Statistics of collision parameters computed from 2D simulations
Áron Süli
Eötvös Loránd University

There are two popular ways to speed up N-body simulations of planet formation via increasing the collision probability: (i) confine motion to 2 spatial dimensions (2D), (ii) artificially enhance the physical radii of the bodies by a factor denoted by Aref. In this paper I have computed the collision parameters for 2 × 50 simulations each containing 104 fully interacting bodies which were confined to 2D using a lower and higher accuracy parameter. A major goal was to determine the probability distribution functions of the collision parameters and to find out the implications for planet formation. A method based on the two-body problem (TBP) is devised to improve the determination of the collision parameters. It was shown that the distribution of the impact parameter is uniform and independent of Aref. For real collisions the impact velocity is greater than 1 mutual escape velocity, a finding that can be explained using the TBP. This casts some doubts on simulations of the terrestrial planets' final accretion that have assumed that all collisions lead to mergers. The shape of the distribution of impact velocity is qualitatively explained. Collision outcome maps were created adopting the fragmentation model of Leinhardt (2012) to estimate the number of different types of collisions. A major result is 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.

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