Does Titan's long-wavelength topography contain information about subsurface ocean dynamics?

The long-wavelength topography of Titan is characterized by relatively small amplitudes (about 1 km peak to peak), an anomalous equatorial bulge (the poles are about 300 m lower than the equator), and small gravity anomalies, indicating a high degree of compensation. In the past years, the nature of Titan's non-hydrostatic topography has been addressed in several studies. The topography has been interpreted in terms of isostatic or viscous models and discussed in connection with tidal heating in the ice shell and surface erosion. Here, we present a model of the shape evolution of Titan's ice shell driven by tidal heating in the shell and spatial variations of the heat flux from a subsurface ocean. The model is obtained by solving a general set of equations coupling the viscoelastic flow of ice with the thermal evolution of the ice shell and phase transitions at the ice/water interface. The equations are solved in a domain with radially varying material properties and moving boundaries. The motion of the boundaries is a consequence of ice flow within the shell, melting and crystallization at the bottom boundary and erosion and deposition at the surface. Our model suggests that Titan's anomalous topographic bulge can be explained by lateral variations of ocean heat flux of the order of 0.1-1 mW m−2, provided that the heat flux is stable over a period of at least 10 Myr and the ice shell has a sufficiently high viscosity, exceeding 1016 Pa s at the base of the shell. Such a high value of viscosity implies that either the ice grains are coarse ( ≳ 10 mm) or the temperature of the ocean is significantly (by more than 40 K) lower than the melting temperature of pure water ice. The heat flux pattern predicted on top of the ocean is consistent with a flow characterized by upwelling of warm water in polar regions and downwelling of cold water at low latitudes. The negative correlation between the topography and geoid at degree 3 reported in a previous study (but not confirmed at higher degrees yet) is shown to be compatible with erosion and deposition occurring at a rate of 0.01-0.1 mm yr−1. Our results underline the importance of gravity and topography measurements for understanding Titan's surface and deep interior processes.