How Big Can a Black Hole Grow? 50 billion times the Sun

How Big Can a Black Hole Grow?

The discovery of mega black holes within the last few years that prompted Andrew King of the University of Leicester, UK to look at the subject. The heaviest black holes we’ve now seen have a mass of up to 40 billion times that of our sun, which led King to calculate how big a black hole would have to be for its outer edge to keep a disc from forming. He also came up with a figure of 50 billion solar masses, firming up the previous findings.

Without a disc, the black hole would stop growing, making this the upper limit. The only way it could grow larger would be if a star fell straight in or another black hole merged with it. But neither process would fatten it up as efficiently as a gas disc. “Unless you merge with another monster, you’ll make almost no difference to the black hole mass,” King says.

There is a physical limit to the mass of a black hole, above which it cannot grow through luminous accretion of gas, and so cannot appear as a quasar or active galactic nucleus. The limit is Mmax simeq 5×10^{10}M_sun for typical parameters, but can reach Mmax simeq 2.7×10^{11}M_sun in extreme cases (e.g. maximal prograde spin). The largest black hole masses so far found are close to but below the limit. The Eddington luminosity simeq 6.5×10^{48} erg/s corresponding to Mmax is remarkably close to the largest AGN bolometric luminosity so far observed. The mass and luminosity limits both rely on a reasonable but currently untestable hypothesis about AGN disc formation, so future observations of extreme SMBH masses can therefore probe fundamental disc physics. Black holes can in principle grow their masses above Mmax by non-luminous means such as mergers with other holes, but cannot become luminous accretors again. They might nevertheless be detectable in other ways, for example through gravitational lensing. I show further that black holes with masses ~ Mmax can probably grow above the values specified by the black-hole — host-galaxy scaling relations, in agreement with observation

The mass limit Mmax for accreting supermassive black holes, compared with the largest observed masses. The curve shows Mmax as a function of black hole spin parameter

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