<p>First off, let us try to clarify a few terms:</p>
<ol>
<li>As usual in astrophysics, <strong>metal-free star</strong> means atomic number <span class="math-container">$Z \leq 3$</span>, i.e. it only consists of the primordial elements hydrogen, helium, and lithium.</li>
<li><strong>Primordial star</strong> literally means <em>original</em> star and refers to the first star(s) (generation) formed after the big bang. It is IMHO equivalent to metal-free, and a <em>primordial metal-free star</em> would be a <a href="https://en.wikipedia.org/wiki/Pleonasm" rel="nofollow noreferrer">pleonasm</a>.</li>
<li><strong>Star</strong> can be most generally be defined as <em>massive, self-luminious gas sphere</em> (see <em>Lexikon der Astronomie</em>, p. 412), which leads to the question what each of these four terms mean exactly. Massive would probably mean at least about  <span class="math-container">$0.09 M_\odot$</span> as 0.09 solar masses is the weight of the smallest star observed, <a href="https://en.m.wikipedia.org/wiki/AB_Doradus" rel="nofollow noreferrer">AB Doradus</a>, which is undergoing nuclear fusion.</li>
<li>A <strong><a href="https://en.wikipedia.org/wiki/Quasi-star" rel="nofollow noreferrer">quasi-star</a></strong> is also worth a definition for the current question. The first paragraph of that Wiki-page summarizes it pretty neatly:</li>
</ol>
<blockquote>
<p>A quasi-star (also called black hole star) is a hypothetical type of extremely massive and luminous star that may have existed early in the history of the Universe. Unlike modern stars, which are powered by nuclear fusion in their cores, a quasi-star's energy would come from material falling into a black hole at its core.</p>
</blockquote>
<p><a href="https://astronomy.stackexchange.com/users/2531/profrob">ProfRob</a> already pointed out that a key issue is the definition of <strong>star</strong>.</p>
<blockquote>
<p>Or is something that starts nuclear fusion, but is always collapsing, a star?</p>
</blockquote>
<p>Related is the question about the <em>stability of a star</em>, which is studied by Isabelle Baraffe <em>et al.</em> in <a href="https://arxiv.org/abs/astro-ph/0009410" rel="nofollow noreferrer">arXiv:astro-ph/0009410 </a>:</p>
<blockquote>
<p>The stability of metal-free very massive stars (<span class="math-container">$ Z= 0; M = 120 \ldots 500 M_\odot$</span>) is analyzed and compared with metal-enriched stars. Such zero-metal stars are unstable to nuclear-powered radial pulsations on the main sequence, but the growth time scale for these instabilities is much longer than for their metal-rich counterparts.</p>
</blockquote>
<p>The metal-free stars analyzed in that manuscript would still be smaller than the quasi-stars, which require at least <span class="math-container">$1000 M_\odot$</span>. Again a <a href="https://en.wikipedia.org/wiki/Quasi-star" rel="nofollow noreferrer">Wikipedia-quote</a>:</p>
<blockquote>
<p>Quasi stars would have had a short maximum lifespan, approximately 7 million years, during which the core black hole would have grown to about <span class="math-container">$10^3 \ldots 10^5 M_\odot$</span> for modern stars.</p>
</blockquote>
<p>To summarize: The maximal size limit varies, depending on what we exactly regard as <strong>primordial metal-free star</strong>, and also how long such an object has to exist/ be stable. I would assume that the upper limit of primordial metal-free stars is probably larger than the upper limit of stability of <span class="math-container">$80 \ldots 100 M_\odot$</span> which holds for modern stars (see p. 458 in <em>Lexikon der Astronomie</em>).</p>
<h3>References</h3>
<ul>
<li>Helmut Zimmermann, Alfred Weigert: <em>Lexikon der Astronomie</em>. Edition 8. Heidelberg/ Berlin 1999. ISBN 3-8274-0575-0. (in German)</li>
</ul>

CC BY-SA 4.0
2021-01-02T00:00:48.107Z
Thanks! I've just asked [Why could Quasi-stars (“black hole stars”) have only existed when everything was hydrogen and helium? (no metal “contamination”)](https://astronomy.stackexchange.com/q/40684/7982)
uhoh
CC BY-SA 4.0
2021-01-01T01:46:22.860Z
2021-01-01T17:08:25.853Z
2021-01-01T17:08:25.853Z
B--rian
<p>This <a href="https://iopscience.iop.org/article/10.1088/0004-637X/706/2/1184" rel="nofollow noreferrer">Okhubo 2009 paper</a> presents two fiducial models: (a) stars between Pop III-1 stars of 40 to 300 M☉ stars not affected by stellar feedback which end in core-instability SN and BHs [they speculate that some became seeds of SMBHs]; and (b) Pop III-2 stars of 40 to 60 M☉ which do include radiative feedback and explode as Type II SNs, seeding the universe with its first metals. There are other papers in this genre but this is a good introduction.</p>
<p>We are missing a point in this preoccupation with mass: how much ionising luminosity did these stars impart to a universe perhaps &gt;10 times denser than today whose gas was neutral hydrogen? IOW were these classes of Pop III stars the sole contributor to reionization? Or did partial reionisation occur until Pop II stars were able to form and undergo the SN cycle and complete ionisation? The literature is not especially abundant on the subject, but it does seem that preoccupation with mass size misses the more important matter of long-term effect galactic assembly.</p>

CC BY-SA 4.0
2021-01-02T00:01:00.820Z
Thanks! just fyi I've just asked [Why could Quasi-stars (“black hole stars”) have only existed when everything was hydrogen and helium? (no metal “contamination”)](https://astronomy.stackexchange.com/q/40684/7982)
uhoh
CC BY-SA 4.0
2021-01-01T09:18:10.563Z
2021-01-01T09:18:10.563Z
Douglas Bullis
<p><a href="https://astronomy.stackexchange.com/a/37127/7982">This answer</a> to <em>Why don't or (can't) stars be more than 325 or so times the mass of the sun? What limits their size?</em> includes the following:</p>
<blockquote>
<p>...The upper limit you refer to is for compositions similar to the Sun. For stars born in the distant past that were metal-poor, or even born from primordial material with no metals, the upper limit could be much higher.</p>
</blockquote>
<p><strong>Question:</strong> What was the absolute limit to the possible sizes of the first stars formed from &quot;primordial material with no metals&quot;? I'm primarily asking about the size that was possible to <em>exist</em> as a star. There may be other limits associated with the possibility of formation in the first place due to matter distribution and that would be interesting to know as well.</p>
<p><strong>NOTE:</strong> There is also the well-received and as yet unanswered question <a href="https://astronomy.stackexchange.com/q/33397/7982">Formation of the First Stars</a> If this topic is better addressed as an answer there instead, then please do so and we can close this as a duplicate.</p>

CC BY-SA 4.0
2020-08-26T05:03:32.183Z
start of answer: radiation pressure imposes the limit to the mass of stars. Too much energy/radiation will push the star apart. The radiation pressure depends upon the composition. Different elements absorb different amounts of radiation at different wavelengths. How much of the gas is ionized depends upon its composition. The fraction of free electrons will change the radiation absorption and hence radiation pressure.
TazAstroSpacial
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2020-08-26T06:01:03.713Z
@TazAstroSpacial Thanks! Hopefully "first stars" and "primordial material with no metals" narrows down questions of composition; based on early comments it looks like the hard part of the problem lies elsewhere.
uhoh
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2020-07-25T07:16:02.253Z
Define "star" ?
ProfRob
CC BY-SA 4.0
2020-07-25T07:28:49.957Z
@RobJeffries wait, hmm.. let me think about this a bit...your questions are usually quite instructive.
uhoh
CC BY-SA 4.0
2020-07-25T07:32:53.877Z
[On the Detection of Supermassive Primordial Stars](https://arxiv.org/abs/1811.08911) and [The Hunt for Enormous Early Stars](https://aasnova.org/2019/01/30/the-hunt-for-enormous-early-stars/) Yikes!
uhoh
CC BY-SA 4.0
2020-07-25T07:33:09.377Z
I mean, is a "quasi-star" a star? Or is something that starts nuclear fusion, but is always collapsing, a star? I guess an answer would need to address this.
ProfRob
CC BY-SA 4.0
2020-07-25T16:56:32.190Z
@RobJeffries Maybe something like a simply connected compact region of space(time) in which (p-p chain?) fusion occurs which either has non-trivial outflux of new fusion products (including those of other fusion chains, s-process, r-process, etc.) or (failing that) does not collapse to a black hole?  Probably needs some sort of bounds on minimum and maximum timescales for the collapse bit that could confound the whole idea, though; and I think it'd technically include brown dwarfs, which might be silly...and possibly the Earth because of all these scientists and bombs...
zibadawa timmy
CC BY-SA 4.0
2020-07-30T12:59:29.183Z
@RobJeffries is it reasonable to define (for this purpose) a "star" as self-supporting against gravity by fusion so that its radius (say the radius containing 90% of its mass) is changing much more slowly than the speed of pressure waves in its interior. I'm looking for a way to allow variable stars and exclude momentary pauses in a continuous collapse, but this is hard.
Steve Linton
CC BY-SA 4.0
2020-07-30T13:10:16.443Z
@SteveLinton perhaps hard questions are better posted as new questions! That provides a lot more space in which to answer them and visibility for a lot more users.
uhoh
CC BY-SA 4.0
2020-12-26T06:25:41.593Z
This paper, MASSIVE STARS IN EXTREMELY METAL-POOR GALAXIES: A WINDOW INTO THE PAST suggests there may not be a good model for local upper mass bounds: https://arxiv.org/pdf/1908.04687.pdf.  See the last paragraph of page 5. This is a great question, but may require a true astrophysicist to answer. I won't be pursuing this bounty.
Connor Garcia
CC BY-SA 4.0
2020-12-26T06:28:33.590Z
@ConnorGarcia I'm pretty flexible, if an informative answer is posted that explains why the question doesn't have a simple answer based on current understanding, that can certainly receive a bounty award. I see that this is hard to answer *but I don't understand why nor might many other future readers* and so an explanation is certainly welcome!
uhoh
CC BY-SA 4.0
2020-12-30T22:28:20.477Z
My 50 cents: I also found https://arxiv.org/abs/astro-ph/0009410 *On the stability of very massive primordial stars* noteworthy.
B--rian
CC BY-SA 4.0
2020-12-31T23:12:26.683Z
@ConnorGarcia bounty expires in 24 hours, plus there is a 24 hour invisible "grace period" when it can still be awarded. Consider writing something at least explaining why the question may not be easily answerable?
uhoh
CC BY-SA 4.0
2020-12-31T23:12:36.747Z
@B--rian *ditto.*
uhoh
<star><stellar-evolution><stellar-astrophysics><early-universe>
What was the absolute limit to the possible sizes of the first stars formed from "primordial material with no metals"?
uhoh
# What was the absolute limit to the possible sizes of the first stars formed from "primordial material with no metals"?

(Asked by: username_0 on 2020-07-25)

[This answer](https://astronomy.stackexchange.com/a/37127/7982) to *Why don't or (can't) stars be more than 325 or so times the mass of the sun? What limits their size?* includes the following:

> ...The upper limit you refer to is for compositions similar to the Sun. For stars born in the distant past that were metal-poor, or even born from primordial material with no metals, the upper limit could be much higher.

**Question:** What was the absolute limit to the possible sizes of the first stars formed from "primordial material with no metals"? I'm primarily asking about the size that was possible to *exist* as a star. There may be other limits associated with the possibility of formation in the first place due to matter distribution and that would be interesting to know as well.

**NOTE:** There is also the well-received and as yet unanswered question [Formation of the First Stars](https://astronomy.stackexchange.com/q/33397/7982) If this topic is better addressed as an answer there instead, then please do so and we can close this as a duplicate.

**Tags:** star, stellar-evolution, stellar-astrophysics, early-universe
> **Comments:**
> **username_2**: Define "star" ?  
> **username_0**: @RobJeffries wait, hmm.. let me think about this a bit...your questions are usually quite instructive.  
> **username_0**: [On the Detection of Supermassive Primordial Stars](https://arxiv.org/abs/1811.08911) and [The Hunt for Enormous Early Stars](https://aasnova.org/2019/01/30/the-hunt-for-enormous-early-stars/) Yikes!  
> **username_2**: I mean, is a "quasi-star" a star? Or is something that starts nuclear fusion, but is always collapsing, a star? I guess an answer would need to address this.  
> **username_3**: @RobJeffries Maybe something like a simply connected compact region of space(time) in which (p-p chain?) fusion occurs which either has non-trivial outflux of new fusion products (including those of other fusion chains, s-process, r-process, etc.) or (failing that) does not collapse to a black hole?  Probably needs some sort of bounds on minimum and maximum timescales for the collapse bit that could confound the whole idea, though; and I think it'd technically include brown dwarfs, which might be silly...and possibly the Earth because of all these scientists and bombs...  
> **username_4**: @RobJeffries is it reasonable to define (for this purpose) a "star" as self-supporting against gravity by fusion so that its radius (say the radius containing 90% of its mass) is changing much more slowly than the speed of pressure waves in its interior. I'm looking for a way to allow variable stars and exclude momentary pauses in a continuous collapse, but this is hard.  
> **username_0**: @SteveLinton perhaps hard questions are better posted as new questions! That provides a lot more space in which to answer them and visibility for a lot more users.  
> **username_1**: start of answer: radiation pressure imposes the limit to the mass of stars. Too much energy/radiation will push the star apart. The radiation pressure depends upon the composition. Different elements absorb different amounts of radiation at different wavelengths. How much of the gas is ionized depends upon its composition. The fraction of free electrons will change the radiation absorption and hence radiation pressure.  
> **username_0**: @TazAstroSpacial Thanks! Hopefully "first stars" and "primordial material with no metals" narrows down questions of composition; based on early comments it looks like the hard part of the problem lies elsewhere.  
> **username_5**: This paper, MASSIVE STARS IN EXTREMELY METAL-POOR GALAXIES: A WINDOW INTO THE PAST suggests there may not be a good model for local upper mass bounds: https://arxiv.org/pdf/1908.04687.pdf.  See the last paragraph of page 5. This is a great question, but may require a true astrophysicist to answer. I won't be pursuing this bounty.  
> **username_0**: @ConnorGarcia I'm pretty flexible, if an informative answer is posted that explains why the question doesn't have a simple answer based on current understanding, that can certainly receive a bounty award. I see that this is hard to answer *but I don't understand why nor might many other future readers* and so an explanation is certainly welcome!  
> **username_6**: My 50 cents: I also found https://arxiv.org/abs/astro-ph/0009410 *On the stability of very massive primordial stars* noteworthy.  
> **username_0**: @ConnorGarcia bounty expires in 24 hours, plus there is a 24 hour invisible "grace period" when it can still be awarded. Consider writing something at least explaining why the question may not be easily answerable?  
> **username_0**: @B--rian *ditto.*  

---

## 2 answers

### Answer by username_6 on 2021-01-01. Score: 2

First off, let us try to clarify a few terms:

1. As usual in astrophysics, **metal-free star** means atomic number $Z \leq 3$, i.e. it only consists of the primordial elements hydrogen, helium, and lithium.
2. **Primordial star** literally means *original* star and refers to the first star(s) (generation) formed after the big bang. It is IMHO equivalent to metal-free, and a *primordial metal-free star* would be a [pleonasm](https://en.wikipedia.org/wiki/Pleonasm).
3. **Star** can be most generally be defined as *massive, self-luminious gas sphere* (see *Lexikon der Astronomie*, p. 412), which leads to the question what each of these four terms mean exactly. Massive would probably mean at least about $0.09 M\_\odot$ as 0.09 solar masses is the weight of the smallest star observed, [AB Doradus](https://en.m.wikipedia.org/wiki/AB_Doradus), which is undergoing nuclear fusion.
4. A **[quasi-star](https://en.wikipedia.org/wiki/Quasi-star)** is also worth a definition for the current question. The first paragraph of that Wiki-page summarizes it pretty neatly:

> A quasi-star (also called black hole star) is a hypothetical type of extremely massive and luminous star that may have existed early in the history of the Universe. Unlike modern stars, which are powered by nuclear fusion in their cores, a quasi-star's energy would come from material falling into a black hole at its core.

[ProfRob](https://astronomy.stackexchange.com/users/2531/profrob) already pointed out that a key issue is the definition of **star**.

> Or is something that starts nuclear fusion, but is always collapsing, a star?

Related is the question about the *stability of a star*, which is studied by Isabelle Baraffe *et al.* in [arXiv:astro-ph/0009410](https://arxiv.org/abs/astro-ph/0009410) :

> The stability of metal-free very massive stars ($ Z= 0; M = 120 \ldots 500 M\_\odot$) is analyzed and compared with metal-enriched stars. Such zero-metal stars are unstable to nuclear-powered radial pulsations on the main sequence, but the growth time scale for these instabilities is much longer than for their metal-rich counterparts.

The metal-free stars analyzed in that manuscript would still be smaller than the quasi-stars, which require at least $1000 M\_\odot$. Again a [Wikipedia-quote](https://en.wikipedia.org/wiki/Quasi-star):

> Quasi stars would have had a short maximum lifespan, approximately 7 million years, during which the core black hole would have grown to about $10^3 \ldots 10^5 M\_\odot$ for modern stars.

To summarize: The maximal size limit varies, depending on what we exactly regard as **primordial metal-free star**, and also how long such an object has to exist/ be stable. I would assume that the upper limit of primordial metal-free stars is probably larger than the upper limit of stability of $80 \ldots 100 M\_\odot$ which holds for modern stars (see p. 458 in *Lexikon der Astronomie*).

### References

* Helmut Zimmermann, Alfred Weigert: *Lexikon der Astronomie*. Edition 8. Heidelberg/ Berlin 1999. ISBN 3-8274-0575-0. (in German)

> **Comments:**
> **username_0**: Thanks! I've just asked [Why could Quasi-stars (“black hole stars”) have only existed when everything was hydrogen and helium? (no metal “contamination”)](https://astronomy.stackexchange.com/q/40684/7982)  

---

### Answer by username_7 on 2021-01-01. Score: 1

This [Okhubo 2009 paper](https://iopscience.iop.org/article/10.1088/0004-637X/706/2/1184) presents two fiducial models: (a) stars between Pop III-1 stars of 40 to 300 M☉ stars not affected by stellar feedback which end in core-instability SN and BHs [they speculate that some became seeds of SMBHs]; and (b) Pop III-2 stars of 40 to 60 M☉ which do include radiative feedback and explode as Type II SNs, seeding the universe with its first metals. There are other papers in this genre but this is a good introduction.

We are missing a point in this preoccupation with mass: how much ionising luminosity did these stars impart to a universe perhaps >10 times denser than today whose gas was neutral hydrogen? IOW were these classes of Pop III stars the sole contributor to reionization? Or did partial reionisation occur until Pop II stars were able to form and undergo the SN cycle and complete ionisation? The literature is not especially abundant on the subject, but it does seem that preoccupation with mass size misses the more important matter of long-term effect galactic assembly.

> **Comments:**
> **username_0**: Thanks! just fyi I've just asked [Why could Quasi-stars (“black hole stars”) have only existed when everything was hydrogen and helium? (no metal “contamination”)](https://astronomy.stackexchange.com/q/40684/7982)  

---

