Why is there no proton degeneracy pressure?

[Pedro de la Torre]

Hello. I usually heard about electron degeneracy pressure and neutron degeneracy pressure. But I´ve never heard about a proton degeneracy pressure.
Why is this?

 

[Nugatory]

Large bodies of matter contain roughly equal amounts of electrons and protons. Under extreme pressure these are forced together to produce neutrons, so by the time that degeneracy pressure would matter for the protons there aren't any protons left, just neutrons.

 

[Pedro de la Torre]

Yes, I can understand that.
What I mean, I have calculated a degeneracy pressure for electrons when a White dwarf is forming. I calculated a degeneracy pressure for neutrons when a Neutron star is going to form. But I have never heard about such pressure for protons.
Does a degeneracy pressure for protons exist? I suppose yes, but I do not know why I have never heard about an explanation of this.

 

[PeterDonis]

Does a degeneracy pressure for protons exist?

Yes, theoretically speaking. But practically speaking, it never gets observed, because, as @Nugatory said, at the densities where it would become significant, protons and electrons are forced together to form neutrons.

In other words, theoretically, if you could assemble, say, $10^{60}$ protons into a compact object like a neutron star, without including any electrons, then yes, the structure of that object would be significantly affected by proton degeneracy pressure. But assembling such an object is impossible in any practical sense, because the protons would repel each other electrically and you would never be able to push them together into a compact enough object in the first place. Neutron stars are able to form because the objects they form from, ordinary stars that go supernova, are electrically neutral--they contain equal numbers of protons and electrons. That is what allows them to get compressed to the point where degeneracy pressure starts to matter--but, as above, by the time proton degeneracy pressure would start to matter, the protons and electrons have all been forced together to form neutrons.

(I have not done the math, but I am skeptical that such a compact "proton star" would be stable even if you could assemble it; I don't think its gravity would be sufficient to hold it together for any long period of time against the combined effects of proton degeneracy pressure and the electrical repulsion between the protons.)

 

[Pedro de la Torre]

Aah. Great! Thank you very much!