Revising the Kepler-10 System for Exoplanet Characteristics & Adding Kepler-10d (KOI-72.X)

Revised Masses and Densities of the Planets around Kepler-10

Authors:

Weiss et al

Abstract:

Determining which small exoplanets have stony-iron compositions is necessary for quantifying the occurrence of such planets and for understanding the physics of planet formation. Kepler-10 hosts the stony-iron world Kepler-10b (K10b), and also contains what has been reported to be the largest solid silicate-ice planet, Kepler-10c (K10c). Using 220 radial velocities (RVs), including 72 precise RVs from Keck-HIRES of which 20 are new from 2014-2015, and 17 quarters of Kepler photometry, we obtain the most complete picture of the Kepler-10 system to date. We find that K10b (Rp=1.47 Re) has mass 3.72±0.42 Me and density 6.46±0.73 g/cc. Modeling the interior of K10b as an iron core overlaid with a silicate mantle, we find that the iron core constitutes 0.17±0.11 of the planet mass. For K10c (Rp=2.35 Re) we measure Mp=13.98±1.79 Me and ρ=5.94±0.76 g/cc, significantly lower than the mass computed in Dumusque et al. (2014, 17.2±1.9 Me). Internal compositional modeling reveals that at least 10% of the radius of Kepler-10c is a volatile envelope composed of hydrogen-helium (0.2% of the mass, 16% of the radius) or super-ionic water (28% of the mass, 29% of the radius). Analysis of only HIRES data yields a higher mass for K10b and a lower mass for K10c than does analysis of the HARPS-N data alone, with the mass estimates for K10c formally inconsistent by 3σ. Splitting the RVs from each instrument leads to inconsistent measurements for the mass of planet c in each data set. This suggests that time-correlated noise is present and that the uncertainties in the planet masses (especially K10c) exceed our formal estimates. Transit timing variations (TTVs) of K10c indicate the likely presence of a third planet in the system, KOI-72.X. The TTVs and RVs are consistent with KOI-72.X having an orbital period of 24, 71, or 101 days, and a mass from 1-7 Me.

Host Star Iron Abundance Correlates With SuperEarth Density

Constraining planet structure from stellar chemistry: the cases of CoRoT-7, Kepler-10, and Kepler-93

Authors:

Santos et al

Abstract:

We explore the possibility that the stellar relative abundances of different species can be used to constrain the bulk abundances of known transiting rocky planets. We use high resolution spectra to derive stellar parameters and chemical abundances for Fe, Si, Mg, O, and C in three stars hosting low mass, rocky planets: CoRoT-7, Kepler-10, and Kepler-93. These planets follow the same line along the mass-radius diagram, pointing toward a similar composition. The derived abundance ratios are compared with the solar values. With a simple stoichiometric model, we estimate the iron mass fraction in each planet, assuming stellar composition. We show that in all cases, the iron mass fraction inferred from the mass-radius relationship seems to be in good agreement with the iron abundance derived from the host star's photospheric composition. The results suggest that stellar abundances can be used to add constraints on the composition of orbiting rocky planets.

 

Examining the Substellar Points of Exoplanets in the Visible Spectrum

A Semi-Analytical Model of Visible-Wavelength Phase Curves of Exoplanets and Applications to Kepler-7 b and Kepler-10 b

Authors:

Hu et al

Abstract:

Kepler has detected numerous exoplanet transits by precise measurements of stellar light in a single visible-wavelength band. In addition to detection, the precise photometry provides phase curves of exoplanets, which can be used to study the dynamic processes on these planets. However, the interpretation of these observations can be complicated by the fact that visible-wavelength phase curves can represent both thermal emission and scattering from the planets. Here we present a semi-analytical model framework that can be applied to study Kepler and future visible-wavelength phase curve observations of exoplanets. The model efficiently computes reflection and thermal emission components for both rocky and gaseous planets, considering both homogeneous and inhomogeneous surfaces or atmospheres. We analyze the phase curves of the gaseous planet Kepler-7 b and the rocky planet Kepler-10 b using the model. In general, we find that a hot exoplanet's visible-wavelength phase curve having a significant phase offset can usually be explained by two classes of solutions: one class requires a thermal hot spot shifted to one side of the substellar point, and the other class requires reflective clouds concentrated on the same side of the substellar point. The two solutions would require very different Bond albedos to fit the same phase curve; atmospheric circulation models or eclipse observations at longer wavelengths can effectively rule out one class of solutions, and thus pinpoint the albedo of the planet, allowing decomposition of the reflection and the thermal emission components in the phase curve. Particularly for Kepler-7 b, reflective clouds located on the west side of the substellar point can best explain its phase curve. We further derive that the reflectivity of the clear part of the atmosphere should be less than 7% and that of the cloudy part should be greater than 80%.

Kepler-10b is Unusually Reflective

Statistical Eclipses of Close-in Kepler Sub-Saturns

Authors:

Sheets et al

Abstract:

We present a method to detect small atmospheric signals in Kepler's planet candidate light curves by averaging light curves for multiple candidates with similar orbital and physical characteristics. Our statistical method allows us to measure unbiased physical properties of Kepler's planet candidates, even for candidates whose individual signal-to-noise precludes the detection of their secondary eclipse. We detect a secondary eclipse depth of 3.83 +1.10/-1.11 ppm for a group of 31 sub-Saturn (R less than 6 Earth radii) planet candidates with the greatest potential for a reflected light signature ((R_p/a)^2 greater than 10 ppm). Including Kepler-10b in this group increases the depth to 5.08 +0.71/-0.72 ppm. For a control group with (R_p/a)^2 less than 1 ppm, we find a depth of 0.36 +/- 0.37 ppm, consistent with no detection. We also analyze the light curve of Kepler-10b and find an eclipse depth of 7.08 +/- 1.06 ppm. If the eclipses are due solely to reflected light, this corresponds to a geometric albedo of 0.22 +/- 0.06 for our group of close-in sub-Saturns, 0.37 +/- 0.05 if including Kepler-10b in the group, and 0.60 +/- 0.09 for Kepler-10b alone. Including a thermal emission model does not change the geometric albedo appreciably, assuming the Bond albedo is 2/3 the geometric albedo. Our result for Kepler-10b is consistent with previous works. Our result for close-in sub-Saturns shows that Kepler-10b is unusually reflective, but our analysis is consistent with the results of Demory (2014) for super-Earths. Our results also indicate that hot Neptunes are typically more reflective than hot Jupiters.

Examining the Formation of the Kepler-10 System

On the formation of the Kepler-10 planetary system

Authors:

Terquem et al

Abstract:

In this paper, we investigate the conditions required for the 3 and 17 Earth mass solid planets in the Kepler-10 system to have formed through collisions and mergers within an initial population of embryos. By performing a large number of N-body simulations, we show that the total mass of the initial population had to be significantly larger than the masses of the two planets, and that the two planets must have built-up farther away than their present location, at a distance of at least a few au from the central star. The planets had to grow fast enough so that they would detach themselves from the population of remaining, less massive, cores and migrate in to their present location. By the time the other cores migrated in, the disc's inner edge would have moved out so that these cores cannot be detected today. We also compute the critical core mass beyond which a massive gaseous envelope would be accreted and show that it is larger than 17 Earth masses if the planetesimal accretion rate onto the core is larger than 10^{-6} Earth mass per year. For a planetesimal accretion rate between 10^{-6} and 10^{-5} Earth mass per year, the 17 Earth mass core would not be expected to have accreted more than about 1 Earth mass of gas. The results presented in this paper suggest that a planetary system like Kepler-10 may not be unusual, although it has probably formed in a rather massive disc.

Tidal dissipation in Io, Mercury & Kepler-10b

Tidal dissipation in a homogeneous spherical body. II. Three examples: Io, Mercury, and Kepler-10 b

Authors:

Makarov et al

Abstract:

In Efroimsky & Makarov (2014), we derived from the first principles a formula for the tidal heating rate in a tidally perturbed homogeneous sphere. We compared it with the formulae used in the literature, and pointed out the differences. Using this result, we now present three case studies - Mercury, Kepler-10b, and a triaxial Io. A very sharp frequency-dependence of k2/Q near spin-orbit resonances yields a similarly sharp dependence of k2/Q on the spin rate. This indicates that physical libration may play a major role in tidal heating of synchronously rotating bodies. The magnitude of libration in the spin rate being defined by the planet's triaxiality, the latter should be a factor determining the dissipation rate. Other parameters equal, a synchronously rotating body with a stronger triaxiality should generate more heat than a similar body of a more symmetrical shape. Further in the paper, we discuss scenarios where initially triaxial objects melt and lose their triaxiality. Thereafter, dissipation in them becomes less intensive; so the bodies freeze. The tidal bulge becomes a new permanent figure, with a new triaxiality lower than the original. In the paper, we also derive simplified, approximate expressions for dissipation rate in a rocky planet of the Maxwell rheology, with a not too small Maxwell time. The three expressions derived pertain to the cases of a synchronous spin, a 3:2 resonance, and a nonresonant rotation; so they can be applied to most close-in super-Earth exoplanets detected thus far. In such bodies, the rate of tidal heating outside of synchronous rotation is weakly dependent on the eccentricity and obliquity, provided both these parameters are small or moderate. According to our calculation, Kepler-10b could hardly survive the great amount of tidal heating without being synchronised, circularised and also reshaped through a complete or partial melt-down.

Revisiting the Kepler-10 System: Is Kepler-10c the First Giant ROCKY Planet? Or a Stripped Gas Giant?

The Kepler-10 planetary system revisited by HARPS-N: A hot rocky world and a solid Neptune-mass planet

Authors:

Dumusque et al

Abstract:

Kepler-10b was the first rocky planet detected by the Kepler satellite and con- firmed with radial velocity follow-up observations from Keck-HIRES. The mass of the planet was measured with a precision of around 30%, which was insufficient to constrain models of its internal structure and composition in detail. In addition to Kepler-10b, a second planet transiting the same star with a period of 45 days was sta- tistically validated, but the radial velocities were only good enough to set an upper limit of 20 Mearth for the mass of Kepler-10c. To improve the precision on the mass for planet b, the HARPS-N Collaboration decided to observe Kepler-10 intensively with the HARPS-N spectrograph on the Telescopio Nazionale Galileo on La Palma. In to- tal, 148 high-quality radial-velocity measurements were obtained over two observing seasons. These new data allow us to improve the precision of the mass determina- tion for Kepler-10b to 15%. With a mass of 3.33 +/- 0.49 Mearth and an updated radius of 1.47 +0.03 -0.02 Rearth, Kepler-10b has a density of 5.8 +/- 0.8 g cm-3, very close to the value -0.02 predicted by models with the same internal structure and composition as the Earth. We were also able to determine a mass for the 45-day period planet Kepler-10c, with an even better precision of 11%. With a mass of 17.2 +/- 1.9 Mearth and radius of 2.35 +0.09 -0.04 Rearth, -0.04 Kepler-10c has a density of 7.1 +/- 1.0 g cm-3. Kepler-10c appears to be the first strong evidence of a class of more massive solid planets with longer orbital periods.