Resonant stratification in Titan's global ocean

Abstract

Titan's ice shell floats on top of a global ocean revealed by the large tidal Love number $k_2 = 0.616\pm0.067$ registered by Cassini. The Cassini observation exceeds the predicted $k_2$ by one order of magnitude in the absence of an ocean, and is 3-$\sigma$ away from the predicted $k_2$ if the ocean is pure water resting on top of a rigid ocean floor. Previous studies demonstrate that an ocean heavily enriched in salts (salinity $S\gtrsim200$ g/kg) can explain the 3-$\sigma$ signal in $k_2$. Here we revisit previous interpretations of Titan's large $k_2$ using simple physical arguments and propose a new interpretation based on the dynamic tidal response of a stably stratified ocean in resonance with eccentricity tides raised by Saturn. Our models include inertial effects from a full consideration of the Coriolis force and the radial stratification of the ocean, typically neglected or approximated elsewhere. The stratification of the ocean emerges from a salinity profile where salt concentration linearly increases with depth. We find multiple salinity profiles that lead to the $k_2$ required by Cassini. In contrast with previous interpretations that neglect stratification, resonant stratification reduces the bulk salinity required by observations by an order of magnitude, reaching a salinity for Titan's ocean that is compatible with that of Earth's oceans and close to Enceladus' plumes. Consequently, no special process is required to enrich Titan's ocean to a high salinity as previously suggested.