Did a discrete asteroid breakup event affect Gaspra's cratering record?

Abstract

Recent analysis of the cratering record on the asteroid (951) Gaspra has indicated an index (exponent of the power law describing the cumulative distribution of craters as a function of diameter) α = −3.3±0.3, definitely steeper than the theoretically derived value of −2.5 expected for a projectile population in collisional equilibrium. A single, very energetic breakup event which locally injected debris into the main-belt population with a size distribution unrelated to the equilibrium value has been proposed as a simple explanation for this finding. I have tested this hypothesis using the numerical algorithm described in Campo Bagatin et al. ( Planet. Space Sci. 42, 1079–1092, 1099–1107, 1994) to model the outcome of impacts between asteroids of very large sizes and to assess their transient consequences on the main-belt size distribution as a function of time. The results show that the previous hypothesis is very unlikely in the case of Gaspra because it requires two ad hoc assumptions: (1) that the assumed impact should have involved two relatively large asteroids, hence its a priori probability of occurring during the whole history of the Solar System would have been low; (2) and that this event should have occurred as recently as ≤ 10 Myr ago.