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

The X-ray–to–UV relation of active galactic nuclei (AGNs), commonly parametrized via the monochromatic luminosities at $2500,\mathring{A}$ 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 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 $0.5 \leq z < 3.0$. 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 $\log L_X({\rm 2,keV})$-$\log L_ν({\rm 2500,\mathring{A}})$ 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.

💡 Research Summary

This research presents a large-scale re-evaluation of the X-ray to UV luminosity relationship in quasars, utilizing an unprecedentedly vast dataset from the SDSS DR16Q catalogue, XMM-Newton, and the eROSITA All-Sky Survey DR1. The study focuses on the fundamental correlation between monochromatic luminosities at $2500,\mathring{A}$ (representing the accretion disc) and $2,keV$ (representing the X-ray corona), a relationship that is vital for understanding the energetic coupling between these two distinct components of Active Galactic Nucleates (AGN).

To ensure statistical rigor, the authors implemented a hierarchical Bayesian framework. This sophisticated approach is particularly significant because it allows for the simultaneous and uniform treatment of both X-ray detections and non-detections (upper limits). By incorporating censored data, the study avoids the common selection biases found in previous literature, providing a more robust inference of the underlying physical parameters across a sample of 136,745 QSOs spanning redshifts $0.5 \leq z < 3.0$.

The findings yield several groundbreaking insights. First, the study confirms a tight, sublinear correlation between UV and X-ray luminosities, though it notes that the normalization at the lower end is lower than previously estimated by other studies. Second, and perhaps most provocatively, the research detects a systematic evolution with redshift. Contrary to the assumption of a redshift-independent relation, the data shows that the relation flattens and the intrinsic scatter decreases at higher redshifts. This suggests that the physical processes governing energy transfer from the disc to the corona, or the role of scattering in disc-dominated emission, may have evolved over cosmic time, potentially implying an evolution in the X-ray bolometric correction.

Finally, the study finds no significant dependence of this relation on the Eddington ratio. This result is particularly noteworthy as it stands in direct tension with several recent accretion flow models that predict a specific dependence on the accretion rate. By challenging existing theoretical frameworks and providing a new empirical baseline, this work sets a new standard for AGN studies in the era of all-sky surveys and provides a critical foundation for future investigations into the co-evolution of supermassive black holes and their host galaxies.