The Influence of Equation of State on the Giant Impact Simulations

We explore the role of various equations of state (EoS) in controlling the composition of the Moon formed by a giant impact (GI) using a density-independent SPH code. A limitation in our previous model Hosono et al. (2019), is improved by replacing the EoS of the solid from Tillotson EoS to M-ANEOS, and we also explored two recently proposed EoSs by Stewart et al. (2020), and Wissing and Hobbs (2020a), ; Wissing and Hobbs (2020b), . The goal is to investigate to what extent we can explain the observed composition of the Moon including the similarity in the isotopic composition and the dissimilarity in the FeO/(FeO + MgO) ratio as compared to that of Earth by the different types of EoS assuming the conventional collision conditions. We found that changing the EoS for solids from Tillotson to M-ANEOS EoS resolves the issues of latent heat, but its effect on the composition of the disk is small compared to the influence of the hard-sphere EoS of magma ocean in controlling the composition of the disk. Similarly, two recently proposed EoSs have small effects on the composition of the disk in comparison to the model where the hard-sphere EoS is used for preexisting magma ocean. We attribute this difference to a fundamental difference in thermodynamic behavior of silicate melts captured by the hard-sphere EoS and by newly proposed EoSs; in the hard-sphere model of silicate melts, configurational entropy dominates in free energy, whereas in the newly proposed model, entropy is dominated by vibrational entropy similar to entropy of solids.