  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.
