Incorporation of melt-scaling laws into models of Earths accretion and core formation

The initial compositions of Earths core and mantle were set in a series of metalsilicate partitioning reactions at high pressures and temperatures. However, the details of this complex process are necessarily simplified in core formation models, and it remains poorly understood how these simplifications may affect our understanding of how the process of core formation affects the compositions of the core and mantle. Traditional core formation models assume increasing pressures and temperatures, along with constant fractions of equilibrating metal and silicate, throughout Earths accretion [1]. However, these values depend on the physical processes, and the extent of melting associated with accretionary impacts. The initial composition of Earths core and mantle are therefore reliant upon the nature and timing of these accretionary impacts, which differ between different types of simulations, each with unique evolutionary scenarios. Here, we combine a melt-scaling law [2] with multiple types of N-body accretion simulations [3, 4, 5, 6] to investigate how equilibration parameters vary throughout Earths accretion for different initial Solar System configurations. These equilibration parameters are used as inputs in a continuous core formation model in which oxygen fugacity is allowed to evolve self-consistently. By using different simulations with different plausible evolutionary scenarios, with equilibration parameters that are dependent on the timing and nature of impacts in each simulation, we are able to compare the compositions of Earth analogs produced in each type of simulation. These compositions are then compared to each other and the Earth itself to evaluate how Earths accretion history is manifested in its final composition. References: [1] Fischer, R.A., et al. (2017), EPSL, 458, 252-262. [2] Nakajima, M., et al. (2021), EPSL, 568, 116983. [3] Clement, M.S. et al. (2021), Icarus, 367, 114585. [4] Kaib, N.A. and Cowan, N.B. (2015), Icarus, 252, 161-174. [5] OBrien, D.P. et al. (2006), Icarus, 184, 39-58. [6] OBrien, D.P. et al. (2014), Icarus, 239, 74-84.