We summarize a study where we test the hypothesis that local black holes ( BH ) are relics of AGN activity .
We compare the mass function of BHs in the local universe with that expected from AGN relics , which are BHs 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 .
The density of BHs in the local universe is \rho _ { \mathrm { BH } } = 4.6 _ { -1.4 } ^ { +1.9 } h _ { 0.7 } ^ { 2 } \times 10 ^ { 5 } ~ { } \mathrm { M } _ % { \odot } \mathrm { Mpc } ^ { -3 } .
The relic BHMF is derived from the continuity equation with the only assumption that AGN activity is due to accretion onto massive BHs and that merging is not important .
We find that the relic BHMF at z = 0 is generated mainly at z < 3 .
Moreover , the BH growth is anti-hierarchical in the sense that smaller BHs ( M _ { \mathrm { BH } } < 10 ^ { 7 } M _ { \odot } ) grow at lower redshifts ( z < 1 ) with respect to more massive ones ( z \sim 1 - 3 ) .
Unlike previous work , we find that the BHMF of AGN relics is perfectly consistent with the local BHMF indicating the local BHs were mainly grown during AGN activity .
This agreement is obtained while satisfying , at the same time , the constraints imposed by the X-ray background .
The comparison with the local BHMF also suggests that the merging process is not important in shaping the relic BHMF , at least at low redshifts ( z < 3 ) .
Our analysis thus suggests the following scenario : local BHs grew during AGN phases in which accreting matter was converted into radiation with efficiencies \varepsilon = 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 \simeq 4.5 \times 10 ^ { 8 } yr for M _ { \mathrm { BH } } < 10 ^ { 7 } M _ { \odot } to \simeq 1.5 \times 10 ^ { 8 } yr for M _ { \mathrm { BH } } > 10 ^ { 9 } M _ { \odot } .