| The Pauli Exclusion Principle in quantum mechanics forbids electrons (and all fermions with half integer spin including neutron) occupying the same state. Basically, each electron must have different energy when they are packed together, as they are in a white dwarf. The number of available low energy states is too small and many electrons are forced into high energy states. When this happens the electrons are said to be degenerate. These high energy electrons make a significant contribution to the pressure. Because this pressure arises from a quantum mechanical effect, it is insensitive to temperature, i.e., the pressure doesn't go down as the star cools. This pressure is known as electron degeneracy pressure and it is the force that supports white dwarf stars against their own gravity. If the star is more massive, the Fermi energy (corresponding to the last-filled |
energy state) goes up and it becomes possible to absorb the electrons into the nucleons, converting protons into neutrons. In this case the Fermi energy reaches to a level above 1 MeV. If the electrons disappear this way, the star collapses suddenly down to a size for which the degeneracy pressure of the neutrons stops the collapse (with quite a shock). Some white dwarfs stay at earth size for a long time as they suck in mass from their surroundings. When they have acquired enough mass, they collapse to form a neutron star and explode as supernova. These are the Type Ia supernovae, which produce nearly same amount of energy. Thus, they have been used to measure the distance of astronomical objects, leading to the discovery of accelerating expansion of the universe. |
For a free fermion gas, the Fermi Energy EF ~ (N/V)2/3, where V is the volume and N is the total number of fermions. Thus the Fermi Energy becomes very high when the fermion gas is compressed into a small volume, i.e., at very high density.