A relationship between supermassive black hole mass and the total gravitational mass of the host galaxy

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 S\ue9rsic index (M bh-n) and the relation between black hole mass and stellar velocity dispersion (M bh-\u3c3sstarf). 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-\u3c3sstarf relation, is log(M bh) = (8.18 \ub1 0.11) + (1.55 \ub1 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.Peer reviewed: YesNRC publication: Ye