Recent orbital evolution and the internal structures of Enceladus and Dione

We study the orbital behavior of Saturn’s satellites Enceladus and Dione during their passage through the 2:1 mean-motion resonances to constrain their interior structures, parameterized by the quantity k 2 / Q (assumed constant). Enceladus’ evolution after escape from the second-order e-Enceladus e-Dione resonance requires that ( k 2 / Q ) Enceladus < 8 × 10 - 4 , for that Q Saturn > 18 , 000 . This result is in agreement with [Meyer, J., Wisdom, J., 2008b. Icarus 193, 213–223]. The present-day libration amplitude of Enceladus requires that ( k 2 / Q ) Enceladus > 1.2 × 10 - 4 , assuming that Q Saturn < 10 5 . Dione’s present-day eccentricity indicates that ( k 2 / Q ) Dione ⩽ 3 × 10 - 4 for Q Saturn > 18 , 000 . Assuming Maxwellian viscoelastic behavior, we find that for Enceladus a convective ice shell overlying an ocean is too dissipative to match the orbital constraints. We conclude that a conductive shell overlying an ocean is more likely, and discuss the implications of this result. Dione’s ice shell is also likely to be conductive, but our results are less constraining.