Astronomy&Astrophysicsmanuscriptno.Fk261 February2,2008 (DOI:willbeinsertedbyhandlater) No magnetic field variation with pulsation phase in the roAp star γ Equulei O.Kochukhov1,T.Ryabchikova2,1,andN.Piskunov3 4 0 1 Institutfu¨rAstronomie,Universita¨tWien,Tu¨rkenschanzstraße17,1180Wien,Austria 0 2 2 InstituteofAstronomy,RussianAcademyofSciences,Pyatnitskaya48,109017Moscow,Russia 3 UppsalaAstronomicalObservatory,Box515,SE-75120Uppsala,Sweden n a J Received/Accepted 7 Abstract.Wepresentananalysisof210high-resolutiontime-resolvedspectropolarimetricobservationsoftheroApstarγEqu 2 obtainedoverthreenightsinAugustandSeptember2003.Radialvelocityvariationsduetop-modenon-radialpulsationsare v clearlydetectedinthelinesofrare-earthelements,inparticularPr,NdandNd.Incontrast,wefindabsolutelynoevidence 8 forthevariationofthemeanlongitudinalmagneticfieldoverthepulsationperiodinγEquatthelevelof110–240Gwhichwas 4 recentlyreportedbyLeone&Kurtz(2003).Ourinvestigationofthevariabilityofcircularlypolarizedprofilesof13Ndlines 0 demonstratesthat,atthe3σconfidencelevel,nomagneticfieldvariationwithanamplitudeabove≈ 40–60Gwaspresentin 1 γEquduringourmonitoringofthisstar. 0 4 Keywords.stars:atmospheres–stars:chemicallypeculiar–stars:individual:γEqu–stars:magneticfields–stars:oscillations 0 / h p 1. Introduction High-resolution analysis of Stokes profiles of individual - o metallinesisamuchmorepromisingtoolformappingatmo- r Sincethediscoveryofhigh-overtonep-modepulsationsinthe sphericpulsationaldisturbancesandinvestigatingpossibleos- t s rapidly oscillating Ap (roAp) stars it became clear that, un- cillations of magnetic field. In a recent paper Leone & Kurtz a like in other stellar pulsators, strong magnetic fields in these : (2003, hereafter LK) announcedthe discovery of variation of v starshaveadefiningroleinexcitingtheoscillationsandshap- themeanlongitudinalfieldhB iwiththe12.1-minutepulsation i ing main pulsational properties. It was found that the ampli- z X periodin oneofthebrightestroApstar γEqu.Magneticvari- tude and phase of the rapid light variation are modulated by r abilitywithanamplitudebetween110and240Gwasinferred a thestellar rotationandthatthephasesoftheextremaofmag- fromthestudyof4Ndlinesin only18circularlypolarized netic field and pulsational amplitude typically coincide with spectra of γEqu, which makes the alleged detection of mag- eachother.Aphenomenologicalobliquepulsatormodel(Kurtz netic variation a statistically marginal result. With the aim of 1982) attributed main characteristics of the photometric pul- verifying the existence of rapid magnetic variability in γEqu sational variation of roAp stars to the oblique dipole modes, wedecidedtoacquireandanalyseamuchmoreextensivetime alignedwiththeaxisofdipolarmagneticfield. seriesspectropolarimetricobservationsofthisstar. Theapparentconnectionbetweenglobalmagneticfieldof roAp stars and their non-radial pulsations led Hubrig et al. (2003)toproposethatatmosphericmagneticstructuremayalso 2. Observations change over the pulsation period and hence pulsational vari- We obtained time-resolved circularly polarized spectra of abilityofthelongitudinalmagneticfieldcaneventuallybeob- γEquusingthecross-dispersedNasmythEchelleSpectrometer served. Hubrig et al. (2003) searched for the magnetic varia- (NES, Panchuk et al. 1999) installed at the 6-m telescope of tionsinasampleofsixroApstarsbutfailedtodetectanyco- the Russian Special Astrophysical Observatory. The NES in- herentmagneticvariability in low-resolutionZeeman spectra. strument is equipped with a Zeeman analyzer consisting of a ThisnullresultisnotunexpectedgiventhatinroApstarslines quarter-waveandhalf-waveretardersandacalcite platesepa- ofdifferentelementsdisplaydramaticallydifferentamplitudes ratingthebeamswithoppositecircularpolarization.A2K×2K and phases of oscillations, which are combined destructively LoralCCDdetectorallowedustorecord26echelleorderswith andresultinanextremelyweakpulsationalsignalwhenaver- nearlycompletewavelengthcoverageinthe4520–6000Å re- agedoverbroadwavelengthregions. gionwithaspectralresolvingpowerofR≈38000. Sendoffprintrequeststo:O.Kochukhov On each of the nights of August 19 and 20, 2003 we ob- e-mail:[email protected] servedγEqufor2.4handhaveobtainedcontinuoussequences 2 O.Kochukhovetal.:NomagneticfieldvariationwithpulsationphaseintheroApstarγEquulei of70StokesI andV spectrausing80s integrationtimewitha Table1.NdlinesusedintheRVandmagneticfieldanalysis readouttimeof42s.Anadditionalseriesof70polarizedspectra of γEqu. The columns give laboratory wavelength, effective of γEqu wassecuredon September11, 2003,whenexposure Lande´ factor, excitation potentials and J values of the lower times of 120s were used. On each of the observingnightsthe andupperlevels. peak S/N ≈ 60–80 was reached in individual time-resolved spectra.ThesoftwarepackageREDUCE(Piskunov&Valenti λ(Å) g Transition(cm−1) eff 2002)wasusedfortheoptimalextractionoftheNESspectra.A 4759.54bc 1.621 5093 –26098 8 7 wavelengthscalewithaninternalaccuracyof50–70ms−1was 4796.49bc 1.553 1138 –21981 5 6 established by means of a 2-D wavelength calibration proce- 4927.49a 1.186 3714 –24003 7 7 dure,whichmadeuseof≈700ThArlinesinallechelleorders. 4942.68b 1.479 3714 –23941 7 6 The left- and right-hand circularly polarized (LCP and RCP) 5012.94d 1.677 50938–250367 beamswere calibratedindependentlyusingthe corresponding 5203.92ad 0.919 11385–203495 5286.75a 1.421 5093 –24003 beamsofthereferencespectrumtakenbeforeandafterstellar 8 7 5294.11a 0.615 0 –18884 observations. 4 4 5677.18a 1.579 5093 –22703 8 7 5802.54c 1.531 2387 –19617 6 5 3. IdentificationofNdlines 5845.02a 1.101 5093 –22197 8 9 5851.54c 1.617 3714 –20799 7 6 Investigation of pulsational variability in the spectral lines of 5987.68a 1.163 3714 –20411 7 7 the rare-earth elements (REE) offers unique potential to ob- serve non-radial p-mode oscillations and to study in detail aPreviouslyidentifiedandclassifiedNdlines the structureof pulsatingcavity in roApstars. Itwas recently bLinesincludedinCrosswhite’s(1976)unpublishedlist demonstrated by Kochukhov & Ryabchikova (2001a, 2001b) cLinesdetectedinthelaboratoryspectrum(Alde´nius2001andprivate that the largest pulsational variability (RV amplitudes up to communication) 1 kms−1) in individual metal lines in γEqu and other roAp dReclassifiedandnewlyclassifiedlines stars is invariably found in the REE spectral lines, in partic- ular strong absorption features of doubly ionized Pr and Nd, center-of-gravityasafunctionoftimeintheStokes I spectra. whilepulsationscouldnotbedetectedinthelinesoflightand Thenarefinedanalysisofpolarizationspectrawascarriedout iron-peakelements.SincethelinesofeachREEionshowvery forthegroupof Ndlinesaimedatdetectionofthemagnetic similar pulsational behaviour, the accuracy of our search for variability.Aninstantaneouspositionofthelinecenterwasde- magnetic oscillations in γEqu can be substantially improved terminedconsistentlyfortheRCPandLCPprofilesbyintegrat- bysimultaneousmultilineanalysisofNdlines,whichconsti- ing over the spectral points below certain residual depth. The tutethemostnumerousgroupofstronglineswithpronounced sameverticalcutoffwasappliedtotheRCPandLCPspectra, variabilityinthespectrumregionavailableinourobservations. butithadtobechosenindividuallyforeachlineduetodiffer- In the present study magnetic field and RV variations entblendingin the far wings. This resultsin up to a factor of weremeasuredusing13unblendedNdlinessomeofwhich twodifferenceintheRVamplitudesforstudiedNdlines,al- werepreviouslyunclassified,butappearedinlaboratoryspec- thoughdeptheffectsmayalsobepartiallyresponsibleforthat. tra(Crosswhite1976;Alde´nius2001)aswellasinthespectra The RV andhBzi werederivedfromthe center-of-gravitiesof ofroApstarsknowntohaveNdlinesofabnormalintensity theRCPandLCPprofiles,λR andλL,usingtheexpressions (Ryabchikovaetal.2001).Weemphasizethatallnewlyclassi- λ +λ hB i= R L , fied Nd lines show strong pulsationalsignatures, consistent z 2.34×10−13g (hλ i+hλ i)2 eff R L (1) withthebehaviourofknownlinesofNd,whichbyitselfpro- RV = c λR+λL −1 , (cid:18)hλ i+hλ i (cid:19) vides a convincingsupportfor our line identification.Table 1 R L containswavelengthsof Nd lines,proposedtransitioniden- wherecisthespeedoflightandhλ icorrespondtothetime- R,L tification based on the energy level calculations by Zhang et averagedlinecenterpositions. al. (2002) and the effective Lande´ factors which were calcu- Preliminarytime seriesanalysisof the Nd linesshowed lated from the g-factorspublishedby Bord (2000) and Zhang negligible difference between the periods and phases of their etal. (2002). The detailsof theline classification willbe pre- RV variability. Therefore, in subsequent least squares sinu- sentedelsewhere,herewenotethattheadoptedLande´ factors soidal fits we allowed for individualamplitudes, but used the andZeemanpatternsareconsistentwiththeobservedZeeman samephaseandpulsationperiodforallNdlines,effectively splittinginthesharp-linedApstarHD144897withthesurface coaddinginformationfrommanylinesintoa singlehighS/N magneticfieldof≈9kG. RV measure.The same strategy wasused to constructthe av- eragevariationofthelongitudinalfieldaftersubtractingacon- stant offset from hB i measurements obtained for each of the 4. Radialvelocityandmagneticfield z Ndlines.Resultsofourinvestigationoftheneodimiumline measurements variability are summarized in Table 1 and are illustrated in ThepulsationalanalysisofγEqufollowedtheprocedureout- Figs. 1 and 2, which show the average RV curves (scaled to lined in Kochukhov & Ryabchikova (2001a). For each spec- nightly mean amplitudes) as well as the average variation of trallineintheavailablewavelengthregionwedeterminedthe hB iandcorrespondingamplitudespectra. z O.Kochukhovetal.:NomagneticfieldvariationwithpulsationphaseintheroApstarγEquulei 3 Fig.1. Pulsational variation of the radial velocity and longitudinal magnetic field measured for Nd lines on the nights of August19and20,2003.TheaveragepulsationalRVcurvesa)arefoldedwiththebest-fitoscillationperiodandarecompared withtheaveragevariationofhB ic).Panelsb)andd)illustratetheamplitudespectrafortheRVandlongitudinalmagneticfield. z Theverticaldashedlinesshow photometricpulsationalperiodsofγEqu.Thehorizontaldashedline in panelsd) indicatesthe maximumamplitudeofpulsationalhB ivariationreportedbyLK. z Table 2. Results of our analysis of the time-resolved polarized spectra of γEqu. The columns list UT date of observation, referenceJuliandate,numberofanalysedspectraandaleast-squaresestimateofthepulsationalperiod,averageamplitudeand phase(measuredin fractionsofthe period)ofthe pulsationalRV variationin 13Nd lines.Thelastthreecolumnsreportthe amplitude of the magnetic variation, standard deviation of the hB i measurements and an amplitude which would have been z detectedwithoutdataatthe3σconfidencelevel. UTDate T − N P hAi ϕ ∆hB i σ(hB i) ∆hB i 0 z z z max 2400000 (min) (ms−1) (G) (G) (G) 13linesofNd 19/08/2003 52871.5140 70 12.212±0.013 963 0.102±0.004 30±17 105 63 20/08/2003 52872.3727 70 12.169±0.012 854 0.382±0.004 37±13 80 48 11/09/2003 52894.2954 70 12.231±0.024 262 0.011±0.012 14±10 59 36 Forallthreenightsthepulsationperioddetectedinourdata and414ms−1(11Sep)andaconstantphaseshiftof0.13±0.02 is consistent with one of the frequencies (P = 12.201 min) ofpulsationperiodwithrespecttotheRVvariationofNd. identifiedinphotometry(Martinezetal.1996).Despiteunam- The procedureof the magneticand RV measurementsap- biguousdetectionofthepulsationalRVshifts,noevidencefor pliedtoREElineswasalsotestedonasampleof19unblended magneticvariabilityisfound.Arigorousstatisticalanalysisin- stronglinesofCa,CrandFe,whicharenotexpectedtoshow dicatesthat,atthe3σconfidencelevel,nomagneticvariability anypulsationalvariabilityofeitherRVorhB i.FromtheAug z with∆hB i>40–60GisseeninγEquduringthenightsofour 19dataweobtainedRV amplitudeof30±19ms−1,∆hB i = z z observations. 18±14Gandstandarddeviationσ(hB i)=84Gfortheselines, z ingoodquantitativeagreementwiththeREEresults.Thispro- In addition to the study of the Nd lines, we identified a vides a complementory indirect argument for the absence of number of Pr and Nd features showing clear pulsational magneticvariabilityinREElines.Sincethevariationofmag- variability. These lines are not so numerous and strong as to neticfieldispredictedtobeproportionaltotheRVoscillations provide an independent and accurate diagnostic of possible (seeHubrigetal.2003),evenformarginalmagneticvariation rapidmagneticchanges.Nevertheless,analysisoftheseionsis onewouldexpecttofindσ(hBziREE)≫σ(hBziCa,Cr,Fe),butthis consistentwith the results obtainedusingthe Nd lines: two isclearlynotobservedinγEqu. linesofPrwiththeaverageRVamplitudebetween950ms−1 (19Aug)and280ms−1 (11Sep)show∆hBzi <∼ 100G,while 5. Discussion ∆hB i≈60±50GisderivedfromfourNdlines.Remarkably, z the lines of singly ionized Nd, which could not be investi- What may be the reason for a major discrepancybetweenthe gated in our first spectroscopic study of pulsations in γEqu resultsreportedbyLKandtheoutcomeofourstudyofγEqu? (Kochukhov& Ryabchikova 2001a), show very high average We consider it improbable that the star itself has changed RV amplitudesof 1416ms−1 (19Aug), 1118ms−1 (20 Aug) its pulsationalbehaviourdramatically.Theoreticalestimate of 4 O.Kochukhovetal.:NomagneticfieldvariationwithpulsationphaseintheroApstarγEquulei Fig.2.ThesameasFig.1forthespectropolarimetricobserva- tionsofγEquobtainedonthenightofSeptember11,2003. possible magnetic variability (Hubrig et al. 2003) hints that magnetic and velocity amplitudes are proportional to each other. Therefore, if magnetic variability really exists, on the nightsof Aug 19 and 20 (whenRV amplitudesof Nd lines were about twice the amplitude measured by LK) we should haveobservedevenlargerhBzivariationthanfoundbyLK. Fig.3. The average Stokes I a) and V b) profilesof the Nd It is possible that the difference between our null result lines at λ 5802.54 and 5845.07 Å. The vertical dashed lines and the alleged positive detection of the magnetic variability illustrate selection of the spectralregionfor the RV andmag- by LK is related to different approachesto measure hB i and netic measurements.The panelc) shows variationof the hB i z z the effects of blending of the Nd lines studied by LK. We measureobtainedfromtheStokesV profiles.Blendingbythe derive longitudinalfield from consistent center-of-gravityde- Pr5844.41ÅleadstospuriousvariationofhB idetermined z termination in the RCP and LCP profiles, while LK analysed fortheNd5845.07Å. the first moment of the Stokes V spectra. Strong Nd lines tendtoshowextendedwingsandhaveunusuallywideStokes Basedonourobservationsweconcludethatweseenoevi- V signatures.Hence,aninsignificantblendinginStokesI may denceforpulsationalvariationofmagneticfieldinγEqucon- correspondtoasubstantialoverlapoftheStokesV profilesof trarytotherecentclaimbyLK.Weshowthatsystematicprob- neighbouringlines.TheNd5845.07Å,whichLKofferedas lemsexistinthelatterstudyandhencetheallegeddetectionof themostprominentcaseofhB ivariation,representsaclearex- z themagneticvariabilityinγEqumaybespurious. ampleoftheblendingproblem.Thislineisblendedbythevari- ablelineof Pratλ5844.41Å,whichappearstobereason- Acknowledgements. WesincerelythankV.PanchukandM.Yushkin ablywellseparatedfromtheNdlineinStokesI,butsignifi- forcarryingouttheobservationsofγEqu.Thisworkwassupported cantlydistortsthecorrespondingStokesV signature.InFig.3 bytheLiseMeitnerfellowshiptoOK(FWFprojectM757-N02),FWF we use our Aug 19 data to illustrate that the blending of the project P14984andhasbeenpartlyfundedbytheSwedishNational Nd5845.07ÅresultsinspuriousvariationofhB iwhenin- Research Council, Swedish Royal Academy of Sciences and by the z tegratingStokesVsignalforthislinewithinafixedwavelength RussianFederalprogram“Astronomy”(part1102). range. In contrast, no variation is seen in the nearby line of Nd5802.54Åwhichisfreefromanyblendsandhashigher References magneticsensitivity. Alde´nius, M. 2001, Master Thesis, Department of Physics, Univ. of We also pointout thatthe results of the RV and magnetic measurements presented by LK for individual Nd lines are Lund Bord,D.J.2000,A&AS,144,517 inconsistent.ThereportedphaseshiftbetweenhB icurvesof, z Crosswhite,H.1976,privatecommunication e.g.,theNd5845.07and6145.07Å,reaches0.20ofthepul- Hubrig,S.,Kurtz,D.W.,Bagnulo,S.,etal.2003,A&A,inpress sationperiod(withatypicallyphaseerrornotexceeding0.03), Kochukhov,O.,&Ryabchikova,T.2001a,A&A,374,615 whilenosuchshiftisseeninRVvariation.Unfortunately,LK Kochukhov,O.,&Ryabchikova,T.2001b,A&A,377,L22 do not comment on this peculiar behaviour of different Nd Kurtz,D.W.1982,MNRAS,200,807 lines. 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