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${\gamma }_{\mathrm{b}\mathrm{r}\mathrm{o}\mathrm{a}\mathrm{d}}$ 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]\mathrm{/}Br$\gamma_{\rm broad})$,dispersion0.47dex,overtheBHmassinterval,$10^6 - 10^8$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 $\propto {M_{\mathrm{B}\mathrm{H}}}^{-1\mathrm{/}4}$.