Until this point we have discussed the observed aspects of the evolution of quasars and AGNs, primarily the evolution of their luminosity functions. Now let us begin to consider their physical evolution, for which estimates of the masses of the central black holes are crucial. Such estimates will enable us to map the growth of the black holes with cosmic epoch.
In this meeting we have heard about three ways to estimate black hole masses: (1) from their gravitational influence on the stellar velocity distributions or gas kinematics in the centers of galaxies, (2) reverberation mapping of the broad-line emission region (Barth 2003), and (3) the use of emission-line widths and continuum luminosities (e.g., C IV, Vestergaard 2002, 2003; Mg II, McClure & Jarvis 2003). The first two provide the underpinnings for the mass estimates but are limited to nearby galaxies and AGNs. The third method, while indirect and subject to more uncertainties, has great potential value because it provides the only practical way we have at the moment of estimating the masses of quasars and AGNs at high redshift.
Vestergaard & Osmer (in preparation) are using methods 2 and 3 to make estimates of the mass functions of quasar samples at low (the BQS, Schmidt & Green 1983) and high (SDSS, Fan et al. 2001a) redshift. Their preliminary results indicate that the SDSS quasars have already achieved masses of > 109 M at z > 3.6, and their cumulative mass density is more than a order of magnitude above the BQS sample. This indicates that luminous quasars at high redshift built up their masses early (see also Vestergaard 2003). The BQS cumulative mass density, on the other hand, is an indicator of how the luminous activity has declined rapidly by the present time, when luminous quasars are quite rare. Interestingly, the SDSS cumulative mass densities appear to fit on the extension of the results from the Padovani, Burg, & Edelson (1990) sample of Seyfert galaxies at low redshift. This is consistent with the idea that both the low-redshift Seyferts and low-luminosity AGNs and the high-redshift SDSS quasars have achieved a substantial fraction of their final black hole mass growth.