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 ($M_{\rm BH}$)
and bolometric luminosity ($L_{\rm bol}$) and found that the fraction changes
depending on both $M_{\rm BH}$ and $L_{\rm bol}$, 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
$M_{\rm BH}-L_{\rm bol}$ plane is affected by the different methods used to
derive $M_{\rm BH}$ and $L_{\rm bol}$, 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 $0.01 \leq z \leq 0.2$. In estimating
$L_{\rm bol}$, we employ two different methods using [O III] and/or [O I]
emission lines, and find that the $L_{\rm bol}$ values obtained from the two
methods agree well. We consider the $M_{\rm BH}-\sigma_*$ relation, the $M_{\rm
BH}-L_{\rm bulge}$ relation and the single-epoch H$\alpha$-based $M_{\rm BH}$
estimate in calculating $M_{\rm BH}$. We find that the trends of the type 1 AGN
fraction with respect to $M_{\rm BH}$ and $L_{\rm bol}$ are similar for the
different derivation methods for $L_{\rm bol}$ but different when using
different methods to derive $M_{\rm BH}$. 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.
