Hysteresis in broad-line regions of active galactic nuclei

The response of emission-line luminosities to changes in the observed continuum in active galaxies is commonly used for reverberation mapping (RM) of the emission-line region. The method assumes regularity in the continuum source and linearity in the line response to the continuum, and that the phase-space distribution of the line-emitting gas is constant in time. The wealth of information contained in the detailed line profiles is under-utilized in current methods of RM. We propose a new method to improve this situation. We define normalized profiles and show how their use enables one to explore details of the emission-line region that have hitherto eluded detection. Furthermore, we investigate the possibility of testing the validity of the assumptions as used in the standard application of RM. We present new methods, the hysteresis test and the Q concept - also based on the line profiles - to test the basic assumptions of RM. The test falls when applied to NGC 4151. We show that there is good evidence either for significantly extended and complex emission-line regions, or for changes in the mass distribution over time-scales of months or more - i.e. on time-scales comparable to the length of typical observing campaigns. We discuss the implication of our results.