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 $\sim$3~orders of magnitude in luminosity. Here we propose a modified version of this relation which involves the broad emission lines' full-width at 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 previous works 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-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. The proposed new relation does not evolve with time, and thus it can be employed as a cosmological indicator to robustly estimate cosmological parameters.
Categories: astro-ph.HE