Distribution of the coronal temperature in Seyfert 1 galaxies

Active galactic nuclei (AGN) produce copious amounts of X-rays through the corona, the region of hot gas that lies close to the accretion disk. The temperature of the corona can be accurately determined by the cut-off signature in the X-ray spectrum. Owing to the high temperatures in the corona, observations well above 10 keV are necessary. Here, we explore the NuSTAR observations of 118 Seyfert 1 AGN selected using Gehrels/Swift. We modelled the spectrum using a single power-law with an exponential cut-off modified by neutral and ionised absorption as well as a reflection component. We found secure spectral cut-off estimates in 62 sources, while for the remaining ones, we derived only the lower limits. The resulting mean value is 103 keV, with a skewed distribution towards large energies with a large dispersion. When we consider the lower limits using survival analysis techniques, the mean cut-off energy becomes significantly larger, that is, about 200 keV. Because of various limitations (e.g., limited spectral passband, photon statistics, model degeneracies), we performed extensive simulations to explore the underlying spectral cut-off distribution. We find that an intrinsic spectral cut-off distribution, which has a Maxwell-Boltzmann shape with a mean value in the range of 160-200 keV, can reproduce the observations sufficiently well. Finally, our spectral analysis places very stringent constraints on both the photon index (Γ = 1.77 ± 0.01) as well as on the reflection component (R = 0.69 ± 0.04) of the Seyfert 1 population. From the values of the spectral cut-off and the photon-index, we deduce that the mean optical depth of the AGN corona is approximately τ_e = 1.82 ± 0.14 and its mean temperature is approximately kT_e = 65 ± 10 keV.