On the Structure of the AGN Torus through the Fraction of Optically-Selected Type 1 AGNs

The ratio in number between unobscured (type 1) and obscured (type 2) AGNs is often used to explore the structure of the torus in the unified scheme for active galactic nuclei (AGNs). Oh et al. (2015) investigated the type 1 AGN fraction on two-dimensional space in terms of black hole mass ($M_{\mathrm{B}\mathrm{H}}$) and bolometric luminosity ($L_{\mathrm{b}\mathrm{o}\mathrm{l}}$) and found that the fraction changes depending on both $M_{\mathrm{B}\mathrm{H}}$ and $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$, forming a ridge-shaped distribution. In this study, based on the up-to-date type 1 AGN catalog of Oh et al. (2015), we examine how the trend of the type 1 AGN fraction in the $M_{\mathrm{B}\mathrm{H}}-L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ plane is affected by the different methods used to derive $M_{\mathrm{B}\mathrm{H}}$ and $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$, and suggest an analytic model to explain the observations. We use galaxies from the Sloan Digital Sky Survey Data Release 7 in the redshift range of $0.01\le z\le 0.2$. In estimating $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$, we employ two different methods using [O III] and/or [O I] emission lines, and find that the $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ values obtained from the two methods agree well. We consider the $M_{\mathrm{B}\mathrm{H}}-{\sigma }_{\ast }$ relation, the $M_{\rm BH}-L_{\rm bulge}$relationandthesingle-epochH$\alpha$-based$M_{\rm BH}$estimateincalculating$M_{\rm BH}$. We find that the trends of the type 1 AGN fraction with respect to $M_{\mathrm{B}\mathrm{H}}$ and $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ are similar for the different derivation methods for $L_{\mathrm{b}\mathrm{o}\mathrm{l}}$ but different when using different methods to derive $M_{\mathrm{B}\mathrm{H}}$. We present a model based on the clumpy-torus scheme that reproduces the ridge-shaped distribution of the fraction parallel to the iso-Eddington ratio lines.