Timescale of Destabilization of a Magma Ocean Cumulate

A common scenario considered during the formation of terrestrial planets is the crystallization of a global magma ocean from the bottom-up. The crystallization of the surface magma ocean is expected to be rapid, on a timescale of the order of 1 Myr. This has lead several authors to assume convection in the solid part of the crystallizing mantle only sets out after the complete solidification of the surface magma ocean. Assuming fractionnal crystallization of this ocean, the magma (and resulting solid) is more and more enriched in FeO as the crystallization progresses. This leads to an unstable stratification and an overturn. After overturn, the resulting solid mantle would be strongly compositionally stratified. The present study tests the assumption that solid-state mantle overturn only occurs after complete crystallization of the surface magma ocean. We model convection in the solid part of the mantle only and parametrize the presence of a magma ocean with boundary conditions. Our model includes through these boundary conditions the possibility for matter to cross the boundary between the solid shell and the magma ocean by melting and freezing. We perfomed a linear stability analysis with respect to the temperature and compositional profiles obtained in a growing magma ocean cumulate to assess the destabilization timescale of such profiles as a function of the crystallized thickness. By comparing this timescale with a model of surface magma ocean crystallization, we deduce the time and crystallized thickness at which the convection timescale is comparable to the age of the solid crystallizing mantle. This time is found to be small ( 1 kyr) compared to the time needed to crystallize the entire surface magma ocean ( 1 Myr).