al. 2007). Themodel wasfitunder the assumption thatthe star is indeed in itsPMS evolutionary phase.Asthe observed frequency spectrum of NGC6530 278 is completeenough, it was possibletocheck whether the oscillations couldalsobereproduced by apost-mainsequence model.So, we thentried to fit post-main sequence modelstothe observedp-modefrequencies the same wayaswedid forthe PMSmodelsusing the same chemical composition andmixing- length parameter (i.e., calibrated to the solarmodel). No post-main sequence model could be found to fit the observed frequencies (Guenther et al. 2007).Therefore, we conclude that, in thiscase, it is possibletodistinguish between apre-and apost-mainsequence star only from the observed frequencies.Based on this, we areabletoconfirmthatNGC 6530 278 is indeed aPMS object.

HD 142666 Asinglepulsation period of ∼1.12 hourswas discovered in the Herbig Ae star HD 142666 (V =8.81mag)byKurtz &M¨u llerin2001. Thepulsational variations were knowntolie on topoflarger irregularvariations caused by adensecircumstellardustdiskseen edge-on (Meeus et al. 1998).For adetailedasteroseismicstudyofthe pulsationsofthe star,additional, longer time-seriesofhigher qualitywereneeded. Hence, HD 142666 wasproposedastarget forthe MOST satellite(Walker et al. 2003) to the MOST ScienceTeam. MOST observations of HD 142666 were conducted for11.5daysin2006 andfor nearly 39 days in 2007. Thelight curvesshowthe typical“UX-Ori type”irregularvariations caused by the circumstellardustdiskwithapeak-to-peak amplitudeof∼1magnitude (see Figure 1: upper panel:2006 data,middlepanel:2007 data). Thepulsational variations at the milli- magnitude levelare showninthe bottomlayer in Figure1.Adetailedfrequency analysisof the data sets from both yearswas performed(formoredetails seeZwintz et al. 2008).12fre- quencies couldbeidentifiedtooriginate from pulsation andweresubject to an asteroseismic analysis. ThelocationofHD142666 in the HR-diagramisquite uncertain,since the star is sur- rounded by adensecircumstellardiskwhich affects the determination of effective temperature andluminosity. Thevalues forthe star’s effective temperaturegiven in the literaturevary

1 Numbering accordingtoZwintz&Weiss(2006) 258 Asteroseismology of pre-main sequencestars

Figure 1: MOST observations of HD 142666: Thetypical “UX-Oritype” irregular light variations are clearlyvisible both in the2006 data (top panel) and in the2007data(middlepanel). Thepulsations are seen in thelower panelwhich showsazoom into the2007 observations. between 7200 K(Vieira et al. 2003) and8500 K(Dominik et al. 2003).The only estimate forthe luminosity is givenbyMonnier et al. (2005) whoobtain L =8.8±2.5 L⊙ derived from arelationbetween thecircumstellardiskradiusand the stellarluminosity. As the input parametersofthe disk itself areuncertain,the result is quite ambiguous. We again used the denseand extensivegridofmodel spectratofind the best match to the observed frequency spectrum.However,inthe case of HD 142666, it wasnot possible to findafit to all 12 identifiedpulsation frequencies simultaneously.Therefore, theanaly- sisfocused on the fivemostdominantmodes,for whichgood model fitsweredetermined (Zwintz et al. 2008). Theasteroseismologically derived values lie significantlyout of the uncertainty boxof the values foreffective temperatureand luminosity takenfromthe literature. Therefore, additional studies of the fundamentalparametersofHD142666 together with itspulsations have to be carriedout to be able to give adefinite solution.

NGC2264 Recently,MOSTobservedthe young open cluster NGC2264 (age ∼3Myr)tosearchfor PMSpulsators apartfromthe twoalready known oscillators, V588 Monand V589 Mon (Breger 1972; Kallinger et al. 2008).Asthe diameter of the cluster waslarger thanthe field-of-viewofMOST, the observations were performedusing twoalternating fields. High- precision time-seriesphotometryfor in total69stars between 7.5th and12th magnitude and with spectral typesfromearly BtoKwasobtained from space. MOST revealed4new pulsating PMSstars in NGC2264, oneexample is showninFig- ure2.The star pulsates with frequencies at 58.1and 61.5 d−1 andwithamplitudes of 11 and15mmag,respectively.Adetailedasteroseismicanalysis of all four newly identified starsisongoing. K. Zwintz,D.Guenther, andT.Kallinger 259

0.02

0.018

0.016

0.014

0.012 [mag] 0.01

0.008 amplitude

0.006

0.004

0.002

0 50 55 60 65 70 75 80 frequency [c/d]

Figure2:Amplitude spectrumofanewPMS pulsatorinNGC 2264 discovered usingMOSTobservations: thedashed lines at ∼ 56.7and 71 d−1 mark 4and 5times theorbit frequencyofMOST, respectively, and thedottedlines arethe corresponding1d−1sidelobes.The twofrequenciesat61.5and 58.1 d−1 aredue to pulsations.

Acknowledgments. KZ andTKacknowledge supportfromthe Austrian Science Funds (FWF; KZ:project T335-N16; TK:project P17580).The Natural Sciences andEngineering Research CouncilofCanadasupports the research of D.B.G. References Breger,M.1972, ApJ, 171, 539 Breger,M., &Pamyatnykh, A. A. 1998, A&A, 332, 958 Dominik, C.,Dullemond, C. P.,Waters, L. B. F. M.,Walch, S. 2003, A&A, 398, 607 Guenther,D.B., &Brown,K.I.T.2004, ApJ, 600, 419 Guenther,D.B., Kallinger, T., Zwintz, K.,etal. 2007, ApJ, 671, 581 Kallinger, T., Zwintz, K.,&Weiss,W.W.2008, A&A, 488, 279 Kurtz, D. W.,&M¨uller, M. 2001, MNRAS, 325, 1341 Marconi,M., &Palla, F. 1998, AJ, 507, L141 Meeus, G., Waelkens,C., &Malfait,K.1998, A&A, 329, 131 Monnier, J. D.,Millan-Gabet, R.,Billmeier,R., et al. 2005,ApJ,624, 832 Palla, F.,&Stahler,S.W.1993, ApJ, 418, 414 Suran, M.,Goupil, M.,Baglin, A., et al. 2001, A&A, 372, 233 vanAltena, W. F.,&Jones, B. F. 1972, A&A, 20, 425 Vieira,S.L.A., Corradi,W.J.B., Alencar, S. H. P.,etal. 2003, AJ, 126, 2971 Walker,G., Matthews, J. M.,Kuschnig, R.,etal. 2003, PASP,115, 1023 Zwintz, K.,&Weiss,W.W.2006, A&A, 457, 237 Zwintz, K. 2008,ApJ,673, 1088 Zwintz, K.,Kallinger, T., Guenther,D.B., et al. 2008, submitted

DISCUSSION Dziembowski: Didyou take into account rotational splitting? Zwintz: No. Weiss: Thereisapaperrecentlypublished by the Italian groupwhich triestotakerotation into account andthey determine very similarfrequencies. Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Internal dynamics from asteroseismology fortwo sdB pulsators in closebinarysystems

V. VanGrootel1,2,S.Charpinet1,G.Fontaine2,P.Brassard2,and D. Reese3

1 Laboratoire d’Astrophysique de Toulouse-Tarbes, Universit´e de Toulouse, CNRS,14Av. E. Belin,F-31400 Toulouse, France 2 D´epartement de Physique,Universit´e de Montr´eal, C.P. 6128, Succ. Centre-Ville,Montr´eal, QC H3C3J7,Canada 3 Department of AppliedMathematics,UniversityofSheffield,HounsfieldRoad, Sheffield, S3 7RH,UK

Abstract

Since theirdiscoveryelevenyears ago, short-period pulsating sdBstars have proved their potential forquantitative asteroseismologicalstudies. We have recentlyupdated our astero- seismicdiagnostic toolsinorder to incorporatethe effects of stellarrotationonpulsations, assuming variousinternalrotationlaws. It is possible, with these new tools, to determine the internalrotationprofile of twoshort-periodpulsating sdBstars residing in closebinarysys- tems, namely Feige48and PG 1336−018. They exhibitorbital periodsof9.024 hand 2.424 hrespectively,asmeasuredfromspectroscopy. For the twostars, we show thatspin-orbit synchronismisreached from the surfacedownto∼0.22 R∗ and0.55 R∗,respectively.The rotation of deeper layers cannot be inferredwiththe type of modes – p-modes –observedin short-period pulsating sdBstars. Theseresults canpotentiallyprovide new elements to test tidalfriction theories,particularlythe angularmomentumtransport,inclose binary systems.

IndividualObjects: Feige48, PG 1336−018 (NYVirginis).

Introduction

Subdwarf B(sdB) starsare hot(Teff =20,000−40,000 K) andcompact (log g =5.2 − 6.2) evolvedExtreme HorizontalBranch stars(EHB).They arecomposedofapartly convec- tive helium-burning core,surrounded by aradiativeheliummantleand averythinradiative hydrogen-richenvelope(Menv < 0.02 M⊙,while the totalmassisaround 0.5 M⊙). They spend about1.5×108 yr on the EHBand then evolve,after core-heliumexhaustion, directly toward the whitedwarf coolingsequence (Dorman et al. 1993). SubdwarfBstarshosttwo groups of nonradial,multiperiodic pulsators. Rapidoscillations (80 − 600 s) in the so-called EC 14026stars, discovered by Kilkenny et al. (1997),are usually identifiedwithlow-degree, low-order p-modes.The longer periods(0.75 − 3h)ofthe PG 1716 stars, discovered more recentlybyGreen et al. (2003),are due to low-degree, mid-order g-modes.The presence of ex- cited pulsation modes in both typesofpulsators is caused by aclassic κ-effect associated with an opacitybumpdue to partial ionization of heavy metals,especiallyiron, locally enhanced by radiativelevitationatworkinthe envelopeofthesestars (Charpinet et al. 2001, 2008). Asignificantfraction of sdBstars reside in closebinaries, with orbitalperiods from hourstodaysand whitedwarfsorMdwarfcompanions(see, e.g.,Maxted et al. 2001 or Green et al. 2001).The Feige48system is madeofashort-period pulsating sdBstarand an unseen companion(most likelyawhitedwarf), with an orbitalperiodof9.024 ± 0.072 h V. VanGrootel,S.Charpinet,G.Fontaine, et al. 261

(O’Toole et al. 2004).PG1336−018 (Porb =2.42438 h; Kilkenny et al. 2000) is oneofthe very few HW Vir-typesdB +dwarf Mclose eclipsing binaries,and the only known–to date –thatexhibitsshort-periodpulsationsfor itssdB component. Tidalforces in binary systems, among other long-termeffects such as circularizationand alignment of the rotation axis to the normalofthe orbit, tend to synchronizethe rotation of the twostars with the orbitalmotion. Theoreticalframeworksontidal interaction have been developed in the lastdecades essentiallybyZahn(1975, 1977, andreferences therein),where turbulent dissipative processesand radiativedampingare invoked. Another model basedon large-scale hydrodynamical currents wasproposedbyTassoul &Tassoul (1992, andrefer- ences therein).The question of the basicvalidity of these competing modelsisstill under debate. Thetheoreticalsynchronization timescan differbyordersofmagnitude depending on the physical mechanism invoked, especiallyinthe case of hotstars with radiativeen- velopes(such as sdBstars),wheretidal forces arelessefficient forsynchronization.Inany case,the confrontation of the theorywiththe observations,through the traditionalphoto- metric or spectroscopictechniques,onlydeals with the surfacelayers. Thesynchronization levelreached in the inner parts, by transportofthe angularmomentum from the surface (Goldreich &Nicholson 1989),isonlyaccessiblebyasteroseismology.Itthereforeconstitutes aunique opportunity to testthe theory of stellarsynchronization andangular momentum transportasafunction of depth.

Theforwardmodeling approach forasteroseismology

Thegroup of rapidlypulsating sdBstars hasprovedits potential forperforming objective asteroseismicanalyses(seeFontaineetal. 2008 forarecentreview).The methodimplements the so-called forwardmodelingapproach, built on the requirement of global optimization: theoreticalpulsation spectracomputed from sdBmodelsmustmatch all the observed periods simultaneaously.The goodnessofthe fit is evaluated throughamerit function defined as

N Xobs “ Pi − Pi ”2 S2 = obs th (1) σ i=1 i where Nobs is the number of observedperiodicities.The methodperforms adouble- optimization procedureinorder to findthe minima of the merit function,which constitutes the potential asteroseismicsolutions(seedetails in Charpinet et al. 2005b). Thecodes have been recentlyimprovedtoincorporatethe effect of the rotation of the star,which lifts the (2l +1)- fold degeneracyofeigenfrequencies of aperfectlyspherically symmetric star (Van Grootel al. 2008).Assuming an internalrotationlaw Ω(r), therotationalmultiplets are calculated, with the perturbative methodtofirst order,by

Z R 2 2 ξr − [l(l +1)−1]ξh − 2ξr ξh 2 σklm = σkl − m Ω(r)Kkl (r)dr ; Kkl = R ρr (2) R 2 2 2 0 0 [ξr + l(l +1)ξh]ρr dr where Kkl is the rotational kernel.The optimal solution givesthe structural parametersof the star (Teff ,log g, M∗,log q(H)) and, of utmostinteresthere, the internaldynamicsΩ(r) as afunction of the radius of the star. Theeffects of higher ordersdue to rotation have been estimated from polytropic (N =3) models, usingafull (nonperturbative) treatment of stellarrotationdeveloped by oneofus (Reese et al. 2006).The mainresults show thatthesehigher-order perturbation effects dueto rotation andtidal deformationofthe star cannot affect in anysignificantway the asteroseismic solution proposed forFeige 48 andPG1336−018 at the present levelofaccuracy(further details aregiven in Charpinet et al. 2008). 262 Internal dynamics from asteroseismology fortwo sdBpulsatorsinclose binary systems

Figure 1: Meritfunction S2 (inlogarithmicunits)asafunction of thecorerotationperiodofthe sdB star in Feige48system. Thesurface rotation is fixed at theoptimal valueof32,500 s(9.028 h) found for solid-bodyrotation. Thetransitionbetween thetwo layers is fixed to 0.3 R∗.

Test of spin-orbit synchronism withasteroseismology

Thepulsating sdBstarinthe Feige48system exhibits nine pulsation periodsinthe range 343 − 383 s, as observed in whitelight photometryatthe 3.6-mCFHTduringsix nights in June 1998 (Charpinet et al. 2005a). Threegroups of modes cannaturallybeconstructed from thispulsation spectrum,ascomponents of rotational multiplets approximatelyevenly distributed in frequency with ameanspacing of about ∼ 28 µHz.Theseninepulsation periods areusedinthe optimization procedure in order to findthe minima of the merit function, assuming several internalrotationlaws. First,the hypothesis of asolid-bodyrotation(Ω(r)= Ω=constant)istested,and the star rotation period Prot =2π/Ωthereforeconstitutes afree parameter in the optimization procedure.Thisleads to thedetermination of the structural parametersofthe star andtoarotation period Prot =9.028 ± 0.48 h(details canbefound in VanGrootel al. 2008),inexcellent agreement with the orbitalperiodofthe system Porb = 9.024 ± 0.072 hmeasuredfromRVvariations.Thisresultstronglysuggests thatthe sdB star is tidally locked in the Feige48system. To investigatethisquestion further,the hypothesis of differential rotation is tested by dividing the star in tworegions that each rotate independentlyassolid structures. In afirst step, thetransitionbetween thetwo layers is fixed to 0.3 R∗,following the sug- gestion of Kawaler&Hostler(2005).The surfacerotationisfixedtoits optimal value of 32,500 s(9.028 h), when thecorerotationisvariedfromaperiod of 4,500 sto40,000 s. Theoptimization procedure on structural parametersiscarried out foreachconfigurationof differential rotation.The best meritfunction S2 foreachconfigurationisplotted in Fig. 1. Averyfastcorerotationcan be rejected from Fig. 1, as it leadstomuch poorermerit functions; while S2 again increasesfor longer core rotation periods. Taking theuncertainties into account,thisresultindicates thatthe sdBrotates as asolid-bodyinthe Feige48system. In asecond step, thetransitionbetween thetwo layers canvaryfrom0.1 to 1.0 R∗,while the structuralparametersare fixed to theiroptimal values.The surfacerotationisfixedto the valueof32,500 s, andthe core rotation period Pcore canvary, as showninFig.2(left), from 5,000 to 45,000 s. Allthe meritfunctionsare showninFig.2,withacolor scale in logarithmic units.The optimal core rotation period Pcore (continuous whiteline) is not V. VanGrootel,S.Charpinet,G.Fontaine, et al. 263

Figure 2: Seismic internal rotation profile of thesdB star in Feige48(left; Porb =9.024 h) andPG 2 1336−018 (right; Porb =2.424 h). This S map(on alogarithmicscale)shows thequalityoffittothe observed pulsationperiods as afunction of theparameters Pcore and RS /R∗.The continuous whiteline indicatesthe minima of themerit function. Thewhite dot-dashedverticallines indicatesthe orbitalperiod. Whitedotted-linecontoursindicatesthe 1-σ,2-σet 3-σ confidencelevel relativetothe best-fitsolution. Thetransitions between theH-richenvelopeand theradiativeHecore; andbetween theradiativeHecore andthe convectiveC-O-He core arealso indicated. significantlydifferent from the surfacerotationperiod(equals to the orbitalperiod, vertical dot-dashed line) in the most part of the star:the sdBcomponent in the Feige48system is tidally locked, from the surfacedownto∼0.22 R∗ at least. Thebluevalley enlarges significantlyunder thislimit,which translates theinsensitivityofthe p-modes to thesedeep regions. Thesame exercise is carried out with the 25 pulsation periodsinthe frequency spectrum of thesdB star in the PG 1336−018 system (Kilkennyetal. 2003).Details on the asteroseismic analysisisreported in Charpinet et al. (2008),and the internal rotation profile is shownin Fig. 2(right). ThesdB star is alsotidally locked, down to ∼ 0.55 R∗ at least. Again,the dynamics of deeper regions(under the H-rich envelopemuch thinner in thiscasecompared to the envelopeofFeige 48), cannot be probed by the p-modes in action here.

Conclusion

We have demonstrated, forthe first time by asteroseismicmeans,thatspin-orbitsynchronism is reached in the most part of twoshort-periodpulsating sdBstars residinginclose binary systems, namely Feige48and PG 1336−018. Both starsrotateassolid bodieswithperiods equaltotheirorbital periodsfromthe surfacedowntoatleast ∼ 0.22 and0.55oftheir radius, respectively.The rotation of deeperlayerscannotbeinferredwiththe type of modes observed in short-period pulsating sdBstars. This observed synchronizationasafunction of depth, achieved within ∼ 1.5×108 yr (thelifetime of asdB star on the EHB),could provideconstraints fortidal evolutiontheories,concerningparticularly the angularmomentum transportfromthe surfacetothe center.Inanextstep, the dynamics of deeper regionsinsdB starsresidinginbinariescould be probed,inprinciple, by the g-modes observed in long-period pulsating sdBstars. 264 Internal dynamics from asteroseismology fortwo sdBpulsatorsinclose binary systems

Acknowledgments. V. VanGrootel thanks the financial supportgranted by the HELAS consortium. References

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DISCUSSION

Shibahashi: Iamwonderinghow one candistinguish clearlyintrinsic pulsationsignalofastar from influencecomingfromits companion, such as thereflectioneffect?Isthere anypossibilityofsuch contamination? VanGrootel: Areflectioneffect canonlypossibly be detected with amain sequencecompanion, and it is indeed observed in thelight curveofPG1336−018 (see Kilkenny et al. 2003).One canalso possibly observe an ellipsoidal deformation of thesdB star in thecase of veryclose systemswithmassive companions.Suchcontaminationeffectshaveverydifferenttimescalesthanthe pulsations in short-period sdB stars(80 − 600 s),and thereforeitiseasy to separate them.Inthe case of PG 1336−018, the reflectioneffect hasbeen removed from thelight curvebeforethe Fourieranalysis to extract pulsation frequencies(Kilkenny et al. 2003).