The EOS/Resolution Conspiracy: Convergence in Proto-Planetary Collision Simulations

TL;DR

This study examines how the choice of equation of state and resolution in proto-planetary collision simulations significantly influences the outcomes, convergence, and physical accuracy of the results, especially regarding phase transitions and material behavior.

Contribution

It demonstrates that using thermodynamically consistent EOS like ANEOS improves convergence and physical realism in giant impact simulations compared to simpler EOS like Tillotson.

Findings

Tillotson EOS leads to excessive vapour production and non-converged results.

ANEOS EOS achieves convergence at lower resolutions for oblique impacts.

Proper resolution of phase transitions is crucial for accurate impact energy thresholds.

Abstract

We investigate how the choice of equation of state (EOS) and resolution conspire to affect the outcomes of giant impact (GI) simulations. We focus on the simple case of equal mass collisions of two Earth-like $0.5\,M_\oplus$ proto-planets showing that the choice of EOS has a profound impact on the outcome of such collisions as well as on the numerical convergence with resolution. In simulations where the Tillotson EOS is used, impacts generate an excess amount of vapour due to the lack of a thermodynamically consistent treatment of phase transitions and mixtures. In oblique collisions this enhances the artificial angular momentum (AM) transport from the planet to the circum-planetary disc reducing the planet's rotation period over time. Even at a resolution of $1.3 \times 10^6$ particles the result is not converged. In head-on collisions the lack of a proper treatment of the solid/liquid-vapour phase transition allows the bound material to expand to very low densities which in turn results in very slow numerical convergence of the critical specific impact energy for catastrophic disruption $Q_{RD}^*$ with increasing resolution as reported in prior work. The simulations where ANEOS is used for oblique impacts are already converged at a modest resolution of $10^5$ particles, while head-on collisions converge when they evidence the post-shock formation of a dense iron-rich ring, which promotes gravitational re-accumulation of material. Once sufficient resolution is reached to resolve the liquid-vapour phase transition of iron in the ANEOS case, and this ring is resolved, the value of $Q_{RD}^*$ has then converged.