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

Abstract

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