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Figure 5.23. The quasar luminosity function from the 2DF for several redshift ranges. The luminosity function evolves in two ways: the overall number of quasars drops with time and the characteristic luminosities of the quasars also decrease with time. In the present epoch, quasars are much fewer in number and less luminous than were quasars in the past. From Croom et al.

translating directly to the left. There are also serious problems with this scenario, among them being that most local AGNs are currently radiating at Eddington ratios m « 0.1, which would have required these AGNs to have been radiating at super-Eddington rates, m ^ 1, at z « 2. Close inspection of Figure 5.23 reveals two important things.

(i) The number of extremely bright quasars (MB < -26 mag) decreases dramatically between z « 2 and z « 0.5.

(ii) There is a clear break in the slope of the luminosity function at some characteristic magnitude M* that evolves towards lower luminosity between z « 2 and z « 0.5.

Since the quasar era at z « 2, the quasar population has diminished in number and in typical luminosity. This is shown even more dramatically in Figure 5.24, which clearly demonstrates that the epoch at which the maximum space density occurs is luminosity-dependent: more-luminous objects reach their maximum density earliest, at the highest redshifts. This phenomenon is often referred to as "cosmic downsizing," to indicate that the AGN population becomes dominated by lower-luminosity objects with time.

5.11.3 Masses of distant quasars

We have already noted the difficulty of measuring the black-hole masses of AGNs. In principle, reverberation mapping should still be viable even for distant AGNs since it does not depend on angular resolution. However, problems become apparent at higher redshift and luminosity. The BLR is larger in higher-luminosity objects, so the

Figure 5.24. The evolution of the soft-X-ray (a) and hard-X-ray (b) luminosity functions for quasars. What this shows is that the higher-luminosity objects reach their highest space density at earlier epochs (higher redshifts) than do lower-luminosity objects. Labels are log of 2-10 keV flux in erg s-1. Adapted from Brandt & Hasinger (2005).

Figure 5.24. The evolution of the soft-X-ray (a) and hard-X-ray (b) luminosity functions for quasars. What this shows is that the higher-luminosity objects reach their highest space density at earlier epochs (higher redshifts) than do lower-luminosity objects. Labels are log of 2-10 keV flux in erg s-1. Adapted from Brandt & Hasinger (2005).

Figure 5.25. Distribution of black-hole masses with redshift. Note that black holes with M > 109 M& are found at redshifts z ~ 6. Adapted from Vestergaard (2006).

emission-line response times are longer and are more geometrically diluted. Also, higher-luminosity sources have lower amplitudes of variability, so the variability signatures are weaker. Moreover, the light curves suffer 1 + z time dilation, requiring even longer reverberation programs.

Although direct measurement of the masses of black holes in distant quasars becomes very difficult, there are secondary methods that we can apply, notably by using the BLR radius-luminosity relationship discussed earlier. The BLR radius can be estimated from the quasar luminosity and the corresponding line width can be measured directly. From these two measurements it is possible to estimate the black-hole mass from a single spectrum. The great utility of this is that the masses of large numbers of AGNs can be estimated through measurements made from single spectra, thus by-passing the laborious reverberation-mapping process. Masses of large populations of AGNs have been measured by several investigators (Vestergaard 2002, 2004; McLure & Jarvis 2002; Kollmeier et al. 2006; Vestergaard & Peterson 2006) in this way. The example shown in Figure 5.25 shows the remarkable result that supermassive black holes with masses M > 109 Mq were already in place by z « 4-6.

Acknowledgments

I wish to thank the organizers, students, and other lecturers for making the XVIII Winter School a valuable and enjoyable experience. I am grateful to The Ohio State University for support of this work through NSF grant AST-0604066.

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