Interior structure models, tidal dissipation, and thermal evolution of Titan: A prospective study for Dragonfly

Despite being comparable in size and mass, the largest moons in the Solar System—Jupiter’s moons Ganymede and Callisto, and Saturn’s moon Titan—exhibit contrasting surface characteristics and varying degrees of internal differentiation, suggesting distinct evolutionary paths. Future geophysical measurements from the upcoming Dragonfly mission (Charnay et al., 2022; Delaroche et al., 2026) will be essential for determining the structure of Titan’s hydrosphere, constraining its thermal state and degree of differentiation, and understanding its origin and evolution.

 

The hydrosphere structure is modeled using the SeaFreeze Python library (Journaux et al., 2020), which provides thermodynamic and elastic properties of water and various ice polymorphs over a wide range of temperatures and pressures. The library also includes similar properties for aqueous NaCl solutions. When integrating the mass, pressure, and temperature equations throughout the hydrosphere, we obtain the necessary properties at each depth using this package.

 

To construct realistic hydrosphere models, it is important to accurately represent the thermal and rheological state of the outer ice shell, as both seismic and tidal deformation measurements are primarily sensitive to this layer. In our models, the outer ice shell consists of pure ice I and, depending on its thickness and the assumed viscosity values, may be either fully conductive or partially convective. To determine the appropriate temperature profile and the relative proportions of conductive and convective layers, we apply scaling laws from Dumoulin et al. (1999), Deschamps and Sotin (2000), and Tobie et al. (2003). The main parameters in our ice shell models are the total shell thickness and the reference viscosity at the melting point, which together determine a corresponding surface heat flux that must be consistent with the available heat sources (radiogenic and tidal). The adopted surface temperature, thermal conductivity, and ocean composition also influence the thermal structure of the ice shell.

 

The ocean is modeled as an aqueous NaCl solution with varying concentrations, and its thermodynamic properties at each pressure and temperature are determined using the SeaFreeze package. The NaCl concentration influences the ice–water phase transition, as well as the ocean’s density and electrical conductivity. The ocean is assumed to follow an adiabatic temperature profile, while the underlying high-pressure ice layer is modeled using various thermal structure scenarios.

 

The deep interior of Titan is modeled with an outer hydrated and/or carbon rich silicate mantle characterized by lower density and weaker mechanical properties and a denser rocky core. For each hydrosphere model, we explore all combinations of radii and densities for the interior layers that produce moments of inertia consistent with observational constraints. Density within each layer increases with depth according to the Adams–Williamson equation. For each deep interior model, we also vary the elastic moduli and viscosity of the interior layers.

 

When computing tidal deformation, it is crucial to properly account for anelasticity. In this work, we adopt Andrade rheology, following the approach described by Amorim and Gudkova (2025). The tidal Love numbers for each model are computed using an algorithm similar to that of Amorim and Gudkova (2024), but with some improvements regarding the governing equations and boundary conditions.

 

We generate millions of interior structure models by varying all relevant parameters that describe Titan’s hydrosphere and deep interior. We compute the tidal Love numbers, which characterize the gravitational potential perturbations, surface displacements, and surface pressure variations caused by tidal forces, along with their associated phase lags and tidal dissipation. Based on the available radiogenic and tidal heating, we assess the most likely present-day hydrosphere structure and how it may have evolved since the moon’s formation.