Super-massive Black Hole Demography: the Match between the Local and Accreted Mass Functions

We have performed a detailed analysis of the local super-massive black-hole (SMBH) mass function based on both kinematic and photometric data and derived an accurate analytical fit in the range 10 6 MBH/M⊙ 6 5 × 10 . We find a total SMBH mass density of (4.2 ± 1.1)× 105M⊙/Mpc , about 25% of which is contributed by SMBHs residing in bulges of late type galaxies. Exploiting up-to-date luminosity functions of hard X-ray and optically selected AGNs, we have studied the accretion history of the SMBH population. If most of the accretion happens at constant ṀBH/MBH, as in the case of Eddington limited accretion and consistent with recent observational estimates, the local SMBH mass function is fully accounted for by mass accreted by Xray selected AGNs, with bolometric corrections indicated by current observations and a standard mass-to-light conversion efficiency ǫ ≃ 10%. The accreted mass function matches the local SMBH mass function if, during the main accretion phases, ǫ ≃ 0.09 (+0.04,−0.03) and the Eddington ratio λ = L/LEdd ≃ 0.3 (+0.3,−0.1) (68% confidence errors). The visibility time, during which AGNs are luminous enough to be detected by the currently available X-ray surveys, ranges from ≃ 0.1Gyr for present day BH masses M BH ≃ 10 M⊙ to ≃ 0.3Gyr for M 0 BH > 10 M⊙. The mass accreted during luminous phases is > 25–30% even if we assume extreme values of ǫ (ǫ ≃ 0.3− 0.4). An unlikely fine tuning of the parameters would be required to account for the local SMBH mass function accomodating a dominant contribution from ’dark’ BH growth (due, e.g., to BH coalescence).