The black hole mass distribution in early-type galaxies: Cusps in Hubble Space Telescope photometry interpreted through adiabatic black hole growth

Hubble Space Telescope (HST) observations show that the surface brightness profiles of early-type galaxies have central cusps. I show that the observe d characteristics of these cusps are consistent with the hypothesis that (1 ) all early-type galaxies have central black holes that grew adiabatically in homogeneous isothermal cores and (2) these "progenitor" cores followed s caling relations similar to those of the fundamental plane. The models studied here are the ones first proposed by P. Young. They predi ct I proportional to r(-1/2) at asymptotically small radii, but I proportio nal to r(-gamma) at the radii observable with HST. The slope gamma can take on all observed values and increases monotonically with mu = M-./M-core. B oth "core" profiles (which have a break at a resolved radius and a shallow slope inside that radius) and "power-law" profiles (which have a steep slop e down to the resolution limit and no clear break) can be reproduced. Observations show that, with few exceptions, galaxies with M-V < -22 have c ore profiles, and galaxies with M-V > -20.5 have power-law profiles; both p rofile types occur in galaxies with -22 < M-V < -20.5. For the models, the scaling relations for early-type galaxies imply that the progenitor core ma ss scales with luminosity as M-core proportional to L-1.5. If, as suggested by various arguments, the black hole (BH) mass M-. scales roughly linearly with luminosity, M-. proportional to L, then mu proportional to L-0.5. Thi s yields larger cusp slopes in lower luminosity galaxies. Models with BH ma sses and progenitor cores that obey established scaling relations predict ( at the distance of the Virgo Cluster) that galaxies with M-V < -21.2 have c ore profiles and galaxies with M-V > -21.2 have power-law profiles. This re produces both the sense and the absolute magnitude of the observed transiti on. Intrinsic scatter in BH and galaxy properties can explain why both type s of galaxies are observed around the transition magnitude. The observed bi modality in cusp slopes may be due to a bimodality in IM,IL, with rapidly r otating disky galaxies having larger M-./L than slowly rotating boxy galaxi es. I 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, log M-. approxim ate to -1.83 + log L in solar units (rms scatter 0.33 dex). This agrees wit h the average relation for nearby galaxies with kinematically determined BH masses. Photometrically and kinematically determined BH masses agree to wi thin similar to 0.25 dex rms for galaxies that have both. These results pro vide additional support to the hypothesis that every galaxy (spheroid) has a central BH. The BH mass distribution inferred here is consistent with qua sar 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 t hat are otherwise unexplained, and it yields BH masses that agree with thos e determined kinematically.