  As a major feature in spectra of active galactic nuclei, broad emission lines
deliver information of kinematics and spatial distributions of ionized gas
surrounding the central supermassive black holes (SMBHs), that is the so-called
broad-line regions (BLRs). There is growing evidence for appearance of spiral
arms in the BLRs. It has been shown by reverberation mapping (RM) campaigns
that the characterized radius of BLRs overlaps with that of self-gravitating
regions of accretion disks. In the framework of the WKB approximation, we show
robust properties of observational features of the spiral arms. The resulting
spiral arms lead to various profiles of the broad emission line. We calculate
RM and differential interferometric features of BLRs with $m=1$ mode spiral
arms. These features can be detected with high-quality RM and differential
interferometric observations via such as GRAVITY onboard Very Large Telescope
Interferometer. The WKB approximation will be relaxed and universalized in the
future to explore more general cases of density wave signals in RM campaigns
and differential spectroastrometry observations.
