Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity

Abstract

In this paper, we present the consistent evolution of short-period exoplanets coupling the tidal and gravothermal evolution of the planet. Contrarily to previous similar studies, our calculations are based on the complete tidal evolution equations of the Hut model, valid at any order in eccentricity, obliquity and spin. We demonstrate, both analytically and numerically, that, except if the system was formed with a nearly circular orbit (e<0.2), solving consistently the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at second order in eccentricity, as done in all previous studies, lead to erroneous tidal evolutions. As a consequence, tidal energy dissipation rates are severely underestimated in all these calculations and the characteristic timescales for the various orbital parameters evolutions can be wrong by up to three orders in magnitude. Based on these complete, consistent calculations, we revisit the viability of the tidal heating hypothesis to explain the anomalously large radius of transiting giant planets. We show that, even though tidal dissipation does provide a substantial contribution to the planet's heat budget and can explain some of the moderately bloated hot-Jupiters, this mechanism can not explain alone the properties of the most inflated objects, including HD 209458b. Indeed, solving the complete tidal equations shows that enhanced tidal dissipation and thus orbit circularization occur too early during the planet's evolution to provide enough extra energy at the present epoch. In that case another mechanisms, such as stellar irradiation induced surface winds dissipating in the planet's tidal bulges, or inefficient convection in the planet's interior must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.