<blockquote>
<p>Under what conditions may a pop III star undergo a supernova, i.e., only certain masses, composition, etc?</p>
</blockquote>
<p>The exact mass range, composition, rotation etc. necessary to for a star to go supernova or to undergo a direct collapse are still uncertain (see for example <a href="https://iopscience.iop.org/article/10.1088/0004-637X/730/2/70" rel="noreferrer">O'Connor &amp; Dott 2011</a>, <a href="https://iopscience.iop.org/article/10.1088/0004-637X/749/1/91" rel="noreferrer">Fryer et al. 2012</a>, <a href="https://iopscience.iop.org/article/10.3847/0004-637X/818/2/124" rel="noreferrer">Ertl et al 2016</a>). If this is uncertain for PopI and PopII stars, you can imagine that for PopIII, lacking any observational evidence, the problems are even worse.</p>
<p>But, even if the exact conditions are not known, the processes that may lead a PopIII star to explode are relatively well understood and were already described in <a href="https://iopscience.iop.org/article/10.1086/375341" rel="noreferrer">Heger et al 2003</a> that you quote.</p>
<p><strong>Why PopIII stars are different from solar metallicity stars</strong></p>
<p>Having a lower metallicity means less efficient stellar winds (<a href="http://www.aanda.org/10.1051/0004-6361:20066176" rel="noreferrer">Grafner &amp; Hamman 2008</a>, <a href="https://arxiv.org/abs/2207.09333" rel="noreferrer">Rickard et al. 2022</a>), so a less pronounced mass loss. This means that the helium core of PopIII stars might not be eroded by winds, even for very massive stars (<span class="math-container">$&gt;100 M_\odot$</span>). Thus, PopIII stars might build massive helium cores, which is not possible for their high metallicity counterparts. And the mass of the helium core is a key factor in determining the final fate of the star.</p>
<p><strong>Core collapse supernovae, direct black hole formation of pair instability</strong></p>
<p>Quoting the numbers from Table 2 of <a href="https://iopscience.iop.org/article/10.1086/375341" rel="noreferrer">Heger et al 2003</a>, a star that at the onset of collapse has an helium core of at most <span class="math-container">$8 M_\odot$</span> will explode as a core collapse supernova. If <span class="math-container">$8 M_\odot &lt; m_{He} &lt; 15 M_\odot$</span> the supernova still occurs, but only little is ejected and most of the material falls back into the black hole. Helium cores in the range <span class="math-container">$15 M_\odot &lt; m_{He} &lt; 42 M_\odot$</span> lead to a direct collapse into a black hole, with no supernova explosion.</p>
<p>Quoting the mass ranges from Section 4.4, above <span class="math-container">$42 M_\odot$</span> things start to change. The helium core is now massive enough that it can reach a temperature of about <span class="math-container">$10^9 K$</span>, at which the production of electron-positron pairs becomes efficient. This soften the equation of state to an adiabatic index below <span class="math-container">$4/3$</span>, reducing the pressure support and inducing the contraction of the core. This process is called pair instability and is thought to occur only for very low metallicity stars that are able to form such massive helium cores. If the helium core has a mass <span class="math-container">$42 M_\odot &lt; m_{He} &lt; 65 M_\odot$</span>, the energy produced during the contraction is able to reverse the collapse. The star will then undergo a series of violent pulsations (<a href="https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stv3002" rel="noreferrer">Yoshida et al. 2016</a>, <a href="https://iopscience.iop.org/article/10.3847/1538-4357/836/2/244" rel="noreferrer">Woosley 2017</a>) until it has lost enough mass to stabilize the pair production, and will (likely?) eventually collapse into a black hole without further explosions.</p>
<p>If instead <span class="math-container">$65 M_\odot &lt; m_{He} &lt; 133 M_\odot$</span>, the first pulsation is strong enough to completely unbind the star, that explodes in a Pair Instability SuperNova (PISN), leaving <em>no remnant</em> behind. These highly energetic events are thought to be important to the early chemical evolution of the universe (due to the large amount of metals expelled) (<a href="https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stw2687" rel="noreferrer">de Bennassuti et al. 2017</a>), but have not been conclusively observed yet, although there is some hope in the next generation of telescopes (see for ex. <a href="https://ui.adsabs.harvard.edu/abs/2022arXiv220408727M" rel="noreferrer">Moriya et al. 2022</a>, <a href="http://arxiv.org/abs/2204.09402" rel="noreferrer">Tanikawa et al. 2022</a>). Since stars in this mass range do not produce a black hole, it is expected that we should observe a gap in the black hole mass distribution, called pair-instability gap, but there is currently no evidence for this (<a href="http://arxiv.org/abs/2111.03634" rel="noreferrer">The LVK collaboration, 2021</a>).</p>
<p>Above an helium core mass of <span class="math-container">$133 M_\odot$</span>, the star is expected to collapse again into a black hole, without any explosion.</p>
<p><a href="https://i.sstatic.net/oHnZl.png" rel="noreferrer"><img src="https://i.sstatic.net/oHnZl.png" alt="initial mass vs black hole mass relation for different metallicities" /></a></p>
<p>A nice way to visualize all these mass ranges is this figure from <a href="https://academic.oup.com/mnras/article/470/4/4739/3883764" rel="noreferrer">Spera &amp; Mapelli (2017)</a> that shows the relation between the initial mass of a star (ZAMS stands for zero-age main sequence) and the mass of the black hole remnant produced. Each curve corresponds to a different metallicity, from <span class="math-container">$Z = 2 \times 10^{-4}$</span> to <span class="math-container">$Z = 2 \times 10^{-2}$</span>. Note that the x axis is the initial mass of the star, not the final mass of the helium core. This means that this figure is assuming a relation between initial mass and final mass of the helium core, which is affected by additional (large) uncertainties.</p>
<p>Look, for reference, at the purple dashed line (<span class="math-container">$Z=2 \times 10^{-4}$</span>) which is the closest to PopIII metallicity. For <span class="math-container">$m_{ZAMS} &lt; 35 M_\odot$</span>,  the core collapse supernova occurs, most of the material is ejected, and a relatively low mass black hole is formed. In the range <span class="math-container">$35 M_\odot &lt; m_{ZAMS} &lt; 60 M_\odot$</span>, there is a direct collapse into a black hole, in fact <span class="math-container">$m_{ZAMS} \approx m_{rem}$</span>. For <span class="math-container">$60 M_\odot &lt; m_{ZAMS} &lt; 110 M_\odot$</span>, pulsational pair instability considerably reduces the final black hole mass, until, for stars with <span class="math-container">$110 M_\odot &lt; m_{ZAMS} &lt; 230 M_\odot$</span>, a PISN occurs and the mass of the remnant is zero. For initial mass greater than <span class="math-container">$230 M_\odot$</span>, the direct collapse resumes.</p>
<p>Keep in mind that these numbers are model dependent and considerably more uncertain than the figures for the helium core mass. Also, all the above is not taking into account rotation, which may be of great importance (<a href="https://arxiv.org/abs/0901.4489" rel="noreferrer">Meynet et al. 2009</a>, <a href="https://arxiv.org/abs/2104.10046" rel="noreferrer">Boyouan et al. 2020</a>)</p>
<p><strong>Second questions</strong></p>
<blockquote>
<p>Does (the core of) a pop III star that undergoes a supernova form a proto-neutron star before forming a black hole?</p>
</blockquote>
<p>Given the above, I would say no, the mechanisms for explosion is not electron-capture, but pair production.</p>
<p><strong>Third question</strong></p>
<p>The <a href="https://iopscience.iop.org/article/10.1088/0004-637X/778/1/17" rel="noreferrer">paper</a> you quote is talking about supermassive Pop III stars, an hypothetical kind of star with thousands of solar masses that could be formed as the result of gravitational instabilities in primordial clouds that are not able to fragment through <span class="math-container">$H_2$</span> cooling, because a near source of Lyman-Werner radiation is dissociating all the molecular hydrogen. The result is thought to be a monolithic collapse of the cloud that leads to the direct formation of a supermassive black hole in the range <span class="math-container">$m \approx 10^{4-5} M_\odot$</span>. The authors of the paper argue that for a narrow mass range, instead of forming a black hole, the cloud could form a supermassive star, and that such star would explode in an extremely energetic event. The reasoning behind the apparent self-contradiction in the statement you quote is, in my opinion, the following:</p>
<blockquote>
<p>if we detected an energetic event such as the one we are predicting, this would be a confirmation that supermassive stars can form from a direct collapse of a primordial cloud. According to the same mechanisms, similar clouds with a little more or little less mass would instead directly form a supermassive black hole. Thus, the observation of such a supernova would be an indirect confirmation that supermassive black hole heavy seeds can indeed form through direct collapse of the primordial cloud. This would help in addressing the open problem of how the observed supermassive black holes at high redshift could form in such a short time.</p>
</blockquote>

CC BY-SA 4.0
2022-08-16T19:43:26.207Z
2022-08-16T19:53:37.010Z
2022-08-16T19:53:37.010Z
Prallax
<p>Population III stars were the first stars to form. They are hypothesised as being very massive, i.e., &gt; 100 M<span class="math-container">$_{\odot}$</span>. My question regards how do these stars end their lives?</p>
<p><a href="https://ui.adsabs.harvard.edu/abs/2003ApJ...591..288H/abstract" rel="noreferrer">An old orthodoxy</a> for high mass stars, i.e. those with mass between ~40 and 100 M<span class="math-container">$_{\odot}$</span>, is that they will form into black holes via direct collapse without producing supernovae (and possibly without receiving natal kicks). This is, however, uncertain and there are papers that explore the possibility of these high mass stars undergoing supernovae (and receiving natal kicks in formation... there are many types of natal kicks possible, and they may be neutrino driven or hydrodynamical driven, its complicated).</p>
<p>On the other hand, I've seen many papers about the (possible) supernovae of pop III stars, e.g.'s, <a href="https://arxiv.org/abs/2103.01643" rel="noreferrer">this</a>, <a href="https://link.springer.com/article/10.1007/s10714-022-02909-4" rel="noreferrer">this</a> and <a href="https://iopscience.iop.org/article/10.1088/0004-637X/778/1/17" rel="noreferrer">this</a>. Naively, I would have suspected that the very massive pop III stars would undergo direct collapse to form black holes.</p>
<p>Questions: <strong>Under what conditions may a pop III star undergo a supernova, i.e., only certain masses, composition, etc? Does (the core of) a pop III star that undergoes a supernova form a proto-neutron star before forming a black hole?</strong> For the second question, I would suspect not, since there would be so much mass around, but maybe this depends on the metallicity?</p>
<p>EDIT:
A related question: maybe I'm just really confused, but how can there be a supernova if the star undergoes direct formation of a black hole? Naively, I'd expect there to be no supernova in a direct collapse process, since there would be no ejected material? Maybe I'm missing something here? For example, on the second page of <a href="https://iopscience.iop.org/article/10.1088/0004-637X/778/1/17" rel="noreferrer">this</a> paper, they state &quot;These stars die as extremely energetic thermonuclear supernovae..... Such events would be the most energetic explosions in the cosmos, and their detection could reveal the birthplaces of SMBHs created by direct collapse...&quot;</p>

CC BY-SA 4.0
2022-08-16T09:34:17.370Z
This is the map of supernova types on Wikipedia, but I'm not sure how up to date it is.  It's based on research from 2003 https://commons.wikimedia.org/wiki/File:Supernovae_as_initial_mass-metallicity.svg
James K
<star><black-hole><supernova>
Do pop III stars undergo supernova or direct collapse?
Daddy Kropotkin
# Do pop III stars undergo supernova or direct collapse?

(Asked by: username_0 on 2022-08-16)

Population III stars were the first stars to form. They are hypothesised as being very massive, i.e., > 100 M$\_{\odot}$. My question regards how do these stars end their lives?

[An old orthodoxy](https://ui.adsabs.harvard.edu/abs/2003ApJ...591..288H/abstract) for high mass stars, i.e. those with mass between ~40 and 100 M$\_{\odot}$, is that they will form into black holes via direct collapse without producing supernovae (and possibly without receiving natal kicks). This is, however, uncertain and there are papers that explore the possibility of these high mass stars undergoing supernovae (and receiving natal kicks in formation... there are many types of natal kicks possible, and they may be neutrino driven or hydrodynamical driven, its complicated).

On the other hand, I've seen many papers about the (possible) supernovae of pop III stars, e.g.'s, [this](https://arxiv.org/abs/2103.01643), [this](https://link.springer.com/article/10.1007/s10714-022-02909-4) and [this](https://iopscience.iop.org/article/10.1088/0004-637X/778/1/17). Naively, I would have suspected that the very massive pop III stars would undergo direct collapse to form black holes.

Questions: **Under what conditions may a pop III star undergo a supernova, i.e., only certain masses, composition, etc? Does (the core of) a pop III star that undergoes a supernova form a proto-neutron star before forming a black hole?** For the second question, I would suspect not, since there would be so much mass around, but maybe this depends on the metallicity?

EDIT:
A related question: maybe I'm just really confused, but how can there be a supernova if the star undergoes direct formation of a black hole? Naively, I'd expect there to be no supernova in a direct collapse process, since there would be no ejected material? Maybe I'm missing something here? For example, on the second page of [this](https://iopscience.iop.org/article/10.1088/0004-637X/778/1/17) paper, they state "These stars die as extremely energetic thermonuclear supernovae..... Such events would be the most energetic explosions in the cosmos, and their detection could reveal the birthplaces of SMBHs created by direct collapse..."

**Tags:** star, black-hole, supernova
> **Comments:**
> **username_1**: This is the map of supernova types on Wikipedia, but I'm not sure how up to date it is.  It's based on research from 2003 https://commons.wikimedia.org/wiki/File:Supernovae_as_initial_mass-metallicity.svg  

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## 1 answers

### Answer by username_2 on 2022-08-16. Score: 6

> Under what conditions may a pop III star undergo a supernova, i.e., only certain masses, composition, etc?

The exact mass range, composition, rotation etc. necessary to for a star to go supernova or to undergo a direct collapse are still uncertain (see for example [O'Connor & Dott 2011](https://iopscience.iop.org/article/10.1088/0004-637X/730/2/70), [Fryer et al. 2012](https://iopscience.iop.org/article/10.1088/0004-637X/749/1/91), [Ertl et al 2016](https://iopscience.iop.org/article/10.3847/0004-637X/818/2/124)). If this is uncertain for PopI and PopII stars, you can imagine that for PopIII, lacking any observational evidence, the problems are even worse.

But, even if the exact conditions are not known, the processes that may lead a PopIII star to explode are relatively well understood and were already described in [Heger et al 2003](https://iopscience.iop.org/article/10.1086/375341) that you quote.

**Why PopIII stars are different from solar metallicity stars**

Having a lower metallicity means less efficient stellar winds ([Grafner & Hamman 2008](http://www.aanda.org/10.1051/0004-6361:20066176), [Rickard et al. 2022](https://arxiv.org/abs/2207.09333)), so a less pronounced mass loss. This means that the helium core of PopIII stars might not be eroded by winds, even for very massive stars ($>100 M\_\odot$). Thus, PopIII stars might build massive helium cores, which is not possible for their high metallicity counterparts. And the mass of the helium core is a key factor in determining the final fate of the star.

**Core collapse supernovae, direct black hole formation of pair instability**

Quoting the numbers from Table 2 of [Heger et al 2003](https://iopscience.iop.org/article/10.1086/375341), a star that at the onset of collapse has an helium core of at most $8 M\_\odot$ will explode as a core collapse supernova. If $8 M\_\odot < m\_{He} < 15 M\_\odot$ the supernova still occurs, but only little is ejected and most of the material falls back into the black hole. Helium cores in the range $15 M\_\odot < m\_{He} < 42 M\_\odot$ lead to a direct collapse into a black hole, with no supernova explosion.

Quoting the mass ranges from Section 4.4, above $42 M\_\odot$ things start to change. The helium core is now massive enough that it can reach a temperature of about $10^9 K$, at which the production of electron-positron pairs becomes efficient. This soften the equation of state to an adiabatic index below $4/3$, reducing the pressure support and inducing the contraction of the core. This process is called pair instability and is thought to occur only for very low metallicity stars that are able to form such massive helium cores. If the helium core has a mass $42 M\_\odot < m\_{He} < 65 M\_\odot$, the energy produced during the contraction is able to reverse the collapse. The star will then undergo a series of violent pulsations ([Yoshida et al. 2016](https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stv3002), [Woosley 2017](https://iopscience.iop.org/article/10.3847/1538-4357/836/2/244)) until it has lost enough mass to stabilize the pair production, and will (likely?) eventually collapse into a black hole without further explosions.

If instead $65 M\_\odot < m\_{He} < 133 M\_\odot$, the first pulsation is strong enough to completely unbind the star, that explodes in a Pair Instability SuperNova (PISN), leaving *no remnant* behind. These highly energetic events are thought to be important to the early chemical evolution of the universe (due to the large amount of metals expelled) ([de Bennassuti et al. 2017](https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/stw2687)), but have not been conclusively observed yet, although there is some hope in the next generation of telescopes (see for ex. [Moriya et al. 2022](https://ui.adsabs.harvard.edu/abs/2022arXiv220408727M), [Tanikawa et al. 2022](http://arxiv.org/abs/2204.09402)). Since stars in this mass range do not produce a black hole, it is expected that we should observe a gap in the black hole mass distribution, called pair-instability gap, but there is currently no evidence for this ([The LVK collaboration, 2021](http://arxiv.org/abs/2111.03634)).

Above an helium core mass of $133 M\_\odot$, the star is expected to collapse again into a black hole, without any explosion.

[![initial mass vs black hole mass relation for different metallicities](https://i.sstatic.net/oHnZl.png)](https://i.sstatic.net/oHnZl.png)

A nice way to visualize all these mass ranges is this figure from [Spera & Mapelli (2017)](https://academic.oup.com/mnras/article/470/4/4739/3883764) that shows the relation between the initial mass of a star (ZAMS stands for zero-age main sequence) and the mass of the black hole remnant produced. Each curve corresponds to a different metallicity, from $Z = 2 \times 10^{-4}$ to $Z = 2 \times 10^{-2}$. Note that the x axis is the initial mass of the star, not the final mass of the helium core. This means that this figure is assuming a relation between initial mass and final mass of the helium core, which is affected by additional (large) uncertainties.

Look, for reference, at the purple dashed line ($Z=2 \times 10^{-4}$) which is the closest to PopIII metallicity. For $m\_{ZAMS} < 35 M\_\odot$, the core collapse supernova occurs, most of the material is ejected, and a relatively low mass black hole is formed. In the range $35 M\_\odot < m\_{ZAMS} < 60 M\_\odot$, there is a direct collapse into a black hole, in fact $m\_{ZAMS} \approx m\_{rem}$. For $60 M\_\odot < m\_{ZAMS} < 110 M\_\odot$, pulsational pair instability considerably reduces the final black hole mass, until, for stars with $110 M\_\odot < m\_{ZAMS} < 230 M\_\odot$, a PISN occurs and the mass of the remnant is zero. For initial mass greater than $230 M\_\odot$, the direct collapse resumes.

Keep in mind that these numbers are model dependent and considerably more uncertain than the figures for the helium core mass. Also, all the above is not taking into account rotation, which may be of great importance ([Meynet et al. 2009](https://arxiv.org/abs/0901.4489), [Boyouan et al. 2020](https://arxiv.org/abs/2104.10046))

**Second questions**

> Does (the core of) a pop III star that undergoes a supernova form a proto-neutron star before forming a black hole?

Given the above, I would say no, the mechanisms for explosion is not electron-capture, but pair production.

**Third question**

The [paper](https://iopscience.iop.org/article/10.1088/0004-637X/778/1/17) you quote is talking about supermassive Pop III stars, an hypothetical kind of star with thousands of solar masses that could be formed as the result of gravitational instabilities in primordial clouds that are not able to fragment through $H\_2$ cooling, because a near source of Lyman-Werner radiation is dissociating all the molecular hydrogen. The result is thought to be a monolithic collapse of the cloud that leads to the direct formation of a supermassive black hole in the range $m \approx 10^{4-5} M\_\odot$. The authors of the paper argue that for a narrow mass range, instead of forming a black hole, the cloud could form a supermassive star, and that such star would explode in an extremely energetic event. The reasoning behind the apparent self-contradiction in the statement you quote is, in my opinion, the following:

> if we detected an energetic event such as the one we are predicting, this would be a confirmation that supermassive stars can form from a direct collapse of a primordial cloud. According to the same mechanisms, similar clouds with a little more or little less mass would instead directly form a supermassive black hole. Thus, the observation of such a supernova would be an indirect confirmation that supermassive black hole heavy seeds can indeed form through direct collapse of the primordial cloud. This would help in addressing the open problem of how the observed supermassive black holes at high redshift could form in such a short time.


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