Modeling of Collisional Outcomes Based on Impact Simulations of Mars-sized Bodies

TL;DR

This work develops a unified analytic model for collisional outcomes of Mars-sized or larger bodies by calibrating against SPH impact simulations. It introduces an overlapping-mass framework and a perpendicular overlap energy $E_{over,\perp}$ to capture transitions among merging, hit-and-run, and erosive/disruptive regimes, with residual energy $E_{res}=E_{imp}-E_{over,\perp}$ compared to the two-body binding energy $E_{2B}$. The model yields explicit formulas for the largest remnant mass $M_{lar}$, the second-largest remnant mass $M_s$, and the fragment mass $M_f$, including angle-averaged versions suitable for statistical planet formation approaches. Remarkably, the framework also aligns with dust-aggregate collision results, linking large-scale planetesimal interactions to small-scale cohesive collisions and enabling more realistic planet formation modeling across size scales.

Abstract

We investigate the outcomes of collisions between Mars-sized bodies through smooth particle hydrodynamics (SPH) simulations, focusing on the transitions among ``merging'', ``hit-and-run'', and catastrophic disruption. By systematically varying impact velocity, angle, and mass ratio, we characterize the dependence of collision outcomes on geometric and energetic parameters. A new analytic model is developed using characteristic energies -- particularly the energy deposited in overlapping regions of the colliding bodies -- to accurately describe the mass of the largest and second-largest remnants. The model successfully reproduces simulation results across a broad range of impact conditions and improves on previous models by better capturing the transitions between ``merging'', ``hit-and-run'', and disruption. We also derive outcome formulas averaged over impact-parameter-weighted angular distributions, enabling more realistic applications to integrated modeling of planet formation. The model further shows consistency with outcomes from dust aggregate collision simulations, highlighting its utility for modeling collisional processes not only for large planetesimals but also for smaller bodies.