Interior structure models and tidal Love numbers of Ganymede, Callisto and Titan: A prospective study for JUICE and 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 geological evolution paths. Characterizing their interior structure and thermal state is crucial for understanding the origin, evolution, and potential habitability of their subsurface oceans. Future geophysical measurements, including tidal monitoring and magnetic induction from the upcoming JUICE and Dragonfly missions (Van Hoolst et al., 2024; Charnay et al., 2022), will be essential for determining the structure of their hydrospheres and constraining their thermal state and degree of differentiation.

 

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 data from this Python package.

 

In our models, the outer ice shell consists primarily of pure ice I and includes an upper crust with different thermodynamic properties (reduced strength and low conductivity). Depending on its thickness and the assumed viscosity values, the shell 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, the crust thickness and the reference viscosity at the melting point. The adopted surface temperature, thermal conductivity, and ocean composition also influence the ice shell thermal structure.

 

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 possibility of using implementing ocean induction constraints such as Jia et al. (2025) in our hydrosphere models is also discussed.

 

The interiors of the moons are modeled with either two or three distinct layers. For Ganymede, the interior consists of a silicate mantle and a liquid iron core, with or without a solid inner core. For Titan and Callisto, we assume an outer hydrated silicate mantle (characterized by low density) and a denser inner rocky core. The presence of a significant fraction of carbon in the form of graphite is also considered. 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 adopted 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.

 

For each moon, we generate tens of thousands of interior structure models by varying all relevant parameters that describe their hydrosphere and deep interior. We compute the tidal Love numbers k2 and h2, which characterize the gravitational potential perturbation and surface displacement caused by tidal forces, respectively, along with their associated phase lags. In particular, we investigate the influence of the ice shell thickness, ocean properties, and the thermal state of both the ice I and high-pressure ice layers on the amplitude and phase lag of the Love numbers. We also assess how these quantities may be constrained by future observations from the JUICE and Dragonfly missions.