Planetesimal Evolution and the Formation of Terrestrial Planets

Abstract

An accurate numerical model of solar system formation requires understanding how planetesimals grow into larger bodies. Traditionally, numerical simulations of planet formation have used extrapolations of impact experiments in the strength regime to model the effects of fragmentation in planetesimal collisions. However, planetesimals, which are large enough to decouple from the gaseous nebula, are dominated by self-gravity not material strength. As a result, such extrapolations may give misleading results since much more energy is needed to disperse than to disrupt a planetesimal in the gravity regime. In order to determine the effects of collision parameters, I have completed parameter-space studies of collisions between kilometer-sized planetesimals. The planetesimals are modeled as ``rubble piles"---gravitational aggregates of particles bound together by gravity. I find that as the mass ratio departs from unity the impact angle has less effect on the collision outcome. At the same time, the probability of planetesimal growth increases. Conversely, for a fixed impact energy, collisions between impactors with mass ratio near unity are more dispersive than those with mass ratio far from unity. For an average mass ratio of 1:5, the accretion probability is ~ 60% over all impact parameters. Results are presented from a dozen direct N-body simulations of terrestrial planet formation with various initial conditions. To increase the realism of the simulations, a self-consistent planetesimal collision model was developed based on the planetesimal model developed and investigated in the parameter space studies summarized above. The results are compared to the best numerical simulations of planet formation in the literature (Kokubo and Ida 2002) in which no fragmentation is allowed---perfect merging is the only collision outcome. After 400,000 years of integration our results are virtually indistinguishable from those of (Kokubo and Ida 2002). We find that the number and masses of protoplanets, and time required to grow a protoplanet, depends strongly on the initial conditions of the disk and is consistent with oligarchic theory. In contrast to the suggestion by (Goldreich et al. 2004), there is negligible debris remaining at the end of oligarchic growth, where ``debris" is defined to be those particles smaller than our resolution limit.