How does gravity acts on the electrons to collapse a neutrons star or white dwarfs against the degeneracy pressure?

Question

if electrons is considered as quantum particle in case neutron star (alluding to quantum statistics) how does gravity makes the star collapse? considering the fact that electrons are quantum particles and have negligible mass.

Answer 1

Chandrasekhar showed in the 1930's that there was a limit, now called the Chandrasekhar limit, on the mass of a white dwarf that is in hydrodynamic equilibrium. The limit is about 1.4 solar masses. This is enough to establish that a heavier star can't be a white dwarf, but by itself it doesn't explain what happens instead.

The reaction $\text{p}+\text{e}^-\rightarrow \text{n}+\nu$ occurs due to the weak nuclear force. When the proton is free, i.e., in hydrogen, it requires an input of 0.8 MeV of energy. A nucleus can absorb an electron and convert a proton into a neutron, and in this context the process is called electron capture. Ordinarily this process will only occur if the nucleus is neutron-deficient; once it reaches a neutron- to-proton ratio that optimizes its binding energy, neutron capture cannot proceed without a source of energy to make the reaction go. In the environment of a white dwarf, however, there is such a source. The annihilation of an electron opens up a hole in the “Fermi sea.” There is now an state into which another electron is allowed to drop without violating the exclusion principle, and the effect cascades upward. In a star with a mass above the Chandrasekhar limit, this process runs to completion, with every proton being converted into a neutron. This results in a neutron star.

A calculation similar to Chandrasekhar's, by Tolman, Oppenheimer, and Volkoff in 1939, shows that there is an upper limit on the mass of a stable neutron star. The limit is currently believed to be about 2 to 3 solar masses. Most likely there is no stable form of matter for stars above this limit, so they become black holes.

Answer 2

The acceleration on a particle due to gravity doesn't depend on its mass; it's just the local gravitational field strength. This is the basis of the equivalence principle.

Answer 3

at the field strengths present in a star near collapse, the mass of the electrons is not negligible. they are gravitationally bound.

Answer 4

Gravitation is not needed. Extremely high pressure is the only thing that is needed. Gravitation is one mechanism that can create the necessary pressure.

Answer 5

Gravity acts on electrons the same way it acts on any other mass. It doesn’t matter how small the electrons mass is. What causes gravity is another question.