Improved parameters of seven Kepler giant companions characterized with SOPHIE and HARPS-N

2.1 MB·English

by  A. S. Bonomo

Astronomy&Astrophysicsmanuscriptno.Bonomoetal˙2015 (cid:13)c ESO2015
January13,2015
Improved parameters of seven Kepler giant companions
characterized with SOPHIE and HARPS-N
A.S.Bonomo1,A.Sozzetti1,A.Santerne2,M.Deleuil3,J.-M.Almenara3,G.Bruno3,R.F.D´ıaz4,G.He´brard5,6,and
C.Moutou3
1 INAF-OsservatorioAstrofisicodiTorino,viaOsservatorio20,10025PinoTorinese,Italy
2 InstitutodeAstrof´ısicaeCieˆnciasdoEspac¸o,UniversidadedoPorto,CAUP,RuadasEstrelas,PT4150-762Porto,Portugal
3 AixMarseilleUniversite´,CNRS,LAM(Laboratoired’AstrophysiquedeMarseille)UMR7326,13388,Marseille,France
4 ObservatoireAstronomiquedel’Universite´deGene`ve,51chemindesMaillettes,1290Versoix,Switzerland
5 ObservatoiredeHaute-Provence,Universite´Aix-Marseille&CNRS,F-04870St.Michell’Observatoire,France
6 Institutd’AstrophysiquedeParis,UMR7095CNRS,Universite´Pierre&MarieCurie,98bisboulevardArago,75014Paris,France
5
1 Received13November2013/Accepted2January2015
0
2 ABSTRACT

n
Radial-velocityobservationsofKeplercandidatesobtainedwiththeSOPHIEandHARPS-Nspectrographshavepermittedunveiling
a
J thenatureofthefivegiantplanetsKepler-41b,Kepler-43b,Kepler-44b,Kepler-74b,andKepler-75b,themassivecompanionKepler-
39b,andthebrowndwarfKOI-205b.Thesecompanionswerepreviouslycharacterizedwithlong-cadence(LC)Keplerdata.Herewe
2
aimatrefiningtheparametersofthesetransitingsystemsbyi)modellingthepublishedradialvelocities(RV)andKeplershort-cadence
1
(SC)datathatprovideamuchbettersamplingofthetransits,ii)performingnewspectralanalysesoftheSOPHIEandESPaDOnS
] spectra,afterimprovingourprocedureforselectingandco-addingtheSOPHIEspectraoffaintstars(Kp (cid:38) 14),andiii)improving
P stellarrotationperiodshencestellarageestimatesthroughgyrochronology,whenpossible,byusingalltheavailableLCdataupto
quarterQ17.PosteriordistributionsofthesystemparameterswerederivedwithadifferentialevolutionMarkovchainMonteCarlo
E
approach.Ourmainresultsareasfollows:a)Kepler-41bissignificantlylargerandlessdensethanpreviouslyfoundbecausealower
h. orbitalinclinationisfavouredbySCdata.Thisalsoaffectsthedeterminationofthegeometricalbedothatislowerthanpreviously
p derived: Ag < 0.135; b) Kepler-44b is moderately smaller and denser than reported in the discovery paper, as a consequence of
- theslightlyshortertransitdurationfoundwithSCdata;c)goodagreementwasachievedwithpublishedKepler-43,Kepler-75,and
o KOI-205systemparameters,althoughthehoststarsKepler-75andKOI-205werefoundtobeslightlyricherinmetalsandhotter,
r respectively;d)thepreviouslyreportednon-zeroeccentricitiesofKepler-39bandKepler-74bmightbespurious.Iftheirorbitswere
t
s circular,the twocompanions wouldbe smallerand denserthan inthe eccentriccase. Theradiusof Kepler-39bis stilllarger than
a predictedbytheoreticalisochrones.Itsparentstarishotterandricherinmetalsthanpreviouslydetermined.
[
Key words. planetary systems: individual (Kepler-39, Kepler-41, Kepler-43, Kepler-44, Kepler-74, Kepler-75, KOI-205) – stars:
1 fundamentalparameters–techniques:photometric–techniques:spectroscopic–techniques:radialvelocities.
v
3
5
6 1. Introduction 423b in the brown-dwarf desert (Bouchy et al. 2011), which
2 couldbeeitheranextremelymassiveplanetoralow-massbrown
Thanks to unprecedented photometric precision and temporal
0 dwarf; and the brown dwarf KOI-205b (D´ıaz et al. 2013). For
coverage, the Kepler space telescope has discovered over two
. two planets, that is for Kepler-74b and Kepler-75b, additional
1 thousandsmall-sizedplanetarycandidateswithradiiR < 4R
p ⊕ radial-velocity measurements were taken with the HARPS-N
0
(Burke et al. 2014). At the same time, it has provided the ex-
5 spectrograph (Cosentino et al. 2012), which has been installed
oplanet community with more than two hundred Jupiter-sized
1 attheTelescopioNazionaleGalileoatLaPalmaislandinSpring
candidates, thus triggering further studies on the structure, for-
: 2012(seeHe´brardetal.2013).
v mation, and evolution of giant companions as well as on their
Xi atmosphere,iftheopticaland/ornIRoccultationsareobserved. AllthesegiantcompanionswerecharacterizedusingKepler
Since2010wehavebeenfollowingupseveralKepler giant data with long-cadence (LC) temporal sampling of 29.42 min,
r
a candidatesorbitingfaintstarswithKepler magnitudes Kp (cid:38) 14 usuallybecauseshort-cadence(SC)photometricmeasurements,
using the SOPHIE spectrograph at the Observatoire de Haute thatisonepointevery58s,werenotavailableatthemomentof
Provence (France). In addition to determining the fraction of publication. However, the long-cadence sampling presents the
false positives among the Kepler giant candidates (Santerne et strong inconvenience of distorting the transit shape. This effect
al. 2012), this intensive follow-up allowed us to characterize leads to longer transit durations, more V-shaped transits, hence
thegiantplanetsKepler-41b/KOI-196b(Santerneetal.2011a), lower ratios between the semi-major axis and the stellar radius
Kepler-43b/KOI-135b and Kepler-44b/KOI-204b (Bonomo et than the true ones. This yields lower stellar densities from the
al. 2012a), Kepler-74b/KOI-200b and Kepler-75b/KOI-889b thirdKeplerlawandthusmakesbothstellarandplanetaryradii
(He´brardetal.2013);themassivecompanionKepler-39b/KOI- appear larger than they actually are (Kipping 2010). To over-
come this problem, Kipping (2010) suggested to perform the
Sendoffprintrequeststo:A.S.Bonomo transit fitting by oversampling the transit model and then bin-
e-mail:[email protected] ning the model samples to those of the LC before computing
1
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
thechi-squareorthelikelihoodfunction.HisEq.(40)suggestsa entBayesianframeworktoderivetheposteriordensitydistribu-
simplewaytochoosetheresamplingresolution,giventhepho- tionsofthefullsetofsystemparameters.
tometric precision of the light curve. Following this prescrip-
tion,Kipping&Bakos(2011)analysedtheLCdataofKepler-4b
throughKepler-8busingabinnumberof4. 2. Data
WhenmodellingthetransitsoftheKeplerplanetsobserved
2.1. Keplerphotometry
with SOPHIE and HARPS-N, we therefore followed this sug-
gestionbyKipping(2010)andoversampledthetransitmodelby Short-cadencemeasurementsobtainedwiththesimple-aperture-
afactorfive,whichishigherthanrecommendedbyhisEq.(40). photometry pipeline1 (Jenkins et al. 2010) were downloaded
However, in some cases, the analysis of short-cadence data is from the MAST archive2. Eleven quarters of SC data (Q3-
mandatoryespeciallywhentheorbitalperiodisclosetoaninte- Q7 and Q10-Q15) are available for Kepler-43; six quarters
ger multiple of the LC sampling δTlc because this prevents the (Q10-Q15)forKepler-75;fourquarters(Q4-Q7)forKepler-41,
transitfrombeingwellsampledinorbitalphase.Themostevi- Kepler-44, Kepler-74, and KOI-205; and three quarters (Q12-
dentcaseisKepler-43b,whoseorbitalperiodisP=147.99·δTlc Q14)forKepler-39.
(see Fig. 5 in Bonomo et al. 2012a). In addition, the massive The medians of the errors of SC measurements of Kepler-
companion Kepler-39b did not present an optimal coverage of 39, Kepler-41, Kepler-43, Kepler-44, Kepler-74, Kepler-75 and
thetransitingressandegressinthequartersQ1andQ2thatwere KOI-205 are 1.20 · 10−3, 1.27 · 10−3, 8.9 · 10−4, 2.02 · 10−3,
analysedbyBouchyetal.(2011)becauseP=1032.14·δTlc(see 1.24·10−3,3.26·10−3,and1.28·10−3 inunitsofrelativeflux,
Fig.9inBouchyetal.2011). respectively.
Moreover,byperforminganhomogeneousanalysisoftran- Foralltargets,thefluxexcessoriginatingfrombackground
sitphotometryfromspaceandoversamplingtheKeplerLCdata stars that are located within the Kepler photometric mask was
by a factor of ten instead of five, Southworth (2012) derived subtractedseparatelyforeachquarterbyusingtheestimatespro-
smaller stellar and planetary radii for some of the aforemen- videdbytheKeplerteam3.Indeed,thiscontaminationofthetar-
tioned giant companions, although his results agree with ours getfluxdilutesthetransits,makingthemappearshallowerthan
within2σ.Thiswouldindicatethatanoversamplingofthetran- theyare,eventhoughitusuallydoesnotexceed5-7%ofthetotal
sitmodelbyafactoroffivemightnotbeidealinallcases,hence collectedflux.
an independent analysis of SC data is certainly recommended. AlltheSCdatawereusedtomodelthetransitsoftheseven
Nevertheless, some of the slightly different results obtained by giantcompanions.Thesignal-to-noiseratiosofthephase-folded
Southworth (2012) are also due to a better ephemeris and tran- transits are of at least ∼ 450 and, in some cases, higher than
sit signal-to-noise ratio (S/N) because, in most cases, he used 1000. Thanks to these high S/N, we were able to derive stel-
longertemporalseriesthanwedid,uptoquarterQ6. lar and planetary radii with uncertainties (cid:46) 3% almost in all
In this paper, we report the results of our analysis of the cases(seeTables2-8).Atthislevelofprecision,errorsonplan-
Kepler SCdataof Kepler-39,Kepler-41,Kepler-43,Kepler-44, etaryradiiaredominatedbytheuncertaintiesonstellarmodels
Kepler-74, Kepler-75, and KOI-205, along with the previously (Southworth2011,2012)and/orontheorbitaleccentricityeand
published radial velocities (RV). Kepler LC data up to quar- argument of periastron ω. Indeed, the uncertainties on e and ω
ter Q17 were used to refine stellar rotation periods by means fromRVobservationspropagateintothetransitparametera/R
(cid:63)
of both generalised Lomb-Scargle periodograms (Zechmeister andthusintothestellardensityfromthethirdKeplerlaw.Stellar
&Ku¨rster2009)andautocorrelationfunctions,whenanunam- densityisthenusedasaproxyforluminositytodeterminestellar
biguouspeakwithFAP<0.01%couldbeidentified.Thisallows henceplanetaryparameters(e.g.,Sozzettietal.2007)whenno
us to estimate system ages through gyrochronology (Mamajek constraintsfromasteroseismologyareavailable.Thismeansthat
& Hillenbrand 2008), after deriving the B-V index colour and inourparticularcasestheadditionaluseofLCdatapractically
its uncertainty from Eq. (3) in Sekiguchi & Fukugita (2000). doesnotyieldanysignificantimprovementonplanetaryparam-
TheIDsandKepler magnitudesoftheparentstarsarelistedin eterswhileintroducingpossiblecovariancesbetweentransitpa-
Table1.Thisworkaimsatrefiningthecharacterizationofthese rameters (Price & Rogers 2014). For this reason, as mentioned
systems and possibly clarifying the apparently unusual proper- before,weusedLCdataonlytoderivestellarrotationperiods.
tiesofKepler-39bandKepler-41b.Indeed,theformerwasfound
to have a larger radius than predicted by theoretical isochrones
of Baraffe et al. (2003), and Bouchy et al. (2011) were unable 2.2. Radial-velocitydata
tofindanyreasonableexplanationforthisbehaviour.Thelatter
The RV observations considered in this work are those listed
seemed to be a non-inflated planet despite its proximity to the
in the announcement papers because no additional observa-
host star, and to occupy an atypical position in the radius-mass
tions with either SOPHIE or HARPS-N were carried out for
and radius-T diagrams of giant planets (see Figs. 9 and 10 in
eq these targets. The SOPHIE measurements were performed in
Santerneetal.2011a). high-efficiency mode with a resolution of ∼ 40000, and expo-
Moreover,weperformednewspectralanalysesoftheplanet-
sure times not exceeding 1 hr. The observations of KOI-200
hosting stars after improving our procedure of selecting, treat-
and KOI-889 carried out with HARPS-N were taken in high-
ing, and co-adding the SOPHIE spectra. A revision of the at-
resolutionmode(theonlyavailableone)witharesolvingpower
mospheric parameters may have a significant impact on stellar, of∼ 110000andexposuresof45minandshorterthan25min,
henceplanetary,parameters.
respectively.BothSOPHIEandHARPS-Nmeasurementswere
We recognize the merit of an approach to revisiting stellar
orplanetaryparametersoftransitingsystemsthatencompasses 1 http://keplergo.arc.nasa.gov/PyKEprimerLCs.shtmlp
muchlargersamples(e.g.,Torresetal.2012;Southworth2012) 2 http://archive.stsci.edu/kepler/data search/search.php
thantheonepresentedhere.Ourworkdiffersinthatitperformsa 3 http://archive.stsci.edu/kepler/kepler fov/search.php; for Season 2
self-consistentre-analysistakingintoaccountbothphotometric dataofKOI-205,thevalueofcrowdingfactorasderivedbyD´ıazetal.
andspectroscopicmeasurementsandconstraintswithinacoher- (2013)wasused(seeD´ıazetal.2013).
2
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Table 1. IDs, coordinates, and magnitudes of the planet-hosting stars Kepler-39, Kepler-41, Kepler-43, Kepler-44, Kepler-74,
Kepler-75,andKOI-205
Keplername Kepler-39 Kepler-41 Kepler-43 Kepler-44
Object KOI-423 KOI-196 KOI-135 KOI-204
KeplerID 9478990 9410930 9818381 9305831
2MASSID 19475046+4602034 19380317+4558539 19005780+4640057 20002456+4545437
KeplermagnitudeK 14.33 14.46 13.96 14.68
p
Keplername Kepler-74 Kepler-75 -
Object KOI-200 KOI-889 KOI-205
KeplerID 6046540 757450 7046804
2MASSID 19322220+4121198 19243302+3634385 19415919+4232163
KeplermagnitudeK 14.41 15.26 14.52
p
performed in obj AB observing mode with fibre A centred on masterspectrumwithS/Nof65inthecontinuumat600nmper
thetargetandfibreBonthesky.Whenneeded,theobservations resolutionelement.Thisco-addedspectrumisanalysedherefor
werecorrectedformoonlightpollution,asdescribedinBonomo thefirsttime.
etal.(2010).
3. Dataanalysis
2.3. Spectra
3.1. Spectralanalysis
Theatmosphericparametersofthehoststars,alongwiththestel-
lar density derived from the transit fitting, are of fundamental To determine the effective temperature (Teff), surface gravity
importancefordeterminingstellar,henceplanetary,parameters (logg),andironabundance[Fe/H],theco-addedSOPHIEspec-
(Sozzettietal.2007).
traobtainedwithourimprovedselectionandthoseacquiredwith
While radial-velocity measurements can accommodate low
ESPaDOnSwerereanalysedfollowingthesameproceduresde-
S/Nspectra,spectralanalysisismorechallenging.Indeed,some
scribed in detail by Sozzetti et al. (2004, 2006) and references
diffuselightintheSOPHIEspectrographmightaffectthespec- therein. A set of ∼ 60 relatively weak lines of Fe I and 10 of
tra at very low S/N acquired in high-efficiency mode. For this
Fe II were selected, and EWs were measured using the TAME
reason,werecentlyimprovedourprocedureoftreatingandse-
software(Kang&Lee2012).Metalabundanceswerederivedas-
lectingtheSOPHIEspectratodeterminestellaratmosphericpa-
suminglocalthermodynamicequilibrium(LTE),usingthe2010
rameters.Inparticular,spectrawithanS/Nlowerthan14were
versionofthespectralsynthesiscodeMOOG(Sneden1973),a
excluded from the co-addition. Those acquired in the presence
gridofKuruczATLASplane-parallelmodelstellaratmospheres
oftheMoonwerecorrectedforthemoonlightcontaminationby
(Kurucz 1993), and imposing excitation and ionisation equilib-
subtractingthebackgroundasestimatedfromfibreB.Asisusu-
rium.Uncertaintiesintheparameterswereestimatedfollowing
allydone,theindividualexposureswerethensetintherestframe
theprescriptionsofNeuforge&Magain(1997)andGonzalez&
andco-addedinasinglemasterspectrum.
Vanture(1998)androundedto25KinTeffand0.05dexinlogg.
InthecaseofKepler-39,theco-addedspectrumobtainedthis
The derived atmospheric parameters are compared in
way shows deeper lines than simply co-adding all the SOPHIE
Sect.4.1withtheliteraturevalues,whichwereobtainedwithi)
spectra, as was previously done by Bouchy et al. (2011). This
theiterativespectralsynthesispackageVWA(Brunttetal.2010)
hasasignificantimpactonthederivationoftheatmosphericpa-
for Kepler-39, Kepler-41, Kepler-74, Kepler-75, and KOI-205,
rameters(seeSect.4.1).
andii)the2002versionoftheMOOGcodewiththemethodol-
The S/N of the SOPHIE master spectra at 600 nm and per
ogydescribedinBonomoetal.(2012a)andMortieretal.(2013)
element of resolution ranges between 100 and 170 for Kepler-
forKepler-43andKepler-44.
39,Kepler-41,Kepler-43,Kepler-44,andKepler-74.Itisequal
to72and65forKOI-205andKepler-75,respectively.
Two host stars, namely KOI-205 and Kepler-39, were also 3.2. CombinedanalysisofKeplerandradial-velocitydata
observed with ESPaDOnS at the 3.6-m Canada-France-Hawaii
Toderivesystemparameters,aBayesiananalysisofKepler SC
Telescope in Mauna Kea as part of a programme dedicated to
the characterization of Kepler planet-hosting stars4. The objec- photometry and radial-velocity measurements was performed,
using a differential evolution Markov chain Monte Carlo (DE-
tiveisindeedtocarryoutabetterspectralanalysisoftheparent
stars with a spectrograph that offers both a higher spectral res- MCMC)method(TerBraak2006;Eastmanetal.2013).Forthis
olution (R (cid:39) 65 000) and an extended spectral coverage (370 purpose,theepochsoftheSOPHIEandHARPS-Nobservations
- 1000 nm). These two targets were observed in ’object+sky’ wereconvertedfromBJDUTCintoBJDTDB(Eastmanetal.2010),
mode. The ESPaDOnS spectrum of KOI-205 with a S/N ∼ 90 whichisthetimestampofKeplerdata.
waspreviouslyusedbyD´ıazetal.(2013)todeterminethehost The transit fitting was performed using the model of
starandbrowndwarfparameters.Kepler-39wasobservedwith Gime´nez (2006, 2009). For this purpose, each transit was nor-
ESPaDOnS on September 28, 2012 and December 1, 2012, in malised by locally fitting a slope to the light-curve intervals of
a series of five exposures of ∼ 40 min. The individual spec- twice the transit duration before its ingress and after its egress.
tra as reduced by the CFHT Upena/Libre-Esprit pipeline were ForKepler-39,alinearfunctionoftimedidnotprovideasatis-
co-added after they were set in the rest frame and resulted in a factorynormalisationbecauseoftheshort-termstellarvariabil-
ity(seeSect.4.2),henceaquadraticfunctionoftimewasused.
4 programme12BF24,PI:M.Deleuil CorrelatednoisewasestimatedfollowingPontetal.(2006)and
3
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Bonomoetal.(2012b),andaddedinquadraturetotheformaler- of system parameters towards a low but non-zero eccentricity
rorbars.However,itturnedouttobeverylow,generallylower e ∼ 0.14 even when including in the global fit the secondary
than one fifth of the formal photometric errors, as expected for eclipse that indicates that e cosω is consistent with zero (e.g.,
high-precisionspace-basedphotometry(e.g.,Aigrainetal.2009, Santerneetal.2011a;Quintanaetal.2013).Thiswouldreduce
Bonomoetal.2012b). theorbitalconfigurationsofapossibleeccentricorbittoω=90
Our global model has 12 free parameters when i) an ec- or 270 deg. However, the expected circularization timescale is
centric model was considered and ii) RV were taken with only shorterthan100Myrbyassumingamodifiedtidalqualityfac-
one instrument (SOPHIE): the transit epoch T ; the orbital pe- torofQ(cid:48) = 107 fortheplanetbecauseofitsshortorbitalperiod
0 p
riodP;thesystemicradialvelocityV;theradial-velocitysemi- P = 1.85days(hencesmallsemi-majoraxisa = 0.031au)and
√ √ r
amplitude K; e cosω and e sinω (e.g., Anderson et al. relatively low mass M ∼ 0.6 M for a Jupiter-sized planet.
p Jup
2011);anadditiveRVjitterterm s toaccountforpossiblejitter Indeed,therearenoplanetswithmasscomparabletoKepler-41
j
intheRVmeasurementsregardlessofitsorigin,suchasinstru- andP<3dwithasignificanteccentricity.Forthesereasons,we
mental effects, stellar activity, additional companions, etc.; the adoptedacircularmodelforKepler-41.
transit duration from first to fourth contact T ; the ratio of the For Kepler-74, our DE-MCMC chains did not converge to-
14
planetary-to-stellarradiiR /R ;theinclinationibetweentheor- wardsauniquesolutionwhenwevariedtheeccentricity,which
p ∗
bitalplaneandtheplaneofthesky;andthetwolimb-darkening resultedinverylowacceptancerates.Thiswasalsonoticedby
coefficients (LDC) q = (u + u )2 and q = 0.5u /(u + u ) He´brardetal.(2013),whoimposedaGaussianpriorontheor-
1 a b 2 a a b
(Kipping2013),whereu andu arethecoefficientsofthelimb- bital eccentricity, solely based on a RV fit, in their combined
a b
darkeningquadraticlaw5.Twoadditionalparameters,thatisthe analysis of Kepler and RV data. However, this prior inevitably
HARPS-N systemic radial velocity and jitter term, were fitted affectstheposteriordistributionsoforbitandtransitparameters.
when HARPS-N data were obtained as well (Kepler-74 and Instead,wepreferredtouseacircularmodelgiventhatcurrent
Kepler-75). Uniform priors were set on all parameters, in par- RVdataevidentlydonotallowustoconstraintheorbitaleccen-
ticularwithboundsof[0,1]forq andq (Kipping2013),lower tricitywell.
1 2
limitofzeroforK and s,andupperboundof1fore(thelower The Kepler-39 system parameters were obtained by using
j √
limitof0simplycomesfromthechoiceoffitting ecosωand both eccentric and circular models because the 2σ significance
√
esinω). of the eccentricity e = 0.112 ± 0.057 cannot exclude that the
The posterior distributions of our free parameters were de- orbitisperfectlycircular(Lucy&Sweeney1971).
termined by means of our DE-MCMC code by maximising a
Gaussian likelihood (see, e.g., Eq. 9 and 10 in Gregory 2005).
4. Results
For each target, a number of chains equal to twice the number
offreeparameterswererunsimultaneouslyafterbeingstartedat
4.1. Stellaratmosphericparameters
differentpositionsintheparameterspacebutreasonablycloseto
thesystemvaluesknownintheliteratureand/orobtainedwithan The Teff and [Fe/H] of Kepler-41, Kepler-43, Kepler-44, and
independent fit that was previously performed with AMOEBA Kepler-74,whichweredeterminedwiththeproceduredescribed
(Nelder & Mead 1965). The jumps for a current chain in the inSect.3.1,areconsistentwithin1σwiththeliteraturevalues.
parameter space were determined from the other chains, ac- ThesurfacegravitiesofKepler-43andKepler-44werefoundto
cordingtotheprescriptionsgivenbyTerBraak(2006),andthe belogg=4.4±0.10(Kepler-43)andlogg=4.1±0.10(Kepler-
Metropolis-Hastings algorithm was used to accept or reject a 44), which are lower than previously found by Bonomo et al.
proposedstepforeachchain. (2012a), that is logg = 4.64±0.103 and 4.59±0.14, respec-
Fortheconvergenceofthechains,werequiredtheGelman- tively.Thesenewlydeterminedvaluesaremoreconsistentwith
Rubin statistics, Rˆ, to be lower than 1.03 for all the parameters thephotometricallyderivedlogg(seeTables4and5).
(Gelmanetal.2003).Stepsbelongingtotheburn-inphasewere The star KOI-205 was found to be slightly hotter than re-
identified following Knutson et al. (2009) and were excluded. ported by D´ıaz et al. (2013), with Teff = 5400±75 K, metal-
The medians of the posterior distributions of the fitted and de- licity[Fe/H]=0.18±0.12,andlogg = 4.7±0.10,bothwiththe
rived parameters and their 34.13% intervals are reported as the ESPaDOnS and the co-added SOPHIE spectrum (see Table 8).
final values and their 1σ error bars. When the distributions of The slightly hotter temperature has only a minor, almost negli-
theeccentricityandtheRVjitterwerefoundtopeakatzero,we gible,influenceonsystemparameters.
providedonlythe1σupperlimitsestimatedasthe68.27%con- Themoststrikingdifferenceswithpreviouslydeterminedat-
fidenceintervalsstartingfromzero.Indeed,themediansofthese mosphericparameterswerefoundforKepler-39andKepler-75.
distributionsmightyieldmisleadingnon-zerovalues. The former is significantly richer in metals and slightly hotter
Finally, the Yonsei-Yale evolutionary tracks (Demarque et than reported by Bouchy et al. (2011): Teff = 6350 ± 100 K,
al. 2004) for the effective temperature, metallicity, and density [Fe/H]=0.10±0.14,andlogg=4.4±0.15,tobecomparedwith
ofthehoststarswereusedtodeterminethestellar,hencecom- thepreviousestimatesTeff =6260±140,[Fe/H]=−0.29±0.10,
panion,parameters(Sozzettietal.2007;Torresetal.2012). andlogg=4.1±0.2.Veryconsistentvalueswerederivedfrom
For Kepler-41 and Kepler-74 only a circular model was theanalysisoftheESPaDOnSspectrum.Thisdifferencecomes
adopted for the following reasons: the RV curve of Kepler-41 from the better selection and treatment of the SOPHIE spectra
isslightlyasymmetricwithrespecttoasinusoid,verylikelybe- beforeco-addingtheindividualspectra(seeSect.2.3).Itisnot
cause of residual effects from the correction of moonlight con- duetothedifferentspectralanalysistechniquethatwasusedby
tamination and/or low S/N (from 13 to 20) spectra. These ar- Bouchy et al. (2011), that is, the VWA package (Bruntt et al.
tificial asymmetries in the RV curve tend to bias the solution 2010). Indeed, when run on the new co-added SOPHIE spec-
trum,VWAprovidedresultsthatarealmostidenticaltothoseob-
in5tenIs(itµy)/aIt(1th)e=c1en−treuao(1f −theµ)d−iscuba(n1d−µµ)=2,wcohserγe,Iγ(1b)eiisngthethsepaencigfilec taanidnelodgwgit=hM4.4O±O0G.3:.TTehffe=se6n3e6w0v±a1lu0e0sKha,v[Feea/nHim]=pa0c.t1o2n±st0e.l1la4r,
betweenthesurfacenormalandthelineofsight. massandage(seeTable2).
4
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Kepler-75isalsofoundtobericherinmetalsthanpreviously
1.4
thought.ItsatmosphericparametersdeterminedwithMOOGare
OGLE-TR-123 b
TWH(seee´ffhebir=lTaear5tdbh2leee0t0T7a±)e.lff1.H0i(s2o0w0cKo1en3,v[s)eF,irse,tth/eaeHntttd]hwie=ffsitee0hr.tie3ennm0c1±epσ0ei.rn1wa2tmiu,trheaetnstahd,lletlihocveigatsylgyuise=steda4meb.r6oipv±uaet0rda.21mb5σy-. Rjup]111...231 WAXSOP--31 8b b KELT-1 b CoRoT-15 b OGLE-TR-122 b KOI-686 b
eotfetrhseohfiKgheeprlemr-e7t5aldliocintyo.tsignificantlychangeasaconsequence adius [1.0 CoRoT-3 b WASP-30 b LRc0K1_OEI-11_8497 b80 b
R
0.9
0.8 KOI-205 b LHC6343 C
4.2. Systemparameters KOI-415 b
0.7
4.2.1. Kepler-39 20 40 60 80 100
Mass [Mjup]
Orbital and transit parameters obtained with our Bayesian DE-
MCMCanalysisintheeccentriccaseagreewellwiththosethat Fig.1. Radius-mass diagram including transiting companions
werepreviously determinedby Bouchyet al.(2011). However, more massive than 10 M . The dashed curves are the Baraffe
Jup
wefoundalowersignificanceofapproximately2σfortheor- et al. (2003) isochrones for 0.5, 1, 5, and 10 Gyr (from top to
bitaleccentricity,thatise = 0.112±0.057,whileBouchyetal. bottom). Both circular (filled red circle) and eccentric (empty
(2011) reported e = 0.122 ± 0.023. Our larger uncertainty on redcircle)solutionsareshownforKepler-39b.Bluelabelsindi-
theeccentricityindicatesthatitmightbespurious,accordingto catethebrowndwarfsthatwerecharacterizedthankstoSOPHIE
Lucy & Sweeney (1971). The Bayes factor of ∼ 3 between the spectroscopicmeasurements(seealsoMoutouetal.2013;D´ıaz
eccentricandthecircularmodel,whichwascomputedbyusing etal.2014).
the truncated posterior mixture method (Tuomi & Jones 2012),
doesnotprovidestrongenoughevidenceeitherforaneccentric
orbit,accordingtoKass&Raftery(1995). phase-folded transit and RV curve and the best solutions ob-
AsdiscussedinSect.4.1,thestellaratmosphericparameters tainedwithbotheccentricandcircularmodels.
were refined thanks to both a better treatment of the SOPHIE
spectra and a new ESPaDOnS spectrum. Specifically, a moder-
atelyhottertemperatureTeff =6350±100Kandasignificantly 4.2.2. Kepler-41
higher metallicity of 0.10 ± 0.14 were found (see Sect. 4.1). The new system parameters determined with SC data signifi-
For these new atmospheric parameters and the transit density, cantlydifferfromthoseobtainedbySanterneetal.(2011a).The
theYonsei-Yaleevolutionarytracksindicateamoremassiveand mostimportantdifferenceinthefittedparametersisfoundforthe
younger star: M(cid:63) = 1.29+−00..0067 M(cid:12), R(cid:63) = 1.40 ± 0.10 R(cid:12), and orbitalinclinationthat,inturn,affectsthedeterminationofa/R(cid:63)
ageof2.1+0.8 Gyr.Thecorrespondingmass,radius,anddensity and the stellar density. Indeed, while Santerne et al. (2011a)
ofKepler-−309.9bare M = 20.1+1.3 M ,R = 1.24+0.09 R ,and found i = 88.3±0.7 deg, our new solution points to a consid-
ρ = 13.0+3.0 g cm−3b.These−c1o.2mpaJnupionbparamete−r0s.1a0reJcuopnsis- erably higher impact parameter with i = 82.51±0.09 deg (see
b −2.2 Table3).
tentwiththosereportedbyBouchyetal.(2011),exceptforthe
By analysing only LC data, Southworth (2012) found two
stellarage,whichisabouthalfthevaluefoundbytheseauthors
solutionsfortheorbitalinclination,onewithi∼90degandthe
(seeTable2).Interestingly,thisupdatedvalueoftheageagrees
otheronewithi∼80−82deg.Heoptedforthefirstbecause“the
wellwiththegyrochronologyestimate(Mamajek&Hillenbrand
2008), that is t = 0.7+0.9 Gyr, for the stellar rotation period i ∼ 80−82 deg family occurs mainly for LD-fixed light-curve
P =4.50±0.g0y7r dinfer−r0e.3dfromtheKeplerLClightcurve. solutions,andresultsinweirdphysicalproperties”.However,by
rot
letting the LDC vary, our DE-MCMC run on SC data always
Figure 1 shows the position of Kepler-39b (empty red cir-
convergedtowardthelattervalueofi.Thisoccurredevenwhen
cle) in the radius-mass diagram of transiting companions with
the chains were all started at values close to i ∼ 90 deg. This
masses between 10 and 100 M for the eccentric case. The
Jup ambivalenceshowsthat,insomecases,fittingtheLDCwithLC
dashed lines from top to bottom show the Baraffe et al. (2003)
datamayleadtolocalminimathatdonotrepresentthetrueso-
isochronesfor0.5,1,5,and10Gyr.AsalreadynotedbyBouchy
lution.
etal.(2011),thecompanionradiusgivenbytheeccentricsolu-
Long-cadence measurements were also used by Quintana
tion would be incompatible with theoretical isochrones with a
et al. (2013) to validate this planet by analysing the phase
probability > 95% (2 σ). However, the solution these authors
curve. Curiously, these authors found an orbital inclination of
proposedtoexplainthelargeradiusofKepler-39b,thatisanin- 85.4+0.4 deg, which is in between the other two solutions.
creasedopacityinthecompanionatmosphere,whichpreviously −0.5
However,wepointoutthatQuintanaetal.(2013)weremorein-
seemedunlikelyforthelowstellarmetallicity,nowmightapply
terestedinanalysingthephasecurveanddidnotexplicitlymen-
for Kepler-39b. Indeed, our new estimate of [Fe/H] is signifi-
tionwhichoversamplingtheyadoptedtomodeltheLCtransits.
cantlyhigher. Our solution with low orbital inclination i = 82.5 deg is
As previously discussed, the eccentricity of Kepler-39b physicallyacceptablebecausethelowestpossibleinclinationfor
might be spurious according to the Lucy-Sweeney criterion. In the transit of Kepler-41b is ∼ 78 deg. The corresponding stel-
thecircularcase,stellarandcompanionradiiareslightlysmaller lar density indicates a star that is larger and older than previ-
than in the eccentric case, which implies a higher bulk density ouslyfoundbySanterneetal.(2011a)forthesameatmospheric
of 17.4+1.6 g cm−3 (see Table 2). The system age would be parameters. The derived logg = 4.278 ± 0.005 is now more
−1.4
1.0+0.9 Gyr. The position of Kepler-39b in the circular case is consistent with the spectroscopic value logg = 4.2±0.10 (see
−0.7
shown in Fig. 1 with a red filled circle. Figure 2 displays the Table3).Alargerstellarradiusimpliesalargerplanetaryradius
5
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Fig.2. Leftpanel.Top:phase-foldedtransitofKepler-39balongwiththetransitmodelsforthecircular(red
solid line) and eccentric (red dotted line) orbits. The two models are indistinguishable. Middle: residuals
ofthecircularorbit.Bottom:residualsoftheeccentricorbit.Rightpanel.Top:phase-foldedradial-velocity
curveofKepler-39and,superimposed,theKeplerianmodelsforthecircular(redsolidline)andeccentric
(reddottedline)orbits.Middle:O-Cofthecircularorbit.Bottom:O-Coftheeccentricorbit.
R = 1.29±0.02R ,whichnowmakesthisplanetmoresimi-
p Jup
lartotheotherclose-inhotJupiters.Indeed,fromtheplanetary
parameters that were previously determined by Santerne et al. 0.14
(2011a)andSouthworth(2012),thisobjectappearedquiterare,
meaning:non-inflateddespiteitsvicinitytotheparentstar(see 0.12
Figs.9and10inSanterneetal.2011a).
Figure3displaysthephase-foldedtransitandradial-velocity do0.10
e
measurementsalongwiththebestsolution. alb0.08
c
onaL/aRspttbhuattnboetcolemaests,etqhueallotwoe5r0i.n2c6li±na0t.i3o6naanlsdo,ihnastuarnn,iamffpeacctst ometri0.06
thedeterminationofthegeometricalbedo(cf.,e.g.,Eq.(14)in Ge
Roweetal.2006).Thelatterwasfoundtobeconsiderablyhigher 0.04
thanthemajorityofhotJupiterswithmeasuredopticalocculta-
tionsbySanterneetal.(2011a),thatisA =0.30±0.07.Onthe 0.02
g
contrary,ournewsolutionwithSCdataindicatesasignificantly
lower geometric albedo of Ag < 0.135 from the most recent 0.00 1600 1800 2000 2200 2400 2600
valueofthesecondary-eclipsedepth(Angerhausenetal.2014), Day-sideequilibriumtemperature[K]
in agreement with theoretical expectations for atmospheres of
Fig.4.GeometricalbedoofKepler-41basafunctionofitsday-
hotJupiterswithoutscatteringclouds(e.g.,Burrowsetal.2008).
sideequilibriumtemperature.T .Theverticaldashedlinesindi-
Figure4showsthealbedovaluesandtheir1σuncertaintiesasa eq
catethevaluesofT assumingperfectheatredistribution(left)
functionoftheplanetday-sideequilibriumtemperatureT .The eq
eq and no redistribution in the atmosphere (right). The grey band
verticaldashedlinesindicatethevaluesofT assumingperfect
eq shows the albedo values allowed by the 1σ uncertainty on the
heat redistribution (left) or no redistribution in the atmosphere
occultationdepthdeterminedbySanterneetal.(2011a).
(right).
4.2.3. Kepler-43
4.2.4. Kepler-44
System parameters derived from our DE-MCMC analysis are
listed in Table 4, and Fig. 5 shows the phase-folded SC transit New system parameters slightly differ from those derived by
and radial-velocity curvealong with the best-fit model. System Bonomo et al. (2012a) (see Table 5). Our analysis with SC
parametersgenerallyagreewithin1σwiththosedeterminedby data reveals a transit duration that is 2σ shorter than found by
Bonomoetal.(2012a),inspiteoftheverypoorsamplingofthe Bonomoetal.(2012a).Thisimpliesaslightlylargera/R(cid:63),hence
phase-folded LC transit (see their Fig. 5). The transit duration a moderately higher stellar density from the Kepler third law.
derivedwithSCdataisslightlyshorter(at1.3σ)thanfoundby In consequence, stellar evolutionary tracks point to a slightly
Bonomo et al. (2012a) but with negligible influence on system smallerstarthanpreviouslyreportedbyBonomoetal.(2012a),
parameters.Theplaneteccentricityisconsistentwithzerowithin with radius and mass of 1.35 ± 0.08 R(cid:12) and 1.12 ± 0.08 M(cid:12),
2σ. respectively. Therefore, also the planet turns out to be smaller
FromthestellarrotationperiodP =12.95±0.25dderived (fromRp/R(cid:63))anddenser:Rp = 1.09±0.07RJup, Mp = 1.00±
withalltheLCdata,thegyrochronorlootgyagetgyr = 1.7+−00..64 Gyr 0.10MJup,andρp =0.93+−00..1197gcm−3(seeTable5).
agreeswellwiththatestimatedfromstellarevolutionarytracks Figure 6 shows the phase-folded transit and radial-velocity
2.3+0.8Gyr,asalreadynotedbyBonomoetal.(2012a). curveand,superimposed,thetransitandtheKeplerianmodels.
−0.7
6
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Fig.3. Left panel: phase-folded transit light curve of Kepler-41b along with the transit model (red solid
line).Rightpanel:phase-foldedradial-velocitycurveofKepler-41and,superimposed,theKeplerianmodel
(redsolidline).
Fig.5. Left panel: phase-folded transit light curve of Kepler-43b along with the transit model (red solid
line).Rightpanel:phase-foldedradial-velocitycurveofKepler-43and,superimposed,theKeplerianmodel
(redsolidline).
4.2.5. Kepler-74 Thetransitandradialvelocitydataalongwiththebestsolu-
tionsareshowninFig.8.
Thecircularsolutionwedecidedtoadoptdiffersfromtheeccen-
tricsystemparametersbyalmostthreestandarddeviations.This
is mainly because the transit density used to determine stellar 4.2.7. KOI-205
parametersisafunctionoftheeccentricity.Foranulleccentric-
AsforKepler-75,theSCorbitalandphysicalparametersagree
ity, the planet becomes smaller and denser, with R = 0.97 ±
p very well with those determined by D´ıaz et al. (2013) (see
0.04R ,M =0.64±0.10M ,andρ =0.86±0.18gcm−3.
Jup p Jup p Table 8). The best fit of the SC transit and radial-velocity ob-
The best fit of the transit and radial velocities is displayed in
servationsisshowninFig.9.
Fig.7.
5. Discussionandconclusions
4.2.6. Kepler-75
The analysis of Kepler SC photometry, RV data, SOPHIE and
The agreement between the system parameters determined by ESPaDONsspectraofsevengiantcompanionshaspermittedus
He´brardetal.(2013)andourDE-MCMCsolutionobtainedwith to refine their orbital and physical parameters. In three cases,
SC data (see Table 7) is excellent, even adopting the slightly namely Kepler-43, Kepler-75, and KOI-205, they agree with
different atmospheric parameters derived with MOOG: Teff = publishedparameterswithin1−1.3σ.
5200±100Kand[Fe/H]=0.30±0.12. ForKepler-44, forwhichonlytwo quartersofLCdata (Q1
ThestellarrotationperiodinferredfromthewholeLClight andQ2)wereanalysedforthediscoveryannouncement,thenew
curve is P = 19.18 ± 0.15 d, in agreement with He´brard transitparametersdeterminedwithourDE-MCMCapproachin-
rot
et al. (2013). The system age estimated from gyrochronology dicate a transit duration shorter by 2 σ, hence a slightly larger
(Mamajek&Hillenbrand2008)is1.6±0.3Gyr,whichisslightly a/R and higher stellar density. This, in turn, implies that the
(cid:63)
lower than the value provided by stellar models, although con- hoststaranditsplanetarycompanionaresmallerthanpreviously
sistentwiththelatterat1.7σ. found.
7
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Fig.6. Left panel: phase-folded transit light curve of Kepler-44b along with the transit model (red solid
line).Rightpanel:phase-foldedradial-velocitycurveofKepler-44and,superimposed,theKeplerianmodel
(redsolidline).
Fig.7. Leftpanel:phase-foldedtransitlightcurveofKepler-74balongwiththetransitmodelforacircular
orbitandtheirresiduals.Rightpanel:phase-foldedradial-velocitycurveofKepler-74.Reddiamondsand
bluecirclesshowSOPHIEandHARPS-Nradialvelocities,respectively.Theblacksolidlinedisplaysthe
Kepleriancircularmodel.
A separate discussion must be made for Kepler-39b and KOI-205andsignificantlyhighermetallicitiesforKepler-39and
Kepler-74bbecausewehaverevisedthesignificanceoftheiror- Kepler-75.
bital eccentricities. That of Kepler-39b is detected with a 2 σ Amongourseventargets,themoststrikingdivergencewith
significanceleveland,accordingtotheLucy-Sweeneycriterion, alreadypublishedparameterswasfoundforKepler-41.Indeed,
itmightbespurious.SlightasymmetriesintheRVcurvecaused SC data point to a considerably lower inclination, higher im-
by residual effects from the correction of moonlight contami- pact parameter, and lower a/R than found by Santerne et al.
(cid:63)
nation (Santerne et al. 2011b) and/or CCD charge transfer in- (2011a) and Southworth (2012). In consequence, both the host
efficiency(Bouchyetal.2009)mightcausefalseeccentricities. starandtheplanethavelargerradiithanpreviouslyderived.This
Indeed,theseeffectsbecomestrongwhenobservingfaintstars. newsolutionalsohasanimpactontheestimationoftheplane-
More radial-velocity observations without moonlight contami- tarygeometricalbedothatissignificantlylowerthanpreviously
nation are required to determine whether Kepler-39b has a low estimated: A < 0.135 . Both the larger radius and the lower
g
eccentricity.Kepler-74wouldalsobenefitfromadditionalhigh- albedo make this planet resemble the majority of hot Jupiters.
accuracyandhigh-precisionRVsbecausethechainsofourDE- Conversely,theanalysisofKepler LCdatahaderroneouslyre-
MCMC combined analysis did not converge towards a unique sultedinpeculiarcharacteristicsforthisplanet.Thisemphasizes
solutionwhenincludingtheeccentricityasafreeparameter.For that, in some cases, SC data are necessary to derive accurate
this reason, we decided to fit only a circular model to Kepler systemparameters,inadditiontoreducingcovariancesbetween
and RV data. For circular orbits, both Kepler-39b and Kepler- transitparameters(Price&Rogers2014)andpermittingtocom-
74bwouldbesmalleranddenserthanpreviouslyfound.Inany pute precise transit timing variations. This will also be consid-
case, the radius of Kepler-39b is still larger than predicted by eredinthelightofthefutureTESSandPLATOspacemissions.
theoreticalisochrones(seeFig.1),ashighlightedbyBouchyet
al.(2011).
Acknowledgements. A.S.BonomoandR.F.D´ıazacknowledgefundingfrom
the European Union Seventh Framework Programme (FP7/2007-2013) under
Ournewspectralanalysesoftheavailableco-addedspectra
Grantagreementnumber313014(ETAEARTH).A.Santerneissupportedby
revealedslightlyhottereffectivetemperaturesofKepler-39and theEuropeanUnionunderaMarieCurieIntra-EuropeanFellowshipforCareer
8
Bonomoetal.2014:ImprovedparametersofsevenKeplergiantcompanions
Fig.8. Left panel: phase-folded transit light curve of Kepler-75b along with the transit model (red solid
line). Right panel: phase-folded radial-velocity curve of Kepler-75. Red diamonds and blue circles show
SOPHIEandHARPS-Nradialvelocities,respectively.TheblacksolidlinedisplaystheKeplerianmodel.
Fig.9. Leftpanel:phase-foldedtransitlightcurveofKOI-205alongwiththetransitmodel(redsolidline).
Right panel: phase-folded radial-velocity curve of KOI-205 and, superimposed, the Keplerian model (red
solidline).
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