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 $T_{\rm{disc}} \propto {M_{\rm BH}}^{-1/4}$.
