The planet-hosting subdwarf B star V391 Pegasi is a hybrid pulsator

0.55 MB·

by  R. Lutz

Astronomy&Astrophysicsmanuscriptno.hs2201 (cid:13)c ESO2009
January28,2009
The planet-hosting subdwarf B star V391 Pegasi is a hybrid
⋆
pulsator
R.Lutz1,4,S.Schuh1,R.Silvotti2,S.Bernabei3,S.Dreizler1,T.Stahn4,andS.D.Hu¨gelmeyer1
9
1 Institutfu¨rAstrophysik,Universita¨tGo¨ttingen,Friedrich-Hund-Platz1,37077Go¨ttingen,Germany
0
e-mail:[email protected]
0
2 INAF-OsservatorioAstronomicodiCapodimonte,viaMoiariello16,80131Napoli,Italy
2
3 INAF-OsservatorioAstronomicodiBologna,viaRanzani1,40127Bologna,Italy

n 4 Max-Planck-Institutfu¨rSonnensystemforschung,Max-Planck-Straße2,37191Katlenburg-Lindau,Germany
a
J Received;accepted

8
ABSTRACT
2

Context.AnoticeablefractionofsubdwarfBstarsshowseithershort-period(p-mode)orlong-period(g-mode)luminosityvariations,
]
R withtwoobjectssofarknowntoexhibithybridbehaviour,i.e.showingbothtypesofmodesatthesametime.Thepulsatingsubdwarf
BstarV391Pegasi(orHS2201+2610),whichisclosetothetwoknownhybridpulsatorsinthelogg–T plane,hasrecentlybeen
S eff
discoveredtohostaplanetarycompanion.
.
h Aims.Inordertolearnmoreabouttheplanetarycompanionanditspossibleinfluenceontheevolutionofitshoststar(subdwarfB
p starformationisstillnotwellunderstood), anaccuratecharacterisationofthehoststarisrequired.Aspartofanongoingeffortto
- significantlyimprovetheasteroseismiccharacterisationofthehoststar,weinvestigatethelow-frequencybehaviourofHS2201+2610.
o
Methods.Weobtainedrapidhighsignal-to-noisephotometricCCD(B-filter)andPMT(clear-filter)dataat2m-classtelescopesand
r
carriedoutacarefulfrequencyanalysisofthelightcurves.
t
s Results.In addition to the previously known short-period luminosity variations in the range 342s−367s, we find a long-period
a
variationwithaperiodof54minandanamplitudeof0.15percent.Thiscanmostplausiblybeidentifiedwithag-modepulsation,so
[
thatHS2201+2610isanewadditiontotheshortlistofhybridsdBpulsators.
1 Conclusions.AlongwiththepreviouslyknownpulsatingsubdwarfBstarsHS0702+6043andBalloon090100001 showinghybrid
v behaviour,thenewhybridHS2201+2610isthethirdmemberofthisclass.ThisimportantpropertyofHS2201+2610canleadtoa
3 bettercharacterisationofthisplanet-hostingstar,helpingthecharacterisationofitsplanetarycompanionaswell.Currentpulsation
2 modelscannotyetreproducehybridsdBVstarsparticularlywellandimprovedpulsationmodelsforthisobjecthavetoincludethe
5 hybridbehaviour.
4 Keywords.subdwarfs-Stars:horizontal-branch-Stars:oscillations-Stars:individual:HS2201+2610
.
1
0
9 1. Introduction acousticpressurewavesareoflowdegreeandlowradialorder.
0
In contrast, the g-mode pulsators have even lower amplitudes
: SubdwarfBstars(sdBs)areevolvedobjectswithmassesaround
v (fewmmag)andlongerperiods(30to90min)atlowertemper-
half a solar mass and are thought to be core helium burning.
i atures.TheclassprototypesareEC14026-2647(Kilkennyetal.
X Having lost mostof their originalhydrogenenvelopein earlier
1997)andPG1716+426(Greenetal.2003),respectively.Both
r stages of their evolution, the remaining H-rich envelope is too modetypesare thoughtto be drivenby the same κ-mechanism
a thin to sustain hydrogen shell burning. The sdBs populate the
duetoanopacitybumpofironandnickel(Charpinetetal.1997;
extreme horizontal branch (EHB) at effective temperatures of
Fontaineetal.2003;Jeffery&Saio2006).HybridsdBpulsators
20000to40000Kandsurfacegravitieslog(g/cms−2)between
show p-andg-modessimultaneouslyandareofparticularinter-
5.0 and 6.2. Instead of evolving towards the asymptotic giant
estsince thetwo modetypesprobedifferentregionswithinthe
branch,the sdBs arepredictedto followtracksleadingdirectly
star.Inthelogg–T diagram,thehybridsarelocatedatthein-
eff
towards the white dwarf region after leaving the extreme hori-
terfaceofthep-modeandg-modeinstabilityregions.Theknown
zontalbranch.AfractionofthesdBstarsshowspulsations:the
hybridsareHS0702+6043(Schuhetal.2005,2006;Lutzetal.
first pulsating sdB star was discoveredin 1997. Variable subd-
2008) and Balloon090100001 (Oreiroetal. 2005; Baranetal.
warfBstars(sdBVstars)canbedividedintotheclassesofrapid
2005).
p-modepulsators(sdBVr)andslowg-modepulsators(sdBVs),
This paper presents the third member of this group:
withtwoobjectsknownsofartobelongtobothclassessimulta-
HS2201+2610 is a 14.3 B-magnitude star having an effective
neously(hybridpulsators,sdBVrs).
temperature of 29300±500 K and a surface gravity logg of
The p-modepulsatorsshowlowamplitudes(fewtenmmag)
5.40±0.10 in cgs units (Østensenetal. 2001). Based on these
and short periods (few minutes) at higher temperatures. The
spectroscopic parameters, which are very similar to those of
⋆ Based on observations collected at the Centro Astrono´mico HS0702+6043 and Balloon090100001, HS2201+2610 was a
HispanoAlema´n(CAHA)atCalarAlto,operatedjointlybytheMax- natural further target to search for simultaneous g-modes in a
Planck Institut fu¨r Astronomie and the Instituto de Astrof´ısica de known p-modepulsatorafterthe discoveryofthe first hybrids.
Andaluc´ıa(CSIC). Thehighsignal-to-noiseobservationsinitiatedtocheckforhy-
2 R.Lutzetal.:Theplanet-hostingsubdwarfBstarV391Pegasiisahybridpulsator
Fig.1.LightcurvesfromtheSeptember/November2006runsat Fig.2. Lomb Scargle Periodograms (LSPs) of the p-mode
Calar Alto. The relative flux is set to 1.0 for the 27.Sep 2006 regime.ThetoppanelshowsthecompleteCalarAltodata.The
lightcurveandprevious(following)nightsareshiftedupwards bottompaneldisplaystheLSPaftersimultaneoussubtractionof
(downwards)by0.1units. fivefrequencies.Horizontaldottedlinesindicate4σconfidence
levelsandthemarkscorrespondtotheIDsinTable1.
bridbehaviourinHS2201+2610fittedinwellwithourongoing
CCDsets.Thisincludesbias-,flatfield-andbackgroundcorrec-
long-term monitoringin order to search for secular changes in
tionsandfinallyyieldsextractedlightcurvesintheformofrela-
the pulsation periods indicative of slow evolutionary changes
tiveflux(incomparisontofourstablereferencestars)asafunc-
in the star (Silvottietal. 2002), which has recently resulted
tion of geocentric Julian date. Additionally, a barycentric time
in the surprising detection of a planetary companion around
correctionwasapplied.Differentialextinctioneffectsonanight-
HS2201+2610 (better known as V391 Pegasi b, Silvottietal.
by-nightbasiswerecorrectedusingsecond-order-polynomials.
2007).Infact,fromafewofthebetter-qualitydatasetsobtained
InadditiontoourCalarAltodatafrom2006,oneofus(R.S.)
withinthisoverallobservationaleffortuptotheendof2005,we
providedolder data from August/September2003, which were
already suspected the presence of additionalpower in the low-
partoftheWholeEarthTelescopeextendedcoverage23(WET
frequencydomainofHS2201+2610.
Xcov23). The data taken at Loiano Observatory (LOI, 1.5 m
InSection2wepresentthephotometricdataobtainedspecif-
telescopeand3channelphotometer)andObservatoiredeHaute-
ically to investigate the gravity mode frequency range, as well
Provence(OHP,1.9mtelescopeand3channelphotometer)were
as suitable confirmationdata obtainedas part of our long-term
providedasextractedlightcurves(totallengthof28hours)and
monitoring. The data reduction and frequency analysis are de-
weusedthemtocross-checkourCalarAltoresults.
scribed in Section 3, and as a result of our investigation we
will present HS2201+2610 as a new member of the group
of hybrid pulsating sdB stars. We discuss the implications of 3. Results
thisdiscoveryfortheongoingasteroseismiccharacterisationof
Wecarriedoutafrequencyanalysisonbothdatasetswithapro-
HS2201+2610,inthecontextofoureffortstoconstrainthemass
gramcalledsinfit,whichispartofTRIPP.Thisincludesleast-
of its planetary companion,in Section 4. Finally, we present a
squaresnon-linearsinusoidalfits to the light curvesand calcu-
concludingoutlookinSection5.
lationofthecorrespondingperiods,amplitudesandphases.The
amplitudesare givenin millimodulationintensityunits(mmi).
In this context 10 mmi means that the luminosity has changed
2. Observations
by one per cent with respect to the mean brightness level. We
The light curves (see Fig.1) were obtained at Calar Alto used the Scargle algorithm (Scargle 1982) to calculate Lomb-
ObservatoryinSeptemberandNovember2006.Theinstrumen- Scargle-Periodograms(LSPs)intheformofpowerspectralden-
tal setup was chosen to consist of the Calar Alto Faint Object sity (psd) as a function of frequency,together with confidence
Spectrograph(CAFOS)focalreducerattachedtothe2.2mtele- levels, which are based on false alarm probabilities(faps). See
scope.A2k×2kCCDchiprecordedthescienceframesthrough Section 4 in Dreizleretal. (2002) for a more detailed descrip-
aJohnsonBfilterwitha2×2binningandanexposuretimeof tion.In ourcase, we derivedthefapsfrom158000white noise
tensecondswithanaveragecycletimeof25.5seconds.Inorder simulations.Thisyieldsaconfidencelevelof4σ,judgingasig-
tosampletheshort-periodp-modesaswellastodetectverylow- nalabovethisleveltoberealwithaprobabilityof99.99366%.
amplitudeg-modes,onehastofindagoodcompromisewiththe Table1summarizestheresultsofourfrequencyanalysesof
exposuretime.Tensecondsturnedouttobesufficienttoresolve bothdatasets.Wecanclearlyrecoverthethreestrongestmodes
the p-modecyclesaswellasprovideaS/Ngoodenoughtore- foundinanextensiverunpublishedbySilvottietal.(2002),here
solvelow-amplitudesignals.We haveatotalofabout26hours labeledwithf1tof3.Thesefrequenciesareassignedtopressure
ofphotometricdata. drivenmodes.TheoriginalandresidualLSPsofourCalarAlto
ThedatareductionwascarriedoutusingtheTimeResolved datainthep-moderegimearedisplayedinFig.2.Inaddition,we
Imaging Photometry Package (TRIPP, see Schuhetal. 2003), findalong-periodicluminosityvariation(f7,showninFig.3)of
which is designed to handle the aperture photometry of large about54minutes.
R.Lutzetal.:Theplanet-hostingsubdwarfBstarV391Pegasiisahybridpulsator 3
Fig.3.Resultsofourfrequencyanalysisintheg-moderegime.Left:September/November2006CalarAltodata.Thetoppanelisa
LombScarglePeriodogramofthethreebestnightsofthefulllightcurvewherefivefrequencieshavealreadybeensubtracted(f1to
f5,seeTable1).Fittingalong-periodicluminosityvariation(f7)tothissubsetofthedataresultsintheresidualLSPdisplayedinthe
middle.Thewindowfunctionisshowninthebottompanel.Right:August/September2003OHP/LOIdata.Thetoppaneldisplays
theLombScarglePeriodogramofthelightcurveafterpre-whiteningofthreefrequencies(f1tof3,seeTable1).TheresidualLSP
aftersubtractionofthelong-periodvariationf7isshowninthemiddleandthewindowfunctionisillustratedinthebottompanel.
Horizontaldashedlinesindicate4σconfidencelevels.
As mentioned before, we looked at suitable WET Xcov23 group,besidethepreviouslyknownhybridsHS0702+6043and
datawiththefocusontheg-modedomaintoconfirmourdetec- Balloon090100001. Other interpretations for the long-period
tion of a long-periodic luminosity variation found in the Calar variation can be excluded with a high probability with simi-
Alto data (left plots in Fig.3). The periodogramof these addi- lar arguments as for HS0702+6043 (Schuhetal. 2006). The
tional data is shown in the right plots of Fig.3. The OHP/LOI same long-period variation, in frequency as well as amplitude,
results (also in Table 1) clearly confirm the detection of a low is present in data sets three years apart. This rules out sky or
frequencyoscillationinHS2201+2610. transparency variations, as well as rotating star spots. The fast
As can be seen in the middle right plot in Fig.3, there is rotation rate that would be requiredfor the latter interpretation
stillfurtherresidualpowerabove4σintheOHP/LOIdataLSP isfurtherunlikelysincerotationperiodsofsinglesdBstarsare
after subtraction of the long-period variation f7. However, this typically much longer. Rotational splitting (for l > 0 modes)
isnotseenintheCalarAltodata(whichweretakenthreeyears has notyet been detected in HS2201+2610,but the split com-
later) so that further high-quality data are required to test the ponents often have lower amplitudes and might be below our
persistenceoftheseresidualpeaks. detectionlimit. With the light-traveltime effectused in the de-
tectionoftheplanetcandidatearoundHS2201+2610initswide
orbit, we would notbe sensitive to a furtherhypotheticalcom-
4. Discussion
panioninaverycloseorbitwitha54minperiod.Abinaryori-
Weidentifythelong-periodlow-amplitudeluminosityvariation ginofthelong-periodvariationisunlikelyforthefollowingrea-
in HS2201+2610 with a gravity driven mode. The presence sons.A54minorbitalperiodwouldbeattheextremelowlimit
of both types of modes within HS2201+2610would therefore of the observedand theoreticalorbitalperioddistributions(see
define this object to be a member of the hybrid sdB pulsator e.g. Fig.2 in Morales-Ruedaetal. 2006). Additionally, a low-
4 R.Lutzetal.:Theplanet-hostingsubdwarfBstarV391Pegasiisahybridpulsator
Table 1. Results of our frequency analysis of HS2201+2610. We refer to the pulsation frequency identifications obtained by
Silvottietal. (2002) and also list the mode degree (l) identification suggested there in Fig.9. Calar Alto data: We estimate the
errorsinthefrequencytobe0.2µHz(FWHMofthecentralpeakinthewindowfunction)andhavingadetectionlimitof1.1mmi,
whichwas calculatedas fourtimesthe meannoise levelin the residualDFT. We used (f4)and(f5)in the prewhitening,because
low-amplitudesignalsatthesefrequencyrangeswerealsofoundinotherruns(Silvottietal.2002).OHP/LOIdata:Wecalculatea
frequencyresolutionof0.54µHz(FWHMofthecentralpeakinthewindowfunction)andadetectionlimitof0.97mmi(fourtimes
themeannoiselevelintheresidualDFT).FromtheWETXcov23runs,theOHPdatafromAugust22/23andtheLOIdatafrom
August29/31andSeptember3/4havebeenincluded.Meansolution:Thefrequenciesofthe”mean”solutionrefertoBJD2452788,
whichcorrespondstothemiddleofthe7-yearlongdatasetinSilvottietal.(2007).Estimatingtheformalfrequencyresolutionof
the7-year”mean”solutionyields0.0045µHz.
CalarAltoData(2006) OHP/LOIData(2003) Meansolution(2000–2007)
ID type l Period Frequency Amplitude Frequency Amplitude Frequency Amplitude
[s] [µHz] [mmi] [µHz] [mmi] [µHz] [mmi]
f1 p 0 349.5 2861.2 6.6 2860.9 12.3 2860.9387 10.4
f2 p 1 354.2 2823.7 3.3 2824.1 3.7 2824.0965 4.2
f3 p 1 347.1 2880.8 1.5 2880.7 1.5 2880.6842 0.7
f4 p 2 2921.8463 0.6
(≈f4alias) 344.1 2906.3 0.4
(f5) p 2
(f5alias) 366.9 2725.9 0.8
(f6) p (2882.0039 0.5)
f7 g 3255.6 307.2 1.5 306.8 1.5
massmain-sequence(M-dwarf)companionasthesourceofthe itytablesandincluding Ni inadditionto Fe totheopacitypro-
54min signal can be excluded by geometrical considerations file shifts the theoretical blue edge close to the empirical one.
(Roche-Limits vs. separation in Keplerian orbits). The same is Bothaspectsofthisopacityproblemare,incloseanalogy,also
trueforasdB+WDconfigurationina54minorbitdowntovery relevantfortheβCep and[SPB]pulsators(Miglioetal. 2007).
lowWD-masses(below0.2M⊙).Inthecaseofdeformationof In fact, the hybrid objects (both in the main-sequence as well
the sdB by a hypothetical WD companion, causing ellipsoidal asin theextremehorizontalbranchpulsatorsgroups)in partic-
variation, the underlying orbital period would be 108min, but ular represent excellent test cases for the adequateness of the
we wouldthenexpecta signalatleast tentimes strongerdown opacitiesused,andshouldprovidestrongconstraints.Frompre-
tolowinclinations,droppingtotheobservedverylowamplitude viousexperience,it appearsto be clear that radiative levitation
atonlyabout10◦.AWDcompanionasthesourceofthesignalis and self-consistentdiffusionof the Fe/Ni groupelements need
thereforealso veryunlikely.Forless massive andhenceharder to be includedin the EHB models. It will be interesting to see
to detect companions it would be increasingly hard to prevent if”third-generationmodels”incorporatingbothradiativelevita-
masstransferin the system. Binaryorbitalmotionasthe cause tion/diffusionandimprovedopacitieswillfinallydeliveranad-
of the long-periodvariation will immediately and conclusively equatedescriptionofthehybridsdBpulsatorswhilestillrepro-
beruledoutifitsmulti-periodicityisconfirmed. ducingthebehaviourofthe p-modepulsatorsasconsistentlyas
The period and amplitude fall within the typical range for before, and at the same time correctly describing the extent of
g-modesdBpulsations,stronglysuggestingthatthevariationis theempiricalg-modeinstabilityregion.
in fact due to a g-mode. Finally, in comparison to the location
of the other two known hybrid sdB pulsators in the logg–T
eff 5. Concludingoutlook
diagram of sdBV stars (see e.g. Fig.1 in Lutzetal. 2008), the
verysimilar parametersofHS2201+2610againimplythathy- As recently published by Silvottietal. (2007), HS2201+2610
bridbehaviourmayplausiblybeexpected.Allthreeobjectsare hasaplanetarycompanionwhichwasdetectedusingasteroseis-
located at the interface between the empirical p-mode and g- mologicaltechniques.Long-termmonitoringofthestrongest p-
modeinstabilityregions.Hybridpulsatorshavealsobeenshown modepulsationsmadeitpossibletoderivesecularvariationsof
toexistinthepartiallyoverlappingregionsoftheβCep/[SPB] the two main pulsation frequencies, leading to an evolutionary
stars,whichresemblethep/g-modesdBpulsatorsinmanyways timescaleofaround5−8·106years,whichmatchestheoretical
(e.g.Handleretal.2004;Jerzykiewiczetal.2005;Handleretal. evolutionarymodelsofextremehorizontalbranchstars.Periodic
2006;Pigulski&Pojman´ski2007a,b).Hybridbehaviourisalso residualsintheO−Cdiagram(observed−calculated)analysis,
observed in the less closely related δSct / γDor stars (e.g. attributabletolight-traveltimeeffects,revealedthepresenceof
Henry&Fekel2005). an msini = 3.2MJup companion around HS2201+2610 in a
Fromatheoreticalpointofview,modelingp-modesdBpul- 3.2yrorbit.Weareintheprocessofcontinuingourregularlong
satorshasbeenverysuccessful.Fontaineetal.(2006)reporton termphotometricmonitoringofHS2201+2610beyondthecur-
the determination of the basic structural parameters of twelve rentcoverageoftwoorbitcycles.Inordertofurthercharacterise
p-mode sdB pulsators. Regarding the g-mode sdB pulsators thecompanion,especiallytodetermineitsmass,itisnecessary
therearestillissues.The”second-generationmodels”presented toconstraintheorbitalinclinationofthesystemandtoderivea
byCharpinetetal.(1997)andFontaineetal.(2003)divergeby moreaccurateasteroseimicmassofthehoststar.
some 4000 K from the observations, i.e. they fall short of the The mass of the host star is in principle accessible through
empiricalblueedgeof theg-modepulsators.A solutionto this asteroseismology, and Silvottietal. (2002) already presented
problemhasbeensuggestedbyJeffery&Saio(2006,2007):In onepossiblesolution.Thedeterminationofthefundamentalpa-
theirmodels,usingOpacityProject(OP)insteadofOPALopac- rametersof the star hashoweveronlyweaklybeen constrained
R.Lutzetal.:Theplanet-hostingsubdwarfBstarV391Pegasiisahybridpulsator 5
in that work due to the small number of modes detected. Now
that we have added HS2201+2610 to the list of hybrid sdB
pulsators, this finding might provide the additional constraints
necessary for a reliable and accurate asteroseismic characteri-
sation. At this point, we emphasize again the current need to
improve on the model calculations first. For the individual ob-
ject HS2201+2610, it will be a special challenge to addition-
allydriveg-modesinanimprovedversionofoneofthepossible
modelsfoundbySilvottietal.(2002).
Acknowledgements. TheLoiano and OHP data were taken during the Whole
EarthTelescope extended coverage run23;wethanktheWETXcov23team:
R. Janulis, J.-E. Solheim, R. Østensen, T. D. Oswalt, I. Bruni, R. Gualandi,
A. Bonanno, G. Vauclair, M. Reed, C.-W. Chen, E. Leibowitz, M. Paparo,
A.Baran,S.Charpinet,N.Dolez,S.Kawaler,D.Kurtz,P.Moskalik,R.Riddle,
S.Zola.PartoftheobservationsatCalarAltowerecarriedoutinservicemode
byU.ThieleandA.Guijarro. Theobservations atCalarAltoweresupported
throughDeutscheForschungsgemeinschaft(DFG)travelgrantSCHU2249/3-1.
References
Baran,A.,Pigulski,A.,Kozieł,D.,etal.2005,MNRAS,360,737
Charpinet,S.,Fontaine,G.,Brassard,P.,etal.1997,ApJ,483,L123
Dreizler,S.,Schuh,S.,Deetjen,J.L.,Edelmann,H.,&Heber,U.2002,A&A,
386,249
Fontaine,G.,Brassard,P.,Charpinet,S.,etal.2003,ApJ,597,518
Fontaine,G.,Brassard,P.,Charpinet,S.,etal.2006,inESASpecialPublication,
Vol. 624, Proceedings of SOHO 18/GONG 2006/HELAS I, Beyond the
sphericalSun
Green,E.M.,Fontaine,G.,Reed,M.D.,etal.2003,ApJ,583,L31
Handler,G.,Jerzykiewicz,M.,Rodr´ıguez,E.,etal.2006,MNRAS,365,327
Handler,G.,Shobbrook,R.R.,Jerzykiewicz,M.,etal.2004,MNRAS,347,454
Henry,G.W.&Fekel,F.C.2005,AJ,129,2026
Jeffery,C.S.&Saio,H.2006,MNRAS,372,L48
Jeffery,C.S.&Saio,H.2007,MNRAS,378,379
Jerzykiewicz,M.,Handler,G.,Shobbrook,R.R.,etal.2005,MNRAS,360,619
Kilkenny,D.,Koen,C.,O’Donoghue,D.,&Stobie,R.S.1997,MNRAS,285,
640
Lutz, R., Schuh, S., Silvotti, R., et al. 2008, in Astronomical Society of the
PacificConferenceSeries,Vol.392,HotSubdwarfStarsandRelatedObjects,
ed.U.Heber,C.S.Jeffery,&R.Napiwotzki,339–+
Miglio,A.,Montalba´n,J.,&Dupret,M.-A.2007,MNRAS,375,L21
Morales-Rueda,L.,Maxted,P.F.L.,Marsh,T.R.,Kilkenny,D.,&O’Donoghue,
D.2006,BalticAstronomy,15,187
Oreiro,R.,Pe´rezHerna´ndez,F.,Ulla,A.,etal.2005,A&A,438,257
Østensen,R.,Solheim,J.-E.,Heber,U.,etal.2001,A&A,368,175
Pigulski,A.&Pojman´ski,G.2007a,A&A,inpress(ArXive-prints0711.3179)
Pigulski,A.&Pojman´ski,G.2007b,A&A,inpress(ArXive-prints0711.2530)
Scargle,J.D.1982,ApJ,263,835
Schuh,S.,Dreizler,S.,Deetjen,J.L.,&Go¨hler,E.2003,BalticAstronomy,12,
167
Schuh,S.,Huber,J.,Dreizler,S.,etal.2006,A&A,445,L31
Schuh, S., Huber, J., Green, E. M., et al. 2005, in Astronomical Society of
thePacificConferenceSeries,Vol.334,14thEuropeanWorkshoponWhite
Dwarfs,ed.D.Koester&S.Moehler,530
Silvotti,R.,Janulis,R.,Schuh,S.,etal.2002,A&A,389,180
Silvotti,R.,Schuh,S.,Janulis,R.,etal.2007,Nature,449,189