Uncertainties in Simulations of Moon-Forming Disks due to Numerical Resolution and EoS

The canonical giant impact origin of the Moon assumes an oblique, low-velocity collision between a Mars-sized impactor (Theia) and the proto-Earth. Extensive vaporization and volatile loss during the impact could explain the Moon's observed volatile element depletion and enrichment of heavy isotopes of moderately volatile elements (MVEs). Smoothed Particle Hydrodynamics (SPH) has been the preferred method for the direct simulation of the impact as well as the first ~50 hours of the formation of the Moon-forming disk, although a known weakness is the low particle resolution of the disk. SPH depends on an equation of state (EoS) to fully resolve the thermodynamics of the system, which directly influences the vapor mass fraction (VMF) and therefore the degree of MVE isotope fractionation. Here, we implement a recently-developed version of the modified analytical EoS ("Stewart M-ANEOS"), which improves the treatment of heat capacity, in our SPH code, FDPS SPH. The results are then compared with simulations using the previous version of M-ANEOS with heat capacities derived from the Dulong-Petit limit. We run 17 SPH simulations of the canonical giant impact with resolutions between 106-107 particles. We find that the higher heat capacities given by Stewart M-ANEOS result in systematically lower values of VMF by up to ~20%. We also investigate the effect of the minimum "cutoff" density in SPH, which is usually set to prevent disk particles from reaching an artificially low density. We find that as disk particle densities approach 5 kg/m3 or below, they become increasingly sensitive to random encounters with other particles. This leads to small, instantaneous density jumps for many disk particles, resulting in continuous artificial shocking of the disk well after the initial and secondary impacts. This prevents the disk from achieving a steady-state entropy and VMF for the entirety of the simulation. We propose using higher cutoff densities to mitigate this numerical problem. Combined, our results show that SPH contains considerable numerical sensitivities and EoS dependencies that must be accounted for in future simulations of the giant impact. These sensitivities can alter the VMF by 10s of percent and change the predicted composition of the Moon.