# White dwarfs

We know the Sun is destined to become a white dwarf but what is that and what happens next?

Main sequence stars, like the Sun, represent a balance between the force of gravity, which is trying to compress the star, and radiation pressure from burning hydrogen, which is trying to make the star expand. In almost all stars these two forces are in perfect balance throughout the star.

Eventually all the hydrogen in its interior will be used up and no further source of energy production will be available. Gravity will then win and the star will contract to a small size.

## Electron degeneracy

If the mass of the star is less than a critical value, called the Chandresekhar limit, after its discoverer, then this contraction to small size is halted by a quantum mechanical effect called degeneracy.

Quantum mechanics shows that if we put electrons inside a box with fixed dimensions then the electrons can only take up a set of defined states each of which is different from that of any other electron. These states are defined by the size of the box. The limit of how many electrons can be added is reached when the momentum of the last electron corresponds to its moving at the speed of light.

The size of the box and the number of electrons are both governed by the mass of the star and the critical value of 1.44 times the mass of the Sun is the most that the mass of a white dwarf can be. If the mass is greater than this the pressure developed by the electronic degeneracy is insufficient to prevent gravitational collapse to a neutron star (see Pulsars).

Observations of white dwarfs

The first white dwarf star to be found was the companion to the bright star Sirius. Sirius and its companion are in mutual orbit about each other and this allows the mass of each to be found. From the brightness of the companion and its temperature we can determine its size which is about 10,000km in diameter – much less than that of the Earth. Yet the mass of the companion is equal to that of the Sun (more than 300,000 times that of the Earth).

White dwarfs are intrinsically very faint and are thus hard to detect. Despite this they are the end state for all medium mass stars and we thus expect that there are very many white dwarfs. Astronomers have succeeded in finding many using a variety of techniques.

## Black takes white

The degenerate pressure in white dwarfs depends only on the star's mass and not on its temperature so that they are stable. Some energy resides in the nuclear particles which are present together with the electrons. The heat associated with the nuclear particles will gradually be radiated away and the stars will gradually cool over some billions of years. At the end of this process the remnant star will cease to emit radiation and will become a 'black dwarf'.