N-Body Simulations of Growth from 1 km Planetesimals at 0.4 AU

We present N-body simulations of planetary accretion beginning with 1 km
radius planetesimals in orbit about a 1 M_Sun star at 0.4 AU. The initial
disk of planetesimals contains too many bodies for any current N-body code
to integrate, therefore we model a sample patch of the disk. Although this
greatly reduces the number of bodies, we still track in excess of 10^5
particles. We consider three initial velocity distributions and monitor
the growth of the planetesimals. The masses of some particles increase by
more than a factor of 100. Additionally the escape velocity of the largest
particle grows considerably faster than the velocity distribution of
particles, suggesting impending runaway growth, although no particle grows
large enough to detach itself from the power law size-frequency
distribution. These results are in general agreement with previous
statistical and analytical results. We compute rotation rates by assuming
conservation of angular momentum around the center of mass at impact and
that merged planetesimals relax to spherical shapes. At the end of our
simulations, the majority of bodies that have undergone at least one
merger are rotating faster than the breakup frequency. This implies that
the assumption of completely inelastic collisions (perfect accretion),
which is made in almost all simulations of planetary growth at sizes 1 km
and above, is inadequate.  Our simulations also reveal that after the
number of particles in the patch has decreased by half, the presence of
larger bodies in neighboring regions of the disk may limit the validity of
simulations employing the patch approximation.