The amplitude–time lag (“ΔA-Δt”) relation is considered in order to describe behaviour of the emission-line spectrum of an active galactic nucleus during a separate active event. Here ΔA, called the amplitude, is the maximum relative increment of the flux in a line, and Δt is the time lag between the maximum of the ionizing continuum flare and the maximum of the flare in a line. As suggested by Shevchenko (1988), the construction and analysis of such relations can be used to discriminate between broad-line region models. Comparison of theoretical “ΔA-Δt” relations with the observed one composed by data for flares in various lines during a separate active event, is proved to be a useful tool for investigating the geometry of a broad-line region, for studies of the form of phase functions of a typical line-emitting cloud in various lines, as well as for clearing up the duration and amplitude of the initial flare in the ionizing continuum. The advantage of this method is that it utilizes the most general observed characteristics of the emission-line flares and nevertheless provides basic information on the allowed BLR models before the detailed modelling of emission-line light curves is performed.
The Amplitude–Time Lag Relation for Emission-Line Flares of AGN