Modeling variable emission lines in active galactic nuclei: Method and application to NGC 5548

We present a new scheme for modeling the broad-line region in active galactic nuclei (AGNs). It involves photoionization calculations of a large number of clouds, in several predetermined geometries, and a comparison of the calculated line intensities with observed emission-line light curves. Fitting several observed light curves simultaneously provides strong constraints on model parameters such as the run of density and column density across the nucleus, the shape of the ionizing continuum, and the radial distribution of the emission-line clouds. When applying the model to the Seyfert 1 galaxy NGC 5548, we were able to reconstruct the light curves of four ultraviolet emission lines in time and in absolute flux. This has not been achieved by any previous work. We argue that the Balmer line light curves, and possibly also the Mg II lambda 2798 light curve, cannot be tested in this scheme because of the limitations of present-day photoionization codes. Our fitting procedure can be used to rule out models in which the particle density scales as r(-2), where r is the distance from the central source. The best models are those in which the density scales as r(-l) or r(-1.5). We can place a lower limit on the column density at a distance of 1 It-day of N-col(r = 1)greater than or similar to 10(23) cm(-2) and limit the particle density to be in the range of 10(12.5) > N(r = 1)> 10(11) cm(-3). We have also tested the idea that the spectral energy distribution (SED) of the ionizing continuum is changing with continuum luminosity. None of the variable-shape SEDs tried resulted in real improvement over a constant-SED case, although models with harder continuum during phases of higher luminosity seem to better fit the observed spectrum. Reddening and/or different composition seem to play a minor role, at least to the extent tested in this work.