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The final parsec problem (or last parsec problem) is an astrophysical problem that would seem to prevent the merger of a binary SMBH, e.g., after a galaxy merger. When the supermassive black holes (SMBHs) are extremely close, they merge because gravitational waves significantly drain their orbital energy. Beyond such extreme closeness, close encounters with stars can remove orbital energy, tightening the orbit, but the odds of encountering a star decreases as the orbit decreases, to a point where the black holes would remain in virtually the same orbit, i.e., the timescale for further decrease is far too long (longer than the age of the universe). Assuming they sometimes do merge, it is not clear how their orbits continue to become smaller through the final parsec: there is a gap within which neither process is sufficient to significantly tighten the orbit.
The problem is often described as an inability to sufficiently refill the loss cone to close the gap between black holes within a timescale of interest. The loss cone is not a cone-shaped region of space, rather it is a region within the phase space (shaped within a graph so as to suggest a cone) of the galaxy's stars within which they have the opportunity for encounters with the orbiting black holes that absorb energy and angular momentum from their orbits.
If there is a mechanism that regularly overcomes the final parsec problem, then it is presumed there are as many SMBH mergers as there are galaxy mergers. How detected SMBHs gain their large masses (SMBH formation) is also a mystery, and such mergers would be a contributor.
The problem has been of interest, and approached a number of ways. Models suggest encounters between SMBH and stars fall to the point that the orbit of the two SMBHs remains virtually static, and one proposed solution to the problem is that the distribution of stars in the galaxy core after a merger differs from models developed from/for simpler galaxies, such simple models not modeling stars' dynamical friction realistically. A triaxial galaxy model (differing "widths" of the galaxies' the three dimensions) may explain more encounters between SMBH and surrounding stars than simplistic models that presume a symmetric disk, such as a spiral galaxy. Another proposed solution is that a circumbinary accretion disk some distance out from accretion disks around the individual black holes, accreting material onto those inner disks (disk coupling) has a means of drawing out orbital angular momentum into ejected material. Other solutions have been proposed, some including possible characteristics of dark matter, and some including the presence of neighboring smaller black holes.