X-ray power law spectra in active galactic nuclei
  X-ray spectra of active galactic nuclei (AGN) are usually described as power
law spectra, characterized by the spectral slope $\alpha$ or photon index
$\Gamma$. Here we discuss the X-ray spectral properties within the framework of
clumpy accretion flows, and estimate the power law slope as a function of the
source parameters. We expect harder spectra in massive objects than in less
massive sources, and steeper spectra in higher accretion rate systems. The
predicted values of the photon index cover the range of spectral slopes
typically observed in Seyfert galaxies and quasars. The overall trends are
consistent with observations, and may account for the positive correlation of
the photon index with Eddington ratio (and the possible anticorrelation with
black hole mass) observed in different AGN samples. Spectral properties are
also closely related to variability properties. We obtain that shorter
characteristic time scales are associated with steeper spectra. This agrees
with the observed `spectral-timing' correlation.
