Complete spin and orbital evolution of close-in bodies using a Maxwell viscoelastic rheology

TL;DR

This paper develops a comprehensive formalism for modeling the spin and orbital evolution of close-in bodies with Maxwell viscoelastic rheology, accounting for complex orbital configurations and validating results with exoplanet data.

Contribution

It generalizes existing models to include spatial and multipole effects, providing a versatile tool for studying tidal interactions in diverse planetary systems.

Findings

Presence of multiple spin-orbit resonances when relaxation time exceeds orbital period

Planetary obliquity generally decreases along resonances, with some cases of growth

Model successfully tested on the exoplanet HD 80606b

Abstract

In this paper, we present a formalism designed to model tidal interaction with a viscoelastic body made of Maxwell material. Our approach remains regular for any spin rate and orientation, and for any orbital configuration including high eccentricities and close encounters. The method is to integrate simultaneously the rotation and the position of the planet as well as its deformation. We provide the equations of motion both in the body frame and in the inertial frame. With this study, we generalize preexisting models to the spatial case and to arbitrary multipole orders using a formalism taken from quantum theory. We also provide the vectorial expression of the secular tidal torque expanded in Fourier series. Applying this model to close-in exoplanets, we observe that if the relaxation time is longer than the revolution period, the phase space of the system is characterized by the presence of several spin-orbit resonances, even in the circular case. As the system evolves, the planet spin can visit different spin-orbit configurations. The obliquity is decreasing along most of these resonances, but we observe a case where the planet tilt is instead growing. These conclusions derived from the secular torque are successfully tested with numerical integrations of the instantaneous equations of motion on HD 80606b. Our formalism is also well adapted to close-in super-Earths in multiplanet systems which are known to have non-zero mutual inclinations.