Abstract
ABSTRACTThere are two popular ways to speed up simulations of planet formation via increasing the collision probability: (i) confine motion to 2D, (ii) artificially enhance the physical radii of the bodies by an expansion factor. In this paper, I have performed 100 simulations each containing 104 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 cast some doubts on simulations of the terrestrial planets’ final accretion that have assumed merge. Collision outcome maps were created adopting the fragmentation model of recent studies 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 differ progressively than the majority of collisions lead to mass growth either via partial accretion or via graze-and-merge collision.
Highlights
According to the most widely accepted model, the nebular hypothesis states that the formation process of the terrestrial planets is the result of a series of three consecutive but partly overlapping stages (Lissauer 1993; Chambers 2004; Morbidelli et al 2012)
Weidenschilling (1977) has described the dust motion in protoplanetary discs and showed that dust grains from micron to a few meters in size experience a radial motion towards the star
The statistics of the collision parameters is investigated with 10000 equal-mass protoplanets under perfect and gasfree accretion
Summary
According to the most widely accepted model, the nebular hypothesis states that the formation process of the terrestrial planets is the result of a series of three consecutive but partly overlapping stages (Lissauer 1993; Chambers 2004; Morbidelli et al 2012). Oligarchic growth ends when the number of planetesimal drops below such a threshold where their damping effect on protoplanet orbits become insufficient to prevent orbit crossing This initiates the last phase of terrestrial planet formation, involving the collision and mutual accretion of protoplanets and embryos the so called giant impacts phase. The numerical N -body simulations that assumed perfect accretion have been successful at reproducing the broad characteristics of the terrestrial planets in our Solar System (Wetherill 1994; Chambers 2001; Quintana et al 2002; Raymond et al 2004, 2006, 2009; O’Brien et al 2006; Quintana & Lissauer 2006, 2014; Quintana et al 2016; Liu, Zhou & Wang 2011) These results were all based on a small (up to a dozen) number of realizations performed for each set of initial conditions.
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