Degenerate Matter - Degenerate Gases

Degenerate Gases

Degenerate gases are gases composed of fermions that have a particular configuration that usually forms at high densities. Fermions are particles with half-integer spin. Their behavior is regulated by a set of quantum mechanical rules called the Fermi–Dirac statistics. One particular rule is the Pauli exclusion principle, which states that there can be only one fermion occupying each quantum state, which also applies to electrons that are not bound to a nucleus but merely confined to a fixed volume, such as in the deep interior of a star. Such particles as electrons, protons, neutrons, and neutrinos are all fermions and obey Fermi–Dirac statistics.

A fermion gas in which all energy states below a critical value are filled is called a fully degenerate fermion gas. The critical value is known as the Fermi energy. The electron gas in ordinary metals and in the interior of white dwarf stars constitute two examples of a degenerate electron gas. Most stars are supported against their own gravitation by normal gas pressure. White dwarf stars are supported by the degeneracy pressure of the electron gas in their interior. For white dwarfs the degenerate particles are the electrons while for neutron stars the degenerate particles are neutrons.

In ordinary gas, most of the electron energy levels (n-spheres) are unfilled and the electrons are free to move about. As particle density is increased electrons progressively fill the lower energy states and additional electrons are forced to occupy states of higher energy. Degenerate gases strongly resist further compression because the electrons cannot move to lower energy levels, which are already filled. The Pauli exclusion principle causes this. Even though thermal energy may be extracted from the gas, it still may not cool down, since electrons cannot give up energy by moving to a lower energy state. This increases the pressure of the fermion gas termed degeneracy pressure. In a degenerate gas, the average pressure opposes the force of gravity and limits its compression.

Under high densities the matter becomes a degenerate gas when the electrons are all stripped from their parent atoms. In the core of a star, once hydrogen burning in nuclear fusion reactions stops, it 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. Degenerate gas is an almost perfect conductor of heat and does not obey the ordinary gas laws. White dwarfs are luminous not because they are generating any energy but rather because they have trapped a large amount of heat. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. When gas becomes super-compressed, particles position right up against each other to produce degenerate gas that behaves more like a solid. In degenerate gases the kinetic energies of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light. Instead of temperature, the pressure in a degenerate gas depends only on the speed of the degenerate particles; however, adding heat does not increase the speed. Pressure is only increased by the mass of the particles, which increases the gravitational force pulling the particles closer together. Therefore, the phenomenon is the opposite of that normally found in matter where if the mass of the matter is increased, the object becomes bigger. In degenerate gas, when the mass is increased, the pressure is increased, and the particles become spaced closer together, so the object becomes smaller. Degenerate gas can be compressed to very high densities, typical values being in the range of 10,000 kilograms per cubic centimeter.

There is an upper limit to the mass of an electron-degenerate object, the Chandrasekhar limit, beyond which electron degeneracy pressure cannot support the object against collapse. The limit is approximately 1.44 solar masses for objects with compositions similar to the sun. The mass cutoff changes with the chemical composition of the object, as this affects the ratio of mass to number of electrons present. Celestial objects below this limit are white dwarf stars, formed by the collapse of the cores of stars that run out of fuel. During collapse, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a neutron star (supported by neutron degeneracy pressure) or a black hole may be formed instead.