Redshift Evolution of the X-Ray and Ultraviolet Luminosity Relation of Quasars: Calibrated Results from SNe Ia

Quasars could serve as standard candles if the relation between their ultraviolet (UV) and X-ray luminosities can be accurately calibrated. Previously, we developed a model-independent method to calibrate quasar standard candles using the distance–redshift relation reconstructed from Type Ia supernovae (SNe Ia) at z < 2 using Gaussian process regression. Interestingly, we found that the calibrated quasar standard candle data set preferred a deviation from ΛCDM at redshifts above z > 2. One possible interpretation of these findings is that the calibration parameters of the quasar UV and X-ray luminosity relationship evolves with redshift. In order to test the redshift dependence of the quasar calibration in a model-independent manner, we divided the quasar sample whose redshift overlaps with the redshift coverage of Pantheon+ SNe Ia compilation into two subsamples: a low-redshift quasar subsample and a high-redshift quasar subsample. Assuming all the quasar samples are reliable, our results show that there is about a 4σ inconsistency between the quasar parameters inferred from the subsamples without considering evolution. This inconsistency suggests the possibility of considering redshift evolution for the relationship between the quasars’ UV and X-ray luminosities. We then test an explicit parameterization of the redshift evolution of the quasar calibration parameters via γ(z) = γ0 + γ1(1 + z) and β(z) = β0 + β1(1 + z). Combining this redshift-dependent calibration relationship with the distance–redshift relationship reconstructed from the Pantheon+ supernova compilation, we find the high-redshift subsample and low-redshift subsample become consistent at the 2σ level, which means that the parameterized form of γ(z) and β(z) works well at describing the evolution of the quasar calibration parameters.