Testing Comptonizing coronae on a long BeppoSAX observation of the Seyfert 1 galaxy NGC 5548

We test accurate models of Comptonization spectra over the high-quality data of the BeppoSAX long look at NGC 5548, allowing for different geometries of the scattering region, different temperatures of the input soft photon field, and different viewing angles. We find that the BeppoSAX data are well represented by a plane-parallel or hemispherical corona viewed at an inclination angle of 30 degrees. For both geometries the best-fit temperature of the soft photons is close to 15(-9)(+3) eV. The corresponding best-fit values of the hot plasma temperature and optical depth are kT(e) similar or equal to 250-260 keV and tau similar or equal to 0.16-0.37 for the slab and hemisphere, respectively. These values are substantially different from those derived fitting the data with a power-law-plus-cutoff approximation to the Comptonization component (kT(e) less than or similar to 60 keV, tau similar or equal to 2.4). In particular, the temperature of the hot electrons estimated from Comptonization models is much larger. This is due to the fact that accurate Comptonization spectra in anisotropic geometries show "intrinsic" curvature that reduces the necessity of a high-energy cutoff. The Comptonization parameter derived for the slab model is larger than predicted for a two-phase plane-parallel corona in energy balance, suggesting that a more "photon-starved" geometry is necessary. The case of a hemispherical corona is consistent with energy balance but requires a large reflection component. The spectral softening detected during a flare that occurred in the central part of the observation corresponds to a decrease of the Comptonization parameter, probably associated with an increase of the soft photon luminosity, the hard photon luminosity remaining constant. The increased cooling fits in naturally with the derived decrease of the coronal temperature kT(e) in the high state.