Collisional evolution of asteroids - Populations, rotations, and velocities

The collisional evolution of various initial populations of asteroids is simulated numerically and compared with the present asteroid size-frequency distribution to find those populations which collisionally relax to the present belt. Both orbital and size distributions are treated, as well as the simultaneous evolution of two collisionally interacting populations with different physical properties. If the initial belt distribution was a power law, the initial belt population at the time when the present high-collision speed was established was probably only modestly larger than the present population. However, other distributions allow a more massive early belt. The rotational evolution due to collisions of asteroids with power-law distributions is also examined and compared with observations, leading to conclusions generally in agreement with those of size evolution. The high-collision speed in the present belt is likely due to Jupiter. Gravitational stirring by massive Jupiter-scattered planetesimals or secular resonances sweeping through the belt are the most probable mechanisms.