Echo Images of Broad-Line Regions in Active Galactic Nuclei

Continuum and emission line variations can be used to form two- dimensional images of gas flows in the nuclear regions of active galaxies. The "echo image," {PSI}(v,t), is the two-dimensional transfer function that maps continuum variations to emission-line variations. Convolving a continuum light curve C(t) with {PSI}(v,t) yields L(v, t), the line light curve at each velocity across the line. A procedure for constructing the echo image of a given BLR model is described. Echo images for several BLR models are presented and discussed. A simulated continuum light curve is generated and convolved with the echo images to produce trailed spectrograms showing variations of the line fluxes and line profiles. Because the echo image incorporates both velocity and time-delay information, it is a far more powerful probe of the structure of the BLR than one-dimensional velocity profiles, transfer functions, or cross-correlation functions.