Tracking Deep Mantle Melting on Mars Using Phobos Tides

We study the deep internal structure and rheological state of Mars by analyzing its response to tidal forces exerted by Phobos and in introducing melt fraction in the mantle layers. We modify the ALMA3 program to compute the tidal Love number (k2) and the dissipation factor (Q) of the planet for a wide range of spherically symmetric internal structures considering an extended version of the Andrade rheology where viscosity and anelastic creep parameter explicitly depend on the local melt fraction. With a 3-layers mantle structure, tidal deformations alone provide a radially dependent melt fraction profile: the two shallowest layers are consistent with solid material, while the deepest layer exhibits partial melting. Adding thermal constraints from recent solidus and liquidus determinations refines these limits, confirming that only the deepest part of the mantle might exhibit significant melting. The inferred densities for the mantle and core align with previous studies and point towards iron-rich mantle layers and a core enriched in light elements. Viscosity and temperature profiles suggest with a transition from solid to partially molten behavior near the core-mantle boundary, consistent with the presence of a thin basal molten layer enriched in iron and radiogenic elements. However, the rheological parameters α and β deviate from laboratory estimates for terrestrial materials, suggesting that the anelastic behavior of the Martian mantle may differ from terrestrial analogues. This highlights the need for experimental studies on iron-rich, melt-bearing compositions representative of Mars.