Coupled Evolution with Tides of the Radius and Orbit of Transiting Giant Planets: General Results

Some transiting extrasolar giant planets have measured radii larger than predicted by the standard theory. In this paper, we explore the possibility that an earlier episode of tidal heating can explain such radius anomalies and apply the formalism we develop to HD 209458b as an example. We find that for strong enough tides the planet's radius can undergo a transient phase of inflation that temporarily interrupts canonical, monotonic shrinking due to radiative losses. Importantly, an earlier episode of tidal heating can result in a planet with an inflated radius, even though its orbit has nearly circularized. Moreover, we confirm that at late times, and under some circumstances, by raising tides on the star itself a planet can spiral into its host. We note that a 3$\times$ to 10$\times$solar planet atmospheric opacity with no tidal heating is sufficient to explain the observed radius of HD 209458b. However, our model demonstrates that with an earlier phase of episodic tidal heating we can fit the observed radius of HD 209458b even with lower (solar) atmospheric opacities. This work demonstrates that, if a planet is left with an appreciable eccentricity after early inward migration and/or dynamical interaction, coupling radius and orbit evolution in a consistent fashion that includes tidal heating, stellar irradiation, and detailed model atmospheres might offer a generic solution to the inflated radius puzzle for transiting extrasolar giant planets such as WASP-12b, TrES-4, and WASP-6b.