Luminosity and Redshift Dependence of the Covering Factor of AGNs viewed with WISE and SDSS

In this work, we investigate the dependence of the covering factor (CF) of active galactic nuclei (AGNs) (i) on the mid-infrared (MIR) luminosity and (ii) on the redshift. We constructed 12- and 22-micron luminosity functions (LFs) at 0.006 < z < 0.3 using the Wide-field Infrared Survey Explorer} (WISE) data. Combining the WISE catalog with the Sloan Digital Sky Survey (SDSS) spectroscopic data, we selected 223,982 galaxies at 12 micron and 25,721 galaxies at 22 micron for spectroscopic classification. We then identified 16,355 AGNs at 12 micron and 4,683 AGNs at 22 micron by their optical emission lines and cataloged classifications in the SDSS. Following that, we estimated the CF as the fraction of type 2 AGN in all AGNs whose MIR emissions are dominated by the active nucleus (not their host galaxies) based on their MIR colors. We found that (i) the CF decreased with increasing MIR luminosity, regardless of the choice of type 2 AGN classification criteria, and (ii) the CF did not change significantly with the redshift for z < 0.2. Furthermore, we carried out various tests to determine the influence of selection bias and confirmed similar dependences exist even when taking these uncertainties into account. The luminosity dependence of the CF can be explained by the receding torus model, but the "modified" receding torus model gives a slightly better fit, as suggested by Simpson.