Electron-Positron Pair Instability Supernova

[debs1]

How does the formation of electron positron pairs increase the energy density and softens the EOS?

I trrying to understand the pair instability supernova. In many texts and articles, it is written that the formation of electron positron pairs lead to instability, the energy density is increased and the adiabatic index drops below 4/3 which softens the equation of state.

• How does the formation of electron positron pairs lead to instability?
• How is the energy density increased?
• What does it mean by 'softening of EOS' and how does it happen?

Ref:
1) https://ui.adsabs.harvard.edu/abs/1967ApJ...148..803R/abstract
2)https://arxiv.org/abs/1910.12874
3)https://arxiv.org/abs/2007.07889

 

[PeroK]

Wherever this gets moved to, you'll need some references for where you've been reading this stuff.

 

[debs1]

Wherever this gets moved to, you'll need some references for where you've been reading this stuff.

I have included some references

 

[Astronuc]

What does it mean by 'softening of EOS' and how does it happen?

The best statement I can readily find states "A stiff equation of state tends to have larger pressure for a given density. This material resists compression and these stars have larger radii. Naturally, a soft equation of state has smaller pressures, is more easily compressed, and produces stars with smaller radii."

The threshold for pair production is 1.022 MeV. A photon of that or greater theshold would produce an electron-proton pair and transform photon energy into rest mass + some kinetic energy, where the kinetic energy would be given by the difference in the total photon energy before and rest energy after. Then shortly thereafter, the positron would find an electron and annihilate, which would produce 2 photons of 0.511 MeV.

How is the energy density increased?

Energy density would increase during the collapse, or as the radius decreases?

Did the questions arise from the following article, which cites Ref 1?
https://en.wikipedia.org/wiki/Pair-instability_supernova

the production of free electrons and positrons in the collision between atomic nuclei and energetic gamma rays, temporarily reduces the internal radiation pressure supporting a supermassive star's core against gravitational collapse.

https://en.wikipedia.org/wiki/Pair-instability_supernova#cite_note-1

From the article,

In very massive, hot stars with interior temperatures above about 300000000 K (3×108 K), photons produced in the stellar core are primarily in the form of very high energy-level gamma rays. The pressure from these gamma rays fleeing outward from the core helps to hold up the upper layers of the star against the inward pull of gravity. If the level of gamma rays (the energy density) is reduced, then the outer layers of the star will begin to collapse inwards.