Semi-empirical calibration of the oxygen abundance for LINER galaxies based on SDSS-IV MaNGA -- The case for strong and weak AGN

In this paper, we present a semi-empirical calibration between the oxygen abundance and the $N2$ emission-line ratio for Low Ionization Nuclear Emission Regions (LINERs). This relation was derived by comparing the optical spectroscopic data of 118 nuclear spaxels classified as LINERs using three different BPT diagrams from the Mapping Nearby Galaxies survey (MaNGA) and sub-classified as weak (wAGN, 84 objects) and strong (sAGN, 34 objects) AGN (active galactic nucleus) from the WHAN diagnostic diagram and photoionization model results obtained with the {\sc cloudy} code assuming gas accretion into a black hole (representing an AGN). We found that our wAGN LINERs exhibit an oxygen abundance in the range of $8.50 \lesssim \mathrm{12+\log(O/H)} \lesssim 8.90 $, with an average value of $\mathrm{12+\log(O/H)}=8.68$, while our sAGN LINERs exhibit an oxygen abundance in the range of $8.51 \lesssim \: \mathrm{12+\log(O/H)} \: \lesssim \: 8.81 $, with an average value of $\mathrm{12+\log(O/H)}=8.65$. Our abundance estimations are in good agreement with those derived for another two different samples one of them with 463 Seyfert 2 objects and the other with 43 LINERs galaxies ionized by post-AGB stars, showing that the assumptions of our models are likely suitable for wAGN and sAGN LINERs. A relation between the equivalent width of the observed H$\alpha$ emission-line and the estimated ionization parameter provided by models was obtained. Our results also suggest that LINERs does not show a clear correlation between oxygen abundances and the stellar mass of the hosting galaxies.