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

Abstract

[1] 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.

Impact of tidal heating on the onset of convection in Enceladus’s ice shell

“…In order to describe the onset of convection in a body undergoing strong tidal friction, we use a numerical tool described in Běhounková et al (2010Běhounková et al ( , 2012. This tool solves simultaneously the long-term viscous flow and the short-term viscoelastic response to a tidal forcing in a 3D spherical shell.…”

“…When the computed viscosity exceeds 10 8 Â g b (viscosity at the bottom of the ice shell), the viscosity is set to this cut-off value. The tidal deformation is recomputed every 50 convection time steps following the procedure described in detail in Běhounková et al (2010), and a convergence parameter equal to 10 À8 is used.…”

“…In particular, our goal is to understand how tidal heating, especially during periods of elevated eccentricity, may influence the onset of convection. To answer this question, we performed 3D simulations of thermal convection including a self-consistent computation of tidal dissipation using the code ANTIGONE previously described in Běhounková et al (2010Běhounková et al ( , 2012. To better simulate the mechanical properties of the ice shell, we considered a composite non-Newtonian rheology including three creep mechanisms following Durham et al (2001) and Goldsby and Kohlstedt (2001), and we defined an effective tidal viscosity reproducing the dissipation function of the Andrade model (Castillo-Rogez et al, 2011).…”

Climate Instability on Tidally Locked Exoplanets

“…These will cause spikes in equilibrium pressure. The rate of resurfacing is very sensitive to mantle composition, tidal heating, and tectonic style (Kite et al 2009;Valencia & O'Connell 2009;Korenaga 2010;Bȇhounková et al 2010Bȇhounková et al , 2011van Summeren et al 2011). Shutdown of volcanism (such that V n 0) extinguishes the possibility of a stable climate equilibrium; P will fall monotonically.…”

Coupled convection and tidal dissipation in Europa’s ice shell using non-Newtonian grain-size-sensitive (GSS) creep rheology

“…In these studies, the tidal heating (if any) was assumed to be constant or to depend only on local temperature, following the predictions of an isothermal Maxwell model with zero spatial dimensions. However, tidal dissipationat a given location depends not only on local temperature, but also on the surrounding temperature Han and Showman, 2010;Behounkova et al, 2010). Han and Showman (2010) performed the first coupled numerical simulations of convection and oscillatory tidal flexing to show that tidal heating, self-consistently calculated with the heterogeneous temperature structure, has a strong impact on thermal evolution in Europa's ice shell.…”