Determining the torus covering factors for a sample of type 1 AGN in the local Universe

In the unified scheme of active galactic nuclei, a dusty torus absorbs and then reprocesses a fraction of the intrinsic luminosity which is emitted at longer wavelengths. Thus, subject to radiative transfer corrections, the fraction of the sky covered by the torus as seen from the central source (known as the covering factor $f_c$) can be estimated from the ratio of the infrared to the bolometric luminosities of the source as $f_c=L_{\rm torus}/L_{\rm Bol}$. However, the uncertainty in determining $L_{\rm Bol}$ has made the estimation of covering factors by this technique difficult, especially for AGN in the local Universe where the peak of the observed SEDs lies in the UV (ultraviolet). Here, we determine the covering factors of an X-ray/optically selected sample of 51 type~1 AGN. The bolometric luminosities of these sources are derived using a self-consistent, energy-conserving model that estimates the contribution in the unobservable far-UV region, using multi-frequency data obtained from SDSS, \textit{XMM-Newton}, \textit{WISE}, 2MASS and UKIDSS. We derive a mean value of $f_c\sim$0.30 with a dispersion of 0.17. Sample correlations, combined with simulations, show that $f_c$ is more strongly anti-correlated with $\lambda_{\rm Edd}$ than with $L_{\rm Bol}$. This points to large-scale torus geometry changes associated with the Eddington-dependent accretion flow, rather than a receding torus, with its inner sublimation radius determined solely by heating from the central source. Furthermore, we do not see any significant change in the distribution of $f_c$ for sub-samples of radio-loud sources or Narrow Line Seyfert~1 galaxies (NLS1s), though these sub-samples are small.