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

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 (1981) 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 less than or similar to 0.2), consistently solving the complete tidal equations is mandatory to derive correct tidal evolution histories. We show that calculations based on tidal models truncated at 2nd order in eccentricity, as done in all previous studies, lead to quantitatively and sometimes even qualitatively 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 of magnitude. These discrepancies can by no means be justified by invoking the uncertainty in the tidal quality factors. 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 209 458b. 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 either a third, so far undetected, low-mass companion must be present to keep exciting the eccentricity of the giant planet, or other mechanisms - stellar irradiation induced surface winds dissipating in the planet's tidal bulges and thus reaching the convective layers, inefficient flux transport by convection in the planet's interior - must be invoked, together with tidal dissipation, to provide all the pieces of the abnormally large exoplanet puzzle.