The Masses of Nuclear Black Holes in Luminous Elliptical Galaxies and Implications for the Space Density of the Most Massive Black Holes^*

Black hole (BH) masses predicted from the M_•-σ relationship conflict with predictions from the M_•-L relationship for high-luminosity galaxies, such as brightest cluster galaxies (BCGs). The M_•-L relationship predicts that some BCGs may harbor BHs with M_• approaching 10¹⁰ M_☉, while the M_•-σ relationship always predicts M_• < 3 × 10⁹ M_☉. We argue that the M_•-L relationship is a plausible description for galaxies of high luminosity. If the cores in central stellar density are formed by binary BHs, the inner core cusp radius, r_γ, may be an independent witness of M_•. Using central structural parameters derived from a large sample of early-type galaxies observed by HST, we argue that L is superior to σ as an indicator of r_γ. Further, the r_γ-M_• relationship for 11 core galaxies with measured M_• appears to be consistent with the M_•-L relationship for BCGs. BCGs have large cores appropriate for their large luminosities that may be difficult to generate with the more modest BH masses inferred from the M_•-σ relationship. M_• ~ M would be expected for BCGs, if they were formed in dissipationless mergers, which should preserve the ratio of BH to stellar mass, M. This scenario appears to be consistent with the slow increase in σ with L and the more rapid increase in effective radii with L seen in BCGs as compared to less luminous galaxies. If BCGs have large BHs commensurate with their luminosities, then the local BH mass function for M_• > 3 × 10⁹ M_☉ would be nearly an order of magnitude richer than that inferred from the M_•-σ relationship. The volume density of the most luminous QSOs may favor the M_•-L relationship.