<p>The article you cite is almost certainly referring to the suggestions put forward by <a href="https://arxiv.org/abs/1511.08502" rel="nofollow noreferrer">King (2016)</a>, <a href="https://arxiv.org/abs/1601.02611" rel="nofollow noreferrer">Inayoshi &amp; Haiman (2016)</a> and <a href="https://arxiv.org/abs/1609.06716" rel="nofollow noreferrer">Yazdi &amp; Afshordi (2017)</a>, that there is a limit imposed by gravitational fragmentation of any accretion disc feeding the black hole.</p>
<p>Black holes are generally fed by gas, in an accretion disc, losing energy and angular momentum, until it reaches the innermost stable circular orbit (ISCO - a feature of General Relativistic orbits). Further loss of energy then results in the material falling rapidly to the event horizon.</p>
<p>To grow a black hole at a significant rate requires that the average mass inflow is roughly equal to the mass of the black hole divided by its age. The bigger this value, the more gas there must be in the accretion disc to accomplish that accretion rate.</p>
<p>However, if the disc is too massive, it becomes &quot;self gravitating&quot; and can begin to fragment and form stars (it breaches the so-called <a href="https://en.wikipedia.org/wiki/Toomre%27s_stability_criterion" rel="nofollow noreferrer">Toomre stability criterion</a>). If it does so, then because orbiting stars do not lose energy or angular momentum anywhere near as easily as hot gas, they won't necessarily fall into the black hole and its mass accretion rate is drastically reduced.</p>
<p>The big idea here is that, when you do the maths, the discs become self-gravitating beyond some outer radius. If that radius become smaller than the ISCO then you cannot get a stable accretion disc to feed the black hole and it stops growing (at a fast rate).</p>
<p>According to the papers above, this occurs at around 50 billion solar masses (but maybe 300 billion solar masses for the fastest possible spinning black holes). Above this limit, black holes could not be accreting sufficiently to grow their masses on timescales of the age of the universe. i e. They could still grow, but only very slowly.</p>
<p>Also note, that this limit applies to luminous accretion from a gaseous disc. It would still be possible to grow these black holes by mergers with other black holes for example. But there is then an observational bias against detecting such black holes, until perhaps we have a low frequency gravitational wave detector in space.</p>

CC BY-SA 4.0
2024-03-24T08:27:38.727Z
2024-03-30T23:51:49.380Z
2024-03-30T23:51:49.380Z
ProfRob
<p>According to this,</p>
<p><a href="https://www.sciencefocus.com/space/how-big-could-a-black-hole-get" rel="nofollow noreferrer">How big could a black hole get</a></p>
<blockquote>
<p>recent studies suggest that UMBHs cannot physically grow much beyond
this (10 billion solar masses) anyway, since they would then begin to
disrupt the accretion discs that feed them, choking the source of new
material.</p>
</blockquote>
<p>I don't understand this. What would happen exactly with the accretion discs if the UMBH grows beyond 10 billion solar masses? How would the accretion discs be disrupted by the black hole?</p>

CC BY-SA 4.0
2024-03-21T02:08:55.017Z
https://astronomy.stackexchange.com/questions/24196/is-there-a-maximum-size-for-a-black-hole https://astronomy.stackexchange.com/questions/14093/is-there-a-limit-to-the-size-of-a-black-hole
Mithoron
CC BY-SA 4.0
2024-03-21T02:14:12.177Z
https://astronomy.stackexchange.com/questions/13111/what-happens-when-an-ultra-massive-black-hole-cannibalize-another
Mithoron
<black-hole>
How ultra massive black holes would " disrupt the accretion discs that feed them" beyond some upper limit to their masses?
Pablo
# How ultra massive black holes would " disrupt the accretion discs that feed them" beyond some upper limit to their masses?

(Asked by: username_0 on 2024-03-21)

According to this,

[How big could a black hole get](https://www.sciencefocus.com/space/how-big-could-a-black-hole-get)

> recent studies suggest that UMBHs cannot physically grow much beyond
> this (10 billion solar masses) anyway, since they would then begin to
> disrupt the accretion discs that feed them, choking the source of new
> material.

I don't understand this. What would happen exactly with the accretion discs if the UMBH grows beyond 10 billion solar masses? How would the accretion discs be disrupted by the black hole?

**Tags:** black-hole
> **Comments:**
> **username_1**: https://astronomy.stackexchange.com/questions/24196/is-there-a-maximum-size-for-a-black-hole https://astronomy.stackexchange.com/questions/14093/is-there-a-limit-to-the-size-of-a-black-hole  
> **username_1**: https://astronomy.stackexchange.com/questions/13111/what-happens-when-an-ultra-massive-black-hole-cannibalize-another  

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## 1 answers

### Answer by username_2 on 2024-03-24. Score: 5 | Accepted answer

The article you cite is almost certainly referring to the suggestions put forward by [King (2016)](https://arxiv.org/abs/1511.08502), [Inayoshi & Haiman (2016)](https://arxiv.org/abs/1601.02611) and [Yazdi & Afshordi (2017)](https://arxiv.org/abs/1609.06716), that there is a limit imposed by gravitational fragmentation of any accretion disc feeding the black hole.

Black holes are generally fed by gas, in an accretion disc, losing energy and angular momentum, until it reaches the innermost stable circular orbit (ISCO - a feature of General Relativistic orbits). Further loss of energy then results in the material falling rapidly to the event horizon.

To grow a black hole at a significant rate requires that the average mass inflow is roughly equal to the mass of the black hole divided by its age. The bigger this value, the more gas there must be in the accretion disc to accomplish that accretion rate.

However, if the disc is too massive, it becomes "self gravitating" and can begin to fragment and form stars (it breaches the so-called [Toomre stability criterion](https://en.wikipedia.org/wiki/Toomre%27s_stability_criterion)). If it does so, then because orbiting stars do not lose energy or angular momentum anywhere near as easily as hot gas, they won't necessarily fall into the black hole and its mass accretion rate is drastically reduced.

The big idea here is that, when you do the maths, the discs become self-gravitating beyond some outer radius. If that radius become smaller than the ISCO then you cannot get a stable accretion disc to feed the black hole and it stops growing (at a fast rate).

According to the papers above, this occurs at around 50 billion solar masses (but maybe 300 billion solar masses for the fastest possible spinning black holes). Above this limit, black holes could not be accreting sufficiently to grow their masses on timescales of the age of the universe. i e. They could still grow, but only very slowly.

Also note, that this limit applies to luminous accretion from a gaseous disc. It would still be possible to grow these black holes by mergers with other black holes for example. But there is then an observational bias against detecting such black holes, until perhaps we have a low frequency gravitational wave detector in space.


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