Investigating close binary supermassive black holes at high angular resolution

Gravitational waves (GW) in the nano-Hz domain are expected to be radiated by close-binaries of supermassive black holes (CB-SMBHs; components bound in a Keplerian binary at mutual distance less than ~ 0.1 pc), which are relicts of galaxy mergers and anticipated to be measured via the Pulsar Timing Array (PTA) technique. The challenge of present CB-SMBH investigations is that their signatures are elusive and not easily disentangled from a single SMBH. PTAs will typically have a glimpse of an early portion of the binary inspiral to catch the frequency evolution of the binary only with sufficiently high mass and initially high eccentricity. Thus, we have to make use of electromagnetic observations to determine orbital parameters of CB-SMBHs and test nano-Hz GW properties. The 2D reverberation mapping (RM) is a powerful tool for probing kinematics and geometry of ionized gas in the SMBHs (single or binary) vicinity, yet it can lose information due to projection on the line of sight of the observer. Nevertheless, spectroastrometry with AMBER, GRAVITY, and successors can provide an independent measurement of the emitting region's size, geometry, and kinematics. These two techniques combined can resolve CB-SMBHs. In this review, we focus on RM and spectroastrometry observational signatures of CB-SMBHs with non-zero eccentricity from recent simulations with particular attention to recent developments and open issues.