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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 $α$ or photon index $Γ$. 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.