degeneracy pressure
What holds up a burnt-out star against its own crushing gravity, when there is no more nuclear fire to push back? Not heat — a white dwarf can be stone cold. The answer is a pressure that exists even at absolute zero, arising purely because fermions refuse to share quantum states. Squeeze them together and the Pauli exclusion principle forces some into higher-momentum states; their zero-point motion pushes back. This is degeneracy pressure, and without it the compact remnants of stars could not exist.
For a degenerate Fermi gas at T = 0, the pressure comes entirely from the filled Fermi sea. For a nonrelativistic gas the pressure scales as P proportional to n^(5/3); explicitly, for electrons, P = (hbar^2 / 5m)(3 pi^2)^(2/3) n^(5/3), equal to (2/5) n E_F. It is completely independent of temperature — cooling the star does not weaken it. When the fermions become ultrarelativistic (as in a very massive white dwarf, where E_F exceeds the electron rest energy), the scaling softens to P proportional to n^(4/3). This softening is fatal: a pressure rising only as n^(4/3) cannot always beat the n^(4/3) demand of self-gravity, which leads directly to the Chandrasekhar limit of about 1.4 solar masses, above which electron degeneracy pressure fails and the star collapses.
Degeneracy pressure supports white dwarfs (electron degeneracy) and neutron stars (neutron degeneracy), and it sets the rigidity of ordinary matter and the incompressibility of the electron gas in metals. The crucial and often-missed point: this pressure is NOT electrostatic repulsion between like charges — a neutral gas of identical fermions would have it too. It is a direct mechanical consequence of the exclusion principle and the zero-point kinetic energy it forces upon the particles.
A white dwarf packs roughly the mass of the Sun into the volume of the Earth. Its electrons form a degenerate gas whose n^(5/3) pressure balances gravity with no help from heat, so the star can cool for billions of years without shrinking — until, above 1.4 solar masses, the relativistic n^(4/3) pressure can no longer win and collapse to a neutron star or supernova follows.
Degeneracy pressure holds a white dwarf up until the Chandrasekhar limit, where relativity defeats it.
Degeneracy pressure is temperature-independent and survives at T = 0; it is a consequence of the Pauli exclusion principle, not of Coulomb repulsion or thermal agitation. The switch from n^(5/3) to n^(4/3) scaling as the gas becomes relativistic is precisely what makes the Chandrasekhar mass limit exist.