The Evolution and Luminosity Function of Quasars from Complete Optical   Surveys
  We use several quasar samples to determine the density and luminosity evolution of quasars. Combining different samples and accounting for varying selection criteria require tests of correlation and the determination of distributions for multiply truncated data. We describe new non-parametric techniques for accomplishing these tasks, which have been developed recently by Efron and Petrosian (1998). We use matter dominated cosmological models with either zero cosmological constant or zero spatial curvature. Of the two most common models of luminosity evolution, L = exp(k t(z)) and L = (1+z)^k', we find the second model to be a better description of the data at all luminosities; we find k' = 2.58 ([2.14,2.91] one sigma region) for the Einstein - de Sitter model.   Using this form of luminosity evolution we determine a global luminosity function and the evolution of the co-moving density for the two types of cosmological models. For the Einstein - de Sitter cosmological model we find a relatively strong increase in co-moving density up to a redshift of about 2, at which point the density peaks and begins to decrease rapidly. This is in agreement with results from high redshift surveys. We find some co-moving density evolution for all cosmological models, with the rate of evolution lower for models with lower matter density. We find that the local cumulative luminosity function exhibits the usual double power law behavior. The luminosity density (i.e. the total rate of energy output of quasars) is found to increase rapidly at low redshift and to peak at around z = 2. Our results for the luminosity density are compared to results from high redshift surveys and to the variation of the star formation rate with redshift. 
Alexander Maloney, Vahe Petrosian