Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius is the brightest star in the night sky with a visual Apparent magnitude of &minus1 The Hubble Space Telescope ( HST; also known colloquially as "the Hubble" or just "Hubble" is a space telescope that was carried into Sirius B, which is a white dwarf, can be seen as a faint dot to the lower left of the much brighter Sirius A.

A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth Degenerate matter is matter which has sufficiently high Density that the dominant contribution to its Pressure rises from the Pauli Exclusion As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense. The Sun (Sol is the Star at the center of the Solar System. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Their faint luminosity comes from the emission of stored heat. Luminosity has different meanings in several different fields of science In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature ^[1] They comprise roughly 6% of all known stars in the solar neighborhood. ^[2] The unusual faintness of white dwarfs was first recognized in 1910 by Henry Norris Russell, Edward Charles Pickering and Williamina Fleming;^{[3], p. Henry Norris Russell ( October 25, 1877 &ndash February 18, 1957) was an American Astronomer who along with Ejnar Edward Charles Pickering ( July 19 1846 – February 3 1919) was an American Astronomer and Physicist, brother Williamina Paton Stevens Fleming ( May 15, 1857 &ndash May 21, 1911) Astronomer, was born in Dundee, Scotland 1} the name white dwarf was coined by Willem Luyten in 1922. Willem Jacob Luyten ( Mar 7 1899, Semarang &ndash Nov 21 1994, Minneapolis) was a Dutch - American ^[4]

White dwarfs are thought to be the final evolutionary state of all stars whose mass is not too high—over 97% of the stars in our Galaxy. Stellar evolution is the process by which a Star undergoes a sequence of radical changes during its lifetime The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply ^{[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. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness A red giant is a luminous Giant star of low or intermediate mass (roughly 0 Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the The triple alpha process is a set of Nuclear fusion reactions by which three Helium nuclei ( Alpha particles are transformed into Carbon. If a red giant has insufficient mass to generate the core temperatures required to fuse carbon, an inert mass of carbon and oxygen will build up at its center. Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 After shedding its outer layers to form a planetary nebula, it will leave behind this core, which forms the remnant white dwarf. A planetary nebula is an Emission nebula consisting of a glowing shell of Gas and plasma formed by certain types of Stars when they die ^[6] Usually, therefore, white dwarfs are composed of carbon and oxygen. It is also possible that core temperatures suffice to fuse carbon but not neon, in which case an oxygen-neon-magnesium white dwarf may be formed. Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 Magnesium (mægˈniːziəm is a Chemical element with the symbol Mg, Atomic number 12 Atomic weight 24 ^[7] Also, some helium^[8][9] white dwarfs appear to have been formed by mass loss in binary systems. Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy, nor is it supported against gravitational collapse by the heat generated by fusion. Gravitational collapse in Astronomy is the inward fall of a massive body under the influence of the force of Gravity. It is supported only by electron degeneracy pressure, which enables it to be extremely dense. Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two Fermions cannot occupy the same Quantum state at the The physics of degeneracy yields a maximum mass for a nonrotating white dwarf, the Chandrasekhar limit—approximately 1. The Chandrasekhar limit limits the mass of bodies made from Electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of Electrons 4 solar masses—beyond which it cannot be supported by degeneracy pressure. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. 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. A Type Ia supernova is a sub-category of cataclysmic Variable Carbon detonation is a violent re-ignition of thermonuclear fusion in a dead star, which produces a Type Ia supernovae. ^[6][1] (SN 1006 is thought to be a famous example. SN 1006 was a Supernova, widely seen on Earth beginning in the year 1006 CE Earth was about 7200 light-years away from the supernova )

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. Color temperature is a characteristic of Visible light that has important applications in lighting photography videography publishing and other fields Over a very long time, a white dwarf will cool to temperatures at which it is no longer visible and become a cold black dwarf. A black dwarf is a hypothetical Star, created when a White dwarf becomes sufficiently cool to no longer emit significant Heat or Light ^[6] However, since no white dwarf can be older than the age of the Universe (approximately 13. The age of the Universe is the time elapsed between the theory of the Big Bang and the present day 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. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic ^[5][1]

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. A star system or stellar system is a small number of Stars which orbit each other bound by gravitational attraction. 40 Eridani (also known as Omicron2 Eridani, or Keid, from the Arabic word qayd, (egg shells) is a triple Star The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness 40 Eridani (also known as Omicron2 Eridani, or Keid, from the Arabic word qayd, (egg shells) is a triple Star A binary star is a Star system consisting of two Stars orbiting around their Center of mass. 40 Eridani (also known as Omicron2 Eridani, or Keid, from the Arabic word qayd, (egg shells) is a triple Star The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool Star, of the Main sequence, either late K 40 Eridani (also known as Omicron2 Eridani, or Keid, from the Arabic word qayd, (egg shells) is a triple Star The pair 40 Eridani B/C was discovered by Friedrich Wilhelm Herschel on January 31, 1783;^{[11], p. Sir Frederick William Herschel FRS KH ( 15 November 1738 – 25 August 1822) was a German -born British Events 1504 - France cedes Naples to Aragon. 1606 - Gunpowder Plot: Guy Fawkes Year 1783 ( MDCCLXXXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or 73} it was again observed by Friedrich Georg Wilhelm Struve in 1825 and by Otto Wilhelm von Struve in 1851. Friedrich Georg Wilhelm von Struve (Vasily Yakovlevich Struve ( April 15, 1793 &ndash November 23, 1864 ( Julian calendar Not to be confused with his grandson Otto Struve (1897&ndash1963 Otto Wilhelm von Struve ( May 7 1819 ( Julian ^[12][13] In 1910, it was discovered by Henry Norris Russell, Edward Charles Pickering and Williamina Fleming that despite being a dim star, 40 Eridani B was of spectral type A, or white. Henry Norris Russell ( October 25, 1877 &ndash February 18, 1957) was an American Astronomer who along with Ejnar Edward Charles Pickering ( July 19 1846 – February 3 1919) was an American Astronomer and Physicist, brother Williamina Paton Stevens Fleming ( May 15, 1857 &ndash May 21, 1911) Astronomer, was born in Dundee, Scotland In Astronomy, stellar classification is a classification of Stars based initially on photospheric temperature and its associated Spectral characteristics ^[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. Walter Sydney Adams ( December 20 1876 &ndash May 11 1956) was an American Astronomer. ^[14]

The companion of Sirius, Sirius B, was next to be discovered. Sirius is the brightest star in the night sky with a visual Apparent magnitude of &minus1 Sirius is the brightest star in the night sky with a visual Apparent magnitude of &minus1 During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used just such precise measurements to determine that the stars Sirius (α Canis Majoris) and Procyon (α Canis Minoris) were changing their positions. Friedrich Wilhelm Bessel (22 July 1784 &ndash 17 March 1846 was a German Mathematician, Astronomer, and systematizer of the Bessel functions This article is about the star Procyon is also the mammalian genus to which raccoons belong 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. H. 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. Events 1504 - France cedes Naples to Aragon. 1606 - Gunpowder Plot: Guy Fawkes Year 1862 was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common year starting on Monday Alvan Graham Clark ( July 10, 1832 &ndash June 9, 1897) born in Fall River, Massachusetts, was an American ^[16] Walter Adams announced in 1915 that he had found the spectrum of Sirius B to be similar to that of Sirius. Walter Sydney Adams ( December 20 1876 &ndash May 11 1956) was an American Astronomer. ^[17]

In 1917, Adriaan Van Maanen discovered Van Maanen's Star, an isolated white dwarf. Adriaan van Maanen ( March 31 1884, Sneek &ndash January 26 1946, Pasadena) was a Dutch - American Van Maanen's star is a White dwarf Star. Out of the white dwarfs known it is the third closest to the Sun after Sirius B and Procyon B ^[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. The proper motion of a Star is the measurement of its change in position in the sky over time after Improper motions are accounted for 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. Willem Jacob Luyten ( Mar 7 1899, Semarang &ndash Nov 21 1994, Minneapolis) was a Dutch - American Sir Arthur Stanley Eddington, OM (28 December 1882 – 22 November 1944 was an English Astrophysicist of the early 20th century ^[23][4] 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. The Sloan Digital Sky Survey or SDSS is a major multi-filter imaging and spectroscopic Redshift survey using a dedicated 2 ^[26]

Composition and structure

Although white dwarfs are known with estimated masses as low as 0. The Hertzsprung-Russell diagram (usually referred to by the abbreviation H-R diagram or HRD, also known as a colour-magnitude diagram, or CMD In Astronomy, stellar classification is a classification of Stars based initially on photospheric temperature and its associated Spectral characteristics Brown dwarfs are sub- stellar objects with a mass below that necessary to maintain Hydrogen -burning Nuclear fusion reactions in their cores as do stars According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool Star, of the Main sequence, either late K A subdwarf star, sometimes denoted by "sd" is Luminosity class VI under the Yerkes spectral classification system The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness Subgiant star is a class of Stars that are slightly brighter than normal Main sequence (dwarf stars of the same spectral class but not as bright as A giant star is a Star with substantially larger Radius and Luminosity than a Main sequence star of the same surface temperature. The luminosity class II in the Yerkes spectral classification is given to bright giants. Supergiants are among the most massive Stars In the Hertzsprung-Russell diagram they occupy the top region of the diagram A hypergiant ( luminosity class 0) is a Star with a tremendous Mass and Luminosity, showing signs of a very high rate of mass loss In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard In Astronomy, absolute magnitude (also known as absolute visual magnitude) is the Apparent magnitude an object would have if it were at a standard 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. In Astronomy, the solar radius is a unit of Length used to express the size of Stars It is equal to the current radius of the Sun. 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. For other uses of the words gram or gramme see Gram (disambiguation. This article is about the tonne or metric ton For other tons see Ton. A cubic centimetre or cubic centimeter (symbol cm3 —the abbreviation cc, though widely used is deprecated is a commonly used unit of Volume ^[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. In Astronomy, the term compact star (sometimes compact object) is used to refer collectively to White dwarfs Neutron stars other exotic A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e A quark star or strange star is a hypothetical type of Exotic star composed of Quark matter, or Strange matter. ^[30]

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. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. This was done for Sirius B by 1910,^[31] yielding a mass estimate of 0. 94 solar mass. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. (A more modern estimate is 1. 00 solar mass. )^[32] 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. Star The effective temperature of a Star is the temperature of a Black body with the same luminosity per surface area (\mathcal{F}_{Bol} A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary infinitely within a continuum. 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". Ernst Julius Öpik ( October 23, 1893 – September 10, 1985) was a notable Estonian astronomer and astrophysicist who spent the last The Sun (Sol is the Star at the center of the Solar System. ^[33] As Arthur Stanley Eddington put it later in 1927:^{[34], p. Sir Arthur Stanley Eddington, OM (28 December 1882 – 22 November 1944 was an English Astrophysicist of the early 20th century 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. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 In Physics, Light or other forms of Electromagnetic radiation of a certain wavelength originating from a source placed in a region of stronger gravitational ^[23] This was confirmed when Adams measured this redshift in 1925. ^[35]

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. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny A chemical bond is the physical process responsible for the attractive interactions between Atoms and Molecules and which confers stability to diatomic and polyatomic In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J 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. An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom ^[23] Eddington, however, wondered what would happen when this plasma cooled and the energy which kept the atoms ionized was no longer present. ^[36] This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Sir Ralph Howard Fowler OBE FRS ( January 17 1889 &ndash July 28 1944) was a British Physicist and Astronomer Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons 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. The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925 In Quantum physics, a quantum state is a mathematical object that fully describes a quantum system. In Statistical mechanics, Fermi-Dirac statistics is a particular case of Particle statistics developed by Enrico Fermi and Paul Dirac that ^[37] 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. In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy Fermi liquid is a generic term for a quantum mechanical Liquid of Fermions that arises under certain physical conditions when the Temperature This state of the electrons, called degenerate, meant that a white dwarf could cool to zero temperature and still possess high energy. Degenerate matter is matter which has sufficiently high Density that the dominant contribution to its Pressure rises from the Pauli Exclusion 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. In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain This means that some electrons must have high momentum and hence high kinetic energy. ^[36][38]

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. ^[36][39] This electron degeneracy pressure is what supports a white dwarf against gravitational collapse. Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two Fermions cannot occupy the same Quantum state at the Gravitational collapse in Astronomy is the inward fall of a massive body under the influence of the force of Gravity. 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^[40] and in 1930 by Edmund C. Stoner. Edmund Clifton Stoner ( October 2, 1899, in Surrey, England – December 27, 1968 in Leeds, England ^[41] The modern value of the limit was first published in 1931 by Subrahmanyan Chandrasekhar in his paper "The Maximum Mass of Ideal White Dwarfs". Padma Vibhushan Subrahmanyan Chandrasekhar, FRS ( Tamil: சுப்பிரமணியன் சந்திரசேகர் English ˌtʃʌndrəˈʃeɪkɑr( ^[42] 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. ^{[43], 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,^[38] leading to the commonly-quoted value of 1. See also List of elements by atomic number In Chemistry and Physics, the atomic number (also known as the proton The atomic mass (ma is the Mass of an atom most often expressed in unified atomic mass units The atomic mass may be considered to be the total mass 4 solar masses. (Near the beginning of the 20th century, there was reason to believe that stars were composed chiefly of heavy elements,^{[41], 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. William Alfred "Willie" Fowler ( August 9, 1911 &ndash March 14, 1995) was an American Astrophysicist. The Nobel Prize in Physics (Nobelpriset i fysik is awarded once a year by the Royal Swedish Academy of Sciences. ^[44] The limiting mass is now called the Chandrasekhar limit. The Chandrasekhar limit limits the mass of bodies made from Electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of Electrons

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 or black hole. In Nuclear physics, a nuclear reaction is the process in which two nuclei or nuclear particles collide to produce products different from the initial particles The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Gravitation is a natural Phenomenon by which objects with Mass attract one another A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e ^[45] 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. A Type Ia supernova is a sub-category of cataclysmic Variable ^[46]

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). Luminosity has different meanings in several different fields of science The Hertzsprung-Russell diagram (usually referred to by the abbreviation H-R diagram or HRD, also known as a colour-magnitude diagram, or CMD 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,^[47] or the even lower-temperature brown dwarfs. The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool Star, of the Main sequence, either late K Brown dwarfs are sub- stellar objects with a mass below that necessary to maintain Hydrogen -burning Nuclear fusion reactions in their cores as do stars ^[48]

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. Potential energy can be thought of as Energy stored within a physical system The kinetic energy of an object is the extra Energy which it possesses due to its motion 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 gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass 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. Degenerate matter is matter which has sufficiently high Density that the dominant contribution to its Pressure rises from the Pauli Exclusion In Quantum physics, the Heisenberg uncertainty principle states that locating a particle in a small region of space makes the Momentum of the particle uncertain The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. 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. ^[38]

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

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:

Solving this for the radius, R, gives^[38]

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:

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

If we equate this to the magnitude of E_g, we find that R drops out and the mass, M, is forced to be^[38]

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.

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. In Physics and Thermodynamics, an equation of state is a relation between state variables More specifically an equation of state is a thermodynamic 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. Fluid statics (also called hydrostatics) is the Science of Fluids at rest and is a sub-field within Fluid mechanics. In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass. ^{[43], 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 Chandrasekhar limit limits the mass of bodies made from Electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of Electrons 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. A Fermi gas, or Free electron gas, is a collection of non-interacting Fermions. 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. ^[49][43]

These computations all assume that the white dwarf is nonrotating. 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. A rotating frame of reference is a special case of a Non-inertial reference frame that is rotating relative to an Inertial reference frame. ^[50] 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,^[51] there is no limit to the mass for which it is possible for a model white dwarf to be in static equilibrium. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress. Sir Fred Hoyle FRS ( 24 June, 1915  &ndash 20 August, 2001) was an English Astronomer primarily Not all of these model stars, however, will be dynamically stable. In physics the term dynamics customarily refers to the time evolution of physical processes ^[52]

Radiation and cooling

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. The main sequence is the name for a continuous and distinctive band of stars that appear on a plot of stellar color versus brightness According to the Hertzsprung-Russell diagram, a red dwarf star is a small and relatively cool Star, of the Main sequence, either late K ^[53] White dwarf effective surface temperatures extend from over 150,000 K^[25] to under 4,000 K. Star The effective temperature of a Star is the temperature of a Black body with the same luminosity per surface area (\mathcal{F}_{Bol} ^[54][55] 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. The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit ^[55] 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. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. This enables the composition and structure of their atmospheres to be studied by soft X-ray and extreme ultraviolet observations. X-ray astronomy is an observational branch of Astronomy, which deals with the study of X-ray emission from celestial objects Ultraviolet astronomy is generally used to refer to observations at Ultraviolet wavelengths between approximately 10 and 320 nanometres ^[56]

A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). IK Pegasi (or HR 8210) is a Binary star system in the Constellation Pegasus. This white dwarf has a surface temperature of 35,500 K.

Unless the white dwarf accretes matter from a companion star or other source, this radiation comes from its stored heat, which is not replenished. In Astrophysics, the term accretion is used for at least two distinct processes White dwarfs have an extremely small surface area to radiate this heat from, so they remain 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. Bergeron, Ruiz, and Leggett, for example, estimate that after a carbon white dwarf of 0. Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 59 solar mass with a hydrogen atmosphere has cooled to a surface temperature of 7,140 K, taking approximately 1. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 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. ^{[57], 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. In Physics and Chemistry, plasma is an Ionized Gas, in which a certain proportion of Electrons are free rather than being bound The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Crystallization is the (natural or artificial process of formation of solid Crystals precipitating from a homogeneous --> identical Solution ^[58] The crystal structure is thought to be a body-centered cubic lattice. The cubic crystal system (or isometric) is a Crystal system where the Unit cell is in the shape of a Cube. ^[59][5] In 1995 it was pointed out that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory,^[60] and in 2004, Travis Metcalfe and a team of researchers at the Harvard-Smithsonian Center for Astrophysics estimated, on the basis of such observations, that approximately 90% of the mass of BPM 37093 had crystallized. Asteroseismology (from Greek grc ἀστήρ astēr, "star" grc σεισμός seismos, "earthquake" and grc -λογία The Harvard-Smithsonian Center for Astrophysics (CfA is arguably the largest and most diverse astrophysical institution in the world where scientists carry out a broad program of research BPM 37093 is a variable White dwarf Star of the DAV or ZZ Ceti, type with a Hydrogen atmosphere and an unusually high mass ^{[58][61][62][63]} Other work gives a crystallized mass fraction of between 32% and 82%. ^[64]

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K. ^[65][26] 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. Selection bias is a distortion of evidence or data that arises from the way that the data are collected ^[66] This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K,^[67] and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,900 K. WD 0346+246 is a White dwarf Star. It was discovered in 1997 when examination of photographs taken for a survey of Brown dwarfs in the ^[54] The reason for this is that, as the Universe's age is finite,^[68] 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. In Astronomy, the luminosity function gives the number of stars or galaxies with a given Luminosity. A disc is a component of Disc galaxies, such as Spiral galaxies, or Lenticular galaxies. ^[66]

A white dwarf will eventually cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. A black dwarf is a hypothetical Star, created when a White dwarf becomes sufficiently cool to no longer emit significant Heat or Light 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. Spectroscopy was originally the study of the interaction between Radiation and Matter as a function of Wavelength (λ Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical 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. Évry Léon Schatzman (born September 16, 1920 in Neuilly-sur-Seine, France) is a French Astrophysicist. The surface gravity, g, of an astronomical or other object is the Gravitational acceleration experienced at its surface ^{[69][70], §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 asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass Stars This is a period of Stellar evolution 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. ^{[55][71], §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. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J 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. An isothermal process is a Thermodynamic process in which the Temperature of the System stays Constant: &Delta T = 0 The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation. ^[55]

The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941,^[53][72] and various classification schemes have been proposed and used since then. Gerard Peter Kuiper ( born Gerrit Pieter Kuiper ( ( December 7 1905, Harenkarspel ( Tuitjenhorn) Netherlands &ndash ^[73][74] The system currently in use was introduced by Edward M. Sion and his 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. Star The effective temperature of a Star is the temperature of a Black body with the same luminosity per surface area (\mathcal{F}_{Bol} 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. Spectroscopic notation provides various ways to specify atomic ionization states, as well as atomic and Molecular orbitals. 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. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Spectroscopic notation provides various ways to specify atomic ionization states, as well as atomic and Molecular orbitals. Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1

The symbols ? and : may also be used if the correct classification is uncertain. ^[53][25]

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority (approximately three-quarters) of all observed white dwarfs. ^[55] The vast majority of the classifiable remainder (DB, DC, DO, DZ, and cool DQ) have helium-dominated atmospheres. A tiny fraction (roughly 0. 1%) have carbon-dominated atmospheres, the "hot" (above 15,000 K) DQ class. ^[75] Assuming that carbon and metals are not present, which spectral classification is seen depends on the effective temperature. Star The effective temperature of a Star is the temperature of a Black body with the same luminosity per surface area (\mathcal{F}_{Bol} 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. ^{[71],§ 2. 4[55]} The reason for the absence of white dwarfs with helium-dominated atmospheres and effective temperatures between 30,000 K and 45,000 K, called the DB gap, is not clear. It is suspected to be due to competing atmospheric evolutionary processes, such as gravitational separation and convective mixing. ^[55]

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. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges The gauss, abbreviated as G is the Cgs unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic Patrick Maynard Stuart Blackett Baron Blackett OM CH FRS ( 18 November 1897 &ndash 13 July 1974) was an In Physics, the angular momentum of a particle about an origin is a vector quantity equal to the mass of the particle multiplied by the Cross product of the position ^[76] This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted. The Blackett effect, also called gravitational magnetism, is the hypothetical generation of a Magnetic field by an uncharged rotating body ^{[77], 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. Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic 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. ^{[70], §8;[78], 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. GJ 742 is a White dwarf Star. Although photographed in the 19th century as part of the Carte du Ciel project it was not determined to be a white In Electrodynamics, circular polarization (also circular polarisation) of Electromagnetic radiation is a Polarization such that the tip of the ^[79] It is thought to have a surface field of approximately 300 million gauss (30 kT). ^{[70], §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). ^[80][81]

Variability

Main article: Pulsating white dwarf

See also: Cataclysmic variables

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. A pulsating white dwarf is a White dwarf Star whose Luminosity varies due to non-radial Gravity wave pulsations within itself Luminosity has different meanings in several different fields of science For the astronomical object see Variable star. Variable Star is a 2006 novel written by Spider Robinson ^{[70], § 7. 1. 1;[84]} 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. HL Tau 76 is a variable White dwarf Star of the DAV (or ZZ Ceti type Arlo U Landolt (born 1935 is an American Astronomer. Landolt has worked principally in Photometry and has published a number of widely used lists of 5 minutes. ^[85] 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. In Fluid dynamics, gravity waves are waves generated in a Fluid medium or at the interface between two media (e ^{[70], § 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;^{[70], pp. 891, 895} DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB;^{[55], p. 3525} and GW Vir stars (sometimes subdivided into DOV and PNNV stars), with atmospheres dominated by helium, carbon, and oxygen. ^{[83],§1. 1, 1. 2;[86],§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. The Hertzsprung-Russell diagram (usually referred to by the abbreviation H-R diagram or HRD, also known as a colour-magnitude diagram, or CMD The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass Stars This is a period of Stellar evolution They may be called pre-white dwarfs. ^{[83], § 1. 1;[87]} 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. Asteroseismology (from Greek grc ἀστήρ astēr, "star" grc σεισμός seismos, "earthquake" and grc -λογία ^[88]

Formation

White dwarfs are thought to represent the end point of stellar evolution for main-sequence stars with masses from about 0. Stellar evolution is the process by which a Star undergoes a sequence of radical changes during its lifetime 07 to 10 solar masses. ^[89][5] 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. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. 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. Helium-4 ( or) is a non- Radioactive and light Isotope of Helium. 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^{[8][9][90][91][92][6]} or mass loss due to a large planetary companion. ^[93]

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. Helium ( He) is a colorless odorless tasteless non-toxic Inert Monatomic Chemical Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the The triple alpha process is a set of Nuclear fusion reactions by which three Helium nuclei ( Alpha particles are transformed into Carbon. Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 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. The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass Stars This is a period of Stellar evolution It will then expel most of its outer material, creating a planetary nebula, until only the carbon-oxygen core is left. A planetary nebula is an Emission nebula consisting of a glowing shell of Gas and plasma formed by certain types of Stars when they die This process is responsible for the carbon-oxygen white dwarfs which form the vast majority of observed white dwarfs. ^[90][94][95]

Stars with medium to high mass

If a star is sufficiently massive, 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 as the mass of its central, non-fusing, core, supported by electron degeneracy pressure, will eventually exceed the largest possible mass supportable by degeneracy pressure. Electron degeneracy pressure is a consequence of the Pauli exclusion principle, which states that two Fermions cannot occupy the same Quantum state at the 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. Gravitational collapse in Astronomy is the inward fall of a massive body under the influence of the force of Gravity. Type II Supernova, or core-collapse supernova, is a sub-category of cataclysmic Variable stars that results from the internal collapse and violent explosion A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e In Astronomy, the term compact star (sometimes compact object) is used to refer collectively to White dwarfs Neutron stars other exotic ^[89][96] 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. The solar mass is a standard way to express Mass in Astronomy, used to describe the masses of other Stars and galaxies. The carbon burning process is a set of Nuclear fusion reactions that take place in massive Stars (at least 4 MSun at birth that have used up The neon burning process is a set of Nuclear fusion reactions that take place in massive Stars (at least 8 MSun) 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. Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the Neon (ˈniːɒn is the Chemical element that has the symbol Ne and Atomic number 10 Magnesium (mægˈniːziəm is a Chemical element with the symbol Mg, Atomic number 12 Atomic weight 24 A supernova (plural supernovae or supernovas) is a stellar Explosion. ^[97][98] 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. A nova (pl novae or novas) is a Cataclysmic nuclear explosion caused by the accretion of hydrogen onto the surface of a White ^[7][99][100]

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. A black dwarf is a hypothetical Star, created when a White dwarf becomes sufficiently cool to no longer emit significant Heat or Light 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. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy A year (from Old English gēr) is the time between two recurrences of an event related to the Orbit of the Earth around the Sun A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth ^{[101], §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. In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus A Type Ia supernova is a sub-category of cataclysmic Variable ^{[101], §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. The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive Some simple grand unified theories predict a proton lifetime of no more than 10⁴⁹ years. Grand Unification, grand unified theory, or GUT refers to any of several very similar unified field theories or models in Physics that In Particle physics, proton decay is a hypothetical form of Radioactive decay in which the Proton decays into lighter Subatomic particles 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. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature In Quantum gravity, a virtual black hole is a Black hole which has a temporary existence as a result of a Quantum fluctuation of Spacetime. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei decay, until it loses so much mass as to become a nondegenerate lump of matter, and finally disappears completely. The nucleus of an Atom is the very dense region consisting of Nucleons ( Protons and Neutrons, at the center of an atom ^{[101], §IV.}

Stellar system

A white dwarf's stellar and planetary system is inherited from its progenitor star and may interact with the white dwarf in various ways. A star system or stellar system is a small number of Stars which orbit each other bound by gravitational attraction. 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. The Spitzer Space Telescope (formerly the Space Infrared Telescope Facility, SIRTF) is an Infrared Space observatory. The Helix Nebula, also known as The helix or NGC 7293, is a large Planetary nebula (PN in the sky and is placed the zodiac Constellation It is possible that infalling material from this may cause X-ray emission from the central star. ^[102][103] 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. Period 110 - 1016 seconds--> Giclas 29-38 is a variable White dwarf Star of the DAV or ZZ Ceti,whose variability is due to The asymptotic giant branch is the region of the Hertzsprung-Russell diagram populated by evolving low to medium-mass Stars This is a period of Stellar evolution ^[104] If a white dwarf is in a binary system with a stellar companion, a variety of phenomena may occur, including novae and Type Ia supernovae. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. A nova (pl novae or novas) is a Cataclysmic nuclear explosion caused by the accretion of hydrogen onto the surface of a White A Type Ia supernova is a sub-category of cataclysmic Variable 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. A super soft X-ray source is an astronomical source of very low energy X-rays.

Type Ia supernovae

Multiwavelength X-ray image of SN 1572 or Tycho's Nova, the remnant of a Type Ia supernova. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. SN 1572 ( Tycho's Supernova, Tycho's Nova) "B Cassiopeiae" (B Cas or 3C 10 was a Supernova of Type Ia in the Tycho Brahe, born Tyge Ottesen Brahe ( December 14 1546 &ndash October 24 1601) was a Danish nobleman

Main article: Type Ia supernova

The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~1. A Type Ia supernova is a sub-category of cataclysmic Variable The Chandrasekhar limit limits the mass of bodies made from Electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of Electrons 4 solar masses. (This limit may increase if the white dwarf is rotating rapidly and nonuniformly. )^[105] White dwarfs in binary systems, however, can accrete material from a companion star, increasing both their mass and their density. A binary star is a Star system consisting of two Stars orbiting around their Center of mass. 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. In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus A neutron star is a type of remnant that can result from the Gravitational collapse of a massive Star during a Type II, Type Ib or Type ^[45]

Accretion provides the currently favored mechanism, the single-degenerate model, for type Ia supernovae. A Type Ia supernova is a sub-category of cataclysmic Variable In this model, a carbon-oxygen white dwarf accretes material from a companion star,^{[46], p. Carbon (kɑɹbən is a Chemical element with the symbol C and its Atomic number is 6 Oxygen (from the Greek roots ὀξύς (oxys (acid literally "sharp" from the taste of acids and -γενής (-genēs (producer literally begetteris the 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. Physical compression is the result of the subjection of a material to Compressive stress, resulting in reduction of Volume. Carbon detonation is a violent re-ignition of thermonuclear fusion in a dead star, which produces a Type Ia supernovae. The carbon burning process is a set of Nuclear fusion reactions that take place in massive Stars (at least 4 MSun at birth that have used up ^[46] 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. Thermal runaway refers to a situation where an increase in temperature changes the conditions in a way that causes a further increase in temperature leading to a destructive result The thermonuclear flame consumes much of the white dwarf in a few seconds, causing a type Ia supernova explosion that obliterates the star. In Physics and Nuclear chemistry, nuclear fusion is the process by which multiple- like charged atomic nuclei join together to form a heavier nucleus ^[1][46][106] 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. ^{[46], p. 14.}

Cataclysmic variables

Main article: Cataclysmic variable star

When accretion of material does not push a white dwarf close to the Chandrasekhar limit, accreted hydrogen-rich material on the surface may still ignite in a thermonuclear explosion. Cataclysmic variable stars ( CV) are stars which irregularly increase in brightness by a large factor then drop back down to a quiescent state Hydrogen (ˈhaɪdrədʒən is the Chemical element with Atomic number 1 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. A nova (pl novae or novas) is a Cataclysmic nuclear explosion caused by the accretion of hydrogen onto the surface of a White Astronomers have also observed dwarf novae, which have smaller, more frequent luminosity peaks than classical novae. A dwarf nova (pl novae) is a type of Cataclysmic variable, consisting of a close Binary star system in which one of the components is a These are thought to not be caused by fusion but rather by the release of gravitational potential energy during accretion. Potential energy can be thought of as Energy stored within a physical system In general, binary systems with a white dwarf accreting matter from a stellar companion are called cataclysmic variables. Cataclysmic variable stars ( CV) are stars which irregularly increase in brightness by a large factor then drop back down to a quiescent state As well as novae and dwarf novae, several other classes of these variables are known. ^{[1][46][107][108]} Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources. X-radiation (composed of X-rays) is a form of Electromagnetic radiation. ^[108]

See also

• 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)

References

External links and further reading

General

• White Dwarf Stars, Steven D. Kawaler, in Stellar remnants, S. D. Kawaler, I. Novikov, and G. Srinivasan, edited by Georges Meynet and Daniel Schaerer, Berlin: Springer, 1997. Lecture notes for Saas-Fee advanced course number 25. ISBN 3540615202.

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 0471873179.
• Physics of white dwarf stars, D. Koester and G. Chanmugam, Reports on Progress in Physics 53 (1990), pp. 837–915.
• White dwarf stars and the Chandrasekhar limit, Dave Gentile, Master's thesis, DePaul University, 1995. DePaul University is a private institution of Higher education and Research in Chicago, Illinois, U
• 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

• Asteroseismology of white dwarf stars, D. E. Winget, Journal of Physics: Condensed Matter 10, #49 (December 14, 1998), pp. Events 1287 - St Lucia's flood: The Zuider Zee sea wall in the Netherlands collapses killing over 50000 people Year 1998 ( MCMXCVIII) was a Common year starting on Thursday (link will display full 1998 Gregorian calendar) 11247–11261. DOI 10. 1088/0953-8984/10/49/014.

Magnetic field

• Magnetism in Isolated and Binary White Dwarfs, D. T. Wickramasinghe and Lilia Ferrario, Publications of the Astronomical Society of the Pacific 112, #773 (July 2000), pp. 873–924.

Frequency

• White Dwarfs and Dark Matter, B. K. Gibson and C. Flynn, Science 292, #5525 (June 22, 2001), p. Events 217 BC - Battle of Raphia: Ptolemy IV of Egypt defeats Antiochus III the Great of the Seleucid kingdom. Year 2001 ( MMI) was a Common year starting on Monday according to the Gregorian calendar. 2211. DOI 10.1126/science.292.5525.2211a.

Observational

• Testing the White Dwarf Mass-Radius Relation with HIPPARCOS, J. L. Provencal, H. L. Shipman, Erik Hog, P. Thejll, The Astrophysical Journal 494 (February 20, 1998), pp. Events 1472 - Orkney and Shetland are left by Norway to Scotland, due to a Dowry payment Year 1998 ( MCMXCVIII) was a Common year starting on Thursday (link will display full 1998 Gregorian calendar) 759–767.
• Discovery of New Ultracool White Dwarfs in the Sloan Digital Sky Survey, Evalyn Gates, Geza Gyuk, Hugh C. Harris, Mark Subbarao, Scott Anderson, S. J. Kleinman, James Liebert, Howard Brewington, J. Brinkmann, Michael Harvanek, Jurek Krzesinski, Don Q. Lamb, Dan Long, Eric H. Neilsen, Jr. , Peter R. Newman, Atsuko Nitta, and Stephanie A. Snedden, The Astrophysical Journal 612, #2 (September 2004), pp. L129–L132.
• Villanova University White Dwarf Catalogue WD, G. P. McCook and E. M. Sion.
• Dufour, P. ; Liebert, James; Fontaine, G. ; Behara, N. (2007). "Rare White dwarf stars with carbon atmospheres". Nature 450: 522-524.