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SOPHIE velocimetry of Kepler transit candidates XI. Kepler-412 system: probing the properties of a new inflated hot Jupiter

We confirm the planetary nature of Kepler-412b, listed as planet candidate KOI-202 in the Kepler catalog, thanks to our radial velocity follow-up program of Kepler-released planet candidates, which is on going with the SOPHIE spectrograph. We performed a complete analysis of the system by combining the Kepler observations from Q1 to Q15, to ground-based spectroscopic observations that allowed us to derive radial velocity measurements, together with the host star parameters and properties. We also analyzed the light curve to derive the star's rotation period and the phase function of the planet, including the secondary eclipse. We found the planet has a mass of 0.939 $\pm$ 0.085 M$_{Jup}$ and a radius of 1.325 $\pm$ 0.043 R$_{Jup}$ which makes it a member of the bloated giant subgroup. It orbits its G3 V host star in 1.72 days. The system has an isochronal age of 5.1 Gyr, consistent with its moderate stellar activity as observed in the Kepler light curve and the rotation of the star of 17.2 $\pm$ 1.6 days. From the detected secondary, we derived the day side temperature as a function of the geometric albedo and estimated the geometrical albedo, Ag, is in the range 0.094 to 0.013. The measured night side flux corresponds to a night side brightness temperature of 2154 $\pm$ 83 K, much greater than what is expected for a planet with homogeneous heat redistribution. From the comparison to star and planet evolution models, we found that dissipation should operate in the deep interior of the planet. This modeling also shows that despite its inflated radius, the planet presents a noticeable amount of heavy elements, which accounts for a mass fraction of 0.11 $\pm$ 0.04.