The Probable Ages of Asteroid Families

There has been considerable debate recently over the ages of the Hirayama families, and in particular if some of the families are very oung(u) It is a straightforward task to estimate the characteristic time of a collision between a body of a given diameter, d_o, by another body of diameter greater of equal to d_1. What is less straightforward is to estimate the critical diameter ratio, d_1/d_o, above which catastrophic disruption occurs, from which one could infer probable ages of the Hirayama families, by knowing the diameter of the parent body, d_o. One can gain some insight into the probable value of d_1/d_o, and of the likely ages of existing families, from the plot below. I have computed the characteristic time between collisions in the asteroid belt of a size ratio greater of equal to d_1/d_o, for 4 sizes of target asteroids, d_o. The solid curves to the lower right are the characteristic times for a single object...