The redshift and X-ray photon index evolutionary <i>L</i> _X - <i>L</i> _UV relations of quasars

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.