SIZE DISTRIBUTION OF COLLISIONALLY EVOLVED ASTEROIDAL POPULATIONS - ANALYTICAL SOLUTION FOR SELF-SIMILAR COLLISION CASCADES

Collision cascades play a prominent role in processing the present ast eroid belt, as well as formative planetary systems. As a first step to ward understanding how this mechanism operates, an analytical solution has been obtained for the steady-state size distribution of a self-si milar collisional fragmentation cascade. It is found that this corresp onds to a power law for the differential mass distribution dn = Cm-alp hadm, where the exponent alpha is very nearly 11/6, equivalent to a di fferential radius distribution dn = Cr-3.5dr. This is in agreement wi th the earlier conclusion of J. S. Dohnanyi (1969, J. Geophys. Res. 74 , 2531-2554). The work of Dohnanyi has been extended considerably to i nclude a full treatment of the simultaneous occurrence of cratering an d catastrophic fragmentation. A more physically realistic model of cat astrophic fragmentation is used in which the size of the largest fragm ent decreases with projectile mass. The average steady-state value of the exponent alpha(1.8333) is found to be extremely insensitive to the assumed physical parameters of the fragmentation process, such as the strength of the target, the threshold for catastrophic fragmentation, the relative contribution of cratering and catastrophic fragmentation , the size and number of the largest fragments, and the size distribut ion of the fragments produced by individual fragmentation events. The robust nature of the result is a consequence of the steady-state solut ion being primarily the consequence of geometrical rather than mechani cal considerations. (C) 1994 Academic Press, Inc.