White dwarf

For other uses, see White dwarf (disambiguation).

Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius B, which is a white dwarf, can be seen as a faint pinprick of light to the lower left of the much brighter Sirius A.

Artist's concept of white dwarf aging.

A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth. Its faint luminosity comes from the emission of stored thermal energy.^[1] In January 2009, the Research Consortium on Nearby Stars project counted eight white dwarfs among the hundred star systems nearest the Sun.^[2] The unusual faintness of white dwarfs was first recognized in 1910 by Henry Norris Russell, Edward Charles Pickering, and Williamina Fleming;^{[3], p. 1} the name white dwarf was coined by Willem Luyten in 1922.^[4]

White dwarfs are thought to be the final evolutionary state of all stars whose mass is not high enough to become a neutron star—over 97% of the stars in our galaxy.^{[5], §1.} After the hydrogen–fusing lifetime of a main-sequence star of low or medium mass ends, it will expand to a red giant which fuses helium to carbon and oxygen in its core by the triple-alpha process. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon, around 1 billion K, an inert mass of carbon and oxygen will build up at its center. After shedding its outer layers to form a planetary nebula, it will leave behind this core, which forms the remnant white dwarf.^[6] Usually, therefore, white dwarfs are composed of carbon and oxygen. If the mass of the progenitor is above 8 solar masses but below 10.5 solar masses,the core temperature suffices to fuse carbon but not neon, in which case an oxygen-neon–magnesium white dwarf may be formed.^[7] Also, some helium white dwarfs^[8][9] appear to have been formed by mass loss in binary systems.

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported by the heat generated by fusion against gravitational collapse. 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 1.4 solar masses—beyond which it cannot be supported by electron degeneracy pressure. A carbon-oxygen white dwarf that approaches this mass limit, typically by mass transfer from a companion star, may explode as a Type Ia supernova via a process known as carbon detonation.^[1][6] (SN 1006 is thought to be a famous example.)

A white dwarf is very hot when it is formed, but since it has no source of energy, it will gradually radiate away its energy and cool down. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool to temperatures at which it will no longer emit significant heat or light, and it will become a cold black dwarf.^[6] However, since no white dwarf can be older than the age of the Universe (approximately 13.7 billion years),^[10] even the oldest white dwarfs still radiate at temperatures of a few thousand kelvins, and no black dwarfs are thought to exist yet.^[1][5]

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 Friedrich Wilhelm Herschel on January 31, 1783;^{[11], p. 73} it was again observed by Friedrich Georg Wilhelm Struve in 1825 and by Otto Wilhelm von Struve in 1851.^[12][13] 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.^[4] In 1939, Russell looked back on the discovery:^{[3], p. 1}

I was visiting my friend and generous benefactor, Prof. Edward C. Pickering. With characteristic kindness, he had volunteered to have the spectra observed for all the stars—including comparison stars—which had been observed in the observations for stellar parallax which Hinks and I made at Cambridge, and I discussed. This piece of apparently routine work proved very fruitful—it led to the discovery that all the stars of very faint absolute magnitude were of spectral class M. In conversation on this subject (as I recall it), I asked Pickering about certain other faint stars, not on my list, mentioning in particular 40 Eridani B. Characteristically, he sent a note to the Observatory office and before long the answer came (I think from Mrs Fleming) that the spectrum of this star was A. I knew enough about it, even in these paleozoic days, to realize at once that there was an extreme inconsistency between what we would then have called "possible" values of the surface brightness and density. I must have shown that I was not only puzzled but crestfallen, at this exception to what looked like a very pretty rule of stellar characteristics; but Pickering smiled upon me, and said: "It is just these exceptions that lead to an advance in our knowledge", and so the white dwarfs entered the realm of study!

The spectral type of 40 Eridani B was officially described in 1914 by Walter Adams.^[14]

The 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 (α Canis Majoris) and Procyon (α Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions:^[15]

If we were to regard Sirius and Procyon as double stars, the change of their motions would not surprise us; we should acknowledge them as necessary, and have only to investigate their amount by observation. But light is no real property of mass. The existence of numberless visible stars can prove nothing against the existence of numberless invisible ones.

Bessel roughly estimated the period of the companion of Sirius to be about half a century;^[15] C. A. F. Peters computed an orbit for it in 1851.^[16] It was not until January 31, 1862 that Alvan Graham Clark observed a previously unseen star close to Sirius, later identified as the predicted companion.^[16] Walter Adams announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius.^[17]

In 1917, Adriaan Van Maanen discovered Van Maanen's Star, an isolated white dwarf.^[18] These three white dwarfs, the first discovered, are the so-called classical white dwarfs.^{[3], p. 2} Eventually, many faint white stars were found which had high proper motion, indicating that they could be suspected to be low-luminosity stars close to the Earth, and hence white dwarfs. Willem Luyten appears to have been the first to use the term white dwarf when he examined this class of stars in 1922;^{[4][19][20][21][22]} the term was later popularized by Arthur Stanley Eddington.^[4][23] Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18 white dwarfs had been discovered by 1939.^{[3], p. 3} Luyten and others continued to search for white dwarfs in the 1940s. By 1950, over a hundred were known,^[24] and by 1999, over 2,000 were known.^[25] Since then the Sloan Digital Sky Survey has found over 9,000 white dwarfs, mostly new.^[26]

Composition and structure

Hertzsprung–Russell Diagram

Spectral Type

Brown dwarfs

White dwarfs

Red dwarfs

Subdwarfs

Main sequence
("dwarfs")

Subgiants

Giants

Bright Giants

Supergiants

Hypergiants

absolute

magni-

tude

(M_V)

Although white dwarfs are known with estimated masses as low as 0.17^[27] and as high as 1.33^[28] solar masses, the mass distribution is strongly peaked at 0.6 solar mass, and the majority lie between 0.5 to 0.7 solar mass.^[28] The estimated radii of observed white dwarfs, however, are typically between 0.008 and 0.02 times the radius of the Sun;^[29] this is comparable to the Earth's radius of approximately 0.009 solar radius. A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically a million times smaller than the Sun's; the average density of matter in a white dwarf must therefore be, very roughly, 1,000,000 times greater than the average density of the Sun, or approximately 10⁶ grams (1 tonne) per cubic centimeter.^[1] White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact stars such as neutron stars, black holes and, hypothetically, quark stars.^[30]

Material	Density in kg/m3	Notes
Water (fresh)	1,000	At STP
Osmium	22,610	Near room temperature
The core of the Sun	~150,000
White dwarf star	1 × 109[1]
Atomic nuclei	2.3 × 1017[31]	Does not depend strongly on size of nucleus
Neutron star core	8.4 × 1016 − 1 × 1018
Black hole	2 × 1030[32]	Critical density of an Earth-mass black hole

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 and 40 Eridani B, it is possible to estimate its mass from observations of the binary orbit. This was done for Sirius B by 1910,^[33] yielding a mass estimate of 0.94 solar mass. (A more modern estimate is 1.00 solar mass.)^[34] Since hotter bodies radiate more than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and hence from its spectrum. If the star's distance is known, its overall luminosity can also be estimated. Comparison of the two figures yields the star's radius. Reasoning of this sort led to the realization, puzzling to astronomers at the time, that Sirius B and 40 Eridani B must be very dense. For example, when Ernst Öpik estimated the density of a number of visual binary stars in 1916, he found that 40 Eridani B had a density of over 25,000 times the Sun's, which was so high that he called it "impossible".^[35] As Arthur Stanley Eddington put it later in 1927:^{[36], p. 50}

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 3,000 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."

As Eddington pointed out in 1924, densities of this order implied that, according to the theory of general relativity, the light from Sirius B should be gravitationally redshifted.^[23] This was confirmed when Adams measured this redshift in 1925.^[37]

Such densities are possible because white dwarf material is not composed of atoms bound by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer to each other than electron orbitals—the regions occupied by electrons bound to an atom—would normally allow.^[23] Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present.^[38] 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 which satisfy the Pauli exclusion principle.^[39] At zero temperature, therefore, electrons could not all occupy the lowest-energy, or ground, state; some of them had 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. Another way of deriving this result is by use of the uncertainty principle: the high density of electrons in a white dwarf means that their positions are relatively localized, creating a corresponding uncertainty in their momenta. This means that some electrons must have high momentum and hence high kinetic energy.^[38][40]

Compression of a white dwarf will increase the number of electrons in a given volume. Applying either the Pauli exclusion principle or the uncertainty principle, we can see that this will increase the kinetic energy of the electrons, causing pressure.^[38][41] This electron degeneracy pressure is what supports a white dwarf against gravitational collapse. It 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 so much greater than that of a low-mass white dwarf that the radius of a white dwarf decreases as its mass increases.^[1]

The existence of a limiting mass that no white dwarf can exceed is another consequence of being supported by electron degeneracy pressure. These masses were first published in 1929 by Wilhelm Anderson^[42] and in 1930 by Edmund C. Stoner.^[43] The modern value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar in his paper "The Maximum Mass of Ideal White Dwarfs".^[44] For a nonrotating white dwarf, it is equal to approximately 5.7/μ_e² solar masses, where μ_e is the average molecular weight per electron of the star.^{[45], eq. (63)} As the carbon-12 and oxygen-16 which predominantly compose a carbon-oxygen white dwarf both have atomic number equal to half their atomic weight, one should take μ_e equal to 2 for such a star,^[40] leading to the commonly quoted value of 1.4 solar masses. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,^{[43], p. 955} so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, μ_e, equal to 2.5, giving a limit of 0.91 solar mass.) Together with William Alfred Fowler, Chandrasekhar received the Nobel prize for this and other work in 1983.^[46] The limiting mass is now called the Chandrasekhar limit.

If a white dwarf were to exceed the Chandrasekhar limit, and nuclear reactions did not take place, the pressure exerted by electrons would no longer be able to balance the force of gravity, and it would collapse into a denser object such as a neutron star.^[47] However, carbon-oxygen white dwarfs accreting mass from a neighboring star undergo a runaway nuclear fusion reaction, which leads to a Type Ia supernova explosion in which the white dwarf is destroyed, just before reaching the limiting mass.^[48]

New research indicates that many white dwarfs—at least in certain types of galaxies—may not approach that limit by way of accretion. In a paper published in the journal Nature in February 2010, astronomers Marat Gilfanov and Akos Bogdan, both of the Max Planck Institute for Astrophysics in Garching, Germany, postulated that at least some of the white dwarfs that become supernovae attain the necessary mass not by accretion but by colliding with one another. Gilfanov and Bogdan said that in elliptical galaxies such collisions are the major source of supernovae. Their hypothesis is based on the fact that the x-rays produced by the white dwarfs' accretion of matter—measured using NASA's Chandra X-Ray Observatory—are no more than 1/30th to 1/50th of what would be expected to be produced by an amount of matter falling into a white dwarf sufficient to produce enough mass to cause the star to go supernova. In other words, at least in some circumstances, accretion simply does not add enough matter to cause a white dwarf to approach the Chandrasekhar limit, and the two astronomers concluded that no more than 5 percent of the supernovae in such galaxies could be created by the process of accretion to white dwarfs. The significance of this finding is that there could be two types of supernovae, which could mean that the Chandrasekhar limit might not always apply in determining when a white dwarf goes supernova, given that two colliding white dwarfs could have a range of masses. This in turn would confuse efforts to use exploding white dwarfs as standard measurements in determining the nature of the universe.^[49]

White dwarfs have low luminosity and therefore occupy a strip at the bottom of the Hertzsprung-Russell diagram, a graph of stellar luminosity versus color (or temperature). They should not be confused with low-luminosity objects at the low-mass end of the main sequence, such as the hydrogen–fusing red dwarfs, whose cores are supported in part by thermal pressure,^[50] or the even lower-temperature brown dwarfs.^[51]

Mass-radius relationship and mass limit

It is simple to derive a rough relationship between the mass and radii of white dwarfs using an energy minimization argument. The energy of the white dwarf can be approximated by taking it to be the sum of its gravitational potential energy and kinetic energy. The gravitational potential energy of a unit mass piece of white dwarf, E_g, will be on the order of −GM/R, where G is the gravitational constant, M is the mass of the white dwarf, and R is its radius. The kinetic energy of the unit mass, E_k, will primarily come from the motion of electrons, so it will be approximately N p²/2m, where p is the average electron momentum, m is the electron mass, and N is the number of electrons per unit mass. Since the electrons are degenerate, we can estimate p to be on the order of the uncertainty in momentum, Δp, given by the uncertainty principle, which says that Δp Δx is on the order of the reduced Planck constant, ħ. Δx will be on the order of the average distance between electrons, which will be approximately n^−1/3, i.e., the reciprocal of the cube root of the number density, n, of electrons per unit volume. Since there are N M electrons in the white dwarf and its volume is on the order of R³, n will be on the order of N M / R³.^[40]

Solving for the kinetic energy per unit mass, E_k, we find that

$E_k \approx \frac{N (\Delta p)^2}{2m} \approx \frac{N \hbar^2 n^{2/3}}{2m} \approx \frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.$

The white dwarf will be at equilibrium when its total energy, E_g + E_k, is minimized. At this point, the kinetic and gravitational potential energies should be comparable, so we may derive a rough mass-radius relationship by equating their magnitudes:

$|E_g|\approx\frac{GM}{R} = E_k\approx\frac{M^{2/3} N^{5/3} \hbar^2}{2m R^2}.$

Solving this for the radius, R, gives^[40]

$R \approx \frac{N^{5/3} \hbar^2}{2m GM^{1/3}}.$

Dropping N, which depends only on the composition of the white dwarf, and the universal constants leaves us with a relationship between mass and radius:

$R \sim \frac{1}{M^{1/3}}, \,$

i.e., the radius of a white dwarf is inversely proportional to the cube root of its mass.

Since this analysis uses the non-relativistic formula p²/2m for the kinetic energy, it is non-relativistic. If we wish to analyze the situation where the electron velocity in a white dwarf is close to the speed of light, c, we should replace p²/2m by the extreme relativistic approximation p c for the kinetic energy. With this substitution, we find

$E_{k\ {\rm relativistic}} \approx \frac{M^{1/3} N^{4/3} \hbar c}{R}.$

If we equate this to the magnitude of E_g, we find that R drops out and the mass, M, is forced to be^[40]

$M_{\rm limit} \approx N^2 \left(\frac{\hbar c}{G}\right)^{3/2}.$

Radius–mass relations for a model white dwarf.

To interpret this result, observe that as we add mass to a white dwarf, its radius will decrease, so, by the uncertainty principle, the momentum, and hence the velocity, of its electrons will increase. As this velocity approaches c, the extreme relativistic analysis becomes more exact, meaning that the mass M of the white dwarf must approach M_limit. Therefore, no white dwarf can be heavier than the limiting mass M_limit, or 1.4 Solar masses.

For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state which describes the relationship between density and pressure in the white dwarf material. If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the hydrostatic equation together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium. In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass.^{[45], eq. (80)} Relativistic corrections will alter the result so that the radius becomes zero at a finite value of the mass. This is the limiting value of the mass—called the Chandrasekhar limit—at which the white dwarf can no longer be supported by electron degeneracy pressure. The graph on the right shows the result of such a computation. It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf. Both models treat the white dwarf as a cold Fermi gas in hydrostatic equilibrium. The average molecular weight per electron, μ_e, has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses.^[45][52]

These computations all assume that the white dwarf is non-rotating. If the white dwarf is rotating, the equation of hydrostatic equilibrium must be modified to take into account the centrifugal pseudo-force arising from working in a rotating frame.^[53] For a uniformly rotating white dwarf, the limiting mass increases only slightly. However, if the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle in 1947,^[54] there is no limit to the mass for which it is possible for a model white dwarf to be in static equilibrium. Not all of these model stars, however, will be dynamically stable.^[55]

Radiation and cooling

The degenerate matter that makes up the bulk of a white dwarf has a very low opacity, because any absorption of a photon requires an electron transition to a higher empty state, which may not be available given the energy of the photon; it also has a high thermal conductivity. As a result, the interior of the white dwarf maintains a constant temperature, approximately 10⁷ K. However, an outer shell of non-degenerate matter cools from approximately 10⁷ K to 10⁴ K. This matter radiates roughly as a black body to determine the visible color of the white dwarf. A white dwarf remains visible for a long time, because it radiates as a roughly 10⁴ K body, while its interior is at 10⁷ K.^[56]

The visible radiation emitted by white dwarfs varies over a wide color range, from the blue-white color of an O-type main sequence star to the red of a M-type red dwarf.^[57] White dwarf effective surface temperatures extend from over 150,000 K^[25] to barely under 4,000 K.^[58][59] In accordance with the Stefan-Boltzmann law, luminosity increases with increasing surface temperature; this surface temperature range corresponds to a luminosity from over 100 times the Sun's to under 1/10,000th that of the Sun's.^[59] Hot white dwarfs, with surface temperatures in excess of 30,000 K, have been observed to be sources of soft (i.e., lower-energy) X-rays. This enables the composition and structure of their atmospheres to be studied by soft X-ray and extreme ultraviolet observations.^[60]

A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.

As was explained by Leon Mestel in 1952, unless the white dwarf accretes matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished.^{[61][62], §2.1.} White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time.^[6] As a white dwarf cools, its surface temperature decreases, the radiation which it emits reddens, and its luminosity decreases. Since the white dwarf has no energy sink other than radiation, it follows that its cooling slows with time. Pierre Bergeron, Maria Tereza Ruiz, and Sandy Leggett, for example, estimate that after a carbon white dwarf of 0.59 solar mass with a hydrogen atmosphere has cooled to a surface temperature of 7,140 K, taking approximately 1.5 billion years, cooling approximately 500 more kelvins to 6,590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6,030 K and 5,550 K) take first 0.4 and then 1.1 billion years.^{[63], Table 2.} Although white dwarf material is initially plasma—a fluid composed of nuclei and electrons—it was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize, starting at the center of the star.^[64] The crystal structure is thought to be a body-centered cubic lattice.^[5][65] In 1995 it was pointed out that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory,^[66] and in 2004, Antonio Kanaan, Travis Metcalfe and a team of researchers with the Whole Earth Telescope estimated, on the basis of such observations, that approximately 90% of the mass of BPM 37093 had crystallized.^[64][67][68] Other work gives a crystallized mass fraction of between 32% and 82%.^[69]

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K.^[26][70] A white dwarf, though, spends more of its lifetime at cooler temperatures than at hotter temperatures, so we should expect that there are more cool white dwarfs than hot white dwarfs. Once we adjust for the selection effect that hotter, more luminous white dwarfs are easier to observe, we do find that decreasing the temperature range examined results in finding more white dwarfs.^[71] This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K,^[72] and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,900 K.^[58] The reason for this is that, as the Universe's age is finite,^[73][74] there has not been time for white dwarfs to cool down below this temperature. The white dwarf luminosity function can therefore be used to find the time when stars started to form in a region; an estimate for the age of the Galactic disk found in this way is 8 billion years.^[71]

A white dwarf will eventually, in many trillion years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. However, no black dwarfs are thought to exist yet.^[1]

Atmosphere and spectra

Although most white dwarfs are thought to be composed of carbon and oxygen, spectroscopy typically shows that their emitted light comes from an atmosphere which is observed to be either hydrogen-dominated or helium-dominated. The dominant element is usually at least 1,000 times more abundant than all other elements. As explained by Schatzman in the 1940s, the high surface gravity is thought to cause this purity by gravitationally separating the atmosphere so that heavy elements are on the bottom and lighter ones on top.^{[75][76], §5–6} This atmosphere, the only part of the white dwarf visible to us, is thought to be the top of an envelope which is a residue of the star's envelope in the AGB phase and may also contain material accreted from the interstellar medium. The envelope is believed to consist of a helium-rich layer with mass no more than 1/100th of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1/10,000th of the stars total mass.^{[59][77], §4–5.}

Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore almost isothermal, and it is also hot: a white dwarf with surface temperature between 8,000 K and 16,000 K will have a core temperature between approximately 5,000,000 K and 20,000,000 K. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.^[59]

White dwarf spectral types^[25]

Primary and secondary features
A	H lines present; no He I or metal lines
B	He I lines; no H or metal lines
C	Continuous spectrum; no lines
O	He II lines, accompanied by He I or H lines
Z	Metal lines; no H or He I lines
Q	Carbon lines present
X	Unclear or unclassifiable spectrum
Secondary features only
P	Magnetic white dwarf with detectable polarization
H	Magnetic white dwarf without detectable polarization
E	Emission lines present
V	Variable

The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941,^[57][78] and various classification schemes have been proposed and used since then.^[79][80] The system currently in use was introduced by Edward M. Sion, Jesse L. Greenstein and their coauthors in 1983 and has been subsequently revised several times. It classifies a spectrum by a symbol which consists of an initial D, a letter describing the primary feature of the spectrum followed by an optional sequence of letters describing secondary features of the spectrum (as shown in the table to the right), and a temperature index number, computed by dividing 50,400 K by the effective temperature. For example:

• A white dwarf with only He I lines in its spectrum and an effective temperature of 15,000 K could be given the classification of DB3, or, if warranted by the precision of the temperature measurement, DB3.5.
• A white dwarf with a polarized magnetic field, an effective temperature of 17,000 K, and a spectrum dominated by He I lines which also had hydrogen features could be given the classification of DBAP3.

The symbols ? and : may also be used if the correct classification is uncertain.^[25][57]

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately 80%) of all observed white dwarfs.^[59] The next class in number is of DBs (approximately 16%).^[81] A small fraction (roughly 0.1%) have carbon-dominated atmospheres, the hot (above 15,000 K) DQ class.^[82] Those classified as DB, DC, DO, DZ, and cool DQ have helium-dominated atmospheres. Assuming that carbon and metals are not present, which spectral classification is seen depends on the effective temperature. Between approximately 100,000 K to 45,000 K, the spectrum will be classified DO, dominated by singly ionized helium. From 30,000 K to 12,000 K, the spectrum will be DB, showing neutral helium lines, and below about 12,000 K, the spectrum will be featureless and classified DC.^{[77],§ 2.4}.^[59]

Magnetic field

Magnetic fields in white dwarfs with a strength at the surface of ~1 million gauss (100 teslas) were predicted by P. M. S. Blackett in 1947 as a consequence of a physical law he had proposed which stated that an uncharged, rotating body should generate a magnetic field proportional to its angular momentum.^[83] This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted.^{[84], pp. 39–43} In the 1960s, it was proposed that white dwarfs might have magnetic fields because of conservation of total surface magnetic flux during the evolution of a non-degenerate star to a white dwarf. A surface magnetic field of ~100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of ~100·100²=1 million gauss (100 T) once the star's radius had shrunk by a factor of 100.^{[76], §8;[85], p. 484} The first magnetic white dwarf to be observed was GJ 742, which was detected to have a magnetic field in 1970 by its emission of circularly polarized light.^[86] It is thought to have a surface field of approximately 300 million gauss (30 kT).^{[76], §8} Since then magnetic fields have been discovered in well over 100 white dwarfs, ranging from 2×10³ to 10⁹ gauss (0.2 T to 100 kT). Only a small number of white dwarfs have been examined for fields, and it has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).^[87][88]

Variability

Main article: Pulsating white dwarf

See also: Cataclysmic variables

DAV (GCVS: ZZA)	DA spectral type, having only hydrogen absorption lines in its spectrum
DBV (GCVS: ZZB)	DB spectral type, having only helium absorption lines in its spectrum
GW Vir (GCVS: ZZO)	Atmosphere mostly C, He and O; may be divided into DOV and PNNV stars
Types of pulsating white dwarf[89][90], §1.1, 1.2.

Early calculations suggested that there might be white dwarfs whose luminosity varied with a period of around 10 seconds, but searches in the 1960s failed to observe this.^{[76], § 7.1.1;[91]} The first variable white dwarf found was HL Tau 76; in 1965 and 1966, Arlo U. Landolt observed it to vary with a period of approximately 12.5 minutes.^[92] The reason for this period being longer than predicted is that the variability of HL Tau 76, like that of the other pulsating variable white dwarfs known, arises from non-radial gravity wave pulsations.^{[76], § 7.} Known types of pulsating white dwarf include the DAV, or ZZ Ceti, stars, including HL Tau 76, with hydrogen-dominated atmospheres and the spectral type DA;^{[76], pp. 891, 895} DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;^{[59], p. 3525} and GW Vir stars (sometimes subdivided into DOV and PNNV stars), with atmospheres dominated by helium, carbon, and oxygen.^{[90],§1.1, 1.2;[93],§1.} GW Vir stars are not, strictly speaking, white dwarfs, but are stars which are in a position on the Hertzsprung-Russell diagram between the asymptotic giant branch and the white dwarf region. They may be called pre-white dwarfs.^{[90], § 1.1;[94]} These variables all exhibit small (1%–30%) variations in light output, arising from a superposition of vibrational modes with periods of hundreds to thousands of seconds. Observation of these variations gives asteroseismological evidence about the interiors of white dwarfs.^[95]

Formation

White dwarfs are thought to represent the end point of stellar evolution for main-sequence stars with masses from about 0.07 to 10 solar masses.^[5][96] The composition of the white dwarf produced will differ depending on the initial mass of the star.

Stars with very low mass

If the mass of a main-sequence star is lower than approximately half a solar mass, it will never become hot enough to fuse helium at its core. It is thought that, over a lifespan exceeding the age (~13.7 billion years)^[10] of the Universe, such a star will eventually burn all its hydrogen and end its evolution as a helium white dwarf composed chiefly of helium-4 nuclei.^[97] Owing to the time this process takes, it is not thought to be the origin of observed helium white dwarfs. Rather, they are thought to be the product of mass loss in binary systems^{[6][8][9][98][99][100]} or mass loss due to a large planetary companion.^[101][102]

Stars with low to medium mass

If the mass of a main-sequence star is between approximately 0.5 and 8 solar masses, its core will become sufficiently hot to fuse helium into carbon and oxygen via the triple-alpha process, but it will never become sufficiently hot to fuse carbon into neon. Near the end of the period in which it undergoes fusion reactions, such a star will have a carbon-oxygen core which does not undergo fusion reactions, surrounded by an inner helium-burning shell and an outer hydrogen-burning shell. On the Hertzsprung-Russell diagram, it will be found on the asymptotic giant branch. It will then expel most of its outer material, creating a planetary nebula, until only the carbon-oxygen core is left. This process is responsible for the carbon-oxygen white dwarfs which form the vast majority of observed white dwarfs.^{[98][103][104]}

Stars with medium to high mass

If a star is massive enough, its core will eventually become sufficiently hot to fuse carbon to neon, and then to fuse neon to iron. Such a star will not become a white dwarf, because the mass of its central, non-fusing core, supported by electron degeneracy pressure, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will collapse and it will explode in a core-collapse supernova which will leave behind a remnant neutron star, black hole, or possibly a more exotic form of compact star.^[96][105] Some main-sequence stars, of perhaps 8 to 10 solar masses, although sufficiently massive to fuse carbon to neon and magnesium, may be insufficiently massive to fuse neon. Such a star may leave a remnant white dwarf composed chiefly of oxygen, neon, and magnesium, provided that its core does not collapse, and provided that fusion does not proceed so violently as to blow apart the star in a supernova.^[106][107] Although some isolated white dwarfs have been identified which may be of this type, most evidence for the existence of such stars comes from the novae called ONeMg or neon novae. The spectra of these novae exhibit abundances of neon, magnesium, and other intermediate-mass elements which appear to be only explicable by the accretion of material onto an oxygen-neon-magnesium white dwarf.^{[7][108][109]}

Fate

A white dwarf is stable once formed and will continue to cool almost indefinitely; eventually, it will become a black white dwarf, also called a black dwarf. Assuming that the Universe continues to expand, it is thought that in 10¹⁹ to 10²⁰ years, the galaxies will evaporate as their stars escape into intergalactic space.^{[110], §IIIA.} White dwarfs should generally survive this, although an occasional collision between white dwarfs may produce a new fusing star or a super-Chandrasekhar mass white dwarf which will explode in a type Ia supernova.^{[110], §IIIC, IV.} The subsequent lifetime of white dwarfs is thought to be on the order of the lifetime of the proton, known to be at least 10³² years. Some simple grand unified theories predict a proton lifetime of no more than 10⁴⁹ years. If these theories are not valid, the proton may decay by more complicated nuclear processes, or by quantum gravitational processes involving a virtual black hole; in these cases, the lifetime is estimated to be no more than 10²⁰⁰ years. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei decay, until it loses enough mass to become a nondegenerate lump of matter, and finally disappears completely.^{[110], §IV.}

Stellar system

The merger process of two co-orbiting white dwarfs produces gravitational waves

A white dwarf's stellar and planetary system is inherited from its progenitor star and may interact with the white dwarf in various ways. Infrared spectroscopic observations made by NASA's Spitzer Space Telescope of the central star of the Helix Nebula suggest the presence of a dust cloud, which may be caused by cometary collisions. It is possible that infalling material from this may cause X-ray emission from the central star.^[111][112] Similarly, observations made in 2004 indicated the presence of a dust cloud around the young white dwarf star G29-38 (estimated to have formed from its AGB progenitor about 500 million years ago), which may have been created by tidal disruption of a comet passing close to the white dwarf.^[113]

If a white dwarf is in a binary star system and is accreting matter from its companion, a variety of phenomena may occur, including novae and Type Ia supernovae. It may also be a super-soft x-ray source if it is able to take material from its companion fast enough to sustain fusion on its surface.^[114] A close binary system of two white dwarfs can radiate energy in the form of gravitational waves, causing their mutual orbit to steadily shrink until the stars merge.^[115][116]

Type Ia supernovae

Composite image of SN 1572 or Tycho's Nova, the remnant of a Type Ia supernova.

Main article: Type Ia supernova

The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~1.4 solar masses. (This limit may increase if the white dwarf is rotating rapidly and nonuniformly.)^[117] White dwarfs in binary systems, however, can accrete material from a companion star, increasing both their mass and their density. As their mass approaches the Chandrasekhar limit, this could theoretically lead to either the explosive ignition of fusion in the white dwarf or its collapse into a neutron star.^[47]

Accretion provides the currently favored mechanism, the single-degenerate model, for type Ia supernovae. In this model, a carbon–oxygen white dwarf accretes material from a companion star,^{[48], p. 14.} increasing its mass and compressing its core. It is believed that compressional heating of the core leads to ignition of carbon fusion as the mass approaches the Chandrasekhar limit.^[48] Because the white dwarf is supported against gravity by quantum degeneracy pressure instead of by thermal pressure, adding heat to the star's interior increases its temperature but not its pressure, so the white dwarf does not expand and cool in response. Rather, the increased temperature accelerates the rate of the fusion reaction, in a runaway process that feeds on itself. The thermonuclear flame consumes much of the white dwarf in a few seconds, causing a type Ia supernova explosion that obliterates the star.^[1][48][118] In another possible mechanism for type Ia supernovae, the double-degenerate model, two carbon-oxygen white dwarfs in a binary system merge, creating an object with mass greater than the Chandrasekhar limit in which carbon fusion is then ignited.^{[48], p. 14.}

Observations have failed to note signs of accretion leading up to type Ia supernovae, and this is now thought to be because the star is first loaded up to above the Chandrasekhar limit while also being spun up to a very fast rate by the same process. Once the accretion stops the star gradually slows down until the spin is no longer fast enough to prevent the explosion.^[119]

Cataclysmic variables

Main article: Cataclysmic variable star

Before accretion of material pushes a white dwarf close to the Chandrasekhar limit, accreted hydrogen-rich material on the surface may ignite in a less destructive type of thermonuclear explosion powered by hydrogen fusion. Since the white dwarf's core remains intact, these surface explosions can be repeated as long as accretion continues. This weaker kind of repetitive cataclysmic phenomenon is called a (classical) nova. Astronomers have also observed dwarf novae, which have smaller, more frequent luminosity peaks than classical novae. These are thought to be caused by the release of gravitational potential energy when part of the accretion disc collapses onto the star, rather than by fusion. In general, binary systems with a white dwarf accreting matter from a stellar companion are called cataclysmic variables. As well as novae and dwarf novae, several other classes of these variables are known.^{[1][48][120][121]} Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.^[121]

See also

	Star portal
	Space portal

• Planetary nebula
• PG 1159 star
• Pulsating white dwarf
• Stellar classification
• Timeline of white dwarfs, neutron stars, and supernovae
• Degenerate matter
• Black dwarf
• Supernova
• Red dwarf
• Brown dwarf
• Robust Associations of Massive Baryonic Objects (RAMBOs)
• Neutron star

References

1. ^ ^{a b c d e f g h i} Johnson, J. (2007). "Extreme Stars: White Dwarfs & Neutron Stars". Lecture notes, Astronomy 162. Ohio State University. http://www.astronomy.ohio-state.edu/~jaj/Ast162/lectures/notesWL22.html. Retrieved 2011-10-17. 
2. ^ Henry, T. J. (1 January 2009). "The One Hundred Nearest Star Systems". Research Consortium On Nearby Stars. http://www.chara.gsu.edu/RECONS/TOP100.posted.htm. Retrieved 2010-07-21. 
3. ^ ^{a b c d} White Dwarfs, E. Schatzman, Amsterdam: North-Holland, 1958.
4. ^ ^{a b c d} Holberg, J. B. (2005). "How Degenerate Stars Came to be Known as White Dwarfs". American Astronomical Society Meeting 207 207: 1503. Bibcode 2005AAS...20720501H. 
5. ^ ^{a b c d} Fontaine, G.; Brassard, P.; Bergeron, P. (2001). "The Potential of White Dwarf Cosmochronology". Publications of the Astronomical Society of the Pacific 113 (782): 409. Bibcode 2001PASP..113..409F. doi:10.1086/319535. 
6. ^ ^{a b c d e} Richmond, M. "Late stages of evolution for low-mass stars". Lecture notes, Physics 230. Rochester Institute of Technology. http://spiff.rit.edu/classes/phys230/lectures/planneb/planneb.html. Retrieved 2007-05-03. 
7. ^ ^{a b} Werner, K.; Hammer, N. J.; Nagel, T.; Rauch, T.; Dreizler, S. (2005). "On Possible Oxygen/Neon White Dwarfs: H1504+65 and the White Dwarf Donors in Ultracompact X-ray Binaries". 14th European Workshop on White Dwarfs 334: 165. arXiv:astro-ph/0410690. Bibcode 2005ASPC..334..165W. 
8. ^ ^{a b} Liebert, J.; Bergeron, P.; Eisenstein, D.; Harris, H. C.; Kleinman, S. J.; Nitta, A.; Krzesinski, J. (2004). "A Helium White Dwarf of Extremely Low Mass". The Astrophysical Journal 606 (2): L147. arXiv:astro-ph/0404291. Bibcode 2004ApJ...606L.147L. doi:10.1086/421462. 
9. ^ ^{a b} "Cosmic weight loss: The lowest mass white dwarf" (Press release). Harvard-Smithsonian Center for Astrophysics. 17 April 2007. http://spaceflightnow.com/news/n0704/17whitedwarf. 
10. ^ ^{a b} Spergel, D. N.; Bean, R.; Doré, O.; Nolta, M. R.; Bennett, C. L.; Dunkley, J.; Hinshaw, G.; Jarosik, N. et al. (2007). "Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology". The Astrophysical Journal Supplement Series 170 (2): 377. arXiv:astro-ph/0603449. Bibcode 2007ApJS..170..377S. doi:10.1086/513700. 
11. ^ Herschel, W. (1785). "Catalogue of Double Stars. By William Herschel, Esq. F. R. S". Philosophical Transactions of the Royal Society of London 75: 40–126. Bibcode 1785RSPT...75...40H. doi:10.1098/rstl.1785.0006. JSTOR 106749. 
12. ^ Van Den Bos, W. H. (1926). "The orbit and the masses of 40 Eridani BC". Bulletin of the Astronomical Institutes of the Netherlands 3: 128. Bibcode 1926BAN.....3..128V. 
13. ^ Heintz, W. D. (1974). "Astrometric study of four visual binaries". The Astronomical Journal 79: 819. Bibcode 1974AJ.....79..819H. doi:10.1086/111614. 
14. ^ Adams, W. S. (1914). "An A-Type Star of Very Low Luminosity". Publications of the Astronomical Society of the Pacific 26: 198. Bibcode 1914PASP...26..198A. doi:10.1086/122337. 
15. ^ ^{a b} "On the variations of the proper motions of Procyon and Sirius". Monthly Notices of the Royal Astronomical Society 6: 136. 1844. Bibcode 1844MNRAS...6..136.. 
16. ^ ^{a b} Flammarion, Camille (1877). "The Companion of Sirius". Astronomical register 15: 186. Bibcode 1877AReg...15..186F. 
17. ^ Adams, W. S. (1915). "The Spectrum of the Companion of Sirius". Publications of the Astronomical Society of the Pacific 27: 236. Bibcode 1915PASP...27..236A. doi:10.1086/122440. 
18. ^ Van Maanen, A. (1917). "Two Faint Stars with Large Proper Motion". Publications of the Astronomical Society of the Pacific 29: 258. Bibcode 1917PASP...29..258V. doi:10.1086/122654. 
19. ^ Luyten, W. J. (1922). "The Mean Parallax of Early-Type Stars of Determined Proper Motion and Apparent Magnitude". Publications of the Astronomical Society of the Pacific 34: 156. Bibcode 1922PASP...34..156L. doi:10.1086/123176. 
20. ^ Luyten, W. J. (1922). "Note on Some Faint Early Type Stars with Large Proper Motions". Publications of the Astronomical Society of the Pacific 34: 54. Bibcode 1922PASP...34...54L. doi:10.1086/123146. 
21. ^ Luyten, W. J. (1922). "Additional Note on Faint Early-Type Stars with Large Proper-Motions". Publications of the Astronomical Society of the Pacific 34: 132. Bibcode 1922PASP...34..132L. doi:10.1086/123168. 
22. ^ Aitken, R. G. (1922). "Comet c 1922 (Baade)". Publications of the Astronomical Society of the Pacific 34: 353. Bibcode 1922PASP...34..353A. doi:10.1086/123244. 
23. ^ ^{a b c} Eddington, A. S. (1924). "On the relation between the masses and luminosities of the stars". Monthly Notices of the Royal Astronomical Society 84: 308. Bibcode 1924MNRAS..84..308E. 
24. ^ Luyten, W. J. (1950). "The search for white dwarfs". The Astronomical Journal 55: 86. Bibcode 1950AJ.....55...86L. doi:10.1086/106358. 
25. ^ ^{a b c d} McCook, George P.; Sion, Edward M. (1999). "A Catalog of Spectroscopically Identified White Dwarfs". The Astrophysical Journal Supplement Series 121: 1. Bibcode 1999ApJS..121....1M. doi:10.1086/313186. 
26. ^ ^{a b} Eisenstein, Daniel J.; Liebert, James; Harris, Hugh C.; Kleinman, S. J.; Nitta, Atsuko; Silvestri, Nicole; Anderson, Scott A.; Barentine, J. C. et al. (2006). "A Catalog of Spectroscopically Confirmed White Dwarfs from the Sloan Digital Sky Survey Data Release 4". The Astrophysical Journal Supplement Series 167: 40. arXiv:astro-ph/0606700. Bibcode 2006ApJS..167...40E. doi:10.1086/507110. 
27. ^ Kilic, M.; Allende Prieto, C.; Brown, Warren R.; Koester, D. (2007). "The Lowest Mass White Dwarf". The Astrophysical Journal 660 (2): 1451. arXiv:astro-ph/0611498. Bibcode 2007ApJ...660.1451K. doi:10.1086/514327. 
28. ^ ^{a b} Kepler, S. O.; Kleinman, S. J.; Nitta, A.; Koester, D.; Castanheira, B. G.; Giovannini, O.; Costa, A. F. M.; Althaus, L. (2007). "White dwarf mass distribution in the SDSS". Monthly Notices of the Royal Astronomical Society 375 (4): 1315. arXiv:astro-ph/0612277. Bibcode 2007MNRAS.375.1315K. doi:10.1111/j.1365-2966.2006.11388.x. 
29. ^ Shipman, H. L. (1979). "Masses and radii of white-dwarf stars. III - Results for 110 hydrogen-rich and 28 helium-rich stars". The Astrophysical Journal 228: 240. Bibcode 1979ApJ...228..240S. doi:10.1086/156841. 
30. ^ Sandin, F. (2005). "Exotic Phases of Matter in Compact Stars". Licentiate thesis. Luleå University of Technology. http://epubl.luth.se/1402-1757/2005/25/LTU-LIC-0525-SE.pdf. Retrieved 2011-08-20. 
31. ^ Nave, C. R.. "Nuclear Size and Density". HyperPhysics. Georgia State University. http://hyperphysics.phy-astr.gsu.edu/HBASE/Nuclear/nucuni.html. Retrieved 2009-06-26. 
32. ^ Adams, Steve (1997). Relativity: an introduction to space-time physics. CRC Press. p. 240. ISBN 0748406212. 
33. ^ Boss, L. (1910). Preliminary General Catalogue of 6188 stars for the epoch 1900. Carnegie Institution of Washington. Bibcode 1910pgcs.book.....B. LCCN 10009645. 
34. ^ Liebert, J.; Young, P. A.; Arnett, D.; Holberg, J. B.; Williams, K. A. (2005). "The Age and Progenitor Mass of Sirius B". The Astrophysical Journal 630: L69. arXiv:astro-ph/0507523. Bibcode 2005ApJ...630L..69L. doi:10.1086/462419. 
35. ^ Öpik, E. (1916). "The Densities of Visual Binary Stars". The Astrophysical Journal 44: 292. Bibcode 1916ApJ....44..292O. doi:10.1086/142296. 
36. ^ Eddington, A. S. (1927). Stars and Atoms. Clarendon Press. LCCN 27015694. 
37. ^ Adams, W. S. (1925). "Tiie Relativity Displacement of the Spectral Lines in the Companion of Sirius". Proceedings of the National Academy of Sciences 11 (7): 382. Bibcode 1925PNAS...11..382A. doi:10.1073/pnas.11.7.382. 
38. ^ ^{a b c} Fowler, R. H. (1926). "On dense matter". Monthly Notices of the Royal Astronomical Society 87: 114. Bibcode 1926MNRAS..87..114F. 
39. ^ Hoddeson, L. H.; Baym, G. (1980). "The Development of the Quantum Mechanical Electron Theory of Metals: 1900-28". Proceedings of the Royal Society of London 371 (1744): 8–23. Bibcode 1980RSPSA.371....8H. doi:10.1098/rspa.1980.0051. JSTOR 2990270. 
40. ^ ^{a b c d e} "Estimating Stellar Parameters from Energy Equipartition". ScienceBits. http://www.sciencebits.com/StellarEquipartition. Retrieved 2007-05-09. 
41. ^ Bean, R.. "Lecture 12 - Degeneracy pressure". Lecture notes, Astronomy 211. Cornell University. http://www.astro.cornell.edu/~rbean/a211/211_notes_lec_12.pdf. Retrieved 2007-09-21.  Archived September 25, 2007 at the Wayback Machine
42. ^ Anderson, W. (1929). "Über die Grenzdichte der Materie und der Energie". Zeitschrift für Physik 56 (11–12): 851. Bibcode 1929ZPhy...56..851A. doi:10.1007/BF01340146. 
43. ^ ^{a b} Stoner, C. (1930). "The Equilibrium of Dense Stars". Philosophical Magazine 9: 944. 
44. ^ Chandrasekhar, S. (1931). "The Maximum Mass of Ideal White Dwarfs". The Astrophysical Journal 74: 81. Bibcode 1931ApJ....74...81C. doi:10.1086/143324. 
45. ^ ^{a b c} Chandrasekhar, S. (1935). "The highly collapsed configurations of a stellar mass (Second paper)". Monthly Notices of the Royal Astronomical Society 95: 207. Bibcode 1935MNRAS..95..207C. 
46. ^ "The Nobel Prize in Physics 1983". The Nobel Foundation. http://nobelprize.org/nobel_prizes/physics/laureates/1983/. Retrieved 2007-05-04. 
47. ^ ^{a b} Canal, R.; Gutierrez, J. (1997). "The Possible White Dwarf-Neutron Star Connection". arXiv:astro-ph/9701225 [astro-ph]. 
48. ^ ^{a b c d e f} Hillebrandt, W.; Niemeyer, J. C. (2000). "Type IA supernova explosion models". Annual Review of Astronomy and Astrophysics 38: 191. arXiv:astro-ph/0006305. Bibcode 2000ARA&A..38..191H. doi:10.1146/annurev.astro.38.1.191. 
49. ^ Overbye, D. (22 February 2010). "From the Clash of White Dwarfs, the Birth of a Supernova". New York Times. http://www.nytimes.com/2010/02/23/science/space/23star.html?hpw. Retrieved 2010-02-22. 
50. ^ Chabrier, G.; Baraffe, I. (2000). "Theory of low-Mass stars and substellar objects". Annual Review of Astronomy and Astrophysics 38: 337. arXiv:astro-ph/0006383. Bibcode 2000ARA&A..38..337C. doi:10.1146/annurev.astro.38.1.337. 
51. ^ Kaler, J.. "The Hertzsprung-Russell (HR) diagram". http://www.astro.uiuc.edu/~kaler/sow/hrd.html. Retrieved 2007-05-05. 
52. ^ "Basic symbols". Standards for Astronomical Catalogues, Version 2.0. VizieR. http://vizier.u-strasbg.fr/doc/catstd-3.2.htx. Retrieved 2007-01-12. 
53. ^ Tohline, J. E.. "The Structure, Stability, and Dynamics of Self-Gravitating Systems". http://www.phys.lsu.edu/astro/H_Book.current/H_Book.html. Retrieved 2007-05-30. 
54. ^ Hoyle, F. (1947). "Stars, Distribution and Motions of, Note on equilibrium configurations for rotating white dwarfs". Monthly Notices of the Royal Astronomical Society 107: 231. Bibcode 1947MNRAS.107..231H. 
55. ^ Ostriker, J. P.; Bodenheimer, P. (1968). "Rapidly Rotating Stars. II. Massive White Dwarfs". The Astrophysical Journal 151: 1089. Bibcode 1968ApJ...151.1089O. doi:10.1086/149507. 
56. ^ Kutner, M. L. (2003). Astronomy: A physical perspective. Cambridge University Press. p. 189. ISBN 9780521529273. http://books.google.com/books?id=2QVmiMW0O0MC&pg=PA189. 
57. ^ ^{a b c} Sion, E. M.; Greenstein, J. L.; Landstreet, J. D.; Liebert, J.; Shipman, H. L.; Wegner, G. A. (1983). "A proposed new white dwarf spectral classification system". The Astrophysical Journal 269: 253. Bibcode 1983ApJ...269..253S. doi:10.1086/161036. 
58. ^ ^{a b} Hambly, N. C.; Smartt, S. J.; Hodgkin, S. T. (1997). "WD 0346+246: A Very Low Luminosity, Cool Degenerate in Taurus". The Astrophysical Journal 489 (2): L157. Bibcode 1997ApJ...489L.157H. doi:10.1086/316797. 
59. ^ ^{a b c d e f g} Fontaine, G.; Wesemael, F. (2001). "White dwarfs". In Murdin, P.. Encyclopedia of Astronomy and Astrophysics. IOP Publishing/Nature Publishing Group. ISBN 0-333-75088-8. 
60. ^ Heise, J. (1985). "X-ray emission from isolated hot white dwarfs". Space Science Reviews 40: 79. Bibcode 1985SSRv...40...79H. doi:10.1007/BF00212870. 
61. ^ Mestel, L. (1952). "On the theory of white dwarf stars. I. The energy sources of white dwarfs". Monthly Notices of the Royal Astronomical Society 112: 583. Bibcode 1952MNRAS.112..583M. 
62. ^ Kawaler, S. D. (1998). "White Dwarf Stars and the Hubble Deep Field". The Hubble Deep Field : Proceedings of the Space Telescope Science Institute Symposium. pp. 252. arXiv:astro-ph/9802217. Bibcode 1998hdf..symp..252K. ISBN 0-521-63097-5. 
63. ^ Bergeron, P.; Ruiz, M. T.; Leggett, S. K. (1997). "The Chemical Evolution of Cool White Dwarfs and the Age of the Local Galactic Disk". The Astrophysical Journal Supplement Series 108: 339. Bibcode 1997ApJS..108..339B. doi:10.1086/312955. 
64. ^ ^{a b} Metcalfe, T. S.; Montgomery, M. H.; Kanaan, A. (2004). "Testing White Dwarf Crystallization Theory with Asteroseismology of the Massive Pulsating DA Star BPM 37093". The Astrophysical Journal 605 (2): L133. arXiv:astro-ph/0402046. Bibcode 2004ApJ...605L.133M. doi:10.1086/420884. 
65. ^ Barrat, J. L.; Hansen, J. P.; Mochkovitch, R. (1988). "Crystallization of carbon-oxygen mixtures in white dwarfs". Astronomy and Astrophysics 199: L15. Bibcode 1988A&A...199L..15B. 
66. ^ Winget, D. E. (1995). "The Status of White Dwarf Asteroseismology and a Glimpse of the Road Ahead". Baltic Astronomy 4: 129. Bibcode 1995BaltA...4..129W. 
67. ^ Diamond star thrills astronomers, David Whitehouse, BBC News, February 16, 2004. Accessed on line January 6, 2007.
68. ^ Kanaan, A.; Nitta, A.; Winget, D. E.; Kepler, S. O.; Montgomery, M. H.; Metcalfe, T. S.; Oliveira, H.; Fraga, L. et al. (2005). "Whole Earth Telescope observations of BPM 37093: A seismological test of crystallization theory in white dwarfs". Astronomy and Astrophysics 432: 219–224. arXiv:astro-ph/0411199. Bibcode 2005A&A...432..219K. doi:10.1051/0004-6361:20041125. 
69. ^ Brassard, P.; Fontaine, G. (2005). "Asteroseismology of the Crystallized ZZ Ceti Star BPM 37093: A Different View". The Astrophysical Journal 622: 572. Bibcode 2005ApJ...622..572B. doi:10.1086/428116. 
70. ^ McCook, G. P.; Sion, E. M.. III/235A "A Catalogue of Spectroscopically Identified White Dwarfs". Centre de données astronomiques de Strasbourg. http://cdsweb.u-strasbg.fr/cgi-bin/Cat?III/235A III/235A. Retrieved 2007-05-09.  Archived February 17, 2007 at the Wayback Machine
71. ^ ^{a b} Leggett, S. K.; Ruiz, M. T.; Bergeron, P. (1998). "The Cool White Dwarf Luminosity Function and the Age of the Galactic Disk". The Astrophysical Journal 497: 294. Bibcode 1998ApJ...497..294L. doi:10.1086/305463. 
72. ^ Gates, E.; Gyuk, G.; Harris, H. C.; Subbarao, M.; Anderson, S.; Kleinman, S. J.; Liebert, J.; Brewington, H. et al. (2004). "Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey". The Astrophysical Journal 612 (2): L129. arXiv:astro-ph/0405566. Bibcode 2004ApJ...612L.129G. doi:10.1086/424568. 
73. ^ Winget, D. E.; Hansen, C. J.; Liebert, J.; Van Horn, H. M.; Fontaine, G.; Nather, R. E.; Kepler, S. O.; Lamb, D. Q. (1987). "An independent method for determining the age of the universe". The Astrophysical Journal 315: L77. Bibcode 1987ApJ...315L..77W. doi:10.1086/184864. 
74. ^ Trefil, J. S. (2004). The Moment of Creation: Big Bang Physics from Before the First Millisecond to the Present Universe. Dover Publications. ISBN 0-486-43813-9. 
75. ^ Schatzman, E. (1945). "Théorie du débit d'énergie des naines blanches". Annales d'Astrophysique 8: 143. Bibcode 1945AnAp....8..143S. 
76. ^ ^{a b c d e f} Koester, D.; Chanmugam, G. (1990). "Physics of white dwarf stars". Reports on Progress in Physics 53 (7): 837. Bibcode 1990RPPh...53..837K. doi:10.1088/0034-4885/53/7/001. 
77. ^ ^{a b} Kawaler, S. D. (1997). "White Dwarf Stars". In Kawaler, S. D.; Novikov, I.; Srinivasan, G.. Stellar remnants. 1997. ISBN 3-540-61520-2. 
78. ^ Kuiper, G. P. (1941). "List of Known White Dwarfs". Publications of the Astronomical Society of the Pacific 53: 248. Bibcode 1941PASP...53..248K. doi:10.1086/125335. 
79. ^ Luyten, W. J. (1952). "The Spectra and Luminosities of White Dwarfs". The Astrophysical Journal 116: 283. Bibcode 1952ApJ...116..283L. doi:10.1086/145612. 
80. ^ Greenstein, J. L. (1960). Stellar atmospheres. University of Chicago Press. Bibcode 1960stat.conf.....G. LCCN 61-9138. 
81. ^ Kepler, S. O.; Kleinman, S. J.; Nitta, A.; Koester, D.; Castanheira, B. G.; Giovannini, O.; Costa, A. F. M.; Althaus, L. (2007). "White dwarf mass distribution in the SDSS". Monthly Notices of the Royal Astronomical Society 375 (4): 1315. arXiv:astro-ph/0612277. Bibcode 2007MNRAS.375.1315K. doi:10.1111/j.1365-2966.2006.11388.x. 
82. ^ Dufour, P.; Liebert, J.; Fontaine, G.; Behara, N. (2007). "White dwarf stars with carbon atmospheres". Nature 450 (7169): 522–4. Bibcode 2007Natur.450..522D. doi:10.1038/nature06318. PMID 18033290. 
83. ^ Blackett, P. M. S. (1947). "The Magnetic Field of Massive Rotating Bodies". Nature 159 (4046): 658–66. Bibcode 1947Natur.159..658B. doi:10.1038/159658a0. PMID 20239729. 
84. ^ Lovell, B. (1975). "Patrick Maynard Stuart Blackett, Baron Blackett, of Chelsea. 18 November 1897-13 July 1974". Biographical Memoirs of Fellows of the Royal Society 21: 1–115. doi:10.1098/rsbm.1975.0001. JSTOR 769678. 
85. ^ Ginzburg, V. L.; Zheleznyakov, V. V.; Zaitsev, V. V. (1969). "Coherent mechanisms of radio emission and magnetic models of pulsars". Astrophysics and Space Science 4 (4): 464. Bibcode 1969Ap&SS...4..464G. doi:10.1007/BF00651351. 
86. ^ Kemp, J. C.; Swedlund, J. B.; Landstreet, J. D.; Angel, J. R. P. (1970). "Discovery of Circularly Polarized Light from a White Dwarf". The Astrophysical Journal 161: L77. Bibcode 1970ApJ...161L..77K. doi:10.1086/180574. 
87. ^ Jordan, S.; Aznar Cuadrado, R.; Napiwotzki, R.; Schmid, H. M.; Solanki, S. K. (2007). "The fraction of DA white dwarfs with kilo-Gauss magnetic fields". Astronomy and Astrophysics 462 (3): 1097. arXiv:astro-ph/0610875. Bibcode 2007A&A...462.1097J. doi:10.1051/0004-6361:20066163. 
88. ^ Liebert, James; Bergeron, P.; Holberg, J. B. (2003). "The True Incidence of Magnetism Among Field White Dwarfs". The Astronomical Journal 125: 348. arXiv:astro-ph/0210319. Bibcode 2003AJ....125..348L. doi:10.1086/345573. 
89. ^ ZZ Ceti variables, Association Française des Observateurs d'Etoiles Variables, web page at the Centre de Données astronomiques de Strasbourg. Accessed on line June 6, 2007.
90. ^ ^{a b c} Quirion, P.‐O.; Fontaine, G.; Brassard, P. (2007). "Mapping the Instability Domains of GW Vir Stars in the Effective Temperature–Surface Gravity Diagram". The Astrophysical Journal Supplement Series 171: 219. Bibcode 2007ApJS..171..219Q. doi:10.1086/513870. 
91. ^ Lawrence, G. M.; Ostriker, J. P.; Hesser, J. E. (1967). "Ultrashort-Period Stellar Oscillations. I. Results from White Dwarfs, Old Novae, Central Stars of Planetary Nebulae, 3c 273, and Scorpius XR-1". The Astrophysical Journal 148: L161. Bibcode 1967ApJ...148L.161L. doi:10.1086/180037. 
92. ^ Landolt, A. U. (1968). "A New Short-Period Blue Variable". The Astrophysical Journal 153: 151. Bibcode 1968ApJ...153..151L. doi:10.1086/149645. 
93. ^ Nagel, T.; Werner, K. (2004). "Detection of non-radial g-mode pulsations in the newly discovered PG 1159 star HE 1429-1209". Astronomy and Astrophysics 426 (2): L45. arXiv:astro-ph/0409243. Bibcode 2004A&A...426L..45N. doi:10.1051/0004-6361:200400079. 
94. ^ O'Brien, M. S. (2000). "The Extent and Cause of the Pre–White Dwarf Instability Strip". The Astrophysical Journal 532 (2): 1078. arXiv:astro-ph/9910495. Bibcode 2000ApJ...532.1078O. doi:10.1086/308613. 
95. ^ Winget, D. E. (1998). "Asteroseismology of white dwarf stars". Journal of Physics: Condensed Matter 10 (49): 11247. Bibcode 1998JPCM...1011247W. doi:10.1088/0953-8984/10/49/014. 
96. ^ ^{a b} Heger, A.; Fryer, C. L.; Woosley, S. E.; Langer, N.; Hartmann, D. H. (2003). "How Massive Single Stars End Their Life". The Astrophysical Journal 591: 288. arXiv:astro-ph/0212469. Bibcode 2003ApJ...591..288H. doi:10.1086/375341. 
97. ^ Laughlin, G.; Bodenheimer, P.; Adams, Fred C. (1997). "The End of the Main Sequence". The Astrophysical Journal 482: 420. Bibcode 1997ApJ...482..420L. doi:10.1086/304125. 
98. ^ ^{a b} Stars Beyond Maturity, Simon Jeffery, online article. Accessed on line May 3, 2007.
99. ^ Sarna, M.J.; Ergma, E.; Gerškevitš, J. (2001). "Helium core white dwarf evolution - including white dwarf companions to neutron stars". Astronomische Nachrichten 322 (5–6): 405. Bibcode 2001AN....322..405S. doi:10.1002/1521-3994(200112)322:5/6<405::AID-ASNA405>3.0.CO;2-6. 
100. ^ Benvenuto, O. G.; De Vito, M. A. (2005). "The formation of helium white dwarfs in close binary systems - II". Monthly Notices of the Royal Astronomical Society 362 (3): 891. Bibcode 2005MNRAS.362..891B. doi:10.1111/j.1365-2966.2005.09315.x. 
101. ^ Nelemans, G.; Tauris, T. M. (1998). "Formation of undermassive single white dwarfs and the influence of planets on late stellar evolution". Astronomy and Astrophysics 335: L85. arXiv:astro-ph/9806011. Bibcode 1998A&A...335L..85N. 
102. ^ "Planet diet helps white dwarfs stay young and trim". NewScientist. 18 January 2008. http://space.newscientist.com/article/mg19726394.900-planet-diet-helps-white-dwarfs-stay-young-and-trim.html. 
103. ^ the evolution of low-mass stars, Vik Dhillon, lecture notes, Physics 213, University of Sheffield. Accessed on line May 3, 2007.
104. ^ the evolution of high-mass stars, Vik Dhillon, lecture notes, Physics 213, University of Sheffield. Accessed on line May 3, 2007.
105. ^ Schaffner-Bielich, Jürgen (2005). "Strange quark matter in stars: A general overview". Journal of Physics G: Nuclear and Particle Physics 31 (6): S651. arXiv:astro-ph/0412215. Bibcode 2005JPhG...31S.651S. doi:10.1088/0954-3899/31/6/004. 
106. ^ Nomoto, K. (1984). "Evolution of 8-10 solar mass stars toward electron capture supernovae. I - Formation of electron-degenerate O + NE + MG cores". The Astrophysical Journal 277: 791. Bibcode 1984ApJ...277..791N. doi:10.1086/161749. 
107. ^ Woosley, S. E.; Heger, A. (2002). "The evolution and explosion of massive stars". Reviews of Modern Physics 74 (4): 1015. Bibcode 2002RvMP...74.1015W. doi:10.1103/RevModPhys.74.1015. 
108. ^ Werner, K.; Rauch, T.; Barstow, M. A.; Kruk, J. W. (2004). "Chandra and FUSE spectroscopy of the hot bare stellar core H?1504+65". Astronomy and Astrophysics 421 (3): 1169. arXiv:astro-ph/0404325. Bibcode 2004A&A...421.1169W. doi:10.1051/0004-6361:20047154. 
109. ^ Livio, Mario; Truran, James W. (1994). "On the interpretation and implications of nova abundances: An abundance of riches or an overabundance of enrichments". The Astrophysical Journal 425: 797. Bibcode 1994ApJ...425..797L. doi:10.1086/174024. 
110. ^ ^{a b c} Adams, Fred C.; Laughlin, Gregory (1997). "A dying universe: The long-term fate and evolutionof astrophysical objects". Reviews of Modern Physics 69 (2): 337. arXiv:astro-ph/9701131. Bibcode 1997RvMP...69..337A. doi:10.1103/RevModPhys.69.337. 
111. ^ Comet clash kicks up dusty haze, BBC News, February 13, 2007. Accessed on line September 20, 2007.
112. ^ Su, K. Y. L.; Chu, Y.-H.; Rieke, G. H.; Huggins, P. J.; Gruendl, R.; Napiwotzki, R.; Rauch, T.; Latter, W. B. et al. (2007). "A Debris Disk around the Central Star of the Helix Nebula?". The Astrophysical Journal 657: L41. arXiv:astro-ph/0702296. Bibcode 2007ApJ...657L..41S. doi:10.1086/513018. 
113. ^ Reach, William T.; Kuchner, Marc J.; Von Hippel, Ted; Burrows, Adam; Mullally, Fergal; Kilic, Mukremin; Winget, D. E. (2005). "The Dust Cloud around the White Dwarf G29-38". The Astrophysical Journal 635 (2): L161. arXiv:astro-ph/0511358. Bibcode 2005ApJ...635L.161R. doi:10.1086/499561. 
114. ^ Di Stefano, R.; Nelson, L. A.; Lee, W.; Wood, T. H.; Rappaport, S. (1997). P. Ruiz-Lapuente, R. Canal, J. Isern. ed. Luminous Supersoft X-ray Sources as Type Ia Progenitors. NATO ASI series: Mathematical and physical sciences. Springer. pp. 148–149. ISBN 079234359X. 
115. ^ Aguilar, David A.; Pulliam, Christine (November 16, 2010). "Astronomers Discover Merging Star Systems that Might Explode". Harvard-Smithsonian Center for Astrophysics. http://www.cfa.harvard.edu/news/2010/pr201024.html. Retrieved 2011-02-16. 
116. ^ Aguilar, David A.;Pulliam, Christine (July 13, 2011). "Evolved Stars Locked in Fatalistic Dance". Harvard-Smithsonian Center for Astrophysics. http://www.cfa.harvard.edu/news/2011/pr201119.html. Retrieved 2011-07-17. 
117. ^ Yoon, S.-C.; Langer, N. (2004). "Presupernova evolution of accreting white dwarfs with rotation". Astronomy and Astrophysics 419 (2): 623. arXiv:astro-ph/0402287. Bibcode 2004A&A...419..623Y. doi:10.1051/0004-6361:20035822. 
118. ^ Blinnikov, S. I.; Röpke, F. K.; Sorokina, E. I.; Gieseler, M.; Reinecke, M.; Travaglio, C.; Hillebrandt, W.; Stritzinger, M. (2006). "Theoretical light curves for deflagration models of type Ia supernova". Astronomy and Astrophysics 453: 229. arXiv:astro-ph/0603036. Bibcode 2006A&A...453..229B. doi:10.1051/0004-6361:20054594. 
119. ^ O'Neill, Ian. "Don't Slow Down White Dwarf, You Might Explode." Discovery Communications, LLC 6 September 2011.
120. ^ Imagine the Universe! Cataclysmic Variables, fact sheet at NASA Goddard. Accessed on line May 4, 2007.
121. ^ ^{a b} Introduction to Cataclysmic Variables (CVs), fact sheet at NASA Goddard. Accessed on line May 4, 2007.

External links and further reading

General

• Kawaler, S. D. (1997). "White Dwarf Stars". In Kawaler, S. D.; Novikov, I.; Srinivasan, G.. Stellar remnants. 1997. ISBN 3-540-61520-2. 

Physics

• Black holes, white dwarfs, and neutron stars: the physics of compact objects, Stuart L. Shapiro and Saul A. Teukolsky, New York: Wiley, 1983. ISBN 0-471-87317-9.
• Koester, D; Chanmugam, G (1990). "Physics of white dwarf stars". Reports on Progress in Physics 53 (7): 837. Bibcode 1990RPPh...53..837K. doi:10.1088/0034-4885/53/7/001. 
• White dwarf stars and the Chandrasekhar limit, Dave Gentile, Master's thesis, DePaul University, 1995.
• Estimating Stellar Parameters from Energy Equipartition, sciencebits.com. Discusses how to find mass-radius relations and mass limits for white dwarfs using simple energy arguments.

Variability

• Winget, D E (1998). "Asteroseismology of white dwarf stars". Journal of Physics: Condensed Matter 10 (49): 11247. Bibcode 1998JPCM...1011247W. doi:10.1088/0953-8984/10/49/014. 

Magnetic field

• Wickramasinghe, D. T.; Ferrario, Lilia (2000). "Magnetism in Isolated and Binary White Dwarfs". Publications of the Astronomical Society of the Pacific 112 (773): 873. Bibcode 2000PASP..112..873W. doi:10.1086/316593. 

Frequency

• Gibson, B. K.; Flynn, C (2001). "White Dwarfs and Dark Matter". Science 292 (5525): 2211a. doi:10.1126/science.292.5525.2211a. PMID 11423620. 

Observational

• Provencal, J. L.; Shipman, H. L.; Hog, Erik; Thejll, P. (1998). "Testing the White Dwarf Mass‐Radius Relation withHipparcos". The Astrophysical Journal 494 (2): 759. Bibcode 1998ApJ...494..759P. doi:10.1086/305238. 
• Gates, Evalyn; Gyuk, Geza; Harris, Hugh C.; Subbarao, Mark; Anderson, Scott; Kleinman, S. J.; Liebert, James; Brewington, Howard et al. (2004). "Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey". The Astrophysical Journal 612 (2): L129. arXiv:astro-ph/0405566. Bibcode 2004ApJ...612L.129G. doi:10.1086/424568. 
• Villanova University White Dwarf Catalogue WD, G. P. McCook and E. M. Sion.
• Dufour, P.; Liebert, J.; Fontaine, G.; Behara, N. (2007). "White dwarf stars with carbon atmospheres". Nature 450 (7169): 522–4. arXiv:0711.3227. Bibcode 2007Natur.450..522D. doi:10.1038/nature06318. PMID 18033290. 

Images

• Astronomy Picture of the Day
  • NGC 2440: Cocoon of a New White Dwarf 2010 February 21
  • Dust and the Helix Nebula 2009 December 31
  • The Helix Nebula from La Silla Observatory 2009 March 3
  • IC 4406: A Seemingly Square Nebula 2008 July 27
  • A Nearby Supernova in Spiral Galaxy M100 2006 March 7
  • White Dwarf Star Spiral 2005 June 1