The black hole mass distribution in early-type galaxies: cusps in HST photometry interpreted through adiabatic black hole growth

HST observations show that the surface brightness profiles of early-type galaxies have central cusps, I ∝ r−γ. Two characteristic profile types are observed: ‘core’ profiles have a break at a resolved radius and γ ≤ 0.3 inside that radius; ‘power-law’ profiles have no clear break and γ > 0.3. With few exceptions, galaxies with MV < −22 have core profiles, and galaxies with MV > −20.5 have power-law profiles. Both profile types occur in galaxies with −22 < MV < −20.5. We show here that these results are consistent with the hypothesis that: (i) all early-type galaxies have central BHs that grew adiabatically in homogeneous isothermal cores; and (ii) these ‘progenitor’ cores followed scaling relations similar to those of the fundamental plane. The models studied here are the ones first proposed by Young. They predict I ∝ r−1/2 at asymptotically small radii, but I ∝ r−γ at the radii observable with HST. The slope γ can take all observed values; it increases monotonically with μ = M•/Mcore. The scaling relations for early-type galaxies imply that the progenitor core mass scales with luminosity as Mcore ∝ L1.5. If, as suggested by various arguments, the black hole (BH) mass M• scales roughly linearly with luminosity, M• ∝ L, then μ ∝ L−0.5. This yields larger cusp slopes in lower-luminosity galaxies. Models with BH masses and progenitor cores that obey established scaling relations predict (at the distance of the Virgo cluster) that galaxies with MV < −21.2 have core profiles and galaxies with MV > −21.2 have power-law profiles. This reproduces both the sense and the absolute magnitude of the observed transition. Intrinsic scatter in BH and galaxy properties can explain why both types of galaxies are observed around the transition magnitude. The observed bimodality in cusp slopes may be due to a bimodality in M•/L, with rapidly rotating disky galaxies having larger M•/L than slowly rotating boxy galaxies. We apply the models to 46 galaxies with published HST photometry. Both core and power-law galaxies are well fitted. The models suggest a roughly linear correlation between BH mass and V -band galaxy luminosity, logM• ≈ −1.83 + logL in solar units (RMS scatter 0.33 dex). This agrees with the average relation for nearby galaxies with kinematically determined BH masses. Photometrically and kinematically determined BH masses agree to within ∼ 0.25 dex RMS for galaxies that have both. These results provide additional support to the hypothesis that every galaxy (spheroid) has a central BH. The BH mass distribution inferred here is consistent with quasar statistics for a BH accretion efficiency of 4%. The proposed scenario is not a unique way to interpret the observed surface brightness cusps of galaxies, but it explains observational correlations that are otherwise unexplained, and it yields BH masses that agree with those determined kinematically. Subject headings: galaxies: elliptical and lenticular, cD — galaxies: kinematics and dynamics — galaxies: nuclei — galaxies: structure.