[supernova87a]

Here's a question I was always curious to hear a good intuitive explanation for --

Why does a neutron star not decay, as it is composed of neutrons, and free neutrons should decay in 15 minutes?

Is it because the neutrons are in an energetic "well" and to decay out would actually require energy? In collapsing under gravity to neutron degeneracy, did the neutrons say, radiate away their ability to decay any more?

[kadoban]

This is the best answer I've seen: https://physics.stackexchange.com/a/63387 which to my layman eyes basically seems to match your theory.

[JumpCrisscross]

Does this mean the neutrons are continuously degrading? Their decay products continuously recombining into new neutrons? (Though that would imply "evaporation" at the surface?)

[kadoban]

I _think_ not, it's just energenically unfavorable so it should ~never happen.

https://en.m.wikipedia.org/wiki/Urca_process this does seem to be going on though, which tbh I just don't understand so it may contradict what I just said, or not.

[savant_penguin]

I'll pretend I understood what the answer says about there not being enough energy and boldly ask: what if the neutron star is spinning _really_ fast?

[jfoutz]

You are spinning pretty fast on the side of the planet, but you don’t go flying out into space. Same deal, I’d guess as a layman.

[sp332]

Well that's the decay rate for a "bare" neutron. Neutrons in atoms obviously last longer than that. And the neutrons in a neutron star are all smashed up next to each other, kinda like a star-sized atom.

[pfdietz]

The neutron would have to emit an electron (and an antineutrino). A neutron star does have electrons (and protons) in it, to the extent that the electrons have filled all energy levels into which a neutron decay electron could go. In other words, the decay is prevented by the presence of these electrons and the Pauli exclusion principle.

[colechristensen]

It seems there are several things going on. Protons absorbing electrons becoming neutrons doing the opposite of decay, a sort of connective cycle that radiates away neutrinos while enabling decay and reverse decay, and plain old Pauli exclusion where there is no room for electrons.

But it all comes down to lots of things being possible in such a crowded place and neutrons not being “free” in a neutron star. Nuclear chemistry is full of crazy stuff happening constantly in stable situations that all kind of balances out.

[cozzyd]

I guess there's probably not enough phase space for that

[adrian_b]

It is approximately what you say.

A free neutron decays spontaneously into a proton, electron and neutrino, because decaying provides energy, because the mass of a neutron is higher than the sum of the masses of the decay products.

A free proton does not decay because none of the possible decay modes can produce particles with a lesser mass.

This is the same reason why your body does not fragment spontaneously in separate parts, but some external energy is required for that, e.g. someone wielding a meat cleaver.

The neutrons forming a neutron star are bound together by the gravitational force. When the neutron star has formed, the energy equal to the binding energy has been lost, so the average mass of a neutron in a neutron star, i.e. the mass of the star divided by the number of neutrons, is less than the mass of a free neutron and it is also less than the mass of a free proton and even less than the average mass of a nucleon inside the nucleus with the highest binding energy (iron 56).

Otherwise the star would have remained composed of ordinary nuclei instead of becoming a neutron star.

To extract a free neutron from a neutron star you must provide an energy at least as large as corresponding to the difference in mass between a free neutron and the mass of a neutron bound in the neutron star.

To make it "decay" (of course, that is not decay, because it is not spontaneous) while remaining in the neutron star, you need to provide some lower energy, which could convert a neutron into a proton, electron and neutrino, creating an excited state of the star, like an excited state of a nucleus or atom. Soon after that, the difference in energy will be radiated, either when the proton and electron would recombine again, or the proton will spontaneously decay into a neutron and a positron (which will later annihilate with the electron).

So a neutron star should behave like any other bound system. The state with the lowest energy is the state when all the nucleons are neutrons, unlike the state with the lowest energy of an ordinary nucleus, where a part of the nucleons must be protons.

This being the state with the lowest energy, no decay processes can exist. External energy can produce excited states, where a few protons, electrons and positrons may exist, but these other particles will decay, combine or annihilate, so the base state will be reached again.

The same happens with atomic nuclei, which are bound by strong nuclear forces instead of gravitational forces. The neutrons in stable nuclei or in nuclei with excess protons do not decay. On the contrary, the protons in nuclei with excess protons over the corresponding stable nucleus decay into neutrons and positrons (or they capture electrons).

So a neutron star behaves in the same way as a nucleus where the state with the lowest energy happens to be the one with no protons.