Tidal synchronization of close-in satellites and exoplanets. III. Tidal dissipation revisited and application to Enceladus

Abstract

This paper deals with a new formulation of the creep tide theory (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 116}, 109, 2013 $-$ Paper I) and with the tidal dissipation predicted by the theory in the case of stiff bodies whose rotation is not synchronous but is oscillating around the synchronous state with a period equal to the orbital period. We show that the tidally forced libration influences the amount of energy dissipated in the body and the average perturbation of the orbital elements. This influence depends on the libration amplitude and is generally neglected in the study of planetary satellites. However, they may be responsible for a 27 percent increase in the dissipation of Enceladus. The relaxation factor necessary to explain the observed dissipation of Enceladus ($\gamma=1.2-3.8\times 10^{-7}\ {\rm s}^{-1}$) has the expected order of magnitude for planetary satellites and corresponds to the viscosity $0.6-1.9 \times 10^{14}$ Pa s, which is in reasonable agreement with the value recently estimated by Efroimsky (2018) ($0.24 \times 10^{14}$ Pa s) and with the value adopted by Roberts and Nimmo (2008) for the viscosity of the ice shell ($10^{13}-10^{14}$ Pa s). For comparison purposes, the results are extended also to the case of Mimas and are consistent with the negligible dissipation and the absence of observed tectonic activity. The corrections of some mistakes and typos of paper II (Ferraz-Mello, Cel. Mech. Dyn. Astron. {\bf 122}, 359, 2015) are included at the end of the paper.