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.