Heat partitioning in terrestrial planets during core formation by negative diapirism

We investigate the gravitational heat partitioning between silicate and metallic phases during core formation by negative diapirism in terrestrial planets. We model the dynamic evolution of an iron diapir, sinking through a solid silicate proto-mantle. Our calculations include viscous heating and strong temperature and composition-dependence of viscosity. We show that the diapir mean temperature evolves towards an asymptotic value Td∞, which depends on the efficiency of viscous heating and heat transfer between the diapir and its surroundings, and on the viscous rheology. We derived a simple analytic model that captures the thermal evolution observed in our numerical experiments. This model can be applied to determine the heat distribution within terrestrial planets with a large number of diapirs, during their growth and early differentiation. We show that the partitioning of core formation heating during negative diapirism depends strongly on the size distribution of the iron diapirs. A large number of small sinking iron diapirs favors metal–silicate heat exchange and leads to a relatively hot core, which allows a sustainable dynamo, as on Earth. A small number of large diapirs have the opposite effect and could correspond to a Mars-like planet with an early dynamo that is no longer active. In all cases, negative diapirism tends to leave the lowermost mantle significantly hotter than its upper part, which could trigger large amounts of melting in the early deep mantle.