Cassini States with Dissipation: Why Obliquity Tides Cannot Inflate Hot Jupiters

Abstract

Some short-period exoplanets (hot Jupiters) are observed by their transits to have anomalously large radii. It has been suggested that these planets are in a resonance involving persistent misalignment and synchronous precession of their spin and orbital angular momenta, a Cassini state, and that the attendant tidal heating inflates the planet. We argue against this. Using explicit tidal integrations, we show that although an oblique Cassini state can dissipate many times the rotational energy of the planet, the rate of dissipation must be much less than hypothesized. Dissipation causes the planetary spin to lie at an angle to the plane containing the orbital and total angular momenta. If dissipation is too rapid, this angle becomes so large that Cassini equilibrium is lost. A separate consideration limits the total energy that can be extracted from the orbit. The source of the torque on the orbit, either an oblique parent star or an inclined third body, aligns with the orbit as it absorbs the angular momentum shed by the planet. Alignment removes the orbital precession required by the Cassini state. In combination with observational bounds on the mass and semimajor axis of a possible second planet and with bounds on the stellar rotation and obliquity, these constraints make it very unlikely that obliquity tides can be the explanation for inflated hot Jupiters, especially HD 209458b.