Implications of Shallow‐Shell Models for Topographic Relaxation on Icy Satellites

Abstract Icy satellites host topography at many length scales, from rifts and craters on the small end to equatorial‐pole shell thickness differences that are comparable to these bodies' circumference. The current paradigm is that icy satellites should not host stable small‐scale topography. This idea comes from previous work using a “shallow”‐shell model (i.e., ice shell circumference much larger than shell thickness) with a rigid outer crust. In this limit, large‐scale topography relaxes over a longer time scale than small‐scale features. Here we revisit this paradigm and analyze relaxation of topography starting from the Stokes equations for viscous fluid flow. For a shell with a viscosity that decreases exponentially with depth, we show numerically that there is a regime where the larger viscosity outer crust acts as a nearly rigid boundary. In this case, the relaxation time scale depends on the wavelength. For the largest spatial scales, however, the time scale becomes independent of wavelength and the value is set by the average shell viscosity. However, the spatial scale that this transition occurs at becomes larger as the viscosity contrast increases, limiting the applicability of the scale‐independent relaxation rate. These results for the relaxation of topography have implications for interpreting relaxed crater profiles, inferences of ice shell thickness from topography, and upcoming observations from missions to the outer solar system.