Quasar tomography: unification of echo mapping and photoionization models

Reverberation mapping aims to use time-delayed variations in photoionized emission lines to map the geometry and kinematics of emission-line gas in the vicinity of an active galactic nucleus. By fitting to a time-variable emission-line profile, we can reconstruct a two-dimensional map Psi(tau, v ), where tau is the time delay and v is the Doppler shift, for each emission line. In this paper we develop quasar tomography, which combines the time delay and velocity information with photoionization physics in order to map the reprocessing region using information assembled from many different emission lines. The observed spectral variations are modelled in terms of direct light from the active nucleus and time-delayed reprocessed light from surrounding gas clouds. We use the photoionization code cloudy to evaluate line and continuum reprocessing efficiencies epsilon(lambda, Phi(H) , n (H) , N (H) , theta) for clouds of hydrogen density n (H) and column density N (H) exposed to hydrogen-ionizing photon flux Phi(H) . The gas distribution is described by a five-dimensional map, the differential covering fraction f (R , theta, n (H) , N (H) , v ), which we reconstruct from the two-dimensional data F (lambda) (lambda, t ) by using maximum entropy techniques. Tests with simulated data and a variety of geometries (shells, rings, discs, clouds, jets) are presented to illustrate some of the capabilities and limitations of the method. Specifically, we reconstruct three-dimensional geometry-density maps, f (R , theta, n (H) ), by fitting to well-sampled light curves for the continuum and seven ultraviolet emission lines. The maps are distorted in ways that we understand and discuss. The most successful test recovers a hollow shell geometry, determining correctly its radius and density. The data constrain the ionization parameter U proportional toR (-2) n (-1) (H) to about 0.1 dex, the radius R to 0.15 dex, and n (H) to 0.3 dex. We expect better constraints to arise from future fits using more lines and velocity profiles as well as velocity-integrated line fluxes. The maps are sensitive to the assumed distance, offering some prospects for using emission-line reverberations to measure the luminosities and distances of active galactic nuclei.