Abstracts

Abstract

We have carried out a set of numerical simulations of the collisional evolution of the main asteroid belt, based on some models of fragmentation and cratering events consistent with the available experimental results on the outcomes of high-velocity impacts. We have taken into account such effects as gravitational self-compression, strain-rate scaling of the impact strength, ejection speed versus mass correlation for fragments, reaccumulation of fragments ejected at speeds smaller than the target’s escape velocity. The asteroidal population has been divided into a sequence of discrete size bins, down from Ceres’ diameter (about 1000 km) to arbitrarily small sizes; the bins have a constant logarithmic width, corresponding to a factor two in the mass of the bodies. A simple particle-in-a-box formula has been used to compute in every time step the number of collisions involving bodies belonging to any given pair of size bins. Then we have numerically integrated over a time of 4.5 billion years a set of first-order differential equations for the populations of the bins, considering the redistribution of the objects caused by collisions and including a sink term modelling the removal of small particles by non-gravitational effects (such as the Poynting-Robertson drag). The initial conditions were chosen to be consistent with a primordial asteroid population following two power-law size distributions, joined at a transition diameter of 100 km.