Enceladus's Limit Cycle

Abstract: Enceladus exhibits some remarkable phenomena, including water geysers spraying through surface cracks, a global ice shell that is librating atop an ocean, a large luminosity, and rapid outward orbital migration. Here we model the coupled evolution of Enceladus's orbit and interior structure. We find that Enceladus is driven into a periodic state: a limit cycle. Enceladus's observed phenomena emerge from the model, and the predicted values for the orbital eccentricity, libration amplitude, shell thickness, and luminosity agree with observations. A single limit cycle lasts around ten million years, and has three distinct stages: (1) freezing, (2) melting, and (3) resonant libration. Enceladus is currently in the freezing stage, meaning that its ice shell is getting thicker. That pressurizes the ocean, which in turn cracks the shell and pushes water up through the cracks. In this stage the orbital eccentricity increases, as Saturn pushes Enceladus deeper into resonance with Dione. Once the eccentricity is sufficiently high, tidal heating begins to melt the shell, which is the second stage of the cycle. In the third stage the shell remains close to 3km thick. At that thickness the shell's natural libration frequency is resonant with the orbital frequency. The shell's librations are consequently driven to large amplitude, for millions of years. Most of the tidal heating of Enceladus occurs during this stage, and the observed luminosity is a relic from the last episode of resonant libration.