# Degeneracy

In a normal ionized gas, thermal motions of the electrons (which move faster than the ions, and hence collide more frequently) provide the pressure support.

PV=nRT

What happens in the dense core of a star where the pressure gets very large, or in cases where the temperature gets very low? The volume can get very small.

Electrons have a (common-sensical) property: no two identical electrons can be in the same place at the same time. More specifically, no two electrons with the same spin and momentum can be in the same place at the same time. This is a general property of particles called fermions, and is called the Pauli Exclusion Principle.

As you make the ratio T/P very small, the volume decreases but only to the point where the electrons all want to have the same low energy. They can't. This forces electrons to have a minimum amount of momentum, which supplies pressure. Such electrons are said to be in a state of degeneracy. The pressure supplied by these electrons is called Fermi Pressure or degenerate electron pressure.

The radius of a degenerate star is proportional to mass-1/3, which means that more massive degenerate stars are smaller!

Degenerate electrons provide about 25% of the pressure support in the solar core. This increases towards lower masses. Brown dwarfs are entirely supported by degenerate pressure.

The burned-out core of a star supported against gravitational collapse by degenerate electrons is called a white dwarf.

You cannot support a star more massive than 1.4 solar masses by degenerate electron pressure. This is called the Chandrasekhar limit. There are no white dwarfs more massive than this.

Neutrons are also fermions, and can also support a star against gravitational collapse. Such stars are called neutron stars. They are about 2000 times smaller than white dwarfs (the ratio of the mass of the neutron to the mass of the electron), or about 10 kilometers in radius.

Neutron stars can support up to about 2.5 solar masses against gravitational collapse.