Emirical calibration for helium abundance determinations in active galactic nuclei

For the first time, a calibration between the He i$\lambda 5876$/H $\beta$ emission line ratio and the helium abundance y = 12 + log(He/H) for Narrow line regions of Seyfert 2 Active Galactic Nuclei is proposed. In this context, observational data (taken from the SDSS-DR15 and from the literature) and direct abundance estimates (via the $T_{\rm e}$-method) for a sample of 65 local ($z \: \lt \: 0.2$) Seyfert 2 nuclei are considered. The resulting calibration estimates the y abundance with an average uncertainty of 0.02 dex. Applying our calibration to spectroscopic data containing only strong emission lines, it yields a helium abundance distribution similar to that obtained via the $T_{\rm e}$-method. Some cautions must be considered to apply our calibration for Seyfert 2 nuclei with high values of electron temperature (${\gtrsim} 20\, 000$ K) or ionization parameter ($\log U \ \gt\ {-}2.0$).