Tidal dissipation in Enceladus' uneven, fractured ice shell

Analysis of Enceladus’ gravity, topography and libration data suggests that the thickness of the ice crust significantly varies, which may have important consequences for the heat transfer across and the tidal dissipation within the ice shell. Understanding these processes is a critical prerequisite for analyzing Enceladus’ thermal evolution and assessing the long-term stability of its subsurface ocean. Here, we investigate the impact of ice shell thickness variations on the tidal deformation of the moon and the associated heat production using a finite-element model that includes faults (“tiger stripes”) in the south polar region (SPR). Since the tidal deformation and the thermal structure of the ice shell are coupled through temperature and deviatoric stress, we simultaneously solve the equations governing the anelastic deformation of ice and also equations which model conductive heat transfer in the ice shell. We find that tidal heating is concentrated in a narrow low viscosity zone near the base of the ice shell and along faults. Outside the SPR, the thickness of this zone is about 1/10 of the local ice thickness and the associated volumetric heating is ≲ 1 0 − 6 W/m 3 , corresponding to less than 1 GW of dissipated power. In the SPR, the tidal effects are enhanced by the combined action of faults and ice shell thinning. Although the volumetric heating in this relatively small region may be larger than 10 −4 W/m 3 , the total heat production in this region does not exceed 1.1 GW. Our computations show that tidal heating in the ice shell can explain only a small fraction of Enceladus’ heat production derived from astrometric observations, implying that Enceladus’ heat engine is powered by dissipation in the core or in the ocean.