<p><a href="https://en.wikipedia.org/wiki/Proton_decay" rel="nofollow noreferrer">Proton decay</a> is thought to produce either anti-muons or positrons along with neutral pions that decay into gamma ray photons. There are perhaps other speculative possibilities.</p>
<p>If the result of the decay is indeed positively charge leptons then I would think that these should immediately annihilate with the abundant electrons and muons within the neutron star, producing more gamma ray photons.</p>
<p>The net result would be the gradual conversion of proton rest mass into photon energy and the loss of pressure support within the star - which is largely from the mutual repulsion between baryons rather than degeneracy pressure. Counter intuitively, the neutron star would expand and its density decreases. Once the rest mass drops below the minimum stable mass for a neutron star (about <span class="math-container">$0.2M_\odot$</span>), the neutrons would combine with protons and the likely outcome that minimised the energy density star would be a low-mass  white dwarf, made up of iron-peak elements (or possibly heavier elements, depending on the timescales on which they could decay to the minimum energy configuration compared with the proton half life), supported by electron degeneracy pressure and I suppose the proton decay process would continue until all the rest mass was converted into energy.</p>
<p>Since the proton is the lightest baryon then the removal of protons would also allow any heavier baryons (even if they were somehow more stable than the proton, which seems unlikely) the chance to decay into protons - a possibility that is otherwise blocked by proton degeneracy.</p>
<p>Maybe the only neutron star model that would interfere with this process would be a neutron star core featuring quark matter. I am not familar enough with proton decay to know how whatever physics causes that might influence the long term future of quark matter.</p>

CC BY-SA 4.0
2024-11-22T22:15:43.610Z
If you decompress neutron star matter, you get r-process nuclei, not protons.
John Doty
CC BY-SA 4.0
2024-11-22T22:29:32.473Z
@JohnDoty I think actually it would end up as a white dwarf made of iron-peak elements as the density gradually decreased.
ProfRob
CC BY-SA 4.0
2024-11-22T23:01:30.630Z
Well, iron-peak is *thermodynamically* favored, but there's no thermal process here. A $10^{34}$ year old neutron star will be very cold. Non-equilibrium nucleosynthesis makes nuclei that are *kinetically* favored.
John Doty
CC BY-SA 4.0
2024-11-22T23:33:01.333Z
@JohnDoty a neutron star that is 1 day old is "cold". Temperature plays no role in determining the internal composition of neutron stars after that. It is density dependent and the Fermi energies of particles are orders of magnitude bigger than thernal energies. The physics at crustal densities is well understood and you get iron-peak elements once densities drop below about $10^{12}$ kg/m$^3$. This is not a sudden change like in a neutron star merger.
ProfRob
CC BY-SA 4.0
2024-11-22T23:41:52.137Z
Different situation. The iron-peak nuclei are not dredged up from lower down. The neutron-rich nuclei at higher densities stay below. But, regardless of how fast you decompress, what pathway is there for heavier nuclei to decay to iron at low temperature?
John Doty
CC BY-SA 4.0
2024-11-22T23:46:32.487Z
The production of iron in the crust *is* thermal: that's what makes x-ray bursts. Pile too much lighter stuff on and bang!
John Doty
CC BY-SA 4.0
2024-11-23T07:59:35.710Z
@JohnDoty accretion onto the neutron star surface produces X-ray bursts. Pathways? We have $>10^{35}$ years. Any pathways you like. But the heavy neutron-rich nuclei formed at factors of 10-1000 below nuclear densities are unstable to fission and decay at lower densities.
ProfRob
CC BY-SA 4.0
2024-11-23T12:59:47.937Z
Yes, they decay to stable isotopes, most of which aren't iron. Iron is the end point of *thermonuclear* processes, either from the initial accretion of the NS, or from subsequent mass transfer in a binary.
John Doty
CC BY-SA 4.0
2024-11-23T14:30:07.653Z
@JohnDoty The elements and isotopes you are discussing are not stable at densities $>10^{10}$ kg/m$^3$. Fission, neutron capture/dripping, electron capture, alpha and beta decay proceed with no thermal activation in degenerate matter. This was set out in the early 70s by Baym, Pethick and Sutherland (1971), who derived the equilibrium state of cold matter as a function of density.
ProfRob
CC BY-SA 4.0
2024-11-23T14:36:01.503Z
But do the kinetics lead to thermodynamic equilibrium here? Fission, neutron capture/dripping, electron capture, alpha and beta decay don't generally lead to iron. Neutron capture turns iron into heavier elements.
John Doty
CC BY-SA 4.0
2024-11-22T14:57:37.043Z
2024-11-23T08:05:12.773Z
2024-11-23T08:05:12.773Z
ProfRob
<p>Proton decay is a hypothesis presented by some GUTs and, although we have zero experimental evidence for that, it's still a possible phenomenon or, at least, it's not ruled-out</p>
<p>If proton decay occurs, neutron stars should decay over time, as the external layer of matter made of protons would decay over extremely long time scales, decreasing the degeneracy pressure, and allowing neutrons to suffer beta-decay, which would form in turn new protons that could eventually decay, decreasing even more the degeneracy pressure and so on</p>
<p>But, could there be neutrons stars with cores composed of particular forms of matter that would survive this proton decay, leaving a remnant?</p>
<p>For instance, in this image (<a href="https://www.researchgate.net/publication/264459294_Properties_of_High-Density_Matter_in_Neutron_Stars/figures?lo=1" rel="noreferrer">https://www.researchgate.net/publication/264459294_Properties_of_High-Density_Matter_in_Neutron_Stars/figures?lo=1</a>) it's shown the different possible compositions of a neutron star core: neutrons, electrons, muons, hyperons, deltas, bosons, condensates...</p>
<p>Are any of these options close to mainstream and verified physics but that at the same time would allow neutron stars to survive proton decay in some sense after all, if it indeed happens?</p>

CC BY-SA 4.0
2024-11-22T14:37:47.820Z
There is no "external layer of matter made of protons" (or provide a reference for that). Do you mean that the crust material contains protons (within nuclei)? If neutrons decay into (lighter) protons and electrons then this has the effect of INCREASING degeneracy pressure - the protons and electrons are also degenerate.
ProfRob
<astrophysics><cosmology><neutron-star><quantum-mechanics>
Could neutron stars leave a "remnant" after decaying (assuming they decay)?
vengaq
# Could neutron stars leave a "remnant" after decaying (assuming they decay)?

(Asked by: username_0 on 2024-11-22)

Proton decay is a hypothesis presented by some GUTs and, although we have zero experimental evidence for that, it's still a possible phenomenon or, at least, it's not ruled-out

If proton decay occurs, neutron stars should decay over time, as the external layer of matter made of protons would decay over extremely long time scales, decreasing the degeneracy pressure, and allowing neutrons to suffer beta-decay, which would form in turn new protons that could eventually decay, decreasing even more the degeneracy pressure and so on

But, could there be neutrons stars with cores composed of particular forms of matter that would survive this proton decay, leaving a remnant?

For instance, in this image (<https://www.researchgate.net/publication/264459294_Properties_of_High-Density_Matter_in_Neutron_Stars/figures?lo=1>) it's shown the different possible compositions of a neutron star core: neutrons, electrons, muons, hyperons, deltas, bosons, condensates...

Are any of these options close to mainstream and verified physics but that at the same time would allow neutron stars to survive proton decay in some sense after all, if it indeed happens?

**Tags:** astrophysics, cosmology, neutron-star, quantum-mechanics
> **Comments:**
> **username_1**: There is no "external layer of matter made of protons" (or provide a reference for that). Do you mean that the crust material contains protons (within nuclei)? If neutrons decay into (lighter) protons and electrons then this has the effect of INCREASING degeneracy pressure - the protons and electrons are also degenerate.  

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## 1 answers

### Answer by username_1 on 2024-11-22. Score: 6

[Proton decay](https://en.wikipedia.org/wiki/Proton_decay) is thought to produce either anti-muons or positrons along with neutral pions that decay into gamma ray photons. There are perhaps other speculative possibilities.

If the result of the decay is indeed positively charge leptons then I would think that these should immediately annihilate with the abundant electrons and muons within the neutron star, producing more gamma ray photons.

The net result would be the gradual conversion of proton rest mass into photon energy and the loss of pressure support within the star - which is largely from the mutual repulsion between baryons rather than degeneracy pressure. Counter intuitively, the neutron star would expand and its density decreases. Once the rest mass drops below the minimum stable mass for a neutron star (about $0.2M\_\odot$), the neutrons would combine with protons and the likely outcome that minimised the energy density star would be a low-mass white dwarf, made up of iron-peak elements (or possibly heavier elements, depending on the timescales on which they could decay to the minimum energy configuration compared with the proton half life), supported by electron degeneracy pressure and I suppose the proton decay process would continue until all the rest mass was converted into energy.

Since the proton is the lightest baryon then the removal of protons would also allow any heavier baryons (even if they were somehow more stable than the proton, which seems unlikely) the chance to decay into protons - a possibility that is otherwise blocked by proton degeneracy.

Maybe the only neutron star model that would interfere with this process would be a neutron star core featuring quark matter. I am not familar enough with proton decay to know how whatever physics causes that might influence the long term future of quark matter.

> **Comments:**
> **username_2**: If you decompress neutron star matter, you get r-process nuclei, not protons.  
> **username_1**: @JohnDoty I think actually it would end up as a white dwarf made of iron-peak elements as the density gradually decreased.  
> **username_2**: Well, iron-peak is *thermodynamically* favored, but there's no thermal process here. A $10^{34}$ year old neutron star will be very cold. Non-equilibrium nucleosynthesis makes nuclei that are *kinetically* favored.  
> **username_1**: @JohnDoty a neutron star that is 1 day old is "cold". Temperature plays no role in determining the internal composition of neutron stars after that. It is density dependent and the Fermi energies of particles are orders of magnitude bigger than thernal energies. The physics at crustal densities is well understood and you get iron-peak elements once densities drop below about $10^{12}$ kg/m$^3$. This is not a sudden change like in a neutron star merger.  
> **username_2**: Different situation. The iron-peak nuclei are not dredged up from lower down. The neutron-rich nuclei at higher densities stay below. But, regardless of how fast you decompress, what pathway is there for heavier nuclei to decay to iron at low temperature?  
> **username_2**: The production of iron in the crust *is* thermal: that's what makes x-ray bursts. Pile too much lighter stuff on and bang!  
> **username_1**: @JohnDoty accretion onto the neutron star surface produces X-ray bursts. Pathways? We have $>10^{35}$ years. Any pathways you like. But the heavy neutron-rich nuclei formed at factors of 10-1000 below nuclear densities are unstable to fission and decay at lower densities.  
> **username_2**: Yes, they decay to stable isotopes, most of which aren't iron. Iron is the end point of *thermonuclear* processes, either from the initial accretion of the NS, or from subsequent mass transfer in a binary.  
> **username_1**: @JohnDoty The elements and isotopes you are discussing are not stable at densities $>10^{10}$ kg/m$^3$. Fission, neutron capture/dripping, electron capture, alpha and beta decay proceed with no thermal activation in degenerate matter. This was set out in the early 70s by Baym, Pethick and Sutherland (1971), who derived the equilibrium state of cold matter as a function of density.  
> **username_2**: But do the kinetics lead to thermodynamic equilibrium here? Fission, neutron capture/dripping, electron capture, alpha and beta decay don't generally lead to iron. Neutron capture turns iron into heavier elements.  

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