Spiral Arms in Broad-line Regions of Active Galactic Nuclei. II. Loosely Wound Cases: Reverberation Properties

There has recently been growing evidence that broad-line regions (BLRs) in active galactic nuclei have regular substructures, such as spiral arms, which are supported by the fact that the radii of BLRs measured by RM observations are generally consistent with the self-gravitating regions of accretion disks. We have shown in Paper I that the spiral arms excited by the gravitational instabilities in these regions may exist in some disk-like BLRs. As the second paper of the series, we investigate the loosely wound spiral arms excited by gravitational instabilities in disk-like BLRs and present their observational characteristics. Following the treatments of Adams et al. (1989), we solve the governing integro-differential equation by a matrix scheme. The emission-line profiles, velocity-delay maps, and velocity-resolved lags of the BLR spiral arms are calculated. We find that the spiral arms can explain some phenomena in observations: (1) the emission-line profiles in the mean and rms spectra have different asymmetries, (2) some velocity-delay maps, e.g., NGC 5548, have complex sub-features (incomplete ellipse), (3) the timescales of the asymmetry changes in emission-line profiles (rms spectra) are short. These features are attractive for modeling the observed line profiles and the properties of reverberation, and for revealing the details of the BLR geometry and kinematics.