The EOS/resolution conspiracy: convergence in proto-planetary collision simulations

Abstract

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⊕ 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 × 106 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 $Q_{\rm {RD}}^{*}$ with increasing resolution as reported in prior work. The simulations where ANalytic Equation Of State (ANEOS) is used for oblique impacts are already converged at a modest resolution of 105 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 $Q_{\rm {RD}}^{*}$ has then converged.