The need to recover the intrinsic distribution of properties for a population of objects from observational data that contain various elements of bias occurs frequently in astronomy. The relevant procedures have been slow in coming into use in the quasar field but applications in other areas, such as binary stars (Duquennoy and Mayor 1991), contain some remarkably close parallels to the problems inherent in quasar surveys. Substantial progress is being made in the development of techniques to calculate P (M, z, SED), and the prejudice that it is necessary to perform ``unbiased'' and ``complete'' quasar surveys is being replaced by the realization of the importance of quantitative determinations of survey selection functions.
Existing quasar surveys have provided a qualitative picture of the evolution of the luminosity function and of the spatial clustering properties of the population. However, the lack of quantitative information on: (a) the intrinsic distribution of quasar SEDs, (b) whether the distribution of SEDs changes as a function of redshift or luminosity, and (c) the resulting uncertainties in the luminosity function and evolution, can be directly ascribed to the lack of surveys for which selection functions have been determined. Given the extensive coverage of the absolute magnitude versus redshift plane (Figure 1) by surveys that lack associated P (M, z, SED) calculations, the scope for significant improvement from such samples is small. Studies that provide a more complete picture of the quasar population will be those where the derivation of P (M, z, SED) is an integral part of the undertaking.
Future analyses of survey results will incorporate improved approximations to quasar SEDs, including the distribution of SED types within the population. Data from a wide variety of sources, including multi-band photometry from U through to the K band, ultraviolet spectroscopy from HST, near-infrared spectroscopy using array detectors, and spectra from X-ray satellites, will provide greatly improved characterizations of quasar SEDs. These, in turn, will improve the parametrization of the evolution of the quasar population and should enable the question of whether the distribution of SEDs changes as a function of cosmic time to be addressed. The criterion for assessing the degree of our progress will be the level of agreement between the determination of the intrinsic properties of the quasar population from surveys undertaken at different wavelengths or using different selection methodologies.
We are grateful to Brian Boyle, Fred Chaffee, Mike Irwin, Pat Osmer, David Schade and Stephen Warren for reading and commenting on earlier drafts. Brian Boyle and Steve Warren both gave generously of their time and effort to provide figures. Our own work on quasar surveys is supported by the National Science Foundation Grant AST-90-01181 and in part by a NATO Collaborative Research Grant to one of us (P.C.H).