Matching of Models of the Internal Structure and Thermal Regime of Partially Differentiated Titan with Gravity Field

Abstract

The problem of matching models of the internal structure of partially differentiated Titan with experimentally measured values of Love number k2 (Iess et al., 2012; Durante et al., 2019) according to results of studying the gravity field of Titan based on flights of the Cassini spacecraft is discussed. The values of k2 obtained presumably point to the presence of large masses of liquid (ocean) in the interior of Titan. However, there are no reliable data about the thickness of the outer ice crust and internal (underice) ocean. In this work, constraints on the heat flow, structure of the water-ice shell, and composition of the Titan ocean which are necessary for matching the calculated (model) and experimental Love numbers are considered. The energy release due to ice crystallization in the ocean is estimated. Estimates for the model Love numbers and maximal surface heat flows for the L/LL chondritic composition of the rock–iron component of Titan are obtained with allowance for the radiogenic energy, as well as for the energy of ice crystallization in the ocean due to the satellite cooling: F ~ 5.8 mW/m2, k2 = 0.53, the thickness of the ice Ih shell $${{H}_{{{{{\text{I}}}_{h}}}}}$$ ~ 100 km, and the ocean depth HW ~ 280 km. Model Love numbers k2 agree with experimental ones (Iess et al., 2012) in the presence of the ocean. To match the model (k2 ≥ 0.55) and recently refined values of Love numbers (k2)D = 0.616 ± 0.067 (Durante et al., 2019), it is necessary to satisfy the constraints on the magnitude of the surface heat flow F ≥ 6.3 mW/m2, which corresponds to a water ocean thickness HW ≥ 310 km under the ice Ih shell with a thickness $${{H}_{{{{{\text{I}}}_{h}}}}}$$ ≤ 90 km. The effect of heat flow variations, ice crust thickness, and water–ammonia ocean density on model values of Love numbers is analyzed and the negligible influence of the NH3 admixture in the ocean on the k2 value is demonstrated. The moment of inertia for models of partially differentiated Titan has constraints: I* ≤ 0.342 at k2 ≥ 0.56.