Degenerate matter

Degenerate matter in physics is a collection of free, non-interacting particles with pressure and other physical characteristics determined by quantum mechanical effects. It is the analogue of an ideal gas in classical mechanics. The degenerate state of matter, insofar as it deviates from an ideal gas, arises at extraordinarily high density (in compact stars) or at extremely low temperatures in laboratories. It occurs for matter particles such as electrons, neutrons, protons, and fermions in general and in which case it is referred to as electron-degenerate matter, neutron-degenerate matter, and so on. In a mixture of particles, such as ions and electrons in white dwarfs or metals, the electrons may be degenerate, while the ions are not.

In a quantum mechanical description, free particles limited to a finite volume may take only a discrete set of energies, called quantum states. The Pauli exclusion principle prevents identical fermions from occupying the same quantum state. At lowest total energy (when the thermal energy of the particles is negligible), all the lowest energy quantum states are filled. This state is referred to as full degeneracy. The pressure (called degeneracy pressure or Fermi pressure) remains nonzero even at absolute zero temperature. Adding particles or reducing the volume forces the particles into higher-energy quantum states. This requires a compression force, and is made manifest as a resisting pressure. The key feature is that this degeneracy pressure does not depend on the temperature but only on the density of the fermions. Degeneracy pressure keeps dense stars in equilibrium, independent of the thermal structure of the star.

Degenerate matter is also called a Fermi gas or a degenerate gas. A degenerate mass whose fermions have velocities close to the speed of light (particle energy larger than its rest mass energy) is called relativistic degenerate matter.

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