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 Sloan Digital Sky Survey and the relation between BH mass and velocity dispersion to estimate the local BH mass density to be ρ • (z = 0) (2.5 ± 0.4) × 10 5 h 2 0.65 M Mpc −3 . We also use the quasistellar object (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 a massto-energy conversion 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. If 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 10 46 erg s −1 ) have a high efficiency (e.g. ∼ 0.2, which is possible for thin-disc accretion on to a Kerr BH) and the growth of high-mass BHs ( 10 8 M ) comes mainly from accretion during optically bright QSO phases, or that luminous QSOs have a superEddington luminosity. If luminous QSOs are not accreting with super-Eddington luminosities and 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 (L bol 10 46 erg s −1 ) is (3-13) × 10 7 yr, which is comparable to the Salpeter time. We also investigate the case in which total BH mass decreases during BH mergers due to gravitational radiation; in the extreme case in which total BH entropy is conserved, the observations again suggest that BHs in most luminous QSOs are Kerr BHs accreting with an efficiency 0.1.Key words: black hole physics -galaxies: active -galaxies: evolution -galaxies: nucleiquasars: general -cosmology: miscellaneous. I N T RO D U C T I O NMost nearby galaxies contain massive dark objects at their centres (e.g. Kormendy & Richstone 1995;Kormendy & Gebhardt 2001), which are presumably black holes (BHs). The existence of these objects was predicted by arguments based on quasi-stellar object (QSO) energetics and demography (e.g. Soltan 1982;Rees 1984). Studies of central BHs in nearby galaxies have also revealed a tight correlation between BH mass and galactic velocity dispersion (Ferrarese & Merritt 2000;Gebhardt et al. 2000), and a less tight correlation between BH mass and the luminosity (or mass) of the hot stellar component of the host galaxy (e.g. Kormendy & Gebhardt 2001, and references therein; by 'hot'component we mean either an elliptical galaxy or the bulge of a spiral or S0 galaxy). These cor-E-mail:yqj@astro.princeton.edu(QY);tremaine@astro.princeton.edu (ST) relations strongly suggest a...

We study three processes that eject hypervelocity (> 10 3 km s −1 ) stars from the Galactic center: (i) close encounters of two single stars; (ii) tidal breakup of binary stars by the central black hole, as originally proposed by Hills; and (iii) threebody interactions between a star and a binary black hole (BBH). Mechanism (i) expels hypervelocity stars to the solar radius at a negligible rate, ∼ 10 −11 yr −1 . Mechanism (ii) expels hypervelocity stars at a rate ∼ 10 −5 (η/0.1) yr −1 , where η is the fraction of stars in binaries with semimajor axis a b 0.3 AU. For solar-mass stars, the corresponding number of hypervelocity stars within the solar radius R 0 = 8 kpc is ∼ 60(η/0.1)(a b /0.1 AU) 1/2 . For mechanism (iii), Sgr A * is assumed to be one component of a BBH. We constrain the allowed parameter space (semimajor axis, mass ratio) of the BBH. In the allowed region (for example, semimajor axis of 0.5 × 10 −3 pc and mass ratio of 0.01), the rate of ejecting hypervelocity stars can be as large as ∼ 10 −4 yr −1 and the expected number of hypervelocity stars within the solar radius can be as large as ∼ 10 3 . Hypervelocity stars may be detectable by the next generation of large-scale optical surveys.

Since many or most galaxies have central massive black holes (BHs), mergers of galaxies can form massive binary black holes (BBHs). In this paper, we study the evolution of massive BBHs in realistic galaxy models, using a generalization of techniques used to study tidal disruption rates around massive BHs. The evolution of BBHs depends on BH mass ratio and host galaxy type. BBHs with very low mass ratios (say, $\la$ 0.001) are hardly ever formed by mergers of galaxies because the dynamical friction timescale is too long for the smaller BH to sink into the galactic center within a Hubble time. BBHs with moderate mass ratios are most likely to form and survive in spherical or nearly spherical galaxies and in high-luminosity or high-dispersion galaxies; they are most likely to have merged in low-dispersion galaxies (line-of-sight velocity dispersion $\la$ 90 km/s) or in highly flattened or triaxial galaxies. The semimajor axes and orbital periods of surviving BBHs are generally in the range 10^{-3}-10 pc and 10-10^5 yr; and they are larger in high-dispersion galaxies than in low-dispersion galaxies, larger in nearly spherical galaxies than in highly flattened or triaxial galaxies, and larger for BBHs with equal masses than for BBHs with unequal masses. The orbital velocities of surviving BBHs are generally in the range 10^2-10^4 km/s. The methods of detecting surviving BBHs are also discussed. If no evidence of BBHs is found in AGNs, this may be either because gas plays a major role in BBH orbital decay or because nuclear activity switches on soon after a galaxy merger, and ends before the smaller BH has had time to spiral to the center of the galaxy.Comment: 32 pages, including 14 figures, submitted to MNRA

QSOs are believed to be powered by accretion onto massive black holes (BHs). In this paper, assuming that each central BH in nearby galaxies has experienced the QSO phase and ignoring BH mergers, we establish a relation between the QSO luminosity function (LF) and the local BH mass function (MF). The QSOLF is jointly controlled by the luminosity evolution of individual QSOs and the triggering history of the accretion onto seed BHs. By comparing the time integral of the QSOLF with that inferred from local BHs, we separate the effect of the luminosity evolution of individual QSOs from the effect of the triggering history. Assuming that the nuclear luminosity evolution includes two phases (first increasing at the Eddington luminosity with growth of BHs and then declining), we find that observations are generally consistent with the expected relation between the QSOLF and the local BHMF and obtain the following constraints on QSO models and BH growth: (i) The QSO mass-toenergy efficiency should be k0.1. (ii) The lifetime (defined directly through the luminosity evolution of individual QSOs here) should be k4 Â 10 7 yr. The characteristic declining timescale in the second phase should be significantly shorter than the Salpeter timescale Sp , and BH growth should not be dominated by the second phase. (iii) The ratio of obscured QSOs/AGNs to optically bright QSOs should be not larger than 7 at M B $ À23 and 3 at M B $ À26 if ¼ 0:31, and not larger than 1 at M B $ À23 and negligible at M B $ À26 if ¼ 0:1. (iv) It is unlikely that most QSOs are accreting at super-Eddington luminosities. We point out that it is hard to accurately estimate the value of the QSO lifetime from the QSOLF and/or the local BHMF, if it is longer than a certain value (e.g., $4 Sp in this study). We discuss the importance of accurate measurements of the intrinsic scatter in the BH mass and velocity dispersion relation of local galaxies and the scatter in the bolometric correction of QSOs. We also discuss some possible applications of the work in this paper, such as to the study of the demography of QSOs and the demography of normal galaxies at intermediate redshift.