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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 <= (M_BH/M_sun) <= 5*10^9. We find a total SMBH mass density of (4.2+/-1.1)*10^5 M_sun/Mpc^3, 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 \dot{M_BH}/M_BH the local SMBH mass function is fully accounted for by mass accreted by X-ray selected AGNs, with bolometric corrections indicated by current observations and a standard mass-to-light conversion efficiency ε~10%. The analysis of the accretion history highlights that the most massive BHs accreted their mass faster and at higher redshifts (z>1.5), while the lower mass BHs responsible for most of the hard X-ray background have mostly grown at z<1.5. The accreted mass function matches the local SMBH mass function if ε~0.09(+0.04,-0.03) and the Eddington ratio λ=L/L_Edd \~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 ~0.1 Gyr for present day BH masses M_BH(z=0) ~10^6 M_sun to ~0.3 Gyr for M_BH(z=0) >= 10^9 M_sun. The mass accreted during luminous phases is >= 25-30% even if we assume extreme values of ε(ε\~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).