The long-term evolution of massive black hole binaries at the centers of galaxies is studied in a variety of physical regimes, with the aim of resolving the “final parsec problem,” i.e. how black hole binaries manage to shrink to separations at which emission of gravity waves becomes efficient. A binary ejects stars by the gravitational slingshot and carves out a loss cone in the host galaxy. Continued decay of the binary requires a refilling of the loss cone. We show that the standard treatment of loss cone refilling, derived for collisionally relaxed systems like globular clusters, can substantially underestimate the refilling rates in galactic nuclei. We derive expressions for non-equilibrium loss-cone dynamics and calculate time scales for the decay of massive black hole binaries following galaxy mergers, obtaining significantly higher decay rates than heretofore. Even in the absence of two-body relaxation, decay of binaries can persist due to repeated ejection of stars returning to the nucleus on eccentric orbits. We show that this recycling of stars leads to a gradual, approximately logarithmic dependence of the binary binding energy on time. We derive an expression for the loss cone refilling induced by the Brownian motion of a black hole binary. We also show that numerical N-body experiments are not well suited to probe these mechanisms over long times due to spurious relaxation.

Publication Date



Also archived in: arXiv:astro-ph/0212459 v2 25 Aug 2003 This work was supported by NSF grants AST 96-17088 and AST 00-71099 and by NASA grants NAG5-6037 and NAG5-9046 and STScI grant HST-AR-08759.ISSN:1538-4357 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