Local supermassive black holes, relics of active galactic nuclei and the X-ray background

We quantify the importance of mass accretion during AGN phases in the growth of supermassive black holes (BH) by comparing the mass function of black holes in the local universe with that expected from AGN relics, which are black holes grown entirely with mass accretion during AGN phases. The local BH mass function (BHMF) is estimated by applying the well-known correlations between BH mass, bulge luminosity and stellar velocity dispersion to galaxy luminosity and velocity functions. We find that different correlations provide the same BHMF only if they have the same intrinsic dispersion. The density of supermassive black holes in the local universe which we estimate is ρBH = 4.6 +1.9 −1.4 h 2.7 × 10 5 M⊙ Mpc −3 . The relic BHMF is derived from the continuity equation with the only assumption that AGN activity is due to accretion onto massive BH’s and that merging is not important. We find that the relic BHMF at z = 0 is generated mainly at z 10 9 M⊙ but can become as large as ∼ 10 9 yr for the lowest acceptable ǫ and λ values.