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

International audienceContext. Hot Jupiters are still a fascinating exoplanet population that presents a diversity we are still far from understanding. High-precision photometric observations combined with radial velocity measurements give us a unique opportunity to constrain their properties better, on both their internal structure and their atmospheric bulk properties. Aims. We initiated a follow-up program of Kepler-released planet candidates with the goal of confirming the planetary nature of a number of them through radial velocity measurements. For those that successfully passed the radial velocity screening, we furthermore performed a detailed exploration of their properties to characterize the systems. As a byproduct, these systematic observations allow us to consolidate the exoplanets' occurrence rate. Methods. We performed a complete analysis of the Kepler-412 system, listed as planet candidate KOI-202 in the Kepler catalog, 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. Results. We secured the planetary nature of Kepler-412b. We found the planet has a mass of 0.939 +/- 0.085 M-Jup and a radius of 1.325 +/- 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 +/- 1.6 days. From the detected secondary we derived the day-side temperature as a function of the geometric albedo. We estimated that the geometrical albedo A(g), should be between 0.094 +/- 0.015 and 0.013 (+0.017)(-0.013) and the brightness of the day side 2380 +/- 40 K. The measured night-side flux corresponds to a night-side brightness temperature of 2154 +/- 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 +/- 0.04