X-ray variability and correlations in the two-phase disk-corona model for Seyfert galaxies

We discuss in detail the broadband X-ray variability expected in Seyfert galaxies in the framework of a Compton-cooled corona model, computing spectral indices in the 2-10 keV range and fluxes in the medium (2-10 keV), hard (30-100 keV), and soft (0.1-0.4, 0.9-2 keV) X-ray bands, for different hypotheses concerning variability ''modes.'' In all cases the soft photons responsible for the cooling are assumed to be proportional to the Comptonized flux (fixed geometry), and the plane-parallel limit is adopted. 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 de finite 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. If,for instance, tau varies while the luminosity remains approximately constant, the Compton spectrum shows a pivoting behavior around similar or equal to 10 keV. In both cases, the coronal temperature decreases for increasing spectral index. In the absence of substantial changes in the structure of the corona, the soft thermal component correlates with the medium and hard Comptonized components. Although the correlation must hold globally, that is, for the integrated power of the two components, the observed intensity in the soft X-ray band is extremely sensitive to the temperature of the thermal component that may vary as a result of variations in luminosity and/or area of the reprocessing region(s). Examples are computed using the ROSAT response matrix, showing that for kT less than or similar to 60 eV the spectrum in the ROSAT range softens with increasing intensity while the opposite is true for larger temperatures. Current observations of NGC 5548 and Mrk 766 showing different behaviors can therefore be reconciled with the model. The spectral behavior of Mrk 766 strongly suggests that the coronal plasma in this source is not pair dominated. The possibility of constraining models through simultaneous observations in the soft, medium, and hard X-ray ranges is discussed.