# Quasars as standard candles I: The physical relation between disc and coronal emission [HEAP]

A tight non-linear relation exists between the X-ray and UV emission in quasars (i.e. $L_{\rm X}\propto L_{\rm UV}^{\gamma}$), with a dispersion of $\sim$0.2~dex over \rev{$\sim$3~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 {\it 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 {\it standard candles}.
Here we propose a modified version of this relation which involves the emission line full-width half maximum, $L_{\rm X}\propto L_{\rm UV}^{\hat\gamma}\upsilon_{\rm fwhm}^{\hat\beta}$. We interpret this new relation through a simple, {\it ad-hoc} model of accretion disc corona, derived from the works of Svensson \& Zdziarski (1994) and Merloni \& Fabian (2002), where it is assumed that reconnection and magnetic loops above the accretion disc can account for the production of the primary X-ray radiation.
We find that the monochromatic optical-UV (2500 \AA) and X–ray (2 keV) luminosities depend on the black hole mass and accretion rate as $L_{\rm UV}\propto M_{\rm BH}^{4/3} (\dot{M}/\dot{M}_{\rm Edd})^{2/3}$ and $L_{\rm X}\propto M_{\rm BH}^{19/21} (\dot{M}/\dot{M}_{\rm Edd})^{5/21}$, respectively. Assuming a broad line region size function of the disc luminosity $R_{\rm blr}\propto L_{\rm disc}^{0.5}$ we finally have that $L_{\rm X}\propto L_{\rm UV}^{4/7} \upsilon_{\rm fwhm}^{4/7}$. Such relation is remarkably consistent with the slopes and the normalization obtained from a fit of a sample of 545 optically selected quasars from SDSS DR7 cross matched with the latest XMM–{\it Newton} catalogue 3XMM-DR6.
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 $L_{\rm X}-L_{\rm UV}$ relation (considering also the effect of $\upsilon_{\rm fwhm}$), 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.

E. Lusso and G. Risaliti
Fri, 17 Mar 17
10/50

Comments: 15 pages, 9 figures, accepted for publication in Astronomy & Astrophysics