A novel black-hole mass scaling relation based on coronal gas, and its dependence with the accretion disc

Using bona-fide black hole (BH) mass estimates from reverberation mapping and the line ratio [SiVI] 1.963$\mu$m/Br$\gamma_{\rm broad}$ as tracer of the AGN ionising continuum, a novel BH-mass scaling relation of the form log($M_{\rm BH}) = (6.40\pm 0.17) - (1.99\pm 0.37) \times$ log ([SiVI]/Br$\gamma_{\rm broad})$, dispersion 0.47 dex, over the BH mass interval, $10^6 - 10^8$ M$_{\odot}$ is found. Following on the geometrically thin accretion disc approximation and after surveying a basic parameter space for coronal lines production, we believe one of main drivers of the relation is the effective temperature of the disc, which is effectively sampled by the [SiVI] 1.963$\mu$m coronal line for the range of BH masses considered. By means of CLOUDY photoionisation models, the observed anti-correlation appears to be formally in line with the thin disc prediction T_disc $\propto {M_{\rm BH}}^{-1/4}$.