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

The experimental results on high-velocity impacts reported in the literature are analyzed in detail, with the purpose: (a) to check the possibility of applying to asteroidal collisions, without a size-dependent scaling, the critical energy densities associated with various degrees of fragmentation; (b) to ascertain which fraction of the projectile's energy is converted into kinetic energy of fragments after a catastrophic breakup.

The results of our analysis on these two problems indicate that: (a) the critical energy density is independent on size only for super-catastrophic events, when no massive core survives, while it slowly decreases for larger targets when the fragmentation is only partial (barely-catastrophic collisions). Therefore the “energy gap” between cratering and complete distruction is probably wider for the asteroids than for the small experimental targets. (b) 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; for asteroidal catastrophic collisions, it probably ranges from 10⁻² to 10⁻¹.