White dwarf

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Image of Sirius A and Sirius B taken by the Hubble Space Telescope. Sirius B, which is a white dwarf, can be seen as a faint point of light to the lower left of the much brighter Sirius A.

 

A white dwarf, also called a degenerate dwarf, is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to that of the Sun, while its volume is comparable to that of Earth. A white dwarf's faint luminosity comes from the emission of stored thermal energy; no fusion takes place in a white dwarf wherein mass is converted to energy. 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 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 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, that of about 10 solar masses. This includes over 97% of the other stars in the Milky Way. After the hydrogen-fusing period of a main-sequence star of low or medium mass ends, such a star will expand to a red giant during which it fuses 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 1 billion K), an inert mass of carbon and oxygen will build up at its center. After such a star sheds its outer layers and forms a planetary nebula, it will leave behind a core, which is the remnant white dwarf. Usually, white dwarfs are composed of carbon and oxygen. If the mass of the progenitor is between 8 and 10.5 solar masses (M_☉), the core temperature will be sufficient to fuse carbon but not neon, in which case an oxygen–neon–magnesium white dwarf may form. Stars of very low mass will not be able to fuse helium, hence, a helium white dwarf may form by mass loss in binary systems. 

The material in a white dwarf no longer undergoes fusion reactions, so the star has no source of energy. As a result, it cannot support itself by the heat generated by fusion against gravitational collapse, but is supported only by electron degeneracy pressure, causing it to be extremely dense. The physics of degeneracy yields a maximum mass for a non-rotating white dwarf, the Chandrasekhar limit—approximately 1.44 times of M_☉—beyond which it cannot be supported by electron degeneracy pressure. 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 thought to be a famous example. 

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. 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. 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 universe (approximately 13.8 billion years), it is thought that no black dwarfs yet exist. The oldest white dwarfs still radiate at temperatures of a few thousand kelvins.

Discovery

The first white dwarf discovered was in the triple star system of 40 Eridani, which contains the relatively bright main sequence star 40 Eridani A, orbited at a distance by the closer binary system of the white dwarf 40 Eridani B and the main sequence red dwarf 40 Eridani C. The pair 40 Eridani B/C was discovered by William Herschel on 31 January 1783. In 1910, Henry Norris Russell, Edward Charles Pickering and Williamina Fleming discovered that, despite being a dim star, 40 Eridani B was of spectral type A, or white. 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 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.

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:

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; C. A. F. Peters computed an orbit for it in 1851. It was not until 31 January 1862 that Alvan Graham Clark observed a previously unseen star close to Sirius, later identified as the predicted companion. 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 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. 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 Stanley 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 the 1940s. By 1950, over a hundred were known, and by 1999, over 2,000 were known. Since then the Sloan Digital Sky Survey has found over 9,000 white dwarfs, mostly new.

Composition and structure

Although white dwarfs are known with estimated masses as low as 0.17 M_☉ and as high as 1.33 M_☉, the mass distribution is strongly peaked at 0.6 M_☉, and the majority lie between 0.5 and 0.7 M_☉. The estimated radii of observed white dwarfs are typically 0.8–2% the radius of the Sun; this is comparable to the Earth's radius of approximately 0.9% solar radius. A white dwarf, then, packs mass comparable to the Sun's into a volume that is typically 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 g/cm³, or 1 tonne per cubic centimeter. A typical white dwarf has a density of between 10⁴ and 10⁷ g/cm³. White dwarfs are composed of one of the densest forms of matter known, surpassed only by other compact stars such as neutron stars, quark stars (hypothetically), and black holes.

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 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 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 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 a density of over 25,000 times the Sun's, which was so high that he called it "impossible". As Arthur Stanley 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 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. This was confirmed when Adams measured this redshift in 1925.

Such densities are possible because white dwarf material is not composed of atoms joined by chemical bonds, but rather consists of a plasma of unbound nuclei and electrons. There is therefore no obstacle to placing nuclei closer than normally allowed by electron orbitals limited by normal matter. Eddington wondered what would happen when this plasma cooled and the energy to keep the atoms ionized was no longer sufficient. This paradox was resolved by R. H. Fowler in 1926 by an application of the newly devised quantum mechanics. Since electrons obey the Pauli exclusion principle, no two electrons can occupy the same state, and they must obey Fermi–Dirac statistics, also introduced in 1926 to determine the statistical distribution of particles which 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 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 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 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. These masses were first published in 1929 by Wilhelm Anderson and in 1930 by Edmund C. Stoner. The modern 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 5.7M_☉/μ_e², where μ_e is the average molecular weight per electron of the star. 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, 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 the Nobel prize for this and other work in 1983. The limiting mass is now called the Chandrasekhar limit. 

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 called a neutron star. 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 may be destroyed, before it reaches the limiting mass.

New research indicates that many white dwarfs—at least in certain types of galaxies—may not approach that limit by way of accretion. It has been postulated that at least some of the white dwarfs that become supernovae attain the necessary mass by colliding with one another. It may be that in elliptical galaxies such collisions are the major source of supernovae. This hypothesis is based on the fact that the X-rays produced by those galaxies are 30 to 50 times less than what is expected to be produced by type Ia supernovas of that galaxy as matter accretes on the white dwarf from its encircling companion. It has been concluded that no more than 5 percent of the supernovae in such galaxies could be created by the process of accretion onto white dwarfs. The significance of this finding is that there could be two types of supernovae, which could mean that the Chandrasekhar limit might not always apply in determining when a white dwarf goes supernova, given that two colliding white dwarfs could have a range of masses. This in turn would confuse efforts to use exploding white dwarfs as standard candles in determining distances.

White dwarfs have low luminosity and therefore occupy a strip at the bottom of the Hertzsprung–Russell diagram, a graph of stellar luminosity versus color or temperature. They should not be confused with low-luminosity objects at the low-mass end of the main sequence, such as the hydrogen-fusing red dwarfs, whose cores are supported in part by thermal pressure, or the even lower-temperature brown dwarfs.

Mass–radius relationship and mass limit

The relationship between the mass and radius of white dwarfs can be derived 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. The gravitational potential energy of a unit mass piece of white dwarf, E_g, will be on the order of −G M ∕ R, where G is the gravitational constant, M is the mass of the white dwarf, and R is its radius. 

${\displaystyle E_{g}\approx {\frac {-GM}{R}}.}$

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. 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, where M is the star's mass and its volume is on the order of R³, n will be on the order of N M ∕ R³.

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

${\displaystyle E_{k}\approx {\frac {N(\Delta p)^{2}}{2m}}\approx {\frac {N\hbar ^{2}n^{2/3}}{2m}}\approx {\frac {M^{2/3}N^{5/3}\hbar ^{2}}{2mR^{2}}}.}$

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: 

${\displaystyle |E_{g}|\approx {\frac {GM}{R}}=E_{k}\approx {\frac {M^{2/3}N^{5/3}\hbar ^{2}}{2mR^{2}}}.}$

Solving this for the radius, R, gives

${\displaystyle R\approx {\frac {N^{5/3}\hbar ^{2}}{2mGM^{1/3}}}.}$

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: 

${\displaystyle R\sim M^{-1/3}}$

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 

${\displaystyle E_{k\ {\rm {relativistic}}}\approx {\frac {M^{1/3}N^{4/3}\hbar c}{R}}.}$

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

${\displaystyle M_{\rm {limit}}\approx N^{2}\left({\frac {\hbar c}{G}}\right)^{3/2}.}$

Radius–mass relations for a model white dwarf. M_limit is denoted as M_Ch

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 a limiting mass of M_limit. Therefore, no white dwarf can be heavier than the limiting mass M_limit, or 1.4 M_☉. 

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. If the density and pressure are both set equal to functions of the radius from the center of the star, the system of equations consisting of the hydrostatic equation together with the equation of state can then be solved to find the structure of the white dwarf at equilibrium. In the non-relativistic case, 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 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 is measured in standard solar radii and mass in standard solar masses.

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

Radiation and cooling

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.

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 an M-type red dwarf. White dwarf effective surface temperatures extend from over 150,000 K to barely under 4,000 K. 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 1/10,000 that of the Sun's. 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 the Urca process. 

A comparison between the white dwarf IK Pegasi B (center), its A-class companion IK Pegasi A (left) and the Sun (right). This white dwarf has a surface temperature of 35,500 K.

 

As was explained by Leon Mestel in 1952, unless the white dwarf accretes matter from a companion star or other source, its radiation comes from its stored heat, which is not replenished. White dwarfs have an extremely small surface area to radiate this heat from, so they cool gradually, remaining hot for a long time. As a white dwarf cools, its surface temperature decreases, the radiation 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. The rate of cooling has been estimated for a carbon white dwarf of 0.59 M_☉ with a hydrogen atmosphere. After initially taking approximately 1.5 billion years to cool to a surface temperature of 7,140 K, 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.

Most observed white dwarfs have relatively high surface temperatures, between 8,000 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 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 4,000 K, and one of the coolest so far observed, WD 0346+246, has a surface temperature of approximately 3,900 K. The reason for this is that the Universe's age is finite; there has not been enough time for white dwarfs to cool below this temperature. The white dwarf luminosity function can therefore be used to find the time when stars started to form in a region; an estimate for the age of our Galactic disk found in this way is 8 billion years. A white dwarf will eventually, in many trillions of years, cool and become a non-radiating black dwarf in approximate thermal equilibrium with its surroundings and with the cosmic background radiation. No black dwarfs are thought to exist yet.

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 its center. The crystal structure is thought to be a body-centered cubic lattice. In 1995 it was suggested that asteroseismological observations of pulsating white dwarfs yielded a potential test of the crystallization theory, and in 2004, observations were made that suggested approximately 90% of the mass of BPM 37093 had crystallized. Other work gives a crystallized mass fraction of between 32% and 82%. As a white dwarf core undergoes crystallization into a solid phase, latent heat is released which provides a source of thermal energy that delays its cooling. This effect 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 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.

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 or helium dominated. 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 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 which is a residue of the star's envelope in the AGB phase and may also contain material accreted from the interstellar medium. The envelope is believed to consist of a helium-rich layer with mass no more than 1/100 of the star's total mass, which, if the atmosphere is hydrogen-dominated, is overlain by a hydrogen-rich layer with mass approximately 1/10,000 of the stars total mass.

Although thin, these outer layers determine the thermal evolution of the white dwarf. The degenerate electrons in the bulk of a white dwarf conduct heat well. Most of a white dwarf's mass is therefore at almost the same temperature (isothermal), and it is also hot: a white dwarf with surface temperature between 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.

The first attempt to classify white dwarf spectra appears to have been by G. P. Kuiper in 1941, and various classification schemes have been proposed and used since then. The system currently in use was introduced by Edward M. Sion, Jesse L. Greenstein and their coauthors in 1983 and has been subsequently revised several times. It classifies a spectrum by a symbol 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:

• 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, DB3.5.
• 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.

The symbols ? and : may also be used if the correct classification is uncertain.

White dwarfs whose primary spectral classification is DA have hydrogen-dominated atmospheres. They make up the majority, approximately 80%, of all observed white dwarfs. The next class in number is of DBs, approximately 16%. The hot, above 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 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 (H₂) has been detected in spectra of the atmospheres of some white dwarfs.

Metal-rich white dwarfs

Around 25–33% of white dwarfs have metal lines in their spectra, which is notable because any heavy elements in a white dwarf should sink into the star's interior in just a small fraction of the star's lifetime. The prevailing explanation for metal-rich white dwarfs is that they have recently accreted rocky planetesimals. The bulk composition of the accreted object can be measured from the strengths of the metal lines. For example, a 2015 study of the white dwarf Ton 345 concluded that its metal abundances were consistent with those of a differentiated, rocky planet whose mantle had been eroded by the host star's wind during its asymptotic giant branch phase.

Magnetic field

Magnetic fields in white dwarfs with a strength at the surface of c. 1 million gauss (100 teslas) were predicted by P. M. S. Blackett in 1947 as a consequence of a physical law he had proposed which stated that an uncharged, rotating body should generate a magnetic field proportional to its angular momentum. This putative law, sometimes called the Blackett effect, was never generally accepted, and by the 1950s even Blackett felt it had been refuted. In the 1960s, it was proposed that white dwarfs might have magnetic fields due to conservation of total surface magnetic flux that existed in its progenitor star phase. A surface magnetic field of c. 100 gauss (0.01 T) in the progenitor star would thus become a surface magnetic field of c. 100·100² = 1 million gauss (100 T) once the star's radius had shrunk by a factor of 100. The first magnetic white dwarf to be discovered was GJ 742 (also known as Grw +70 8247) which was identified by James Kemp, John Swedlund, John Landstreet and Roger Angel in 1970 to host a magnetic field by its emission of circularly polarized light. It is thought to have a surface field of approximately 300 million gauss (30 kT).

Since 1970 magnetic fields have been discovered in well over 200 white dwarfs, ranging from 2 × 10³ to 10⁹ gauss (0.2 T to 100 kT). 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. It has been estimated that at least 10% of white dwarfs have fields in excess of 1 million gauss (100 T).

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.

Chemical bonds

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.

Variability

Early calculations suggested that there might be white dwarfs whose luminosity varied with a period of around 10 seconds, but searches in the 1960s failed to observe this. The first variable white dwarf found was HL Tau 76; in 1965 and 1966, and was observed to vary with a period of approximately 12.5 minutes. The reason for this period being longer than predicted is that the variability of HL Tau 76, like that of the other pulsating variable white dwarfs known, arises from non-radial gravity wave pulsations. Known types of pulsating white dwarf include the DAV, or ZZ Ceti, stars, including HL Tau 76, with hydrogen-dominated atmospheres and the spectral type DA; DBV, or V777 Her, stars, with helium-dominated atmospheres and the spectral type DB; and GW Vir stars, sometimes subdivided into DOV and PNNV stars, with atmospheres dominated by helium, carbon, and oxygen. GW Vir stars are not, strictly speaking, white dwarfs, but are stars which are in a position on the Hertzsprung-Russell diagram between the asymptotic giant branch and the white dwarf region. They may be called pre-white dwarfs. These variables all exhibit small (1%–30%) variations in light output, arising from a superposition of vibrational modes with periods of hundreds to thousands of seconds. Observation of these variations gives asteroseismological evidence about the interiors of white dwarfs.

Formation

White dwarfs are thought to represent 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.

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 in its core. It is thought that, over a lifespan that considerably exceeds the age of the Universe (c. 13.8 billion years), such a star will eventually burn all its hydrogen, for a while becoming a blue dwarf, and end its evolution as a helium white dwarf composed chiefly of helium-4 nuclei. Due to the very long time this process takes, it is not thought to be the origin of the observed helium white dwarfs. Rather, they are thought to be the product of mass loss in binary systems or mass loss due to a large planetary companion.

Stars with low to medium mass

If the mass of a main-sequence star is between 0.5 and 8 M_☉ like our sun, 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 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. 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 which form the vast majority of observed white dwarfs.

Stars with medium to high mass

If a star is massive enough, its core will eventually become sufficiently hot to fuse carbon to neon, and then to fuse neon to iron. Such a star will not become a white dwarf, because the mass of its central, non-fusing core, initially supported by electron degeneracy pressure, will eventually exceed the largest possible mass supportable by degeneracy pressure. At this point the core of the star will collapse and it will explode in a core-collapse supernova which will leave behind a remnant neutron star, black hole, or possibly a more exotic form of compact star. Some main-sequence stars, of perhaps 8 to 10 M_☉, although sufficiently massive to fuse carbon to neon and magnesium, may be insufficiently massive to fuse neon. Such a star may leave a remnant white dwarf composed chiefly of oxygen, neon, and magnesium, provided that its core does not collapse, and provided that fusion does not proceed so violently as to blow apart the star in a supernova. Although a few white dwarfs have been identified which 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 which appear to be only explicable by the accretion of material onto an oxygen-neon-magnesium white dwarf.

Type Iax supernovae

Type Iax supernova, 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 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.

Fate

Artist's impression of debris around a white dwarf

 

A white dwarf is stable once formed and will continue to cool almost indefinitely, eventually to become a black dwarf. 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. White dwarfs should generally survive galactic dispersion, 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. The subsequent lifetime of white dwarfs is thought to be on the order of the lifetime of the proton, known to be at least 10³⁴–10³⁵ years. Some grand unified theories predict a proton lifetime between 10³⁰ and 10³⁶ years. If these theories are not valid, the proton may decay by complicated nuclear reactions or through quantum gravitational processes involving a virtual black hole; in these cases, the lifetime is estimated to be no more than 10²⁰⁰ years. If protons do decay, the mass of a white dwarf will decrease very slowly with time as its nuclei decay, until it loses enough mass to become a non-degenerate lump of matter, and finally disappears completely.

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.

Debris disks and planets

Comet falling into white dwarf (artist's impression)

 

The merger process of two co-orbiting white dwarfs produces gravitational waves

 

A white dwarf's stellar and planetary system is inherited from its progenitor star and may interact with the white dwarf in various ways. 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. 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. Some estimations based on the metal content of the atmospheres of the white dwarfs consider that at least a 15% of them may be orbited by planets and/or asteroids, or at least their debris. 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.

There is a planet in the white dwarf–pulsar binary system PSR B1620-26. 

There are two circumbinary planets around the white dwarf–red dwarf binary NN Serpentis.

The metal-rich white dwarf WD 1145+017 is the first white dwarf observed with a disintegrating minor planet which transits the star. The disintegration of the planetesimal generates a debris cloud which passes in front of the star every 4.5 hours, causing a 5-minute-long fade in the star's optical brightness. The depth of the transit is highly variable.

Habitability

It has been proposed that white dwarfs with surface temperatures of less than 10,000 kelvins could harbor a habitable zone at a distance of c. 0.005 to 0.02 AU that would last upwards of 3 billion years. This is so close that any habitable planets would be tidally locked. The goal is to search for transits of hypothetical Earth-like planets that could have migrated inward and/or formed there. As a white dwarf has a size similar to that of a planet, these kinds of transits would produce strong eclipses. Newer research casts some doubts on this idea, given that the close orbits of those hypothetical planets around their parent stars would subject them to strong tidal forces that could render them uninhabitable by triggering a greenhouse effect. Another suggested constraint to this idea is the origin of those planets. Leaving aside formation from the accretion disk surrounding the white dwarf, there are two ways a planet could end in a close orbit around stars of this kind: by surviving being engulfed by the star during its red giant phase, and then spiraling inward, or inward migration after the white dwarf has formed. The former case is implausible for low-mass bodies, as they are unlikely to survive being absorbed by their stars. In the latter case, the planets would have to expel so much orbital energy as heat, through tidal interactions with the white dwarf, that they would likely end as uninhabitable embers.

Binary stars and novae

If a white dwarf is in a binary star system and is accreting matter from its companion, a variety of phenomena may occur, including novae and Type Ia supernovae. 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 close binary system of two white dwarfs can radiate energy in the form of gravitational waves, causing their mutual orbit to steadily shrink until the stars merge.

Type Ia supernovae

The mass of an isolated, nonrotating white dwarf cannot exceed the Chandrasekhar limit of ~1.4 M_☉. This limit may increase if the white dwarf is rotating rapidly and nonuniformly. White dwarfs in binary systems can accrete material from a companion star, increasing both their mass and their density. 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.

Accretion provides the currently favored mechanism called the single-degenerate model for Type Ia supernovae. In this model, a carbon–oxygen white dwarf accretes mass and compresses its core by pulling mass from a companion star. It is believed that compressional heating of the core leads to ignition of carbon fusion as the mass approaches the Chandrasekhar limit. 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. The thermonuclear flame consumes much of the white dwarf in a few seconds, causing a Type Ia supernova explosion that obliterates the star. 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.

Observations have failed to note signs of accretion leading up to Type Ia supernovae, and this is now thought to be because the star is first loaded up to above the Chandrasekhar limit while also being spun up to a very high rate by the same process. Once the accretion stops the star gradually slows until the spin is no longer enough to prevent the explosion.

Cataclysmic variables

Before accretion of material pushes a white dwarf close to the Chandrasekhar limit, accreted hydrogen-rich material on the surface may ignite in a less destructive type of thermonuclear explosion powered by hydrogen fusion. These surface explosions can be repeated as long as the white dwarf's core remains intact. This weaker kind of repetitive cataclysmic phenomenon is called a (classical) nova. Astronomers have also observed dwarf novae, which have smaller, more frequent luminosity peaks than the classical novae. These are thought to be caused by the release of gravitational potential energy when part of the accretion disc collapses onto the star, rather than through a release of energy due to fusion. In general, binary systems with a white dwarf accreting matter from a stellar companion are called cataclysmic variables. As well as novae and dwarf novae, several other classes of these variables are known, including polars and intermediate polars, both of which feature highly magnetic white dwarfs. Both fusion- and accretion-powered cataclysmic variables have been observed to be X-ray sources.

Red giant

From Wikipedia, the free encyclopedia

 

A red giant is a luminous giant star of low or intermediate mass (roughly 0.3–8 solar masses (M_☉)) in a late phase of stellar evolution. The outer atmosphere is inflated and tenuous, making the radius large and the surface temperature around 5,000 K (4,700 °C; 8,500 °F) or lower. The appearance of the red giant is from yellow-orange to red, including the spectral types K and M, but also class S stars and most carbon stars.

 

The most common red giants are stars on the red-giant branch (RGB) that are still fusing hydrogen into helium in a shell surrounding an inert helium core. Other red giants are the red-clump stars in the cool half of the horizontal branch, fusing helium into carbon in their cores via the triple-alpha process; and the asymptotic-giant-branch (AGB) stars with a helium burning shell outside a degenerate carbon–oxygen core, and a hydrogen burning shell just beyond that.

Characteristics

Mira, a variable asymptotic giant branch red giant

 

Red giants are stars that have exhausted the supply of hydrogen in their cores and have begun thermonuclear fusion of hydrogen in a shell surrounding the core. They have radii tens to hundreds of times larger than that of the Sun. However, their outer envelope is lower in temperature, giving them a reddish-orange hue. Despite the lower energy density of their envelope, red giants are many times more luminous than the Sun because of their great size. Red-giant-branch stars have luminosities up to nearly three thousand times that of the Sun (L_☉), spectral types of K or M, have surface temperatures of 3,000–4,000 K, and radii up to about 200 times the Sun (R_☉). Stars on the horizontal branch are hotter, with only a small range of luminosities around 75 L_☉. Asymptotic-giant-branch stars range from similar luminosities as the brighter stars of the red giant branch, up to several times more luminous at the end of the thermal pulsing phase. 

Among the asymptotic-giant-branch stars belong the carbon stars of type C-N and late C-R, produced when carbon and other elements are convected to the surface in what is called a dredge-up. The first dredge-up occurs during hydrogen shell burning on the red-giant branch, but does not produce a large carbon abundance at the surface. The second, and sometimes third, dredge up occurs during helium shell burning on the asymptotic-giant branch and convects carbon to the surface in sufficiently massive stars. 

The stellar limb of a red giant is not sharply defined, contrary to their depiction in many illustrations. Rather, due to the very low mass density of the envelope, such stars lack a well-defined photosphere, and the body of the star gradually transitions into a 'corona'. The coolest red giants have complex spectra, with molecular lines, emission features, and sometimes masers, particularly from thermally pulsing AGB stars.

Another noteworthy feature of red giants is that, unlike Sun-like stars whose photospheres have a large number of small convection cells (solar granules), red-giant photospheres, as well as those of red supergiants, have just a few large cells, the features of which cause the variations of brightness so common on both types of stars.

Evolution

This image tracks the life of a Sun-like star, from its birth on the left side of the frame to its evolution into a red giant on the right after billions of years.

 

Red giants are evolved from main-sequence stars with masses in the range from about 0.3 M_☉ to around 8 M_☉. When a star initially forms from a collapsing molecular cloud in the interstellar medium, it contains primarily hydrogen and helium, with trace amounts of "metals" (in stellar structure, this simply refers to any element that is not hydrogen or helium i.e. atomic number greater than 2). These elements are all uniformly mixed throughout the star. The star reaches the main sequence when the core reaches a temperature high enough to begin fusing hydrogen (a few million kelvin) and establishes hydrostatic equilibrium. Over its main sequence life, the star slowly converts the hydrogen in the core into helium; its main-sequence life ends when nearly all the hydrogen in the core has been fused. For the Sun, the main-sequence lifetime is approximately 10 billion years. More-massive stars burn disproportionately faster and so have a shorter lifetime than less massive stars.

When the star exhausts the hydrogen fuel in its core, nuclear reactions can no longer continue and so the core begins to contract due to its own gravity. This brings additional hydrogen into a zone where the temperature and pressure are adequate to cause fusion to resume in a shell around the core. The outer layers of the star then expand greatly, thus beginning the red-giant phase of the star's life. As the star expands, the energy produced in the burning shell of the star is spread over a much larger surface area, resulting in a lower surface temperature and a shift in the star's visible light output towards the red—hence it becomes a red giant. At this time, the star is said to be ascending the red-giant branch of the Hertzsprung–Russell (H–R) diagram.

Mira A is an old star, already shedding its outer layers into space.

The evolutionary path the star takes as it moves along the red-giant branch, which ends with the complete collapse of the core, depends on the mass of the star. For the Sun and stars of less than about 2 M_☉ the core will become dense enough that electron degeneracy pressure will prevent it from collapsing further. Once the core is degenerate, it will continue to heat until it reaches a temperature of roughly 10⁸ K, hot enough to begin fusing helium to carbon via the triple-alpha process. Once the degenerate core reaches this temperature, the entire core will begin helium fusion nearly simultaneously in a so-called helium flash. In more-massive stars, the collapsing core will reach 10⁸ K before it is dense enough to be degenerate, so helium fusion will begin much more smoothly, and produce no helium flash. The core helium fusing phase of a star's life is called the horizontal branch in metal-poor stars, so named because these stars lie on a nearly horizontal line in the H–R diagram of many star clusters. Metal-rich helium-fusing stars instead lie on the so-called red clump in the H–R diagram.

An analogous process occurs when the central helium is exhausted and the star collapses once again, causing helium in a shell to begin fusing. At the same time hydrogen may begin fusion in a shell just outside the burning helium shell. This puts the star onto the asymptotic giant branch, a second red-giant phase. The helium fusion results in the build up of a carbon–oxygen core. A star below about 8 M_☉ will never start fusion in its degenerate carbon–oxygen core. Instead, at the end of the asymptotic-giant-branch phase the star will eject its outer layers, forming a planetary nebula with the core of the star exposed, ultimately becoming a white dwarf. The ejection of the outer mass and the creation of a planetary nebula finally ends the red-giant phase of the star's evolution. The red-giant phase typically lasts only around a billion years in total for a solar mass star, almost all of which is spent on the red-giant branch. The horizontal-branch and asymptotic-giant-branch phases proceed tens of times faster. 

If the star has about 0.2 to 0.5 M_☉, it is massive enough to become a red giant but does not have enough mass to initiate the fusion of helium. These "intermediate" stars cool somewhat and increase their luminosity but never achieve the tip of the red-giant branch and helium core flash. When the ascent of the red-giant branch ends they puff off their outer layers much like a post-asymptotic-giant-branch star and then become a white dwarf.

Stars that do not become red giants

Very low mass stars are fully convective and may continue to fuse hydrogen into helium for up to a trillion years until only a small fraction of the entire star is hydrogen. Luminosity and temperature steadily increase during this time, just as for more-massive main-sequence stars, but the length of time involved means that the temperature eventually increases by about 50% and the luminosity by around 10 times. Eventually the level of helium increases to the point where the star ceases to be fully convective and the remaining hydrogen locked in the core is consumed in only a few billion more years. Depending on mass, the temperature and luminosity continue to increase for a time during hydrogen shell burning, the star can become hotter than the Sun and tens of times more luminous than when it formed although still not as luminous as the Sun. After some billions more years, they start to become less luminous and cooler even though hydrogen shell burning continues. These become cool helium white dwarfs.

Very-high-mass stars develop into supergiants that follow an evolutionary track that takes them back and forth horizontally over the HR diagram, at the right end constituting red supergiants. These usually end their life as a type II supernova. The most massive stars can become Wolf–Rayet stars without becoming giants or supergiants at all.

Planets

Red giants with known planets: the M-type HD 208527, HD 220074 and, as of February 2014, a few tens of known K-giants including Pollux, Gamma Cephei and Iota Draconis.

Prospects for habitability

Although traditionally it has been suggested the evolution of a star into a red giant will render its planetary system, if present, uninhabitable, some research suggests that, during the evolution of a 1 M_☉ star along the red-giant branch, it could harbor a habitable zone for several times 10⁹ years at 2 AU out to around 10⁸ years at 9 AU out, giving perhaps enough time for life to develop on a suitable world. After the red-giant stage, there would for such a star be a habitable zone between 7 and 22 AU for an additional 10⁹ years. Later studies have refined this scenario, showing how for a 1 M_☉ star the habitable zone lasts from 10⁸ years for a planet with an orbit similar to that of Mars to 2.1×10⁸ yr for one that orbits at Saturn's distance to the Sun, the maximum time (3.7×10⁸ yr) corresponding for planets orbiting at the distance of Jupiter. However, for planets orbiting a 0.5 M_☉ star in equivalent orbits to those of Jupiter and Saturn they would be in the habitable zone for 5.8×10⁹ yr and 2.1×10⁹ yr respectively; for stars more massive than the Sun, the times are considerably shorter.

Enlargement of planets

As of June 2014, 50 giant planets have been discovered around giant stars. However, these giant planets are more massive than the giant planets found around solar-type stars. This could be because giant stars are more massive than the Sun (less massive stars will still be on the main sequence and will not have become giants yet) and more massive stars are expected to have more massive planets. However, the masses of the planets that have been found around giant stars do not correlate with the masses of the stars; therefore, the planets could be growing in mass during the stars' red giant phase. The growth in planet mass could be partly due to accretion from stellar wind, although a much larger effect would be Roche lobe overflow causing mass-transfer from the star to the planet when the giant expands out to the orbital distance of the planet.

Well known examples

Many of the well known bright stars are red giants, because they are luminous and moderately common. The red giant branch variable star Gamma Crucis is the nearest M class giant star at 88 light years. The K0 red giant branch star Arcturus is 36 light years away.

Red-giant branch

• Aldebaran (α Tauri)
• Arcturus (α Bootis)
• Gacrux (γ Crucis)

Red-clump giants

• Hamal (α Arietis)
• κ Persei
• δ Andromedae

Asymptotic giant branch

• Mira (ο Ceti)
• χ Cygni
• α Herculis

The Sun as a red giant

The current size of the Sun (now in the main sequence) compared to its estimated maximum size during its red-giant phase in the future

 

In about 5 to 6 billion years, the Sun will have depleted the hydrogen fuel in its core. It will shrink, with the hydrogen outside the core able to compress enough for hydrogen there to fuse, and will begin to expand into a subgiant. Eventually, the pressure builds up so much that the core will begin to fuse helium, and will expand even more into a red giant. At its largest, its surface (photosphere) will approximately reach the current orbit of Earth. It will then lose its atmosphere completely; its outer layers forming a planetary nebula and the core a white dwarf. The evolution of the Sun into and through the red-giant phase has been extensively modeled, but it remains unclear whether Earth will be engulfed by the Sun or will continue in orbit. The uncertainty arises in part because as the Sun burns hydrogen, it loses mass causing Earth (and all planets) to orbit farther away. There are also significant uncertainties in calculating the orbits of the planets over the next 5–6.5 billion years, so the fate of Earth is not well-understood. At its brightest, the red-giant Sun will be several thousand times more luminous than today but its surface will be at about half the temperature.

Eschatology

From Wikipedia, the free encyclopedia

Four horsemen of the apocalypse, as depicted in the Apocalypse work by Albrecht Dürer

Eschatology is a part of theology concerned with the final events of history, or the ultimate destiny of humanity. This concept is commonly referred to as the "end of the world" or "end times".

The word arises from the Greek ἔσχατος eschatos meaning "last" and -logy meaning "the study of", and first appeared in English around 1844. The Oxford English Dictionary defines eschatology as "the part of theology concerned with death, judgment, and the final destiny of the soul and of humankind".

In the context of mysticism, the term refers metaphorically to the end of ordinary reality and to reunion with the Divine. Many religions treat eschatology as a future event prophesied in sacred texts or in folklore. 

History is often divided into "ages" (aeons), which are time periods each with certain commonalities. One age comes to an end and a new age or world to come, where different realities are present, begins. When such transitions from one age to another are the subject of eschatological discussion, the phrase, "end of the world", is replaced by "end of the age", "end of an era", or "end of life as we know it". Much apocalyptic fiction does not deal with the "end of time" but rather with the end of a certain period, the end of life as it is now, and the beginning of a new period. It is usually a crisis that brings an end to current reality and ushers in a new way of living, thinking, or being. This crisis may take the form of the intervention of a deity in history, a war, a change in the environment, or the reaching of a new level of consciousness.

Most modern eschatology and apocalypticism, both religious and secular, involve the violent disruption or destruction of the world; whereas Christian and Jewish eschatologies view the end times as the consummation or perfection of God's creation of the world, albeit with violent overtures, such as the Great Tribulation. For example, according to some ancient Hebrew worldviews, reality unfolds along a linear path (or rather, a spiral path, with cyclical components that nonetheless have a linear trajectory); the world began with God and is ultimately headed toward God's final goal for creation, the world to come.

Eschatologies vary as to their degree of optimism or pessimism about the future. In some eschatologies, conditions are better for some and worse for others, e.g. "heaven and hell". They also vary as to time frames. Groups claiming imminent eschatology are also referred to as Doomsday cults.

Religion

Bahá'í

In Bahá'í belief, creation has neither a beginning nor an end. Instead, the eschatology of other religions is viewed as symbolic. In Bahá'í belief, human time is marked by a series of progressive revelations in which successive messengers or prophets come from God. The coming of each of these messengers is seen as the day of judgment to the adherents of the previous religion, who may choose to accept the new messenger and enter the "heaven" of belief, or denounce the new messenger and enter the "hell" of denial. In this view, the terms "heaven" and "hell" are seen as symbolic terms for the person's spiritual progress and their nearness to or distance from God. In Bahá'í belief, the coming of Bahá'u'lláh, the founder of the Bahá'í Faith, signals the fulfillment of previous eschatological expectations of Islam, Christianity and other major religions.

Christianity

Christian eschatology is the study concerned with the ultimate destiny of the individual soul and the entire created order, based primarily upon biblical texts within the Old and New Testament. 

Christian eschatology looks to study and discuss matters such as death and the afterlife, Heaven and Hell, the Second Coming of Jesus, the resurrection of the dead, the Rapture, the Tribulation, Millennialism, the end of the world, the Last Judgment, and the New Heaven and New Earth in the world to come. 

Eschatological passages are found in many places in the Bible, both in the Old and the New Testaments. In the Old Testament, apocalyptic eschatology can be found notably in Isaiah 24–27, Isaiah 56–66, Joel, Zechariah 9–14 as well as closing chapters of Daniel, and Ezekiel. In the New Testament, applicable passages include Matthew 24, Mark 13, the parable of "The Sheep and the Goats" and in the Book of Revelation—although Revelation often occupies a central place in Christian eschatology. 

The Second Coming of Christ is the central event in Christian eschatology within the broader context of the fullness of the Kingdom of God. Most Christians believe that death and suffering will continue to exist until Christ's return. There are, however, various views concerning the order and significance of other eschatological events.

The Book of Revelation is at the core of Christian eschatology. The study of Revelation is usually divided into four interpretative methodologies or hermeneutics. In the Futurist approach, Revelation is treated mostly as unfulfilled prophecy taking place in some yet undetermined future. In the Preterist approach, Revelation is chiefly interpreted as having prophetic fulfillment in the past, principally the events of the first century CE.

In the Historicist approach, Revelation provides a broad view of history, and passages in Revelation are identified with major historical people and events. This is view the Jewish scholars held, along with the early Christian church, and it was prevalent in Wycliffe's writings, and other Reformers such as Martin Luther, John Calvin,  John Wesley,  and Sir Isaac Newton,  and many others.

In the Idealist approach, the events of Revelation are neither past nor future, but are purely symbolic, dealing with the ongoing struggle and ultimate triumph of good over evil.

Hinduism

Contemporary Hindu eschatology is linked in the Vaishnavite tradition to the figure of Kalki, the tenth and last avatar of Vishnu before the age draws to a close who will reincarnate as Shiva and simultaneously dissolve and regenerate the universe. 

Most Hindus believe that the current period is the Kali Yuga, the last of four Yuga that make up the current age. Each period has seen successive degeneration in the moral order, to the point that in the Kali Yuga quarrel and hypocrisy are the norm. In Hinduism, time is cyclic, consisting of cycles or "kalpas". Each kalpa lasts 4.1 – 8.2 billion years, which is one full day and night for Brahma, who in turn will live for 311 trillion, 40 billion years. The cycle of birth, growth, decay, and renewal at the individual level finds its echo in the cosmic order, yet is affected by vagaries of divine intervention in Vaishnavite belief. Some Shaivites hold the view that Shiva is incessantly destroying and creating the world.

Islam

Islamic eschatology is documented in the sayings of the Prophet Muhammad, regarding the Signs of the Day of Judgement. The Prophet's sayings on the subject have been traditionally divided into Major and Minor Signs. He spoke about several Minor Signs of the approach of the Day of Judgment, including:

• Abu Hurairah reported that Muhammad said: "If you survive for a time you would certainly see people who would have whips in their hands like the tail of an ox. They would get up in the morning under the wrath of God and they would go into the evening with the anger of God."
• Abu Hurairah narrated that Muhammad said, "When honesty is lost, then wait for the Day of Judgment." It was asked, "How will honesty be lost, O Messenger of God?" He said, "When authority is given to those who do not deserve it, then wait for the Day of Judgment."
• 'Umar ibn al-Khattāb, in a long narration, relating to the questions of the angel Gabriel, reported: "Inform me when the Day of Judgment will be." He [the Prophet Muhammad] remarked: "The one who is being asked knows no more than the inquirer." He [the inquirer] said: "Tell me about its indications." He [the Prophet Muhammad] said: "That the slave-girl gives birth to her mistress and master, and that you would find barefooted, destitute shepherds of goats vying with one another in the construction of magnificent buildings."
• "Before the Day of Judgment there will be great liars, so beware of them."
• "When the most wicked member of a tribe becomes its ruler, and the most worthless member of a community becomes its leader, and a man is respected through fear of the evil he may do, and leadership is given to people who are unworthy of it, expect the Day of Judgment."

Regarding the Major Signs, a Companion of the Prophet narrated: "Once we were sitting together and talking amongst ourselves when the Prophet appeared. He asked us what it was we were discussing. We said it was the Day of Judgment. He said: 'It will not be called until ten signs have appeared: Smoke, Dajjal (the Antichrist), the creature (that will wound the people), the rising of the sun in the West, the Second Coming of Jesus, the emergence of Gog and Magog, and three sinkings (or cavings in of the earth): one in the East, another in the West and a third in the Arabian Peninsula.'" (note: the previous events were not listed in the chronological order of appearance)

Judaism

Jewish eschatology is concerned with events that will happen in the end of days, according to the Hebrew Bible and Jewish thought. This includes the in gathering of the exiled diaspora, the coming of the Jewish Messiah, afterlife, and the revival of the dead Tzadikim. 

In Judaism, the end times are usually called the "end of days" (aḥarit ha-yamim, אחרית הימים), a phrase that appears several times in the Tanakh. The idea of a messianic age has a prominent place in Jewish thought and is incorporated as part of the end of days. 

Judaism addresses the end times in the Book of Daniel and numerous other prophetic passages in the Hebrew scriptures, and also in the Talmud, particularly Tractate Avodah Zarah.

Zoroastrianism

Frashokereti is the Zoroastrian doctrine of a final renovation of the universe when evil will be destroyed, and everything else will then be in perfect unity with God (Ahura Mazda). The doctrinal premises are (1) good will eventually prevail over evil; (2) creation was initially perfectly good, but was subsequently corrupted by evil; (3) the world will ultimately be restored to the perfection it had at the time of creation; (4) the "salvation for the individual depended on the sum of [that person's] thoughts, words and deeds, and there could be no intervention, whether compassionate or capricious, by any divine being to alter this." Thus, each human bears the responsibility for the fate of his own soul, and simultaneously shares in the responsibility for the fate of the world.

Analogies in science and philosophy

Futures studies and transhumanism

Researchers in futures studies and transhumanists investigate how the accelerating rate of scientific progress may lead to a "technological singularity" in the future that would profoundly and unpredictably change the course of human history, and result in Homo sapiens no longer being the dominant life form on Earth.

Astronomy

A diagram showing the life cycle of the Sun

Occasionally the term "physical eschatology" is applied to the long-term predictions of astrophysics. The Sun will turn into a red giant in approximately 6 billion years. Life on Earth will become impossible due to a rise in temperature long before the planet is actually swallowed up by the Sun. Even later, the Sun will become a white dwarf.

What Is Enlightenment? by Immanuel Kant

Enlightenment is man's emergence from his self-imposed nonage. Nonage is the inability to use one's own understanding without another's guidance. This nonage is self-imposed if its cause lies not in lack of understanding but in indecision and lack of courage to use one's own mind without another's guidance. Dare to know! (Sapere aude.) "Have the courage to use your own understanding," is therefore the motto of the enlightenment. 

Laziness and cowardice are the reasons why such a large part of mankind gladly remain minors all their lives, long after nature has freed them from external guidance. They are the reasons why it is so easy for others to set themselves up as guardians. It is so comfortable to be a minor. If I have a book that thinks for me, a pastor who acts as my conscience, a physician who prescribes my diet, and so on--then I have no need to exert myself. I have no need to think, if only I can pay; others will take care of that disagreeable business for me. Those guardians who have kindly taken supervision upon themselves see to it that the overwhelming majority of mankind--among them the entire fair sex--should consider the step to maturity, not only as hard, but as extremely dangerous. First, these guardians make their domestic cattle stupid and carefully prevent the docile creatures from taking a single step without the leading-strings to which they have fastened them. Then they show them the danger that would threaten them if they should try to walk by themselves. Now this danger is really not very great; after stumbling a few times they would, at last, learn to walk. However, examples of such failures intimidate and generally discourage all further attempts.

Thus it is very difficult for the individual to work himself out of the nonage which has become almost second nature to him. He has even grown to like it, and is at first really incapable of using his own understanding because he has never been permitted to try it. Dogmas and formulas, these mechanical tools designed for reasonable use--or rather abuse--of his natural gifts, are the fetters of an everlasting nonage. The man who casts them off would make an uncertain leap over the narrowest ditch, because he is not used to such free movement. That is why there are only a few men who walk firmly, and who have emerged from nonage by cultivating their own minds.

It is more nearly possible, however, for the public to enlighten itself; indeed, if it is only given freedom, enlightenment is almost inevitable. There will always be a few independent thinkers, even among the self-appointed guardians of the multitude. Once such men have thrown off the yoke of nonage, they will spread about them the spirit of a reasonable appreciation of man's value and of his duty to think for himself. It is especially to be noted that the public which was earlier brought under the yoke by these men afterwards forces these very guardians to remain in submission, if it is so incited by some of its guardians who are themselves incapable of any enlightenment. That shows how pernicious it is to implant prejudices: they will eventually revenge themselves upon their authors or their authors' descendants. Therefore, a public can achieve enlightenment only slowly. A revolution may bring about the end of a personal despotism or of avaricious tyrannical oppression, but never a true reform of modes of thought. New prejudices will serve, in place of the old, as guide lines for the unthinking multitude.

This enlightenment requires nothing but freedom--and the most innocent of all that may be called "freedom": freedom to make public use of one's reason in all matters. Now I hear the cry from all sides: "Do not argue!" The officer says: "Do not argue--drill!" The tax collector: "Do not argue--pay!" The pastor: "Do not argue--believe!" Only one ruler in the world says: "Argue as much as you please, but obey!" We find restrictions on freedom everywhere. But which restriction is harmful to enlightenment? Which restriction is innocent, and which advances enlightenment? I reply: the public use of one's reason must be free at all times, and this alone can bring enlightenment to mankind.

On the other hand, the private use of reason may frequently be narrowly restricted without especially hindering the progress of enlightenment. By "public use of one's reason" I mean that use which a man, as scholar, makes of it before the reading public. I call "private use" that use which a man makes of his reason in a civic post that has been entrusted to him. In some affairs affecting the interest of the community a certain [governmental] mechanism is necessary in which some members of the community remain passive. This creates an artificial unanimity which will serve the fulfillment of public objectives, or at least keep these objectives from being destroyed. Here arguing is not permitted: one must obey. Insofar as a part of this machine considers himself at the same time a member of a universal community--a world society of citizens--(let us say that he thinks of himself as a scholar rationally addressing his public through his writings) he may indeed argue, and the affairs with which he is associated in part as a passive member will not suffer. Thus it would be very unfortunate if an officer on duty and under orders from his superiors should want to criticize the appropriateness or utility of his orders. He must obey. But as a scholar he could not rightfully be prevented from taking notice of the mistakes in the military service and from submitting his views to his public for its judgment. The citizen cannot refuse to pay the taxes levied upon him; indeed, impertinent censure of such taxes could be punished as a scandal that might cause general disobedience. Nevertheless, this man does not violate the duties of a citizen if, as a scholar, he publicly expresses his objections to the impropriety or possible injustice of such levies. A pastor, too, is bound to preach to his congregation in accord with the doctrines of the church which he serves, for he was ordained on that condition. But as a scholar he has full freedom, indeed the obligation, to communicate to his public all his carefully examined and constructive thoughts concerning errors in that doctrine and his proposals concerning improvement of religious dogma and church institutions. This is nothing that could burden his conscience. For what he teaches in pursuance of his office as representative of the church, he represents as something which he is not free to teach as he sees it. He speaks as one who is employed to speak in the name and under the orders of another. He will say: "Our church teaches this or that; these are the proofs which it employs." Thus he will benefit his congregation as much as possible by presenting doctrines to which he may not subscribe with full conviction. He can commit himself to teach them because it is not completely impossible that they may contain hidden truth. In any event, he has found nothing in the doctrines that contradicts the heart of religion. For if he believed that such contradictions existed he would not be able to administer his office with a clear conscience. He would have to resign it. Therefore the use which a scholar makes of his reason before the congregation that employs him is only a private use, for no matter how sizable, this is only a domestic audience. In view of this he, as preacher, is not free and ought not to be free, since he is carrying out the orders of others. On the other hand, as the scholar who speaks to his own public (the world) through his writings, the minister in the public use of his reason enjoys unlimited freedom to use his own reason and to speak for himself. That the spiritual guardians of the people should themselves be treated as minors is an absurdity which would result in perpetuating absurdities.

But should a society of ministers, say a Church Council, . . . have the right to commit itself by oath to a certain unalterable doctrine, in order to secure perpetual guardianship over all its members and through them over the people? I say that this is quite impossible. Such a contract, concluded to keep all further enlightenment from humanity, is simply null and void even if it should be confirmed by the sovereign power, by parliaments, and the most solemn treaties. An epoch cannot conclude a pact that will commit succeeding ages, prevent them from increasing their significant insights, purging themselves of errors, and generally progressing in enlightenment. That would be a crime against human nature whose proper destiny lies precisely in such progress. Therefore, succeeding ages are fully entitled to repudiate such decisions as unauthorized and outrageous. The touchstone of all those decisions that may be made into law for a people lies in this question: Could a people impose such a law upon itself? Now it might be possible to introduce a certain order for a definite short period of time in expectation of better order. But, while this provisional order continues, each citizen (above all, each pastor acting as a scholar) should be left free to publish his criticisms of the faults of existing institutions. This should continue until public understanding of these matters has gone so far that, by uniting the voices of many (although not necessarily all) scholars, reform proposals could be brought before the sovereign to protect those congregations which had decided according to their best lights upon an altered religious order, without, however, hindering those who want to remain true to the old institutions. But to agree to a perpetual religious constitution which is not publicly questioned by anyone would be, as it were, to annihilate a period of time in the progress of man's improvement. This must be absolutely forbidden.

A man may postpone his own enlightenment, but only for a limited period of time. And to give up enlightenment altogether, either for oneself or one's descendants, is to violate and to trample upon the sacred rights of man. What a people may not decide for itself may even less be decided for it by a monarch, for his reputation as a ruler consists precisely in the way in which he unites the will of the whole people within his own. If he only sees to it that all true or supposed [religious] improvement remains in step with the civic order, he can for the rest leave his subjects alone to do what they find necessary for the salvation of their souls. Salvation is none of his business; it is his business to prevent one man from forcibly keeping another from determining and promoting his salvation to the best of his ability. Indeed, it would be prejudicial to his majesty if he meddled in these matters and supervised the writings in which his subjects seek to bring their [religious] views into the open, even when he does this from his own highest insight, because then he exposes himself to the reproach: Caesar non est supra grammaticos. 2    It is worse when he debases his sovereign power so far as to support the spiritual despotism of a few tyrants in his state over the rest of his subjects.

When we ask, Are we now living in an enlightened age? the answer is, No, but we live in an age of enlightenment. As matters now stand it is still far from true that men are already capable of using their own reason in religious matters confidently and correctly without external guidance. Still, we have some obvious indications that the field of working toward the goal [of religious truth] is now opened. What is more, the hindrances against general enlightenment or the emergence from self-imposed nonage are gradually diminishing. In this respect this is the age of the enlightenment and the century of Frederick [the Great].

A prince ought not to deem it beneath his dignity to state that he considers it his duty not to dictate anything to his subjects in religious matters, but to leave them complete freedom. If he repudiates the arrogant word "tolerant", he is himself enlightened; he deserves to be praised by a grateful world and posterity as that man who was the first to liberate mankind from dependence, at least on the government, and let everybody use his own reason in matters of conscience. Under his reign, honorable pastors, acting as scholars and regardless of the duties of their office, can freely and openly publish their ideas to the world for inspection, although they deviate here and there from accepted doctrine. This is even more true of every person not restrained by any oath of office. This spirit of freedom is spreading beyond the boundaries [of Prussia] even where it has to struggle against the external hindrances established by a government that fails to grasp its true interest. [Frederick's Prussia] is a shining example that freedom need not cause the least worry concerning public order or the unity of the community. When one does not deliberately attempt to keep men in barbarism, they will gradually work out of that condition by themselves.

I have emphasized the main point of the enlightenment--man's emergence from his self-imposed nonage--primarily in religious matters, because our rulers have no interest in playing the guardian to their subjects in the arts and sciences. Above all, nonage in religion is not only the most harmful but the most dishonorable. But the disposition of a sovereign ruler who favors freedom in the arts and sciences goes even further: he knows that there is no danger in permitting his subjects to make public use of their reason and to publish their ideas concerning a better constitution, as well as candid criticism of existing basic laws. We already have a striking example [of such freedom], and no monarch can match the one whom we venerate.

 

But only the man who is himself enlightened, who is not afraid of shadows, and who commands at the same time a well disciplined and numerous army as guarantor of public peace--only he can say what [the sovereign of] a free state cannot dare to say: "Argue as much as you like, and about what you like, but obey!" Thus we observe here as elsewhere in human affairs, in which almost everything is paradoxical, a surprising and unexpected course of events: a large degree of civic freedom appears to be of advantage to the intellectual freedom of the people, yet at the same time it establishes insurmountable barriers. A lesser degree of civic freedom, however, creates room to let that free spirit expand to the limits of its capacity. Nature, then, has carefully cultivated the seed within the hard core--namely the urge for and the vocation of free thought. And this free thought gradually reacts back on the modes of thought of the people, and men become more and more capable of acting in freedom. At last free thought acts even on the fundamentals of government and the state finds it agreeable to treat man, who is now more than a machine, in accord with his dignity.