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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 (⁠|$\log U \ \gt\ {-}2.0$|⁠). [ABSTRACT FROM AUTHOR]

We present maps for the electron temperature in the inner kpc of three luminous Seyfert galaxies: Mrk 79, Mrk 348, and Mrk 607 obtained from Gemini Multi-Object Spectrograph-integral field unit observations at spatial resolutions of ∼110–280 pc. We study the distributions of electron temperature in active galaxies and find temperatures varying in the range from ∼8000 to |$\gtrsim 30\, 000\,$| K. Shocks due to gas outflows play an important role in the observed temperature distributions of Mrk 79 and Mrk 348, while standard photoionization models reproduce the derived temperature values for Mrk 607. In Mrk 79 and Mrk 348, we find direct evidence for shock ionization with overall orientation orthogonal to the ionization axis, where shocks can be easily observed as the active galactic nuclei radiation field is shielded by the nuclear dusty torus. This also indicates that even when the ionization cones are narrow, the shocks can be much wider angle. [ABSTRACT FROM AUTHOR]