The stationary size distribution of main-belt asteroids: Comparing recent observation with theory

Recent observations of main-belt asteroids (Jedicke and Metcalfe, 1998; Ivecic et al., 2001) help to extend theoretical understanding of collisional evolution to sub-kilometer sizes. Previous theoretical models treated the collisional evolution as a stochastic process where the outcome of pairwise collisions between asteroids is sampled using Monte-Carlo techniques (Davis et al., 1985; Davis et al., 1989; Davis et al., 1994; Campo Bagatin, 1994), leading to a time-dependent model which depends on assumptions about the initial state. Alternative theoretical investigations (Dohnanyi, 1969; Williams and Wetherill, 1994) for the stationary case have been restricted to simplified functional relationships for the outcome of collisions and for the critical specific energy of catastrophic fragmentation, and in these cases a power law as analytical solution has been found. The present model solves the quasi-stationary form of the collisional balance of mass, assuming the size distribution of very large asteroids as given.