# Electron Degeneracy Pressure and the Pauli Exclusion Principle

I have read that what keeps white dwarfs from gravitational collapse is electron degeneracy pressure. How does this pressure prevent further collapse, and how is it related to the Pauli Exclusion Principle?

## 2 Answers

Basically, the Pauli exclusion principle says that two fermions (in this case, electrons) can't be in the same quantum state. To expand: No two electrons in an atom can share the same numbers for their four quantum numbers, properties that help describe the state of a particle. What are quantum numbers? The important consequence here is that no two electrons can have the same spin and energy level.

In a white dwarf or a neutron star, the fermions are packed very close together, and there's quite a lot of force due to gravity. However, the exclusion principle triumphs. Fermions near each other must have different energy levels; this leads to energy differences and degeneracy pressure pressure, which counteracts the force of gravity. Above a certain mass limit (the Chandrasekhar limit, roughly $\sim1.40M_{\odot}$), electron degeneracy pressure is no longer sufficient; the white dwarf collapses to a neutron star. There appears to be a similar limit for neutron stars, where neutron degeneracy pressure cannot support the remnant against gravity, and it collapses into a black hole.

And here's another way to frame the situation. Degeneracy is not responsible for the pressure in the electrons in a white dwarf, they would have that same pressure once the star contracts to the same size even if it was all ideal gas (say, if the electrons were distinguishable). What is meant by "degeneracy pressure" is the perfectly mundane kinetic gas pressure that happens to be reached at the point where the Pauli exclusion principle makes it impossible for the star to lose any more heat, so it cannot contract any further. Notice this also means that the "degeneracy pressure" limit for a given star is the maximum pressure the star can attain. This surprises some people, who are inclined to think of degeneracy pressure as a kind of minimum below which the pressure cannot fall, but that would be true for a gas in a box of constant volume, not a self-gravitating contracting star.

• Finally a proper explanation! – nbubis Oct 18 '17 at 7:14