Testing Comptonizing coronae on a long BeppoSAX observation of the Seyfert1 galaxy NGC 5548

We test accurate models of Comptonization spectra over the high-quality dat a of the BeppoSAX long look at NGC 5548, allowing for different geometries of the scattering region, different temperatures of the input soft photon f ield, and different viewing angles. We find that the BeppoSAX data are well represented by a plane-parallel or hemispherical corona viewed at an incli nation 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 val ues of the hot plasma temperature and optical depth are kT(e) similar or eq ual to 250-260 keV and tau similar or equal to 0.16-0.37 for the slab and h emisphere, respectively. These values are substantially different from thos e derived fitting the data with a power-law-plus-cutoff approximation to th e Comptonization component (kT(e) less than or similar to 60 keV, tau simil ar or equal to 2.4). In particular, the temperature of the hot electrons es timated from Comptonization models is much larger. This is due to the fact that accurate Comptonization spectra in anisotropic geometries show "intrin sic" curvature that reduces the necessity of a high-energy cutoff. The Comp tonization parameter derived for the slab model is larger than predicted fo r a two-phase plane-parallel corona in energy balance, suggesting that a mo re "photon-starved" geometry is necessary. The case of a hemispherical coro na is consistent with energy balance but requires a large reflection compon ent. The spectral softening detected during a flare that occurred in the ce ntral part of the observation corresponds to a decrease of the Comptonizati on parameter, probably associated with an increase of the soft photon lumin osity, 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.