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A binary supermassive black hole leaves an imprint on a galactic nucleus inthe form of a "mass deficit," a decrease in the mass of the nucleus due toejection of stars by the binary. The magnitude of the mass deficit is inprinciple related to the galaxy's merger history, but the relation has neverbeen quantified. Here, high-accuracy N-body simulations are used to calibratethis relation. Mass deficits are shown to be approximately 0.5M_{12}, withM_{12} the total mass of the binary; the coefficient in this relation dependsonly weakly on the binary mass ratio or on the galaxy's pre-existing densityprofile. Hence, after N mergers, the mass deficit is ~0.5 N M_h with M_h thefinal (current) black hole mass. When compared with observed mass deficits,this result implies between 1 and 3 mergers for most galaxies, in accord withhierarchical galaxy formation models. Implications for binary stalling radii,the origin of hyper-velocity stars, and the distribution of dark matter at thecenters of galaxies are discussed.Comment: 11 pages, uses emulateapj.st

Mass Deficits, Stalling Radii, and the Merger Histories of Elliptical Galaxies