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  • 1. Accepted for publication in ApJL Preprint typeset using L TEX style emulateapj v. 8/13/10 A THE HIGH ALBEDO OF THE HOT JUPITER KEPLER-7 B Brice-Olivier Demory , Sara Seager1 , Nikku Madhusudhan2 , Hans Kjeldsen3 , Jørgen Christensen-Dalsgaard3 , 1 Micha¨l Gillon4 , Jason F. Rowe5 , William F. Welsh6 , Elisabeth R. Adams7 , Andrea Dupree7 , Don McCarthy8 , e Craig Kulesa8 , William J. Borucki5 , David G. Koch5 and the Kepler Science Team Accepted for publication in ApJL ABSTRACTarXiv:1105.5143v1 [astro-ph.EP] 25 May 2011 Hot Jupiters are expected to be dark from both observations (albedo upper limits) and theory (alkali metals and/or TiO and VO absorption). However, only a handful of hot Jupiters have been observed with high enough photometric precision at visible wavelengths to investigate these expectations. The NASA Kepler mission provides a means to widen the sample and to assess the extent to which hot Jupiter albedos are low. We present a global analysis of Kepler-7 b based on Q0-Q4 data, published radial velocities, and asteroseismology constraints. We measure an occultation depth in the Kepler bandpass of 44±5 ppm. If directly related to the albedo, this translates to a Kepler geometric albedo of 0.32±0.03, the most precise value measured so far for an exoplanet. We also characterize the planetary orbital phase lightcurve with an amplitude of 42±4 ppm. Using atmospheric models, we find it unlikely that the high albedo is due to a dominant thermal component and propose two solutions to explain the observed planetary flux. Firstly, we interpret the Kepler-7 b albedo as resulting from an excess reflection over what can be explained solely by Rayleigh scattering, along with a nominal thermal component. This excess reflection might indicate the presence of a cloud or haze layer in the atmosphere, motivating new modeling and observational efforts. Alternatively, the albedo can be explained by Rayleigh scattering alone if Na and K are depleted in the atmosphere by a factor of 10-100 below solar abundances. Subject headings: planetary systems - stars: individual (Kepler-7, KIC 5780885, 2MASS 19141956+4105233) - techniques: photometric 1. INTRODUCTION visible, two orders of magnitude less than mid-infrared More than 30 hot Jupiters benefit from observations signatures. of their emitted radiation from near to mid-infrared, To date, eleven planets have an upper limit constraint where the measurement of their thermal emission is on their geometric albedo : τ Boo b (Charbonneau et al. the most favorable. Spitzer made a significant con- 1999; Leigh et al. 2003a; Rodler et al. 2010), υAnd b tribution by producing a flurry of results allowing us (Collier Cameron et al. 2002), HD75289A b (Leigh et al. to derive general properties of hot-Jupiter atmospheres 2003b; Rodler et al. 2008), HD209458b (Rowe et al. (Deming & Seager 2009). Those planets are strongly 2008), CoRoT-1b (Alonso et al. 2009; Snellen et al. irradiated by their host stars and their equilibrium 2009), CoRoT-2b (Alonso et al. 2010; Snellen et al. temperatures were early estimated to be above 1000K 2010), HAT-P-7b (Christiansen et al. 2010; Welsh et al. (Seager & Sasselov 2000). Those observations confirm 2010), Kepler-5b (Kipping & Bakos 2011; Desert et al. that hot Jupiters efficiently reprocess the incident stellar 2011), Kepler-6b (Kipping & Bakos 2011; Desert et al. flux into thermal reemission, exhibiting low flux at vis- 2011), Kepler-7b (Kipping & Bakos 2011) and ible wavelengths (Marley et al. 1999; Seager et al. 2000; HD189733b (Berdyugina et al. 2011). Sudarsky et al. 2003). Eight of them corroborate early theoretical predic- Characterization of transiting hot-Jupiter reflected tions: with Ag < 0.3 (3σ upper limit) hot Jupiters light suffers from the scarcity of observations. The plan- are dark in the visible. However Collier Cameron et al. etary to stellar flux ratio is of the order of 10−5 in the (2002) determined Ag < 0.42 (3σ) from spectroscopy in the 380-650nm range for υAnd b, Kipping & Bakos 1 Department of Earth, Atmospheric and Planetary Sciences, (2011) reported Ag = 0.38 ± 0.129 for Kepler-7 b and Massachusetts Institute of Technology, 77 Massachusetts Ave., Berdyugina et al. (2011) determined a V -band albedo of Cambridge, MA 02139, USA. demory@mit.edu 2 Department of Astrophysical Sciences, Princeton University, Ag = 0.28 ± 0.16 for HD189733b from polarimetry, sug- gesting dominance of reflected light over thermal emis- Princeton, New Jersey 08544, USA. 3 Department of Physics and Astronomy, Aarhus University, sion. DK-8000 Aarhus C, Denmark. Solar system giant planets have geometric albedos of 4 Institut d’Astrophysique et de G´ophysique, Universit´ de e e 0.32 (Uranus) to 0.50 (Jupiter) in a bandpass similar to Li`ge, All´e du 6 Aoˆt, 17, Bat. B5C, Li`ge 1, Belgium. e e u e Kepler ’s (Karkoschka 1994). Those objects harbor bright 5 NASA Ames Research Center, Moffett Field, CA 94035, USA. cloud decks made of ammonia and water ice that are 6 Astronomy Department, San Diego State University, San highly reflective at visible wavelengths. In contrast to the Diego, CA 92182, USA. solar system giant planets, atmosphere models show that 7 Smithsonian Astrophysical Observatory, 60 Garden St., Cambridge, MA 02138, USA 8 Steward Observatory, University of Arizona, 933 N. Cherry 9 Determined in the Kepler bandpass, which has a >5% response Ave, Tucson, AZ 85721, USA between 423 and 897 nm (Koch et al. 2010)
  • 2. 2the presence of alkali metals in hot-Jupiter atmospheres Spectrograph) observations and applied to both transit(Na and K) as well as TiO and VO (at the hotter range) and occultation photometry.causes significant absorption at visible wavelengths. The excellent sampling of the transit lightcurve moti- We report in this letter the characterization of the hot vated us to fit for the limb-darkening (LD) coefficients.Jupiter Kepler-7 b (Latham et al. 2010), based on Kepler For this purpose, we assumed a quadratic law and usedQ0-Q4 data. We present the photometry and data anal- c1 = 2u1 + u2 and c2 = u1 − 2u2 as jump parameters,ysis in Sect. 2, while corresponding results are shown in where u1 and u2 are the quadratic coefficients.Sect. 3. Discussion and atmospheric analysis are finally The MCMC has the following set of jump parameters:presented in Sect. 4. the planet/star flux ratio, the impact parameter b, the 2. OBSERVATIONS AND DATA ANALYSIS transit duration from first to fourth contact, the time of √ minimum light, the orbital period, K = K 1 − e2 P 1/3 , 2.1. Kepler photometry where K is the radial-velocity semi-amplitude, the occul- Kepler-7 b belongs to the first set of new planets pub- tation depth, the√ LD combinations c1 and c2 and the two √lished by the Kepler science team in early 2010. Kepler- two parameters e cos ω and e sin ω. A uniform prior7 b is a 4.8-day period hot Jupiter orbiting a V =13.04 distribution is assumed for all jump parameters.sub-giant G star with M = 1.347 ± 0.07M and R =1.843 ± 0.07R (Latham et al. 2010). Like all objects lo- 2.2.1. Model and systematicscated in the Kepler field, Kepler-7 benefits from nearly The transit and occultation photometry are modeledcontinuous photometric monitoring since mid-2009. with the Mandel & Agol (2002) model, multiplied by a We base our analysis on the Q0-Q4 quarters, which second order polynomial accounting for stellar and in-represent nearly one year of observations. Data recorded strumental variability. Baseline model coefficients areduring each quarter are differentiated in short- and long- determined for each lightcurve with the SVD methodcadence timeseries, that are binnings per 58.84876s and (Press et al. 1992) at each step of the MCMC. Correlated29.4244min respectively of the same CCD readouts. Five noise was accounted for following Winn et al. (2008);long-cadence (Jenkins et al. 2010) and six short cadence Gillon et al. (2010), to ensure reliable error bars on the(Gilliland et al. 2010) datasets are used as part of this fitted parameters. For this purpose, we compute a scal-study, representing 272,719 photometric datapoints and ing factor based on the standard deviation of the binned311.68 effective days of observations, out of which 175.37 residuals for each lightcurve with different time bins. Thedays have also been recorded in short cadence. We used error bars are then multiplied by this scaling factor. Wethe raw photometry for our purpose. obtained a mean scaling factor of 1.04 for all photometry, Kepler-7 is a photometrically quiet star: apart from the denoting a negligible contribution from correlated noise.4.88-day period transit signals, no evidence of significant The mean global photometric RMS per 30-min bin is 96stellar variability is apparent in the data. parts per million (ppm). 2.2. Data analysis 2.2.2. Asteroseismology For the purpose of this global analysis, we usedthe implementation of the Markov Chain Monte-Carlo The data series for Kepler-7 contains 9 months of(MCMC) algorithm presented in Gillon et al. (2009, data at a cadence of 1 minute. The power spectrum2010). MCMC is a Bayesian inference method based on shows a clear excess of power near 1.05mHz. Thestochastic simulations that samples the posterior prob- asteroseismic analysis of the data was performed us-ability distributions of adjusted parameters for a given ing the pipeline developed at the Kepler Asteroseis-model. Our MCMC implementation uses the Metropolis- mic Science Operations Center as described in detail byHastings algorithm to perform this sampling. Our nom- Christensen-Dalsgaard et al. (2008, 2010); Huber et al.inal model is based on a star and a transiting planet on (2009); Gilliland et al. (2011). Using the matched fil-a Keplerian orbit about their center of mass. ter approach we determine a value for the large separa- Our global analysis was performed using 199 transit tion of 56µHz. Locating the asymptotic frequency struc-and occultation lightcurves in total, out of which 70 ture in the folded power allows a robust identification ofwere acquired in short cadence mode. We discarded 13 13 individual p-mode frequencies and an estimate of thelightcurves because of discontinuities due to spacecraft scatter on those frequencies (0.9µHz). The frequenciesroll, change of focus, pointing offsets or safe mode events. resulting from this analysis were fitted to stellar modelsInput data also include the 9 radial velocity points in the same manner as in Christensen-Dalsgaard et al.obtained from NOT/FIES (FIber-fed Echelle Spectro- (2010), using also the effective temperature and metal-graph) that were published in Latham et al. (2010). licity ([Fe/H]) determined by Latham et al. (2010). The As the focus of this study is on using the transits models did not include diffusion and settling. Modelsand occultations to refine the system parameters, for the were computed without overshoot from the convectivemodel fitting we use only the photometry near the eclipse core, as well as with overshoot of 0.1Hp and 0.2Hp , whereevents. Windows of width 0.6 days (12.3% of the or- Hp is the pressure scale height at the edge of the convec-bit) surrounding eclipses were used to measure the local tive core. The observed frequencies and effective temper-out-of-transit baseline, while minimizing the computa- ature were fitted to the models in a least-squares sense,tion time. A dilution of 2.7±0.5% was determined from resulting in a weighted average of the stellar properties.MMT/ARIES10 (ARizona Infrared imager and Echelle Interestingly, only models with overshoot provided ac- ceptable fits to the frequencies within the observed range 10 MMT is a joint facility of the Smithsonian Institution and of the effective temperature.University of Arizona. We used the resulting stellar density (see Table 1) as
  • 3. 3a Bayesian prior in the MCMC and the corresponding to 0.9 µm. Albedo values reported in this paper forstellar mass to derive the system’s physical parameters. Kepler-7 b are averaged over this spectral domain. For the highly irradiated exoplanets, a significant part of the 2.2.3. Phase curve thermal emission leaks into the red end of this bandpass, About 312 days of Kepler-7 observations are covered making the occultation depth larger. With a 4.9-d longin Q0-Q4 data. This motivated us to search for the orbit, Kepler-7 b would not be expected to be one of theplanetary phase signature. We first removed the tran- hottest giant planets found to date. However, its hostsits and fitted the long and short cadence data to re- star with a Teff =5933K, 1.4 M and 2.0 R , is aboutmove temporal linear trends. Stellar and instrumental in- 4.5 times more luminous than the Sun. These compen-duced modulation on the photometry was then removed sating factors make it necessary to estimate the relativeby pre-whitening the raw data using Period04 software contributions of thermal emission and reflected light to(Lenz & Breger 2005). This step allowed us to filter out the occultation depth.all frequencies below the orbital frequency and those that The possible relative contributions of thermal emis-are not connected with the planetary orbit period. sion and reflected light to the observed flux in the Ke- 3. RESULTS pler bandpass are shown in Fig. 3. The thermal emis- sion is represented by an effective brightness tempera- We present Kepler-7 b’s system parameters in Table ture (TB ), and the reflected light by the geometric albedo1. Each value is the median of the marginal posterior (Ag ). Also shown are the dayside equilibrium tempera-distribution obtained for the relevant parameter. Error tures corresponding to atmosphere with efficient versusbars are the corresponding 68.3% probability interval. inefficient energy redistribution (dotted lines). The de-Figure 1 shows the phase-folded transit photometry of generacy between TB and Ag is evident. The observedKepler-7 b. occultation depth allows for geometric albedos as high Our results confirm the very low density of Kepler- as 0.35 for TB = 1500K in the Kepler bandpass. On7 b. The external constraint from asteroseismology mod- the other hand, allowing for a zero geometric albedo re-eling causes the planet radius to significantly increase as quires an extremely high TB of 2500-2600K, which is ∼compared to the discovery paper (Latham et al. 2010). 400K higher than the maximum equilibrium tempera-Our MCMC analysis yields a planetary radius of RP = ture. Completely breaking the degeneracy between Ag1.61 ± 0.02RJup and a mass of MP = 0.44 ± 0.04MJup , and TB requires additional observations in the visiblewhich gives a surprisingly low density of ρP = 0.14±0.01 and near-infrared. However, tentative constraints can beg cm−3 . Interestingly, Kepler-7b’s properties are close placed on the various sources of opacity and scatteringto WASP-17b’s (Anderson et al. 2010), the least dense using a physical model atmosphere.transiting planet discovered so far with ρP = 0.12±0.06 g The thermal and reflection spectra of the planetarycm−3 . Both planets are of similar mass and orbit evolved atmosphere depend on the various atomic and molec-stars. ular opacities, sources of scattering, and the temper- We find a marginal orbital eccentricity of e = 0.001 ± ature structure, all of which constitute a large num-0.001. ber of free parameters under-constrained by the single We determine an occultation depth of 44±5 ppm. The data point available. Nevertheless, the precise mea-corresponding phase-folded lightcurve is shown on bot- surement allows us to constrain regions of the param-tom panel of Fig. 2. eter space, given plausible assumptions about energy Finally we find an orbital phase curve of 42±4 ppm am- balance and atmospheric chemistry. We use the exo-plitude that is consistent with the occultation depth and planet atmospheric modeling and retrieval technique ofphased with Kepler-7 b’s transits and occultations. We Madhusudhan & Seager (2009). The model computesmodel the phase curve assuming a Lambert law phase- line-by-line radiative transfer in a plane-parallel atmo-dependent flux-ratio (Sobolev 1975) : sphere, with the assumption of hydrostatic equilibrium Rp 2 sin(α) + (π − α) cos(α) and global energy balance, and parametrized chemical φ(α) = Ag composition and temperature structure. A key aspect a π of the model is the flexibility to explore a wide range ofwhere α is the orbital phase, Ag is the geometric albedo, molecular abundances and pressure-temperature (P -T )Rp is the planetary radius and a is the orbital semi- profiles, without any assumptions of chemical or radia-major axis. A value of Ag = 0.31 ± 0.03 is deduced tive equilibrium. We consider all the major sources offrom the phase curve using Rp and a values from Ta- opacity in the visible and near-infrared: H2 -H2 collision-ble 1. Although a perfectly reflecting Lambertian sphere induced absorption, Na, K, Rayleigh scattering, TiO andhas Ag = 2 , the Lambert law can represent a scatterer VO (with a condensation curve), H2 O, CO, CH4 and 3which takes on a lower Ag value for an atmosphere with CO2 (Christiansen et al. 2010; Madhusudhan & Seagersome absorption (Seager 2010). The resulting lightcurve 2010, 2011). However, given the availability of the Ke-is shown on top panel of Fig. 2, with the best-fit model pler observation alone in the present work, the numbersuperimposed. No ellipsoidal variations are detected of free parameters far exceed the single data point. Con-(−1 ± 3ppm). sequently, we explore a range of 1-D P -T profiles and chemical composition to explore possible explanations of 4. THE HIGH ALBEDO OF KEPLER-7 B the observed flux in the Kepler bandpass. If directly related to the albedo, the measured occul- Our results indicate that a high geometric albedo istation depth of 44±5 ppm translates to a 0.32±0.03 geo- the most plausible explanation of the observed eclipsemetric albedo as measured by Kepler. The Kepler band- depth. The major sources of opacity in the Kepler band-pass encompasses a large range of wavelengths, from 0.4 pass are atomic Na and K, molecular TiO and VO where
  • 4. 4 Fig. 1.— Top : Kepler-7 b phase-folded transit lightcurve with best-fit model superimposed. Binned per 15min. Error bars are smallerthan the plotted datapoints. Bottom : residuals. Fig. 2.— Top : Kepler-7 b orbital phase curve with best-fit model (see text) superimposed. Transits are omitted. Bottom : Kepler-7 bphase-folded occultation lightcurve with best-fit model. Binned per 15min.
  • 5. 5 TABLE 1 Kepler-7 system parameters Parameters ValueJump parametersPlanet/star area ratio (Rp /Rs )2 0.006772+0.000018 −0.000021b = a cos i/R [R ] 0.5565+0.0060 −0.0063Transit width [d] 0.21777+0.00023 −0.00021T0 - 2450000 [HJD] 4967.27599+0.00019 −0.00020Orbital period P [d] 4.8854830+0.0000042 −0.0000041RV K [m s−1 d1/3 ] 73.1+6.7 −6.8√ e cos ω 0.0376+0.0143 −0.0153√ e sin ω −0.0016+0.0026 −0.0022c1 = 2u1 + u2 0.922+0.011 −0.011c2 = u1 − 2u2 −0.143+0.022 −0.022Occultation depth 0.000044+0.000005 −0.000006Deduced stellar parametersu1 0.344+0.007 −0.007u2 0.232+0.009 −0.009Density ρstar [g cm−3 ] 0.231+0.004 −0.004Surface gravity log g∗ [cgs] 3.960+0.005 −0.005Mass M [M ] 1.36+0.03 −0.03Radius R [R ] 2.02+0.02 −0.02Asteroseismic parametersDensity ρstar [g cm−3 ] 0.252 ± 0.003Mass Mstar [M ] 1.359 ± 0.031Radius Rstar [R ] 1.966 ± 0.013Stellar age [Gyr] 3.3 ± 0.4Surface gravity log g∗ [cgs] 3.984 ± 0.006Deduced planet parametersRV K [m s−1 ] 43.1+3.9 −4.0btransit [R ] 0.557+0.006 −0.006boccultation [R ] 0.556+0.006 −0.006Toccultation - 2450000 [HJD] 4974.6086+0.0040 −0.0028Orbital semi-major axis a [AU] 0.06246+0.00046 −0.00046Orbital inclination i [deg] 85.18+0.076 −0.074Orbital eccentricity e 0.001+0.001 −0.001Argument of periastron ω [deg] 357.1+4.4 −2.8Density ρP [g cm−3 ] 0.14+0.01 −0.01 +0.04Surface gravity log gP [cgs] 2.62−0.04Mass MP [MJ up ] 0.443+0.041 −0.042Radius RP [RJ up ] 1.614+0.015 −0.015
  • 6. 6 contributions from thermal emission and Rayleigh scat- tering (with a geometric albedo of 0.17). However, two problems confront this scenario. Firstly, requiring such a high thermal flux implies that all the stellar incident flux on the dayside of the planet must be reradiated on the same side, with almost no energy recirculation to the night side. The Kepler phase curve of Kepler-7 b, shown in Fig. 2, could support this scenario if all the flux were purely due to thermal emission. However, because there is still a 50% contribution due to Rayleigh scattering required to explain the net flux at occultation, the Ke- pler phase curve cannot be interpreted as solely due to a large day-night temperature contrast. Furthermore, at the high pressures (P ∼ 1 bar) probed by the Ke- pler bandpass, the temperature should be homogenized across day and night side, exhibiting small thermal or- bital phase variation. Secondly, at the high tempera- Fig. 3.— Model-independent domain of allowed geometric albedo ture of ∼2600K probed by Kepler, it seems unlikely thatAg (reflected light) and brightness temperature TB (thermal emis- TiO/VO can be depleted by factors of 103 below chemicalsion) combinations, constrained by the observed Kepler occultation equilibrium at ∼ 1 bar pressure, although the difficultydepth. The shaded area represents the 1σ confidence domain foundusing a Kurucz spectrum for the star and blackbody emission for of sustaining TiO/VO at high altitudes (P 10−3 bar)the planet. The dotted lines depict the equilibrium temperature has been reported in literature (Spiegel et al. 2009).assuming full redistribution (left) and no redistribution (right). In our final scenario, we investigate if Rayleigh scat- tering alone can contribute dominantly to the observed flux. The strongest absorbers of Rayleigh scattered light,temperatures are higher than the condensation tempera- as shown in the first two panels of Fig. 4, are atomic Nature, Rayleigh scattering, and any possible contribution and K. We find that if we allow depletion of Na and Kdue to clouds and/or hazes. Consequently, we examine by a factor of 10-100 of the equilibrium composition, thethe constraints on each of these opacity sources due to observed flux in the Kepler bandpass can be fit extremelythe Kepler point. We assume all other molecules (H2 O, well with a geometric albedo of 0.32 from Rayleigh scat-CO, CH4 and CO2 ) to be in chemical equilibrium, assum- tering alone along with a nominal contribution due toing solar abundances. We find that the observed Kepler thermal emission. The resultant model also yields effi-flux can be explained under three scenarios, shown in the cient day-night energy circulation.three panels of Fig. 4. We finally note that the large planetary radius and In a first scenario, we consider a model where all the very low density would make appealing the hypothe-major absorbers, i.e. Na, K, TiO, and VO, are in chem- sis of Kepler-7 b being a very young planet that wouldical equilibrium with solar abundances, and we nomi- still be in its cooling phase. However, the asteroseismol-nally vary only the P -T profile to find a close match to ogy results presented in Sect. 2 produce a stellar age ofthe data. In this scenario, we find that the observed 3.3±0.4Gyr, which argues for a planetary evolutionaryflux cannot be accounted for by thermal emission and state beyond the collapsing phase (Fortney et al. 2005),Rayleigh scattering alone, both of which together provide and a negligible contribution from internal heat to thea net flux contrast of ∼ 20 ppm, with Rayleigh scatter- occultation depth.ing contributing a geometric albedo of 0.15. In principle,one might expect that hotter temperature profiles might 5. CONCLUSIONSlead to greater thermal emission which could contribute Given the three scenarios described in Sect. 4, we in-to the observed flux. However, warmer P -T profiles in- terpret the Kepler observed planetary flux as due to atercept longer absorption columns of TiO/VO which fur- combination of Rayleigh scattering and the presence ofther lower the emergent thermal flux. Therefore, under clouds or a haze layer (e.g., Lecavelier Des Etangs et al.the assumption of solar abundances of all species, excess 2008; Sing et al. 2009) in the atmosphere of Kepler-7 b,flux in the form of reflected light, potentially from clouds yielding an averaged geometric albedo of ∼ 0.3 in theand/or hazes, is required to explain the observed Kepler Kepler bandpass. A detailed cloud or haze model is be-flux, implying a net geometric albedo of ∼ 0.3. yond the scope of the present work. Our results motivate In a second scenario, we investigate if thermal emission new modeling and observational efforts to investigate thecan be a predominant contributor to the observed Kepler nature of clouds and hazes that might be possible in aflux. The strongest absorber in the redder regions of the low gravity atmosphere such as that of Kepler-7 b.Kepler bandpass, where thermal emission dominates, isTiO, followed by VO. As discussed in the equilibriumscenario above, TiO absorption precludes high bright- Authors thank the Kepler Giant Planet Workingness temperatures due to thermal emission in the Kepler Group, P.-O. Quirion, M. Holman, D. Ragozzine, J.bandpass. Conversely, we find that thermal emission can Jenkins, J.-M. D´sert, B. Benneke and D. Latham for econtribute substantially to the observed flux, if TiO and useful discussions. We thank E. Dunham, W. CochranVO are assumed to be depleted by over 103 in the lower and the referee for helpful comments that improved theatmosphere (P ∼ 0.1 − 1 bar). Such a scenario just man- manuscript. B.-O.D. acknowledges support from theages to fit the data at the lower error bar, with equal Swiss NSF and thanks kindly R. Stewart, P.L. Vidale
  • 7. 7 Fig. 4.— Model spectra of Kepler-7 b in the Kepler bandpass. Each panel corresponds to each scenario (1 to 3, left to right) described inSect.4. The Kepler data point is shown in red. In each panel, the black solid curve shows the net emergent spectrum. The net emergentflux integrated in the Kepler bandpass is shown in green. The cyan and purple curves show the contributions of thermal emission andreflected light to the emergent spectrum. The black dashed line shows a black body spectrum of the planet at 2550K, divided by a Kuruczmodel spectrum for the star. The relevant Pressure-Temperature profiles are shown for each atmospheric model in the insets, with the TiOcondensation curve in dotted line.and A. Verhoef from the University of Reading (UK), support from NASA Kepler Participating Science Pro-where part of this work has been carried out. M.G. gram NNX10AD67G. Funding for this Discovery Missionis Belgian FNRS Research Associate. We acknowledge is provided by NASA’s Science Mission Directorate. Facilities:Kepler,MMT REFERENCESAlonso, R., et al. 2009, A&A, 506, 353 Leigh, C., Collier Cameron, A., Udry, S., Donati, J.-F., Horne,Alonso, R., Deeg, H. J., Kabath, P., & Rabus, M. 2010, AJ, 139, K., James, D., & Penny, A. 2003, MNRAS, 346, L16 1481 Lenz, P., & Breger, M. 2005, Communications inAnderson, D. R., et al. 2010, ApJ, 709, 159 Asteroseismology, 146, 53Berdyugina, S. V., Berdyugin, A. V., Fluri, D. M., & Piirola, V. Madhusudhan, N., & Seager, S. 2011, ApJ, 729, 41 2011, ApJ, 728, L6 Madhusudhan, N., & Seager, S. 2010, ApJ, 725, 261Collier Cameron, A., Horne, K., Penny, A., & Leigh, C. 2002, Madhusudhan, N., & Seager, S. 2009, ApJ, 707, 24 MNRAS, 330, 187 Mandel, K., & Agol, E. 2002, ApJ, 580, L171Charbonneau, D., Noyes, R. W., Korzennik, S. G., Nisenson, P., Marley, M. S., Gelino, C., Stephens, D., Lunine, J. I., & Jha, S., Vogt, S. S., & Kibrick, R. I. 1999, ApJ, 522, L145 Freedman, R. 1999, ApJ, 513, 879Christensen-Dalsgaard, J., et al. 2010, ApJ, 713, L164 Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery,Christensen-Dalsgaard, J., Arentoft, T., Brown, T. M., Gilliland, B. P. 1992, Cambridge: University Press, —c1992, 2nd ed., R. L., Kjeldsen, H., Borucki, W. J., & Koch, D. 2008, Rodler, F., K¨rster, M., & Henning, T. 2008, A&A, 485, 859 u Communications in Asteroseismology, 157, 266 Rodler, F., K¨rster, M., & Henning, T. 2010, A&A, 514, A23 uChristiansen, J. L., et al. 2010, ApJ, 710, 97 Rowe, J. F., et al. 2008, ApJ, 689, 1345Deming, D., & Seager, S. 2009, Nature, 462, 301 Seager, S., & Sasselov, D. D. 2000, ApJ, 537, 916Desert, J.-M., et al. 2011, arXiv:1102.0555 Seager, S., Whitney, B. A., & Sasselov, D. D. 2000, ApJ, 540, 504Fortney, J. J., Marley, M. S., Hubickyj, O., Bodenheimer, P., & Seager, S. 2010, Exoplanet Atmospheres: Physical Lissauer, J. J. 2005, Astronomische Nachrichten, 326, 925 Processes. Princeton University Press, 2010. ISBN:Gilliland, R. L., et al. 2010, ApJ, 713, L160 978-1-4008-3530-0.Gilliland, R. L., McCullough, P. R., Nelan, E. P., Brown, T. M., Sing, D. K., D´sert, J.-M., Lecavelier Des Etangs, A., Ballester, e Charbonneau, D., Nutzman, P., Christensen-Dalsgaard, J., & G. E., Vidal-Madjar, A., Parmentier, V., Hebrard, G., & Henry, Kjeldsen, H. 2011, ApJ, 726, 2 G. W. 2009, A&A, 505, 891Gillon, M., et al. 2009, A&A, 506, 359 Snellen, I. A. G., de Mooij, E. J. W., & Albrecht, S. 2009, Nature,Gillon, M., et al. 2010, A&A, 511, A3 459, 543Jenkins, J. M., et al. 2010, ApJ, 713, L120 Snellen, I. A. G., de Mooij, E. J. W., & Burrows, A. 2010, A&A,Huber, D., Stello, D., Bedding, T. R., Chaplin, W. J., Arentoft, 513, A76 T., Quirion, P.-O., & Kjeldsen, H. 2009, Communications in Sobolev, V. V. 1975, Oxford and New York, Pergamon Press Asteroseismology, 160, 74 (International Series of Monographs in NaturalKarkoschka, E. 1994, Icarus, 111, 174 Philosophy. Volume 76)Kipping, D., & Bakos, G. 2011, ApJ, 730, 50 Spiegel, D. S., Silverio, K., & Burrows, A. 2009, ApJ, 699, 1487Koch, D. G., et al. 2010, ApJ, 713, L79 Sudarsky, D., Burrows, A., & Hubeny, I. 2003, ApJ, 588, 1121Latham, D. W., et al. 2010, ApJ, 713, L140 Welsh, W. F., Orosz, J. A., Seager, S., Fortney, J. J., Jenkins, J.,Lecavelier Des Etangs, A., Pont, F., Vidal-Madjar, A., & Sing, D. Rowe, J. F., Koch, D., & Borucki, W. J. 2010, ApJ, 713, L145 2008, A&A, 481, L83 Winn, J. N., et al. 2008, ApJ, 683, 1076Leigh, C., Cameron, A. C., Horne, K., Penny, A., & James, D. 2003, MNRAS, 344, 1271