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STARS Oscillations and Stellar Models

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STARS Oscillations and Stellar Models 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
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