Ice rheology and tidal heating of Enceladus

Abstract

For the saturnian satellite Enceladus, the possible existence of a global ocean is a major issue. For the stability of an internal ocean, tidal heating is suggested as an effective heat source. However, assuming Maxwell rheology ice, it has been shown that a global scale ocean on Enceladus cannot be maintained (Roberts, J.F., Nimmo, F. [2008]. Icarus 194, 675–689). Here, we analyze tidal heating and the stability of a global ocean from the aspect of anelastic behavior. The Maxwell model is the most typical and widely used viscoelastic model. However, in the tidal frequency domain, energy is also dissipated by the anelastic response involving time-dependent or transient creep mechanisms, which is different from the viscoelastic response caused by steady-state creep. The Maxwell model cannot adequately address anelasticity, which has a large effect in the high viscosity range. Burgers and Andrade models are suggested as suitable models for the creep behavior of ice in the frequency domain. We calculate tidal heating in the ice layer and compare it with the radiated heat assuming both convection and conduction of the ice layer. Though anelastic behavior increases the heating rate, it is insufficient to maintain a global subsurface ocean if the ice layer is convecting, even though a wide parameter range is taken into account. One possibility to maintain a global ocean is that Enceladus’ ice shell is conductive and its tidal response is similar to that of the Burgers body with comparatively small transient shear modulus and viscosity. If the surface ice with large viscosity is dissipative by anelastic response, the heat produced in the ice layer would supersede the cooling rate and a subsurface ocean could be maintained without freezing.