A fast method for finding bound systems in numerical simulations: Results from the formation of asteroid binaries

We present a new code (companion) that identifies bound systems of particles in O ( N log N ) time. Simple binaries consisting of pairs of mutually bound particles and complex hierarchies consisting of collections of mutually bound particles are identifiable with this code. In comparison, brute force binary search methods scale as O ( N 2 ) while full hierarchy searches can be as expensive as O ( N 3 ) , making analysis highly inefficient for multiple data sets with N ≳ 10 3 . A simple test case is provided to illustrate the method. Timing tests demonstrating O ( N log N ) scaling with the new code on real data are presented. We apply our method to data from asteroid satellite simulations [Durda et al., 2004. Icarus 167, 382–396; Erratum: Icarus 170, 242; reprinted article: Icarus 170, 243–257] and note interesting multi-particle configurations. The code is available at http://www.astro.umd.edu/zoe/companion/ and is distributed under the terms and conditions of the GNU Public License.