Revisiting the X-ray-to-UV relation of quasars in the era of all-sky surveys

ABSTRACT The X-ray-to-UV relation of active galactic nuclei (AGNs), commonly parametrized via the monochromatic luminosities at 2500 Å and 2 keV, reflects the energetic interplay between the accretion disc and the X-ray-emitting corona, and is key for understanding accretion physics. Previous studies suggest that disc-dominated emission becomes more prominent with increasing optical luminosity. However, the redshift evolution of this relation remains debated, and a dependence on Eddington ratio, predicted by accretion flow models, is still observationally unconstrained. We revisit this relation using a large nearly all-sky sample by combining the Sloan Digital Sky Survey Quasar Catalog Data Release 16 quasar (QSO) catalogue with X-ray data from XMM–Newton and the SRG/eROSITA All-Sky Survey Data Release 1, yielding 136 745 QSOs at redshifts $0.5 \le z < 3.0$. We introduce a hierarchical Bayesian framework that treats X-ray detections and upper limits uniformly, enabling robust inference from both parametric and non-parametric models. We confirm a tight sublinear $\log L_X({\rm 2\, keV})$–$\log L_{\nu }({\rm 2500\, \mathring{A}})$ correlation, but with a normalization at the lower end of previous estimates. Contrary to most literature results, we detect a mild but systematic redshift evolution: the relation flattens and its intrinsic scatter decreases at higher redshift. This trend is consistent with disc emission increasingly dominated by scattering and enhanced energy transfer to the X-ray corona, potentially indicating redshift evolution in the X-ray bolometric correction. We find no significant dependence on Eddington ratio, in tension with recent accretion flow models.