Heat transport in partially molten bodies with strong internal heating

Recent geochemical and astrophysical studies suggest that Mars formed in the first few million years of the solar system. The decay of short-lived aluminium-26 would release a significant amount of energy, melting the planetary interior. Here, we develop a simple model for heat transport in partially molten bodies with strong internal heating. In our model, the energy released by the radioactive decay is consumed by the latent heat of melting and transported outward to the planetary surface by melt migration. The melt ascending to the surface forms a mostly-liquid layer, which undergoes crystallization and supplies solid materials to sustain the partially molten interior. The system enters a quasi-steady state with relatively low melt fractions (<~20%). This result indicates that Mars may have undergone chemical differentiation in a different mode than the commonly assumed fractional crystallization of a completely molten magma ocean. Additionally, the model presented in this study may apply to planetary bodies undergoing strong tidal heating. For example, Jupiter's moon Io is thought to contain a partially molten layer in its mantle. The role of melt migration is crucial for understanding the chemical differentiation that redistributes and modifies materials in planetary interiors.