To test $R_{NLRs}~-~L_{O3}$ relation for narrow emission line regions of AGN through low redshift Type-2 AGN in SDSS

Abstract

Sizes of narrow emission line regions (NLRs) of AGN could be estimated by [O~{\sc 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 AGN. In this manuscript, a method is proposed to test the $R_{NLRs}-L_{O3}^{\sim0.25}$ empirical relations for AGN NLRs through SDSS Type-2 AGN having few orientation effects on NLRs sizes expected by AGN unified model, after considering sizes $R_{fib}$ of SDSS fiber covered regions. Comparing $R_{fib}$ and $R_{NLRs}$ estimated by $L_{O3}$, Type-2 AGN with $R_{fib}>R_{NLRs}$ (Sample-II) and with $R_{fib}<R_{NLRs}$ (Sample-I) should have different physical properties of NLRs. Accepted electron density gradients in AGN NLRs, statistically higher electron densities (traced by lower flux ratio $R_{S2}$ of [S~{\sc ii}]$\lambda6717$\AA~ to [S~{\sc ii}]$\lambda6731$\AA) could be expected for the Type-2 AGN in the Sample-I. Then, through the collected 1062 SDSS Type-2 AGN in the Sample-I and 3658 SDSS Type-2 AGN in the Sample-II, statistically lower $R_{S2}$ for the Type-2 AGN 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 $R_{NLRs}~\propto~L_{O3}^{0.25}$ empirical relation is preferred to estimate NLRs sizes of SDSS AGN through SDSS fiber spectroscopic results, and also to support the commonly expected electron density gradients in AGN NLRs.