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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 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 (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 HST 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 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 supermassive black hole properties are determined by the halo properties of the host galaxy.