The Evolution and Luminosity Function of Quasars from Complete Optical Surveys

We use several quasar samples to determine the density and luminosityevolution of quasars. Combining different samples and accounting for varyingselection criteria require tests of correlation and the determination ofdistributions for multiply truncated data. We describe new non-parametrictechniques for accomplishing these tasks, which have been developed recently byEfron and Petrosian (1998). We use matter dominated cosmological models witheither zero cosmological constant or zero spatial curvature. Of the two mostcommon models of luminosity evolution, L = exp(k t(z)) and L = (1+z)^k', wefind the second model to be a better description of the data at allluminosities; 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 luminosityfunction and the evolution of the co-moving density for the two types ofcosmological models. For the Einstein - de Sitter cosmological model we find arelatively strong increase in co-moving density up to a redshift of about 2, atwhich point the density peaks and begins to decrease rapidly. This is inagreement with results from high redshift surveys. We find some co-movingdensity evolution for all cosmological models, with the rate of evolution lowerfor models with lower matter density. We find that the local cumulativeluminosity function exhibits the usual double power law behavior. Theluminosity density (i.e. the total rate of energy output of quasars) is foundto increase rapidly at low redshift and to peak at around z = 2. Our resultsfor the luminosity density are compared to results from high redshift surveysand to the variation of the star formation rate with redshift.Comment: 28 pages, 16 Encapsulated Postscript figures, AAS-Latex. Submitted to the Astrophysical Journa