Quasars as standard candles. IV. Analysis of the X-ray and UV indicators of the disc-corona relation

Context. A non-linear relation between quasar monochromatic luminosities at 2500 Å and 2 keV holds at all observed redshifts and luminosities, and it has been used to derive quasar distances and to build a Hubble diagram of quasars. The choice of the X-ray and UV indicators has so far been somewhat arbitrary and has typically relied on photometric data.
Aims: We aim to determine the X-ray and UV proxies that provide the smallest dispersion of the relation in order to obtain more precise distance estimates and to confirm the reliability of the X-ray-to-UV relation as a distance indicator.
Methods: We performed a complete UV spectroscopic analysis of a sample of ∼1800 quasars with SDSS optical spectra and XMM-Newton X-ray serendipitous observations. In the X-rays, we analysed the spectra of all the sample objects at redshift z > 1.9, while we relied on photometric measurements at lower redshifts. As done in previous studies, we analysed the relation in small redshift bins, using fluxes instead of luminosities.
Results: We show that the monochromatic fluxes at 1 keV and 2500 Å are, respectively, the best X-ray and UV continuum indicators among those that are typically available. We also find a tight relation between soft X-ray and Mg IIλ2800 Å line fluxes, and a marginal dependence of the X-ray-to-UV relation on the width of the Mg II line.
Conclusions: Our analysis suggests that the physical quantities that are more tightly linked to one another are the soft X-ray flux at ∼1 keV and the ionising UV flux blueward of the Lyman limit. However, the `usual' monochromatic fluxes at 2 keV and 2500 Å estimated from photometric data provide an almost as tight X-ray-to-UV relation, and can be used to derive quasar distances. The Hubble diagram obtained using spectroscopic indicators is fully consistent with the one presented in previous papers, based on photometric data.