Binary Starsas CriticalTools & Testsin Contemporary Astrophysics Proceedings IAU Symposium No. 240, 2007 (cid:13)c 2007International AstronomicalUnion W. Hartkopf, E. Guinan, and P. Harmanec, eds. DOI:00.0000/X000000000000000X Asteroseismology of close binary stars Conny Aerts1,2 1Instituut voor Sterrenkunde,Celestijnenlaan 200D, B-3001 Leuven,Belgium email: [email protected] 2 Department of Astrophysics, RadboudUniversity Nijmegen, P.O.Box 9010, 6500 GL Nijmegen, The Netherlands Abstract.Inthisreviewpaper,wesummarisethegoalsofasteroseismic studiesofclosebinary stars. We first briefly recall the basic principles of asteroseismology, and highlight how the binarity of a star can be an asset, but also a complication, for the interpretation of the stellar 7 oscillations. Wediscussafewsamplestudiesofpulsationsinclosebinariesandsummarisesome 0 case studies. This leads us to conclude that asteroseismology of close binaries is a challenging 0 fieldofresearch,butwithlargepotentialfortheimprovementofcurrentstellarstructuretheory. 2 Finally, we highlight the best observing strategy tomake efficient progress in thenear future. n Keywords. (stars:) binaries: general, (stars:) binaries (including multiple): close, (stars:) bi- a naries: eclipsing, stars: early-type,stars: evolution, stars: interiors, stars: oscillations (including J pulsations), (stars:) subdwarfs, stars: variables: other, stars: statistics 6 1 1 1. Goals and current status of asteroseismology v 9 The main goal of asteroseismologyis to improve the input physics of stellar structure 5 and evolution models by requiring such models to fit observed oscillation frequencies. 4 The latter are a very direct and high-precision probe of the stellar interior, which is 1 otherwise impossible to access. In particular, asteroseismology holds the potential to 0 7 provide a very accurate stellar age estimate from the properties of the oscillations near 0 thestellarcore,whosecomposition,stratificationandextentiscapturedbythefrequency / behaviour. In general, the oscillations are characterised by their frequency ν and their h p threewavenumbers(ℓ,m,n)determining the shapeofthe eigenfunction(e.g.Unnoetal. - 1989).Seismictuningofinteriorstellarstructurebecomeswithinreachwhenauniqueset o ofvalues(ν,ℓ,m,n)isassignedtoeachoftheobservedoscillationmodes.Inpractice,the r t number of identified modes needed to improve current structure models depends on the s a kindofstar.ForB-typestarsonthemainsequence,e.g.,eventwoorthreewell-identified : modescansometimesbesufficienttoputconstraintsontheinternalrotationprofile(e.g. v i Aerts et al. 2003, Pamyatnykh et al. 2004) and/or on the extent of the convective core X (e.g. Aerts et al. 2006, Mazumdar et al. 2006). r Asteroseismology received a large impetus after the very successful application of the a technique to the Sun during the past decade. Helioseismology indeed revolutionised our understanding of the solar structure, including the solar interior rotation and mixing (e.g.Christensen-Dalsgaard2002foranextensivereview).Thisremainstruetoday,even though helioseismologyis presently undergoing somewhat of a crisis with the revisionof thesolarabundances(Asplundetal.2005,andreferencestherein).Theseledtoaslightly diminished precision, but still the relative agreement between the observed solar oscil- lation properties and those derived from the best solar structure models remains below 0.5% for most of the basic quantities, such as the interior sound speed and composition profiles (while it used to be below 0.1%with the old solarabundances). Helioseismology thus provided us with a unique calibrator to study the structure of other stars. 1 2 Conny Aerts However, the Sun is just one simple star. It is a slow rotator, it is hardly evolved, it does not possess a convective core, it does not suffer from severe mass loss, etc. There are thus a number of effects, of great importance for stellar evolution, that have not yet been tested with high accuracy. Since stars of different mass and evolutionary stage have very different structure, we cannot simply extrapolate the solar properties across the whole HR diagram. Stellar oscillations allow us to evaluate our assumptions on the input physics of evolutionary models for stars in which these effects are of appreciable importance.Forthemoment,suchoscillationsaretheonlyaccurateprobeoftheinterior physics that we have available. At present, the interior mixing processes in stars are often described by parametrised laws,suchasthetime-independentmixinglengthformulationforconvection.Valuesnear the solar ones for the mixing length and the convective overshootare often assumed, by lack of better information. Similarly, rotation is either not included or with an assumed rotationlawinstellarmodels,whileanaccuratedescriptionofrotationalmixingiscrucial for the evolution of massive stars (e.g. Maeder & Meynet 2000). Fortunately, both core overshoot and rotation modify the frequencies of the star’s oscillations and they do it in a different way. Core overshoot values can be derived from zonal oscillation modes, which have m = 0, because they are not affected by the rotation of the star for cases where the centrifugal force can be ignored, but they are strongly affected if an overshoot region surrounds the well-mixed convective core. On the other hand, the rotationalsplitting of the oscillation frequencies is dependent of the internal rotation profile. This can be mapped from the identification of the modes with m6=0 once the central m=0 component of these modes has been fixed by the models. Adequateseismicmodelling ofcoreconvectionandinteriorrotationisthuswithinreach, provided that one succeeds in the identification of at least two, and preferably a much largersetof(ν,ℓ,m,n).Thisobservationalrequirementdemandscombinedhigh-precision multicolour photometric and high-resolution spectroscopic measurements with a high duty cycle (typically above 50%). For an extensive introduction into asteroseismology, its recent successes, and its challenges, I advise the review papers by Kurtz (2006) and by De Ridder (2006). None of the successful cases so far concerns a close binary ... 2. The specific case of oscillations in close binaries Close binary stars have always played a crucial role in astrophysics,not only because, besides pulsating stars, they allow stringent tests of stellar evolution models, but also because they are laboratoriesin which specific physicalprocesses,which do not occur in single stars,takeplace.Understanding these processesis importantbecause atleasthalf of all stars occur in multiple systems. Closebinaries aresubjected to tidalforcesand canevolvequite differently than single stars.Seismic massandageestimatesofpulsating componentsinclosebinariesofdiffer- entstagesof evolution,wouldallow to refine the binaryscenariosinterms of energyloss and to probe the interior structure of stars subject to tidal effects in terms of angular momentum transport through non-rigid internal rotation. 2.1. Overview of observational data Two excellent review papers on pulsating stars in binaries and multiple systems (in- cluding clusters) are available in Pigulski (2006) and Lampens (2006). These are highly recommendedtothereaderwhowantstogetaclearoverviewoftheobservationalstatus and become familiar with this subfield of binary star research. One learns from these works that numerous pulsating stars are known in binaries, that lots of open questions Asteroseismology of close binary stars 3 remain concerning the confrontation between tidal theory and observational data, and that the best cases to monitor in the future are pulsating stars in eclipsing binaries. Eclipsing binaries have indeed revealed values for the core extent in B stars in excess of those found from asteroseismology of single B stars (Guinan et al. 2000). A natural thing to do would be to repeat the type of asteroseismic studies that led to the core overshoot value and internal rotation profile of single stars, as discussed in the previous section,butthenforpulsatingstarsineclipsingbinaries.Thiswouldallowtodisentangle the coreovershootfrom the internalrotationwith higher confidence levelthan for single stars. In this respect, I refer to Pigulski et al., Golovin & Pavlenko and Latkovic (these proceedings) for new discoveries of pulsating stars in eclipsing binaries and to Bru¨ntt et al. (these proceedings) for the best quality data available of such systems to date. 2.2. Mode identification through eclipse mapping A remark worth giving here is the potential to perform mode identification through the technique ofeclipsemapping ineclipsing binarieswitha pulsating component.This idea wasputforwardmorethan30yearsagobyNather&Robinson(1974)whointerpretedthe ◦ phase jumps of 360 in the nova-like binary UXUMa in terms of non-radial oscillation modes of ℓ = 2. We now know that this interpretation was premature and that the observedphasephenomenonisfarbetterexplainedintermsofanobliquerotatormodel. Mkrtichianet al.(2004)excluded odd ℓ+m combinations for the Algol-type eclipsing binary star ASEri from the fact that the disk-integrated amplitude disappears during the eclipse. Gamarova et al. (2005) and Rodr´ıguez et al. (2004) made estimates of the wavenumbers for the Algol-type eclipsing binaries ABCas and found a dominant radial mode, in agreement with the out-of-eclipse identification. By far the best documented version of mode identification from photometric data using eclipse mapping is available inReedetal.(2005).Whiletheirprimarygoalwastosearchforevidenceoftidallytipped pulsationaxesinclosebinaries,they alsomade extensive simulations,albeitfor the very specific case of eclipse mapping of pulsating subdwarf B star binaries. They find that ℓ>2 modes become visible during an eclipse while essentially absent outside of eclipse. Their tools have so far only been applied to the concrete cases of KPD1930+2752 and of PG1336-018(Reed et al. 2006) but without clear results. We must conclude that, still today, more than 30 years after the original idea, mode identification from eclipse mapping is hardly applied successfully in practice, and it cer- tainly has notbeen able to provideconstraintsonthe wavenumbersfor starswhichhave been modelled seismically. New promising work along this path is, however, in progress (Mkrtichian, private communication). 2.3. Pressure versus gravity modes One thing to keep in mind is that there are two types of oscillations from the viewpoint of the acting forces,and that only one type is relevant in the context of tidal excitation. One either has pressure modes, for which the dominant restoring force is the pressure, or gravity modes, for which the dominant restoring force is buoyancy. Tidal excitation can only occur whenever the orbital frequency is an integer multiple of the pulsation frequency,theintegertypicallybeingsmallerthanten.Thisfollowsfromtheexpressionof thetide-generatinggravitationalpotential(e.g.Claretetal.2005,andreferencestherein). Moreover,inthatcase,oneexpectsonlyℓ=2modestobeexcited,withanm-valuethat provides the good combination between the rotation, oscillation and orbital frequencies to achieve a non-linear resonance. Such a situation is much more likely to occur for gravity modes, which have, in main-sequence stars, oscillation periods of order days, than for pressuremodes which havemuch shorterperiods of hours.The same holds true 4 Conny Aerts for compact oscillators, whose pressure modes have short periods of minutes while their gravity modes have periodicities of hours and these may be of the same order as the orbital periods. Tidalforcescan,ofcourse,alterthefreeoscillationsexcitedincomponentsofbinaries. In that case, one expects to see shifts of the frequencies of the free oscillation modes with values that have something to do with the orbital frequency. This alteration can, but does not need to be, accompanied with ellipsoidal variability. In the latter case, the tides have deformed the oscillator from spherical symmetry, and one needs to take into account this deformation in the interpretation of the oscillation modes. 2.4. Sample studies Soydugan et al. (2006) have presented a sample study of 20 eclipsing binaries with a δSct-type component. They came up with a linear relation between the pulsation and orbital period: P = (0.020±0.002) P − (0.005±0.008). (2.1) puls orb This observationalresult implies that tidal excitation cannot be active in this sample of binaries, because this would demand a coefficient larger than typically 0.1 as mentioned above, i.e. an order of magnitude larger than the observed one. A similar conclusion was reached by Fontaine et al. (2003), who investigated if the oscillations in pulsating subdwarf B stars could be tidally induced, given that 2/3 of suchstarsareinclosebinaries.Tidalexcitationcan,atmost,explainsomeofthegravity modesobservedinsomesuchstarsbutthisisnotyetprovenobservationally.Ontheother hand,alltheformationchannelsforsubdwarfBstarsinvolveclosebinaryevolution(Han etal.,Pulstylnik&Pustynski,Morales-Ruedaetal.,theseproceedings).Anasteroseismic high-precisionmassandageestimate ofsuchastarwouldimplystringentconstraintson the proposed scenarios and on the role of the binarity for the oscillatory behaviour (see Hu et al., these proceedings). Aerts&Harmanec(2004),finally,madeacompilationofsome50confirmedline-profile variables in close binaries (mainly OBA-type stars). They could not find any significant relation between the binary and variability parameters of these stars. We come to the important conclusion that we have by no means a good statistical understanding of the effects of binarity on the components’ oscillations. This situation can only be remedied by performing several case studies of pulsating close binaries in much more depth than those existing at present. 3. Towards successful seismic modelling of binaries In general, we have to make a distinction between three different situations when studying oscillations in close binaries with the goal to make seismic inferences of the stellar structure. 3.1. Reduction of the error box of fundamental parameters Inafirstcase,thebinarityissimplyanassetfortheasteroseismologist,becauseitallows for a reduction of the observational error box of the fundamental parameters of the pulsating star. This case is relevant whenever we lack an accurate parallax value, and thusagoodestimateoftheluminosityandthemass.ThisismainlythecaseforOB-type stars,but sometimes also for cooler stars or compact objects. In absence of a good mass or luminosity estimate, the asteroseismologist cannot discriminate sufficiently between theseismicmodelsfulfillingtheobservedandidentifiedoscillationmodes.Itwasrecently Asteroseismology of close binary stars 5 shown that a combined observational effort based on interferometry and high-precision spectroscopy can enhance significantly the precision of luminosity and mass estimates in double-lined spectroscopic binaries with a pulsating component (Davis et al., these proceedings), if need be after spectroscopic disentangling as in Ausseloos et al. (2006). Suchspectroscopyisinanycasealsoneededtoderivetheoscillationwavenumbers(ℓ,m) (e.g. Briquet & Aerts 2003, Zima 2006). The best casestudy of apulsating star whosebinaritywas ofgreathelpin the seismic interpretation is the one of αCenA+B with two pulsating components (Miglio & Mon- talban2006,andreferencestherein). The binarity gavesuchstringentconstraintsin this case,that in-depthinformationonthe interiorofboth components wasfound.In partic- ular, it was found that the components seem to have different values of the convective overshootingparameterandthattheprimary,beingofthesamespectraltypeastheSun, is right at the limit of having or not a small convective core. The seismic analysis also providedanaccurateageestimateofthesystem.WerefertoMiglio&Montalban(2006), and references therein, for the latest results and an overview of the stellar modelling. Other well-known,but less successfulexamples are the δSct star θ2Tau (Breger et al. 2002,Lampensetal.theseproceedings)andtheB-typepulsatorsβCen(Ausseloosetal. 2006),λSco(Tangoetal.2006)andψCen(Bru¨nttetal.2006).Forthesefourstars,which areallfairlyrapidrotators,ourcomprehensionoftheobservedpulsationalbehaviourisat presentinsufficientfordetailedseismicinferenceoftheirinteriorstructure.Inparticular, welackreliablemodeidentificationofthedetectedfrequencies.Notbeingabletoidentify theoscillationmodesproperlyisthelargeststumblingblockinasteroseismologyofsingle stars as well. 3.2. Tidal perturbations of free oscillations The second case concerns seismic targets whose free oscillation spectrum is affected by thetides.ThefirstsuchsituationwasreportedfortheδSctstar14AurA,a3.8dcircular binary whose close frequency splitting of an ℓ = 1 mode does not match the one of a single rotating star and was interpreted in terms of a tidal effect by Fitch & Wisniewski (1979).Alterationsofthefreeoscillationmodesbytidaleffectshavealsobeenclaimedfor the three βCep stars αVir (also named Spica) which has an orbital period P = 4.1d orb andaneccentricitye=0.16(Aufdenberg,these proceedings,Smith 1985a,b),σScowith P =33d, e= 0.44 (Goossens et al. 1984) and ηOriAab with P =8d, e =0.01 (De orb orb Mey et al. 1996). When, besides oscillation frequencies, the orbital frequency and its harmonic is found inthe frequencyspectrum,oneisdealingwithoscillationsinanellipsoidalvariable.This caseoccursfortheβCepstarsψ2OriwithP =2.5d,e=0.05(Teltingetal.2001)and orb νCen with P = 2.6d, e = 0 (Schrijvers & Telting 2002), as well as for the δSct stars orb θTucwithP =7d,e=0(DeMeyetal.1998),XXPyxwithP =1.2d,e=0(Aerts orb orb etal.2002)andHD207251withP =1.5d,e=0(Henryetal.2004).Thedeformation orb ofthepulsatorhassofarbeenneglectedintheinterpretationoftheoscillationfrequencies in these binaries. The reason is clear: the complexity of the mathematical description of non-radialoscillations for a deformed star is huge compared to the case of a spherically- symmetric star. Aerts et al. (2002) have pointed out that this omission may well be the reason why the extensive efforts to model XXPyx seismically, as in Pamyatnykh et al. (1998), have failed so far. 3.3. Tidally-excited oscillations There are at present only two cases known that meet the requirement of having tidally- excited oscillation modes. It concerns the slowly pulsating B star HD177863 (B8V), for 6 Conny Aerts Figure 1. Observed radial velocities of HD209295 (symbols) phased with the orbital solution (fullline).Foranexplanationofthesymbols,werefertoHandleretal.(2002), from whichthis figurewas reproduced with permission from MNRAS. which De Cat et al. (2000) found an oscillation mode whose pulsation frequency is an exactmultiple of10.00times theorbitalfrequency.Theorbitofthe starisveryeccentric with e = 0.77 which provides a good situation to achieve a resonance between an ℓ = 2 mode with a period of 1 day and the orbit of 10 days. Willems & Aerts (2002) made computationsbasedontidaloscillationtheoryforthis starandindeedcameupwith the possibility that it is undergoing a non-linear resonantly excited ℓ = 2 oscillation mode. Thisstarhasonlyoneconfirmedoscillationsofar,suchthatseismicmodellingisnotyet possible since this requires at least two well-identified modes. By far the most interesting case of tidally-induced oscillations was found by Handler et al. (2002).They discoveredthe star HD209295(A9/F0V) to be a binary with P = orb 3.11dande=0.352(see Fig.1) exhibiting oneδSct-type pressuremode and nine γDor- typegravitymodes,ofwhichfivehaveanoscillationfrequencywhichisanexactmultiple of the orbital frequency. The frequency spectra of the star, after subsequent stages of prewhitening, are shown in Fig.2. The authors also predicted frequencies of tidally- excitedmodes forappropriatefundamentalparametersofthe primaryandfoundseveral suchgravitymodes to agreewith the observedones,after having correctedthe latter for the surface rotation of the star (see Fig.3). The unfortunate situation of not being able Asteroseismology of close binary stars 7 Figure 2. Left: Spectral window and amplitude spectra of the B filter time-series photometry of HD209295 after subsequent stages of prewhitening. Top Right: amplitude spectra of the combinedBandscaledVfilterdata,afterprewhiteningwiththe6-frequencysolution shownin the left panel. Several harmonics of the orbital frequency are found. Bottom Right: amplitude spectraofthedifferentialmagnitudesofthecomparison stars. Figurereproducedfrom Handler et al. (2002) with permission from MNRAS. to identify the modes occurs againfor this star,such that seismic tuning of its structure was not achieved so far. 4. Conclusions and outlook Werecallthattherequirementsforsuccessfulseismicmodellingofastararestringent. We need accurate frequency values, reliable identification of the spherical wavenumbers (ℓ,m) and accurate fundamental parameters with a precision better than typically 10% before being able to start the modelling process. These requirements demand long-term high signal-to-noise and time-resolved spectroscopy and multicolour photometry with a duty cycle above, say, 50%. It is important that the data cover the overall beat-period of the oscillations, ranging from a few days for compact oscillators up to severalmonths for main-sequence gravity-mode oscillators. These requirements have been met recently 8 Conny Aerts Figure 3. Predicted amplitudes of tidally induced radial velocity variations in a model for HD209295, for two slightly different values of the rotation frequency (1.852d−1: full line; 1.854d−1: dashed line). The orbital frequency of the star is indicated by the dotted vertical line. Figure reproduced from Handler et al. (2002) with permission from MNRAS. for a few bright single stars, with impressive improvement for their interior structure modelling, but not yet for a pulsating star in a close binary. For those candidates that came close to meeting these requirements, the problem of mode identification occurred and prevented seismic tuning. We come to the conclusion that the potential of seismic modelling of close binaries is extremely good, particularly for eclipsing binaries. At the same time, its application is extremely demanding from an observational point of view. It is clear that efficient progress in this field can only be achieved from coordinated multisite multitechnique observing campaigns, preferrably in combination with uninterrupted space photometry. I strongly encourage the binary and asteroseismology communities to collaborate and take up this challenging project. Asteroseismology of close binary stars 9 Acknowledgements The author is much indebted to the Research Council of the Catholic University of Leuven for significant support during the past years under grant GOA/2003/04. 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Analytical computations of energy loss are availabe in, e.g., Willems et al. 2003, A&A, 397, 973. Numerical computations were made by, e.g., Witte & Savonije 2002, A&A, 386, 222. All these works, however, predict too long timescales if we compare them with those derived from data of high-mass X-ray binaries (the only observed cases available). This might be due to the much stronger radiative damping during resonances than anticipated so far. Besides the orbital energy loss, one also has to keep in mind that the oscillations probably imply significant angular momentum loss of the components through non-rigid internal rotation. P. Lampens: How much time was needed to reach the significant new insight for single stars from the oscillations that you discussed (non-rigid internal rotation and estimate of core overshoot), given that the combination of pulsation and binarity is even more demanding? C. Aerts: We managed to derive the non-rigid internal rotation in two main-sequence B starsso far.These starshavemultiple oscillationperiods ofthe orderofseveralhours. One star was monitored with one and the same instrument from a single site during 21 years! The other one was monitored during a well-coordinated multisite photometric and spectroscopic campaign lasting 5 months and involving about 50 observers (see references in the paper). It is therefore clear that asteroseismic inference requires long- term monitoring. I think that the binarity does not impose the necessity of even longer runs(atleastnotforclosebinaries),becausethe moststringentdemandisthefrequency accuracyandthemodeidentification,whiletheorbitaldeterminationwillresultnaturally and efficiently from a multsite spectroscopic effort.