Orbital evolution of Saturn's mid-sized moons and the tidal heating of Enceladus

TL;DR

This study uses N-body simulations to explore how Saturn's mid-sized moons evolved orbitally, highlighting the role of ring torque in avoiding resonance trapping and explaining Enceladus's high heat flow through eccentricity excitation.

Contribution

It demonstrates that ring torque can prevent resonance trapping and sustain eccentricity, providing a plausible explanation for Enceladus's observed heat flow, which previous models struggled to explain.

Findings

Ring torque influences orbital evolution, avoiding resonance trapping.

Eccentricity excitation from rings can account for Enceladus's heat.

Most simulations show potential for collision, but ring mass decrease may prevent it.

Abstract

The formation and orbital evolution of Saturn's inner mid-sized moons are still debated. The most puzzling aspects are 1) how the Tethys-Dione pair and the Mimas-Enceladus pair passed through their strong 3:2 mean-motion resonances during the tidal orbital evolution, and 2) the current strong heat flow from Enceladus, which is a few orders of magnitude higher than the tidal energy dissipation caused by the present orbital eccentricity of Enceladus. Here we perform N-body simulations of the moons' orbital evolution from various initial conditions -- assuming that the moons were formed from Saturn's hypothetical massive ring -- and investigate possible paths to solve the above difficulties. If the influence of the rings is neglected, we find that the Tethys-Dione pair cannot avoid becoming trapped in the mean-motion resonances as they recede from Saturn, and that the Tethys-Enceladus pair cannot avoid collisions after the resonance trapping, in case Saturn's quality factor is smaller than 15,000. These findings are inconsistent with the current orbital configuration. However, taking into account both the eccentricity excitation and the orbital expansion caused by the ring torque, we find that these resonance captures are avoided. With the high eccentricity pumped up by the torque, Enceladus passes through the resonances with Tethys, and the Dione-Tethys pair passes through their 2:1 and possibly the 3:2 resonance as well. After Enceladus resides beyond the 2:1 resonance with the outer ring edge, the eccentricity can be tidally damped. While this is a promising path of evolution, in most runs, Enceladus collides with Tethys by the excited eccentricity. There is a hint that a ring mass decrease could avoid the collision. The tidal heat due to the eccentricity excitation by the ring torque is stored in the moons and slowly radiated away. It may account for the current high heat flow.