Session 2B: MODES Mode Identification

Session 2B:MODES Mode identiﬁcation Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Pulsationalmodeidentiﬁcationfrommulti-colourphotometry − an observer’spoint of view

G. Handler

Institut f¨ur Astronomie,T¨u rkenschanzstraße 17, A-1180 Vienna,Austria

Abstract

We review the methods available to performmodeidentiﬁcationfromtime-series photometric measurements.Following the developments in time,wediscussthe rootsofthe method, its basicmethodology, extensions andimprovements.Suggestionsonthe optimal choice of ﬁlterstoapplythe methodare quoted andseveral practicalapplications arecited, with a focus on howadditional astrophysicalinformationwas obtained at the same time.Finally, some practicalconsiderations concerning observationalmodediscriminationfromphotometry aregiven, some pitfallsare discussedand abrief glimpseatfuturespace data is made.

IndividualObjects: 12 Lac,G226-29, PG 1351+489, 44 Tau, ν Eri, θ Oph

Whydoweneed observational mode identiﬁcations?

Thegoalofany proper asteroseismicstudyisthe gain of knowledgeofstellarstructure andevolution.Thisisfacilitated by the comparison of observed pulsational mode spectra with those predicted by theoreticalmodels. Thedecisive requirement forany stellarmodel thatdeservestobecalled seismicmodel is itsuniqueness: each individualoscillationmode observed must be identifiedwithits pulsationalquantum numbers k, ℓ and m beyond any doubt, and(withinreasonablelimits) only onestellarmodel exists thatcan explain themall. Unfortunately, the pulsationmodes in real starsdonot comelabelledwiththeirk,ℓand m. In some cases, we areluckytoobserve afairly complete setofpulsational signals over some rangeoffrequency.Becausethe frequencies of the stellareigenmodes arenot randomly distributed, frequency groups thathavecertain structure(e.g.,frequency ratios of radial modes,equidistantlyspaced frequencies/periods of p/gmodes,rotationally split frequency multiplets)can aid the identificationofthe pulsation modesthatcause them. This technique is called pattern recognition andhas been appliedsuccessfully to whitedwarf stars(e.g. Winget et al. 1991, 1994). For most pulsators, the observed mode spectraare toosparse or toocomplicated (e.g. if rotationallysplit patterns of modes with different kand/or ℓ overlap in frequency)to facilitatepatternrecognition. In such cases, we must resort to observationalmethods that give additional clues towards ℓ andm.Bothphotometric andspectroscopictechniques have been developed forthispurpose.Whereasthe latter arereviewedbyTelting (2008), we will discussthe photometric methods in what follows. Numerous excellent reviewsonphotometric mode identificationare present in the literature, most recentlybyDaszyń ska-Daszkiewicz (2008). Becausethe latestoverviewarticles emphasizedthe theoreticalaspects of mode identification, we hereattempt to stress the issues relevant to observation. G. Handler 107

Acautionarytale Even in the presence of sparse observationalmodespectra, it is tempting to applypattern recognition methods (alsonamed”mode identificationbymagic numbers”,Breger 1989). One(in)famous example is the β Cephei star 12 Lacertae. Itsfive dominant pulsation frequencies have been knownfor alongtime(Jerzykiewicz 1978). Among them,anexactlyequally spaced frequency tripletispresent, andthe obvious assumption is thatitisdue to rotational splitting.However,all interpretations in thisdirection failedbecausethe splitting was”tooequidistant”.Therefore, hypothesesconcerningresonant mode couplingwereinvoked to explain thistriplet, andseveral papers were written on the subject. Besides the equally spaced triplet, the present authornoticed thatthe frequency ratioof twoofthe fivethen knownpulsation modes wasconsistent with thatofradial fundamental andfirst overtone mode pulsations-to the fourth digit! This wouldalsosolve the dilemma of the equally spaced tripletasthe hypothesizedfirst overtone mode corresponded to oneof the tripletcomponents. Consequently, aphotometric multisitecampaignon12Lacertaewas organized(Han- dler et al. 2006).Fromits multicolourdataitbecame clearthatthe apparent rotationally split mode tripletconsisted of an ℓ =1,anℓ=0,and an ℓ =2mode. Thesuspected radial modes both turnedout to be ℓ =2.Aspectroscopicmultisite campaign (Desmetetal. 2008) confirms these results. We conclude: apparent recognition of frequency patterns wherethereare none canlead to alot of unnecessary work.

Thebasic idea

Dziembowski(1977) expressedthe fluxvariations of anonradiallyoscillatingstarmathemat- ically. He thenpointed outthatthe Baade-Wesselinkmethod(developed to determine the radiiofCepheids by combining radial velocity andtwo-colourphotometryoverthe pulsation cycle) canbeusedtoinfer the stellarradiusifthe spherical harmonicdegree ℓ of the oscillation is knownor, vice versa,toinfer ℓ if the star’s radius is known. Buta &Smith (1979) andBalona &Stobie(1979a,b)reformulated Dziembowski’s(1977) expressionsfor easier usewithobservational data andpresented the first applications of the method. In particular,Balona &Stobie(1979b)showedthatpulsation modes of different ℓ separate in aphotometric amplitude ratiovs. phase shiftdiagram. Robinson et al. (1982) adapted the calculations to the light variations of pulsating white dwarfstars andrefined the methodbyincluding stellarmodel atmospheres,replacingthe previously used blackbodyspectral distributionsorempirical colour-brightness relations,and at the same time providingamore realisticlimb-darkening law. This work hadtwo important ”side” results: first,Robinsonetal. (1982) showed thatthe oscillations of whitedwarf stars arecausedbyg-mode(as opposedtor-mode) pulsation andsecond, thattheseare due temperaturevariations only.

Generalconsiderations and optimaluse of themethod

Watson (1988) explored the behaviourofphotometric amplitudes andphasesfor alarge varietyofpulsating star models. He started with the expression forthe ﬂuxchangefor nonradial pulsation in the linearregime:

Δm(λ, t)=−1.086ǫPℓ,|m|(µ0)((T1 + T2)cos(ωt + ψT )+(T3+T4+T5)cos(ωt)), whereΔm(λ,t)isthe time andwavelength dependent magnitude variationofanoscillation, −1.086ǫ is an amplitude parameter transformedfromﬂuxes to magnitudes, Pℓ,|m| is the 108 Pulsationalmodeidentiﬁcation from multi-colourphotometry

associated Lagrange polynomial, µ0 is the cosine of the inclinationofthe stellarpulsation axis with respect to the observer, ω is the angularpulsation frequency, t is time and ψT is the phaselag between the changes in temperatureand localgeometry. Theterm T1 is the localtemperaturechangeonthe stellarsurface, T2 is the temperature-dependent limb darkening variation, T3 is the localgeometrychangeonthe stellarsurface, T4 is the local surfacepressure change and T5 is the gravity-dependent limbdarkening variation. Therelativeimportanceofthe Ti terms wasevaluated formodelsofdifferent typesof pulsators, rangingfromwhite dwarftoRCrB stars, Mirasand Cepheids, δ Scuti and β Cephei stars, as well as solar-likeoscillatorsand roAp stars. For instance, the geometrytermwas found to be of virtually no importance forthe high radial overtone pulsators(Watson 1988). Theresults of thisworkallowanoptimal choice of photometric filtersfor efficient mode discrimination:one wants to observeatone wavelength wherethe geometry variationis significant, while the temperaturetermiswellconstrained at the same time. Finally,Watson(1988) computed ”areas of interest” in amplitude ratiovs. phase shift diagrams, i.e. the loci in whichmodes of agiven ℓ wouldbecontained (alsocalled ”diagnostic diagrams” in the literature). Such diagrams arestill in usefor mode identificationtoday.

Adaptations, extensions, improvements and additional astrophysics

After thisverybroad work,specialistsonvarious classesofpulsators took the stage. Garrido et al. (1990) performedcomputationsofdiagnostic diagrams for δ Scuti starsinthe Strömgren photometric system,tryingtofind the most efficient filter combinations formode identification(usingtwo filters, v and y seem to be best). Later, Heynderickx et al. (1994) tested β Cephei modelsinthe Genevaand Walraven systems, finding thatthe mode discrim- inationisbestdonevia the evaluationofamplitude ratios,and thatknowledge of ultraviolet amplitudes is crucial. Cugier et al. (1994),alsoexamining modelsofβCephei stars, performednonadiabatic calculations of photometric andradial velocity amplitudevariations andphase shifts forthe first time.Theirresults impliedthattheseparametersmay be dependent on stellarmassand thatdiscriminationofthe overtone of radial modes mayalsobepossible. An apparent setback formodeidentificationofδScuti starswas discussedby Balona &Evers (1999):the shallow convection zones of these starsaffect the theoretical predictions of the photometric observables, depending on theassumedconvective efficiency. However, Daszyńska-Daszkiewicz et al. (2003) realizedthat thisdependence maybeturned into an asset: when introducing asuitablethird filter into theobservations, onecan constrain the convective efficiency simultaneously with obtainingpulsational mode identifications.In other words, onecan learnadditional physics when applying the photometric method. Thephotometric methodhas been extended further andfurtherinthe recent past.For instance, Garrido (2000) modernizedWatson’s(1988) work withafocus on δ Scuti stars, andpresented diagnostic diagrams for γ Doradus starsfor the first time.Balona et al. (2001) pointed outthatthe incorporationofJohnson Ifilter data greatlyimprovesthe relative accuracyofthe measuredphase shifts andthereforeprovided clearermodediscriminationfor δ Scuti stars. On the side of theory, Townsend (2003) andDaszyń ska-Daszkiewicz et al. (2007) formu- lated the methodfor gravitymodes in rapidlyrotatingstars, whererotationcan no longer be treated with aperturbation approach.Dupretetal. (2005) included theirtime-dependent convection model to derivemodeidentifications for δ Scuti stars, andlater applieditto γDoradus starsaswell(Dupret et al. 2006). Daszyńska-Daszkiewicz et al. (2005) combined the photometricmethodwithradial veloc- itydata, andsuggested a χ2-test(Daszyńska-Daszkiewicz et al. 2003) formodediscrimination in the combined measurements.Thisincreasesthe objectivity of the process: previously,iden- G. Handler 109 tifications were obtained by visual inspection of the amplitude/phase vs.wavelength behaviour andoften critically depended on the wavelength of the normalization, whichcould sometimes mislead the eye. Thepotential of photometric mode identificationhas alsobeenrecognizedfor the pulsating subdwarf Bstars (Randall et al. 2005).Theseauthors computed amplituderatiosand phase shifts forawide rangeofparameter space, including long-and short-period sdBpulsators as well as nonadiabatic effects,and examined the systematicsthoroughly. Similartothe β Cephei stars, thatare similarintemperaturetothe sdBoscillators, amplituderatiosare the observationalquantity most sensitivetoℓ,but data of high accuracyare requiredand discrimination between the modes of ℓ ≤ 2isdifficulttoobtain.

Applications to diﬀerenttypes of pulsators

Starting with the pulsatingwhite dwarfstars, it must be mentioned thatlimbdarkening is by farthe strongestcontributing factortothe wavelength dependence of pulsation amplitudes. Ultravioletmeasurements arenecessary to achievegood mode discrimination.Combining ground-basedphotometryand ultravioletspectroscopyfromthe HST, Kepler et al. (2000) derived mode identifications forthe DA whitedwarf star G226-29, andatthe same time determined its Teff andlog g by combining the amplitudeinformationfromall modes.In the same paper, Kepler et al. (2000) could notfind aunique ℓ assignment forthe strongest mode of the DB pulsatorPG1351+489, but resolved the ambiguity by consideringthe spectroscopiclog g valueofthe star.Thesetwo examplesagain illustrate thatadditional astrophysicalinformationcan be obtained when applying mode identificationmethods. Alongsimilarlines,the potential to learnsomething aboutsurface convection usingmul- ticolour data on δ Scuti starshas alreadybeen pointed out. In their study of 44 Tau, Lenz et al. (2008) identifiedseveral low-ℓ modes,and at the same time constrained the mixing length parameter with αMLT ≤ 0.2withintheirtreatment of surfaceconvection. As afinalexample,Pamyatnykh et al. (2004) used theirknowledge of the radial mode detected in the β Cephei star ν Eridani, combined with the frequencies of the three ℓ =1 triplets,toconstrain the star’s position in the HR diagramand to obtain atight constraint on the convective core overshooting parameter.

Practicalconsiderations, pitfallsand spacedata

Thereader should notget the impression thatobservational identifications of all observed pulsation modes of anygiven star arerequiredfor successful asteroseismology.Itisjustnecessary to identify a sufficient numberofmodes to rule outall possiblealternative interpretations andmodels. As another example,seven pulsation modes were detected forthe β Cephei star θ Ophiuchi (Handler et al. 2005),but only four of themhad unique determinationsofℓfrom photometry. However, these identifications sufficed to tagall modes as:one radial mode, arotationally split ℓ =1triplet, andthree components of arotationally split ℓ =2quintuplet, with an ambiguity which m the observed components wouldhave. Spectroscopycame to the rescue (Briquet et al. 2005):withthe photometric ℓ values,parameter spacecould be sufficiently restricted to obtain m forthe strongest ℓ =2mode. Theproblem thatmisinterpretations of mode identificationdiagrams canbecausedby visual inspection hasalready been mentioned.Another problem onemustbeaware of is the accuracyofthe underlyingdata. Examinations of multisitetimeseriesphotometrysug- gestthatformal errorestimates mayunderestimatethe real errors by aboutafactorof2 (Handler et al. 2000, Jerzykiewiczetal. 2005),probablyaconsequence of correlated noise. However, when consideringamplitude ratios andphase shifts between different filters, at least 110 Pulsationalmodeidentification from multi-colourphotometry part of the correlated noise maycancel andthereforethe formalerrorestimates maynot be toofar from the truth (Breger 2008).Inany case,the useofmorethantwo photometric filtersmay helptoinvestigate the possibleoccurrence of systematic errors. Asteroseismology puts enormous hope on dedicated spacemissions,which will yield(and do alreadyyield)time-resolved photometryofextremely high precision.However,the presently active asteroseismicspace missions operateinasingle colour only, andthe colour information of CoRoTinthe exoplanet fieldsiscrude. This meansthatasteroseismicmodellingmay still be difficultdespite awealthoffrequency information.The first spacemission thatwill be able to provideaccuratecolourinformationisBRITE-Constellation (e.g. Zwintz &Kaiser 2008) thathopefully will have been launched when theseproceedingsare published; Daszyńska- Daszkiewicz(2008) thoroughlyexamined the prospects of mode identificationwithBRITE- Constellation.

Some (trivial) conclusions

Photometricmodeidentificationmethods have nowmatured to apoint wherethey canbe widelyappliedtodifferent classesofpulsators. Successeshavebeen obtained forpulsating whitedwarf andsubdwarfstars, andalong the mainsequence for γ Doradus, δ Scuti,SPB and β Cephei stars. In severalcases,interesting astrophysicalinformationhas been obtained as a”by-product” such as thatwhite dwarfpulsate in gmodes ratherthaninrmodes, constraints on the efficiency of surfaceconvection of δ Scuti starswerefound, and Teff and log g determinationsweremadefor some stars. Thechoiceofthe most suitable setoffiltersfor mode identificationisacrucial pointin planning observations;atone wavelength the geometry variationshouldbesignificant, and the temperaturevariationshouldbewellconstrained in the combinationwithasecond filter (Watson1988). To be able to estimatethe possibleeffects of systematic measurement errors, redun- dancy should be sought, i.e. athird photometric filter wouldaid the reliabilityofthe mode identificationand can, in some cases, provideadditional astrophysicalinformation. External constraints,such as temperatureorgravity estimates of the target object, canalsoassist in the correct mode identification. Finally,iffeasible, photometric mode identificationshouldgo hand in hand with spectroscopicobservationstoprovide the largestpossibleset of information to the asteroseismologist.

Acknowledgments. Iamgrateful to the organizers of thisexcellent workshop forinviting me to give thispresentation andtoHELASfor the ﬁnancial support. Travel supportwas provided by the Austrian Fonds zurF¨o rderung der wissenschaftlichen Forschung under grant P18339-N08. References

Balona,L.A., &Stobie, R. S. 1979a,MNRAS,187, 217 Balona,L.A., &Stobie, R. S. 1979b, MNRAS, 189, 649 Balona,L.A., &Evers, E. A. 1999, MNRAS, 302, 349 Balona,L.A., Bartlett, B.,Caldwell, J., et al. 2001, MNRAS321, 239 Breger,M.1989, DSSN,1,7 Breger,M.2008, CoAst, 156, 6 Briquet, M.,Lefever,K., Uytterhoeven,K., &Aerts,C.2005, MNRAS, 362, 619 Buta,R.J., &Smith,M.A.1979, ApJ, 232, 213 Cugier,H., Dziembowski, W. A., &Pamyatnykh, A. A. 1994, A&A, 291, 143 G. Handler 111

Daszyń ska-Daszkiewicz,J.2008, CoAst, 152, 140 Daszyń ska-Daszkiewicz,J., Dziembowski, W. A., &Pamyatnykh, A. A. 2003, A&A, 407, 999 Daszyń ska-Daszkiewicz,J., Dziembowski, W. A., &Pamyatnykh, A. A. 2005, A&A, 441, 641 Daszyń ska-Daszkiewicz,J., Dziembowski, W. A., &Pamyatnykh, A. A. 2007, Acta Astron.,57, 11 Desmet,M., Briquet, M.,Thoul, A., et al.,2008, MNRAS, submitted Dupret,M.-A., Grigahcè ne,A., Garrido, R.,etal. 2005, MNRAS, 361, 476 Dupret,M.-A., Grigahcè ne,A., Garrido, R.,etal. 2006, Mem. S. A. It., 77, 121 Dziembowski, W. 1977, AcA, 27, 3, 203 Garrido, R. 2000,inDeltaScutiand RelatedStars,eds.M.Breger&M. Montgomery, ASPC 210, 67 Garrido, R.,Garcia-Lobo, E.,&Rodriguez,E.1990, A&A, 234,262 Handler,G., Arentoft,T., Shobbrook,R.R., et al. 2000, MNRAS, 318, 511 Handler,G., Shobbrook,R.R., &Mokgwetsi, T. 2005, MNRAS, 362, 612 Handler,G., Jerzykiewicz,M., Rodriguez,E., et al. 2006, MNRAS 365, 327 Heynderickx, D.,Waelkens, C.,&Smeyers, P. 1994, A&AS,105,447 Jerzykiewicz,M.1978, AcA, 28, 465 Jerzykiewicz,M., Handler,G., Shobbrook,R.R., et al. 2005,MNRAS,360, 619 Kepler,S.O., Robinson,E.L., Koester, et al. 2000, ApJ, 539,379 Lenz, P.,Pamyatnykh, A. A., Breger,M., &Antoci, V. 2008, A&A, 478, 855 Pamyatnykh,A.A., Handler,G., &Dziembowski, W. A. 2004, MNRAS, 350, 1022 Randall,S.K., Fontaine, G., Brassard,P., &Bergeron, P. 2005, ApJS, 161, 456 Robinson, E. L.,Kepler, S. O.,&Nather, R. E. 1982, ApJ, 259, 219 Telting, J. H. 2008, CoAst, 157, 112 Townsend, R. H. D. 2003, MNRAS, 343, 125 Watson, R. D. 1988, Ap&SS, 140, 255 Winget, D. E.,Nather, R. E.,Clemens,J.C., et al.,1991, ApJ, 378, 326 Winget, D. E.,Nather, R. E.,Clemens,J.C., et al.,1994, ApJ, 430, 839 Zwintz,K., &Kaiser, A. 2008, (eds.),CoAst,Vol.152

DISCUSSION

Zahn: Havethere been recentdeterminations of internal rotation profiles, usingmultiplemodes? Handler: Thereisconvincing evidencefor differential rotation in anumberofβCep stars, but we have toosmall anumberofmodes to obtain somethingthatdeserves thename”rotation profile”. Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Constraints on angularnumbers of pulsation modesfromspectroscopy

J. H. Telting

Nordic OpticalTelescope,Santa Cruz de La Palma, Spain,[email protected]

Abstract

Asteroseismology reliesonaccurateobservational mode identification. High-resolution spectroscopyallows to detectsuch crucial information as the pulsationaldegree ℓ,the azimuthal number m,and pulsation amplitudes,directlyfromtimeseriesofobservations. Theadvan- tage of usingbothstandardphotometric techniques andhigh-resolution spectroscopyisthat notonlypulsational temperaturevariations canbedetected, but alsothe pulsational velocity field,yieldingvaluable extrainformation. In thispaper Ireviewthe spectroscopicmode-identificationmethods thathavebeen developed over the lastdecades,withemphasisonthe applicationtohot stars.

IndividualObjects: Balloon090100001

Introduction

Thestudyofstellarpulsationsprovides apromising tool to further reﬁneour knowledgeofthe internalstructureofstars. Provided thatone canconclusivelyderivepulsational parameters from the observations,asteroseismology canconstrain stellarstructureand evolution models. In general, there aretwo complementary and independent methods to derive observational mode identiﬁcations: • photometric/spectroscopicamplitude ratios,atechnique thatprobesthe pulsational variations of temperature, gravity, andmorerecentlyalsoradial velocity,and thataims to derive the degree ℓ of the modes.

• line-profile variability, atechnique thatprobesthe 3D pulsational velocity field,and that aims to derive the degree ℓ andthe azimuthalnumber m of the modes. It hasbecomeevident thatthe most conclusiveresults have been obtained from applying both methods simultaneously.HereIwill focus on the topicofspectroscopicmodeidentifi- cation; seeHandler (2008) forareview on photometric methods. Thetheory of nonradial pulsation wasdeveloped by Lord Kelvin (Thomson1863) before thatofradial pulsation.Through the interestinCepheids,the theory of radial pulsation madealotofprogressinthe first half of the previous century; the lackofapplicability kept the development of nonradial oscillationtheory at aslowpace. It wasonlyinthe 1950’sthatLedoux (1951) suggested thatthe observed variabilityinthe broadening of the spectral lines of β CMa(aprototype of the β Cephei variables) is due to nonradial pulsations. Osaki (1971) calculated lineprofilesofnonradiallypulsating starsand compared them with observations available at thattime. With the work of Smith(1977),who used asimilarmodel to fit line-profile variations,the field of spectroscopicpulsation-modeidentificationgot off J. H. Telting 113 the ground. Furthermore,the work of Vogt &Penrod (1983) sparkedthe applicationofthe Doppler-imagingtechnique forspectroscopicmodeidentification. Alloverthe Hertzsprung-Russell diagramthereare typesofstars thatpulsate in nonradial modes.The mode identificationmethods discussedinthispaper aremostlybased on high- resolution spectroscopyand aretypically appliedtoearly-typestars, such as δ Scuti variables and β Cephei variables. Thesestars have apparent pulsation periodsofabout 20 minutes to afew hours, andwiththe present observing facilitiesharmonicdegrees up to ℓ ∼20 can be derived spectroscopically (Doppler imaging).Morerecently, applications to longer-period g-mode pulsators such as γ Doradus starsand Slowly PulsatingB-stars have been presented in the literature. Very recentlyhigh-resolution spectroscopyhas been appliedtothe relatively faintsubdwarfBstars, whichhavepulsation periodsofacoupleofminutes to hours, for pulsation-modeidentification(seenextsections). Even forDAV whitedwarfs, it hasbeen shownthatthe harmonicdegree canbeidentified usingtime-series of low-resolution spectroscopy(seenextsections). Excellent in-depth reviewsonmodernanalysismethods forspectroscopicpulsation-mode identificationwerepresented by Aerts&Eyer (2000),Balona (2000),and Mantegazza (2000). Theaim of thiscurrent paperistolistthe latestdevelopments since the review presented by Telting(2003).

High-resolution spectroscopy forpulsation-mode identiﬁcation

Stellarpulsationsare reflected as line-profile variations in absorption lines formedinthe pho- tosphere. For slowly-rotatingstars, modes with ℓ ∼<4giverisetodetectable line-profile variations. In rotating stars, wherethe Doppler-imagingprincipleapplies, the line-profile variations due to nonradial pulsationsappearasblue-to-redmovingbumps (Vogt &Penrod 1983),and modes with ℓ ∼<20 canbedetected. In general, the line-profile variations arecausedbythe stellarpulsational velocity field,and by the photospheric pulsational temperaturevariations. Effects induced by localsurface gravityvariations areusually neglected, whichisavalid assumption if hydrogen lines arenot used in the analysis, norany other lines nearthe coresof the hydrogen lines. Thetemperaturevariations give rise to localchanges in brightness, andtolocal changes of the equivalent width (EW)ofthe intrinsicstellarlineprofile (e.g. Buta &Smith 1979, Lee et al. 1992).For absorption lines with lowthermal broadening andsmallintrinsicEW variations the pulsational line-profile variations aredominated by velocity effects,implying thatthermal pulsational effects maybeneglected in the modellingofthe profile variations. Such absorption lines providethe idealcase, as the 3D pulsational velocity field is relatively simple to model (see e.g. Schrijvers&Telting1999), andallows to derive both the degree ℓ of the mode as well as the azimuthalnumbermofthe mode. In rotating stars, the pulsationalvelocityfieldcannotbedescribed by asinglespherical harmonic. In the case of slow rotation,toroidalterms areinduced due to the Coriolis force (e.g. Aerts&Waelkens 1993);inthe case thatthe pulsation frequency in the corotating frame, ωcor,iscomparabletothe rotation frequency,Ω,awholeseriesofspherical harmonic functionsisneeded to describeaneigenfunction (Lee &Saio 1990, Townsend 1997). Afurther complicationinthe interpretation of line-profile variations is thatthe inclination angleofthe star, i ,isgenerallynot known. Other parametersthatplayarole in the appearance of the line-profile variations are: the limb-darkening coefficient, the intrinsicprofile width, the equatorial rotational velocity,the ratioofhorizontaltoverticalpulsational motion,the amplitudeofthe localbrightness variations,the amplitudeofthe localequivalent width variations,and the non-adiabatic phase lag between velocity andtemperaturevariations.Not all of these arefreeparameters: some parametersdepend on the valueofothers, andsome canbemodelledwithline-profile synthesis codes andwithnon-adiabatic pulsation codes. 114 Constraints on angularnumbers of pulsation modesfromspectroscopy

Figure1:Lineproﬁles at one particular phase of an (ℓ=3,|m|=3)and a(ℓ=4,|m|=3)(right)mode. All otherstellarand pulsationalparameters, exceptthe pulsation amplitude,are thesame. It is evident that forpole-on inclinations (hereIused i=35o )the pulsationally distortedlineproﬁles of (ℓ,m)and (ℓ+1,m) modeslookverysimilar.

Nevertheless, it is clearthatinorder to get reliable values forthe three parametersthat onewants to obtain from high-resolution spectroscopy, the degree ℓ,the azimuthalnumber m, andthe pulsational velocity amplitude, onehas to performavery carefulanalysisonadata setwithhighsignal-to-noise ratio. Depending on the line-profile shape, the degree of the mode, andthe identificationmethodthatone uses,aspectral resolution of R=20000–60000 is sufficient formode-identification. Doppler imagingand profile-fitting methods used for modes with high ℓ values require the highestspectral resolution.The idealdataset is such thatone-dayaliasingdoesnot play arole, andthatall the intrinsicfrequencies as well as the harmonic, sumand beat frequencies,thatare caused by the non-linearmapping of the stellar variations onto the lineprofiles, areunambiguously resolved. In reality,mostdatasets arefar from ideal, but experience hasshown thatfromthe best data sets we areabletoestimate values of ℓ and |m| with an accuracyof±1orbetter.For anymode-ID methodbased on line- profile variations it is difficulttodistinguish amode(ℓ,m)fromamode (ℓ+1,m), especially forpole-on orientationsofthe symmetryaxisofthe mode (see Figure 1).

High-resolution spectroscopy: new developments of mode-ID methods Irefer to the review presented by Telting(2003) forageneral andlessconcise description of the most-usedspectral analysisand mode-identificationtechniques (MomentMethod, Doppler imaging, IPS/PPM method, etc.).Itisimportant to realise that manyimplementationsof these methods still rely on asimpledescription of the pulsational-velocity field of anon- rotating star,possiblywithout accounting forthe pulsational temperature/gravityeffects mentioned above. Thereforeitiscrucial to select the best absorption lines,i.e.those lines thatare notaffected by these effects,typically lines of elements heavier thanHelium. J. H. Telting 115

TheMomentMethod(MM, seee.g.Balona 1986, Aerts1996) analyses the velocity moments of the lineprofiles; moment variations aredetectable formodes with ℓ ∼<4. The MM is more sensitivetozonal modes (m=0)thantosectoralmodes (|m|=ℓ). TheIPS/PPM method(seee.g.Gies&Kullavanijaya1988; Telting&Schrijvers 1997) analysesthe intensity variations (orbumps)acrossthe lineprofile;bumps canbeseen for modes with ℓ ∼<20. TheIPS/PPM methodismoresensitivetosectoralmodes thantozonal modes.The latter impliesthatthe MM andIPS/PPM methods arecomplementary to each other,and should both be appliedinorder to get the best results. Special attention hastobegiven heretothe latestextensionofthe IPSmethodby Zima (2006ab), whoappliedthe new methodtoidentify numerous modes in the δ Scuti star FG Vir. Zima hasdeveloped an elaboratefitting method(theFPF method), to fit the amplitudeand phase diagrams thattogether form the primediagnostic of the IPSmethod. Furthermore,the FPFmethodisavailable as part of the freelyaccessibleFAMIASpackage (Zima2008),which alsocomprises an implementation of the MM method. Arecent refinement to the Moment Method, to account formulti-periodicity in the MM, waspresented by Briquet &Aerts (2003) whoappliedthe improved methodtothe multi- periodic stars: β Cru,ENLac,HD74195. Kochukhov (2005) discussedthe MM forthe case of oblique pulsators. Schoenaers&Lynas-Gray(2008) introduced the syntheticmoment method(SMM),toaccount forpulsational temperature/gravityeffects in sdB-star atmospheres,and in particular forthe g-mode pulsating subdwarf HD 4539. Kochukhov (2004) developed amethodtomakeDoppler-Imagingmapsofsurface-velocity fields, andfound forthe bright roAp star HR 3831 thatthe LPVare due to oblique axisym- metric ℓ=1 modes.

Low-resolutionspectroscopy forpulsation-mode identiﬁcation

Low-resolution spectroscopycan be used forpulsation-modeidentification, aimingtoderive the pulsationaldegree ℓ of the mode.Informationonthe azimuthalnumber m andthe inclinationofthe symmetryaxisofthe mode (usually the stellarrotationaxis) cannot be derived from low-resolution spectroscopy. Somenewly developed methods have been applied recently. As presented by Daszyńska-Daszkiewicz (2005) forthe β Cepstars δ Cetand ν Eri, radial- velocity measurements obtained from time seriesoflow-resolution spectroscopy, obtained simultaneously with the photometricdata, canbeusedtodrastically improvethe diagnostic valueofthe photometric mode-ID methods. Clemens et al. (2000) measuredchromatic amplitudes (pulsation amplitudeateachwave- length bin) across the hydrogen Balmer lines in the DAVwhite dwarfG29-38, anddemon- strated thatspectral variations canindeed be used to identify the spherical degree. Usingthis method, Thompson et al. (2008) findthat4outof11spectroscopically identifiedmodes in G29-38 have ℓ>1.

Arecentapplication: thesubdwarfBstar Balloon090100001

Teltingetal. (2008) obtained time seriesofhigh-resolution spectroscopyonthe relatively bright (V=12.1) pulsating subdwarf BstarBalloon090100001, in 2006 at the Nordic Optical Telescope. Thedominantmodeinthisstarhas apulsation period of 356 seconds,and a radial-velocity amplitudeofabout 14.5km/s(in 2006).After foldingthe individualspectrato pulsational phase,and after combiningthe pulsational variations of about60heavy-element absorption lines,the resultingcombined proﬁleshavehighenoughsignal-to-noise ratiofor mode identiﬁcation(seeFigure2). 116 Constraints on angularnumbers of pulsation modesfromspectroscopy

Figure 2: Best-fitradial pulsationmodel (left),and best-fit ℓ=2 model(right), overplottedonprocessed time-resolved high-resolution spectra of thepulsatingsubdwarfBalloon09010000 (V=12.1).Pulsational phase is running upwards, andthe averagespectrumisplottedatthe top. Themodel on theright does not fit thedataasgood as themodel on theleft. Basedonsuchfits,Telting et al. (2008) exclude an ℓ ≥2originfor thedominant mode in this sdB star.

Basedonχ2minimisationofmodel fits, Teltingetal. (2008) conclusivelyconstrain the modalparametersofthe dominant pulsation in thissdB star,implyingthe first successful applicationofhigh-resolution spectroscopyfor mode-identificationinsdB stars. They can excludeanℓ≥2originfor the dominant mode in thissdB star,which is in good agreement with the resultsofphotometric mode-identificationtechniques (Baran et al. 2008; Charpinet et al. 2008).

Animations forpresentations, educationand publicoutreach Basedonthe model of the pulsational eigenfunction described in Schrijvers et al. (1997) andSchrijvers &Telting (1999),Ihave madeaWWW form thatallowsyou to make acolouranimationofapulsating star with corresponding line-profile variation, i.e. the animated form of the plotsshown in Figure 1. TheWWW form allows formanydif- ferent stellarand pulsational parameterstobespecified, andcan currentlybefound at http://staff.not.iac.es/∼jht/science/nrpform/.Pleasebepatient when usingthisfeature: the generationofthe animationisabitslow. J. H. Telting 117

References Aerts, C.,&Waelkens,C.1993, A&A, 273, 135 Aerts, C. 1996, A&A, 314, 115 Aerts, C.,&Eyer,L.2000, ASPC, 210, 113 Balona,L.A.1986, MNRAS, 219, 111 Balona,L.A. 2000, ASPC, 210, 170 Baran, A., Pigulski, A., &O’Toole,S.J.2008, MNRAS, 385, 255 Briquet, M.,&Aerts, C. 2003, A&A, 398, 687 Buta,R.J., &Smith,M.A.1979, ApJ, 232, 213 Charpinet, S., Fontaine, G., Brassard,P., et al. 2008, ASPC,392, 297 Clemens, J. C.,Van Kerkwijk,M.H., Wu,Y.2000, MNRAS, 314, 220 Daszyńska-Daszkiewicz, J., Dziembowski, W.,&Pamyatnykh,A.2005, A&A, 441, 641 Gies,D.R., &Kullavanijaya, A. 1988, ApJ, 326, 813 Handler,G.2008, CoAst, 157, 106 Kochukhov,O.2004, ApJ, 615, L149 Kochukhov,O.2005, A&A, 438, 219 Ledoux,P.1951, ApJ, 114, 373 Lee, U.,&Saio,H.1990, ApJ, 349, 570 Lee, U.,Jeffery, C. S.,&Saio,H.1992, MNRAS, 254, 185 Mantegazza,L.2000, ASPC, 210, 138 Osaki, Y. 1971, PASJ,23, 485 Schoenaers,C., &Lynas-Gray, A. E. 2008, ASPC, 392, 253 Schrijvers, C.,Telting, J. H.,Aerts,C., et al. 1997, A&AS,121, 343 Schrijvers, C.,&Telting, J. H. 1999, A&A, 342, 453 Smith, M. A. 1977, ApJ, 215, 574 Telting, J. H. 2003, Ap&SS, 284, 85 Telting, J. H.,&Schrijvers, C. 1997, A&A, 317, 723 Telting, J. H.,Geier,S., Østensen,R.H., et al. 2008, A&A, 492, 815 Thompson, S. E.,Van Kerkwijk,M.H., &Clemens,J.C.2008, MNRAS, 389, 93 Thomson, W. 1863, Phil. Trans. RoyalSoc.London, 153, 612 Townsend, R. H. D. 1997, MNRAS, 284, 839 Vogt,S.S., &Penrod, G. D. 1983, ApJ, 275, 661 Zima, W. 2006, A&A, 455, 227 Zima, W.,Wright,D., Bentley, J., et al. 2006, A&A, 455, 235 Zima, W. 2008, CoAst, 155, 17 DISCUSSION Bruntt: Your work on an extensivesampleofB-typestars showsthat50% or more arevariable.However, in theMOSTphotometry it is found that more than 50% Bstars arenon-variable.Isthissimplydue to your method beingmoresensitivetohigh-l modes? Telting: That is probablypartofthe explanation. It is importanttonotethatour sampleisfullina narrowrange in spectraltype, while theMOSTsampleincludesall B-type stars. Weiss: Aremarkconcerning thehistory: TheDI-technique wasintroduced by ArminDeutsch in the 1960’s, developed further by Michel Floquet(Paris) andVeraKhokhlova(Moscow) in the1970’s. Telting: Thankyou foryour comment.Ididnot intend to give theimpressionthatthe DI method was solely developed in theVogt &Penrod(1983) paper. Ionlywantedtostate theimportanceofthispaper formodeidentification methods. Michel: Ijustwanttocall your attentiontoawork whereweinvestigate to whichextentthe moment method canbeappliedtosolar-likepulsation(seeposter). Telting: Thankyou foryour comment. Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

High-resolution spectroscopyand mode identiﬁcationinnon-radially pulsating stars

K.R. Pollard1,D.J.Wright1,2,W.Zima3,P.L.Cottrell1,and P. De Cat2

1 Department of Physics&Astronomy, UniversityofCanterbury, NewZealand 2 RoyalObservatory of Belgium, Brussels, Belgium 3 Instituut voor Sterrenkunde,Leuven University, Leuven,Belgium

Abstract

We have obtained high-resolution spectroscopicdataofasample of non-radiallypulsating starswiththe HERCULESspectrograph on the 1.0-mtelescopeatthe Mt JohnUniversity ObservatoryinNew Zealand. We have developed andusedanew technique whichcross- correlates stellarspectrawithscaleddelta function templates to obtain high signal-to-noise representative spectral line proﬁlesfor further analysis. Usingtheseproﬁles, andemploying the FourierParameter Fitmethod, we have been able to placeconstraints on the degree, ℓ, andazimuthalorder, m,ofthe non-radial pulsation modes in one β Cephei star,V2052 Oph andtwo γ Doradus stars, QW Pupand HD 139095.

IndividualObjects: V2052 Oph, QW Pup, HD 139095

Introduction

Slowly pulsating Bstars and γ Dorstars canbeconsidered as the g-mode counterpartsofthe β Cepstars and δ Sctstars respectively.The theoreticalfrequency spectraofg-modes are much denser comparedtothose of p-mode pulsators andtheirpulsation periodsare generally longer (0.3–3.0d−1). Since most of the g-mode pulsators aremulti-periodic, theobserved variations have long beat-periods andare generallyrather complex. Hence, largeobservational eﬀorts arerequiredfor in-depth studies of these stars. Ourrecent interesthas been to develop an observingprogrammeand variousanalysistools to study pulsation modes in asample of non-radiallypulsators, including the γ Dorand β Cepstars.

Instrumentation and observing programmes at MJUO

Observations at the Mt JohnUniversity Observatory(MJUO)are carried out with the 1.0-m telescope equipped with the fibre-fedHighEfficiency andResolution CanterburyUniversity LargeEchelle Spectrograph (HERCULES,Hearnshaw et al. 2002).HERCULES allowsstable, high-precision,high-resolution spectroscopywhich is idealfor mode identificationofreason- ably bright (V <8) targets (Pollard et al. 2007).Asanexample,wehavebeen able to monitor lineprofile variations in a V =7.5 star in 30 minutes,withS/N of ∼120–150. Ourabilityto acquire long sequences of observingtimemeans we areabletoundertake interesting single-site studies of pulsating stars. In addition,the southerly latitude (44◦S) andthe useful longitude (170◦ E) meansthatMJUOcan makesignificantcontributionstomulti-sitespectroscopic campaigns. K.R.Pollard,D.J.Wright, W. Zima,etal. 119

Thescaleddelta function crosscorrelationtechnique

When carryingout high-resolution spectroscopicobservations forasteroseismology,itisim- portanttoobtain agood temporalcoverageofthe stellarvariabilitywhilstmaintainingreason- able S/N.Extensivesimulations were carried out to determine whichmethods of extracting ahighS/N lineprofile from an echelle spectrum were best.Simulated spectrawithdifferent numbers of lines,linedensity, linedepth, lineposition, amounts of noiseand normalisation errors were created andthe variousmethods of extracting arepresentative lineprofile were comparedwiththe input lineprofile usingastatisticaltest. We comparedthe best single lineprofile andthe resultingrepresentative lines profilesand found thatthe scaleddelta function cross-correlationprofile performedbestand wasanexcellent representation of the input lineprofile.Inthismethod, an object’sspectrum is cross-correlated with atemplate of delta functionswhich arepositioned at the correct wavelength anddepth of each line (Wrightetal. 2007, Wright 2008),thus optimizing the S/N whilstpreservingthe scientific integrity of the stellarlineprofiles. It should be noted thatthistechnique is only valid forlines similarlydistorted by the pulsationsince we do notwishtoadd together lines whichexhibit different variationwith pulsational phase.Weverifiedthatthismethodwas applicable to the γ Dorstars by visually examiningmanylineprofilesfromthe relevant spectra. In the β CepstarV2052 Oph, the behaviourofthe He Ilines andSiIII lines were quite different,withthe linedepths varying almostinantiphase.Thus,for V2052 Oph, three individuallineprofileswereexamined and analysed.

Results of themodeidentiﬁcationanalysis

Once high S/N stellarlineprofileswereobtained, the frequencies present in the variationof the lineprofilesweredetermined usingthe pixel-by-pixel period analysispackage included in the FAMIASsoftware(Zima 2008).For each frequency,the variations in the observed line profileswerematched to thoseinsyntheticlineprofilesfor variousnon-radial modes using the FourierParameter Fit(FPF) methodinFAMIAS. We appliedthismodeidentification analysis to one β Cepstar, V2052 Oph, andtwo γ Dorstars, QW Pupand HD 139095.

The β CepstarV2052 Ophiuchi V2052 OphisaB1-2 IV-V β Cepstarwithtwo previously identifiedpulsation modes:anℓ=0 −1 radial mode at f1=7.164 d (Cugieretal. 1994, Heynderickx et al. 1994, Neiner et al. 2003) −1 andanℓ=3 or 4non-radial mode at f2=6.82d (Neineretal. 2003).V2052 Ophwas observed at MJUO as part of amulti-sitecampaignorganised by Aertsetal. (2004) with ν Eridaniasthe primarytarget.Weobtained 88 spectraoverthe time span of twomonths (2004 May–July)withtypical exposure timesof10minutes giving S/N∼200. Threespectral lines were used in the analysis: a4553 AS˚ iIII line, and twoHeIlines at 4713 Aa˚ nd 5876 A.˚ Clearprofile variations were seen in all lines.Figure1showsthe pixel-by-pixel Fouriertransform of the 4713 AH˚ eIline. From analysing the selected spectral lines,the consistentlydetected frequencies were: −1 −1 f1=7.148±0.005 d ,the rotation frequency (f2=frot=0.2748±0.03 d ), twicethe rotation −1 −1 frequency (f3=2frot=0.5496±0.03 d )and f4=6.827±0.02 d ,which canall be associated with frequencies identifiedbyNeiner et al. (2003). TheFPF mode identificationtechnique (Zima2006) wasthen appliedtothe data.For −1 the dominant frequency,f1=7.148 d ,the best fit to the zero pointprofile andphase and amplitudeacrossthe profile is a ℓ=1, m=0 non-radial pulsation mode (see Figure 2).From the FPFoptimization it is clearthatf1is a m=0 mode, thoughitislessobvious whether ℓ=0,1or 2. The ℓ=1 mode givesthe best fit,but the ℓ=0 fit is only marginally worse and 120 High-resolutionspectroscopyand mode identificationinnon-radially pulsating stars

Figure 1: Pixel-by-pixel frequencyanalysis appliedtothe He I4713 Al˚ ineinV2052 Oph(main panel). Thetop panelshows themeanlineproﬁleand thestandard deviation. Variations in thelineproﬁleare symmetric about thelinecore, with maximumdeviations in thered andbluewings andlittlevariationin −1 thelinecoreitself. Themeanfrequencyspectrum(right panel) shows astrong peak at f1=7.148 d .

Figure 2: Thebestfit(solidline) to thelineprofilezeropoint,and amplitude andphase across theprofile −1 forfrequencyf1=7.148 d is an l=1, m=0 non-radial mode. K.R.Pollard,D.J.Wright, W. Zima,etal. 121 is consistentwithpreviousphotometrywhich unambiguously identifiedthisasaradial mode. We quote ℓ=0±1and m=0 as ourfinalmodeidentification. Thelineprofile residuals phased −1 to the f1=7.148 d frequency areinexcellent agreement with theoreticalprofiles, giving us confidence in the derivedbestfitparametersand the mode identification. −1 For the second pulsational frequency at f4=6.827 d ,the best fit is anon-radial ℓ=4, m=2 mode. Althoughthe best fitting mode wasaℓ=4, m=2 mode, the nextbestfitwas an ℓ=4, m=4 mode. After an examinationofthe best fitsfor different ℓ and m combinations, we give amodeidentificationofl=4±1and m =2±2.

The γ DorstarQWPuppis

QW Pup(HD 5589) hasbeen classifiedasaγDorstarbyPorettietal. (1997) basedonthe presence of lineprofile variations in itsspectraand the four independent frequencies around 1day from multi-site photometry.Nopreviousmodeidentificationhas been published. We obtained 179spectroscopicobservationsofQWPup from twosites (MJUOand SAAO,South Africa)overatime span of twomonths (2004 Feb–April).Typical exposure timeswere15 minutes.Weusedthe scaleddelta function cross-correlationtechnique to define high S/N lineprofilesfor analysis. Clearlineprofile variabilitywas observed in QW Pup(Figure3). Apixel-by-pixel frequency analysiswas carried out andeight frequencies detected. An examinationofthe zero point phase andamplitude fitsfor the three strongestfrequencies (2.122, 2.038, 6.229 d−1)shows reasonable fitsfor the first twofrequencies andlineprofile variations consistentwithnon-radial pulsations, but apoorfitfor the third frequency.Wecontinued with amodeidentification forthe first twofrequencies.The best fitsare for ℓ=8, m=6 and ℓ=8, m=4 forthe 2.122 and2.038 d−1 frequencies respectively.Althoughthe zero pointprofile andthe phase were able to be fitted well, the amplitudewas fitted less well in all cases. Therewas more variation in the extremewings of the lineprofile when comparedwiththe theoreticalprofiles. This is possiblydue to the higher horizontalmotions present in g-mode pulsationsinthe γ Dorstars or perhapsdue to rotational effects.After an examinationofthe best fitsfor different ℓ and m combinations,wegiveamode identificationofℓ=8±3, m=6±2and ℓ=8±2, m=4±1for the 2.122 and2.038 d−1 frequencies respectively.

The γ DorstarHD139095

HD 139095 hasbeen classifiedasamultiperiodic γ Dorstarwithadominant period of 0.634 d−1 from HIPPARCOS photometry(Handler 1999, Henry&Fekel2002, Handler & Shobbrook2002).HD139095 wasobservedduringthe campaign forwhich QW Pupwas the primarytarget.Weobtained 57 spectraoverthree weeksatSAAOand MJUO.The analysismethods were very similartothatcarried out forQWPup, usingscaleddelta function cross-correlationtodefine the lineprofilesfor analysisusing the FPFsoftware. Line profile variations were obvious. Thepixel-to-pixelFourier analysisshowedmanyfrequencies present in the dataset, althoughthe data were very noisy, raisingthe possibilityofspurious peaks. A numberoffrequencies whichshowedprofile variations consistentwithnon-radial pulsations −1 (f1=2.353, f2=9.560, f3=8.638 andf4=10.14 d )wereusedinthe FPFanalysis. Thebest −1 mode forfrequency f4=10.14 d was ℓ=7±1, m=5±2whilstthe other frequencies hadpoor fitsand arelikelyspurious.Itislikelythatthe small quantityand poorer qualityofthe data is the mainfactorlimitingthe analysisand further,longer baselineand high S/N data will be requiredfor amoreprecise analysis. 122 High-resolutionspectroscopyand mode identificationinnon-radially pulsating stars

Figure 3: Thelineprofilevariationfor QW Pup. Thestandard deviationfromthe mean profile (top), the setofcross correlationlineprofiles from SAAO spectra (middle) andthe deviations from themeanprofile plottedversusobservation number (bottom).

Summary

As part of an observationalstudy of asample of non-radiallypulsating stars, we have de- velopedand tested ascaleddelta function cross-correlationmethod (Wrightetal. 2007, Wright 2008) whichproduceshighS/N representativelineprofiles. We present theresults from the subsequent mode identificationanalysisofone β Cepstarand two γ Dorstars using the FPFmethod (Zima2006).The FPFmethod givesexcellent resultsfor the β Cepstar, but some discrepancies areseen in the analysisofthe γ Dorstars, possiblydue to the greater horizontalmotionpresent in the g-mode pulsationsorperhaps rotational effects.Further research is in progress.

Acknowledgments. KRPwould liketothank the LOCand SOCfor ﬁnancial supportwhich enabled her to attend the conferenceinWroclaw,Poland. K.R.Pollard,D.J.Wright, W. Zima,etal. 123

References

Aerts, C.,DeCat,P., Handler,G., et al. 2004, MNRAS, 347, 463 Cugier,H., Dziembowski, W.A., &Pamyatnykh, A.A. 1994, A&A, 291, 143 Handler,G.1999, MNRAS, 309, L19 Handler,G., &Shobbrook R.R2002, MNRAS, 333, 251 Hearnshaw, J.B.,BarnesS.I., KershawG.M., et al. 2002, Exp. Astr., 13, 59 Henry, G.W., &Fekel,F.C.2002, PASP,114, 988 Heynderickx, D.,WaelkensC., &Smeyers,P.1994, A&ASS, 105,447 Neiner,C., Henrichs H.F.,Floquet, M.,etal. 2003, A&A, 411,565 Pollard,K.R., Wright D.J., Cottrell, P.L.,etal. 2007, CoAst, 150, 133 Poretti,E., Koen C.,Martinez, P.,etal. 1997, MNRAS, 292, 621 Wright,D.J, Pollard,K.R., &Cottrell, P.L. 2007, CoAst, 150, 135 Wright,D.J. 2008, PhDThesis, UniversityofCanterbury Zima, W. 2006, A&A, 455, 227 Zima, W. 2008, CoAst, 155, 17

Coﬀeebreak between talks Comm. in Asteroseismology Vol. 157, 2008, WrocMl aw HELASWorkshop 2008 M. Breger,W.Dziembowski,&M. Thompson,eds.

Spectroscopic mode identiﬁcationofthe δ Scuti star4CVn

B. G. Castanheira1,M.Breger1,P.G.Beck1,A.Elmasli1,2, P. Lenz1,and R. E. Falcon3

1 Institut f¨ur Astronomie,T¨u rkenschanzstrasse 17, A-1180Vienna,Austria 2 Ankara University, Astronomyand SpaceSciences Department,Tandogan,06100, Ankara,Turkey 3 Department of Astronomyand McDonald Observatory, UniversityofTexas, Austin,TX78712, USA

Abstract

We studied the δ Scuti star 4CVn through time-seriesspectroscopy1 ,since photometryalone is insufficient to provideaunique solution to mode identification. However, the combination of multifilter photometryand high-resolution spectroscopy, similartothe data we obtained andanalyzed, allowsthe necessary reliable mode identification. We have obtained 38 nights of time-serieshigh-resolution spectroscopyatthe 2.1m telescopeatMcDonald Observatory for4CVn.Wehavedonemodeidentificationfor fiveindependent frequencies detected by spectroscopy, whichwerepreviouslydetected with photometric observations.

IndividualObjects: 4CVn

Introduction

Asteroseismology is oneofthe most powerful toolstostudystructureand stellarevolution. Pulsations probethe internalstructureofthe stars, as everypulsational mode is,inprinciple, an independent measurement providingindependent information. Even from just onepulsa- tion mode, we canderivefundamentalproperties, such as stellarmassfor pulsating white dwarfs (Castanheira &Kepler 2008). However, when manymodes areexcited anddetected, the structureofastar canbedetermined in greatdetail (Dziembowski&Pamyatnykh 2008). δ Scuti starsare the perfect targets to applythe full powerofasteroseismology.These 1.5–2.5M⊙ starsare on andabove the mainsequence, pulsating in radial andnon–radial p and g–modes with periodsbetween 0.4and 8h.They areparticularlysuitablefor study- ingthe poorly understood hydrodynamical processoccurring in stellarinteriors, such as the extentofconvective overshooting,the efficiency andtreatment of convection (Daszyń ska- Daszkiewicz et al. 2003, Montalbá n&Dupret 2007), rotationally induced mixing of elements, andthe redistribution of the angularmomentum.Arecent analysis of the solarspectrum by Asplund et al. (2004, 2005) ledtoadownward revision of thesolar heavy element abun- dances,destroyingthe good agreement between the standard solarand helioseismicmodels. With the δ Scuti stars, we cantestwhether the new solarabundances or the seismological modelsare problematic.Theirunderstanding is mandatory in constrainingtheoreticalstellar models. Finally, δ Scuti starsallowustoinvestigate whyand howsomepulsating starsshow strong amplitudeand small frequency variabilities. Thehypothesis thatthe beatingoftwo closemodes causes thisvariabilitycan be tested by the followingtwo predictions it makes.

1Based on observations at McDonald ObservatoryofThe UniversityofTexas at Austin B. G. Castanheira, M. Breger,P.G.Beck,etal. 125

First,amplitude andphase variations arerelated in time,accordingtobeating. Second, due to cancellationeffects,atagivenobservedfrequency,the low-ℓ mode (few nodes on the surface) will be dominant photometrically,but spectroscopically the higher-ℓ mode is more likelyto be seen. Thefirst prediction hasalready been verifiedfor δ Scuti (Breger &Bischof 2002, Breger &Pamyatnykh 2006) andRRLyr stars(Guggenberger &Kolenberg2007),but the second one requireslarge aperturetelescopes with high-resolution time-seriesspectroscopy. That is the hypothesisweare investigatinginthiswork. Thereare three fundamentalrequirements to do seismology of δ Scuti stars. It is necessary to obtain high-accuracymultifilter photometry. We have obtained thousands of hoursof data in the past yearswithdedicated automatic photoelectric telescopes(Breger et al. 2005), detecting more than75frequencies forsomestars. Having detected thatmanyfrequen- cies,sophisticated modelsofstellarstructureand pulsation arenecessary.The modelscom- puted by ourgroup/collaboratorsare state-of-the-artand constantlyimproving (Daszyń ska- Daszkiewicz et al. 2005, Dziembowski2006). However, frequency information alone is insufficient to constrain all model parameters requiredfor aunique model fit.Obtainingmodeidentifications (ℓ, m and n quantum numbers) foreachmodeusedfor seismologicalstudiesisthe third requirement. Photometry alone canpossiblyconstrain the ℓ value. Even with near-infinite amounts of photometry, the modelswould still notprovide aunique solution.Fortunately, the combinationofmultifilter photometryand high-resolution spectroscopyallows reliable mode identifications.

Observationsand datareduction We have obtained 38 nights from January to Mayin2008 of time-serieshigh-resolution spectra usingthe Sandiford Cassegrain Echelle Spectrograph at the Otto Struve 2.1m telescope at McDonald Observatory. Theintegrationtimes were between 7and 15 minutes,depending on the weather conditions, to achieveS/N>200. Theexposuretimes couldnot be longer than thesevalues,becausedominantmodes have periodsbetween 3and 5hours. Theaverage readoutplusthe writingtimeis32s. We used aresolving powerofR∼60 000. Thegridwas centered to ∼ 4500A,˚ because 4CVn is afastrotator (v sin i > 120 km/s). Therefore, most of the lines areblended. This is the best region to observethisstarwhereafewunblended iron lines canbefound. We reduced the data with standard IRAFroutines. First,weappliedflat field andbias corrections.The wavelength calibration is averyimportant step to determine precise line profile variations.Tocorrect forany variations in wavelength duetothe Cassegrain mount, we took 2to3sThArcomparisonspectraafter each science frame. Data analysis and preliminary mode identification In the normalized spectral region,the only twolines thatwerenot blended were the Fe II lines at 4508.2860Aa˚ nd 4549.4790A.˚ Thelines were converted to Doppler velocities and averaged out to study the effects of the pulsations in the lineprofile.The processeddata were analyzedwiththe FourierParameter FitMethoddeveloped by Wolfgang Zima usingthe FAMIASsoftware(Zima 2008). In ourdataset, we found fiveindependent pulsation modes.All of these periodicities have previously been detected by time-seriesphotometry. Oneofthe goals of thisproject wastocheck if the strong amplitudevariationobservedfor 4CVn couldbeexplained by high degree(ℓ)frequencies closetothe photometric ones.Thesehighdegree modes,due to cancellationeffects,cannotbedetected by time-seriesphotometry. However, these modes,if present, couldeasilybeseen in time-serieshigh-resolution spectroscopy. Usingthe FAMIASsoftware, we identifiedthe most likelysolutions for ℓ and m values for the spectroscopicmodes (see Table1). We areusing the convention that m > 0are prograde and m < 0are retrograde. 126 Spectroscopic mode identificationofthe δ Scutistar4CVn

Table1:List of modesdetected spectroscopically and theminimainχ2 forthe best ℓ and m solutions.

Photometricfrequencies Periodicity(cd−1) ℓ m χ2

f5=5.8498 5.852 11 4.48 21 4.65

f2=7.3760 7.374 2-13.05 1-14.44

f3=5.0480 5.044 1-13.32 2-13.34

f1=8.5943 8.596 211.042 111.270

f8=6.9764 6.976 200.645 000.697 100.702

Becauseour data were obtained in only onesite, we cannot look forpulsational frequencies smallerthanone cycleper daynor multiples. Theintegrationtimes of ≤ 15 min, the minimum to achievethe necessary signal–to–noise formodeidentiﬁcation(seeZima2006 fordetails), do notallowustolookfor frequencies larger than48cyclesper day. From time-series photometry, the dominant modes areinthe frequency rangebetween 4and 9cd−1. For the ﬁvefrequencies detected spectroscopically,wewereabletounivocally determine the m value.

Preliminary results

Having detected andidentifiedfive modes,thesewill be used to constrain the modelsfor 4CVn.Thiswill allowustolearn more aboutthe physicalprocess, including convection, taking placeinthe interiorofthisstar. Ournew mode identifications areinagreement with the previous ℓ=1 identificationof f1,f2,and f3 derived by meansofphotometric phase differences (Breger et al. 1999).As stated in Breger &Pamyatnykh (2002),the almost equalspacing of these ℓ =1modes canbeexplained by mode trapping in the acoustic cavity.The model presented in their study predicts trapped ℓ=1 modes closetothe observed frequency values,but with amassof 2.4 M⊙,the luminosity log(L/L⊙)=1.76 is significantlyhigher thanthe valuederived from observations (1.53 ± 0.065). Theadditional knowledgeofmvalues from spectroscopycan be used to improvethe mod- elsof4CVn.Becauseofthe uncertainties in ℓ determinations, it is notclear if components belongingtothe same rotationallysplit multipletare present. Consequently, the rotation of the star couldnot be fully constrained. Preliminaryresults show thatthe identified ℓ =1 modes canbefitbyamodel with 2.1to2.2 M⊙ andarotational velocity of 120 km/s and slightlyabove.Thismay suggestahigh stellarinclinationwhich wouldexplain the non- detection of non-radial m =0modes.The predicted luminosity of these modelsisinbetter agreement with the observed values thanfor the oldmodel. B. G. Castanheira, M. Breger,P.G.Beck,etal. 127

Acknowledgments. This research hasbeen supported by the FWFP17441-N02. References

Asplund, M.,Grevesse,N., Sauval, A. J., et al. 2004, A&A, 417, 751 Asplund, M.,Grevesse,N., &Sauval, A. J. 2005, ASPC, 336, 25 Breger,M., &Bischof, K. M. 2002,A&A,385, 537 Breger,M., Lenz, P.,Antoci, V., et al. 2005, A&A, 435, 955 Breger,M., Handler,G., Garrido, R.,etal. 1999, A&A, 349, 225 Breger,M., &Pamyatnykh, A. A. 2002, ASPC, 259, 388 Breger,M., &Pamyatnykh, A. A. 2006, MNRAS, 368, 571 Castanheira, B. G., &Kepler, S. O. 2008, MNRAS, 385, 430 Daszyń ska-Daszkiewicz,J., Dziembowski, W. A., &Pamyatnykh, A. A. 2003, A&A, 407, 999 Daszyń ska-Daszkiewicz,J., Dziembowski, W. A., Pamyatnykh,A.A., et al. 2005, A&A, 438, 653 Dziembowski, W. A. 2006, MmSAI, 77, 348 Dziembowski, W. A., &Pamyatnykh, A. A. 2008, MNRAS, 385, 2061 Guggenberger, E.,&Kolenberg, K. 2007, CoAst, 150, 379 Montalbá n, J., &Dupret, M.-A.2007, A&A, 470, 991 Zima, W. 2006, A&A, 455, 227 Zima, W. 2008, CoAst, 155, 17 Marc-AntoineDupret...

... andhis audience.