The dust covering factor in active galactic nuclei
  The primary source of emission of active galactic nuclei (AGN), the accretion
disk, is surrounded by an optically and geometrically thick dusty structure
("the so-called dusty torus"). The infrared radiation emitted by the dust is
nothing but a reprocessed fraction of the accretion disk emission, so the ratio
of the torus to the AGN luminosity ($L_{\text{torus}}/L_{\text{AGN}}$) should
correspond to the fraction of the sky obscured by dust, i.e. the covering
factor. We undertook a critical investigation of the
$L_{\text{torus}}/L_{\text{AGN}}$ as the dust covering factor proxy. Using
state-of-the-art 3D Monte Carlo radiative transfer code, we calculated a grid
of spectral energy distributions (SEDs) emitted by the clumpy two-phase dusty
structure. With this grid of SEDs, we studied the relation between
$L_{\text{torus}}/L_{\text{AGN}}$ and the dust covering factor for different
parameters of the torus. We found that in the case of type 1 AGNs the torus
anisotropy makes $L_{\text{torus}}/L_{\text{AGN}}$ underestimate low covering
factors and overestimate high covering factors. In type 2 AGNs
$L_{\text{torus}}/L_{\text{AGN}}$ always underestimates covering factors. Our
results provide a novel easy-to-use method to account for anisotropy and obtain
correct covering factors. Using two samples from the literature, we
demonstrated the importance of our result for inferring the obscured AGN
fraction. We found that after the anisotropy is properly accounted for, the
dust covering factors show very weak dependence on $L_{\text{AGN}}$, with
values in the range of $\approx0.6-0.7$. Our results also suggest a higher
fraction of obscured AGNs at high luminosities than those found by X-ray
surveys, in part owing to the presence of a Compton-thick AGN population
predicted by population synthesis models.
