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

Abstract

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

An analysis of the CoRoT-2 system: a young spotted star and its inflated giant planet

“…As originally proposed by Bodenheimer et al (2001) and Gu et al (2003) and later studied by many authors (e.g. Jackson et al 2008;Ibgui & Burrows 2009;Miller et al 2009), stellar tides provide a way to transfer gravitational energy from the planetary orbit into the planet and either slow its contraction, or even produce a size inflation.…”

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

“…Following Bodenheimer et al (2001) and Gu et al (2003), attempts have been made to explain the observed large radius of some transiting close-in gas giant exoplanets -the so-called "Hot Jupiters" -by means of tidal heating (Jackson et al 2008;Miller et al 2009;). All these models, however, use tidal models truncated to a low (2nd) order in eccentricity, in spite of initial eccentricities, as determined from the tidal evolution calculations, which can be as large as e = 0.8!…”

The TRAPPIST survey of southern transiting planets

“…Their relatively large mass and small semimajor axis imply tidal interactions with the host star that should lead in most cases to a slow spiral-in of the planet and to a transfer of angular momentum to the star (e.g. Barker & Ogilvie 2009;Jackson et al 2009;Mastumura et al 2010), the end result being the planet's disruption at its Roche limit (Gu et al 2003). The timescale of this final disruption depends mostly on the timescale of the migration mechanism, the tidal dissipation efficiency of both bodies, and the efficiency of angular momentum losses from the system due to magnetic braking.…”