The intrinsic X-ray luminosity distribution of an optically-selected SDSS quasar population

In active galactic nuclei, the relationship between UV and X-ray luminosity is well studied (often characterised by ${\alpha }_{\text{ox}}$) but often with heterogeneous samples. We have parametrized the intrinsic distribution of X-ray luminosity, $L_{\text{X}}$, for the optically-selected sample of SDSS quasars in the Stripe 82 and XXL fields across redshifts 0.5-3.5. We make use of the available XMM observations and a custom pipeline to produce Bayesian sensitivity curves that are used to derive the intrinsic X-ray distribution in a hierarchical Bayesian framework. We find that the X-ray luminosity distribution is well described by a Gaussian function in ${\log }_{10}{L}_{\text{X}}$ space with a mean that is dependent on the monochromatic 2500A UV luminosity, $L_{2500}$. We also observe some redshift dependence of the distribution. The mean of the $L_{\text{X}}$ distribution increases with redshift while the width decreases. This weak but significant redshift dependence leads to $L_{2500}$-$L_{\text{X}}$ and $L_{2500}$-${\alpha }_{\text{ox}}$ relations that evolve with redshift, and we produce a redshift- and $L_{2500}$-dependent ${\alpha }_{\text{ox}}$ equation. Neither black hole mass nor Eddington ratio appear to be potential drivers of the redshift evolution.