Electron Degeneracy Pressure

In a gas of electrons, there are two sources of pressure: the "normal" pressure coming from the motion of the particles, and the degeneracy pressure, which is a purely quantum mechanical effect that is present even at zero temperature (right panel). At normal densities only the former is important, but at very high densities the degeneracy pressure becomes the most important source of pressure.

In the cores of massive stars and in white dwarfs, the primary source of the pressure supporting the star is electron degeneracy. In neutron stars, the pressure is produced by degeneracy in the neutrons rather than in the electrons, but the principle is the same.

In a normal plasma, most of the pressure is supplied by the light, fast electrons and only a little by the heavy, slow positive ions; heating the plasma causes the electrons to move faster and the pressure increases. In a degenerate plasma the principles of quantum mechanics make it difficult for electrons to absorb energy and move faster. When a degenerate plasma is heated the energy goes primarily into the heavier ions and this has little effect on the pressure.

Thermonuclear Runaways

The behavior of gases plays a central role in astronomy. Under "normal" conditions, gases obey approximately a set of rules called the ideal gas law. For example, one property of ideal gases is that an increase in the temperature at constant volume causes an increase in the pressure (see the right panel).

Degenerate Gases
Under conditions of very high density, gases can behave in a quite different way. These gases are called degenerate gases and their properties are governed by the principles of quantum mechanics. One very important property of degenerate gases is that the pressure is independent of the temperature. Thus, contrary to our usual experience, if we could heat a balloon of degenerate gas it would not expand. This has very large consequences for thermonuclear reactions that occur under conditions of very high density.

Thermonuclear Reactions in Ideal Gases
If a thermonuclear reaction is ignited in matter it quickly raises the temperature to values approaching a billion degrees. For a normal ideal gas this raises the pressure, causing the hot gas to expand rapidly. This lowers the density and causes the thermonuclear reactions to slow down. Thus, normal explosions are "self-limiting" because the explosion tends to separate the fuel for the explosion, causing it to stop after a certain point.

Thermonuclear Reactions in Degenerate Gases
In degenerate matter the situation is completely different. Because the pressure does not increase with the temperature, as the temperature approaches a billion degrees the thermonuclear fuel is heated but not separated by the explosion. This causes the reactions to go even faster, because thermonuclear reaction rates increase rapidly with temperature. This is called a thermonuclear runaway, and can lead to gigantic explosions. Thermonuclear ignition under degenerate conditions is thought to be a key component in nova explosions, X-ray bursters, type Ia supernovae, and the helium flash in red giant stars. These are all topics to be addressed in this chapter.

Fermions and Bosons

Subatomic particles may be separated into two broad classes: fermions, which carry a quantum number called spin that takes half-integer values, and bosons, which carry integer spins. Electrons, neutrons, and protons carry spin 1/2 and are examples of fermions, while a photon carries spin 1 and is an example of a boson. Degeneracy pressure is ultimately a result of the Exclusion Principle, which applies only to fermions. This principle requires that no two fermions can have exactly the same set of quantum numbers. In practical terms, this means that in high density fermion gases it is very difficult to force the fermions to be close to each other so the gas resists compression, even at zero temperature.