Empirical calibration for helium abundance determinations in Active Galactic Nuclei

For the first time, a calibration between the HeI $\lambda5876$/H$\beta$ emission line ratio and the helium abundance $y$=12+log(He/H) for Narrow line regions (NLRs) of Seyfert~2 Active Galactic Nuclei (AGN) 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 ($z \: < \: 0.2$) 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 ($\log U > -2.0$).