Structural analysis of rubble-pile asteroids applied to collisional evolution

Solar system small bodies come in a wide variety of shapes and sizes, which are achieved following very individual evolutional paths through billions of years. This paper focuses on the reshaping process of rubble-pile asteroids driven by meteorite impacts. In our study, numerous possible equilibrium configurations are obtained via Monte Carlo simulation, and the structural stability of these configurations is determined via eigen analysis of the geometric constructions. The eigen decomposition reveals a connection between the cluster's reactions and the types of external disturbance. Numerical simulations are performed to verify the analytical results. The gravitational N-body code pkdgrav is used to mimic the responses of the cluster under intermittent non-dispersive impacts. We statistically confirm that the stability index, the total gravitational potential and the volume of inertia ellipsoid show consistent tendency of variation. A common regime is found in which the clusters tend towards crystallization under intermittent impacts, i.e., only the configurations with high structural stability survive under the external disturbances. The results suggest the trivial non-disruptive impacts might play an important role in the rearrangement of the constituent blocks, which may strengthen these rubble piles and help to build a robust structure under impacts of similar magnitude. The final part of this study consists of systematic simulations over two parameters, the projectile momentum and the rotational speed of the cluster. The results show a critical value exists for the projectile momentum, as predicted by theory, below which all clusters become responseless to external disturbances; and the rotation proves to be significant for it exhibits an "enhancing" effect on loose-packed clusters, which coincides with the observation that several fast-spinning asteroids have low bulk densities.