Statistics and universality in simplified models of planetary formation

Abstract

In this paper, we modify Laskar's simplified model of planetary evolution and accretion to account for the full conservation of the total angular momentum of the system, and extend it to incorporate an accretion probability that depends on the mass and relative velocity of the colliding particles. We present statistical results for the mass and eccentricity of the planets formed, in terms of their semimajor axes, for a large number of realizations of different versions of the model. In particular, we find that by combining the mass-dependent accretion probability and the velocity-selection mechanism, the planets formed display a systematic occurrence at specific locations. By introducing properly scaled variables, our results are universal with respect to the total angular momentum of the system, the mass of the planetesimal disc and the mass of the central star. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.