Forming Binary Near-Earth Asteroids From Tidal Disruptions

2.2 Method2.2.1 SimulationsAll simulations were done using pkdgrav, a parallelized tree code designed for efficientN-body gravitational and collisional simulations (Richardson et al. 2000; Leinhardt et al.2000; Stadel 2001; Leinhardt & Richardson 2002; Richardson et al. 2005). The simulationsused a timestep of 10 −5 yr/2π, (about 50 seconds, or ∼ 2% of the dynamical timefor the particles) and all simulations were initially run for 10,000 timesteps (∼ 5.8 days).Simulations that produced binaries or systems of bound bodies were run an additional20,000 timesteps to reach a total of 30,000 timesteps (∼ 17.4 days). The collisions ofindividual particles were governed by coefficients of restitution, both normal (ε n ) andtangential (ε t ), which determine how much energy is dissipated during collisions. Thenormal coefficient of restitution, ε n , was fixed at 0.8 in these simulations, similar to previousstudies, and ε t was fixed at 1.0 (no surface friction). Previous work has shown thatε n has little effect on the outcome of a tidal disruption so long as ε n < 1.0 (Richardsonet al. 1998).2.2.2 ProgenitorsThe rubble pile models used in these simulations consist of identical rigid spheres boundto one another by gravity alone. There were five separate progenitors used in the simulations,each with different elongations: 1.0, 1.25, 1.5, 1.75, and 2.0 (here elongationis defined as e = a/c with a, b and c representing the long, intermediate and short axislength of a tri-axial ellipsoid; in our simulations, b was set to ∼ c). The bodies were allconstructed using particles with an internal density of 3.4 g cm −3 , but the bulk densityof the body would vary depending on its packing efficiency, which was usually around27