  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, high-accuracy N-body simulations are used to calibrate
this relation. Mass deficits are shown to be approximately 0.5M_{12}, with
M_{12} the total mass of the binary; the coefficient in this relation depends
only weakly on the binary mass ratio or on the galaxy's pre-existing density
profile. Hence, after N mergers, the mass deficit is ~0.5 N M_h with M_h the
final (current) black hole mass. When compared with observed mass deficits,
this result implies between 1 and 3 mergers for most galaxies, 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.
