Statistics of the Hubble diagram. I. Determination of q0 and luminosity evolution with application to quasars.
A set of very general and assumption-free techniques is developed for extracting information on the luminosity function and the luminosity-distance-redshift relation of a complete sample of extragalactic objects, which need not be standard candles, from the Hubble diagram of that sample. The only assumption required concerning intrinsic source properties is that the luminosity function be of constant functional form throughout space and at all epochs. A rank statistic version of the classical magnitude-redshift deceleration-parameter (q0) test is outlined, methods of testing for luminosity evolution are presented, and techniques are given for determining either the deceleration parameter or the luminosity evolution when the other is known a priori. Analysis of a sample of optically identified 3CR and 4C quasars indicates that the radio luminosity function is a relatively featureless power law and that the quasar optical Hubble diagram is consistent (95% confidence) with a deceleration parameter of 2 to 32 and a best fit of approximately 5.