Analysis of Io's tidal response as a function of the properties of the partially molten layer

Abstract

Io's internal heat is generated by Jupiter-driven tidal dissipation and Laplace resonance. This energy partially melts the mantle, but the melt fraction, depth, and spatial distribution of dissipation remain poorly constrained. Tidal deformation is linked to the mantle's physical state via a parametric approach accounting for melting onset depth and latent heat of fusion. Io is modeled as a three-layer body comprising a fluid core, a viscoelastic mantle, and an elastic lithosphere. The degree-2 potential Love number k2 is computed by solving spheroidal oscillation equations with an adapted California Planetary Geophysics Code (CPGC). Mantle properties (viscosity, shear modulus, Andrade parameter beta) are iteratively updated based on the local melt fraction, and mantle compressibility is explicitly incorporated. Results show a self-consistent shallow-mantle enhancement of tidal heating. Melt presence decreases effective viscosity and increases anelasticity, amplifying upper-mantle dissipation. Reproducing the observed real part of k2 in 1D models requires melt fractions below the rheologically critical threshold. Compressibility yields higher values for the real part of k2, reinforcing this upper bound. Mass flux analysis confirms melt percolation capacity exceeds thermodynamic production, implying efficient drainage. The reference Andrade parameter beta strongly influences the imaginary Love numbers (k2, h2, l2) and the predicted libration amplitude. These constraints support a heterogeneous mantle characterized by a magmatic sponge structure rather than a global magma ocean, establishing a quantitative framework linking Io's interior, partial melting, and tidal dissipation to Juno observations.