Narrow-line regions excited by active galactic nuclei ( AGN ) are important for studying AGN photoionization and feedback .
Their strong [ O III ] lines can be detected with broadband images , allowing morphological studies of these systems with large-area imaging surveys .
We develop a new technique to reconstruct the [ O III ] images using the Subaru Hyper Suprime-Cam ( HSC ) Survey aided with spectra from the Sloan Digital Sky Survey ( SDSS ) .
The technique involves a careful subtraction of the galactic continuum to isolate emission from the [ O III ] \lambda 5007 and [ O III ] \lambda 4959 lines .
Compared to traditional targeted observations , this technique is more efficient at covering larger samples with less dedicated observational resources .
We apply this technique to an SDSS spectroscopically selected sample of 300 obscured AGN at redshifts 0.1 - 0.7 , uncovering extended emission-line region candidates with sizes up to tens of kpc .
With the largest sample of uniformly derived narrow-line region sizes , we revisit the narrow-line region size – luminosity relation .
The area and radii of the [ O III ] emission-line regions are strongly correlated with the AGN luminosity inferred from the mid-infrared ( 15 \micron rest-frame ) with a power-law slope of 0.62 ^ { +0.05 } _ { -0.06 } \pm 0.10 ( statistical and systemic errors ) , consistent with previous spectroscopic findings .
We discuss the implications for the physics of AGN emission-line region and future applications of this technique , which should be useful for current and next-generation imaging surveys to study AGN photoionization and feedback with large statistical samples .