SPH calculations of Mars-scale collisions: The role of the equation of state, material rheologies, and numerical effects

TL;DR

Using ~1 million-particle SPH simulations of ≈2000 km impacts on a Mars-like planet at 4 km/s, the authors compare material strength, Tillotson vs ANEOS/M-ANEOS equations of state, and numerical schemes. They find material strength substantially changes post-impact temperature and impactor-material distributions, while EoS differences are subtle below ~4000 K and numerical density/rotation issues are manageable with appropriate corrections.

Key findings

• Material strength is substantial even at this scale: 27 wt% of the impactor’s core remains inside the mantle with solid rheology versus 3 wt% with fluid rheology; impact-generated heat spreads over a broader region with solid rheology, and the temperature increase around the impact zone is about 10–20 wt% for ANEOS and a bit less for Tillotson. Ejected/orbiting impactor silicate accounts for 13 wt% (fluid) and 18 wt% (solid), with about one sixth of that still bound and the rest escaping; fluid runs produce roughly 30% less escaping mass than solid runs.
• EoS differences are subtle: Tillotson and ANEOS post-impact temperature distributions are quite similar below ~4000 K, diverging above about 4000 K because ANEOS includes latent heat of vaporisation while Tillotson overestimates high temperatures. The EoS changes body radius by ~4% (about 3440 km with ANEOS vs 3290 km with Tillotson) but has little influence on material and heat distributions.
• Numerical effects: without the correction tensor for rigid-body rotation, angular momentum is reduced by almost 25% over ~20 h versus <1% with correction, and the target rotated about 20 degrees less at 18 h; the artificial core-mantle-boundary temperature increase is ~1000 K with correction versus ~5000 K without. Density summation vs integration shows no major final differences, though density integration gives a better-defined surface at the adopted resolution; disc masses are at most a few 10⁻⁴ M_Mars and are under-resolved.
• Oblique-impact rotation periods are comparable to Mars’ present rotation period: all fluid rheology runs have similar periods (1.11–1.14 Martian sidereal days), while solid rheology usually leads to slightly slower rotation except for the Tillotson EoS with density summation, which rotates faster.

Methods

• The authors use an updated SPH code based on SPHLATCH, including self-gravity, a newly implemented pressure- and temperature-dependent shear strength model, and either Tillotson or ANEOS/M-ANEOS equations of state; the code uses a 3D cubic spline kernel, artificial viscosity, and tree-code gravity.
• Initial conditions: a Mars-mass target (r = 3400 km) and a 1000 km radius impactor, both with an iron core of half the body radius and SiO₂ mantles; impact speed is the mutual escape velocity (4 km/s), with 0° (head-on) and 45° (oblique) impacts, giving 16 simulations. The target uses about one million SPH particles, with smoothing length approximately 60 km.
• Analysis compares post-impact material and temperature distributions, ejecta/disc/escaping masses, and rotation periods, and tests numerical effects including density summation vs integration, a correction tensor for rigid-body rotation, and constant vs evolved initial internal energy.

Limitations

• The paper states that neither Tillotson nor ANEOS includes the latent heat of melting, so temperatures above the melt temperature are overestimated; for silicates, neither EoS accounts for the latent heat of melting, and Tillotson uses the approximation T = u/c_p.
• The paper states that small-scale features are under-resolved even at ~1 million particles, disc masses are under-resolved (138–332 SPH particles for density summation and up to 74 for density integration), peak pressures and temperatures in the initial stages may not be fully resolved, and more consistent boundary treatment plus higher resolution are required.
• Evident from the text: the mantle is simplified as SiO₂, the target crust is not resolved or explicitly included, only two impact angles and one impact speed are tested, and an artificial core-mantle-boundary temperature feature arises from the setup routine.