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 Sersic index (M(bh)-n) and the relation between black hole mass and stellar velocity dispersion (M(bh) - sigma(*)). 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) - sigma(*) relation, is log(M(bh)) = (8.18 +/- 0.11) + (1.55 +/- 0.31)(log(M(tot))-13.0) over 2 orders of magnitude in Mbh. 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.