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

¹ Departamento de Física, I3N, Universidade de Aveiro, Campus de Santiago, 3810-193 Aveiro, Portugal
e-mail: correia@ua.pt
² ASD, IMCCE-CNRS UMR8028, Observatoire de Paris, UPMC, 77 Av. Denfert-Rochereau, 75014 Paris, France
³ Instituto de Geociências e Ciências Exatas, UNESP, Av. 24-A 1515, CEP 13506-900, Rio Claro, SP, Brazil

Received: 14 May 2014
Accepted: 24 September 2014

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.