Resonant Tides in Close Orbiting Planets

Abstract

The outer layers of a gas giant planet in a close orbit are isothermal because of heating by the star, and therefore these layers are convectively stable. A resonant tidal torque is exerted at the outer boundary of the interior convection zone. Tidal dissipation occurs through nonlinear damping. This process is similar to that previously considered for high-mass binary stars. Two novel aspects of the planet case are (1) the torque is exerted in a region where H/rp 1, for density scale height H and planet radius rp, and (2) at high spin rates, effects of Coriolis forces are critical in permitting a resonance to occur. Gravity waves carrying angular momentum are launched outward from the resonant region. As these waves damp by nonlinear processes, an oversynchronous planet is spun down toward synchronism with the orbit. The torques are powerful enough to have spun down planet 51 Peg B below Jupiter's spin rate in about 102 yr and to approximate synchronism (ωspin ~ ωorbit) in about 105 yr. These estimates ignore effects of tidal heating, which are likely important at the spin rate of Jupiter or higher. Fast-rotating Jupiter-mass planets with orbital periods of up to about 40 days can be spun down to less than one-tenth the spin rate of Jupiter within 1010 yr. A planet's photosphere would be spun down even more effectively than is estimated above if its outer layers can rotate differentially. A crude estimate suggests that eccentricity is damped on timescales of about 1010 yr, so a more detailed analysis is required to determine the significance of this effect.