Tidal Dissipation in a Partially Molten Asthenosphere on Io

The rocky Jovian moon, Io, exhibits global volcanism that is driven by heat dissipated by tidal deformation. The large rate of heat exported by this volcanism, in conjunction with evidence in the form of magnetic induction, suggests that the mantle may contain a significant fraction of partial melt. This melt may be present in regions where both solid and liquid coexist at the macroscale. Nevertheless, existing models to investigate the location and magnitude of tidal heating consider an internal structure consisting of layers of pure solid or liquid. Such models are not appropriate for tidal deformation of partially molten materials. Building upon recent advancements in the theory of gravitational poroviscoelastic dynamics, we model tidal heating within Io, taking into account the effect of a two-phase, partially molten asthenosphere. 

The solid regions are modelled as a Maxwell viscoelastic material, and the top and bottom of the asthenosphere are treated as impermeable boundaries. We find that tidal dissipation within the fluid-filled pores depends on the ratio of the asthenosphere’s permeability to the melt’s viscosity. Thus, a low-viscosity melt and highly permeable pore-network favour enhanced tidal dissipation within the fluid. When this ratio, representing the Darcy drag, is large enough, fluid dissipation can exceed that within the solid grains when solid viscosity is high (> 10¹⁷ Pa s) or ultra-low (< 10¹¹ Pa s). Tidal dissipation by the pore-hosted melt exhibits its own distinct tidal heating pattern, which always produces enhanced heating towards low latitudes.