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White dwarfs

Stellar stability and evolution

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

As a star uses up its nuclear fuel by converting hydrogen near its centre into helium this balance is disturbed and in low mass stars where no other source of energy is available the gravitational contraction wins over the radiation pressure. Thus the centre of the star contracts liberating gravitational energy which heats the gas and provides short term stability.

The lifetime of a star in this hydrogen burning stage is very long (the Sun will last for billions of years before becoming a white dwarf) but 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 box can be filled with electrons each of which has a particular energy but any additional electrons must take higher energies than those already in 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.

In the very hot centre of an evolved star all the atoms have lost their electrons and these then correspond to the example of the electrons in the box which is defined by the gravitational field of the star. 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 the pamphlet on 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, less than that of the Earth! Yet the mass of the companion is equal to that of the Sun which is 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 techniques which either depend on their being companions to other stars or from their being hot stars with large motions relative to the other stars (indicating that they are much nearer than main sequence stars of the same temperature) and from their emission of high energy radiation such as ultraviolet light.

Evolution of white dwarfs

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'.

The presence of white dwarf stars in binary systems has been very important for the understanding of many violent outbursts in stellar systems. Supernovae of Type I, novae and cataclysmic variable stars are all cases where the companion to a white dwarf star has reached a point in its evolution where it is increasing in diameter and losing mass to the white dwarf. The deposition of material into an accretion disk about the white dwarf or on to the white dwarf's surface will determine the nature of any outburst. (See our supernovae fact file.)

The white dwarf Sirius B

The apparently brightest star in the sky, Sirius, was observed by Bessell in 1844 to show a 'wobble' in its movement across the sky. Bessell attributed this to the presence of a companion star but no companion was seen until Alvan Clark, while testing a new telescope, saw a faint companion star. In 1925 the spectrum of the companion confirmed that it was a star with approximately the same temperature as Sirius A.

The binary has a period of 50 years with a maximum separation in the sky of 7.6 arcseconds. The difference in luminosity between Sirius A and B amounts to a factor of more than 8000. The solution of their orbital motion yielded masses of 2.3 and 1 times the mass of the Sun for A and B. Sirius A has a radius of about 1,000,000 km whereas Sirius B has a radius of only 10,000 km.

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