Coupling mantle convection and tidal dissipation: Applications to Enceladus and Earth-like planets

Abstract

Anelastic dissipation of tidal forces likely contributes to the thermal budget of several satellites of giant planets and Earth-like planets closely orbiting other stars. In order to address how tidal heating influences the thermal evolution of such bodies, we describe here a new numerical tool that solves simultaneously mantle convection and tidal dissipation in a three-dimensional spherical geometry. Since the two processes occur at different timescales, tidal dissipation averaged over a forcing period is included as a volumetric heat source for mantle dynamics. For the long-term flow, a purely viscous material is considered, whereas a Maxwell-like formalism is employed for the tidal viscoelastic problem. Due to the strongly temperature dependent rheological properties of both mechanisms, the coupling is achieved via the temperature field. The model is applied to two examples: Enceladus and an Earth-like planet. For Enceladus, our new 3-D method shows that the tidal strain rates are strongly enhanced in hot upwellings when compared with classical methods. Moreover, the heat flux at the base of Enceladus' ice shell is strongly reduced at the poles, thus favoring the preservation of a liquid reservoir at depth. For Earth-like planets, tidal dissipation patterns are predicted for different orbital configuration. Thermal runaway is observed for orbital periods smaller than a critical value (e.g., 30 days for an eccentricity of 0.2 and 3:2 resonance). This is likely to promote large-scale melting of the mantle and Io-like volcanism. Copyright 2010 by the American Geophysical Union.