Direct N-body Simulations of Rubble Pile Collisions

There is increasing evidence that many km-sized bodies in the Solar System are piles of rubble bound together by gravity. We present results from a project to map the parameter space of collisions between km-sized spherical rubble piles. The results will assist in parameterization of collision outcomes for Solar System formation models and give insight into fragmentation scaling laws. We use a direct numerical method to evolve the positions and velocities of the rubble pile particles under the constraints of gravity and physical collisions. We test the dependence of the collision outcomes on impact parameter and speed, impactor spin, mass ratio, and coefficient of restitution. Speeds are kept low (< 10 m/s, appropriate for dynamically cool systems such as the primordial disk during early planet formation) so that the maximum strain on the component material does not exceed the crushing strength. We compare our results with analytic estimates and hydrocode simulations. Off-axis collisions can result in fast-spinning elongated remnants or contact binaries while fast collisions result in smaller fragments overall. Clumping of debris escaping from the remnant can occur, leading to the formation of smaller rubble piles. In the cases we tested, less than 2% of the system mass ends up orbiting the remnant. Initial spin can reduce or enhance collision outcomes, depending on the relative orientation of the spin and orbital angular momenta. We derive a relationship between impact speed and angle for critical dispersal of mass in the system. We find that our rubble piles are relatively easy to disperse, even at low impact speed, suggesting that greater dissipation is required if rubble piles are the true progenitors of protoplanets.