Numerical experiments with rubble piles: equilibrium shapes and spins

We present numerical experiments investigating the shape and spin limits of self-gravitating “perfect” rubble piles that consist of identical, smooth, rigid, spherical particles with configurable normal coefficient of restitution and no sliding friction. Such constructs are currently employed in a variety of investigations, ranging from the formation of asteroid satellites to the dynamical properties of Saturn's densest rings. We find that, owing to cannonball stacking behavior, rubble piles can maintain non-spherical shapes without bulk spin, unlike a fluid, and can spin faster than a perfect fluid before shedding mass, consistent with the theory for the more general continuum rubble pile model (Holsapple, 2004, Icarus 172, 272-303). Rubble piles that reassemble following a catastrophic disruption reconfigure themselves to lie within stability limits predicted by the continuum theory. We also find that coarse configurations consisting of a small number of particles are more resistant to tidal disruption than fine configurations with many particles. Overall this study shows that idealized rubble piles behave qualitatively in a manner similar to certain granular materials, at least in the limit where global shape readjustments and/or mass shedding begins. The limits obtained here may provide constraints on the possible internal structure of some small Solar System bodies that have extreme shapes or are under high stress. Amalthea is presented as a case study.