White Dwarf 267 Pdf

[Brandi Wendelberger]

A white dwarf is very hot when it forms, but because it has no source of energy, it will gradually cool as it radiates its energy away. This means that its radiation, which initially has a high color temperature, will lessen and redden with time. Over a very long time, a white dwarf will cool and 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.[5] Because the length of time it takes for a white dwarf to reach this state is calculated to be longer than the current age of the known universe (approximately 13.8 billion years),[9] it is thought that no black dwarfs yet exist.[1][4] 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.[10]

The white dwarf companion of Sirius, Sirius B, was next to be discovered. During the nineteenth century, positional measurements of some stars became precise enough to measure small changes in their location. Friedrich Bessel used position measurements to determine that the stars Sirius (α Canis Majoris) and Procyon (α Canis Minoris) were changing their positions periodically. In 1844 he predicted that both stars had unseen companions:[14]

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

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.[22] This was confirmed when Adams measured this redshift in 1925.[34]

Compression of a white dwarf will increase the number of electrons in a given volume. Applying the Pauli exclusion principle, this will increase the kinetic energy of the electrons, thereby increasing the pressure.[38][41] 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.[1]

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

Rotating white dwarfs and the estimates of their diameter in terms of the angular velocity of rotation has been treated in the rigorous mathematical literature.[56] The fine structure of the free boundary of white dwarfs has also been analysed mathematically rigorously.[57]

The degenerate matter that makes up the bulk of a white dwarf has a very low opacity, because any absorption of a photon requires that an electron must transition to a higher empty state, which may not be possible as the energy of the photon may not be a match for the possible quantum states available to that electron, hence radiative heat transfer within a white dwarf is low; 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 108 K shortly after the formation of the white dwarf and reaching less than 106 K for the coolest known white dwarfs.[58] An outer shell of non-degenerate matter sits on top of the degenerate core. The outermost layers, which have temperatures below 105 K, 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.

Most observed white dwarfs have relatively high surface temperatures, between 8,000 K and 40,000 K.[25][67] 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.[68] This trend stops when we reach extremely cool white dwarfs; few white dwarfs are observed with surface temperatures below 4,000 K,[69] and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,800 K.[60][70] The reason for this is that the Universe's age is finite;[71][72] 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.[68] A white dwarf will eventually, in many trillions of years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. No black dwarfs are thought to exist yet.[1]

Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore at almost the same temperature (isothermal), and it is also hot: a white dwarf with surface temperature between 8,000 K and 16,000 K will have a core temperature between approximately 5,000,000 K and 20,000,000 K. The white dwarf is kept from cooling very quickly only by its outer layers' opacity to radiation.[61]

The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941,[59][91] and various classification schemes have been proposed and used since then.[92][93] The system currently in use was introduced by Edward M. Sion, Jesse L. Greenstein and their coauthors in 1983 and has been subsequently revised several times. It classifies a spectrum by a symbol which consists of an initial D, a letter describing the primary feature of the spectrum followed by an optional sequence of letters describing secondary features of the spectrum (as shown in the adjacent table), and a temperature index number, computed by dividing 50,400 K by the effective temperature. For example:

Since 1970, magnetic fields have been discovered in well over 200 white dwarfs, ranging from 2103 to 109 gauss (0.2 T to 100 kT).[104] 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 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.[105] It has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).[106][107]

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, resulting in what has been initially described as "magnetized matter" in research published in 2012.[109]

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.[119] It is thought that, over a lifespan that considerably exceeds the age of the universe (c. 13.8 billion years),[9] 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.[120] 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 the product of mass loss in binary systems[5][7][8][121][122][123] or mass loss due to a large planetary companion.[124][125]

A white dwarf can also be cannibalized or evaporated by a companion star, causing the white dwarf to lose so much mass that it becomes a planetary mass object. The resultant object, orbiting the former companion, now host star, could be a helium planet or diamond planet.[136][137]

A white dwarf's stellar and planetary system is inherited from its progenitor star and may interact with the white dwarf in various ways. There are several indications that a white dwarf has a remnant planetary system.[citation needed]

The least common observable evidence of planetary systems are detected major or minor planets. Only a handful of giant planets and a handful of minor planets are known around white dwarfs.[150] It is a growing list with discoveries of around 6 exoplanets expected with Gaia.[151] Exoplanets with JWST are expected to be .thumbcaptiontext-align:center}

Infrared spectroscopic observations made by NASA's Spitzer Space Telescope of the central star of the Helix Nebula suggest the presence of a dust cloud, which may be caused by cometary collisions. It is possible that infalling material from this may cause X-ray emission from the central star.[154][155] Similarly, observations made in 2004 indicated the presence of a dust cloud around the young (estimated to have formed from its AGB progenitor about 500 million years ago) white dwarf G29-38, which may have been created by tidal disruption of a comet passing close to the white dwarf.[148] Some estimations based on the metal content of the atmospheres of the white dwarfs consider that at least 15% of them may be orbited by planets or asteroids, or at least their debris.[156] Another suggested idea is that white dwarfs could be orbited by the stripped cores of rocky planets, that would have survived the red giant phase of their star but losing their outer layers and, given those planetary remnants would likely be made of metals, to attempt to detect them looking for the signatures of their interaction with the white dwarf's magnetic field.[157] Other suggested ideas of how white dwarfs are polluted with dust involve the scattering of asteroids by planets[158][159][160] or via planet-planet scattering.[161] Liberation of exomoons from their host planet could cause white dwarf pollution with dust. Either the liberation could cause asteroids to be scattered towards the white dwarf or the exomoon could be scattered into the Roche radius of the white dwarf.[162] The mechanism behind the pollution of white dwarfs in binaries was also explored as these systems are more likely to lack a major planet, but this idea cannot explain the presence of dust around single white dwarfs.[163] While old white dwarfs show evidence of dust accretion, white dwarfs older than 1 billion years or >7000 K with dusty infrared excess were not detected[164] until the discovery of LSPM J0207+3331 in 2018, which has a cooling age of 3 billion years. The white dwarf shows two dusty components that are being explained with two rings with different temperatures.[142]

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