The role of subsurface ocean dynamics and phase transitions in forming the topography of icy moons

In order to comprehend the thermo-mechanical evolution of icy moons, it is crucial to consider the interaction between the solid ice crust and the liquid water ocean. This interaction is controlled by the heat flux in the ocean and the material properties of ice. In recent years, the mass and energy exchange between the crust and the ocean has been studied using two different approaches. While the first approach (Kvorka et al., Icarus 2018) assumes that the heat flux from the ocean is governed by the internal dynamics of the ocean and is independent of the processes at the phase boundary, the other approach (e.g., Labrosse et al., J. Fluid Mech. 2018) suggests that the heat flux from the ocean is solely controlled by variations in the melting temperature along the phase boundary. Here, we present a new method for modeling the heat transfer in the interior of icy moons. Our approach is based on solving the governing equations simultaneously in the ice shell and the ocean. This enables us to capture the interaction between the global ocean circulation and the melting temperature variations arising from the deformation of the phase boundary. The method is used to study the role of ocean circulation in the formation of surface and ice-water interface topographies. Numerical simulations are performed for an icy moon whose size and internal structure are similar to those of Titan, one of the few icy satellites for which topography (the distance of the surface from the geoid) is known and its origin has been discussed in a number of studies. Our results show that the surface topography exhibits a latidutinal profile dominated by polar depressions about 500 meters deep. While this depth is less pronounced when compared to models assuming a constant melting temperature, the topography is not entirely erased as hypothesized by Kihoulou et al. (Icarus 2023) because the meridional thermal winds, which were proposed to eliminate the topography, are restrained by strong zonal flows occurring at low latitudes. Our results are in agreement with observations (Corlies et al., GRL 2017), indicating that the zonal character of surface topography found on Titan might be a common feature of icy moons with buried water oceans.