The critical energy density and the inelasticity coefficient for asteroidal catastrophic collisions

Experimental results on high-velocity impacts reported in the literature are analyzed in detail. The purpose of the analysis is twofold: (1) to assess the possibility of applying to asteroidal collisions (without a size-dependent scaling) the critical energy densities associated with various degrees of fragmentation; and (2) to determine which fraction of the projectile's energy is converted into the kinetic energy of fragments after a catastrophic breakup. It is shown that the critical energy density is independent of size only for supercatastrophic events when no massive core survives, whereas it slowly decreases for larger targets when the fragmentation is only partial. The energy gap between cratering and complete destruction is therefore probably wider for the asteroids than for the small experimental targets. It is also shown that the inelasticity coefficient (i.e., the resulting fraction of kinetic energy) depends both on the impact velocity and on the projectile-to-target mass ratio; this coefficient probably ranges from 0.01 to 0.1 for asteroidal catastrophic collisions.