The distribution of the coronal temperature in Seyfert 1 galaxies
  The Active Galactic Nuclei (AGN) produce copious amounts of X-rays through
the corona that is the 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 large temperatures of the corona,
observations well above 10 keV are necessary. Here, we explore the NuSTAR
observations of 118 Gehrels/Swift selected Seyfert 1 AGN. We model 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 find secure spectral
cut-off estimates in 62 sources while for the remaining ones we derive only
lower limits. The mean value is 103 keV with a skewed distribution towards
large energies with large dispersion. When we consider the lower limits using
survival analysis techniques, the mean cut-off energy becomes significantly
larger, about 200 keV. Because of various limitations (e.g. limited spectral
passband, photon statistics, model degeneracies) we perform 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
sufficiently well the observations. Finally, our spectral analysis places very
stringent constraints on both the photon index (Gamma=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 tau=1.82+/-0.14 and its mean
temperature approximately kT=65+/-10 keV.
