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 $2500\mathring{A}$ and $2keV$, 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 SDSS DR16Q QSO catalogue with X-ray data from XMM-Newton and the SRG/eROSITA All-Sky Survey DR1, 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 $\log L_X(2\mathrm{keV})$-$\log L_{\nu }(2500\mathring{\mathrm{A}})$ 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.

arXiv comment18+4 pages, 12+6 figures, Published at MNRAS

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