3.1. X-ray Measurements of AGN Evolution and the Growth of Supermassive Black Holes
Optical studies of AGN evolution have historically focused on luminous quasars (e.g., Hewett & Foltz 1994; Osmer 2004). These have been known to evolve positively with redshift since 1968 (Schmidt 1968), having a comoving space density at z 2 that is 100 times higher than at z 0. Pure luminosity evolution (PLE) models provide acceptable fits to large optically selected samples such as 16, 800 luminous AGN from a combination of the recent 2dF and 6dF surveys out to z = 2.1 (Croom et al. 2004). At z 2.7, the space density of luminous quasars selected in wide-field optical multicolor and emission-line surveys shows a strong decline with redshift (e.g., Schmidt, Schneider & Gunn 1995; Fan et al. 2001). Deep optical AGN surveys, such as COMBO-17, have recently discovered significant numbers of moderate-luminosity AGN (with MB > - 23) at z 1-4 (Wolf et al. 2003). Like luminous quasars, the moderate-luminosity AGN found in these surveys also appear to peak in comoving space density around z 2. Although a careful merging of the COMBO-17 data with a large sample of higher luminosity AGN has yet to be published, there are hints that the comoving space density of moderate-luminosity AGN peaks at smaller redshift (L. Wisotzki, pers. comm.).
As described in Sections 1.3 and 2.3, deep X-ray surveys efficiently select AGN significantly less luminous than those found in optical surveys out to high redshift. Deep plus wide X-ray surveys can therefore cover an extremely broad range of luminosity. Contrary to the PLE model for optically selected luminous quasars, the moderate-luminosity AGN selected in the 0.5-2 keV and 2-10 keV bands require luminosity-dependent density evolution (LDDE; e.g., Miyaji, Hasinger & Schmidt 2000; Cowie et al. 2003; Fiore et al. 2003; Steffen et al. 2003; Ueda et al. 2003; Hasinger, Miyaji & Schmidt 2005). Figure 7 shows the X-ray luminosity function based on 950 AGN selected in the 0.5-2 keV band from deep Chandra and XMM-Newton surveys as well as deep plus wide ROSAT surveys (Hasinger, Miyaji & Schmidt 2005). Strong positive evolution from z 0-2 is only seen at high luminosities; lower luminosity AGN evolve more mildly. The evolutionary behavior measured in the 2-10 keV band is similar. These results are robust to incompleteness of the spectroscopic follow up, although clearly they are still dependent upon the completeness of AGN X-ray selection (see Section 2.4). At a basic level, LDDE is not unexpected as simple PLE and pure density evolution (PDE) models have physical difficulties (see, e.g., Weedman 1986 and Peterson 1997). Simple PLE models tend to overpredict the number of 1010 M black holes in the local universe, while simple PDE models tend to overpredict the local space density of quasars and the CXRB intensity.
Figure 7. The 0.5-2 keV luminosity function for type 1 AGN in six redshift shells. The dashed curves show the best LDDE fit to the data. For ease of comparison, the dot-dashed curves in each panel show the best-fit model for the z = 0.015-0.2 redshift shell. Adapted from Hasinger, Miyaji & Schmidt (2005).
Figure 8 shows estimates of the comoving space density of AGN in different X-ray luminosity ranges as a function of redshift. Figure 8a has been constructed for the 0.5-2 keV band using the Hasinger, Miyaji & Schmidt (2005) sample. Figure 8b is for the 2-10 keV band, utilizing a combination of Chandra, ASCA, and 1 surveys with 247 AGN in total (Ueda et al. 2003). These plots illustrate that (1) the AGN peak space density moves to smaller redshift with decreasing luminosity, and (2) the rate of evolution from the local universe to the peak redshift is slower for less-luminous AGN. It appears that SMBH generally grow in an "anti-hierarchical" fashion: while the 107.5 - 109 M SMBH in rare, luminous AGN could grow efficiently at z 1-3, the 106 - 107.5 M SMBH in more-common, less-luminous AGN had to wait longer to grow (z 1.5). In the 0.5-2 keV band the sensitivity and statistics are good enough to detect a clear decline of the AGN space density toward higher redshifts (also see Silverman et al. 2004); such a high-redshift decline is also hinted at in some 2-10 keV band analyses (Fiore et al. 2003; Steffen et al. 2003).
Figure 8. (a) The comoving space density of AGN selected in the 0.5-2 keV band as a function of redshift. Results are shown for five luminosity ranges; these are labeled with logarithmic luminosity values. Adapted from Hasinger, Miyaji & Schmidt (2005). (b) The same for AGN selected in the 2-10 keV band using three luminosity ranges. Adapted from Ueda et al. (2003).
The AGN luminosity function can be used to predict the masses of remnant SMBH in galactic centers. This is done using the ingenious Soltan (1982) continuity argument, adopting an AGN mass-to-energy conversion efficiency and bolometric correction factor. The local mass density of SMBH in dormant quasar remnants originally predicted by Soltan (1982) was > 0.47 0.1-1 × 105 M Mpc-3, where 0.1 is the mass-to-energy conversion efficiency of the accretion process divided by 0.1. For a Schwarzschild black hole, is expected to be 0.054 or larger, depending upon the accretion-disk torque at the marginally stable orbit around the black hole (e.g., Agol & Krolik 2000). For a rapidly rotating Kerr black hole, can be as high as 0.36. More recent determinations of from optical quasar luminosity functions are around 2 0.1-1 × 105 M Mpc-3 (e.g., Chokshi & Turner 1992; Yu & Tremaine 2002). Estimates from the CXRB spectrum, including obscured accretion power, originally obtained even larger values: 6-9 (Fabian & Iwasawa 1999) or 8-17 (Elvis, Risaliti & Zamorani 2002) in the above units. However, these were derived assuming that the evolution of moderate-luminosity AGN is the same as that of quasars (i.e., that moderate-luminosity peak in number density at z 2), and they need to be revised downward by a factor of 3 in light of the currently observed evolution of CXRB sources (Fabian 2004). Values derived from the infrared band (Haehnelt & Kauffmann 2001) or multiwavelength observations (Barger et al. 2001b) are high (8-9 in the above units). Arguably the most reliable determination comes from an integration of the Ueda et al. (2003) hard X-ray luminosity function including a revised bolometric correction (which ignores infrared emission to avoid the double counting of luminosity) and a plausible correction for missed Compton-thick AGN: 3.5 0.1-1 × 105 M Mpc-3 (Marconi et al. 2004).
The SMBH masses measured in local galaxies are correlated with the velocity dispersions and luminosities of their host bulges (e.g., Kormendy & Gebhardt 2001 and references therein). Using these correlations with velocity dispersion functions or luminosity functions for local galaxies, the total SMBH density in galactic bulges can be estimated. Scaled to the same assumption for the Hubble constant (see Section 1), several recent papers arrive at different values of , mainly depending on assumptions about the SMBH-galaxy correlations. For example, Yu & Tremaine (2002) derive (2.9 ± 0.5) × 105 M Mpc-3 while Marconi et al. (2004) derive (4.6-1.4+1.9) × 105 M Mpc-3. These values are plausibly consistent with the current best estimates of accreted mass density for 0.1. Marconi et al. (2004) and Shankar et al. (2004) also demonstrate that the observed accretion can plausibly explain the measured distribution function of local SMBH masses.