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

Context. Io’s internal heat, generated by Jupiter-driven tidal dissipation and the Laplace resonance, partially melts the mantle. However, the resulting melt fraction, depth, and spatial distribution of dissipation remain poorly constrained. Aims. We use Io’s tidal response to constrain its internal structure, focusing on partial melt distribution and dissipation mechanisms. We link the observed tidal deformation to the mantle physical state through a parametric approach accounting for melting onset depth and latent heat of fusion. Methods. We modeled Io as a three-layer body with a fluid core, a viscoelastic mantle, and an elastic lithosphere. The degree-2 potential Love number k2 was computed by solving spheroidal oscillation equations with an adapted California Planetary Geophysics Code (CPGC).We iteratively updated the mantle properties, viscosity, shear modulus, and the Andrade parameter (beta) based on the local melt fraction (phi(r)). Moving beyond state-of-the-art models, we explicitly incorporated mantle compressibility into our framework. Results. Within the adopted rheological framework, reproducing the observed Re(k2) requires melt fractions below the rheologically critical melt fraction. Our analysis indicates that a limited mantle enhancement in tidal dissipation emerges naturally, although the deep mantle is the primary region of tidal heating. The presence of melt reduces the e ective viscosity and increases anelasticity, enhancing tidal dissipation in the upper mantle. Incompressible models provide conservative upper bounds on the melt fraction, whereas compressible models yield slightly higher values of Re(k2), strengthening this interpretation. An a posteriori mass-flux analysis showed that melt percolation capacity exceeds the thermodynamic production rate, indicating e cient drainage. The reference Andrade parameter  beta0 strongly a ects the imaginary components of the Love numbers (k2, h2, l2) and the predicted libration amplitude. Conclusions. These combined constraints support a heterogeneous, partially molten mantle characterized by a "magmatic sponge" structure rather than a global magma ocean. The proposed framework links Io’s internal structure and tidal dissipation to recent observations from the Juno mission.