A white dwarf is a very dense type of star: in an Earth-sized volume, it packs a mass that is comparable to the Sun. A white dwarf radiates light from residual heat and eventual crystallization, not from nuclear fusion. Stars like the Sun, whose mass is not high enough to collapse into a neutron star or black hole, are expected to become white dwarf stars later in their evolution. The nearest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. 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 would become known as the first white dwarf. The name white dwarf was coined by Willem Jacob Luyten in 1922. In 1931 Subrahmanyan Chandrasekhar developed a physical model of white dwarfs and he won the 1983 Nobel Prize in Physics for studies in the evolution of stars. These compact stars are composed mostly of a highly compressed form of matter. The composition of the white dwarf produced will depend on the initial mass of the star. 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. Observed white dwarf masses are largely between 0.5 and 0.7 M☉. White dwarfs are very hot when they form, but cool gradually as they radiate their energy. This radiation, which initially has a high color temperature, lessens and reddens over time. Eventually, white dwarfs may become cool enough that their material will begin to crystallize, but they are expected to exist for 1038 years.
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 his now famous luminosity (brightness) versus spectral type (color) diagram. Publicly 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 (α Canis Majoris) and Procyon (α Canis Minoris) 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. Eighteen 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 The extreme density of white dwarf stars was initially a theoretical puzzle. 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 0.94 M☉ (which compares well with a more modern estimate of 1.00 M☉). Since hotter bodies radiate more energy than colder ones, a star's surface brightness can be estimated from its effective surface temperature, and star's spectrum gives its temperature. 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 25000 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. 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 5.7 M☉ / μe2, where μe 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 μe equal to 2 for such a star, leading to the commonly quoted value of 1.4 M☉. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements, so, in his 1931 paper, Chandrasekhar set the average molecular weight per electron, μe, equal to 2.5, giving a limit of 0.91 M☉.) 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.
Occurrence Galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs. There are currently thought to be eight white dwarfs among the one hundred star systems nearest to the Sun. The nearest and brightest known white dwarf is Sirius B, at 8.6 light years, the smaller component of the Sirius binary star. The population of white dwarf stars is expected to grow. Existing stars with masses from about 0.07 to 10 M☉ include over 97% of the stars in the Milky Way and these stars will evolve into white dwarfs.
Composition and structure Although white dwarfs are known with estimated masses as low as 0.17 M☉ and as high as 1.33 M☉, the mass distribution is strongly peaked at 0.6 M☉, and the majority lie between 0.5 and 0.7 M☉. 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, 1000000 times greater than the average density of the Sun, or approximately 106 g/cm3, or 1 tonne per cubic centimetre. A typical white dwarf has a density of between 104 and 107 g/cm3. 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.
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 1.2×10−12 m, substantially less than a Bohr radius, 5.3×10−11 m, 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 hot thermal gas of atoms like the core of the Sun, the heat in the core of a white dwarf is associated with vibrating nuclei and the gas-like aspect providing pressure is due to the free electrons. This unusual source of pressure is known as electron degeneracy pressure, a consequence of quantum mechanics. The uncertainty principle requires the product of position uncertainty, Δ x {\displaystyle \Delta x} , and momentum uncertainty, Δ p x {\displaystyle \Delta p_{x}} , to be larger than half of the reduced Planck constant: Δ x × Δ p x > ℏ / 2. {\displaystyle \Delta x\times \Delta p_{x}>\hbar /2.} If the position uncertainty is small, the momentum uncertainty must increase. This uncertainty ultimately derives from the Pauli principle of quantum mechanics that says no two electrons will occupy the same quantum state. Qualitatively, the electrons resist being forced into a single place and this force counteracts the gravitational force compressing the star. The balanced 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 K. While these conditions would fuse hydrogen the low luminosity of white dwarf stars implies the necessary nuclei are not present.
Core types
A typical white dwarf star, a CO white dwarf, is 99% carbon and oxygen by mass, with the remainder being a thin layer of He and H. Main sequence stars close to the upper mass limit of 10 M☉ are thought to fuse carbon into neon, forming O-Ne white dwarf stars. Very light stars, below 0.6 M☉ never fuse He into carbon and oxygen so they form He-core white dwarfs. It takes more time than the age of the universe for a light star to burn through its fuel, so any observed He-core white dwarfs are expected to result from mass loss to a companion in an interacting binary star system. If a carbon-oxygen white dwarf accreted enough matter to reach the Chandrasekhar limit of about 1.44 solar masses (for a non-rotating star), it would no longer be able to support the bulk of its mass through electron degeneracy pressure and, in the absence of nuclear reactions, would begin to collapse. The current view is that this limit is not normally attained; increasing temperature and density inside the core ignite carbon fusion as the star approaches the limit (to within about 1%) before collapse is initiated. In contrast, for a core primarily composed of oxygen, neon and magnesium, the collapsing white dwarf will typically form a neutron star. In this case, only a fraction of the star's mass will be ejected during the collapse. If a white dwarf star accumulates sufficient material from a stellar companion to raise its core temperature enough to ignite carbon fusion, it will undergo runaway nuclear fusion, completely disrupting it. There are three avenues by which this detonation is theorised to happen: stable accretion of material from a companion, the collision of two white dwarfs, or accretion that causes ignition in a shell that then ignites the core. The dominant mechanism by which Type Ia supernovae are produced remains unclear. Despite this uncertainty in how Type Ia supernovae are produced, Type Ia supernovae have very uniform properties and are useful standard candles over intergalactic distances. Some calibrations are required to compensate for the gradual change in properties or different frequencies of abnormal luminosity supernovae at high redshift, and for small variations in brightness identified by light curve shape or spectrum.
Mass–radius relationship
The relationship between the mass and radius of white dwarfs can be estimated using the nonrelativistic Fermi gas equation of state, which gives
R R ⊙ ≈ 0.012 ( M M ⊙ ) − 1 / 3 ( μ e 2 ) − 5 / 3 , {\displaystyle {\frac {R}{R_{\odot }}}\approx 0.012\left({\frac {M}{M_{\odot }}}\right)^{-1/3}\left({\frac {\mu _{e}}{2}}\right)^{-5/3},}
where R is the radius, M is the mass of the white dwarf, and the subscript ⊙ {\displaystyle \odot } indicates the Sun; therefore R / R ⊙ {\displaystyle {R}/{R_{\odot }}} is the radius in units of solar radius and M / M ⊙ {\displaystyle {M}/{M_{\odot }}} is the mass in units of solar mass. The chemical potential, μ e {\displaystyle \mu _{e}} is a thermodynamic property giving the change in energy as one electron is added or removed; it relates to the composition of the star. Numerical treatment of more complete models have been tested against observational data with good agreement. Since this analysis uses the non-relativistic formula p2 / 2m for the kinetic energy, it is non-relativistic. When the electron velocity in a white dwarf is close to the speed of light, the kinetic energy formula approaches pc where c is the speed of light, and it can be shown that the Fermi gas model has no stable equilibrium in the ultrarelativistic limit. In particular, this analysis yields the maximum mass of a white dwarf, which is:
M l i m i t ≈ 1.46 ( μ e 2 ) − 2 {\displaystyle M_{\rm {limit}}\approx 1.46\left({\frac {\mu _{e}}{2}}\right)^{-2}}
The observation of many white dwarf stars implies that either they started with masses similar to the Sun or something dramatic happened to reduce their mass.
For a more accurate computation of the mass-radius relationship and limiting mass of a white dwarf, one must compute the equation of state that 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, the radius is inversely proportional to the cube root of the mass. 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, μe, has been set equal to 2. Radius is measured in standard solar radii and mass in standard solar masses. 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. For a uniformly rotating white dwarf, the limiting mass increases only slightly. If the star is allowed to rotate nonuniformly, and viscosity is neglected, then, as was pointed out by Fred Hoyle in 1947, 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 will be dynamically stable. Rotating white dwarfs and the estimates of their diameter in terms of the angular velocity of rotation has been treated in the rigorous mathematical literature. The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously.
Radiation and cooling
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, or the even lower-temperature brown dwarfs. The visible radiation emitted by white dwarfs varies over a wide color range, from the whitish-blue color of an O-, B- or A-type main sequence star to the yellow-orange of a late K- or early M-type star. White dwarf luminosity varies over 7 orders of magnitude, from over 100 times that of the Sun to under 1/ 10000 that of the Sun. Assuming the Stefan–Boltzmann law, relating luminosity to the fourth power of the effective surface temperature, white dwarf effective surface temperatures extend from over 150000 K to barely under 4000 K. Hot white dwarfs, with surface temperatures in excess of 30000 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. White dwarfs also radiate neutrinos through the Urca process. This process has more effect on hotter and younger white dwarfs. Because neutrinos can pass easily through stellar plasma, they can drain energy directly from the dwarf's interior; this mechanism is the dominant contribution to cooling for approximately the first 20 million years of a white dwarf's existence. The degenerate matter that makes up the bulk of a white dwarf has a very low opacity, because any absorption of a photon requires that an electron must transition to a higher empty state, which may not be possible as the energy of the photon may not be a match for the possible quantum states available to that electron, hence radiative heat transfer within a white dwarf is low, but it has a high thermal conductivity. As a result, the interior of the white dwarf maintains an almost uniform temperature as it cools down, starting at approximately 108 K shortly after the formation of the white dwarf and reaching less than 106 K for the coolest known white dwarfs. An outer shell of non-degenerate matter sits on top of the degenerate core. The outermost layers, which are cooler than the interior, radiate roughly as a black body. A white dwarf remains visible for a long time, as its tenuous outer atmosphere slowly radiates the thermal content of the degenerate interior.
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. White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time. As a white dwarf cools, its surface temperature decreases, the radiation that 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. The rate of cooling has been estimated for a carbon white dwarf of 0.59 M☉ with a hydrogen atmosphere. After initially taking approximately 1.5 billion years to cool to a surface temperature of 7140 K, cooling approximately 500 more kelvins to 6590 K takes around 0.3 billion years, but the next two steps of around 500 kelvins (to 6030 K and 5550 K) take first 0.4 and then 1.1 billion years. Most observed white dwarfs have relatively high surface temperatures, between 8000 K and 40000 K. However this is a selection effect: hotter, more luminous white dwarfs are easier to observe. A white dwarf spends more of its lifetime at cooler temperatures: more cool white dwarfs than hot white dwarfs exist. This trend stops at extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4000 K, and one of the coolest so far observed, WD J2147–4035, has a surface temperature of approximately 3050 K. The reason for this is that the Universe's age is finite; there has not been enough time for white dwarfs to cool 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 our galactic disk found in this way is 8 billion years. A white dwarf will eventually, in many trillions of years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. No black dwarfs are thought to exist yet. At very low temperatures (<4000 K) white dwarfs with hydrogen in their atmosphere will be affected by collision induced absorption (CIA) of hydrogen molecules colliding with helium atoms. This affects the optical red and infrared brightness of white dwarfs with a hydrogen or mixed hydrogen-helium atmosphere. This makes old white dwarfs with this kind of atmosphere bluer than the main cooling sequence. White dwarfs with hydrogen-poor atmospheres, such as WD J2147–4035, are less affected by CIA and therefore have a yellow to orange color.
White dwarf core material is a completely ionized plasma—a mixture of nuclei and electrons—that is initially in a fluid state. It was theoretically predicted in the 1960s that at a late stage of cooling, it should crystallize into a solid state, starting at its center. The crystal structure is thought to be a body-centered cubic lattice. In 1995 it was suggested that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory, and in 2004, observations were made that suggested approximately 90% of the mass of BPM 37093 had crystallized. Other work gives a crystallized mass fraction of between 32% and 82%. As a white dwarf core undergoes crystallization into a solid phase, latent heat is released, which provides a source of thermal energy that delays its cooling. Another possible mechanism that was suggested to explain this cooling anomaly in some types of white dwarfs is a solid–liquid distillation process: the crystals formed in the core are buoyant and float up, thereby displacing heavier liquid downward, thus causing a net release of gravitational energy. Chemical fractionation between the ionic species in the plasma mixture can release a similar or even greater amount of energy. This energy release was first confirmed in 2019 after the identification of a pile up in the cooling sequence of more than 15000 white dwarfs observed with the Gaia satellite. Low-mass helium white dwarfs (mass < 0.20 M☉), often referred to as extremely low-mass white dwarfs (ELM WDs), are formed in binary systems. As a result of their hydrogen-rich envelopes, residual hydrogen burning via the CNO cycle may keep these white dwarfs hot for hundreds of millions of years. In addition, they remain in a bloated proto-white dwarf stage for up to 2 Gyr before they reach the cooling track.
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 that is observed to be either hydrogen or helium dominated. The dominant element is usually at least 1000 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 below and the lighter above. This atmosphere, the only part of the white dwarf visible to us, is thought to be the top of an envelope that 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/ 100 of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1/ 10000 of the star's total mass. 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 at almost the same temperature (isothermal), and it is also hot: a white dwarf with surface temperature between 8000 K and 16000 K will have a core temperature between approximately 5000000 K and 20000000 K. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.
The first attempt to classify white dwarf spectra appears to have been by G.P. Kuiper in 1941, and various classification schemes have been proposed and used since then. 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 that 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 adjacent table), and a temperature index number, computed by dividing 50400 K by the effective temperature. For example, a white dwarf with only He I lines in its spectrum and an effective temperature of 15000 K could be given the classification of "DB3", or, if warranted by the precision of the temperature measurement, "DB3.5". Likewise, a white dwarf with a polarized magnetic field, an effective temperature of 17000 K, and a spectrum dominated by He I lines that also had hydrogen features could be given the classification of DBAP3. The symbols "?" and ":" may also be used if the correct classification is uncertain. White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority, approximately 80%, of all observed white dwarfs. The next class in number is of DBs, approximately 16%. The hot, above 15000 K, DQ class (roughly 0.1%) have carbon-dominated atmospheres. 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 100000 K to 45000 K, the spectrum will be classified DO, dominated by singly ionized helium. From 30000 K to 12000 K, the spectrum will be DB, showing neutral helium lines, and below about 12000 K, the spectrum will be featureless and classified DC. Molecular hydrogen (H2) has been detected in spectra of the atmospheres of some white dwarfs. While theoretical work suggests that some types of white dwarfs may have stellar corona, searches at X-ray and radio wavelengths, where coronae are most easily detected, have been unsuccessful. A few white dwarfs have been observed to have inhomogeneous atmosphere with one side dominated by hydrogen and the other side dominated by helium.
Metal-rich white dwarfs
Around 25–33% of white dwarfs have metal lines in their spectra, which is notable because any heavy elements in a white dwarf should sink into the star's interior in just a small fraction of the star's lifetime. The prevailing explanation for metal-rich white dwarfs is that they have recently accreted rocky planetesimals. The bulk composition of the accreted object can be measured from the strengths of the metal lines. For example, a 2015 study of the white dwarf Ton 345 concluded that its metal abundances were consistent with those of a differentiated, rocky planet whose mantle had been eroded by the host star's wind during its asymptotic giant branch phase.
Magnetic field Magnetic fields in white dwarfs with a strength at the surface of c. 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. This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted. In the 1960s, it was proposed that white dwarfs might have magnetic fields due to conservation of total surface magnetic flux that existed in its progenitor star phase. A surface magnetic field of c. 100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of c. 100 × 1002 = 1 million gauss (100 T) once the star's radius had shrunk by a factor of 100. The first magnetic white dwarf to be discovered was GJ 742 (also known as GRW +70 8247), which was identified by James Kemp, John Swedlund, John Landstreet and Roger Angel in 1970 to host a magnetic field by its emission of circularly polarized light. It is thought to have a surface field of approximately 300 million gauss (30 kT). Since 1970, magnetic fields have been discovered in well over 200 white dwarfs, ranging from 2×103 to 109 gauss (0.2 T to 100 kT). Many of the presently known magnetic white dwarfs are identified by low-resolution spectroscopy, which is able to reveal the presence of a magnetic field of 1 megagauss or more. Thus the basic identification process also sometimes results in discovery of magnetic fields. White dwarf magnetic fields may also be measured without spectral lines, using the techniques of broadband circular polarimetry, or maybe through measurement of their frequencies of radio emission via the electron cyclotron maser. It has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T). The magnetic fields in a white dwarf may allow for the existence of a new type of chemical bond, perpendicular paramagnetic bonding, in addition to ionic and covalent bonds, though detecting molecules bonded in this way is expected to be difficult. The highly magnetized white dwarf in the binary system AR Scorpii was identified in 2016 as the first pulsar in which the compact object is a white dwarf instead of a neutron star. A second white dwarf pulsar was discovered in 2023.
Variability
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. The first variable white dwarf found was HL Tau 76; in 1965 and 1966, and was observed to vary with a period of approximately 12.5 minutes. 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. 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; DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB; and GW Vir stars, sometimes subdivided into DOV and PNNV stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars are not, strictly speaking, white dwarfs, but are stars that 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. 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.
Formation After the hydrogen-fusing period of a main-sequence star of low or intermediate mass ends, such a star will expand onto the red giant branch, and eventually to the asymptotic giant branch with an outer hydrogen shell fusing to helium and an expanding helium shell that fuses to create a carbon and oxygen core by the triple-alpha process. Alternate fusing of the helium shell and hydrogen shells creates thermal pulses; these pulses combine with convective currents to create dust grains that are driven outward by radiation pressure creating strong stellar winds. The ejected mass forms a planetary nebula leaving behind a core, which is the remnant white dwarf. A white dwarf radiates light from residual heat, not from nuclear fusion.
Stars with very low mass White dwarf stars with less than 25% of a solar mass are all found in binary star systems. The proportion of white dwarfs in binary systems declines to 34% for masses in the range 0.5–0.75 M☉. These objects all have helium cores. It is thought that, over a lifespan that considerably exceeds the age of the universe (c. 13.8 billion years), such a star will eventually burn all its hydrogen, for a while becoming a blue dwarf, and end its evolution as a helium white dwarf composed chiefly of helium-4 nuclei. Due to the very long time this process takes, it is not thought to be the origin of the observed helium white dwarfs. Rather, they are believed to be mostly the product of mass loss in binary systems. Proposals to explain those helium white dwarfs that are not part of binary systems include mass loss due to a large exoplanetary companion, stars being stripped of material by companions exploding as supernovae, and various types of stellar mergers.
Stars with low to medium mass If the mass of a main-sequence star is between 0.5 and 8 M☉, 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 neon. Near the end of the period in which it undergoes fusion reactions, such a star will have a carbon–oxygen or oxygen-neon core that 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 to form a planetary nebula, leaving only the carbon–oxygen core. White dwarfs with a mass greater than 1.05 M☉ are termed ultramassive white dwarfs. When formed in single-star systems, these are expected to have an oxygen-neon core. However, a significant fraction (~20%) of ultramassive white dwarfs are formed through white dwarf mergers. In this case the result is a carbon-oxygen ultramassive white dwarf.
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, initially 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 that will leave behind a remnant neutron star, black hole, or possibly a more exotic form of compact star. Some main-sequence stars, of perhaps 8 to 10 M☉, 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. Although a few white dwarfs have been identified that may be of this type, most evidence for the existence of such comes from the novae called ONeMg or neon novae. The spectra of these novae exhibit abundances of neon, magnesium, and other intermediate-mass elements that appear to be only explicable by the accretion of material onto an oxygen–neon–magnesium white dwarf.
Type Iax supernova Type Iax supernovae, that involve helium accretion by a white dwarf, have been proposed to be a channel for transformation of this typ