The L_ X -L_ UV relation serves as a cornerstone for extending the Hubble diagram to higher redshift by utilizing quasars as standard candles. However, the constancy of the L_ X -L_ UV relation has been embroiled in controversy recently. In this work, we discuss the possible physical origins of evolution in the luminosity relation and provide explicit forms for the redshift and Γ_ X dependences. By calibrating quasar distances with the baryon acoustic oscillation measurements from the Dark Energy Spectroscopic Instrument Data Release 2 in combination with the cosmic microwave background measurements from Planck, the parameters in different luminosity relations are constrained with a clean quasar sample. Our analysis indicates strongly that the L_ X -L_ UV relation varies simultaneously with redshift and Γ_ X, and this conclusion is robust under the cosmological model assumptions. Furthermore, the dependence on redshift and Γ_ X implies that the L_ X -L_ UV relation is influenced by the properties of accreting supermassive black holes.
Li et al. (Thu,) studied this question.