A Simplified Model for the Forced Libration of Icy Moons with Subsurface Oceans: Application to Enceladus and Mimas

TL;DR

The paper develops a concise two-layer viscoelastic framework (prestressed icy crust over an effective fluid core) to reproduce forced longitudinal librations and diagnose subsurface oceans. By deriving the rotational dynamics from a Lagrangian with a gravitational spring, Maxwell prestress, and Rayleigh dissipation, it links observed librations to interior properties and core-mantle coupling. Applied to Enceladus and Mimas with Cassini data, the model reproduces observed librations and identifies crustal thicknesses around ~22 km for Enceladus and ~28 km for Mimas, while revealing resonant behavior and comparable dissipation scales (~2 GW) that imply additional heating from oceans or cores not captured in the simplified framework. The approach offers a rapid, first-pass diagnostic tool for ocean detection and interior characterization, particularly useful for mission planning, though it cannot unambiguously distinguish oceans from deep fluid cores and requires complementary geophysical constraints to resolve parameter degeneracies.

Abstract

We investigate a simple two-layered viscoelastic rheological model capable of replicating the forced librations of an icy moon with a subsurface ocean. We show that the model, composed only of a prestressed icy crust lying over an effective fluid core (a fixed mantle cavity), can effectively describe the librational behavior of icy moons, thus holding the potential to predict the presence of a subsurface ocean through the analysis of longitudinal librations. The proposed model is applied to the longitudinal librations of Enceladus and Mimas, two small icy moons of Saturn for which relevant data is available from the Cassini mission.

Figures (11)

• Figure 1: Three possible internal structures for icy satellites.
• Figure 2: Mantle rheological model. The spring $\gamma$ represents the effect of gravity. The damper $\eta$ and the Maxwell element $(\mu_0, \eta_0)$ represent the effect of the macroscopic (spatial average) rheology of the mantle; $\varepsilon$, $\varepsilon_0$ and $\tilde{\varepsilon}_0$ denote strains and $\sigma$ the stress.
• Figure 3: Amplitude of Enceladus's longitudinal libration (in degrees) as a function of ice shell thickness.
• Figure 4: Amplitude of Enceladus's longitudinal libration (in degrees) as a function of ice shell thickness. The red line with dots stands for the shell libration and the blue line with squares for the librations of bodies Tisserand frame. The thin hatched (line-like) interval shows the measured libration amplitude with the uncertainty.
• Figure 5: Amplitude of Enceladus's longitudinal libration (in degrees) as a function of ice shell thickness for three values of the prestress-elastic constant. The thin hatched (line-like) interval shows the measured libration amplitude with the uncertainty.