To test RNLRs−LO3 relation for narrow emission line regions of AGNs through low-redshift Type-2 AGNs in SDSS

ABSTRACT Sizes of narrow emission line regions (NLRs) of active galactic nuclei (AGNs) could be estimated by [O iii] line luminosity LO3 through the known RNLRs−LO3 empirical relations. Unfortunately, it is not convenient to test the RNLRs− LO3 empirical relations through structure properties of spatially resolved NLRs of large samples of AGNs. In this manuscript, a method is proposed to test the $R_{\mathrm{ NLRs}}\!\!-\!\!L_{\mathrm{ O3}}^{\sim 0.25}$ empirical relations for AGN NLRs through Sloan Digital Sky Survey (SDSS) Type-2 AGNs having few orientation effects on NLR sizes expected by the AGN unified model, after considering sizes Rfib of SDSS fibre-covered regions. Comparing Rfib and RNLRs estimated by LO3, Type-2 AGNs with Rfib > RNLRs (Sample-II) and with Rfib < RNLRs (Sample-I) should have different physical properties of NLRs. Accepting electron density gradients in AGN NLRs, statistically higher electron densities (traced by lower flux ratio RS2 of [S ii] λ6717 Å to [S ii] λ6731 Å) could be expected for the Type-2 AGNs in the Sample-I. Then, through the collected 1062 SDSS Type-2 AGNs in the Sample-I and 3658 SDSS Type-2 AGNs in the Sample-II, statistically lower RS2 for the Type-2 AGNs in the Sample-I can be confirmed with confidence level higher than 5σ, even after considering necessary effects. Therefore, the results in this manuscript can provide strong clues to support that the reported $R_{\mathrm{ NLRs}}~\propto ~L_{\mathrm{ O3}}^{0.25}$ empirical relation is preferred to estimate NLR sizes of SDSS AGNs through SDSS fibre spectroscopic results, and also to support the commonly expected electron density gradients in AGN NLRs.