On the size distribution of asteroid families:: The role of geometry

The steep slopes of the size distributions of the presently known asteroid families have long represented a debated problem. The reason is that it is not easy to reproduce them by the usual modeling techniques based on the application of standard power-laws as suggested by laboratory experiments. In this paper, we suggest that the failures of the previous models were due to the fact that geometric effects were not taken into account. In other words, the finite sizes of the parent bodies and the fact that fragments tend to have convex shapes cannot be disregarded. Following this approach, we find that steep size distributions are necessarily produced by fragmentations of the parent bodies. Moreover, we have been able to reproduce fairly well the observed size distributions of the major families, and we have also obtained some reasonable constraints on the original sizes of the parent bodies. Some anomalous mass depletions, probably due to injection of fragments in nearby resonances have also been found, not unexpectedly, in a few cases (Maria, Themis). (C) 1999 Academic Press.