A new equation of state applied to planetary impacts

Abstract

We present a new analytical equation of state (EOS), which correctly models high pressure theory and fits well to the experimental data of ɛ-Fe, SiO2, Mg2SiO4, and the Earth. The cold part of the EOS is modeled after the Varpoly EOS. The thermal part is based on a new formalism of the Gruneisen parameter, which improves behavior from earlier models and bridges the gap between elasticity and thermoelasticity. The EOS includes an expanded state model, which allows for the accurate modeling of material vapor curves. The EOS is compared to both the Tillotson EOS and ANEOS model, which are both widely used in planetary impact simulations. The complexity and cost of the EOS is similar to that of the Tillotson EOS, while showing improved behavior in every aspect. The Hugoniot state of shocked silicate material is captured relatively well and our model reproduces vapor curves similar to that of the ANEOS model. To test its viability in hydrodynamical simulations, the EOS was applied to the lunar-forming impact scenario and the results are presented in Paper II and show good agreement with previous work.

The Influence of Equation of State on the Giant Impact Simulations

“…However, we believe that the effect is less significant than the effect of the type of EoS. Hard-sphere EoS Wissing and Hobbs (2020a).…”

“…Karato (2014) and Hosono et al (2019) demonstrated the importance of unique thermodynamic properties of silicate melts in controlling the fate of a giant impact. However, there have been a few new papers on the issues of EoS in a giant impact (e.g., Stewart et al, 2020;Wissing & Hobbs, 2020b, 2020a) that presented somewhat different EoSs and pointed out a problem in Hosono et al (2019)'s treatment of EoS across the solid vapor transition.…”

“…Point (5) shows that the details of EoS of the magma ocean matter. Wissing and Hobbs (2020b); Wissing and Hobbs (2020a)'s EoS includes important details on the behavior of the Grüneisen parameter. However, their EoS does not capture the important role of configurational entropy.…”

“…In the following, we discuss some key features of equations of state used in the present study, including M-ANEOS (Melosh, 2007), modified M-ANEOS (Stewart et al, 2020), Wissing and Hobbs (2020b); Wissing and Hobbs (2020a) model, and a revised Hosono et al (2019) model. Details of M-ANEOS (Melosh, 2007) and the modified hard-sphere EoS (Hosono et al, 2019;Jing & Karato, 2011) are given by original papers.…”

“…First, we extended our previous study (Hosono et al, 2019) (a) by using the M-ANEOS equation of state for the solid part to rectify the inconsistency of using the (Tillotson, 1962) for the solid part and the hard-sphere EoS for the magma ocean part and (b) we investigate the influence of temperature and density dependence of hard-sphere radii (i.e., a "soft-sphere" model). Second, we explore newly proposed equations of state for the giant impact simulation, including the ones by Stewart et al (2020) and the one by Wissing and Hobbs (2020b); Wissing and Hobbs (2020a) using DISPH.…”