Kinematic signatures of reverberation mapping of close binaries of
  supermassive black holes in active galactic nuclei III. The case of
  elliptical orbits
  An intense search for kinematic signatures of reverberation mapping of close
binary SMBH (SMBBH) is currently ongoing. Elliptical SMBBH systems (i.e. both
orbits and disc-like broad-line regions (BLR) are elliptic) have not been
assessed in two-dimensional transfer functions (2DTF) studies. We aim to
numerically infer such a 2DTF because the geometry of the unresolved region is
imprinted on their optical emission. Through this, we determine their specific
kinematical signatures. We simulated the geometry and kinematics of SMBBH whose
components are on elliptical orbits. Each SMBH had a disc-like elliptical BLR.
The SMBHs were active and orbited each other tightly at a subparsec distance.
  Here we calculate for the first time 2DTF, as defined in the velocity-time
delay plane, for several elliptical configurations of SMBBH orbits and their
BLRs. We find that these very complex configurations are clearly resolved in
maps. These results are distinct from those obtained from circular and
disc-wind geometry. We calculate the expected line variability for all SMBBH
configurations. We show that the line shapes are influenced by the orbital
phase of the SMBBH. Some line profiles resemble observed profiles, but they can
also be much deformed to look like those from the disc-wind model.
  First, our results imply that using our 2DTF, we can detect and quantify
kinematic signatures of elliptical SMBBH. Second, the calculated expected line
profiles share some intriguing similarities with observed profiles, but also
with some profiles that are synthesised in disc-wind models. To overcome the
non-uniqueness of the spectral line shapes as markers of SMBBH, they must be
accompanied with 2DTF.
