A new assessment of the completeness of quasar surveys: Implications for the luminosity function

We apply a simple statistical method to estimating the completeness of quas ar surveys. It requires that an area has been covered by two or more, prefe rably different, selection techniques. We use three suitable data sets with separate selections from the following: variability and UV excess (170 qua sars); objective prism and UV excess (141 quasars); and multicolor and X-ra y (ROSAT, 19 quasars). We find that, for selection by UV excess, the common limit of U-B less than or equal to -0.35 +/- -0.05 leads to losses of simi lar to 35%, typically missing low-luminosity (M-B greater than or similar t o -24.5) quasars, independently of redshift. Systematic incompleteness will therefore affect the new generation of large quasar surveys that select by U-B less than or equal to -0.35. By correcting for this incompleteness, we find from the first data set (B < 21.0 and z < 2.2) that the evolution of the quasar luminosity function (LF) is best described by joint luminosity a nd density evolution. When extrapolated to z = 0, the LF matches that of lo cal Seyfert galaxies better than any previous determination. The LF shows a n increase in the number of low-luminosity quasars at low redshifts and of brighter quasars at intermediate redshifts, relative to the 1990 LF of Boyl e and coworkers. This result is consistent with models in which quasars fad e from an initial bright phase.