X-ray variability and correlations in the two phase disk-corona model   for Seyfert galaxies
  We discuss in detail the broad band X-ray variability expected in Seyfert galaxies in the framework of a Compton cooled corona model. Variations in the optical depth tau of the corona cause spectral changes in the Comptonized emission in the sense that the spectrum steepens and the temperature decreases with increasing tau. If the corona is pair dominated, tau is determined by the compactness (proportional to luminosity for fixed size). This yields a definite relation between spectral shape and intensity implying a variation in intensity of a factor 10 for a change of 0.2 in the 2-10 keV spectral index. For low pair density coronae, no definite prediction is possible. In the absence of substantial changes in the structure of the corona, the soft thermal component correlates with the medium-hard Comptonized component. Examples are computed using the ROSAT response matrix, showing that current observations of NGC 5548 and Mrk 766 showing different behaviours can be reconciled with the model. The spectral behaviour of Mrk 766 strongly suggests that the coronal plasma in this source is not pair dominated. 
Francesco Haardt, Laura Maraschi and Gabriele Ghisellini