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 and the total gravitational mass of the host galaxy (Mtot). 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 (Mbh - n) and the relation between black hole mass and stellar velocity dispersion (Mbh - sigma). We use the enclosed mass within R200, 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 Mbh is determined from Mbh - sigma relation, is log(Mbh) = (8.18 +/- 0.11) + (1.55 +/- 0.31) (log(Mtot) - 13.0) over 2 orders of magnitude in Mbh. From a variety of tests, we find that we cannot reliably infer a connection between Mbh and Mtot from the Mbh - n relation. The Mbh - Mtot 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.
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