Astron. Nachr./AN333,No.10,1088–1091(2012)/DOI10.1002/asna.201211832 Properties of extrasolar planets and their host stars – a case study of HAT-P-7 V.VanEylen1,2,(cid:63),H.Kjeldsen1,J.Christensen-Dalsgaard1,andC.Aerts2 1 StellarAstrophysicsCentre,DepartmentofPhysicsandAstronomy,AarhusUniversity,NyMunkegade120, DK-8000AarhusC,Denmark 2 InstituutvoorSterrenkunde,KatholiekeUniversiteitLeuven,Celestijnenlaan200B,B-3001Heverlee,Belgium Received15August2012,accepted15August2012 3 Publishedonline3December2012 1 0 2 Keywords stars:individual(HAT-P-7)–stars:oscillations–planetarysystems–stars:fundamentalparameters n DatafromtheKeplersatellite(Q0-Q11)areusedtostudyHAT-P-7.Thesatellite’sdataareextremelyvaluableforastero- a seismicstudiesofstarsandforobservingplanetarytransits;inthisworkwedoboth.Anasteroseismicstudyofthehoststar J improvestheaccuracyofthestellarparametersderivedbyChristensen-Dalsgaardetal.(2010),whofollowedlargelythe 8 sameprocedurebutbasedtheanalysisononlyonemonthofKeplerdata.Thestellarinformationiscombinedwithtransit observations,phasevariationsandoccultationstoderiveplanetaryparameters.Inparticular,weconfirmthepresenceof ] ellipsoidalvariationsasdiscoveredbyWelshetal.(2010),butrevisetheirmagnitude,andwerevisetheoccultationdepth R (Boruckietal.2009),whichleadstodifferentplanetarytemperatureestimates.Allotherstellarandplanetaryparameters S arenowmoreaccuratelydetermined. . h (cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim p - o 1 Introduction et al. (2010), based on early Kepler data (Q0-Q1). After r t the initial discovery of its exoplanet HAT-P-7b (Pa´l et al. s a TheKeplermissionwaslaunchedonMarch6,2009.Itwas 2008),phasevariationsandplanetaryoccultationsweredis- [ designed explicitly to be able to detect earth-size planets, coveredinKepler’sQ0data(Boruckietal.2009),andcon- 1 includingthoseinthehabitablezone.Thedetectionmethod sequently the planetary temperature and atmosphere were v forKeplertoachievethisgoalismeasuringplanetarytran- studied(Christiansenetal.2010;Spiegel&Burrows2010). 2 sits to a high level of photometric precision. To improve Additionalellipsoidalvariationswerelaterdiscoveredinthe 7 the chances of detection, a large number of stars have to light curve (Welsh et al. 2010) and the system is currently 4 bemonitoredforalongperiodoftime,preferablycontinu- the only planetary case where this effect has been found. 1 . ously.ItwasquicklyrealisedthatKeplerwouldalsoprovide HAT-P-7 has a surprising inclination angle: a study of the 1 extremelyvaluabledatatostudystellarpulsations.Datafor Rossiter-McLaughlineffectinradialvelocitydatahasfound 0 this purpose are obtained from a subset of the about 500 ittoberetrogradeorpolar(Winnetal.2009).Theseauthors 3 1 stars that are sampled every 58.8 seconds (short cadence), also suggest the presence of a third body. A study of tran- : outofamuchlargersetofabout150000starsobservedat sit timings based on EPOXI data found no evidence of an v i arateof29.4minutes(Boruckietal.2008). additionalplanet(Ballardetal.2011). X Thesatelliteorbitsinanearth-trailingheliocentricorbit Here, we make a preliminary anaysis of the system r (ETHO),witha55◦Sunavoidanceangle,andcontinuously basedonalmostthreeyearsofKeplerdata.Wederivestellar a observesapatchoftheskycentredontheCygnus-Lyrare- pulsation frequencies and perform an asteroseismic mod- gion.Thedataareorganisedintoquarters;aftereachquarter elling to derive the properties of the host star. The plane- thephotometerisrolled90◦tokeepthesolararrayspointed tary system is then studied making use of these newly de- attheSun.Thiscausesa42hourdatagap(Haasetal.2010). terminedstellarproperties. This work uses Q0-Q11 data of HAT-P-7, which has been continuouslyobservedinKepler’sshortcadencemode. 2 Stellarproperties HAT-P-7(KIC10666592,visualmagnitude10.46,spec- traltypeF8)hasbeenidentifiedasaplanethostbyground- Stellar pulsations cause temperature variations, which lead based observations prior to the start of the Kepler mission to flux variations. The frequencies are observed from the (Pa´l et al. 2008). It is one of the most extensively studied power spectrum. Different models are then compared with star-planet systems known to date. A study of the stellar the observed frequencies and the best fit leads to the stel- pulsations has been carried out by Christensen-Dalsgaard lar properties. The procedure followed here resembles the (cid:63) Correspondingauthor:e-mail:[email protected] asteroseismic analysis of HAT-P-7 based on only the first monthofKeplerdata(Christensen-Dalsgaardetal.2010). (cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim Astron.Nachr./AN(2012) 1089 Fig.2 Ane´chellediagramshowingtheobservedfrequen- cies(red)andthebestmodel(blue). µHz (compared to a previous accuracy of 1.4 µHz). They areillustratedinFigure2. Fig.1 Topfigure:oversampled(red)andsmoothedpower spectrum(black),showingregularspacingsgovernedbythe 2.2 Modelling asymptotic equation (eq. 1). Bottom figure (zoom): mode identificationforthreeobservedfrequencies.Analgorithm Tocalculateevolutionmodelsandadiabaticoscillationfre- determinesthemaximainthesmoothedspectrum,therele- quencies,weusetheAarhuscodes(Christensen-Dalsgaard vant maxima (vertical lines) are selected manually making 2008a,b). Evolution tracks were calculated for a grid of use of the asymptotic equation. Sometimes, an average of models with mass range 1.33-1.70 M(cid:12) and metallicity twomaximaisused(e.g.l=2modeinthisfigure). 0.015-0.035.Theconvectivecorewasmodelledwithover- shootinunitsofthepressurescaleheightofαov = 0,0.1 and0.2.Basedontheobservedlargeseparationanestimate 2.1 Observationsanddataanalysis ofthedensityisobtained(Whiteetal.2011),whichisused to select relevant time steps in the stellar evolution tracks, The raw Kepler data are detrended and normalised, and forwhichfrequenciesarethencalculated. transit-like features are removed using a specifically de- Thecalculatedfrequenciesarecomparedwiththeobser- signed median filter. The filtered photometry is then used vations,aftercorrectingfornear-surfaceeffectsthatarenot tocalculateapowerspectrum.Aspectrumwithasampling modelledproperly.Theempiricalcorrectionlawisgivenby rateof0.005µHzisused,whichmeansanoversamplingof (Kjeldsenetal.2008): about three times. A median filter with a period of 1 µHz is used to smooth the power spectrum, to remove the fine (cid:20)ν (n)(cid:21)b ν (n)−ν (n)=a obs , (2) structure of the spectrum, caused by the finite lifetime of obs best ν 0 themodes. whereν isareferencefrequencyandaandbareparameters The location of individual frequencies is governed by 0 to be determined. In addition, we set ν (n) = rν (n), theasymptoticequation(Tassoul1980): best ref where r should be close to one as the reference model (cid:18) 1 (cid:19) should be close to the initial best model. In practice, we ν ≈∆ν n+ l+(cid:15) −δν . (1) n,l 2 0l setb = 4.90(thesolarvalue)andwefindthebestfitforr anda(foreachmodelindividually).Wecanthencalculate In this equation, νn,l is the frequency with radial order n thereferencemodel,forcomparisonwiththeobservedfre- andangulardegreel(neglectingrotationalsplittingsothere quencies. The best model is then picked by comparing the is no dependence on m), and ∆ν and δν0l the large and observedfrequencieswiththecorrectedmodelfrequencies. small separations while (cid:15) is an offset coming from second We use a χ2 minimisation to determine which model fits order and near-surface effects. This theoretical relation is best: used to identify the individual modes, from the smoothed power spectrum. The entire procedure is illustrated in Fig- χ2 = 1 (cid:88)(cid:16)ν(obs)−ν(mod)(cid:17)2. (3) (N −1)σ2 nl nl ure1. ν nl Wehavedetermined14(l = 0),13(l = 1)and16(l = The frequencies of the best model are shown together 2)frequencies,whichconstituteatotaloftenmorefrequen- with the observational frequencies in the e´chelle diagram cies than the initial asteroseismic analysis (Christensen- inFigure2.Withtheexceptionofanumberoffrequencies Dalsgaard et al. 2010). The frequencies were determined (between1200and1400µHz)forl=1,thefrequenciesare with an average standard error estimated to be σ = 0.75 modelledverywell,resultinginχ2 =3.65.Gaussiannoise ν www.an-journal.org (cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim 1090 V.VanEylenetal.:Propertiesofextrasolarplanetsandtheirhoststars Table 1 Parameters obtained for star (HAT-P-7) and its the bottom of the transit depends on the limb darkening, planet(HAT-P-7b). modelledbyaquadraticintensityprofile(Winn2010): HAT-P-7 I(X,Y)∝1−u (1−µ)−u (1−µ)2, (4) 1 2 Mass(M(cid:12)) 1.361±0.021 √ Z 0.01904±0.0015 with µ = 1−X2−Y2 and (X,Y) the coordinates on 0 [Fe/H] 0.13 aunitcircle.Thecoefficientsuk areconstantsdefiningthe Age(Gyr) 2.19±0.12 precise shape of the limb-darkening law. We have simply Radius(R(cid:12)) 1.904±0.010 used them as fitting parameters. The modelled transit is Temperature(K) 6259±32 shown in Figure 3. We have also made a new estimate of Density(g/cm−3) 0.2781±0.0017 theplanetarymass,usingtheradialvelocityvaluesderived Luminosity(L ) 4.996±0.098 (cid:12) byPa´letal.(2008). logg(cgs) 4.98±0.13 Ellips.var.d(ppm) 59±1 3.3 Phasevariations HAT-P-7b Orbitalperiod(d) 2.20473506(11) Theplanetarysystemistidallylocked,whichcausesthestar Orbitalinclinationi(◦) 86.68±0.14 toalways‘see’thesamesideoftheplanet,whileadistant M (M ) 1.741±0.028 p J observerseestheplanetarydaysideandnightsideatdiffer- R (R ) 1.431±0.011 p J T (K) 2470±10 ent times. However, for HAT-P-7 the situation is slightly day T (K) 1772±10 complicated. The close orbit of the planet has induced a night A 0.193±0.002 tidal distortion on the star: rather than being oblate due to g rotation, it has its longest axis towards the planet and the shortestaxisperpendiculartotheorbitalplane.Thiscauses ellipsoidal variations (which peak at phases near 0.25 and was added to the observational frequencies to create 1000 0.75),whichshouldbeaddedtothephasevariations(Pfahl differentfrequencysets.Foreach,thebestmodeliscalcu- et al. 2008; Welsh et al. 2010). HAT-P-7 is the only cur- latedandthestellarparametersarecalculated.Theaverage rentlyknownsystemwithellipsoidalvariationscausedbya andstandarddeviationoftheseparametersarepresentedin planet.Wemodelthefluxthroughoutoneorbitalphaseas Table1. (cid:18)R (cid:19)2 sin(α)+(π−α)cos(α) 3 Planetaryproperties f(Φ,i) = A p (5) g a π cos(2α) 3.1 Period −d π Thetimeofeachindividualtransitismeasuredandusedto with the orbital phase Φ ∈ [0,1] taken as 0 at maximum determine the planetary period. Assuming a perfectly Ke- radial velocity of the star, so that the phase angle α is de- plerian orbit, we fit a straight line through all transit times fined as cosα = −sinisin2πΦ. The first part of f(Φ,i) (taking gaps into account; whenever a transit is measured istheLambertlawforasphere(Charbonneauetal.1999), incompletelyitisignored).Duetothelargeamountofmea- where A is the planetary albedo and a is the semi-major g sured transits (286), the period is determined very accu- axis. A non-zero value for d corresponds to the ellipsoidal rately. An O-C plot has been calculated, which compares variations.WerefertoTable1forvaluesandtoFigure3for the observed and the calculated transit times to look for a thebestfit. gravitational influence from additional bodies in the sys- tem.Nosinuisoidalpatternwasdetected,andvariationsare 3.4 Occultation at the level of the observational error level for individual transit times (≈ 0.00015 days). After the period has been When the planet moves behind the star, an occultation oc- calculated,thetimeseriesisfolded(calculatedmodulothe curs. The depth δ (λ) gives information about the plan- flux period). etary dayside temperature. By combining the information with the phase variations, we can also obtain the night- side temperature. We approximate both star and planet as 3.2 Transitshape ablackbodyanduse From the folded time series, the transit is modelled. The (cid:18)R (cid:19)2 B (T ) transit duration determines the impact parameter, which is δflux(λ)= Rp Bλ(Tp), (6) directly related to the orbital inclination. The transit depth ∗ λ (cid:63) determinestherelativeplanetaryradius,whichcanbecom- where B (T) is the Planck function (Winn 2010), which λ bined with the stellar radius (derived in the previous sec- we integrate over the Kepler bandpass. The exact occulta- tion),toobtaintheabsoluteplanetaryradius.Theshapeof tion depth is calculated by simply comparing the averages (cid:13)c 2012WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim www.an-journal.org Astron.Nachr./AN(2012) 1091 We have not been able to model a few frequencies prop- erly (see Figure 2), a problem that did not present itself in the earlier analysis by Christensen-Dalsgaard et al. (2010) becauseofthefewerfrequenciesobserved,andalowerob- servational accuracy. Ellipsoidal variations were found by Welsh et al. (2010), and we confirm that the phase curve cannot be fit without including this effect. Welsh et al. (2010) find a variation of 37 ppm (no errors quoted, based on Kepler Q0-Q1 data), which is considerably lower than our value of 59 ± 1ppm. All planetary values have im- provedaccuracy.Mostareingeneralagreementwithearlier work. Our planetary temperatures are significantly lower than all earlier temperature determinations (Borucki et al. 2009;Christiansenetal.2010;Pa´letal.2008;Welshetal. 2010).Theyallusedanoccultationdepthof130±11ppm (Boruckietal.2009),which isalmosttwiceashighasthe valuederivedinthiswork;theanalysiswasdonebasedonly onKeplerQ0data,andthemodellingdidnotincludeellip- soidal variations as they were not yet discovered in HAT- P-7 at the time. On the other hand, the temperature in this work assumes a blackbody, which is an oversimplification andalsocausesthetemperatureerrortobeunderestimated. Welshetal.(2010)andChristiansenetal.(2010)usedmore realisticatmospheremodels,anditshouldbeinterestingto seehowtheyareaffectedbytherevisedoccultationdepth. This work shows the excellent quality Kepler can now deliver, both for studying stellar pulsations and planetary Fig.3 Aftertheplanetaryperiodisdetermined,theobser- transits. Asteroseismology is likely to take up an increas- vations(blue)arefolded.Thisallowsforadetailedstudyof inglyimportantroleinstudyinghoststarsofexoplanets. the planetary transit (top figure), phase variations (caused by planetary day-nightside and ellipsoidal variations, mid- Acknowledgements. Theresearchleadingtotheseresultshasre- dle figure), and planetary occultation (bottom). The black ceivedfundingfromtheEuropeanResearchCouncilundertheEu- lineshowsadatafit,thecoloreddatapointsareusedincal- ropeanCommunity’sSeventhFrameworkProgramme(FP7/2007– culatingtheoccultationdepth. 2013)/ERC grant agreements n◦227224 (PROSPERITY) and n◦267864 (ASTERISK). Funding for the Stellar Astrophysics CentreisprovidedbyTheDanishNationalResearchFoundation. of data points inside and just outside the occultation, as WearegratefultotheentireKeplerteamfortheeffortsleadingto shown in Figure 3. We find an occultation depth of 71.85 thishighlysuccessfulmission. ±0.23partspermillion.Weassumethatallplanetaryflux comes from radiation (albedo zero), so the quoted temper- References aturevalueisanupperlimit.Theindicatedaccuracyofthe quotedtemperaturesshouldbeseenastheinternalerrorof Ballard,S.,Christiansen,J.L.,Charbonneau,D.,etal.2011,ApJ, usingablack-bodyspectrumtodescribethespectrumofthe 732,41 exoplanet.Sincetheblack-bodyfluxintheKeplerbandpass Borucki,W.,Koch,D.,Basri,G.,etal.2008,inIAUSymposium, forexoplanettemperatureswillchangealotevenforasmall Vol. 249, IAU Symposium, ed. Y.-S. Sun, S. Ferraz-Mello, & changeintemperatureonecanestimatetheblack-bodytem- J.-L.Zhou,17–24 Borucki,W.J.,Koch,D.,Jenkins,J.,etal.2009,Science,325,709 peratureprecisely.Wefindtheoccultationtobe4.90±0.25 Charbonneau, D., Noyes, R. W., Korzennik, S. G., et al. 1999, ppmdeeperthanthevaluejustoutsidetransit. ApJ,522,L145 Christensen-Dalsgaard,J.2008a,Ap&SS,316,13 4 Discussion —.2008b,Ap&SS,316,113 Christensen-Dalsgaard,J.,Kjeldsen,H.,Brown,T.M.,etal.2010, ApJ,713,L164 The asteroseismic analysis of the host star has followed Christiansen,J.L.,Ballard,S.,Charbonneau,D.,etal.2010,ApJ, largely the same methods as applied by Christensen- 710,97 Dalsgaard et al. (2010) for Kepler’s Q0 and Q1 data. With Haas,M.R.,Batalha,N.M.,Bryson,S.T.,etal.2010,ApJ,713, elevenquartersnowavailable,allparametersaredetermined L115 to higher accuracy. The agreement is fairly good, but we Kjeldsen, H., Bedding, T. R., & Christensen-Dalsgaard, J. 2008, have derived a slightly lower mass, radius and metallicity. 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