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

TL;DR

This study applies the creep tide theory to analyze the spin dynamics of close-in satellites, Mercury, and exoplanets, revealing multiple attractors influenced by viscosity and eccentricity, and examining implications for stellar and planetary rotation.

Contribution

It extends the creep tide theory to include detailed spin dynamics of Mercury and exoplanets, highlighting multiple attractors and their dependence on physical properties.

Findings

Mercury's rotation is at the 3/2 attractor, consistent with observations.

Gaseous planets tend toward classical synchronized rotation, with eccentricity causing higher frequency attractors.

Stellar rotation can be slowed by stellar wind, affecting attractor positions.

Abstract

This paper deals with the application of the creep tide theory (Ferraz-Mello, CeMDA 116, 109, 2013) to the rotation of close-in satellites, Mercury, close-in exoplanets and their host stars. The solutions show 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 towards a stationary solution which is synchronized, but, if the orbit is elliptical, with 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 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 -- 27 x 10^{-9} s^{-1} (equivalent to a quality factor roughly constrained to the interval 5<Q<50). The stars have 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 towards 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 the study of the energy dissipation and the evolution of the orbital eccentricity.