Mass Spectrum and Velocity Dispersions during Planetesimal Accumulation. II. Fragmentation

Abstract

The increase of the velocity dispersions which occurs during the growth of the planetesimals (P. Barge and R. Pellat, 1991, Icarus 93, 270-287) strongly suggested that fragmentation could come at work in the final stages of the accumulation scenario.Fragmentation has been modeled assuming that mass and energy are redistributed in a simple way between the various fragments; it is found to play a role whose importance is greater than previously believed and depends on the average characteristic size of the primordial planetesimals but not on their mass distribution. In the small size range the mass spectrum is strongly modified with the formation of a small bodies tail but, on the other hand, the growth of the most massive objects is significantly slowed down. With the recent fragmentation model of K. R. Housen, R. M. Schmidt, and K. R. Holsapple (1991, Icarus 94, 180-190) it is found that 10-km-sized objects can grow into planetary embryos (size of the order of 1000 km) in a time scale of the order of 105 or 107 years (depending on the fragmentation properties of the planetesimals) whereas 1-km-sized objects cannot on a reasonable time scale. The formation of planetary embryos much more massive than the rest of the swarm is delayed; nevertheless, the time scale problem for the growth of the outer planets is not revived. The elasticity of the collisions is found to play a negligible role in the investigated size range.