White dwarf
A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. These are very dense objects: in an Earth-sized volume, it packs a mass that is comparable to the Sun. A white dwarf radiates light from residual heat, not from nuclear fusion. The nearest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. There are currently thought to be eight white dwarfs among the one hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910. The name white dwarf was coined by Willem Jacob Luyten in 1922.
White dwarfs are thought to be the final evolutionary state of main-sequence stars whose mass is not high enough to become a neutron star or black hole. These stars with masses from about include over 97% of the stars in the Milky Way. The composition of the white dwarf produced will depend on the initial mass of the star. Galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs.
Once formed, the material in a white dwarf no longer undergoes fusion reactions and thus lacks a heat source to support it against gravitational collapse. Instead, it is supported only by electron degeneracy pressure, causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit approximately 1.44 times the mass of the Sun beyond which electron degeneracy pressure cannot support it. A carbon–oxygen white dwarf that approaches this limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as carbon detonation; SN 1006 is a likely example.
A white dwarf, very hot when it forms, gradually cools as it radiates its energy. This radiation, which initially has a high color temperature, lessens and reddens over time. Eventually, a white dwarf will cool enough that its material will begin to crystallize into a cold black dwarf. The oldest known white dwarfs still radiate at temperatures of a few thousand kelvins, which establishes an observational limit on the maximum possible age of the universe.
History
Discovery
The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the relatively bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C. The pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783. In 1910, Henry Norris Russell, Edward Charles Pickering and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white. This star was far out of the normal pattern when Russell first created is now famous luminosity versus spectral type diagram. Publically Russell suggested that the spectral type may not be correct. However the spectral type of 40 Eridani B was independently confirmed in 1914 by Walter Adams. In 1939, Russell looked back on the discovery and noted that Pickering had suggested that such exceptions lead to breakthroughs and in this case it led to the discovery of white dwarfs.The white dwarf companion of Sirius, Sirius B, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius and Procyon were changing their positions periodically. In 1844 he predicted that both stars had unseen companions. Bessel roughly estimated the period of the companion of Sirius to be about half a century; C.A.F. Peters computed an orbit for it in 1851. It was not until 31 January 1862 that Alvan Graham Clark observed a previously unseen star close to Sirius, later identified as the predicted companion. Adams announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius.
In 1917, Adriaan van Maanen discovered van Maanen's Star, an isolated white dwarf. These three white dwarfs, the first discovered, are the so-called classical white dwarfs.
In 1922 Willem Luyten published a series of three papers on faint white stars that had high proper motion, meaning they were low-luminosity white stars close to the Earth. In his third paper he used the term dwarf; the term was later popularized by Arthur Eddington as white dwarf. 18 white dwarfs had been discovered by 1939. Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known, and by 1999, over 2000 were known. Since then the Sloan Digital Sky Survey has found over 9000 white dwarfs, mostly new.
Theory development
White dwarfs were found to be extremely dense soon after their discovery. If a star is in a binary system, as is the case for Sirius B or 40 Eridani B, it is possible to estimate its mass from observations of the binary orbit. This was done for Sirius B by 1910, yielding a mass estimate of, which compares well with a more modern estimate of. Since hotter bodies radiate more energy than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and that from its spectrum. If the star's distance is known, its absolute luminosity can also be estimated. From the absolute luminosity and distance, the star's surface area and its radius can be calculated. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that due to their relatively high temperature and relatively low absolute luminosity, Sirius B and 40 Eridani B must be very dense. When Ernst Öpik estimated the density of visual binary stars in 1916, he found that 40 Eridani B had a density of over times that of the Sun, which was so high that he called it "impossible". As Eddington put it in 1927:We learn about the stars by receiving and interpreting the messages which their light brings to us. The message of the companion of Sirius when it was decoded ran: "I am composed of material 3000 times denser than anything you have ever come across; a ton of my material would be a little nugget that you could put in a matchbox." What reply can one make to such a message? The reply which most of us made in 1914 was—"Shut up. Don't talk nonsense."
Such densities are possible because white dwarf material is not composed of atoms joined by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer than normally allowed by electron orbitals limited by normal matter. Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient. This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles that satisfy the Pauli exclusion principle. At zero temperature, therefore, electrons cannot all occupy the lowest-energy, or ground, state; some of them would have to occupy higher-energy states, forming a band of lowest-available energy states, the Fermi sea. This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy.
Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure. This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases.
The existence of a limiting mass that no white dwarf can exceed without collapsing to a neutron star is another consequence of being supported by electron degeneracy pressure. Such limiting masses were calculated for cases of an idealized, constant density star in 1929 by Wilhelm Anderson and in 1930 by Edmund C. Stoner. This value was corrected by considering hydrostatic equilibrium for the density profile, and the presently known value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar in his paper "The Maximum Mass of Ideal White Dwarfs". For a non-rotating white dwarf, it is equal to approximately, where is the average molecular weight per electron of the star.
As the carbon-12 and oxygen-16 that predominantly compose a carbon–oxygen white dwarf both have atomic numbers equal to half their atomic weight, one should take equal to 2 for such a star, leading to the commonly quoted value of. Together with William Alfred Fowler, Chandrasekhar received the Nobel Prize for this and other work in 1983. The limiting mass is now called the Chandrasekhar limit.
Composition and structure
Although white dwarfs are known with estimated masses as low as and as high as, the mass distribution is strongly peaked at, and the majority lie between. The estimated radii of observed white dwarfs are typically 0.8–2% the radius of the Sun; this is comparable to the Earth's radius of approximately 0.9% solar radius. A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically one millionth of the Sun's; the average density of matter in a white dwarf must therefore be, very roughly, times greater than the average density of the Sun, or approximately, or 1 tonne per cubic centimetre. A typical white dwarf has a density of between 104 and. White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact stars such as neutron stars and the hypothetical quark stars.| Material | Density | Notes |
| Water | 1000 | At STP |
| Osmium | Near room temperature | |
| The core of the Sun | ||
| White dwarf | ||
| Atomic nuclei | Does not depend strongly on size of nucleus | |
| Neutron star core | – |
At these densities the nuclei within the star are much closer than nuclei in ordinary matter. Two nuclei in a white dwarf are separated by about, substantially less than a Bohr radius,, the rough size of a hydrogen atom. The white dwarf matter is pressure ionized: there is no room for bound electron orbitals. Rather than a gas of atoms as in star like the Sun, the gas-like aspect inside of a white dwarf is solely due to the free electrons.
The pressure at the center of a white dwarf will be on the order of 1.5 million times the pressure in the center of the Sun. The central temperature will exceed 10 million degrees K. While these conditions would fuse hydrogen the low luminosity of white dwarf stars implies the necessary nuclei are not present.