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Dependence of Narrow-line Region Sizes on [O iii] Luminosity in Low-redshift Active Galactic Nuclei with Double-peaked Broad Balmer Emission Lines

In this paper, simple but interesting results are reported on the upper limits of narrow-line region (NLR) sizes of a small sample of 38 low-redshift (z < 0.1) active galactic nuclei (AGN) with double-peaked broad emission lines (double-peaked BLAGN), in order to check whether the NLR sizes in type-1 AGN (broad line) and type-2 AGN (narrow line) obey a similar empirical dependence on [O iii] luminosity. In order to correct the inclination effects on projected NLR sizes of type-1 AGN, the accretion disk origin is commonly applied to describe the double-peaked broad Hα line, leading to the determined inclination angles of central disk-like broad-line regions of 38 double-peaked BLAGN. Then, considering the fixed Sloan Digital Sky Survey (SDSS) fiber radius, the upper limits of the NLR sizes of the 38 double-peaked BLAGN can be estimated. Meanwhile, a strong linear correlation between continuum luminosity and [O iii] luminosity is applied to confirm that the [O iii] emissions of the 38 double-peaked BLAGN are totally covered in the SDSS fibers. Considering the reddening-corrected measured [O iii] luminosity, the upper limits of the NLR sizes of the 38 double-peaked BLAGN are within a 99.9999% confidence interval of the expected results from the empirical relation between NLR size and [O iii] luminosity in type-2 AGN. In the current understanding, there are no challenges to the unified model of AGN through the space properties of NLRs.