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M.C. Aller, D.O. Richstone (University of Michigan)
Using a basic assumption that the bulge velocity dispersion of a galaxy can be used to predict the mass of its supermassive black hole, it is possible to estimate the mass density of black holes in the universe. Constructing the number density as a function of galaxy velocity dispersion from published data, an expression for the number density of black holes as a function of mass can be constructed. By taking a Schechter-type luminosity function for a given galaxy type, and applying an appropriate bulge-to-total galaxy magnitude correction, the number density as a function of bulge luminosity can be obtained. This function may then be combined with a Faber-Jackson power law relating velocity dispersion and luminosity to obtain a velocity dispersion function for each galaxy type. By coupling this dispersion function with a relationship between the mass of the black hole and the velocity dispersion of its host galaxy, it is possible to produce an expression for the number density of black holes as a function of black hole mass for each galaxy type, which is of a similar form to a Schechter function. By integrating this function over all black hole mass, an estimate of the mass density of black holes for a given galaxy type may be obtained. Summing over all galaxy types, the cumulative mass density of black holes is found to be 6 \cdot 105 solar masses per cubic megaparsec for an h=1 universe.
The authors acknowledge support from NASA/Space Telescope Science Institute.