Resonant Stratification in Titan’s Global Ocean

Abstract

Titan’s ice shell floats on top of a global ocean, as revealed by the large tidal Love number k _2 = 0.616 ± 0.067 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 σ 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 ≳ 200 g kg ^−1 ) can explain the 3 σ 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 the 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.

Keywords

• Titan
• Saturnian satellites
• Ocean tides
• Gravitational fields
• Planetary interior
• Astrophysical fluid dynamics