Electron degeneracy pressure

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Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without it collapsing into a neutron star or black hole. It is an important factor in stellar physics because it is responsible for the existence of white dwarfs.

Also relevant to the understanding of electron degeneracy pressure is the Heisenberg uncertainty principle, which states that

$\Delta x \Delta p \ge \frac{\hbar}{2}$

where $\hbar$ is Planck's constant (h) divided by 2π, Δx is the uncertainty of the position measurements and Δp is the uncertainty (standard deviation) of the momentum measurements.

A material subjected to ever increasing pressure will become ever more compressed, and for electrons within it, the uncertainty in position measurements, Δx, becomes ever smaller. Thus, as dictated by the uncertainty principle, the uncertainty in the momenta of the electrons, Δp, becomes larger. Thus, no matter how low the temperature drops, the electrons must be traveling at this "Heisenberg speed," contributing to the pressure. When the pressure due to the "Heisenberg speed" exceeds that of the pressure from the thermal motions of the electrons, the electrons are referred to as degenerate, and the material is termed degenerate matter.

Electron degeneracy pressure will halt the gravitational collapse of a star if its mass is below the Chandrasekhar Limit (1.44 solar masses). This is the pressure that prevents a white dwarf star from collapsing. A star exceeding this limit and without usable nuclear fuel 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.