Modeling the polar motion of Titan

The angular momentum of the atmosphere and of the hydrocarbon lakes of Titan have a large equatorial component that can excite polar motion, a variable orientation of the rotation axis of Titan with respect to its surface. We here use the angular momentum obtained from a General Circulation Model of the atmosphere of Titan and from an Ocean Circulation Model for Titan’s polar lakes to model the polar motion of Titan as a function of the interior structure. Besides the gravitational torque exerted by Saturn on Titan’s aspherical mass distribution, the rotational model also includes torques arising due to the presence of an ocean under a thin ice shell as well as the influence of the elasticity of the different layers.
The Chandler wobble period of a solid and rigid Titan without its atmosphere is about 279 years. The period of the Chandler wobble is mainly influenced by the atmosphere of Titan (166 years) and the presence of an internal global ocean (+135 to 295 years depending on the internal model) and to a lesser extent by the elastic deformations (+3.7 years).
The forced polar motion of a solid and rigid Titan is elliptical with an amplitude of about 50 m and a main period equal to the orbital period of Saturn. It is mainly forced by the atmosphere of Titan while the lakes of Titan are at the origin of a displacement of the mean polar motion, or polar offset. The
subsurface ocean can largely increase the polar motion amplitude due to resonant amplification with a wobble free mode of Titan. The amplitudes as well as the main periods of the polar motion depend on whether and which forcing period is close to the period of a free mode. For a thick ice shell, the polar motion mainly has an annual period and an amplitude of about 1 km. For thinner ice shells, the polar motion amplitude can reach several tens of km and shorter periods become dominant. We demonstrate that for thick ice shells, the ice shell rigidity weakly influences the amplitude of the polar motion. For thin ice shells, the level of the resonant amplification of the polar motion amplitude depends on the ice shell rigidity. Future observations of the polar motion of Titan could help constraining some properties of its interior structure as the ice shell thickness and ocean density.