Quasars as standard candles: I. the physical relation between disc and coronal emission

Context. A tight non-linear relation exists between the X-ray and UV emission in quasars (i.e. L-X proportional to L-UV(gamma)), with a dispersion of similar to 0.2 dex over approximately three orders of magnitude in luminosity. Such observational evidence has two relevant consequences: (1) an ubiquitous physical mechanism must regulate the energy transfer from the accretion disc to the X-ray emitting corona; and (2) the non-linearity of the relation provides a new, powerful way to estimate the absolute luminosity, turning quasars into a new class of standard candles. Aims. Here we propose a modified version of this relation, which involves the emission line full-width half maximum, L-X proportional to L-UV((gamma) over cap) upsilon((beta) over cap)(fwhm) Methods. We interpret this new relation through a simple, ad hoc model of accretion disc corona, derived from previous works in the literature where it is assumed that reconnection and magnetic loops above the accretion disc can account for the production of the primary X-ray radiation. Results. We find that the monochromatic optical-UV (2500 angstrom) and X-ray (2 keV) luminosities depend on the black hole mass and accretion rate as L-UV proportional to M-BH(4/3) ((M) over dot/(M) over dot(Edd))(2/3) and L-X /M-BH(19/21) ((M) over dot/(M)(Edd))(5/21), respectively. Assuming a broad line region size function of the disc luminosity R-blr/L-disc(0.5) we finally have that L-X proportional to /L-UV(4/7) upsilon(4/7)(fwhm). Such relation is remarkably consistent with the slopes and the normalisation obtained from a fit of a sample of 545 optically selected quasars from SDSS DR7 cross matched with the latest XMM-Newton catalogue 3XMM-DR6. Conclusions. The homogeneous sample used here has a dispersion of 0.21 dex, which is much lower than previous works in the literature and suggests a tight physical relation between the accretion disc and the X-ray emitting corona. We also obtained a possible physical interpretation of the L-X-L-UV relation (considering also the effect of upsilon(fwhm)), which puts the determination of distances based on this relation on a sounder physical grounds. The proposed new relation does not evolve with time, and thus it can be employed as a cosmological indicator to robustly estimate cosmological parameters.