STATISTICALLY EFFICIENT PARALLEL TESTING OF THE HUBBLE AND LUNDMARK LAWS IN THE PREEVOLUTIONARY X-RAY-BAND

The Hubble (linear) and Lundmark (homogeneous quadratic) redshift-dist ance laws are subjected to statistically efficient parallel tests on t he basis of the complete sample of X-ray active galactic nuclei of Gio ia et al. (1990), Maccacaro et al. (1991), and Stocke et al. (1991). T he samples treated to this end consist of bright flux-limited subsampl es in a variety of redshift ranges. Luminosity functions are estimated by an optimal non-parametric procedure that makes no assumptions rega rding the spatial distribution of the sources and is compatible with m issing redshifts. It assumes only that the discrimination against obje cts on the basis of flux is inconsequential above a suitable limit, wh ich may depend on the position of the object. This is subject to a pos teriori testing, which is provided. The Hubble and Lundmark laws are t ested in successively higher redshift ranges up to z = 0.4, within whi ch range Maccacaro et al. find only weak evolution. Directly observed quantities are compared with the predictions of both cosmologies, and objective statistical significance levels estimated. The Hubble law ap pears inconsistent with the observations, unless evolution effectively equivalent to its replacement by the Lundmark law is postulated. For example, the dispersion in log flux invariably exceeds the observed va lue, as does also the correlation of log luminosity with redshift. The Lundmark law fits the observations closely and moreover predicts that the predictions of the Hubble law will be deviant in the amounts obse rved. Very bright optical subsamples give similar results. In the full redshift range of the sample, z < 3, the chronometric predictions for directly observed quantities, which involve no adjustable parameters such as q0, and which assume no evolution, are quite accurate. The lar ge deviations of the Friedmann predictions from these values, which ma y be ascribed to unobservable evolutionary effects, are statistically coincident with the chronometric prediction for the results of analysi s predicated on Friedmann cosmology.