Tidal synchronization of close-in satellites and exoplanets: II. Spin dynamics and extension to Mercury and exoplanet host stars

摘要

This paper deals with the application of the creep tide theory (Ferraz-Mello, Celest Mech Dyn Astron 116: 109, 2013a) to the rotation of close-in satellites, Mercury, close-in exoplanets, and their host stars. The solutions show different behaviors with two extreme cases: close-in giant gaseous planets with fast relaxation (low viscosity) and satellites and Earth-like planets with slow relaxation (high viscosity). The rotation of close-in gaseous planets follows the classical Darwinian pattern: it is tidally driven toward a stationary solution that is synchronized with the orbital motion when the orbit is circular, but if the orbit is elliptical, it has a frequency larger than the orbital mean motion. The rotation of rocky bodies, however, may be driven to several attractors whose frequencies are 1/2, 1, 3/2, 2, 5/2, ... times the mean motion. The number of attractors increases with the viscosity of the body and with the orbital eccentricity. The final stationary state depends on the initial conditions. The classical example is Mercury, whose rotational period is 2/3 of the orbital period (3/2 attractor). The planet behaves as a molten body with a relaxation that allowed it to cross the 2/1 attractor without being trapped but not to escape being trapped in the 3/2 one. In that case, the relaxation is estimated to lie in the interval 4.6 < gamma < 27x10(-9) s(-1) (equivalent to a quality factor roughly constrained to the interval 5 < Q < 50). The stars have a relaxation similar to the hot Jupiters, and their rotation is also driven to the only stationary solution existing in these cases. However, solar-type stars may lose angular momentum due to stellar wind, braking the rotation and displacing the attractor toward larger periods. Old, active host stars with big close-in companions generally have rotational periods larger than the orbital periods of the companions. The paper also includes a study of energy dissipation and the evolution of orbital eccentricity.