Rarefied Broad-Line Regions in Active Galactic Nuclei: Anomalous Responses in Reverberation Mapping and Implications for Weak Emission-Line Quasars

Reverberation mapping (RM) is a widely-used method for probing the physics of broad-line regions (BLRs) in active galactic nuclei (AGNs). There are increasing preliminary evidences that the RM behaviors of broad emission lines are influenced by BLR densities, however, the influences have not been investigated systematically from theoretical perspective. In the present paper, we adopt locally optimally emitting cloud model and use CLOUDY to obtain the one-dimensional transfer functions of the prominent UV and optical emission lines for different BLR densities. We find that the influences of BLR densities to RM behaviors have mainly three aspects. First, rarefied BLRs (with low gas densities) may show anomalous responses in RM observations. Their emission-line light curves inversely response the variations of continuum light curves, which may have been observed in some UV RM campaigns. Second, the different BLR densities in AGNs may result in correlations between the time lags and equivalent widths of emission lines, and may contribute to the scatters of the radius-luminosity relationships. Third, the variations of BLR densities may explain the changes of time lags in individual objects in different years. Some weak emission-line quasars (WLQs) are probably extreme cases of rarefied BLRs. We predict that their RM observations may show the anomalous responses.