As a direct result of advances in the QSO survey techniques described in Chapter 10, the number of QSOs known as of the early 1990s was of order 104 (Véron-Cetty and Véron 1991, Hewitt and Burbidge 1993). It is therefore possible to explore the distribution of QSOs as a function of z, to compute their comoving space density, and to determine how the AGN population evolves with time.

Simple Tests for Evolution

Determination of the space density and luminosity function of QSOs is a difficult undertaking, and as seen in Chapter 10, the results are sensitive to many different types of selection effects. Despite these many difficulties, it was clear even during the first decade of QSO research that the comoving density of QSOs varies strongly with redshift, with an especially large number of QSOs at z ∼ 2. However, it is also at about this redshift that UV-excess techniques are most sensitive, since this is where the Lya emission line falls in the U band, so originally it was not entirely clear to what extent the inferred high densities of QSOs at z ∼ 2 were due to selection effects rather than a real peak in the comoving space density. For this reason we begin this chapter with a discussion of simple tests for changes in space density as a function of z, or equivalently, lookback time.

The Log N – Log S Test in a Non-Euclidean Universe

The classic test for a constant space density of sources is the log N - log S test that was introduced in Chapter 10.