DDA 2015 – Recent dynamical evolution of Mimas and Enceladus

This is one of a series of notes taken during the 2015 meeting of the AAS Division on Dynamical Astronomy, 3-7 May, at CalTech. An index to this series (all the papers presented at the meeting) is here.

Session: Moon Formation and Dynamics III

Maja Cuk (SETI Institute)


Mimas and Enceladus are the smallest and innermost mid-sized icy moons of Saturn. They are each caught in a 2:1 orbital resonance with an outer, larger moon: Mimas with Tethys, Enceladus with Dione. This is where the similarities end. Mimas is heavily cratered and appears geologically inactive, while Enceladus has a young surface and high tidal heat flow. Large free eccentricity of Mimas implies low tidal dissipation, while Enceladus appears very dissipative, likely due to an internal ocean. Their resonances are very different too. Mimas is caught in a 4:2 inclination type resonance with Tethys which involves inclinations of both moons. Enceladus is in a 2:1 resonance with Dione which affects only Enceladus’s eccentricity. The well-known controversy over the heat flow of Enceladus can be solved by invoking a faster tidal evolution rate than previously expected (Lainey et al. 2012), but other mysteries remain. It has been long known that Mimas has very low probability of being captured into the present resonance, assuming that the large resonant libration amplitude reflects sizable pre-capture inclination of Mimas. Furthermore, Enceladus seems to have avoided capture into a number of sub-resonances that should have preceded the present one. An order of magnitude increase in the rate of tidal evolution does not solve these problems. It may be the time to reconsider the dominance of tides in the establishment of these resonances, especially if the moons themselves may be relatively young. An even faster orbital evolution due to ring/disk torques can help avoid capture into smaller resonances. Additionally, past interaction of Mimas with Janus and Epimetheus produce some of the peculiarities of Mimas’ current orbit. At the meeting I will present numerical integrations that confirm the the existence of these problems, and demonstrate the proposed solutions.


  • tidal rates $\dfrac{1}{a}\dfrac{d a}{d t}$: Mimas = 59, Enceladus = 23
  • numerical integrations — brute force
    • artificial migration
    • slow
  • the trouble with Mimas
    • Mimas and Tethys in inclination-type 4:2 MMR
    • inclination of both moons affected by the resonance
    • libration amp. of resonance is large, ~100 deg $\rightarrow$ primordial Mimas inclination — doesn’t work
    • eccentricity of Tethys has complex effects
    • Mimas-Tethys evolution rate: $\dfrac{da_{moon}}{dt} \propto \dfrac{R^5_{planet}}{a^{3/2}}$
  • introduce ad hoc ring torques — artificial torque on Prometheus
    • gives Tethys resonance a kick
    • $\therefore$ don’t take Mimas-Tethys resonance too seriously
  • …more ad hoc games…
  • rings-Janus-Mimas-Enceladus-Dione system evolution is very complex

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