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Maximum mass limit

There is a natural upper limit to how large supermassive black holes can grow. Supermassive black holes in any quasar or active galactic nucleus (AGN) appear to have a theoretical upper limit of physically around 50 billion M for typical parameters, as anything above this slows growth down to a crawl (the slowdown tends to start around 10 billion M) and causes the unstable accretion disk surrounding the black hole to coalesce into stars that orbit it. A study concluded that the radius of the innermost stable circular orbit (ISCO) for SMBH masses above this limit exceeds the self-gravity radius, making disc formation no longer possible.

A larger upper limit of around 270 billion M was represented as the absolute maximum mass limit for an accreting SMBH in extreme cases, for example its maximal prograde spin with a dimensionless spin parameter of a = 1, although the maximum limit for a black hole's spin parameter is very slightly lower at a = 0.9982. At masses just below the limit, the disc luminosity of a field galaxy is likely to be below the Eddington limit and not strong enough to trigger the feedback underlying the M–sigma relation, so SMBHs close to the limit can evolve above this.

It was noted that, black holes close to this limit are likely to be rather even rarer, as it would require the accretion disc to be almost permanently prograde because the black hole grows and the spin-down effect of retrograde accretion is larger than the spin-up by prograde accretion, due to its ISCO and therefore its lever arm. This would require the hole spin to be permanently correlated with a fixed direction of the potential controlling gas flow, within the black hole's host galaxy, and thus would tend to produce a spin axis and hence AGN jet direction, which is similarly aligned with the galaxy. Current observations do not support this correlation.

The so-called 'chaotic accretion' presumably has to involve multiple small-scale events, essentially random in time and orientation if it is not controlled by a large-scale potential in this way. This would lead the accretion statistically to spin-down, due to retrograde events having larger lever arms than prograde, and occurring almost as often. There is also other interactions with large SMBHs that trend to reduce their spin, including particularly mergers with other black holes, which can statistically decrease the spin. All of these considerations suggested that SMBHs usually cross the critical theoretical mass limit at modest values of their spin parameters, so that 5 × 10 M in all but rare cases.

Although modern UMBHs within quasars and galactic nuclei cannot grow beyond around (5–27) × 10 M through the accretion disk and as well given the current age of the universe, some of these monster black holes in the universe are predicted to still continue to grow up to stupendously large masses of perhaps 10 M during the collapse of superclusters of galaxies in the extremely far future of the universe.