We use direct-summation N-body integrations to follow the evolution of binary black holes at the centers of galaxy models with large, constant-density cores. Particle numbers as large as 0.4 × 106 are considered. The results are compared with the predictions of loss-cone theory, under the assumption that the supply of stars to the binary is limited by the rate at which they can be scattered into the binary’s influence sphere by gravitational encounters. The agreement between theory and simulation is quite good; in particular, we are able to quantitatively explain the observed dependence of binary hardening rate on N. We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that the hardening rate of the binary stabilizes when N exceeds a particular value, or that Brownian wandering of the binary has a significant effect on its evolution. When scaled to real galaxies, our results suggest that massive black hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave coalescence in a Hubble time. (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/10.1086/491598

© 2005 The American Astronomical Society

Also archived in: arXiv:astro-ph/0507260 v1 11 Jul 2005

Support from grants AST- 0206031, AST-0420920 and AST-0437519 from the NSF, grant NNG04GJ48G from NASA, and grant HST-AR-09519.01-A from STScI. PB and RS acknowledge support from grant SFB-439 from the Deutsche Forschungsgemeinschaft. This work was supported in part by the Center for Advancing the Study of Cyberinfrastructure at the Rochester Institute of Technology.

Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2014.

Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus