The redshift and X-ray photon index evolutionary L_X-L_UV relations of quasars

¹ China Institute of Atomic Energy Beijing 102413, China
² Jinping Deep Underground Frontier Science and Dark Matter Key Laboratory of Sichuan Province Liangshan 615000, China
³ School of Nuclear Science and Technology, University of Chinese Academy of Sciences Beijing 101408, China

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Received: 1 August 2025
Accepted: 9 January 2026

Abstract

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.