The Effect of Tidal Inflation Instability on the Mass and Dynamical Evolution of Extrasolar Planets with Ultra-Short Periods

We investigate the possibility of substantial inflation of short-period Jupiter-mass planets, as a result of their internal tidal dissipation associated with the synchronization and circularization of their orbits. We employ the simplest prescription based on an equilibrium model with a constant lag angle for all components of the tide. We show that 1) in the low-eccentricity limit, the synchronization of the planets’ spin with their mean motion is established before tidal dissipation can significantly modify their internal structure. 2) But, above a critical eccentricity, which is a function of the planets’ semimajor axis, tidal dissipation of energy during the circularization process can induce planets to inflate in size before their eccentricity is damped. 3) For moderate eccentricities, the planets adjust to stable thermal equilibria in which the rate of their internal tidal dissipation is balanced by the enhanced radiative flux associated with their enlarged radii. 4) For sufficiently large eccentricities, the planets swell beyond two Jupiter radii and their internal degeneracy is partially lifted. Thereafter, their thermal equilibria become unstable and they undergo runaway inflation until their radii exceed the Roche radius. 5) We determine the necessary and sufficient condition for this tidal inflation instability. 6) These results are applied to study short-period planets. We show that for young Jupiter-mass planets, with a period less than 3 days, an initial radius about 2 Jupiter radii, and an orbital eccentricity greater than 0.2, the energy dissipated during the circularization of their orbits is sufficiently intense and protracted to inflate their sizes up to their Roche radii. 7) We estimate the mass loss rate, the asymptotic planetary masses, and the semi-major axes for various planetary initial orbital parameters. The possibility of gas overflow through both inner (L1) and outer (L2) Lagrangian points for the planets with short periods or large eccentricities is discussed. 8) Planets with more modest eccentricity (< 0.3) and semi-major axis (> 0.03 − 0.04 AU) lose mass via Roche-lobe overflow mostly through the inner Lagrangian (L1) point. Due to the conservation of total angular momentum, these mass-losing planets migrate outwards, such that their semi-major