Poro-viscoelastic Tidal Heating of Io

Io’s tidally driven global volcanism indicates widespread partial melting in its mantle. The role this melt plays in tidal dissipation is poorly understood. We model Io’s tidal deformation by treating its upper mantle as a two-phase (solid and melt) system. By combining poro-viscous and poro-elastic compaction theories in a Maxwell viscoelastic framework into the classic equations of tidal deformation and self-gravitation, we produce the first self-consistent evaluation of Io’s tidal heating rate due to deformation arising from shearing, compaction, and Darcy flow.

We find that Darcy dissipation—viscous dissipation as melt flows through pore space—can potentially exceed the shear heating rate, but only for melt fractions of 5–20%, and if the grain size is large or melt viscosity ultra-low. Since grain sizes larger than 1 cm are unlikely, this suggests that Darcy dissipation is secondary to shear dissipation. Compaction dissipation is maximized when the asthenosphere is highly resistive to isotropic (compaction) stresses, but contributes at most 1% of Io’s observed heating rate. This work represents a crucial step toward a self-consistent quantitative theory for the tidal dynamics of Io’s partially molten interior, and the inevitable feedback between tidal heating and melt generation.