Abstract
The majority of confirmed terrestrial exoplanets orbits close to their host stars and their evolution was likely altered by tidal interaction. Nevertheless, due to their viscoelastic properties on the tidal frequencies, their response cannot be described exactly by standardly employed constant-lag models.We therefore introduce a tidal model based on the numerical evaluation of a continuum mechanics problem describing the deformation of viscoelastic (Maxwell or Andrade) planetary mantles subjected to external force.
We apply the method on amodel Earth-size planet orbiting a low-mass star and study the effect of the orbital eccentricity, the mantle viscosity and the chosen rheology on the tidal dissipation, the complex Love numbers and the tidal torque. The number of stable spin states (i.e., zero tidal torque) grows with increasing mantle viscosity, similarly to the analytical model of Correia et al. (Astron Astrophys 571:A50, 2014) for homogeneous bodies.
This behavior is only slightly influenced by the rheology used. Similarly, the Love numbers do not distinctly depend on the considered rheological model.
The increase in viscosity affects the amplitude of their variations. The tidal heating described by the Maxwell rheology attains local minima associated with low spin-orbit resonances, with depth and shape depending on both the eccentricity and the viscosity.
For the Andrade rheology, the minima at low resonances are very shallow and the tidal heating for all viscosities resembles a "fluid limit." The tidal heating is the quantity influenced the most by the rheology, having thus possible impact on the internal thermal evolution.