Planetesimals to protoplanets. I. Effect of fragmentation on terrestrial planet formation

We present results from a dozen direct N-body simulations of terrestrial planet formation with various initial conditions. In order to increase the realism of our simulations and investigate the effect of fragmentation on proto-planetary growth, we have developed a self-consistent planetesimal collision model that includes fragmentation and accretion of debris. In our model we treat all planetesimals as gravitational aggregates so that gravity is the dominant mechanism determining the collision outcome. We compare our results to those of Kokubo & Ida in which no fragmentation is allowed; perfect merging is the only collision outcome. After 400,000 yr of integration our results are virtually indistinguishable from those of Kokubo & Ida. We find that the number and masses of protoplanets and the time required to grow a protoplanet depend strongly on the initial conditions of the disk and are consistent with oligarchic theory. We have found that the elasticity of the collisions, which is controlled by the normal component of the coefficient of restitution, does not significantly affect planetesimal growth over a long timescale. In addition, it appears that there is a negligible amount of debris remaining at the end of oligarchic growth, where debris'' is defined as particles too small to be resolved in our method, although we caution that these results are for an initial debris mass fraction of 1%. The debris component is not massive enough to alter the dynamics of the protoplanets.