EXPLORATIONS INTO THE VIABILITY OF COUPLED RADIUS-ORBIT EVOLUTIONARY MODELS FOR INFLATED PLANETS

The radii of some transiting extrasolar giant planets are larger than would be expected by the standard theory. We address this puzzle with the model of coupled radius-orbit tidal evolution developed by Ibgui & Burrows. The planetary radius is evolved self-consistently with orbital parameters, under the influence of tidal torques and tidal dissipation in the interior of the planet. A general feature of this model, which we have previously demonstrated in the generic case, is that a possible transient inflation of the planetary radius can temporarily interrupt its standard monotonic shrinking and can lead to the inflated radii that we observe. Importantly, we demonstrate that the use of a constant time lag model for the orbital evolution does not improve the accuracy of the evolutionary calculations. First, though formulated in a closed form by the equations of Hut, it is not valid at large eccentricities, as for the constant phase lag model truncated at the second order in eccentricity that we adopt; ambiguities in tidal theories are perhaps the most significant source of uncertainty in evolutionary calculations. Second, we find evolutionary tracks that fit within the 1 sigma error bars, the radius, the eccentricity, and the semimajor axis of HD 209458b in its current estimated age range, using the constant time lag model, as we find fitting tracks with the constant phase lag model. Both models show that a bloated planet with a circular orbit may still be inflated, due to thermal inertia. We have modified our constant phase lag model to include an orbital period dependence of the tidal dissipation factor in the star, Q'(*) alpha P-gamma, -1 <= gamma <= 1. For some inflated planets (WASP-6b and WASP-15b), we find fitting tracks; for another (TrES-4), we do not; and for others (WASP-4b and WASP-12b), we find fitting tracks, but our model might imply that we are observing the planets at a special time. Finally, we stress a 2-3 order-of-magnitude timescale uncertainty of the inspiraling phase of the planet into its host star, arising from uncertainties in Q'(*).