The evolution and luminosity function of quasars from complete optical surveys

We use several quasar samples (Large Bright QSO Survey, Homogeneous Bright QSO Survey, Durham/AAT, and Edinburgh QSO Survey) to determine the density functions and the luminosity evolution of quasars. Combining these different samples and accounting for varying selection criteria require tests of correlation and the determination of density functions for multiply truncated data. We describe new nonparametric techniques for accomplishing these tasks, which have been developed recently by Efron & Petrosian. With these methods, the luminosity evolution can be found through an investigation of the correlation of the bivariate distribution of luminosities and redshifts. Here, one assumes a cosmological model to convert the observed fluxes into luminosities. We use matter-dominated models with either zero cosmological constant or zero spatial curvature. Of the two most commonly used models for luminosity evolution, L proportional to e(kt(z)) and L proportional to (1 + z)(k'), we find that the second functional form is a better description of the data at all luminosities; we find k' = 2.58 ([2.14, 2.91] 1 sigma region) for the Einstein-de Sitter cosmological model. Using this form of luminosity evolution, we determine a global luminosity function and the evolution of the comoving density for the two types of cosmological models. For the Einstein-de Sitter cosmological model we find a relatively strong increase in comoving density up to z less than or similar to 2, at which point the density peaks and begins to decrease rapidly. This is in agreement with results from high-redshift surveys. However, we nd that pure luminosity evolution, i.e., constant comoving density, is possible for some cosmological models for 3 less than or similar to 2. We find that the local luminosity function Phi(L-0) exhibits the usual double power-law behavior. The luminosity density L(z) = integral L Psi(L, z) dL, where Psi(L, z) is the luminosity function, is found to increase rapidly at low redshift and to reach a peak at around z approximate to 2. Our results for L(z) are compared to results from high-redshift surveys and to the variation of the star formation rate with redshift.