Fragmentation and Distribution of Asteroids

Abstract

As a result of mutual inelastic collisions, frequent on a geologic time scale, the mass distribution of asteroids undergoes constant change. Using a simplified velocity distribution for asteroids, the redistribution of their masses caused by collisions can be mathematically modeled as a stochastic process and the distribution of asteroidal masses can then be obtained as the solution. This paper is a review of recent progress on this problem.The most detailed discussion of this problem considers the influence of the following collisional processes on the asteroidal mass distribution: (1) loss of asteroids by catastrophic breakup, (2) creation of new objects from the fragments of a catastrophically disrupted one, (3) erosive reduction in the masses of individual asteroids, and (4) erosive creation of new objects (i.e., production of secondary ejecta during erosive cratering by projectiles not large enough to catastrophically disrupt the target object). The main result is that after a sufficiently long period of time the population of asteroids may reach a quasi-steady-state distribution, regardless of the initial distribution. This final distribution is a product of a slowly decreasing function of time by a power law of index 11/6 for masses smaller than the largest asteroids. For the largest asteroids, an additional factor is included that expresses the influence on the distribution of the absence of masses larger than those observed. The observed distribution of bright asteroids from the McDonald asteroidal survey and that of faint ones from the Palomar-Leiden asteroidal survey are each individually consistent with the theoretical distribution, although they differ from each other by a numerical factor.