In 1844. F.W.Bessel deduced from the motion of Sirius that it must have an unseen companion. This companion, Sirius B, was dis¬covered in 1862 by A.clark ; it is a tenth-magnitude object, eleven magnitudes fainter than Sirius A. and yet both components have the same surface temperature. The large difference in brightness must therefore be due to a difference in size. This means that Sirius B must be smaller in radius than Sirius A by a factor of about 100. Since Sirius A has a radius of about 106 km, the radius of Sirius B is about 104 km. which is less than the diameter of the Earth. On the other hand, a study of the orbital motion of the two stars indicates that Sinus B has a mass of about 1 M0. We conclude therefore that Sirius B must be a white dwarf

Many more white dwarfs have since been discovered, both as single stars and as members of binary systems. No correlation is found between the radii of white dwarfs and their temperatures, in agreement with our finding that degeneracy pressure is independent of temperature. The radius of a white dwarf is fixed by its mass and by the proportions of the various chemical elements it contains. Once an isolated white dwarf has been formed, it has no alternative but to cool – eventually to very low temperatures – since no nuclear reactions are taking place to replenish its lost heat. Unlike an ordinary star, it does not need energy to provide the pressure required to support it against gravity. Indeed the only white dwarfs we can see are the hotter, more luminous ones. In the Galaxy, there are undoubtedly huge numbers of cool white dwarfs, which we should perhaps call black dwarfs, that are too faint to be visible. Our Sun will eventually become such an object, though, of course, not for another 1010 years or so.

The optical spectra of white dwarfs are varied. Some show absorption lines of hydrogen and others very few, if any, features. The atmospheres of some white dwarfs appear to contain no hydrogen at all. The spectral lines are always broad, due to pressure broadening. A few white dwarfs rotate fast enough for rotational broadening to become important as well. Centrifugal forces become important at high rotation rates and may provide sufficient additional support against gravity to enable some white dwarfs to exceed the Chandrasekhar limit by up to a factor of about two. If the rotation period is much less than 10 seconds, however, these centrifugal forces will rip the star apart. Prom some white dwarfs, polarized light has been detected, indicating surface magnetic fields of up to 104 tesla (108 gauss), about a billion times more than Earth’s field.

Since the mass of a white dwarf cannot exceed about 1.4Mo, single stars less massive than this probably evolve to form white dwarfs. The time they take to do so is 1010 years or longer. From this we can see that unless stars Jose mass during their lifetimes, white dwarfs should only be seen in old stellar systems where such ancient stars have had time to evolve. The fact that white dwarfs are seen in young clusters, such as the Hyades (perhaps 20 million years old), and in binary systems containing young stars (for example Sirius) is proof that mass Joss must occur during the evolution of some stars. In a binary system the mass can be shed by dumping it onto the companion, but if the star is single the mass must be expel led in the form of a wind. Planetary nebulae appear to be new-born white dwarfs which have just expelled a large quantity of material.

Although an isolated white dwarf continues to cool indefinitely. a white dwarf with a eio.se binary companion can remain luminous for much longer. Such an attendant can spill over some of its material to the white dwarf and the energy released when the material crashes onto the surface of the white dwarf corresponds to about 1013Jkg-1. (One kilogram of material therefore releases as much energy as a 100 megawatt power station generates in a day.) This gravitational energy is then radiated by the white dwarf .For example Mira B,the white-dwarf companion to the variable star Mira (o Ceti) appears luminous because it is gathering material from the dense stellar wind emitted by Mira itself

NOVAE are binary systems in which material is being transferred slowly from one star (a low-mass, main-sequence star) to its companion white dwarf. In dwarf novae the accretion takes place onto the white dwarf in sporadic bursts, producing flares at irregular intervals. In novae, the matter appears to accumulate on the white dwarf at a steady rate. The density of the accreted material, once it has settled on the surface, it quite high (more than about 107kgm-3). As more matter accumulates the density rises, and nuclear burning of hydrogen can occur spontaneously. Thus if the transferred material is mostly hydrogen, when a sufficient amount (about 10-4Mo) has accumulated on the surface the hydrogen starts to burn. However, since the burning matter is degenerate, the temperature increase due to the burning does not affect the pressure and so the density initially stays the same. Since a slight increase in temperature yields a large increase in burning, the nuclear reactions run out of control and an explosion results. Such an explosion is thought to be the cause of a nova outburst.

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