Self consistent model of core formation and the effective metal-silicate partitioning

It has been long known that the formation of the core transforms gravitational energy into heat and is able to heat up the whole Earth by about 2000 K. However, the distribution of this energy within the Earth is still debated and depends on the core formation process considered. Iron rain in the surface magma ocean is supposed to be the first mechanism of separation for large planets, iron then coalesces to form a pond at the base of the magma ocean [Stevenson 1990]. The time scale of the separation can be estimated from falling velocity of the iron phase, which is estimated by numerical simulation [Ichikawa et al., 2010] as ∼ 10cm/s with iron droplet of centimeter-scale. A simple estimate of the metal-silicate partition from the P-T condition of the base of the magma ocean, which must coincide with between peridotite liquidus and solidus by a single-stage model, is inconsistent with Earth's core-mantle partition. P-T conditions where silicate equilibrated with metal are far beyond the liquidus or solidus temperature for about ∼ 700K. For example, estimated P-T conditions are: 40GPa at 3750K for Wade and Wood, 2005, T ≧ 3600K for Chabot and Agee, 2003 and 35GPa at T ≧ 3300K for Gessmann and Rubie, 2000. Meanwhile, Rubie et al., 2003 shown that metal couldn't equilibrate with silicate on the base of the magma ocean before crystallization of silicate. On the other hand, metal-silicate equilibration is achieved only ∼ 5 s in the state of iron rain. Therefore metal and silicate simultaneously separate and equilibrate each other at the P-T condition during the course to the iron pond. Taking into account the release of gravitational energy, temperature of the middle of the magma ocean would be higher than the liquidus. Estimation of the thermal structure during the iron-silicate separation requires the development of a planetary-sized calculation model. However, because of the huge disparity of scales between the cm-sized drops and the magma ocean, a direct numerical simulation is impossible. In this study, we made 1D numerical simulations of the whole magma ocean incorporating a parameterization based on direct numerical simulation results of a 10cm-scale emulsion of liquid iron in liquid silicates. We computed the evolution of the thermal and chemical structure during the separation of iron phase. The maximum temperature, which exceeds peridotite melting temperature for several thousands Kelvin, is obtained at the boundary between the metal ponds (or the core if the whole planet is liquid) and the silicate layer. We have found effective P-T conditions for chemical equilibrium in the magma ocean, which is the P-T condition estimated from the resulting partitioning of elements, is not on the melting curve of silicate.