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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 \citet{Ibgui_and_Burrows_2009}. 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. In particular, a bloated planet with even a circular orbit may still be inflated due to an earlier episode of tidal heating. We have modified our model to include an orbital period dependence of the tidal dissipation factor in the star, $Q'_{\ast} \propto P^γ$, $-1 \leqslant γ\leqslant 1$. With this model, we search, for a tidally heated planet, orbital and radius evolutionary tracks that fall within the observational limits of the radius, the semimajor axis, and the eccentricity of the planet in its current estimated age range. We find that, for some inflated planets (WASP-6b and WASP-15b), there are such tracks; for another (TrES-4), there are none; and for still others (WASP-4b and WASP-12b), there are such tracks, but our model might imply that we are observing the planets at a special time. Finally, we stress that there is a two to three order-of-magnitude timescale uncertainty of the inspiraling phase of the planet into its host star, arising from uncertainties in the tidal dissipation factor in the star $Q'_{\ast}$.