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

Abstract

The surface brightness profiles of early-type galaxies have central cusps. Two characteristic profile types are observed with HST: `core' profiles have a break at a resolved radius and logarithmic cusp slope gamma < 0.3 inside that radius; `power-law' profiles have no clear break and gamma > 0.3. With few exceptions, galaxies with M_V < -22 have core profiles, and galaxies with M_V > -20.5 have power-law profiles. Both profile types occur in galaxies with -22 < M_V < -20.5. We show that these results are consistent with the hypothesis that: (i) all early-type galaxies have black holes (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. Models with BH masses and progenitor cores that obey established scaling relations predict (at Virgo) that galaxies with M_V < -21.2 have core profiles and galaxies with M_V > -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_bh/L, with rapidly rotating disky galaxies having larger M_bh/L than slowly rotating boxy galaxies. Application to individual galaxies with HST photometry yields a roughly linear correlation between BH mass and V-band galaxy luminosity, log M_bh = -1.83 + log L (solar units). This agrees with the average relation for nearby galaxies with kinematically determined BH masses, and also with predictions from quasar statistics (shortened abstract).