Kinematic signatures of reverberation mapping of close binaries of
  supermassive black holes in active galactic nuclei
  Close binaries of supermassive black holes (CB-SMBHs) with separations of
$\lesssim 0.1$pc as the final stage of galaxy mergers are sources of low
frequency gravitational waves (GW), however, they are still elusive
observationally because they are not spatially resolved. Fortunately,
reverberation as echoes of broad emission lines to ionizing continuum conveys
invaluable information of the dynamics of broad-line regions (BLRs) governed by
supermassive black holes in the central regions of active galactic nuclei
(AGNs). In this paper, we demonstrate how to composite the hybrid 2-dimensional
transfer functions of binary BLRs around the CB-SMBHs in AGNs, providing an
opportunity of identifying them from reverberation mapping (RM) data. It is
found that there are variation-coupling effects in the transfer functions,
arising from the coupling of CB-SMBH light curves in the Fourier space. We
provide semi-analytical formulations of the transfer functions for kinematic
maps of the gas. For cases with the simplest variation-coupling effects, we
make calculations for several BLR models and reveal significant distinctions
from those of single active black holes. In principle, the difference is caused
by the orbital motion of the CB-SMBH systems. In order to search for CB-SMBHs
in time-domain space, selection of target candidates should focus on local AGNs
with H$\beta$ double-peaked profiles and weaker near-infrared emission.
High-fidelity RM-campaigns of monitoring the targets in future will provide
opportunities to reveal these kinematic signatures of the CB-SMBHs and hence
for measurements of their orbital parameters.
