Testing redshift variation in the X-ray and ultraviolet luminosity relations of quasars*

Abstract Quasars serve as important cosmological probes; constructing accurate luminosity relations for them is essential for their use in cosmology. If the coefficients of such luminosity relations vary with redshift, they could introduce biases into cosmological constraints derived from quasars. In this paper, we conduct a detailed analysis of the redshift variation in the X-ray and ultraviolet (UV) luminosity ( - ) relations of quasars. For the standard - relation, we show that the relation coefficients exhibit a strong and linear correlation with redshift that is not attributable to the selection effect. Additionally, we examine two three-dimensional, redshift-evolving - relations and show that the inclusion of a redshift-dependent term does not eliminate the impact of redshift evolution, given that the relation coefficients continue to evolve with redshift. Finally, we construct a new - relation in which the redshift evolution of the relation coefficients is nearly eliminated. By calibrating the luminosity relations using Hubble parameter measurements, we demonstrate that quasars based on the proposed relation yield effective constraints on cosmological parameters that are consistent with results from Planck CMB data, unlike constraints derived from the standard relation.