Determining the covering factor of Compton-thick active galactic nuclei with NuSTAR

The covering factor of Compton-thick obscuring material associated with the torus in active galactic nuclei (AGN) is at present best understood through the fraction of sources exhibiting Compton-thick absorption along the line of sight ($N_{H}>1.5\times10^{24}$ cm$^{-2}$) in the X-ray band, which reveals the average covering factor. Determining this Compton-thick fraction is difficult however, due to the extreme obscuration. With its spectral coverage at hard X-rays ($>$10 keV), NuSTAR is sensitive to the AGN covering factor since Compton scattering of X-rays off optically thick material dominates at these energies. We present a spectral analysis of 10 AGN observed with NuSTAR where the obscuring medium is optically thick to Compton scattering, so called Compton-thick (CT) AGN. We use the torus models of Brightman & Nandra which predict the X-ray spectrum from reprocessing in a torus and include the torus opening angle as a free parameter and aim to determine the covering factor of the Compton-thick gas in these sources individually. Across the sample we find mild to heavy Compton-thick columns, with $N_{H}$ measured from $10^{24}-10^{26}$ cm$^{-2}$, and a wide range of covering factors, where individual measurements range from 0.2-0.9. We find that the covering factor, $f_{c}$, is a strongly decreasing function of the intrinsic 2-10 keV luminosity, $L_{X}$, where $f_{c}=(-0.41\pm0.13)$log$_{10}$($L_{X}$/erg s$^{-1}$)$+18.31\pm5.33$, across more than two orders of magnitude in $L_{X}$ (10$^{41.5}-10^{44}$ erg s$^{-1}$). The covering factors measured here agree well with the obscured fraction as a function of $L_{X}$ as determined by studies of local AGN with $L_{X}>10^{42.5}$ erg s$^{-1}$.