Distorted, non-spherical transiting planets: impact on the transit depth and on the radius determination.

In this paper, we quantify the systematic impact of the non-spherical shape of transiting planets, due to tidal forces and rotation, on the observed transit depth. Such a departure from sphericity leads to a bias in the derivation of the transit radius from the light curve and affects the comparison with planet structure and evolution models which assume spherical symmetry. As the tidally deformed planet projects its smallest cross section area during the transit, the measured effective radius is smaller than the one of the unperturbed spherical planet (which is the radius predicted by 1D evolution models). This effect can be corrected by calculating the theoretical shape of the observed planet. Using a variational method and a simple polytropic assumption for the gaseous planet structure, we derive simple analytical expres-sions for the ellipsoidal shape of a fluid object (star or planet) accounting for both tidal and rotational deformations. We determine the characteristic polytropic indexes describing the structures of irradiated close-in planets within the mass range 0.3 MJ < Mp < 75 MJ, at different ages, by comparing polytropic models with the inner density profiles calculated with the full evolution code. Our cal-culations yield a 20 % effect on the transit depth, i.e. a 10 % decrease of the measured radius, for the extreme case of a 1MJ planet orbiting a Sun-like star at 0.01AU, and the effect can be larger for smaller mass objects. For the closest planets detected so far (. 0.05 AU), the effect on the radius is of the order of 1 to 10 % (three times more for the mean density), by no means a negligible effect, enhancing the puzzling problem of the anomalously large bloated planets. These corrections must thus be taken into account for