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Obliquity of the Galilean satellites: The influence of a global internal liquid layer

The obliquity of the Galilean satellites is small but not yet observed. Studies of cycloidal lineaments and strike-slip fault patterns on Europa suggest that Europa's obliquity is about 1 deg, although theoretical models of the obliquity predict the obliquity to be one order of magnitude smaller for an entirely solid Europa. Here, we investigate the influence of a global liquid layer on the obliquity of the Galilean satellites. Io most likely has a fully liquid core, while Europa, Ganymede, and Callisto are thought to have an internal global liquid water ocean beneath an external ice shell. We use a model for the obliquity based on a Cassini state model extended to the presence of an internal liquid layer and the internal gravitational and pressure torques induced by the presence of this layer. We find that the obliquity of Io only weakly depends on the different internal structure models considered, because of the weak influence of the liquid core which is therefore almost impossible to detect through observations of the obliquity. The obliquity of Europa is almost constant in time and its mean value is smaller (0.033-0.044 deg) with an ocean than without (0.055 deg). An accuracy of 0.004 deg (about 100 m on the spin pole location at the surface) would allow detecting the internal ocean. The obliquity of Ganymede and Callisto depends more on their interior structure because of the possibility of resonant amplifications for some periodic terms of the solution. Their ocean may be easily detected if, at the measuring time, the actual internal structure model lead to a very different value of the obliquity than in the solid case. A long-term monitoring of their shell obliquity would be more helpful to infer information on the shell thickness.