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 10 10 M ☉ , while the M • -σ relationship always predicts M • < 3 × 10 9 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 × 10 9 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.