We derive improved versions of the relations between supermassive black hole mass (M BH ) and host-galaxy bulge velocity dispersion (σ) and luminosity (L) (the M-σ and M-L relations), based on 49 M BH measurements and 19 upper limits. Particular attention is paid to recovery of the intrinsic scatter (ε 0 ) in both relations. We find log(M BH /M ) = α + β log(σ/200 km s −1 ) with (α, β, ε 0 ) = (8.12 ± 0.08, 4.24 ± 0.41, 0.44 ± 0.06) for all galaxies and (α, β, ε 0 ) = (8.23 ± 0.08, 3.96 ± 0.42, 0.31 ± 0.06) for ellipticals. The results for ellipticals are consistent with previous studies, but the intrinsic scatter recovered for spirals is significantly larger. The scatter inferred reinforces the need for its consideration when calculating local black hole mass function based on the M-σ relation, and further implies that there may be substantial selection bias in studies of the evolution of the M-σ relation. We estimate the M-L relationship as log(M BH /M ) = α + β log(L V /10 11 L ,V ) of (α, β, ε 0 ) = (8.95 ± 0.11, 1.11 ± 0.18, 0.38 ± 0.09); using only early-type galaxies. These results appear to be insensitive to a wide range of assumptions about the measurement errors and the distribution of intrinsic scatter. We show that culling the sample according to the resolution of the black hole's sphere of influence biases the relations to larger mean masses, larger slopes, and incorrect intrinsic residuals.

Black hole masses predicted from the M • − σ relationship conflict with those predicted from the M • − L relationship for the most luminous galaxies, such as brightest cluster galaxies (BCGs). This is because stellar velocity dispersion, σ, increases only weakly with luminosity for BCGs and other giant ellipticals. The M • − L relationship predicts that the most luminous BCGs may harbor black holes with M • approaching 10 10 M ⊙ , while the M • − σ relationship always predicts M • < 3 × 10 9 M ⊙ . Lacking direct determination of M • in a sample of the most luminous galaxies, we advance arguments that the M • − L relationship is a plausible or even preferred description for BCGs and other galaxies of similar luminosity. Under the hypothesis that cores in central stellar density are formed by binary black holes, 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 in luminous galaxies. Further, the observed 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 black hole masses inferred from the M • − σ relationship. M • ∼ L may be expected to hold for BCGs, if they were formed in dissipationless mergers, which should preserve ratio of black hole to stellar mass. This picture appears to be consistent with the slow increase in σ with L and the more rapid increase in effective radii, R e , with L seen in BCGs as compared to less luminous galaxies. If BCGs have large BHs commensurate with their high luminosities, then the local black hole mass function for M • > 3 × 10 9 M ⊙ may be nearly an order of magnitude richer than what would be inferred from the M • − σ relationship. The volume density of the most luminous QSOs at earlier epochs may favor the predictions from the M • − L relationship.

We present observations of 77 early-type galaxies imaged with the PC1 CCD of the Hubble Space Telescope (HST ) WFPC2. ''Nuker-law'' parametric fits to the surface brightness profiles are used to classify the central structure into ''core'' or ''power-law'' forms. Core galaxies are typically rounder than power-law galaxies. Nearly all power-law galaxies with central ellipticities ! 0:3 have stellar disks, implying that disks are present in powerlaw galaxies with < 0:3 but are not visible because of unfavorable geometry. A few low-luminosity flattened core galaxies also have disks; these may be transition forms from power-law galaxies to more luminous core galaxies, which lack disks. Several core galaxies have strong isophote twists interior to their break radii, although power-law galaxies have interior twists of similar physical significance when the photometric perturbations implied by the twists are evaluated. Central color gradients are typically consistent with the envelope gradients; core galaxies have somewhat weaker color gradients than power-law galaxies. Nuclei are found in 29% of the core galaxies and 60% of the power-law galaxies. Nuclei are typically bluer than the surrounding galaxy. While some nuclei are associated with active galactic nuclei (AGNs), just as many are not; conversely, not all galaxies known to have a low-level AGN exhibit detectable nuclei in the broadband filters. NGC 4073 and 4382 are found to have central minima in their intrinsic starlight distributions; NGC 4382 resembles the double nucleus of M31. In general, the peak brightness location is coincident with the photocenter of the core to a typical physical scale of <1 pc. Five galaxies, however, have centers significantly displaced from their surrounding cores; these may be unresolved asymmetric double nuclei. Finally, as noted by previous authors, central dust is visible in about half of the galaxies. The presence and strength of dust correlates with nuclear emission; thus, dust may outline gas that is falling into the central black hole. The prevalence of dust and its morphology suggest that dust clouds form, settle to the center, and disappear repeatedly on $10 8 yr timescales. We discuss the hypothesis that cores are created by the decay of a massive black hole binary formed in a merger. Apart from their brightness profiles, there are no strong differences between core galaxies and power-law galaxies that demand this scenario; however, the rounder shapes of core, their lack of disks, and their reduced color gradients may be consistent with it.

We combine several HST investigations on the central structure of early-type galaxies to generate a large sample of surface photometry. The studies selected were those that used the ''Nuker law'' to characterize the inner light distributions of the galaxies. The sample comprises WFPC1 and WFPC2 V-band observations published earlier by our group, R-band WFPC2 photometry of Rest et al., NICMOS H-band photometry by Ravindranath et al. and Quillen et al., and the brightest cluster galaxy WFPC2 I-band photometry of Laine et al. The distribution of the logarithmic slopes of the central brightness profiles strongly affirms that the central structure of elliptical galaxies with M V < À19 is bimodal, based on both parametric and nonparametric analysis. At the HST resolution limit, most galaxies are either power-law systems, which have steep cusps in surface brightness, or core systems, which have shallow cusps interior to a steeper envelope brightness distribution. A rapid transition between the two forms occurs over the luminosity range À22 < M V < À20, with cores dominating at the highest luminosities and power laws at the lowest. There are a few ''intermediate'' systems that have both cusp slopes and total luminosities that fall within the core/power-law transition, but they are rare and do not fill in the overall bimodal distribution.

Supermassive black holes are thought to be relics of quasars, and their numbers and masses are therefore related to the quasar luminosity function and its evolution with redshift. We have used the relationship between black hole mass and bulge velocity dispersion (the M • − σ relation) to make an improved estimate of the mass density and mass spectrum of supermassive black holes. Uncertainties in the M • − σ relation have little effect on the mass density. We find a mass density of (4.8 ± 1.6)h 2 · 10 5 M ⊙ Mpc −3 . Some of the variance in published density estimates comes from the use of different values of the Hubble constant.