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104-472: Ross 548 is a white dwarf in the equatorial constellation of Cetus . With a mean apparent visual magnitude of 14.2 it is much too faint to be visible to the naked eye. Based on parallax measurements, it is located at a distance of 107  light years from the Sun . It was found to be variable in 1970 and in 1972 it was given the variable star designation ZZ Ceti . This is a pulsating white dwarf of

208-447: A Planck star would form. Regardless, it is argued that gravitational collapse ceases at that stage and a singularity, therefore, does not form. The radii of larger mass neutron stars (about 2.8 solar mass) are estimated to be about 12 km, or approximately 2 times their equivalent Schwarzschild radius. It might be thought that a sufficiently massive neutron star could exist within its Schwarzschild radius (1.0 SR) and appear like

312-730: 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 40 000  K . 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

416-418: A main-sequence star of low or intermediate mass ends, such a star will expand to a red giant and fuse helium to carbon and oxygen in its core by the triple-alpha process . If a red giant has insufficient mass to generate the core temperatures required to fuse carbon (around 10  K ), an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms

520-468: A planetary nebula , it will leave behind a core, which is the remnant white dwarf. Usually, white dwarfs are composed of carbon and oxygen ( CO white dwarf ). If the mass of the progenitor is between 7 and 9  solar masses ( M ☉ ), the core temperature will be sufficient to fuse carbon but not neon , in which case an oxygen–neon– magnesium ( ONeMg or ONe ) white dwarf may form. Stars of very low mass will be unable to fuse helium; hence,

624-531: A planetary nebula . If it has a companion star , a white dwarf-sized object can accrete matter from the companion star. Before it reaches the Chandrasekhar limit (about one and a half times the mass of the Sun, at which point gravitational collapse would start again), the increasing density and temperature within a carbon-oxygen white dwarf initiate a new round of nuclear fusion, which is not regulated because

728-506: A band of lowest-available energy states, the Fermi sea . This state of the electrons, called degenerate , meant that a white dwarf could cool to zero temperature and still possess high energy. Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing

832-541: A black hole remains rather controversial. According to theories based on quantum mechanics , at a later stage, the collapsing object will reach the maximum possible energy density for a certain volume of space or the Planck density (as there is nothing that can stop it). This is the point at which it has been hypothesized that the known laws of gravity cease to be valid. There are competing theories as to what occurs at this point. For example loop quantum gravity predicts that

936-479: A black hole without having all the mass compressed to a singularity at the center; however, this is probably incorrect. Within the event horizon , the matter would have to move outward faster than the speed of light in order to remain stable and avoid collapsing to the center. No physical force, therefore, can prevent a star smaller than 1.0 SR from collapsing to a singularity (at least within the currently accepted framework of general relativity ; this does not hold for

1040-514: 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

1144-611: 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

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1248-447: A density of between 10 and 10  g/cm . 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 . White dwarfs were found to be extremely dense soon after their discovery. If a star is in a binary system, as is the case for Sirius B or 40 Eridani B, it is possible to estimate its mass from observations of

1352-412: A density of over 25 000  times that of the Sun , which was so high that he called it "impossible". As Arthur Eddington put it later, 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;

1456-432: A gradual gravitational collapse of interstellar medium into clumps of molecular clouds and potential protostars . The compression caused by the collapse raises the temperature until thermonuclear fusion occurs at the center of the star, at which point the collapse gradually comes to a halt as the outward thermal pressure balances the gravitational forces. The star then exists in a state of dynamic equilibrium . During

1560-413: A helium white dwarf may form by mass loss in an interacting binary star system. Because the material in a white dwarf no longer undergoes fusion reactions, it 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,

1664-415: A high color temperature , will lessen and redden with time. Over a very long time, a white dwarf will cool enough that its material will begin to crystallize, starting with the core. The star's low temperature means it will no longer emit significant heat or light, and it will become a cold black dwarf . Because the length of time it takes for a white dwarf to reach this state is calculated to be longer than

1768-408: A hydrogen or mixed hydrogen-helium atmosphere. This makes old white dwarfs with this kind of atmosphere bluer than the main cooling sequence. Hence these white dwarfs are called IR-faint white dwarfs . 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 –

1872-404: 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

1976-428: A luminosity from over 100 times that of the Sun to under 1 ⁄ 10 000 that of the Sun. Hot white dwarfs, with surface temperatures in excess of 30 000  K , have been observed to be sources of soft (i.e., lower-energy) X-rays . This enables the composition and structure of their atmospheres to be studied by soft X-ray and extreme ultraviolet observations . White dwarfs also radiate neutrinos through

2080-405: A match for the possible quantum states available to that electron, hence radiative heat transfer within a white dwarf is low; it does, however, have 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 10  K shortly after the formation of the white dwarf and reaching less than 10  K for

2184-416: 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

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2288-441: 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 absoption (CIA) of hydrogen molecules colliding with helium atoms. This affects the optical red and infrared brightness of white dwarfs with

2392-531: 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. White dwarfs are thought to represent

2496-401: A rather simple form describable by the historic Schwarzschild metric in the spherical limit and by the more recently discovered Kerr metric if angular momentum is present. If the precursor has a magnetic field, it is dispelled during the collapse, as black holes are thought to have no magnetic field of their own. On the other hand, the nature of the kind of singularity to be expected inside

2600-527: 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

2704-598: 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. White dwarfs have low luminosity and therefore occupy

2808-411: A skin or "atmosphere" of normal matter on the order of a millimeter thick, underneath which they are composed almost entirely of closely packed neutrons called neutron matter with a slight dusting of free electrons and protons mixed in. This degenerate neutron matter has a density of about 6.65 × 10  kg/m . The appearance of stars composed of exotic matter and their internal layered structure

2912-465: 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 50 400  K by the effective temperature . For example, a white dwarf with only He I lines in its spectrum and an effective temperature of 15 000  K could be given

3016-499: A star will have a carbon–oxygen 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, creating a planetary nebula , until only the carbon–oxygen core is left. This process is responsible for the carbon–oxygen white dwarfs that form

3120-424: 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, μ e , equal to 2.5, giving a limit of 0.91  M ☉ .) Together with William Alfred Fowler , Chandrasekhar received

3224-458: 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 relationship between the mass and radius of low-mass white dwarfs can be estimated using

Ross 548 - Misplaced Pages Continue

3328-515: 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 . This was confirmed when Adams measured this redshift in 1925. Such densities are possible because white dwarf material

3432-439: A white dwarf, which is 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

3536-488: 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 effective surface temperatures extend from over 150 000  K to barely under 4000 K. In accordance with the Stefan–Boltzmann law , luminosity increases with increasing surface temperature (proportional to T ); this surface temperature range corresponds to

3640-430: 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 15 000  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

3744-520: 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. 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

3848-414: Is called the star's death (when a star has burned out its fuel supply), it will undergo a contraction that can be halted only if it reaches a new state of equilibrium. Depending on the mass during its lifetime, these stellar remnants can take one of three forms: The collapse of the stellar core to a white dwarf takes place over tens of thousands of years, while the star blows off its outer envelope to form

3952-412: 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. Early calculations suggested that there might be white dwarfs whose luminosity varied with a period of around 10 seconds, but searches in

4056-487: 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 . 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

4160-438: 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

4264-412: 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

Ross 548 - Misplaced Pages Continue

4368-419: 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; 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

4472-455: 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

4576-417: Is radiating 0.3% of the luminosity of the Sun at an effective temperature of 12,281 K. Ross 548 is spinning with a period of ~38 hours. The dominant pulsation mode of this object has a period of 213.1326 seconds. It has up to 11 known pulsation modes in total. White dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter . A white dwarf

4680-431: Is seen depends on the effective temperature. Between approximately 100 000  K to 45 000  K , the spectrum will be classified DO, dominated by singly ionized helium. From 30 000  K to 12 000  K , the spectrum will be DB, showing neutral helium lines, and below about 12 000  K , the spectrum will be featureless and classified DC. Molecular hydrogen ( H 2 ) has been detected in spectra of

4784-458: 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

4888-440: 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 thought to be

4992-403: 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 × 10 to 10  gauss (0.2 T to 100 kT). The large number of presently known magnetic white dwarfs is due to the fact that most white dwarfs are identified by low-resolution spectroscopy, which

5096-501: Is unclear since any proposed equation of state of degenerate matter is highly speculative. Other forms of hypothetical degenerate matter may be possible, and the resulting quark stars , strange stars (a type of quark star), and preon stars , if they exist, would, for the most part, be indistinguishable from a neutron star : In most cases, the exotic matter would be hidden under a crust of "ordinary" degenerate neutrons. According to Einstein's theory, for even larger stars, above

5200-405: 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

5304-460: Is very dense : its mass is comparable to the Sun 's, while its volume is comparable to Earth 's. No nuclear fusion takes place in a white dwarf. Instead, the light it radiates comes from the residual heat stored in it. The nearest known white dwarf is Sirius B , at 8.6 light years, the smaller component of the Sirius binary star . There are currently thought to be eight white dwarfs among

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5408-518: The Chandrasekhar limit — approximately 1.44 times M ☉ — beyond which electron degeneracy pressure cannot support it. 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 ; SN 1006 is a likely example. A white dwarf is very hot when it forms, and it will gradually cool as it radiates its energy away. This means that its radiation, which initially has

5512-473: 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

5616-556: The Nobel Prize for this and other work in 1983. The limiting mass is now called the Chandrasekhar limit . 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. However,

5720-473: 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. As was explained by Leon Mestel in 1952, unless the white dwarf accretes matter from

5824-536: 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 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 10   g/cm , or 1  tonne per cubic centimetre. A typical white dwarf has

5928-454: 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. This trend stops when we reach 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

6032-597: 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. 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%

6136-436: 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

6240-478: The CNO cycle may keep these white dwarfs hot on a long timescale. In addition, they remain in a bloated proto-white dwarf stage for up to 2 Gyr before they reach the cooling track. 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

6344-517: The DAV type that is the prototype of the ZZ Ceti variable class. This DA-class white dwarf is the surviving core of a red giant star that ceased nuclear fusion while shedding its outer envelope. It has a (presumably) homogeneous core of carbon and oxygen, a relatively thin outer envelope of hydrogen, and a helium mantle. The object has 65% of the mass of the Sun , with 1.2% of the Sun's radius . It

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6448-437: The Earth, and hence white dwarfs. Willem Luyten appears to have been the first to use the term white dwarf when he examined this class of stars in 1922; the term was later popularized by Arthur Eddington . Despite these suspicions, the first non-classical white dwarf was not definitely identified until the 1930s. 18 white dwarfs had been discovered by 1939. Luyten and others continued to search for white dwarfs in

6552-682: The Landau–Oppenheimer–Volkoff limit, also known as the Tolman–Oppenheimer–Volkoff limit (roughly double the mass of the Sun) no known form of cold matter can provide the force needed to oppose gravity in a new dynamical equilibrium. Hence, the collapse continues with nothing to stop it. Once a body collapses to within its Schwarzschild radius it forms what is called a black hole, meaning a spacetime region from which not even light can escape. It follows from general relativity and

6656-451: 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 a number of visual binary stars in 1916, he found that 40 Eridani B had

6760-442: The accretion of material onto an oxygen–neon–magnesium white dwarf. Type Iax supernovae , that involve helium accretion by a white dwarf, have been proposed to be a channel for transformation of this type of stellar remnant. In this scenario, the carbon detonation produced in a Type Ia supernova is too weak to destroy the white dwarf, expelling just a small part of its mass as ejecta, but produces an asymmetric explosion that kicks

6864-433: The atmospheres of some 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

6968-457: 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 that from its spectrum . If the star's distance is known, its absolute luminosity can also be estimated. From

7072-461: 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 17 000  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

7176-424: 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

7280-405: 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. The visible radiation emitted by white dwarfs varies over

7384-407: 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

7488-411: 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

7592-404: The current age of the known universe (approximately 13.8 billion years), it is thought that no black dwarfs yet exist. The oldest known white dwarfs still radiate at temperatures of a few thousand kelvins , which establishes an observational limit on the maximum possible age of the universe . The first white dwarf discovered was in the triple star system of 40 Eridani , which contains

7696-430: 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

7800-479: 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

7904-533: The end point of stellar evolution for main-sequence stars with masses from about 0.07 to 10  M ☉ . The composition of the white dwarf produced will depend on the initial mass of the star. Current galactic models suggest the Milky Way galaxy currently contains about ten billion white dwarfs. If the mass of a main-sequence star is lower than approximately half a solar mass , it will never become hot enough to ignite and fuse helium in its core. It

8008-417: The equation of state can then be solved to find the structure of the white dwarf at equilibrium. In the non-relativistic case, we will still find that the radius is inversely proportional to the cube root of the mass. 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

8112-502: The gravitational potential energy must equal twice the internal thermal energy. If a pocket of gas is massive enough that the gas pressure is insufficient to support it, the cloud will undergo gravitational collapse. The critical mass above which a cloud will undergo such collapse is called the Jeans mass . This mass depends on the temperature and density of the cloud but is typically thousands to tens of thousands of solar masses . At what

8216-483: The hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first recognized in 1910. The name white dwarf was coined by Willem Jacob Luyten in 1922. White dwarfs are thought to be the final evolutionary state of stars whose mass is not high enough to become a neutron star or black hole . This includes over 97% of the stars in the Milky Way . After the hydrogen - fusing period of

8320-524: 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 can not all occupy the lowest-energy, or ground , state; some of them would have to occupy higher-energy states, forming

8424-406: The non-relativistic formula T = p  / 2 m 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 T = pc where c is the speed of light, and it can be shown that there is no stable equilibrium in the ultrarelativistic limit . In particular, this analysis yields the maximum mass of

8528-399: The nonrelativistic Fermi gas equation of state, which gives where R is the radius, M is the total mass of the star, N is the number of electrons per unit mass (dependent only on composition), m e is the electron mass , ℏ {\displaystyle \hbar } is the reduced Planck constant , and G is the gravitational constant . Since this analysis uses

8632-477: The predicted companion. Walter 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 . Eventually, many faint white stars that had high proper motion were found, indicating that they could be suspected to be low-luminosity stars close to

8736-526: 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 ☉ / μ e , where μ e 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 μ e equal to 2 for such

8840-412: The pressure. This electron degeneracy pressure supports a white dwarf against gravitational collapse. The pressure depends only on density and not on temperature. Degenerate matter is relatively compressible; this means that the density of a high-mass white dwarf is much greater than that of a low-mass white dwarf and that the radius of a white dwarf decreases as its mass increases. The existence of

8944-438: The product of mass loss in binary systems or mass loss due to a large planetary companion. 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 carbon into neon . Near the end of the period in which it undergoes fusion reactions, such

9048-456: The progenitor star would thus become a surface magnetic field of c. 100 × 100  = 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

9152-429: 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

9256-402: The rigorous mathematical literature. The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously. 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

9360-417: 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

9464-492: 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 ⁄ 10 000 of the star's total mass. Although thin, these outer layers determine

9568-404: The star's evolution a star might collapse again and reach several new states of equilibrium. An interstellar cloud of gas will remain in hydrostatic equilibrium as long as the kinetic energy of the gas pressure is in balance with the potential energy of the internal gravitational force . Mathematically this is expressed using the virial theorem , which states that to maintain equilibrium,

9672-408: The star's weight is supported by degeneracy rather than thermal pressure, allowing the temperature to rise exponentially. The resulting runaway carbon detonation completely blows the star apart in a type Ia supernova . Neutron stars are formed by the gravitational collapse of the cores of larger stars. They are the remnant of supernova types Ib , Ic , and II . Neutron stars are expected to have

9776-453: The star, often known as a zombie star , to high speeds of a hypervelocity star . The matter processed in the failed detonation is re-accreted by the white dwarf with the heaviest elements such as iron falling to its core where it accumulates. These iron-core white dwarfs would be smaller than the carbon–oxygen kind of similar mass and would cool and crystallize faster than those. Gravitational collapse Star formation involves

9880-404: 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: 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

9984-450: 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 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

10088-401: The theorem of Roger Penrose that the subsequent formation of some kind of singularity is inevitable. Nevertheless, according to Penrose's cosmic censorship hypothesis , the singularity will be confined within the event horizon bounding the black hole, so the spacetime region outside will still have a well-behaved geometry, with strong but finite curvature, that is expected to evolve towards

10192-420: 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 16 000  K will have a core temperature between approximately 5 000 000  K and 20 000 000  K . The white dwarf

10296-426: The vast majority of observed white dwarfs. 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

10400-436: The white dwarf can no longer be supported by electron degeneracy pressure. The graph on the right shows the result of such a computation. It shows how radius varies with mass for non-relativistic (blue curve) and relativistic (green curve) models of a white dwarf. Both models treat the white dwarf as a cold Fermi gas in hydrostatic equilibrium. The average molecular weight per electron, μ e , has been set equal to 2. Radius

10504-407: 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

10608-455: Was first confirmed in 2019 after the identification of a pile up in the cooling sequence of more than 15 000 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

10712-486: Was of spectral type  A, or white. In 1939, Russell looked back on the discovery: 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

10816-435: Was suggested to explain the seeming delay in the cooling of some types of white dwarves 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

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