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

Maria Chira, Antonis Georgakakis, Angel Ruiz, Shi-Jiang Chen, Johannes Buchner, Amy L. Rankine, Elias Kammoun, Catarina Aydar, Mara Salvato, Andrea Merloni, Mirko Krumpe

TL;DR

This work reevaluates the quasar X-ray–to–UV relation using an unprecedented all-sky dataset by combining SDSS DR16Q with XMM-Newton and eROSITA observations and applies a hierarchical Bayesian framework to uniformly treat detections and upper limits. It finds a tight sublinear correlation between $L_X({\rm 2\,keV})$ and $L_ν({2500Å})$, with normalization at the low end of previous studies and a mild redshift evolution toward a flatter relation accompanied by reduced intrinsic scatter. The analysis reports no strong dependence on the Eddington ratio, challenging some accretion-flow predictions (e.g., qsosed) and implying potential redshift evolution of the X-ray bolometric correction within kynsed. These results have implications for AGN accretion physics and the use of the LX–Lν relation in cosmology, and they demonstrate the value of all-sky X-ray surveys and robust Bayesian inference for large, incomplete multiwavelength datasets.

Abstract

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.

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

TL;DR

This work reevaluates the quasar X-ray–to–UV relation using an unprecedented all-sky dataset by combining SDSS DR16Q with XMM-Newton and eROSITA observations and applies a hierarchical Bayesian framework to uniformly treat detections and upper limits. It finds a tight sublinear correlation between and , with normalization at the low end of previous studies and a mild redshift evolution toward a flatter relation accompanied by reduced intrinsic scatter. The analysis reports no strong dependence on the Eddington ratio, challenging some accretion-flow predictions (e.g., qsosed) and implying potential redshift evolution of the X-ray bolometric correction within kynsed. These results have implications for AGN accretion physics and the use of the LX–Lν relation in cosmology, and they demonstrate the value of all-sky X-ray surveys and robust Bayesian inference for large, incomplete multiwavelength datasets.

Abstract

The X-ray--to--UV relation of active galactic nuclei (AGNs), commonly parametrized via the monochromatic luminosities at and , 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 . 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 - 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.

Paper Structure

This paper contains 23 sections, 15 equations, 18 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Data
  3. Optical Quasar Catalogue: DR16Q
  4. X-ray Data
  5. XMM-Newton
  6. eROSITA
  7. Additional Filtering
  8. SED fitting: calculation of the UV luminosity.
  9. Hierarchical Bayesian Methodology
  10. Results
  11. Exploring the luminosity and redshift dependence of the X-ray--to--UV correlation
  12. Comparison to literature results
  13. Exploring the Eddington ratio dependence of the X-ray--to--UV correlation
  14. Discussion
  15. Redshift Evolution of the X-ray/UV correlation
  16. ...and 8 more sections

Figures (18)

  • Figure 1: Distribution of the DR16Q QSO sample on the $\log{L_\nu(\mathrm{2500\mathring{A}})} - z$ plane. Projected frequency histograms of the redshift and the $\rm 2500\mathring{A}$ luminosity are presented in the barred plots on the horizontal and vertical axis respectively.
  • Figure 2: Normalised posterior distribution of $\log{L_X(\rm 2\,keV)}$ in bins of $\log{L_\nu(\rm 2500 \mathring{A})}$ (increasing from left to right) and redshift, $z$ (increasing from top to bottom). The green, solid vertical line shows the median of each distribution. The vertical black line corresponds to $\log{L_X(\rm 2\,keV)} =26$ and is plotted to facilitate comparisons between different panels. The number, $\rm N$, of DRQ16 QSOS in each subsample is shown in the corresponding panel. The dotted line in the first row corresponds to the expected position of the peak of the $\log{L_X(\rm 2\,keV)}$ distribution with increasing $\log{L_\nu(\rm 2500 \mathring{A})}$, assuming a linear $\log{L_X(\rm 2\,keV)}-\log{L_\nu(\rm 2500 \mathring{A})}$ correlation.
  • Figure 3: The correlation between the monochromatic luminosities at 2 keV and 2500Å. The red data points correspond to the mean of the Gaussian model for the $\log{L_X(\rm 2\,keV)}$ distribution (see Equation \ref{['equation:model-flavour-1']}) at fixed $\log{L_\nu(\rm 2500 \mathring{A})}$ luminosity intervals for the redshift bin $z =1.0-1.5$. The x-axis values represent the centers of the $\log{L_\nu(\rm 2500\,\mathring{A})}$ intervals, each with a width of $\Delta \log{L_\nu(\rm 2500\,\mathring{A})} = 0.5$. The red, solid errorbars, correspond to the $1\sigma$ statistical error while, the black, dashed errorbars to the inferred intrinsic Gaussian scatter. The relation of LR2016 is plotted as a green, dashed line and is consistent with the distribution of our data albeit somewhat steeper. The purple, dotted line shows the linear relation.
  • Figure 4: Constraints on the redshift dependence of the monochromatic luminosity $\log{L_X(\rm 2\,keV)}$ distribution, as quantified by the parameter $\Delta \mu (z)$ (Equation \ref{['equation:model-flavour-2']}) measured with respect to the reference redshift bin, $z =1.0-1.5$. The inferred median $\Delta \mu (z)$ values for each redshift interval are shown with solid lines. The shaded regions correspond to the $1\sigma$ uncertainties. The different colors represent different $\log{L_\nu(\rm 2500 \mathring{A})}$ bins as denoted in the key. The $z - \log{L_\nu(\rm 2500 \mathring{A})}$ bins are the same as in Figure \ref{['fig:LUV_z_bins']}.
  • Figure 5: Inferred $L_X({\rm 2\,keV}) - L_\nu(\rm 2500 \mathring{A})$ correlation assuming the log-linear model of Equation \ref{['eq:model-flavour-3']}. The lines correspond to the median of the posterior distributions for the slope ($A$) and intercept ($x_0$), also shown in Table \ref{['tab:parameters']}. The different colours correspond to the redshift intervals indicated in the legend. The light shaded regions associated with each line correspond to the 68th ($1\sigma$) confidence interval around the median. The complex convex shaded regions are density contours that correspond to the superposition of the posterior distributions of individual QSOs within a given redshift bin. The inner and outer boundaries of each convex shaded region correspond to the iso-density contours that enclose, respectively, $1\sigma$ (68%) and $2\sigma$ (95%) of the posterior at fixed UV luminosity. The inner area of these regions, i.e. the one enclosed by the $1\sigma$ iso-density contour, is left empty for clarity and to facilitate the visualization. A typical value of the intrinsic scatter ($\sigma \approx0.4$ dex, see Fig. \ref{['fig:params_z']}) around the log-linear correlation of Equation \ref{['eq:model-flavour-3']} is shown with the gray shaded vertical line on the top left.
  • ...and 13 more figures