We explore whether an independent determination of the distance‒redshift relation, and hence cosmological model parameters, can be obtained from the apparent correlations between two different wave-band luminosities or fluxes, as has been claimed in recent works using the X-ray and ultraviolet luminosities and fluxes of quasars. We show that such an independent determination is possible only if the correlation between luminosities is obtained independently of the cosmological model and measured fluxes and redshifts, for example, based on sound theoretical models or unrelated observations. In particular, we show that if the correlation is determined empirically for two luminosities obtained from fluxes and redshifts, then the method suffers from circularity. In the case where the observed correlation between fluxes in very narrow redshift bins is used as a proxy for the luminosity correlation, we show that one is dealing with a pure tautology with no information on distances and cosmological model. We argue that the problem arises because of the incomplete treatment of the correlation, and we use numerical methods with a joint X-ray and ultraviolet quasar data set to demonstrate this shortcoming.

We explore the evolution of the X-ray luminosity function of quasars and the intrinsic correlation between the X-ray and 2500 Å ultraviolet luminosities, utilizing techniques verified in previous works and a sample of over 4000 quasars detected with Chandra and XMM-Newton in the range 0 < z < 5. We find that quasars have undergone significantly less evolution with redshift in their total X-ray luminosity than in other wave bands. We then determine that the best-fit intrinsic power-law correlation between the X-ray and ultraviolet luminosities, of the form L X ′ ∝ ( L UV ′ ) γ , is γ = 0.28 ± 0.03, and we derive the luminosity function and density evolution in the X-ray band. We discuss the implications of these results for models of quasar systems.