Titan’s internal structure inferred from its gravity field, shape, and rotation state

Abstract

Several quantities measured by the Cassini-Huygens mission provide insight into the interior of Titan: the second-degree gravity field coefficients, the shape, the tidal Love number, the electric field, and the orientation of its rotation axis. The measured obliquity and tides, as well as the electric field, are evidence for the presence of an internal global ocean beneath the icy shell of Titan. Here we use these different observations together to constrain the density profile assuming a four-layer interior model (ice I shell, liquid water ocean, high pressure ice mantle, and rock core). Even though the observed second degree gravity field is consistent with the hydrostatic relation J2=10C22/3, which is a necessary but not sufficient condition for a synchronous satellite to be in hydrostatic equilibrium, the observed shape of the surface as well as the non-zero degree-three gravity signal indicate some departure from hydrostaticity. Therefore, we do not restrain our range of assumed density profiles to those corresponding to the hydrostatic value of the moment of inertia (0.34). From a range of density profiles consistent with the radius and mass of the satellite, we compute the obliquity of the Cassini state and the tidal Love number k2. The obliquity is computed from a Cassini state model for a satellite with an internal liquid layer, each layer having an ellipsoidal shape consistent with the measured surface shape and gravity field. The observed (nearly hydrostatic) gravity field is obtained by an additional deflection of the ocean–ice I shell interface, assuming that the layers have uniform densities. We show that the measured obliquity can be reproduced only for internal models with a dense ocean (between 1275 and 1350kgm−3) above a differentiated interior with a full separation of rock and ice. We obtain normalized moments of inertia between 0.31 and 0.33, significantly lower than the expected hydrostatic value (0.34). Evolutionary mechanisms leading to a significant departure from hydrostatic equilibrium while J2=10C22/3 remain an open issue. The tidal Love number is found to be mostly sensitive to the ocean density and to a lesser extent to the ice shell thickness. By combining obliquity and tidal Love number constraints, we show that the thickness of the outer ice shell is at least 40km and the ocean thickness is less than 100km, with an averaged density of 1300–1350kgm−3. The elevated density (>3400kgm−3) found for the rocky core further suggests that it might possess a significant fraction of iron.