Deformation and tidal evolution of close-in planets and satellites using a Maxwell viscoelastic rheology

TL;DR

This paper introduces a new method for modeling the tidal deformation and evolution of close-in planets using Maxwell viscoelastic rheology, capable of handling large eccentricities and complex perturbations.

Contribution

It presents a differential equation-based approach to compute celestial bodies' deformation, extending tidal theory to include chaotic motions and transient events.

Findings

Spin-orbit equilibria at half-integers of mean motion for large relaxation times.

Equilibria can persist at very low eccentricities for super-Earths.

Method applicable to planets with complex internal structures.

Abstract

In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method allows large eccentricities and it is not limited to quasi-periodic perturbations. It can take into account an extended class of perturbations, including chaotic motions and transient events. We apply our model to some already detected eccentric hot Jupiters and super-Earths in planar configurations. We show that when the relaxation time of the deformation is larger than the orbital period, spin-orbit equilibria arise naturally at half-integers of the mean motion, even for gaseous planets. In the case of super-Earths, these equilibria can be maintained for very low values of eccentricity. Our method can also be used to study planets with complex internal structures and other rheologies.