<p>The problem with your argument is that you incorrectly assume that increasing nuclear fusion increases the pairs/photons ratio.</p>
<p>It is certainly true that increase in temperature increases the nuclear fusion rates and therefore the production of photons. More photons means greater possibility to produce electron-positron pairs, but why do you think that the <em>ratio</em> pairs/photons should increase as well?</p>
<p>Since pulsational pair instability doesn't always lead to a runaway fusion reaction, this means that injecting more photons into the system actually <em>decreases</em> the pairs/photons ratio, halting the collapse and triggering the pulsation mechanism.</p>
<p>The only way to find out that this is indeed the case, is to solve the complete system of equations for the rates of the processes involved.</p>
<p>I think that the first to have brought up the possibility of pair production supernovae were Fowler &amp; Hoyle (1964) in <a href="http://articles.adsabs.harvard.edu/pdf/1964ApJS....9..201F" rel="nofollow noreferrer">Neutrino Processes and Pair Formation in Massive Stars and Supernovae</a></p>

CC BY-SA 4.0
2021-08-30T14:27:11.260Z
Does PPI mean pulsational pair instability?
zucculent
CC BY-SA 4.0
2021-08-30T14:50:53.617Z
@zucculent Yes, sorry for not specifying it
Prallax
CC BY-SA 4.0
2021-08-30T15:03:49.040Z
Does this mean that the cores of stars susceptible to PISNs will have brief periods of more intense pair production, and sooner or later one of these "pulses" will trigger a runaway feedback loop and cause a PISN?
zucculent
CC BY-SA 4.0
2021-08-30T15:13:01.847Z
@zucculent It depends on the mass of the core. In some cases the star would undergo some pulsations, loose a lot of mass and then stabilize itself. In some other cases one pulsation is sufficient to trigger the supernova. Otherwise, the star may start with small pulsations that slowly grow in amplitude until the last pulse makes the star explode. Have a look at [Pulsational Pair-Instability Supernovae](https://arxiv.org/abs/1608.08939) by Woosley, that explores all these scenarios with hydrodynamical simulations
Prallax
CC BY-SA 4.0
2021-08-30T15:16:40.313Z
Do you have any thoughts on the role of metallicity? The Wikipedia article is pretty vague on that score. It just states that these supernovae occur in low-metallicity stars, eg formed by merged pop III stars.
PM 2Ring
CC BY-SA 4.0
2021-08-30T15:42:40.290Z
@PM2Ring dunno, probably the reason is that in order to reach such high temperatures, you need a very massive core. And only low metallicity stars are able to achieve it, due to being more massive from the start (at zero age main sequence) and to being able to retain that mass through their life, because they don't loose much mass in stellar winds
Prallax
CC BY-SA 4.0
2021-08-30T12:54:16.657Z
2021-08-30T14:53:21.860Z
2021-08-30T14:53:21.860Z
Prallax
<p><a href="https://en.wikipedia.org/wiki/Pair-instability_supernova" rel="nofollow noreferrer">The Wikipedia article</a> on pair-instability supernovas (PISNs) doesn't seem to give a very good explanation of what causes a PISN. My understanding of the process it describes is this: Once the core gets hot enough, it starts producing gamma rays with enough energy to produce electron-positron pairs when they interact with atomic nuclei, although these pairs will annihilate eventually, forming a sort of equilibrium between gamma rays and E/P pairs. Since radiation pressure is what keeps the core from collapsing, the fact that a portion of the radiation energy is now in the form of E/P pairs means the radiation pressure decreases, causing the core to contract. This contraction means that fusion will accelerate, and the core will heat up, creating more energetic gamma rays, which lend themselves to pair production even better. It also means that nuclei will be much closer together, meaning gamma rays will interact with them and form E/P pairs much faster, increasing the amount of energy in the form of E/P pairs compared to the amount of energy in the form of gamma rays. This means an overall reduction in radiation pressure, which  causes the core to continue to collapse. This is a positive-feedback loop that inevitably leads to a runaway fusion reaction.</p>
<p>There are two problems with this explanation. The first is that it seems like this positive-feedback loop should start the moment fusion begins. The other is that it doesn't seem like there's a way for the runaway fusion reaction to overcome the fact that pair formation is taking away energy that could help prevent core collapse. It seems like the core should collapse directly into a black hole. Where's the gap in my understanding?</p>

CC BY-SA 4.0
2021-08-30T10:12:02.170Z
Why should it start the moment fusion begins? p-p chain fusion runs at much lower temperatures than the pair-instability process. Eg, the solar core temperature is ~15.7 MK, but according to your link, you need >300 MK for significant pair production.
PM 2Ring
CC BY-SA 4.0
2021-08-30T14:55:26.110Z
So does that mean a PISN won't happen until the star's core reaches 300 MK?
zucculent
CC BY-SA 4.0
2021-08-30T15:13:19.280Z
You need the right combination of temperature, pressure, and low metallicity to get pair-production instability. There are lower mass stars with even hotter cores, eg carbon fusion runs at ~500 MK. So you need thermal photons with enough energy to cause pair production (>1.022MeV), and a sufficiently high density of the right nuclei to get the pair production rate up. (Sorry, I don't know why too many heavier nuclei prevent PISN).
PM 2Ring
CC BY-SA 4.0
2021-08-30T15:38:36.970Z
I think metallicity, which I assume is what you meant by "heavier nuclei, prevents a PISN by increasing the rate at which a star loses mass, meaning that by the time a PISN, would have occurred, the star isn't massive enough.
zucculent
<star><supernova><hypernova>
How does pair production cause a pair-instability supernova instead of leading to the formation of a black hole?
zucculent
# How does pair production cause a pair-instability supernova instead of leading to the formation of a black hole?

(Asked by: username_0 on 2021-08-30)

[The Wikipedia article](https://en.wikipedia.org/wiki/Pair-instability_supernova) on pair-instability supernovas (PISNs) doesn't seem to give a very good explanation of what causes a PISN. My understanding of the process it describes is this: Once the core gets hot enough, it starts producing gamma rays with enough energy to produce electron-positron pairs when they interact with atomic nuclei, although these pairs will annihilate eventually, forming a sort of equilibrium between gamma rays and E/P pairs. Since radiation pressure is what keeps the core from collapsing, the fact that a portion of the radiation energy is now in the form of E/P pairs means the radiation pressure decreases, causing the core to contract. This contraction means that fusion will accelerate, and the core will heat up, creating more energetic gamma rays, which lend themselves to pair production even better. It also means that nuclei will be much closer together, meaning gamma rays will interact with them and form E/P pairs much faster, increasing the amount of energy in the form of E/P pairs compared to the amount of energy in the form of gamma rays. This means an overall reduction in radiation pressure, which causes the core to continue to collapse. This is a positive-feedback loop that inevitably leads to a runaway fusion reaction.

There are two problems with this explanation. The first is that it seems like this positive-feedback loop should start the moment fusion begins. The other is that it doesn't seem like there's a way for the runaway fusion reaction to overcome the fact that pair formation is taking away energy that could help prevent core collapse. It seems like the core should collapse directly into a black hole. Where's the gap in my understanding?

**Tags:** star, supernova, hypernova

> **Comments:**
> **username_1**: Why should it start the moment fusion begins? p-p chain fusion runs at much lower temperatures than the pair-instability process. Eg, the solar core temperature is ~15.7 MK, but according to your link, you need >300 MK for significant pair production.  
> **username_0**: So does that mean a PISN won't happen until the star's core reaches 300 MK?  
> **username_1**: You need the right combination of temperature, pressure, and low metallicity to get pair-production instability. There are lower mass stars with even hotter cores, eg carbon fusion runs at ~500 MK. So you need thermal photons with enough energy to cause pair production (>1.022MeV), and a sufficiently high density of the right nuclei to get the pair production rate up. (Sorry, I don't know why too many heavier nuclei prevent PISN).  
> **username_0**: I think metallicity, which I assume is what you meant by "heavier nuclei, prevents a PISN by increasing the rate at which a star loses mass, meaning that by the time a PISN, would have occurred, the star isn't massive enough.  

---

## 1 answers

### Answer by username_2 on 2021-08-30. Score: 1

The problem with your argument is that you incorrectly assume that increasing nuclear fusion increases the pairs/photons ratio.

It is certainly true that increase in temperature increases the nuclear fusion rates and therefore the production of photons. More photons means greater possibility to produce electron-positron pairs, but why do you think that the *ratio* pairs/photons should increase as well?

Since pulsational pair instability doesn't always lead to a runaway fusion reaction, this means that injecting more photons into the system actually *decreases* the pairs/photons ratio, halting the collapse and triggering the pulsation mechanism.

The only way to find out that this is indeed the case, is to solve the complete system of equations for the rates of the processes involved.

I think that the first to have brought up the possibility of pair production supernovae were Fowler & Hoyle (1964) in [Neutrino Processes and Pair Formation in Massive Stars and Supernovae](http://articles.adsabs.harvard.edu/pdf/1964ApJS....9..201F)

> **Comments:**
> **username_0**: Does PPI mean pulsational pair instability?  
> **username_2**: @username_0 Yes, sorry for not specifying it  
> **username_0**: Does this mean that the cores of stars susceptible to PISNs will have brief periods of more intense pair production, and sooner or later one of these "pulses" will trigger a runaway feedback loop and cause a PISN?  
> **username_2**: @username_0 It depends on the mass of the core. In some cases the star would undergo some pulsations, loose a lot of mass and then stabilize itself. In some other cases one pulsation is sufficient to trigger the supernova. Otherwise, the star may start with small pulsations that slowly grow in amplitude until the last pulse makes the star explode. Have a look at [Pulsational Pair-Instability Supernovae](https://arxiv.org/abs/1608.08939) by Woosley, that explores all these scenarios with hydrodynamical simulations  
> **username_1**: Do you have any thoughts on the role of metallicity? The Wikipedia article is pretty vague on that score. It just states that these supernovae occur in low-metallicity stars, eg formed by merged pop III stars.  
> **username_2**: @PM2Ring dunno, probably the reason is that in order to reach such high temperatures, you need a very massive core. And only low metallicity stars are able to achieve it, due to being more massive from the start (at zero age main sequence) and to being able to retain that mass through their life, because they don't loose much mass in stellar winds  

---

