Crystallization and Cooling of a Deep Silicate Magma Ocean

Impact and accretion simulations of terrestrial planet formation suggest that giant impacts are both common and expected to produce extensive melting. The moon-forming impact, for example, likely melted the majority of Earth's mantle to produce a global magma ocean that subsequently cooled and crystallized (e.g. Nakajima and Stevenson, 2015). Understanding the cooling process is critical to determining magma ocean lifetimes and recognizing possible remnant signatures of the magma ocean in present-day mantle heterogeneities (i.e. Labrosse et al., 2007). Modeling this evolution is challenging, however, due to the vastly different timescales and lengthscales associated with turbulent convection (magma ocean) and viscous creep (present-day mantle), in addition to uncertainties in material properties and chemical partitioning. We consider a simplified spherically-symmetric (1-D) magma ocean to investigate both its evolving structure and cooling timescale. Extending the work of Abe (1993), mixing-length theory is employed to determine convective heat transport, producing a high resolution model that captures the ultra-thin boundary layer (few cms) at the surface of the magma ocean. The thermodynamics of mantle melting are represented using a pseudo-one-component model, which retains the simplicity of a standard one-component model while introducing a finite temperature interval for melting (important for multi-component systems). We derive a new high P-T equation of state (EOS) formulation designed to capture the energetics and physical properties of the partially molten system using parameters that are readily interpreted in the context of magma ocean crystallization. This model is used to determine the cooling timescale for a variety of plausible thermodynamic models, with special emphasis on comparing the center-outwards vs bottom-up cooling scenarios that arise from the assumed EOS (e.g., Mosenfelder et al., 2009; Stixrude et al., 2009).