We present a clear N-body realization of the growth of a Bahcall-Wolf f µE^1/4 (µr^−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 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 = 0.25×10^6. 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, for various choices of N and of the black hole mass. Our results demonstrate the feasibility of direct-force integration techniques for simulating the evolution of galactic nuclei on relaxation time scales (Refer to PDF file for exact formulas).

Publication Date



This is the pre-print of an article published by the American Astronomical Society. The final, published version is available here: https://doi.org/10.1086/425139

© 2004 The American Astronomical Society

Also archived in: arXiv:astro-ph/0406324 v2 9 Jul 2004

We are indebted to Sverre Aarseth and Seppo Mikkola who were tireless in their advice and support during the coding of the chain regularization algorithm. We gratefully acknowledge useful discussions with Marc Freitag and Simon Portegies Zwart. This work was supported via grants NSF AST 02-0631, NASA NAG5-9046 and HST-AR-09519.01-A to DM, and by the German Science Foundation (DFG) via grant SFB439 at the University of Heidelberg to RS and MP. MP also acknowledges financial support from the Fundação para a Ciência e Tecnologia (FCT), Portugal, through grant SFRH/BD/3444/2000.

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Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus