Title: Structural analysis of rubble-pile asteroids applied to collisional evolution,
Abstract: 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.