An Artist’s conception of the evolution of our Sun (left) through the red giant stage (center) and onto a white dwarf (right).
what is a white dwarf star
Our knowledge of white dwarfs began in 1850 with the discovery of a companion to Sirius, called Sirius B. It was 10,000 times fainter than Sirius A, however its mass was 0.98 a solar mass. Since its temperature was measured to be 10,000K, its small mass and faint luminosity did not make sense in the context of the mass-luminosity relation for stars.
The only way it could be both hot and faint was for Sirius B to be very, very small, and so they were called white dwarf stars. White dwarf stars are much smaller than normal stars, such that a white dwarf of the mass of the Sun is only slightly larger than the Earth.
It was soon realized that the gas inside a white dwarf was too dense to behave as an ideal gas and, instead, was degenerate. For normal stars, if you increase the mass, the star gets larger, its radius increases. However, for white dwarfs, the opposite is true, increasing the mass shrinks the star. Notice that at some mass the radius of the star goes to zero.
The size of a star is a balance between pressure and gravity. Gravity pulls the outer layers of the star inward. Pressure pushes those layers upward. In a degenerate gas, increasing the density does not increase the pressure (opposite to a normal gas). But increased density does increase gravity. So, as you add mass to a white dwarf, the gravity increases, but the pressure only changes a small amount. Gravity wins and the star shrinks.
Notice that the mass-radius relation for white dwarfs means you cannot keep adding mass to a star, for eventually its radius goes to zero. This also means the massive stars (with masses greater than 1.4 solar masses) must shed most of their mass as planetary nebula or the final contraction to a white dwarf cannot be stopped by the degenerate electrons. If the mass can not be shed they will become neutron stars or black holes.
White dwarfs are quite common, being found in binary systems and in clusters. Since they are remnants of stars born in the past, their numbers build up in the Galaxy over time. It is only because they are so faint that we fail to detect any except for the very closest ones.
Once a white dwarfs contracts to its final size, it no longer has any nuclear fuel available to burn. However, a white dwarf is still very hot from its past as the core of a star. So, as time passes, the white dwarf cools by radiating its energy outward. Notice that higher mass white dwarfs are small in size, and therefore radiate energy slower than larger, small mass white dwarfs.
Radiative cooling is one way for a white dwarf to cool, another way is neutrino cooling. At very high temperatures, around 30 million degrees K, gamma-rays can pass near electrons and produce a pair of neutrinos. The neutrinos immediately escape from the white dwarf (because they interact very weakly with matter) removing energy.
On the other hand, as a white dwarf cools, the ions can arrange themselves in a organized lattice structure when their temperature falls below a certain point. This is called crystallization and will release energy that delays the cooling time up to 30%.
The cooling process is very slow for white dwarfs. After a billion years the typical white dwarf is down to 0.001 the luminosity of the Sun. But the end result is unstoppable as the white dwarf will eventually give up all its energy and become a solid, crystal black dwarf.