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

The covering factor of Compton-thick (CT) obscuring material associated with the torus in active galactic nuclei (AGNs) is at present best understood through the fraction of sources exhibiting CT absorption along the line of sight (NH > 1.5 × 10²⁴ cm^-2) in the X-ray band, which reveals the average covering factor. Determining this CT fraction is difficult, however, due to the extreme obscuration. With its spectral coverage at hard X-rays (>10 keV), Nuclear Spectroscopic Telescope Array (NuSTAR) is sensitive to the AGNs covering factor since Compton scattering of X-rays off optically thick material dominates at these energies. We present a spectral analysis of 10 AGNs observed with NuSTAR where the obscuring medium is optically thick to Compton scattering, so-called CT AGNs. We use the torus models of Brightman & Nandra that 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 CT gas in these sources individually. Across the sample we find mild to heavy CT columns, with NH measured from 10²⁴ to 10²⁶ cm^-2, and a wide range of covering factors, where individual measurements range from 0.2 to 0.9. We find that the covering factor, fc, is a strongly decreasing function of the intrinsic 2-10 keV luminosity, LX, where fc = (-0.41 ± 0.13)log10(LX/erg s^-1)+18.31 ± 5.33, across more than two orders of magnitude in LX (10^41.5-10⁴⁴ erg s^-1). The covering factors measured here agree well with the obscured fraction as a function of LX as determined by studies of local AGNs with LX > 10^42.5 erg s^-1.