Coronal gas excitation as a tracer of supermassive black hole mass: on the mid-IR coronal [Ne v] lines
Coronal lines (CL) may be a reliable proxy of supermassive black hole (SMBH) masses in active galactic nuclei (AGN) because the production of these high ionisation potential (IP) lines is sensitive to the shape of the ionising continuum which, for a thin accretion disc, relies on the black hole mass. In this work we study the connection between the [Ne\,v] coronal lines and the SMBH mass. We analyse the \textit{Spitzer spectra} of a sample of 27 AGN spanning three orders of magnitude in SMBH mass. Fluxes and the electron density in the coronal gas medium were measured after fitting Gaussians to both the $\rm [Ne\,v]14\mu m$ and $\rm [Ne\,v]24\mu m$ lines where detected at high signal to noise. Line fluxes were normalised to the Br$\gamma_{\rm broad}$ emission from the broad line region. We found strong correlations between the $\rm [Ne\,v]14\mu m/Br\gamma_{\rm broad}$ and $\rm [Ne\,v]24\mu m/Br\gamma_{\rm broad}$ line ratios and the SMBH mass. For this sample of 27 AGN we find scatters of 0.54 and 0.53 dex, respectively. These correlations support the theory that the coronal gas excitation is sensitive to a range of SMBH masses because of the dependence on the shape of the ionising continuum. The electron densities of the coronal medium are of the order 1000$\rm cm^{-3}$ supporting their nuclear origin. A comparison with density values derived from JWST for a subsample of objects confirm this conclusion. These results further demonstrate the ability to use CL as a SMBH mass proxy, allowing for accurate SMBH mass measurements in AGN.