Electron degeneracy pressure

In astrophysics and condensed matter physics, electron degeneracy pressure is a quantum mechanical effect critical to understanding the stability of white dwarf stars and metal solids.

It is a manifestation of the more general phenomenon of quantum degeneracy pressure.

The term "degenerate" here is not related to degenerate energy levels, but to Fermi–Dirac statistics close to the zero-temperature limit[1] (temperatures much smaller than the Fermi temperature, which for metals is about 10000 K.) In metals and in white dwarf stars, electrons can be modeled as a gas of non-interacting electrons confined to a finite volume.

Instead, the confinement makes the allowed energy levels quantized, and the electrons fill them from the bottom upwards.

[2][3]: 32–39 In white dwarf stars, the positive nuclei are completely ionized – disassociated from the electrons – and closely packed – a million times more dense than the Sun.

This force is balanced by the electron degeneracy pressure keeping the star stable.

[4] In metals, the positive nuclei are partly ionized and spaced by normal interatomic distances.

Gravity has negligible effect; the positive ion cores are attracted to the negatively charged electron gas.

Fermions, like the proton or the neutron, follow Pauli's principle and Fermi–Dirac statistics.

In general, for an ensemble of non-interacting fermions, also known as a Fermi gas, each particle can be treated independently with a single-fermion energy given by the purely kinetic term,

When particle energies reach relativistic levels, a modified formula is required.

A star exceeding this limit and without significant thermally generated pressure will continue to collapse to form either a neutron star or black hole, because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity.