The Saturnian satellite Titan is one of the main targets of the Cassini-Huygens mission, which revealed in particular Titan's shape, gravity field, and rotation state. The shape and gravity field suggest that Titan is not in hydrostatic equilibrium, that it has a global subsurface ocean, and that its ice shell is both rigid (at tidal periods) and of variable thickness. The rotational state of Titan consists of an expected synchronous rotation rate and an unexpectedly high obliquity (0.3○) explained by Baland et al. (2011) to be a resonant behavior. We here combine a realistic model of the ice shell and interior and a 6-degrees of freedom rotational model, in which the librations, obliquity and polar motion of the rigid core and of the shell are modelled, to constrain the structure of Titan from the observations. We consider the gravitational pull of Saturn on the 2 rigid layers, the gravitational coupling between them, and the pressure coupling at the liquid-solid interfaces.
We confirm the influence of the resonance found by Baland et al., that affects between 10 and 13% of the possible Titans. It is due to the 29.5-year periodic annual forcing. The resonant Titans can be obtained in situations in which a mass anomaly at the shell-ocean boundary (bottom loading) is from 80 to 92% compensated. This suggests a 250 to 280 km thick ocean below a 130 to 140 km thick shell, and is consistent with the degree-3 analysis of Hemingway 26 et al. (2013).