A Relationship Between Supermassive Black Hole Mass and the Total Gravitational Mass of the Host Galaxy

Abstract

We investigate the correlation between the mass of a central supermassive black hole (SMBH) and the total gravitational mass of the host galaxy (M _tot). The results are based on 43 galaxy-scale strong gravitational lenses from the Sloan Lens ACS Surveys (SLACS) Survey whose black hole masses were estimated through two scaling relations: the relation between black hole mass and Sérsic index (M _bh-n) and the relation between black hole mass and stellar velocity dispersion (M _bh-σ_sstarf). We use the enclosed mass within R ₂₀₀, the radius within which the density profile of the early type galaxy exceeds the critical density of the universe by a factor of 200, determined by gravitational lens models fitted to Hubble Space Telescope imaging data, as a tracer of the total gravitational mass. The best-fit correlation, where M _bh is determined from M _bh-σ_sstarf relation, is log(M _bh) = (8.18 ± 0.11) + (1.55 ± 0.31)(log(M _tot)-13.0) over 2 orders of magnitude in M _bh. From a variety of tests, we find that we cannot reliably infer a connection between M _bh and M _tot from the M _bh-n relation. The M _bh-M _tot relation provides some of the first, direct observational evidence to test the prediction that SMBH properties are determined by the halo properties of the host galaxy.