Combining N-body accretion simulations with partitioning experiments in a statistical model of terrestrial planet accretion and core formation

The terrestrial planets accreted in a series of increasingly large and violent collisions. Simultaneously, metallic cores segregated from their silicate mantles, acquiring their modern compositions through high pressure (P), high temperature (T) partitioning reactions. Here we present a model that couples these aspects of early planetary evolution, building on recent accretion simulations and experimental results. We have run 100 N-body simulations of terrestrial planet accretion, with Jupiter and Saturn on either circular (CJS) or eccentric (EJS) orbits, to gain insight into the statistics of this highly stochastic process (Fischer and Ciesla, 2014). An Earth (Mars) analogue forms in 84-92% (2-10%) of our simulations. We draw on our recent high P-T metal-silicate partitioning experiments of Ni, Co, V, Cr, Si, and O in a diamond anvil cell to 100 GPa and 5500 K. In our model, N-body simulations describe the delivery, masses, and original locations of planetary building blocks. As planets accrete, their core and mantle compositions are modified by high P-T reactions with each collision (Rubie et al., 2011). By utilizing a large number of N-body simulations, we obtain a statistical view and observe a wide range of outcomes. We use this model to predict the core compositions of Earth-like planets. For partial equilibration of the mantle at 50% of the core-mantle boundary (CMB) pressure, we find that their cores contain 6.9 ± 1.8 wt% Si and 4.8 ± 2.3 wt% O (Figure), with this uncertainty due entirely to variations in accretion history in our 100 simulations. This composition is consistent with the seismologically-inferred density of Earth's core, based on comparisons to high P-T equations of state (Fischer et al., 2011, 2014). Earth analogues experience 0.7 ± 0.1 or 0.9 ± 0.2 log units of oxidation during accretion in EJS or CJS simulations respectively, which is due to both the effects of high P-T partitioning and the temporal evolution of the Earth analogue's feeding zone. The model can reveal the relative importance of various accretionary processes, highlighting targets for future experimental and numerical studies. For example, changing the depth of partitioning to 70% of the CMB pressure leads to an increase of 1.7 ± 2.8 wt% Si and 2.2 ± 3.5 wt% O in Earth analogue cores, comparable to variations due to accretion history.