Tidal evolution of Mimas, Enceladus, and Dione

The tidal evolution through several resonances involving Mimas, Enceladus, and/or Dione is studied numerically with an averaged resonance model. We find that, in the Enceladus–Dione 2:1 e-Enceladus type resonance, Enceladus evolves chaotically in the future for some values of k 2 / Q . Past evolution of the system is marked by temporary capture into the Enceladus–Dione 4:2 e e ′ -mixed resonance. We find that the free libration of the Enceladus–Dione 2:1 e-Enceladus resonance angle of 1.5° can be explained by a recent passage of the system through a secondary resonance. In simulations with passage through the secondary resonance, the system enters the current Enceladus–Dione resonance close to tidal equilibrium and thus the equilibrium value of tidal heating of 1.1 ( 18 , 000 / Q S ) GW applies. We find that the current anomalously large eccentricity of Mimas can be explained by passage through several past resonances. In all cases, escape from the resonance occurs by unstable growth of the libration angle, sometimes with the help of a secondary resonance. Explanation of the current eccentricity of Mimas by evolution through these resonances implies that the Q of Saturn is below 100,000. Though the eccentricity of Enceladus can be excited to moderate values by capture in the Mimas–Enceladus 3:2 e-Enceladus resonance, the libration amplitude damps and the system does not escape. Thus past occupancy of this resonance and consequent tidal heating of Enceladus is excluded. The construction of a coherent history places constraints on the allowed values of k 2 / Q for the satellites.