The Anelastic Equilibrium Tide in Giant Planets

International audienceOnce a planetary system is formed, its dynamical evolution is governed by gravitational interactions between its components, be it a star-planet or planet-satellite interaction. By converting kinetic energy into heat, the tides pertub their orbital and rotational properties. The rate at which the system evolves depends on the physical properties of tidal dissipation. Therefore, to understand the past history and predict the fate of a binary system, one has to identify the dissipative processes that achieve this conversion of energy. Planetary systems display a large diversity of planets by their composition. Since tidal mechanism is closely related with the internal structure of the perturbed body, one has to investigate its effects on either its fluid and solid layers. Studies have been carried out on tidal effects in fluid bodies such as stars and envelopes of giant planets. However, the planetary solid regions may also contribute to tidal dissipation, be it the mantles of Earth-like planets that have been investigated by many works, or the cores of giant planets. The purpose of our study is to determine the tidal dissipation in the solid central regions of giant planets, taking into account the presence of a fluid envelope. We derive the different Love numbers that describe the anelastic deformation and discuss the dependence of the quality factor Q on the rheological parameters and the size of the core. Taking plausible values for these parameters, and discussing the frequency-dependence of the solid dissipation, we show how this mechanism may compete with the dissipation in fluid layers, when applied to Jupiter- and Saturn-like planets. We also discuss the case of the icy giants Uranus and Neptune. Finally, we present the way to implement the results in the equations that describe the dynamical evolution of planetary systems