A binary supermassive black hole leaves an imprint on a galactic nucleus in the form of a “mass deficit,” a decrease in the mass of the nucleus due to ejection of stars by the binary. The magnitude of the mass deficit is in principle related to the galaxy’s merger history, but the relation has never been quantified. Here, highaccuracy N-body simulations are used to calibrate this relation. Mass deficits are shown to be Mde f ≈ 0.5M12, with M12 the total mass of the binary; the coefficient in this relation depends only weakly on M2/M1 or on the galaxy’s pre-existing density profile. Hence, after N mergers, Mde f ≈ 0.5N M• with M• the final (current) black hole mass. When compared with observed mass deficits, this result implies 1∼ < N ∼ < 3, in accord with hierarchical galaxy formation models. Implications for binary stalling radii, the origin of hyper-velocity stars, and the distribution of dark matter at the centers of galaxies are discussed.

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© 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.

This is an author-created, un-copyedited version of an article accepted for publication/published in the Astrophysical Journal. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1086/506139

Also archived in: arXiv:astro-ph/0603439 v3 Jun 13 2007

Document Type


Department, Program, or Center

School of Physics and Astronomy (COS)


RIT – Main Campus