The Luminosity Function of Quasars

We propose a new evolutionary model for the optical luminosity function of quasars. Our analytical model is derived from fits to the empirical luminosity function estimated by Hartwick & Schade and Warren, Hewett, & Osmer on the basis of more than 1200 quasars over the range of redshifts 0 <~ z <~ 4.5. We find that the evolution of quasars over this entire redshift range can be well fitted by a Gaussian distribution, while the shape of the luminosity function can be well fitted by either a double power law or an exponential L^1/4^ law. The predicted number counts of quasars, as a function of either apparent magnitude or redshift, are fully consistent with the observed ones. Our model indicates that the evolution of quasars reaches its maximum at z ~ 2.8 and declines at higher redshifts. An extrapolation of the evolution to z ~> 4.5 implies that quasars may have started their cosmic fireworks at z_f_ ~ 5.2-5.5. Forthcoming surveys of quasars at these redshifts will be critical to constrain the epoch of quasar formation. All the results we derived here are based on observed quasars and are therefore subject to the bias of obscuration by dust in damped Lyα systems. Future surveys of these absorption systems at z ~> 3 will also be important if the formation epoch of quasars is to be known unambiguously.