How did the Holm 15A Galaxy BH reach 40 Billion Solar Masses?

The most massive supermassive black hole discovered to date lies within the Abell 85 galaxy cluster. At the heart of this cluster is the galaxy Holm 15A, containing an estimated 2 trillion solar masse in stars. At the heart of this galaxy is a GARGANTUAN black hole that has been measured at 40 BILLION solar masses. (This is alone 2.3% the mass of the Milky Way galaxy.)

How did this BH reach this truly massive size? Is there enough time in the universe for collisions of multiple Super Massive BH's to have been drawn together and merged? Or is there some other cause for its size?

Bonus question... (I am making the assumption that it is a rotating BH due to the galaxy rotating)... Ca we determine how large would the singularity would be?

• Your estimate for the mass of the Milky Way seems off by at least an order of magnitude. Dec 28 '20 at 0:09
• Sorry you are correct. It should have read 2.3% of the milky way. I fixed that.
– Rick
Dec 28 '20 at 2:36

Black holes grow by mergers and by accreting mass in the form of gas. The latter offers the biggest reservoir of available mass - as you say, the black hole is a small fraction of the mass of its host galaxy.

Feeding a black hole is not necessarily easy. There may be a limit to the accretion rate caused by radiative feedback and pressure from the hot gas as it is funneled into the black hole. A common way if thinking about this is to talk about the Eddington limit, which is the maximum accretion rate allowed at the Eddington luminosity for spherical accretion. Since this limiting accretion rate is proportional to the mass of the black hole, it implies an exponential growth with a characteristic timescale known as the Salpeter time, which has a numerical value of about 50 million years (see also https://physics.stackexchange.com/a/167279/43351 ).

If a black hole is $$4\times 10^{10} M_{\odot}$$ after say 10 billion years of growth (this galaxy is in the relatively local universe), then it has had 200 e-folding times to grow - i.e. it can have grown by a factor of $$e^{200}$$. Thus given a gas supply, there is no reason such a black hole cannot grow from a small, stellar-sized black hole, formed early in the galaxy's history.

The more problematic cases are the billion solar mass black holes inferred to be present in young, high redshift quasars ($$z>6$$), which have had a limited time to grow in this way (see for example Yang et al. 2020). There, it may be that you have to start off with larger seed black holes (primordial stars may have produced 1000 solar-mass black holes) or black holes may have initially merged to produce even larger seed black holes, or there are various ways (e.g. non-spherical accretion; low radiative efficiency) that the Eddington limit might be exceeded.

• Hypothetically, if a large spherically symmetric cloud of primordial hydrogen is collapsing under its own gravity with no angular momentum, wouldn't the gravity overcome any radiation pressure and create a SMBH fairly fast? Dec 28 '20 at 15:28
• @Safesphere SMBHs are not formed by drect collapse. As I said in my answer, intermediate BHs of mass ~1000 solar-masses may be formed first. Fragmentation is not dependent on there being angular momentum. Dec 28 '20 at 15:39
• Thanks for your insight and +1 for a great answer, but could you please clarify why my hypothetical case is impossible? "SMBHs are not formed by drect collapse" - Well, perhaps not typically, but what happens, if there is a large spherically symmetric cloud of primordial hydrogen collapsing under its own gravity? Why would it not form a SMBH? Dec 28 '20 at 16:49
• @safesphere because it would fragment into smaller clumps. It might be possible to form $\sim 10^5$ solar mass black holes in very specific circumstances. Dec 28 '20 at 19:17
• I am sure you are right, but for a non-specialist it is not self evident why or how the spherical symmetry would be broken in this case. Could you please clarify why and by what mechanism the gas would fragment instead of proceeding with a spherically symmetric collapse? Dec 29 '20 at 14:59