Perfect-SSDEM: A Hybrid N-body Collisional Model for Gravitational Collapse

Jackson T. Barnes, Stephen R. Schwartz, Seth A. Jacobson

The foremost planetesimal formation hypothesis invokes the collapse of a self-gravitating cloud of pebble-sized (~mm-cm) objects directly into large ~10-100 km-sized planetesimals. We cannot directly verify this theory with observational evidence, as it occurs at a scale too fine to resolve in distant protoplanetary disks and only relict planetesimals remain in our own Solar System. We must therefore use numerical models to simulate gravitational collapse.

The principal challenge of modeling gravitational collapse is that collapsing clouds initially contain ~10^{21} pebbles?an impossible number to ever simulate directly. Therefore, current models use lower-resolution super-particle systems with up to 10^{5} super-particles, which demonstrate that gravitational collapse is a viable mechanism to reproduce the dynamics of binary Kuiper Belt systems. The evolution and behavior of these super-particles is critical to the interpretation of gravitational collapse models.

In this work, we present the initial results of our novel hybrid collisional model, Perfect-SSDEM. Many models use a perfect-merging method that, while computationally efficient, removes planetesimal shape and spin information and assumes efficient energy dissipation via perfectly inelastic collisions. We previously used a soft-sphere discrete element method (SSDEM)?which ensures that colliding particles stick and rest upon one another?within the PKDGRAV N-body integrator to simulate collapse. Using the SSDEM in the late-stages of gravitational collapse is advantageous, because we can model when planetesimals begin to take shape and fully resolve their orbits, but perfect-merger models are more suitable for the early stages when innumerable particle collisions are occurring, and their shapes are not as important. With Perfect-SSDEM, we combine the perfect-merger model at early times and the SSDEM at late times. Thus, we will be able to effectively model the innumerable collisions that occur at the start of collapse and the masses, orbits, shapes, and spins of planetesimals as particle-aggregates at the end of collapse.