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

We quantify the importance of mass accretion during active galactic nuclei (AGN) phases in the growth of supermassive black holes (BHs) 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 that we estimate is PBH = 4.6(-1.4)(+1-9)h(0.7)(2) x 10(5) M-circle dot Mpc(-3). The relic BHMF is derived from the continuity equation with the only assumption that AGN activity is due to accretion on to massive BHs and that merging is not important. We find that the relic BHMF at z = 0 is generated mainly at z < 3 where the major part of the growth of a BH takes place. Moreover, BH growth is antihierarchical in the sense that smaller BHs (M-BH < 10(7) M-circle dot) grow at lower redshifts (z < 1) with respect to more massive ones (z similar to 1-3). Unlike previous work, we find that the BHMF of AGN relics is perfectly consistent with the local BHMF, indicating that local BHs were mainly grown during AGN activity. This agreement. is obtained while satisfying, at the same time, the constraints imposed from the X-ray background (XRB). The comparison between the local and relic BHMFs also suggests that the merging process is not important in shaping the relic BHMF, at least at low redshifts (z < 3), and allows us to estimate the average radiative efficiency (epsilon), the ratio between emitted and Eddington luminosity (lambda) and the average lifetime of active BHs. Our analysis thus suggests the following scenario: local BHs grew during AGN phases in which accreting matter was converted into radiation with efficiencies epsilon = 0.04-0.16 and emitted at a fraction lambda = 0.1-1.7 of the Eddington luminosity. The average total lifetime of these active phases ranges from similar or equal to 4.5 x 10(8) yr for M-BH < 10(8) M-circle dot to similar or equal to 1.5 x 10(8) yr for M-BH > 10(9) M-circle dot, but can become as large as similar to10(9) yr for the lowest acceptable epsilon and lambda values.