Forced libration of tidally synchronized planets and moons

TL;DR

This paper analyzes the mechanisms and characteristics of forced librations in tidally synchronized planets and moons, emphasizing how tidal and triaxial torques influence libration shape, amplitude, and orbital evolution.

Contribution

It provides a comprehensive model for understanding the shape and amplitude of forced librations considering both tidal and triaxial torques, applicable to various celestial bodies.

Findings

Librations can be tidal or deformation dominated depending on physical parameters.

The libration shape influences the orbital damping rates of semimajor axis and eccentricity.

Exoplanets may exhibit mixed libration types based on their internal properties.

Abstract

Tidal dissipation of kinetic energy, when it is strong enough, tends to synchronize the rotation of planets and moons with the mean orbital motion, or drive it into long-term stable spin-orbit resonances. As the orbital motion undergoes periodic acceleration due to a finite orbital eccentricity, the spin rate oscillates around the equilibrium mean value too, giving rise to the forced, or eccentricity-driven, librations. Both the shape and amplitude of forced librations of synchronous viscoelastic planets and moons are defined by a combination of two different types of perturbative torque, the tidal torque and the triaxial torque. Consequently, forced librations can be tidally dominated (e.g., Io and possibly Titan) or deformation-dominated (e.g., the Moon) depending on a set of orbital, rheological, and other physical parameters. With small eccentricities, for the former kind, the largest term in the libration angle can be minus cosine of the mean anomaly, whereas for the latter kind, it is minus sine of the mean anomaly. The shape and the amplitude of tidal forced librations determine the rate of orbital evolution of synchronous planets and moons, i.e., the rate of dissipative damping of semimajor axis and eccentricity. The known super-Earth exoplanets can exhibit both kinds of libration, or a mixture thereof, depending on, for example, the effective Maxwell time of their rigid mantles. Our approach can be extended to estimate the amplitudes of other libration harmonics, as well as the forced libration in non-synchronous spin-orbit resonances.