SRG/eROSITA-SDSS view on the relation between X-ray and UV emission for quasars

Motivated by the idea of using quasars as standardizable candles for cosmology, we examine the relation between X-ray (at 2 keV, $L_{\rm 2keV}$) and ultraviolet (at 2500 Angstrom, $L_{\rm 2500}$) monochromatic luminosities of quasars using a sample of 2414 X-ray sources from the SRG/eROSITA all-sky survey cross-matched with the Sloan Digital Sky Survey data release 16 quasar catalogue (SDSS DR16Q), at redshifts between 0.5 and 2.5. These objects are bright both in X-rays and in the optical, so that the sample is characterized by nearly 100% statistical completeness. We have developed a new method for determining the $L_{\rm 2keV}-L_{\rm 2500}$ relation, which consistently takes into account (i) X-ray and UV flux limited object selection, (ii) X-ray and UV variability of quasars, and (iii) the decreasing space density of quasars with increasing luminosity. Assuming a linear relation between $l_{\rm X}\equiv\log(L_{\rm 2keV}/[{\rm erg\,s^{-1}\,Hz^{-1}}])$ and $l_{\rm UV}\equiv\log(L_{\rm 2500}/[{\rm erg\,s^{-1}\,Hz^{-1}}])$, we find the slope, $\gamma=0.69\pm0.02$ (hereafter all uncertainties are quoted at the 68% confidence level), and normalization, $l_{\rm X}=26.47\pm0.02$ at $l_{\rm UV}=30.5$, of the $L_{\rm 2keV}$ ($L_{\rm 2500}$) dependence. These values are not substantially different from the results of previous studies. A key novel aspect of our work is allowance for intrinsic scatter (which adds to the dispersion induced by quasar variability and flux measurement uncertainties) of the $L_{\rm 2keV}-L_{\rm 2500}$ relation in both variables, i.e. in X-ray and UV luminosity. The intrinsic X-ray scatter ($\sigma^2_{\rm intX}=0.063\pm0.005$) strongly dominates over the UV one ($\sigma^2_{\rm intUV}=0.002^{+0.003}_{-0.002}$). Further studies should seek to explain this behaviour in terms of accretion onto supermassive black holes and orientation of quasars with respect to the observer.