NASA's Hubble Space Telescope has detected for the first time a population of white dwarfs embedded in the hub of our Milky Way galaxy. The Hubble images are the deepest, most detailed study of the galaxy's central bulge of stars. The smoldering remnants of once-vibrant stars can yield clues to our galaxy's early construction stages that happened long before Earth and our sun formed.
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In the present Letter, we address this important issue by introducing new improved static models for white-dwarf asteroseismology that incorporate luminosity profiles accounting for residual contraction and energy losses from neutrino emission processes (Sect. 2). In Sect. 3, the impact of this correction on the g-mode frequency spectrum is investigated, specifically for the optimal model uncovered by Giammichele et al. (2018), and is compared to results of Timmes et al. (2018). A reanalysis of KIC 08626021 based on the improved models then follows in Sect. 4, and the revised seismic solution is discussed in Sect. 5.
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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]
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 a uniform temperature, approximately 107 K. An outer shell of non-degenerate matter cools from approximately 107 K to 104 K. This matter radiates roughly as a black body. A white dwarf remains visible for a long time, as its tenuous outer atmosphere of normal matter begins to radiate at about 107 K, upon formation, while its greater interior mass is at 107 K but cannot radiate through its normal matter shell.[58]
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][86] and various classification schemes have been proposed and used since then.[87][88] 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).[99] 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.[100] It has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).[101][102]
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.[104]
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 in its core. 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.[114] 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][115][116][117] or mass loss due to a large planetary companion.[118][119]
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.[130][131]
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.
The least common observable evidence of planetary systems are detected major or minor planets. Only a handful giant planets and a handful of minor planets are known around white dwarfs.[144] It is a growing list with discoveries of around 6 exoplanets expected with Gaia[145] and 4 exoplanets with JWST.[146].mw-parser-output .tmulti .multiimageinnerdisplay:flex;flex-direction:column.mw-parser-output .tmulti .trowdisplay:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box.mw-parser-output .tmulti .tsinglemargin:1px;float:left.mw-parser-output .tmulti .theaderclear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%.mw-parser-output .tmulti .thumbcaptionbackground-color:transparent.mw-parser-output .tmulti .text-align-lefttext-align:left.mw-parser-output .tmulti .text-align-righttext-align:right.mw-parser-output .tmulti .text-align-centertext-align:center@media all and (max-width:720px).mw-parser-output .tmulti .thumbinnerwidth:100%!important;box-sizing:border-box;max-width:none!important;align-items:center.mw-parser-output .tmulti .trowjustify-content:center.mw-parser-output .tmulti .tsinglefloat:none!important;max-width:100%!important;box-sizing:border-box;text-align:center.mw-parser-output .tmulti .tsingle .thumbcaptiontext-align:left.mw-parser-output .tmulti .trow>.thumbcaptiontext-align:center 2ff7e9595c
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