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A binary SMBH (binary supermassive black hole or BSMBH) is two co-orbiting supermassive black holes. Other terms found in publications: SMBHB for SMBH binary or supermassive black hole binary and SMBBH for supermassive binary black hole. (A common convention is that an "XYZ binary" is a binary system that includes an XYZ, and a "binary XYZ" is specifically a pair of XYZs; however, nothing is really comparable to an SMBH except another SMBH, and the term "SMBH binary" is unlikely to be used for an SMBH and something else).
There are some good BSMBH candidates, but far fewer than accepted individual SMBH detections. None of the recent GW detections has been a BSMBH merger and current gravitational-wave detectors are not set up to detect them.
A reason for interest in BSMBHs is that gravitational waves they would produce could be detected in the future. Pulsar timing arrays (PTAs) are intended to detect them. Unlike existing GW detections, these would not be those of actual mergers, which would be very rare (the inspiral would take much more time than those of stellar-mass black holes), but the GW waves generated when the orbits are somewhat small. Galaxies merge, typically each hosting a SMBH, and it is theorized that their respective SMBHs can fall into orbit. The resulting gravitational waves could be detectable in cases where their orbital periods are sufficiently small.
When the black holes orbit, the energy loss from gravitational waves draw them together, i.e., a black hole merger, but above a certain distance apart, this would be taking too long, e.g., longer than the age of the universe. Sufficiently tightening the orbit, and even entering orbit necessarily requires interaction with other masses. Dynamical friction from stars explains some tightening of such orbits, but analysis of its effect suggest it is insufficient; the tightening would virtually cease before gravitational waves increase to the point that there could be such mergers already. The final parsec problem is the question of how the orbit might continue to tighten while within the gap between these two influences.