<p>The answer to this is unknown at the present time.</p>
<p>The issue is that an accreting &quot;seed black hole&quot; can only accrete at a limited rate. The limitation is provided by radiation pressure from the material it is accreting. This provides negative feedback and defines a maximum accretion rate for spherical accretion known as the <a href="https://en.wikipedia.org/wiki/Eddington_luminosity" rel="noreferrer">Eddington limit</a>, which defines a maximum luminosity and hence a maximum accretion rate (since accretion provides the luminosity).</p>
<p>The net result is that the black hole can grow exponentially, with a growth timescale of about 30-40 million years. That is, it can roughly double in mass in that timescale.</p>
<p>Now the first, primordial stars may have been much more massive than big stars in the universe today, as a result of their pure hydrogen/helium composition. Even if they were able to form up to a few hundred solar mass black holes, it would still take almost a billion years to build a <span class="math-container">$10^9 M_\odot$</span> black hole, even if it accreted at the maximum Eddington rate for all of that time.</p>
<p>This is a bit of a stretch so alternative solutions are being sought. These include</p>
<ol>
<li><p>Maybe you can form even bigger black holes from early collapsing gas clouds. There are some ideas that if the primordial gas gets ionised by the very first massive stars then it doesn;t fragment into &quot;stellar&quot; objects. This can enable you to form very, very massive &quot;stars&quot; (sometimes called <a href="https://en.wikipedia.org/wiki/Quasi-star" rel="noreferrer">&quot;quasi-stars&quot;</a>), which have black holes at their centres rather than nuclear-fusing cores. These might grow rapidly to be of order <span class="math-container">$10^5 M_{\odot}$</span> This can shave of many exponential growth timescales by starting off with a more massive seed.</p>
</li>
<li><p>Maybe you can merge black holes. We now know from gravitational wave detections that mergers can proceed between black holes with tens of solar masses to form <span class="math-container">$\sim 100M_\odot$</span> black holes. Perhaps in the early universe there may have been clusters of high-mass black holes that managed to merge with each other on short timescales. These would then form a massive seed black hole that could grow relatively quickly.</p>
</li>
<li><p>There are some ideas about how the Eddington limit can be circumvented and mass accretion can proceed at higher rates, perhaps by suppressing the radiative efficiency of the accreting black hole (e.g. <a href="https://academic.oup.com/mnras/article/424/2/1461/1001493" rel="noreferrer">Li et al. 2012</a>).</p>
</li>
</ol>

CC BY-SA 4.0
2021-01-22T01:33:55.503Z
Aren't black holes not subject to the Eddington limit, since an unlimited amount of energy can be lost down the hole without contributing to overall luminosity?
Vikki
CC BY-SA 4.0
2021-01-22T08:31:34.023Z
@Sean cramming matter into the event horizon inevitably leads to it heating up and emitting radiation. Most of this radiation comes from well outside the event horizon. What you are suggesting is that the matter could be "advected" into the black hole without heating up. That isn't really possible.
ProfRob
CC BY-SA 4.0
2021-01-22T15:46:31.590Z
Why would the growth of the hypothetical black holes in the midst of gas clouds not be restricted by the same radiation pressure as that of "standard" black holes? Or do you mean that the black hole *starts* at 10^5 solar masses?
Peter - Reinstate Monica
CC BY-SA 4.0
2021-01-22T16:50:22.400Z
@Peter-ReinstateMonica The Eddington limit assumes that the accreting gas is not being "forced in" (other than by gravity). In a quasi-star the black hole sits in the middle of a massive "star", so my understanding is that the Eddington rate in this case is that for the TOTAL mass of the object, not just the black hole, so it can grow to $10^5M\odot$ quickly.
ProfRob
CC BY-SA 4.0
2021-01-22T17:02:47.690Z
Ah, I missed that the BH "replaces" the core of a star, thanks. But then: What other forces than gravity "force in" the matter of that star?
Peter - Reinstate Monica
CC BY-SA 4.0
2021-01-22T17:05:05.947Z
@Peter-ReinstateMonica I'll come back with an edit later. I need to read a paper. I probably badly expressed it. The fact you have the weight of the envelope pressing the stuff inwards. I believe that term is neglected in the standard Eddington treatment.
ProfRob
CC BY-SA 4.0
2021-01-22T17:25:35.043Z
This layman here appreciates your time and effort. No worries. All misunderstandings are mine! :-)
Peter - Reinstate Monica
CC BY-SA 4.0
2021-01-22T20:49:08.530Z
Let's not make too much of the Eddington limit. It's not a fundamental property of accretion flow. We have strong evidence of hyper-Eddington accretion in the engines driving gamma-ray bursts.
John Doty
CC BY-SA 4.0
2021-01-21T18:10:04.353Z
2021-01-21T18:10:04.353Z
ProfRob
<p>A supermassive black hole was discovered <a href="https://phys.org/news/2021-01-earliest-supermassive-black-hole-quasar.html?utm_source=nwletter&amp;utm_medium=email&amp;utm_campaign=daily-nwletter" rel="noreferrer">recently</a> that is 13 billion years old. This blackhole is 1.6 billion times the mass of the sun. How can this blackhole have formed so quickly after the big bang? Do theories predict supermassive black holes forming so quickly?</p>

CC BY-SA 4.0
2021-01-21T17:27:26.603Z
My guess is that a cluster of massive stars formed in a large (more than 100 million solar masses of material) nebula. One of them collapsed into a black hole, upwards of 1000-5000 solar masses. Then the other stars were sucked into the black hole or merged with the black hole. The black hole then drew in most of the remaining matter in the nebula. I don't know this for sure, just a wild guess.
WarpPrime
CC BY-SA 4.0
2021-01-21T21:25:38.053Z
If a body forms a black hole (by implosion via supernova or something), it's not more likely to "suck" distant objects in as the gravitational attraction at a given distance from the center of the black hole wouldn't change. I'd go for the likelihood that things were just more crowded at the start before accretion thinned out the neighborhood. The furthest galaxies are also seen in the more distant past so they're accumulating stuff in the black hole fast enough to be quasars, less distant are Seyfert galaxies, and nearby galaxies are relatively quiescent.
Arthur Kalliokoski
<supermassive-black-hole>
How can a supermassive black hole be 13 billion years old?
Natsfan
# How can a supermassive black hole be 13 billion years old?

(Asked by: username_0 on 2021-01-21)

A supermassive black hole was discovered [recently](https://phys.org/news/2021-01-earliest-supermassive-black-hole-quasar.html?utm_source=nwletter&utm_medium=email&utm_campaign=daily-nwletter) that is 13 billion years old. This blackhole is 1.6 billion times the mass of the sun. How can this blackhole have formed so quickly after the big bang? Do theories predict supermassive black holes forming so quickly?

**Tags:** supermassive-black-hole

> **Comments:**
> **username_1**: My guess is that a cluster of massive stars formed in a large (more than 100 million solar masses of material) nebula. One of them collapsed into a black hole, upwards of 1000-5000 solar masses. Then the other stars were sucked into the black hole or merged with the black hole. The black hole then drew in most of the remaining matter in the nebula. I don't know this for sure, just a wild guess.  
> **username_2**: If a body forms a black hole (by implosion via supernova or something), it's not more likely to "suck" distant objects in as the gravitational attraction at a given distance from the center of the black hole wouldn't change. I'd go for the likelihood that things were just more crowded at the start before accretion thinned out the neighborhood. The furthest galaxies are also seen in the more distant past so they're accumulating stuff in the black hole fast enough to be quasars, less distant are Seyfert galaxies, and nearby galaxies are relatively quiescent.  

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## 1 answers

### Answer by username_3 on 2021-01-21. Score: 25 | Accepted answer

The answer to this is unknown at the present time.

The issue is that an accreting "seed black hole" can only accrete at a limited rate. The limitation is provided by radiation pressure from the material it is accreting. This provides negative feedback and defines a maximum accretion rate for spherical accretion known as the [Eddington limit](https://en.wikipedia.org/wiki/Eddington_luminosity), which defines a maximum luminosity and hence a maximum accretion rate (since accretion provides the luminosity).

The net result is that the black hole can grow exponentially, with a growth timescale of about 30-40 million years. That is, it can roughly double in mass in that timescale.

Now the first, primordial stars may have been much more massive than big stars in the universe today, as a result of their pure hydrogen/helium composition. Even if they were able to form up to a few hundred solar mass black holes, it would still take almost a billion years to build a $10^9 M\_\odot$ black hole, even if it accreted at the maximum Eddington rate for all of that time.

This is a bit of a stretch so alternative solutions are being sought. These include

1. Maybe you can form even bigger black holes from early collapsing gas clouds. There are some ideas that if the primordial gas gets ionised by the very first massive stars then it doesn;t fragment into "stellar" objects. This can enable you to form very, very massive "stars" (sometimes called ["quasi-stars"](https://en.wikipedia.org/wiki/Quasi-star)), which have black holes at their centres rather than nuclear-fusing cores. These might grow rapidly to be of order $10^5 M\_{\odot}$ This can shave of many exponential growth timescales by starting off with a more massive seed.
2. Maybe you can merge black holes. We now know from gravitational wave detections that mergers can proceed between black holes with tens of solar masses to form $\sim 100M\_\odot$ black holes. Perhaps in the early universe there may have been clusters of high-mass black holes that managed to merge with each other on short timescales. These would then form a massive seed black hole that could grow relatively quickly.
3. There are some ideas about how the Eddington limit can be circumvented and mass accretion can proceed at higher rates, perhaps by suppressing the radiative efficiency of the accreting black hole (e.g. [Li et al. 2012](https://academic.oup.com/mnras/article/424/2/1461/1001493)).

> **Comments:**
> **username_4**: Aren't black holes not subject to the Eddington limit, since an unlimited amount of energy can be lost down the hole without contributing to overall luminosity?  
> **username_3**: @Sean cramming matter into the event horizon inevitably leads to it heating up and emitting radiation. Most of this radiation comes from well outside the event horizon. What you are suggesting is that the matter could be "advected" into the black hole without heating up. That isn't really possible.  
> **username_5**: Why would the growth of the hypothetical black holes in the midst of gas clouds not be restricted by the same radiation pressure as that of "standard" black holes? Or do you mean that the black hole *starts* at 10^5 solar masses?  
> **username_3**: @username_5-ReinstateMonica The Eddington limit assumes that the accreting gas is not being "forced in" (other than by gravity). In a quasi-star the black hole sits in the middle of a massive "star", so my understanding is that the Eddington rate in this case is that for the TOTAL mass of the object, not just the black hole, so it can grow to $10^5M\odot$ quickly.  
> **username_5**: Ah, I missed that the BH "replaces" the core of a star, thanks. But then: What other forces than gravity "force in" the matter of that star?  
> **username_3**: @username_5-ReinstateMonica I'll come back with an edit later. I need to read a paper. I probably badly expressed it. The fact you have the weight of the envelope pressing the stuff inwards. I believe that term is neglected in the standard Eddington treatment.  
> **username_5**: This layman here appreciates your time and effort. No worries. All misunderstandings are mine! :-)  
> **username_6**: Let's not make too much of the Eddington limit. It's not a fundamental property of accretion flow. We have strong evidence of hyper-Eddington accretion in the engines driving gamma-ray bursts.  

---

