Introductory Astronomy: Degenerate Pressure

When atoms are subjected to extremely high temperature and pressure, the atoms are stripped of their electrons. In other words, they become ionized. The pressure of the gas inside of a star is due to the electrons, or the electron pressure. If the density is high, the particles are forced close together. The law of physics put constraints on the motion of the electrons. Electrons are only allowed to exist at certain energy levels, and no two electrons are allowed to exist at the same level (unless they spin in opposite directions). Therefore, in a dense gas, all of the lower energy levels become filled with electrons. This gas is termed degenerate matter. Electrons in this state exert a degenerate electron pressure which resists the force of gravity trying to push them closer together (because if they were pushed closer together, their energy would change and they would have to exist in an energy level that is already filled, which they can't do).

The same thing occurs in neutron stars, but in this case the degenerate pressure is due to neutrons rather than electrons. In neutron stars, the gravitational pressure is higher, high enough to push protons and electrons close enough together that they combine into neutrons. The neutrons are then pushed closer together until gravity is balanced by a degenerate neutron pressure.