The forced libration of Europa's deformable shell and its dependence on interior parameters

One of the most important goals of future missions to jovian moon Europa will be to unambiguously determine and characterize the putative subsurface ocean, as well as characterizing the overlying ice shell. In addition to magnetic, altimetry and gravity measurements, observations of Europa's librations are expected to contribute to the realization of such an important goal. The longitudinal libration of Europa's shell in the presence of a subsurface ocean has been previously studied assuming that Europa's internal solid layers behave rigidly. However, at the frequency of the acting diurnal tides and external gravitational torques, the response of Europa's interior is not rigid but rather viscoelastic. In this paper, we develop a differential libration model that takes into account the effect of diurnal deformation on the forced longitudinal libration of Europa's internal solid layers. We apply our libration model to a rather large range of possible interior models of Europa to investigate the dependence of the shell libration amplitude on the geophysical parameters that characterize the interior of Europa, in particular the shell. From all analyzed interior parameters, we find that the poorly constrained rigidity of the shell has the largest effect on the libration amplitude. This results suggests thus that future libration observations could be very useful to constrain the value of this parameter for Europa. However, we also notice that the effect of the viscosity of a dissipating ice sublayer at the bottom of the shell (if present) on the libration amplitude of the shell would not allow for an unambiguous determination of the shell rigidity. Furthermore, the dependence of the shell libration amplitude on the shell thickness and density is rigidity-dependent and weak in comparison to the dependence on the rigidity. As a result, libration observations would not be able to provide any information on the thickness and/or density of the shell without previous determination of the rigidity.