N-Body Growth of a Bahcall-Wolf Cusp around a Black Hole

We present a clear N-body realization of the growth of a Bahcall-Wolf f ∝ E1/4 (ρ ∝ r-7/4) density cusp around a massive object ("black hole") at the center of a stellar system. Our N-body algorithm incorporates a novel implementation of the Mikkola-Aarseth chain regularization to handle close interactions between star and black hole particles. Forces outside the chain were integrated on a GRAPE-6A/8 special-purpose computer with particle numbers up to N = 0.25 × 106. We compare our N-body results with predictions of the isotropic Fokker-Planck equation and verify that the time dependence of the density (both configuration and phase-space) predicted by the Fokker-Planck equation is well reproduced by the N-body algorithm. Our results highlight the usefulness of direct N-body techniques for simulating the dynamical evolution of galactic nuclei containing supermassive black holes.

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