Degenerate matter
The term is used in astrophysics to refer to dense stellar objects such as white dwarfs and neutron stars, where thermal pressure alone is not enough to prevent gravitational collapse.
Degenerate matter is usually modelled as an ideal Fermi gas, an ensemble of non-interacting fermions.
The Pauli exclusion principle prevents identical fermions from occupying the same quantum state.
[3]: 437 The electron degeneracy pressure occurs in the ground state systems which are non-degenerate in energy levels.
Degenerate matter exhibits quantum mechanical properties when a fermion system temperature approaches absolute zero.
The fermions, forced in to higher levels by the Pauli principle, exert pressure preventing further compression.
At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by
Given a sufficiently drastic increase in temperature (such as during a red giant star's helium flash), matter can become non-degenerate without reducing its density.
Degenerate gases strongly resist further compression because the electrons cannot move to already filled lower energy levels due to the Pauli exclusion principle.
Under high densities, matter becomes a degenerate gas when all electrons are stripped from their parent atoms.
The core of a star, once hydrogen burning nuclear fusion reactions stops, becomes a collection of positively charged ions, largely helium and carbon nuclei, floating in a sea of electrons, which have been stripped from the nuclei.
White dwarfs are luminous not because they are generating energy but rather because they have trapped a large amount of heat which is gradually radiated away.
Degenerate gas can be compressed to very high densities, typical values being in the range of 10,000 kilograms per cubic centimeter.
The limit is approximately 1.44[6] solar masses for objects with typical compositions expected for white dwarf stars (carbon and oxygen with two baryons per electron).
[7] The limit may also change with the chemical composition of the object, as it affects the ratio of mass to number of electrons present.
During this shrinking, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse.
This phenomenon is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs.
At densities greater than those supported by neutron degeneracy, quark matter is expected to occur.
The equations of state for the various proposed forms of quark-degenerate matter vary widely, and are usually also poorly defined, due to the difficulty of modelling strong force interactions.
[10] In 1914 Walther Nernst described the reduction of the specific heat of gases at very low temperature as "degeneration"; he attributed this to quantum effects.
In subsequent work in various papers on quantum thermodynamics by Albert Einstein, by Max Planck, and by Erwin Schrödinger, the effect at low temperatures came to be called "gas degeneracy".
[11] A fully degenerate gas has no volume dependence on pressure when temperature approaches absolute zero.
Early in 1927 Enrico Fermi and separately Llewellyn Thomas developed a semi-classical model for electrons in a metal.
Later in 1927, Arnold Sommerfeld applied the Pauli principle via Fermi-Dirac statistics to this electron gas model, computing the specific heat of metals; the result became Fermi gas model for metals.
Sommerfeld called the low temperature region with quantum effects a "wholly degenerate gas".
Eddington had suggested that the atoms in Sirius B were almost completely ionised and closely packed.
Fowler described white dwarfs as composed of a gas of particles that became degenerate at low temperature; he also pointed out that ordinary atoms are broadly similar in regards to the filling of energy levels by fermions.
[16] In 1927 Ralph H. Fowler applied Fermi's model to the puzzle of the stability of white dwarf stars.
