Collisional evolution of asteroid families

Most asteroid dynamical families are thought to be the outcomes of collisional disruption of parent asteroids destroyed by high-velocity impacts with other asteroids. However, subsequent collisions modify both the sizes and the orbits of family members, so the distributions that we see today may be very different from those following the breakup of the parent body. We study the post-breakup evolution of family asteroids with a numerical model which keeps track of both the sizes and the orbits of the fragments as they collisionally interact with the field population of asteroids. Using this model we visualize how the family appears at different evolutionary stages. In particular we find that the size distribution of a family becomes less steep with time. We have simulated the possible evolutionary history of the three most populous Hirayama families, Koronis, Eos, and Themis. By matching the distribution of sizes and orbits with those observed for the families, we obtain significant constraints on the properties of their parent bodies and on some collisional response parameters, together with the evolutionary ages of the families. The Themis family appears as the outcome of the catastrophic disruption of one of the largest asteroids, probably a unique event over the history of the Solar System. On the other hand, the Koronis and Eos families appear to have been formed from smaller parent bodies, but peculiar features may require specific processes or events. Koronis' size distribution has several bodies of comparable size at the large diameter end, which can be explained if the largest fragment of the initial breakup underwent subsequent fragmentation. The 'anistrophic' orbital distribution of the Eos family requires either a peculiar fragment velocity field or the action of poorly understood dynamical processes on the orbits of its members. For both the Koronis and the Themis families we derive an estimate of the age of the order of 2 Byr. The uncertainties affecting our estimates of family ages and of the properties of the parent bodies are mainly due to the present limited understanding of collisional breakup processes for bodies hundreds of kilometers in size and to the poor knowledge of the size distribution of small asteroids.