Modelling the Feedback of Io’s Tidally Induced Heterogeneous Interior on Tidal Dissipation

Undergoing extreme tidal dissipation, Io serves as an archetype of tidally heated rocky exoplanets and exomoons. Therefore, understanding Io’s dissipative processes and their interactions with Io's interior provides insights into the evolution of these tidally heated bodies. Tidal dissipation depends on Io’s rheological structure and is thought to be radially and laterally non-uniformly distributed within Io’s interior. We explore whether the heterogeneous nature of tidal heating causes regional variations of Io's temperature-dependent melt fraction and rheology. Furthermore, we investigate to which extent these regional variations in turn change Io’s tidal dissipation pattern. To study the spatial effect of the heterogeneous heat production on Io's interior structure we developed a model that couples Io's non-uniform heating pattern with Io's main heat transport mechanisms [1]. The initial tidal heating pattern is calculated from a 1-dimensional rheological structure. From the resulting temperature and melt distribution we derive the regionally varying viscosity and rigidity structure. In a second step, we use a finite-element model to re-calculate Io’s tidal dissipation pattern using the updated tidally induced three-dimensional viscosity and rigidity distribution. Our results reveal that for models with a magma-dominating heat transport peak-to-peak variations in the global temperature field of up to 190 K arise. However, for models with a convection-dominating heat transport and low reference viscosities of the convective layer, variations are fully damped. In particular for models with strong tidally-induced lateral variations, the newly obtained dissipation patterns strongly differ from the initial dissipation patterns resulting from 1-dimensional structures. The updated patterns show asymmetric contributions towards the 0°/180°W/E plane and contain additional spherical components with degrees > 4. Our results show that three-dimensional structures are inevitable for bodies with strong tidal dissipation, and 3D modelling approaches for the computation of thermal heat transport and tidal dissipation are necessary. [1] Steinke, T., et al.,2019, Icarus, Tidally induced lateral variations of Io's interior.