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-center dot-sigma relationship conflict with predictions from the M-center dot-L relationship for high-luminosity galaxies, such as brightest cluster galaxies ( BCGs). The M-center dot-L relationship predicts that some BCGs may harbor BHs with M-center dot approaching 10(10) M-circle dot, while the M-center dot-sigma relationship always predicts M-center dot < 3 x 10(9) M-circle dot. We argue that the M-center dot-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(gamma), may be an independent witness of M-center dot. Using central structural parameters derived from a large sample of early-type galaxies observed by HST, we argue that L is superior to sigma as an indicator of r(gamma). Further, the r(gamma)-M-center dot relationship for 11 core galaxies with measured M-center dot appears to be consistent with the M-center dot-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-center dot-sigma relationship. M-center dot similar to 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 sigma 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-center dot > 3 x 10(9) M-circle dot would be nearly an order of magnitude richer than that inferred from the M-center dot-sigma relationship. The volume density of the most luminous QSOs may favor the M-center dot-L relationship.