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

Sizes of narrow emission line regions (NLRs) of active galactic nuclei (AGNs) could be estimated by [O III] line luminosity L-O3 through the known R-NLRs-L-O3 empirical relations. Unfortunately, it is not convenient to test the R-NLRs- L-O3 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-NLRs-L-O3(similar to 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 R-fib of SDSS fibre-covered regions. Comparing R-fib and R-NLRs estimated by L-O3, Type-2 AGNs with R-fib > R-NLRs (Sample-II) and with R-fib < R-NLRs (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 R-S2 of [S II] lambda 6717 angstrom to [S II] lambda 6731 angstrom) 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 R-S2 for the Type-2 AGNs in the Sample-I can be confirmed with confidence level higher than 5 sigma, even after considering necessary effects. Therefore, the results in this manuscript can provide strong clues to support that the reported R-NLRs proportional to L-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.