Optical depth of the nuclear component from the spectral decomposition fits to the CONquest sample (Falstad et al. 2021) against the surface brightness of HCN-vib (left) and the strength of HCN-vib to L_IR (right). Linear fits are shown in the dashed black lines, with 1σ confidence intervals shown in grey. The upper limits of HCN-vib measurements are shown for objects with τ_N > 2.5 and β > 0.4. The dashed grey lines show the CON identification threshold from Falstad et al. (2021) on the x-axis and the corresponding τ_N on the y-axis.