A test for Io's magma ocean: Modeling tidal dissipation with a partially molten mantle

Magnetic induction measurements and astrometry provide constraints on the internal structure of Io, a volcanically active moon of Jupiter. We model the tidal response of a partially molten Io using an Andrade rheology which is supported by silicate deformation experiments. This model uses material properties similar to the Earth's mantle and includes feedbacks between partial melting, tidal heat production, and melt transport. We are able to satisfy constraints provided by the measured imaginary part of the tidal Love number Im(k(2)), the inferred depth and melt fraction of a near-surface partially molten layer, and the observed equatorial concentration of volcanic landforms. We predict a value for the real part of the tidal Love number of Re(k(2)) = 0.09 +/- 0.02, much smaller than the value of Re(k(2)) approximate to 0.5 predicted for an Io with a fluid magma ocean. Future spacecraft observations should be able to measure this value and test which model is correct.