Supermassive black hole demography: the match between the local and accreted mass functions

We have performed a detailed analysis of the local supermassive black hole (SMBH) mass function based on both kinematic and photometric data and we have derived an accurate analytical fit in the range 10(6) less than or equal to M-BH M-circle dot less than or equal to 5 x 10(9). We find a total SMBH mass density of (4.2 +/- 1.1) x 10(5) M-circle dot Mpc(-3), about 25 per cent 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 active galactic nuclei (AGNs), we have studied the accretion history of the SMBH population. If most of the accretion occurs at constant MBH 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 X-ray selected AGNs, with bolometric corrections indicated by current observations and a standard mass-to-light conversion efficiency epsilon similar or equal to 10 per cent. The analysis of the accretion history highlights that the most massive BHs (associated with bright optical quasi-stellar objects) accreted their mass faster and at higher redshifts (typically at 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, during the main accretion phases, ε &SIME; 0.09 (+0.04, -0.03) and the Eddington ratio λ = L/L-Edd &SIME;0.3 (+0.3,-0.1) (68 per cent confidence errors). The visibility time, during which AGNs are luminous enough to be detected by the currently available X-ray surveys, ranges from &SIME;0.1 Gyr for present-day BH masses M-BH(0) similar or equal to 10(6) M-circle dot to similar or equal to0.3 Gyr for M-BH(0) greater than or equal to 10(9) M-circle dot. The mass accreted during luminous phases is greater than or equal to25-30 per cent even if we assume extreme values of epsilon (epsilon similar or equal to 0.3-0.4). An unlikely fine tuning of the parameters would be required to account for the local SMBH mass function accommodating a dominant contribution from 'dark' BH growth (due, for example, to BH coalescence).