Observational constraints on growth of massive black holes

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  • 6 March 2002
Abstract
We study the observational constraints on the growth of massive black holes (BHs) in galactic nuclei. We use the velocity dispersions of early-type galaxies obtained by the SDSS and the relation between BH mass and velocity dispersion to estimate the local BH mass density to be 1.7x10^5 Msun/Mpc^3 in the cosmological model (Omega_m,Omega_Lambda,h)=(0.3,0.7,0.65). We also use the QSO luminosity function from the 2dF Redshift Survey to estimate the BH mass density accreted during optically bright QSO phases. The local BH mass density is consistent with the density accreted during optically bright QSO phases if QSOs have an efficiency 0.1. By studying the continuity equation for the BH mass distribution, including the effect of BH mergers, we find relations between the local BH mass function and the QSO luminosity function. In the classical case where the BH mass is assumed to be conserved during BH mergers, comparison of the predicted relations with the observations suggests that luminous QSOs (L_{bol}$\ga$ 10^{46} erg/s) have a high efficiency (e.g. 0.2-0.3) and that the growth of high-mass BHs ($\ga$10^8 Msun) comes mainly from accretion during optically bright QSO phases. If the growth of low-mass BHs also occurs mainly during optically bright QSO phases, less luminous QSOs must accrete with a low efficiency <0.1; alternatively, they may accrete with high efficiency, but a significant fraction should be obscured. We estimate that the mean lifetime of luminous QSOs is (4-60)x10^7 yr; the lower end of this range is comparable to the Salpeter time. We also investigate the extreme case in which total BH mass decreases during BH mergers due to gravitational radiation while total BH entropy is conserved; in this case the observations again suggest that BHs in most luminous QSOs accrete with high efficiency.

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