Statistics of collision parameters computed from 2D simulations

Abstract

There are two popular ways to speed up simulations of planet formation via increasing the collision probability: ({\it i}) confine motion to 2D, ({\it ii}) artificially enhance the physical radii of the bodies by an expansion factor. In this paper I have performed 100 simulations each containing $10^4$ interacting bodies and computed the collision parameters from the results of the runs. Each run was executed for a lower and a higher accuracy parameter. The main goal is to determine the probability distribution functions of the collision parameters and their dependence on the expansion factor. A simple method is devised to improve the determination of the collision parameters from the simulation data. It was shown that the distribution of the impact parameter is uniform and independent of the expansion factor. For real collisions the impact velocity is greater than 1 mutual escape velocity, a finding that can be explained using the two-body problem. The results casts some doubts on simulations of the terrestrial planets' final accretion that have assumed merge. Collision outcome maps were created adopting the fragmentation model of \cite{Leinhardt2012} to estimate the number of different types of collisions. A detailed comparison with earlier works indicates that there are similarities as well as significant differences between the different works. The results indicate that as the planetary disc matures and the masses of the bodies differs progressively than the majority of collisions lead to mass growth either via partial accretion or via graze-and-merge collision.