A novel black-hole mass scaling relation based on Coronal lines and supported by accretion predictions

Getting insights on the shape and nature of the ionizing continuum in astronomical objects is often done via indirect methods as high energy photons are absorbed by our Galaxy. This work explores the ionization continuum of active galactic nuclei (AGN) using the ubiquitous coronal lines. Using bona-fide BH mass estimates from reverberation mapping and the line ratio [Si VI] 1.963 micron/Br$\gamma_{\rm broad}$ as tracer of the AGN ionizing 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 ([Si VI]/Br$\gamma_{\rm broad})$, over the BH mass interval, $10^6 - 10^8$ M$_{\odot}$ with dispersion 0.47 dex is found. Following on the thin accretion disc approximation and after surveying a basic parameter space for coronal lines production, we believe that a key parameter driving this anti-correlation is the effective temperature of the accretion disc, this being effectively sampled by the coronal line gas. Accordingly, the observed anti-correlation becomes formally in line with the thin accretion disc prediction $T_{\rm{disc}} \propto {M_{\rm BH}}^{-1/4}$.