Someday the Sun will run out of fuel. According to the projections of astrophysical theory, this will happen in about five billion years, and the Sun will turn into a degenerate dwarf star. Nuclear fusion reactions in the central parts of the Sun supply the energy that keeps the Sun shining. The raw material for these reactions is hydrogen gas. When the hydrogen in the central parts of the Sun is used up, the Sun will have a brief career as a red giant star. During this time the core of the Sun will collapse; a shell of hydrogen gas on the edge of this collapsed core will be compressed and heated by the collapse of the core. Thermonuclear reactions involving the fusion of hydrogen nuclei and helium nuclei will produce a new surge of power in the central regions of the star. The outer layers of the Sun will expand until the Sun has a diameter a hundred times its present value. The oceans will boil and the mountains will melt. Then, in a few hundred million years, the shell of hydrogen gas will be used up, and the Sun will collapse to form a white dwarf star about the size of Earth. When this happens the Sun will be at most a few percent as bright as it now is.
White dwarfs were the first type of collapsed star to be discovered. In the nineteenth century, the German mathematician and astronomer Frederick Bessel concluded from the wobbly motion of the bright star Sirius that it must have a nearby companion star with a mass about equal to that of the Sun. Shortly thereafter an American astronomer, Alvan Clark, found the dim companion to Sirius. It was called Sirius B. Sirius B was found to have a mass about equal to that of the Sun, as expected. However, its luminosity is only about 2 percent that of the Sun. The luminosity of a star depends on its surface temperature and its diameter. The abnormally low luminosity of Sirius B can be explained by assuming that Sirius B has a very low temperature or a very small diameter. The temperature was found to be even higher than that of the Sun; thus, the inescapable conclusion is that Sirius B has a diameter of only about a hundredth of that of the Sun. Because of the white color of the star, it was called a "white dwarf" star. This was an extraordinary discovery. It meant that the same amount of material contained in the Sun is packed into a volume one millionth the size of the Sun. The density of material in Sirius B must be a million times denser than that of ordinary matter. That is, a cubic centimeter of Sirius B matter has the same mass as a small automobile!
How such a state of matter could exist was beyond the understanding of physicists until a new theory of matter, quantum mechanics, was  developed in the 1920s. This theory showed that matter can exist in so-called "degenerate" states of extremely high density.
Even though the degenerate state of matter cannot be produced in a terrestrial laboratory, it is very common in the universe at large. Almost all of the mass of white dwarfs is in the form of degenerate matter, and most stars eventually become white dwarfs, or degenerate dwarfs, as they are also called. It has been estimated that there are a billion or more degenerate dwarfs in our galaxy. Despite their ubiquity, the study of degenerate dwarfs remains a difficult business, because they are so dim. A degenerate dwarf gives off at most a few percent as much optical radiation as does a star such as the Sun; most of them give off much less. X-ray observations have provided an important new method for studying degenerate matter. A few degenerate dwarfs, such as Sirius B, are still sufficiently hot that they give off detectable fluxes of X-rays. On the whole, however, as with neutron stars, the most favorable conditions for observing degenerate dwarfs occur when the degenerate dwarf is accreting matter from a nearby companion star. Sirius A is too far from Sirius B to be an effective source of matter, so this process does not work for Sirius B. However, it does for many other star systems. As a result of the HEAO programs, about 50 degenerate dwarf X-ray sources have been observed.
The details of the X-ray production by an accreting degenerate dwarf depend on several factors, such as the mass of the degenerate dwarf, its rate of rotation, its surface magnetic field, and the rate at which matter is supplied to the star. By disentangling these effects through careful observation and theory, the properties of the star and the physical conditions on the surface of the star can be deduced. For example, the analysis of the HEAO observations of the degenerate dwarf star AM Hercules shows that the mass of the star is about 70 percent that of the Sun, and the radius is about one-hundredth that of the Sun. That is, the star is about the same size as Earth. AM Hercules is apparently locked in synchronous rotation with its companion star. In other words, as AM Hercules orbits around its companion, it always keeps the same face toward it, just as the Moon always keeps the same face toward Earth.
The accreting gas apparently flows in a steady stream from the companion star toward AM Hercules. Near the star it is funneled toward the magnetic pole by the strong magnetic forces there. As the gas is drawn near the surface of the degenerate dwarf, it falls ever faster because of the increasingly strong gravitational forces. Eventually a shock wave is produced, heating the material to very high temperatures, producing an intense source of X-ray emission.
The conditions in X-ray emitting gas around AM Hercules are remarkably similar to those needed to make fusion reactors on Earth work. The temperature is several hundred million degrees in both cases, the density is about the same, and the magnetic field strengths are similar. Of course,  there are important differences. The strength of the gravitational field and the overall size of the heated region are much larger on the degenerate dwarf. Nevertheless, detailed studies of degenerate dwarf X-ray sources should sharpen our understanding of processes that occur in high temperature gases, as well as the degenerate state of matter.
In some degenerate dwarf X-ray sources, the matter apparently falls onto the star erratically, in clumps, producing irregular bursts of X-ray and optical radiation. Regular X-ray pulses have been observed during these outbursts. These pulses could be associated with oscillations in the flow of matter onto the surface of the star, or they could be associated with vibrations of the surface of the star. This last possibility would be particularly exciting. Just as the study of vibrations on Earth produced by earthquakes reveals the interior structure of Earth, so could studies of X-ray pulsations tell us about the interior of white degenerate dwarfs. The studies of the X-ray pulses from degenerate dwarf sources are just beginning, but with the data accumulated by the X-ray "eyes" of the HEAO instruments, we may eventually be able to "see," albeit indirectly, inside a degenerate dwarf.