home > Theology > White dwarfs: origin, structure and interesting facts. White dwarfs Which star turns into a white dwarf

White dwarfs: origin, structure and interesting facts. White dwarfs Which star turns into a white dwarf

The message was met with skepticism, since the dark satellite remained unobservable, and its mass should have been quite large - comparable to the mass of Sirius.

Density paradox

“I was visiting my friend ... Professor E. Pickering on a business visit. With his characteristic kindness, he offered to obtain the spectra of all the stars that Hincks and I observed ... with a view to determining their parallaxes. This piece of seemingly routine work turned out to be very fruitful - it led to the discovery that all stars of very small absolute magnitude (that is, low luminosity) have spectral class M (that is, very low surface temperature). As I remember, while discussing this question, I asked Pickering about some other faint stars..., mentioning in particular 40 Eridani B. In his characteristic manner, he immediately sent a request to the (Harvard) Observatory office, and was soon answered (I think from Mrs. Fleming) that the spectrum of this star was A (that is, high surface temperature). Even in those Paleozoic times I knew enough about these things to immediately realize that there was an extreme discrepancy between what we would then call the “possible” values of surface brightness and density. Apparently, I did not hide the fact that I was not just surprised, but literally amazed by this exception to what seemed to be a completely normal rule for the characteristics of stars. Pickering smiled at me and said: “It is precisely such exceptions that lead to the expansion of our knowledge” - and white dwarfs entered the world under study.”

The high density of white dwarfs remained unexplained within the framework of classical physics and astronomy and was explained only within the framework of quantum mechanics after the advent of Fermi-Dirac statistics. In 1926, Fowler, in his article “Dense Matter” ( “On dense matter,” Monthly Notices R. Astron. Soc. 87, 114-122) showed that, unlike main sequence stars, for which the equation of state is based on the ideal gas model (standard Eddington model), for white dwarfs the density and pressure of matter are determined by the properties of the degenerate electron gas (Fermi gas).

The next stage in explaining the nature of white dwarfs was the work of Yakov Frenkel and Chandrasekhar. In 1928, Frenkel pointed out that there should be an upper limit on the mass of white dwarfs, and in 1931 Chandrasekhar in his work "The Maximum Mass of an Ideal White Dwarf" ( "The maximum mass of ideal white dwarfs", Astroph. J. 74, 81-82) showed that there is an upper limit on the masses of white dwarfs, that is, these stars with a mass above a certain limit are unstable (Chandrasekhar limit) and must collapse.

Origin of white dwarfs

Fowler's solution explained the internal structure of white dwarfs, but did not clarify the mechanism of their origin. Two ideas played a key role in explaining the genesis of white dwarfs: the idea of astronomer Ernst Epic that red giants are formed from main sequence stars as a result of the burnout of nuclear fuel, and the assumption of astronomer Vasily Fesenkov, made shortly after World War II, that main sequence stars should lose mass , and such mass loss should have a significant impact on the evolution of stars. These assumptions were completely confirmed.

Triple helium reaction and isothermal nuclei of red giants

During the evolution of main sequence stars, hydrogen “burns out” - nucleosynthesis with the formation of helium (see Bethe cycle). This burnout leads to the cessation of energy release in the central parts of the star, compression and, accordingly, to an increase in temperature and density in its core. An increase in temperature and density in the stellar core leads to conditions in which a new source of thermonuclear energy is activated: helium burnup (triple helium reaction or triple alpha process), characteristic of red giants and supergiants.

At temperatures on the order of 10 8 K, the kinetic energy of helium nuclei becomes high enough to overcome the Coulomb barrier: two helium nuclei (4He, alpha particles) can fuse to form an unstable beryllium isotope:

Most 8 Be decays again into two alpha particles, but when 8 Be collides with a high-energy alpha particle, a stable carbon 12 C nucleus can be formed:

+ 7.3 MeV.

Despite the very low equilibrium concentration of 8 Be (for example, at a temperature of ~10 8 K the concentration ratio [ 8 Be]/[ 4 He] ~10 −10), the rate is such triple helium reaction turns out to be sufficient to achieve a new hydrostatic equilibrium in the hot core of the star. The dependence of the energy release on temperature in the ternary helium reaction is extremely high, for example, for the temperature range ~1-2·10 8 K the energy release is:

where is the partial concentration of helium in the core (in the considered case of hydrogen “burnout” it is close to unity).

It should be noted, however, that the triple helium reaction is characterized by a significantly lower energy release than the Bethe cycle: in terms of per unit mass energy release during the “burning” of helium is more than 10 times lower than during the “burning” of hydrogen. As helium burns out and the energy source in the core is exhausted, more complex nucleosynthesis reactions are possible, however, firstly, such reactions require increasingly higher temperatures, and, secondly, the energy release per unit mass in such reactions decreases as the mass mass increases. number of nuclei reacting.

An additional factor apparently influencing the evolution of red giant nuclei is the combination of the high temperature sensitivity of the triple helium reaction and fusion reactions of heavier nuclei with the mechanism neutrino cooling: at high temperatures and pressures, photons can be scattered by electrons with the formation of neutrino-antineutrino pairs, which freely carry away energy from the core: the star is transparent to them. The speed of this volumetric neutrino cooling, in contrast to classical superficial photon cooling is not limited by the processes of energy transfer from the interior of a star to its photosphere. As a result of the nucleosynthesis reaction, a new equilibrium is reached in the stellar core, characterized by the same core temperature: isothermal core(Fig. 2).

In the case of red giants with a relatively small mass (on the order of the Sun), the isothermal cores consist mainly of helium, in the case of more massive stars - of carbon and heavier elements. However, in any case, the density of such an isothermal core is so high that the distances between the electrons of the plasma forming the core become commensurate with their De Broglie wavelength, that is, the conditions for degeneracy of the electron gas are satisfied. Calculations show that the density of isothermal nuclei corresponds to the density of white dwarfs, that is The cores of red giants are white dwarfs.

Thus, for white dwarfs, there is an upper mass limit (the Chandrasekhar limit). Interestingly, there is a similar lower limit for observed white dwarfs: since the rate of evolution of stars is proportional to their mass, we can observe as low-mass white dwarfs only the remnants of those stars that managed to evolve during the time from the initial period of star formation of the Universe to the present day.

Features of spectra and spectral classification

White dwarfs are classified into a separate spectral class D (from the English. Dwarf- dwarf), a classification is currently used that reflects the features of the spectra of white dwarfs, proposed in 1983 by Edward Sion; in this classification the spectral class is written in the following format:

D [subclass] [spectrum features] [temperature index],

the following subclasses are defined:

DA - lines of the Balmer series of hydrogen are present in the spectrum, lines of helium are not observed
DB - helium He I lines are present in the spectrum, hydrogen or metal lines are absent
DC - continuous spectrum without absorption lines
DO - strong helium He II lines are present in the spectrum, He I and H lines may also be present
DZ - metal lines only, no H or He lines
DQ - carbon lines, including molecular C 2

and spectral features:

P - polarization of light in a magnetic field is observed
H - polarization is not observed in the presence of a magnetic field
V - ZZ Ceti type stars or other variable white dwarfs
X - peculiar or unclassifiable spectra

The evolution of white dwarfs

Rice. 8. Protoplanetary nebula NGC 1705. A series of spherical shells are visible, shed by the red giant, the star itself is hidden by a dust belt.

White dwarfs begin their evolution as the exposed degenerate cores of red giants that have shed their shell - that is, as the central stars of young planetary nebulae. The temperatures of the photospheres of the cores of young planetary nebulae are extremely high - for example, the temperature of the central star of the nebula NGC 7293 ranges from 90,000 K (estimated from absorption lines) to 130,000 K (estimated from the X-ray spectrum). At such temperatures, most of the spectrum consists of hard ultraviolet and soft x-rays.

At the same time, the observed white dwarfs, according to their spectra, are mainly divided into two large groups - “hydrogen” spectral class DA, in the spectra of which there are no helium lines, which make up ~80% of the population of white dwarfs, and “helium” spectral class DB without hydrogen lines in the spectra, making up most of the remaining 20% of the population. The reason for this difference in the composition of the atmospheres of white dwarfs remained unclear for a long time. In 1984, Ico Iben considered scenarios for the "exit" of white dwarfs from pulsating red giants located on the asymptotic giant branch, at various pulsation phases. At a late stage of evolution in red giants with masses up to ten solar, as a result of the “burning out” of the helium core, a degenerate core is formed, consisting mainly of carbon and heavier elements, surrounded by a non-degenerate helium layer source, in which a triple helium reaction occurs. In turn, above it there is a layered hydrogen source, in which thermonuclear reactions of the Bethe cycle take place, converting hydrogen into helium, surrounded by a hydrogen shell; thus, the external hydrogen layer source is the helium “producer” for the helium layer source. Helium combustion in a layer source is subject to thermal instability due to its extremely high temperature dependence, and this is exacerbated by the higher rate of conversion of hydrogen to helium compared to the rate of helium burnup; the result is the accumulation of helium, its compression until degeneration begins, a sharp increase in the rate of the triple helium reaction and the development layered helium flash.

In an extremely short time (~30 years), the luminosity of the helium source increases so much that helium combustion goes into convective mode, the layer expands, pushing out the hydrogen layer source, which leads to its cooling and the cessation of hydrogen combustion. After excess helium burns out during a flare, the luminosity of the helium layer decreases, the outer hydrogen layers of the red giant contract, and a new ignition of the hydrogen layer source occurs.

Iben suggested that a pulsating red giant can shed its envelope, forming a planetary nebula, both in the phase of a helium flash and in a quiescent phase with an active layered hydrogen source, and since the envelope separation surface depends on the phase, then when the envelope is shed during a helium flash a “helium” white dwarf of spectral class DB is exposed, and when the shell is shed by a giant with an active layered hydrogen source, a “hydrogen” dwarf DA is exposed; The duration of the helium burst is about 20% of the duration of the pulsation cycle, which explains the ratio of hydrogen and helium dwarfs DA:DB ~ 80:20.

Large stars (7-10 times heavier than the Sun) at some point “burn” hydrogen, helium and carbon and turn into white dwarfs with an oxygen-rich core. The stars SDSS 0922+2928 and SDSS 1102+2054 with an oxygen-containing atmosphere confirm this.

Since white dwarfs do not have their own thermonuclear energy sources, they radiate from their heat reserves. The radiation power of an absolutely black body (integrated power over the entire spectrum) per unit surface area is proportional to the fourth power of the body temperature:

where is the power per unit area of the radiating surface, and W/(m²·K 4) is the Stefan-Boltzmann constant.

As already noted, temperature is not included in the equation of state of a degenerate electron gas - that is, the radius of the white dwarf and the emitting area remain unchanged: as a result, firstly, for white dwarfs there is no mass - luminosity relationship, but there is an age - luminosity relationship (depending only on temperature, but not on the area of the emitting surface), and, secondly, superhot young white dwarfs should cool quite quickly, since the radiation flux and, accordingly, the cooling rate are proportional to the fourth power of temperature.

Astronomical phenomena involving white dwarfs

X-ray emission from white dwarfs

Rice. 9 Soft X-ray image of Sirius. The bright component is the white dwarf Sirius B, the dim component is Sirius A

The surface temperature of young white dwarfs - the isotropic cores of stars after the shedding of their shells - is very high - more than 2·10 5 K, but drops quite quickly due to neutrino cooling and radiation from the surface. Such very young white dwarfs are observed in the X-ray range (for example, observations of the white dwarf HZ 43 by the ROSAT satellite). In the X-ray range, the luminosity of white dwarfs exceeds the luminosity of main sequence stars: photographs of Sirius taken by the Chandra X-ray telescope (see Fig. 9) can serve as an illustration - in them the white dwarf Sirius B looks brighter than Sirius A of spectral class A1, which optical range ~10,000 times brighter than Sirius B.

The surface temperature of the hottest white dwarfs is 7·10 4 K, the coldest - ~5·10 3 K (see, for example, Van Maanen's Star).

A peculiarity of the radiation of white dwarfs in the X-ray range is the fact that the main source of X-ray radiation for them is the photosphere, which sharply distinguishes them from “normal” stars: the latter have an X-ray corona heated to several million kelvins, and the temperature of the photosphere is too low for X-ray emission.

Accretion onto white dwarfs in binary systems

During the evolution of stars of different masses in binary systems, the rates of evolution of the components are not the same, while a more massive component can evolve into a white dwarf, while a less massive one can remain on the main sequence by this time. In turn, when a less massive component leaves the main sequence during its evolution and transitions to the red giant branch, the size of the evolving star begins to grow until it fills its Roche lobe. Since the Roche lobes of the components of the binary system touch at the Lagrange point L1, then at this stage of the evolution of the less massive component of which, through the L1 point, the flow of matter from the red giant to the Roche lobe of the white dwarf begins and further accretion of hydrogen-rich matter onto its surface (see Fig. 10), which leads to a number of astronomical phenomena:

Non-stationary accretion onto white dwarfs if the companion is a massive red dwarf, leads to the emergence of dwarf novae (U Gem (UG) type stars) and nova-like catastrophic variable stars.
Accretion onto white dwarfs, which have a strong magnetic field, is directed to the region of the white dwarf's magnetic poles, and the cyclotron mechanism of radiation from the accreting plasma in the circumpolar regions of the dwarf's magnetic field causes strong polarization of the radiation in the visible region (polars and intermediate polars).
Accretion of hydrogen-rich matter onto white dwarfs leads to its accumulation on the surface (consisting predominantly of helium) and heating to helium fusion reaction temperatures, which, in the event of thermal instability, leads to an explosion observed as a nova.
Sufficiently long and intense accretion onto a massive white dwarf leads to its mass exceeding the Chandrasekhar limit and gravitational collapse, observed as a type Ia supernova explosion (see Fig. 11).

Notes

Ya. B. Zeldovich, S. I. Blinnikov, N. I. Shakura.. - M.: MSU, 1981.
Sinuosités observées dans le mouvement propre de Sirius, Fig. 320, Flammarion C., Les étoiles et les curiosités du ciel, supplément de “l’Astronomie populaire”, Marpon et Flammarion, 1882
On the proper motions of Procyon and Sirius (English). (12/1844). Archived
Flammarion C. (1877). "The Companion of Sirius". Astronomical register 15 : 186-189. Retrieved 2010-01-05.
van Maanen A. Two Faint Stars with Large Proper Motion. Publications of the Astronomical Society of the Pacific(12/1917). - Vol. 29, No. 172, pp. 258-259. Archived from the original on August 23, 2011.
V.V. Ivanov. White dwarfs. Astronet(17.09.2002). Archived from the original on August 23, 2011. Retrieved May 6, 2009.
Fowler R.H. On dense matter (English). Monthly Notices of the Royal Astronomical Society(12/1926). Archived from the original on August 23, 2011. Retrieved July 22, 2009.
Chandrasekhar S. The Maximum Mass of Ideal White Dwarfs. Astrophysical Journal(07/1931). Archived from the original on August 23, 2011. Retrieved July 22, 2009.
Shklovsky I. S. On the nature of planetary nebulae and their cores // Astronomical Journal. - 1956. - T. 33. - No. 3. - P. 315-329.
A proposed new white dwarf spectral classification system, E. M. Sion, J. L. Greenstein, J. D. Landstreet, J. Liebert, H. L. Shipman, and G. A. Wegner, The Astrophysical Journal 269 , #1 (June 1, 1983), pp. 253-257.
Leahy, D. A.; C. Y. Zhang, Sun Kwok (1994). "Two-temperature X-ray emission from the planetary nebula NGC 7293." The Astrophysical Journal 422 : 205-207. Retrieved 2010-07-05.
Iben Jr, I. (1984). "On the frequency of planetary nebula nuclei powered by helium burning and on the frequency of white dwarfs with hydrogen-deficient atmospheres." The Astrophysical Journal 277 : 333-354. ISSN 0004-637X.
Sofia Neskuchnaya A dwarf breathes oxygen (Russian). newspaper.ru (13.11.09 10:35). Archived from the original on August 23, 2011. Retrieved May 23, 2011.
Sirius A and B: A Double Star System In The Constellation Canis Major // Photo Album of Chandra X-Ray Observatory
Ivanov V.V. White dwarfs. Astronomical Institute named after. V.V. Soboleva. Archived from the original on August 23, 2011. Retrieved January 6, 2010.

Literature

Deborah Jean Warner. Alvan Clark and Sons: Artists in Optics. - Smithsonian Press, 1968.
Ya. B. Zeldovich, S. I. Blinnikov, N. I. Shakura. Physical basis of the structure and evolution of stars. - M., 1981.
Shklovsky I. S. Stars: their birth, life and death. - M.: Nauka, 1984.
Steven D. Kawaler, Igorʹ Dmitrievich Novikov, Ganesan Srinivasan, G. Meynet, Daniel Schaerer. Stellar remnants. - Springer, 1997. - ISBN 3540615202, 9783540615200
Kippenhan R. (English) Russian 100 Billion Suns: The Birth, Life and Death of Stars = 100 Milliarden Sonnen / Transl. with him. A. S. Dobroslavsky, B. B. Straumal, ed. I. M. Khalatnikova, A. V. Tutukova. - World . - M., 1990. - 293 p. - 88,000 copies. - ISBN 5-03-001195-1
White dwarfs // Physics of space: Little encyclopedia. - M.: Soviet Encyclopedia, 1986.

Links

White dwarf
Education	Chandrasekhar limit · PG 1159 star · Stellar evolution · Hertzsprung-Russell diagram · Mirids
Evolution

White dwarfs- evolved stars with a mass not exceeding the Chandrasekhar limit, deprived of their own sources of thermonuclear energy. These are compact stars with masses comparable to the mass of the Sun, but with radii of ~100 and, accordingly, luminosities of ~10,000 times less than the Sun. The density of white dwarfs is about 10 6 g/cm³, which is almost a million times higher than the density of ordinary main sequence stars. In terms of numbers, white dwarfs make up, according to various estimates, 3-10% of the stellar population of our Galaxy.
The figure shows the comparative sizes of the Sun (right) and the binary system IK Pegasus component B - a white dwarf with a surface temperature of 35,500 K (center) and component A - a star of spectral type A8 (left).

Opening In 1844, the director of the Königsberg Observatory, Friedrich Bessel, discovered that Sirius, the brightest star in the northern sky, periodically, although very weakly, deviates from a rectilinear trajectory along the celestial sphere. Bessel came to the conclusion that Sirius should have an invisible “dark” satellite, and the period of revolution of both stars around a common center of mass should be about 50 years. The message was met with skepticism, since the dark satellite remained unobservable, and its mass should have been quite large - comparable to the mass of Sirius.
In January 1862 A.G. Clark, adjusting an 18-inch refractor, the largest telescope in the world at that time (Dearborn Telescope), supplied by the Clark family firm to the Chicago Observatory, discovered a dim star in the immediate vicinity of Sirius. This was the dark satellite of Sirius, Sirius B, predicted by Bessel. The surface temperature of Sirius B is 25,000 K, which, taking into account its anomalously low luminosity, indicates a very small radius and, accordingly, an extremely high density - 10 6 g/cm³ (Sirius density ~0.25 g/cm³, Sun density ~ 1.4 g/cm³).
In 1917, Adrian Van Maanen discovered the next white dwarf - Van Maanen's star in the constellation Pisces.

Density paradox At the beginning of the 20th century, Hertzsprung and Russell discovered a pattern regarding the spectral class (temperature) and luminosity of stars - the Hertzsprung-Russell diagram (H-R diagram). It seemed that the entire diversity of stars fit into two branches of the H-R diagram - the main sequence and the red giant branch. In the course of work on accumulating statistics on the distribution of stars by spectral class and luminosity, Russell turned to Professor E. Pickering in 1910. Russell describes further events as follows:

“I was visiting my friend ... Professor E. Pickering on a business visit. With characteristic kindness, he offered to obtain the spectra of all the stars that Hincks and I had observed... with a view to determining their parallaxes. This piece of seemingly routine work turned out to be very fruitful - it led to the discovery that all stars of very small absolute magnitude (i.e., low luminosity) have spectral class M (i.e., very low surface temperature). As I remember, while discussing this question, I asked Pickering about some other faint stars ..., mentioning in particular 40 Eridani B. In his characteristic behavior, he immediately sent a request to the office of the (Harvard) Observatory, and a reply was soon received (I think from Mrs. Fleming) that the spectrum of this star is A (i.e. high surface temperature). Even in those Paleozoic times I knew enough about these things to immediately realize that there was an extreme discrepancy here between what we would then call the "possible" values of surface brightness and density. Apparently, I did not hide the fact that I was not just surprised, but literally amazed by this exception to what seemed to be a completely normal rule for the characteristics of stars. Pickering smiled at me and said: “It is precisely such exceptions that lead to the expansion of our knowledge” - and white dwarfs entered the world under study.”

Russell’s surprise is quite understandable: 40 Eridani B refers to relatively close stars, and from the observed parallax one can quite accurately determine the distance to it and, accordingly, the luminosity. The luminosity of 40 Eridani B turned out to be anomalously low for its spectral class - white dwarfs formed a new region on the H-R diagram. This combination of luminosity, mass and temperature was incomprehensible and could not be explained within the standard main sequence model of stellar structure developed in the 1920s.
The high density of white dwarfs was explained only within the framework of quantum mechanics after the advent of Fermi-Dirac statistics. In 1926, Fowler, in his article “Dense matter”, Monthly Notices R. Astron. Soc. 87, 114-122, showed that, unlike main sequence stars, for which the equation of state is based on the ideal gas model ( standard Eddington model), for white dwarfs the density and pressure of matter are determined by the properties of the degenerate electron gas (Fermi gas).
The next step in explaining the nature of white dwarfs was the work of Ya. I. Frenkel and Chandrasekhar. In 1928, Frenkel pointed out that there must be an upper mass limit for white dwarfs, and in 1930 Chandrasekhar, in The maximum mass of ideal white dwarfs (Astroph. J. 74, 81-82), showed that white dwarfs above 1.4 solar masses are unstable (Chandrasekhar limit) and must collapse.

Origin of white dwarfs
Fowler's solution explained the internal structure of white dwarfs, but did not clarify the mechanism of their origin. Two ideas played a key role in explaining the genesis of white dwarfs: the idea of E. Epik that red giants are formed from main sequence stars as a result of the burning out of nuclear fuel and the assumption of V.G. Fesenkov, made shortly after World War II, that main sequence stars must lose mass, and such mass loss must have a significant impact on the evolution of stars. These assumptions were completely confirmed.
During the evolution of main sequence stars, hydrogen is “burned out” with the formation of helium (the Bethe cycle). Such burnup leads to the cessation of energy release in the central parts of the star, compression and, accordingly, to an increase in temperature and density in its core, which leads to conditions in which a new source of thermonuclear energy is activated: helium burnup at temperatures of the order of 10 8 K ( triple helium reaction or triple alpha process), characteristic of red giants and supergiants:
He 4 + He 4 = Be 8 - two helium nuclei (alpha particles) merge and an unstable beryllium isotope is formed;
Be 8 + He 4 \u003d C 12 + 7.3 MeV - most of Be 8 again decays into two alpha particles, but when Be 8 collides with a high-energy alpha particle, a stable C 12 carbon nucleus can be formed.
However, it should be noted that the triple helium reaction is characterized by a much lower energy release than the Bethe cycle: in terms of a unit mass energy release during the “burning” of helium is more than 10 times lower than during the “burning” of hydrogen. As helium burns out and the energy source in the nucleus is exhausted, more complex nucleosynthesis reactions are also possible, however, firstly, such reactions require ever higher temperatures and, secondly, the energy release per unit mass in such reactions decreases as the mass numbers increase. reacting nuclei.
An additional factor that apparently influences the evolution of red giant nuclei is the combination of the high temperature sensitivity of the triple helium reaction and fusion reactions of heavier nuclei with the mechanism neutrino cooling: at high temperatures and pressures, photons can be scattered by electrons with the formation of neutrino-antineutrino pairs, which freely carry away energy from the core: the star is transparent to them. The speed of this volumetric neutrino cooling, in contrast to classical superficial photon cooling is not limited by the processes of energy transfer from the interior of a star to its photosphere. As a result of the nucleosynthesis reaction, a new equilibrium is reached in the stellar core, characterized by the same core temperature: isothermal core.
In the case of red giants with a relatively small mass (on the order of the Sun), the isothermal cores consist mainly of helium, in the case of more massive stars - of carbon and heavier elements. However, in any case, the density of such an isothermal core is so high that the distances between the electrons of the plasma forming the core become commensurate with their De Broglie wavelength λ = h / mv , that is, the conditions for degeneracy of the electron gas are satisfied. Calculations show that the density of isothermal nuclei corresponds to the density of white dwarfs, i.e. The cores of red giants are white dwarfs.

Mass loss from red giants
Nuclear reactions in red giants occur not only in the core: as hydrogen burns out in the core, helium nucleosynthesis spreads to the still hydrogen-rich regions of the star, forming a spherical layer at the boundary of the hydrogen-poor and hydrogen-rich regions. A similar situation arises with the triple helium reaction: as helium burns out in the core, it also concentrates in a spherical layer at the boundary between helium-poor and helium-rich regions. The luminosity of stars with such “two-layer” regions of nucleosynthesis increases significantly, reaching about several thousand luminosities of the Sun, while the star “inflates”, increasing its diameter to the size of the Earth’s orbit. The helium nucleosynthesis zone rises to the surface of the star: the fraction of mass inside this zone is ~70% of the star's mass. “Blowing up” is accompanied by a fairly intense outflow of matter from the surface of the star; such objects are observed as protoplanetary nebulae, for example Nebula HD44179 ( drawing).
Such stars are clearly unstable, and in 1956 I.S. Shklovsky proposed a mechanism for the formation of planetary nebulae through the shedding of the shells of red giants, while the exposure of the isothermal degenerate cores of such stars leads to the birth of white dwarfs (this scenario for the end of the evolution of red giants is generally accepted and supported by numerous observational data). The exact mechanisms of mass loss and further shedding of the envelope for such stars are not yet completely clear, but the following factors can be assumed that could contribute to the loss of the envelope:

In extended stellar envelopes, instabilities can develop, leading to strong oscillatory processes, accompanied by changes in the thermal regime of the star. On drawing Density waves of matter ejected by the star are clearly visible, which may be the consequences of such fluctuations.
Due to the ionization of hydrogen in regions below the photosphere, strong convective instability can develop. Solar activity has a similar nature, but in the case of red giants, the power of convective flows should significantly exceed the solar one.
Due to the extremely high luminosity, the light pressure of the star’s radiation flux on its outer layers becomes significant, which, according to calculations, can lead to the loss of the shell within several thousand years.

One way or another, a fairly long period of relatively quiet outflow of matter from the surface of red giants ends with the shedding of its shell and exposure of its core. Such an ejected shell is observed as a planetary nebula. The expansion velocities of protoplanetary nebulae are tens of km/s, i.e., close to the value of parabolic velocities on the surface of red giants, which serves as additional confirmation of their formation by the release of “excess mass” of red giants.

Features of the spectra
The spectra of white dwarfs are very different from the spectra of main sequence stars and giants. Their main feature is a small number of highly broadened absorption lines, and some white dwarfs (spectral class DC) do not contain noticeable absorption lines at all. The small number of absorption lines in the spectra of stars of this class is explained by the very strong broadening of the lines: only the strongest absorption lines, while broadening, have sufficient depth to remain noticeable, and the weak ones, due to their shallow depth, practically merge with the continuous spectrum.
The features of the spectra of white dwarfs are explained by several factors. Firstly, due to the high density of white dwarfs, the acceleration of gravity on their surface is ~10 8 cm/s² (or ~1000 Km/s²), which, in turn, leads to small extents of their photospheres, huge densities and pressures in them and the broadening of absorption lines. Another consequence of the strong gravitational field on the surface is the gravitational redshift of the lines in their spectra, equivalent to velocities of several tens of km/s. Secondly, some white dwarfs with strong magnetic fields exhibit strong polarization of radiation and splitting of spectral lines due to the Zeeman effect.

X-ray emission from white dwarfs
The surface temperature of young white dwarfs - the isotropic cores of stars after the shedding of their shells - is very high - more than 2·10 5 K, but drops quite quickly due to neutrino cooling and radiation from the surface. Such very young white dwarfs are observed in X-rays. The surface temperature of the hottest white dwarfs is 7·10 4 K, the coldest - ~5·10³ K.
A peculiarity of the radiation of white dwarfs in the X-ray range is the fact that the main source of X-ray radiation for them is the photosphere, which sharply distinguishes them from “normal” stars: the latter have an X-ray corona heated to several million kelvins, and the temperature of the photosphere is too low for X-ray emission.
In the absence of accretion, the source of luminosity for white dwarfs is the stored thermal energy of ions in their interior, so their luminosity depends on age. A quantitative theory of the cooling of white dwarfs was built in the late 1940s by S.A. Kaplan.

Accretion onto white dwarfs in binary systems

Nonstationary accretion onto white dwarfs when the companion is a massive red dwarf leads to the formation of dwarf novae (U Gem (UG) type stars) and nova-like catastrophic variable stars.
Accretion onto white dwarfs with a strong magnetic field is directed towards the magnetic poles of the white dwarf, and the cyclotron mechanism of radiation from the accreting plasma in the circumpolar regions of the field causes a strong polarization of the radiation in the visible region (polars and intermediate polars).
Accretion of hydrogen-rich matter onto white dwarfs leads to its accumulation on the surface (consisting predominantly of helium) and heating to helium fusion reaction temperatures, which, in the event of thermal instability, leads to an explosion observed as a nova.

With masses on the order of the mass of the Sun (M?) and radii approximately 100 times smaller than the radius of the Sun. The average density of the substance of white dwarfs is 10 8 -10 9 kg/m 3. White dwarfs make up several percent of all stars in the Galaxy. Many white dwarfs are part of binary star systems. The first star classified as a white dwarf was Sirius B (a satellite of Sirius), discovered by the American astronomer A. Clark in 1862. In the 1910s, white dwarfs were identified as a special class of stars; their name is associated with the color of the first representatives of this class.

With the mass of a star and the size of a small planet, a white dwarf has a colossal gravitational pull near its surface that tends to compress the star. But it maintains a stable equilibrium, since the gravitational forces are resisted by the pressure of the degenerate gas of electrons: at a high density of matter, characteristic of white dwarfs, the concentration of practically free electrons in it is so high that, according to the Pauli principle, they have a large momentum. The pressure of the degenerate gas is practically independent of its temperature, so the white dwarf does not shrink as it cools.

The greater the mass of a white dwarf, the smaller its radius. The theory indicates an upper mass limit for white dwarfs of about 1.4 M? (the so-called Chandrasekhar limit), exceeding which leads to gravitational collapse. The presence of such a limit is due to the fact that as the density of a gas increases, the speed of electrons in it approaches the speed of light and cannot increase further. As a result, the pressure of the degenerate gas is no longer able to withstand the force of gravity.

Are white dwarfs formed at the end of the evolution of ordinary stars with an initial mass of less than 8M? after they have exhausted their supply of thermonuclear fuel. During this period, the star, having passed through the stage of a red giant and a planetary nebula, sheds its outer layers and exposes a core that has a very high temperature. Gradually cooling, the core of the star passes into the state of a white dwarf, continuing to shine for a long time due to the thermal energy stored in the depths. The luminosity of a white dwarf decreases with age. At an age of about 1 billion years, the luminosity of the white dwarf is a thousand times lower than that of the Sun. The surface temperature of the studied white dwarfs lies in the range from 5·10 3 to 10 5 K.

Some white dwarfs exhibit optical variability with periods ranging from several minutes to half an hour, which is explained by the manifestation of gravitational non-radial oscillations of the star. Analysis of these oscillations using asteroseismology methods makes it possible to study the internal structure of white dwarfs. In the spectra of about 3% of white dwarfs, strong polarization of radiation or Zeeman splitting of spectral lines is observed, which indicates the existence of magnetic fields with an induction of 3·10 4 -10 9 G.

If a white dwarf is part of a close binary system, then a significant contribution to its luminosity can come from thermonuclear burning of hydrogen flowing from a neighboring star. This burning is often non-stationary in nature, which manifests itself in the form of outbursts of novae and nova-like stars. In rare cases, the accumulation of hydrogen on the surface of a white dwarf leads to a thermonuclear explosion with complete destruction of the star, observed as a supernova explosion.

Lit.: Blinnikov S.I. White dwarfs. M., 1977; Shapiro S., Tyukolski S. Black holes, white dwarfs and neutron stars: Part 2 M., 1985.

White dwarfs are a common type of star with low luminosity and enormous mass. In our galaxy they make up several percent of the total number of stars. These are compact objects, approximately . The temperature inside them is low, so nuclear reactions do not occur. The stored energy is gradually reduced due to the emission of electromagnetic waves. The surface temperature of white dwarfs ranges from 5,000° K for old, “cold” stars to 50,000° K for young and “hot” stars.

The masses of white dwarfs do not exceed 1.4 solar masses, although the density is quite decent - 1,000,000 - 100,000,000 g/cm³

White dwarfs are objects in the last stage of evolution. The density of the matter of white dwarfs is a million times greater than the density of ordinary stars, and their prevalence among stars is 3–10%. Also, white dwarfs differ from stars in that thermonuclear reactions do not occur in their depths.

When all the helium runs out (in 100 - 110 million years), it will turn into a white dwarf.

Young white dwarfs have temperatures greater than 2. 10 5 °K on the surface. A classic example is photographs of the brightest star in our sky, Sirius.

They were obtained using the Chandra X-ray telescope. In optics, Sirius A is 10,000 times brighter than its companion, Sirius B, but in the X-ray range the white dwarf is b O greater brightness.

What are they made of?

White dwarfs are not as simple and boring as they might seem at first glance. Indeed, if nuclear reactions do not occur and the temperature is low, then where does the high pressure that restrains the gravitational compression of matter come from? It turns out that the quantum properties of electrons play a decisive role. Under the influence of gravity, matter is compressed so much that the nuclei of atoms penetrate into the electron shells of neighboring atoms. Electrons no longer belong to specific nuclei, but are free to fly throughout space inside the star. The nuclei form a tightly connected system like a crystal lattice. Then the most interesting thing happens. Although the white dwarf cools down as a result of radiation into the surrounding space, the average speed of the electrons does not decrease. This is due to the fact that, according to the laws of quantum mechanics, two electrons, having half-integer spin, cannot be in the same state (Pauli principle). This means that the number of different states of electrons in a white dwarf cannot be less than the number of electrons. But it is clear that the number of states decreases with decreasing electron velocities. In the limiting case, if the speed of all electrons became equal to zero, they would all be in one state (more precisely, in two, taking into account the spin projection). Since there are many electrons in a white dwarf, there must be many states, and this is ensured by the conservation of their velocities. Well, high particle speeds create high pressure, counteracting gravitational compression. Of course, if the object's mass is too great, gravity will overcome this barrier.

Evolution

Most white dwarfs are one of the last stages in the evolution of normal, not very massive stars. The star, having exhausted its reserves of nuclear fuel, enters the red giant stage, loses some of its matter, turning into a white dwarf. In this case, the outer shell - heated gas - scatters in outer space and from the Earth it is observed as. Over hundreds of thousands of years, such nebulae dissipate in space, and their dense cores, white dwarfs, gradually cool down like a hot piece of metal, but very slowly, since its surface is small. Over time, they should turn into brown (black) dwarfs - clumps of matter with ambient temperatures. True, as calculations show, this may take many billions of years.

Obviously, the discovery of brown dwarfs is hampered by their weak luminosity. One of the brown dwarfs is located in the constellation Hydra. Its magnitude is only 22.3. The uniqueness of the discovery lies in the fact that previously discovered brown dwarfs were part of binary systems, which is why they could be detected, and this one is single. It was found only due to its proximity to Earth: it is only 33 light years away.

It is assumed that the current brown dwarfs are not cooled white dwarfs (too little time has passed), but “underdeveloped” stars. As is known, stars are born from a gas and dust cloud, and one cloud gives birth to several stars of different masses. If the compressed clump of gas has a mass 10-100 times less than the Sun, brown dwarfs are formed. They are quite strongly heated by the forces of gravitational compression and emit in the infrared range. Nuclear reactions do not occur in brown dwarfs.

Opening

By the beginning of the 30s. XX century In general terms, a theory of the internal structure of stars was developed. By specifying the mass of the star and its chemical composition, theorists could calculate all the observable characteristics of the star - its luminosity, radius, surface temperature, etc. However, this harmonious picture was disrupted by an inconspicuous star 40 Eridani B, discovered by the English astronomer William Herschel in 1783. For its high temperature, it had too little luminosity, and therefore, too small dimensions. From the point of view of classical physics, this could not be explained. After some time, other unusual stars were found. The most famous of these discoveries was the discovery of Sirius B - the invisible satellite of the brightest star - Sirius. Astronomer Friedrich Wilhelm Bessel (German mathematician and astronomer), observing Sirius, discovered that it was not moving in a straight line, but “slightly in a sinusoid.” About ten years of observation and reflection led Bessel to the conclusion that there was a second star near Sirius, exerting a gravitational influence on it.

Bessel's prediction was confirmed after A. Clark constructed a telescope with a lens with a diameter of 46 cm in 1862, at that time the largest telescope in the world. To check the quality of the lens, it was sent to Sirius, the brightest star. Another dim star appeared in the telescope’s field of view, which Bessel had predicted.

The temperature of Sirius B turned out to be 25,000 K - 2.5 times higher than that of bright Sirius A. Taking into account the size of the star, this indicated an extremely high density of its matter - 106 g/cm³. A thimble of such a substance would weigh a million tons on Earth.

As it turns out, white dwarfs are stellar “cinders” that originate from ordinary stars. The equilibrium of ordinary stars is maintained by the pressure force of hot plasma, which opposes the force of gravity (gravity). In order for balance to be maintained, internal sources of energy are necessary, otherwise the star, losing energy to emit streams of light into the surrounding space, would not be able to withstand the confrontation with the forces. Such an internal source is the thermonuclear reaction of converting hydrogen into helium. As soon as all the hydrogen “burns out” in the central regions of the star, the equilibrium is disrupted and the star begins to shrink under the influence of its own gravity. The typical density of the objects around us is several grams per 1 cm³ (approximately the characteristic density of an atom). Stars like our Sun have the same average density. However, if an ordinary star is compressed 100 times, the atoms will “press” into each other and the star will turn into one giant atom, in which the energy levels of individual atoms will “lock” together. At such densities, electrons form the so-called degenerate electron gas - a special quantum state in which all the electrons of the white dwarf “feel” each other and form a single collective - it is this that resists gravitational compression. This is how the star turns into a dense core - a white dwarf.

White dwarfs - one of the most fascinating topics in the history of astronomy: for the first time, celestial bodies were discovered that have properties very far from those with which we deal under earthly conditions. And, in all likelihood, the solution to the mystery of white dwarfs marked the beginning of research into the mysterious nature of matter hidden somewhere in different parts of the Universe.

There are many white dwarfs in the Universe. At one time they were considered rare, but a careful study of photographic plates obtained at the Mount Palomar Observatory (USA) showed that their number exceeds 1500. It was possible to estimate the spatial density of white dwarfs: it turns out that in a sphere with a radius of 30 light years there should be about 100 such stars. The history of the discovery of white dwarfs dates back to the beginning of the 19th century, when Friedrich Wilhelm Bessel, tracing the movement of the brightest star Sirius, discovered that its path is not a straight line, but has a wave-like character. The star's own motion did not occur in a straight line; it seemed as if she was moving barely noticeably from side to side. By 1844, about ten years after the first observations of Sirius, Bessel came to the conclusion that there is a second star next to Sirius, which, being invisible, has a gravitational effect on Sirius; it is revealed by fluctuations in the movement of Sirius. Even more interesting was the fact that if a dark component really exists, then the orbital period of both stars relative to their common center of gravity is approximately 50 years.

Fast forward to 1862. and from Germany to Cambridge, Massachusetts (USA). Alvan Clark, the largest telescope builder in the United States, was commissioned by Mississippi State University to construct a telescope with an 18.5-inch (46 cm) diameter lens, which was to be the largest telescope in the world. After Clark finished processing the telescope lens, it was necessary to check whether the necessary accuracy of the shape of its surface was ensured. For this purpose, the lens was installed in a movable tube and directed towards Sirius - the brightest star, which is the best object for testing lenses and identifying their defects. Having fixed the position of the telescope tube, Alvan Clark saw a faint “ghost” that appeared at the eastern edge of the telescope’s field of view in the reflection of Sirius. Then, as the sky moved, Sirius himself came into view. Its image was distorted - it seemed that the "ghost" represented a defect in the lens that should have been corrected before the lens was put into service. However, this faint star that appeared in the field of view of the telescope turned out to be the component of Sirius predicted by Bessel. In conclusion, it should be added that due to the outbreak of World War I, the Clark telescope was never sent to Mississippi - it was installed at the Dearbon Observatory, near Chicago, and the lens is still used to this day, but in a different installation.

Thus, Sirius has become the subject of general interest and much research, for the physical characteristics of the binary system intrigued astronomers. Taking into account the peculiarities of the movement of Sirius, its distance to the Earth and the amplitude of deviations from rectilinear motion, astronomers were able to determine the characteristics of both stars of the system, named Sirius A and Sirius B. The total mass of both stars turned out to be 3.4 times greater than the mass of the Sun. It was found that the distance between the stars is almost 20 times greater than the distance between the Sun and the Earth, that is, approximately equal to the distance between the Sun and Uranus; The mass of Sirius A, obtained from measurements of orbital parameters, turned out to be 2.5 times greater than the mass of the Sun, and the mass of Sirius B was 95% of the mass of the Sun. After the luminosities of both stars were determined, it was discovered that Sirius A is almost 10,000 times brighter than Sirius B. From the absolute magnitude of Sirius A, we know that it is approximately 35.5 times brighter than the Sun. It follows that the luminosity of the Sun is 300 times higher than the luminosity of Sirius B. The luminosity of any star depends on the temperature of the star’s surface and its size, that is, diameter. The proximity of the second component to the brighter Sirius A makes it extremely difficult to determine its spectrum, which is necessary to establish the temperature of the star. In 1915 Using all the technical means available at the largest observatory of that time, Mount Wilson (USA), successful photographs of the spectrum of Sirius were obtained.

This led to an unexpected discovery: the temperature of the satellite was 8000 K, while the Sun has a temperature of 5700 K. Thus, the satellite actually turned out to be hotter than the Sun, which meant that the luminosity per unit of its surface was also greater. In fact, a simple calculation shows that every centimeter of this star emits four times more energy than a square centimeter of the Sun's surface. It follows that the surface of the satellite should be 300 * 10 4 times smaller than the surface of the Sun, and Sirius B should have a diameter of about 40,000 km. However, the mass of this star is 95% of the mass of the Sun. This means that a huge amount of matter must be packed into an extremely small volume, in other words, the star must be dense. As a result of simple arithmetic operations, we find that the density of the satellite is almost 100,000 times higher than the density of water. A cubic centimeter of this substance on Earth would weigh 100 kg, and 0.5 liters of such a substance would weigh about 50 tons.

This is the story of the discovery of the first white dwarf. Now let’s ask ourselves: how can a substance be compressed so that one cubic centimeter weighs 100 kg? When matter is compressed to high densities as a result of high pressure, as in white dwarfs, another type of pressure comes into play, the so-called “degenerate pressure.” It appears during the strongest compression of matter in the interior of a star. It is compression, and not high temperatures, that causes degenerate pressure.

Due to strong compression, the atoms become so tightly packed that electron shells begin to penetrate one another. The gravitational contraction of a white dwarf takes place over a long period of time, and the electron shells continue to penetrate each other until the distance between the nuclei becomes of the order of the radius of the smallest electron shell. The inner electron shells are an impenetrable barrier that prevents further compression. At maximum compression, the electrons are no longer bound to individual nuclei, but move freely relative to them. The process of separation of electrons from nuclei occurs as a result of pressure ionization. When the ionization becomes complete, the electron cloud moves relative to the lattice of heavier nuclei, so that the matter of the white dwarf acquires certain physical properties characteristic of metals. In such a substance, energy is transferred to the surface by electrons, just as heat is distributed along an iron rod heated from one end.

But electronic gas also exhibits unusual properties. As the electrons are compressed, their speed increases more and more, because, as we know, according to the fundamental physical principle, two electrons located in the same element of the phase volume cannot have the same energy. Therefore, in order not to occupy the same volume element, they must move at tremendous speeds. The smallest allowable volume depends on the range of electron velocities. However, on average, the lower the speed of electrons, the larger the minimum volume they can occupy. In other words, the fastest electrons occupy the smallest volume.

Although individual electrons rush around at speeds corresponding to internal temperatures on the order of millions of degrees, the temperature of the entire ensemble of electrons as a whole remains low. It has been established that the gas atoms of an ordinary white dwarf form a lattice of densely packed heavy nuclei, through which a degenerate electron gas moves. Closer to the surface of the star, the degeneracy weakens, and on the surface the atoms are not completely ionized, so that part of the matter is in the usual gaseous state. Knowing the physical characteristics of white dwarfs, we can construct a visual model of them. Let's begin with white dwarfs have an atmosphere. Analysis of the spectra of dwarfs leads to the conclusion that the thickness of their atmosphere is only a few hundred meters. In this atmosphere, astronomers detect various familiar chemical elements. Known white dwarfs two types - cold and hot. The atmospheres of hotter white dwarfs contain some hydrogen, although it is probably less than 0.05%. Nevertheless, hydrogen, helium, calcium, iron, carbon, and even titanium oxide were detected from the lines in the spectra of these stars. The atmospheres of cool white dwarfs are composed almost entirely of helium; hydrogen probably accounts for less than one atom in a million. The surface temperatures of white dwarfs vary from 5000 K for "cold" stars to 50,000 K for "hot" ones. Under the atmosphere of a white dwarf lies a region of non-degenerate matter containing a small number of free electrons. The thickness of this layer is 160 km, which is approximately 1% of the radius of the star. This layer may change over time, but the diameter of the white dwarf remains constant and equal to about 40,000 km.

Usually, white dwarfs do not decrease in size after reaching this state. They behave like a cannonball heated to a high temperature; the core can change temperature by radiating energy, but its dimensions remain unchanged. What determines the final diameter of a white dwarf?? It turns out to be its mass. The greater the mass of a white dwarf, the smaller its radius; the minimum possible radius is 10,000 km. Theoretically, if the mass of a white dwarf exceeds the mass of the Sun by 1.2 times, its radius can be indefinitely small. It is the pressure of the degenerate electron gas that prevents the star from any further compression, and although the temperature can vary from millions of degrees in the core of the star to zero on the surface, its diameter does not change. Over time, the star becomes a dark body with the same diameter as when it entered the white dwarf stage. Below the top layer of the star, the degenerate gas is practically isothermal, that is, the temperature is almost constant all the way to the very center of the star; it amounts to several million degrees - the most realistic figure is 6 million K.

Now that we have some ideas about the structure of a white dwarf, the question arises: why does it glow? One thing is obvious: thermonuclear reactions are excluded. There is no hydrogen inside the white dwarf to support this energy generation mechanism. The only type of energy a white dwarf has is thermal energy. The atomic nuclei are in random motion as they are scattered by the degenerate electron gas. Over time, the movement of the nuclei slows down, which is equivalent to a cooling process. Electron gas, which is unlike any other gas known on Earth, has exceptional thermal conductivity, and the electrons conduct thermal energy to the surface, where this energy is radiated through the atmosphere into outer space.

Astronomers compare the cooling process of a hot white dwarf to the cooling of an iron rod removed from a fire. The white dwarf cools quickly at first, but as the temperature inside it drops, the cooling slows. According to estimates, over the first hundreds of millions of years, the luminosity of a white dwarf drops by 1% of the luminosity of the Sun.

Eventually the white dwarf must disappear and become a black dwarf. However, this may take trillions of years, and, according to many scientists, it seems highly doubtful that the Universe will be old enough for black dwarfs to appear in it. Other astronomers believe that even in the initial phase, when the white dwarf is still quite hot, the cooling rate is low. And when the temperature of its surface drops to a value on the order of the temperature of the Sun, the cooling rate increases and extinction occurs very quickly. When the white dwarf's interior cools enough, it will solidify. One way or another, if we accept that the age of the Universe exceeds 10 billion years, there should be much more red dwarfs in it than white ones. Knowing this, astronomers are searching for red dwarfs.

So far they have been unsuccessful. The masses of white dwarfs are not determined accurately enough. They can be installed reliably for components of dual systems, as in the case of Sirius. But only a few white dwarfs are part of double stars. In the three most well-studied cases, the masses of white dwarfs, measured with an accuracy of over 10%, turned out to be less than the mass of the Sun and amounted to about half of it. Theoretically, the limiting mass for a completely degenerate non-rotating star should be 1.2 times the mass of the Sun. However, if the stars rotate, and in all likelihood they do, then masses several times larger than the Sun are quite possible.

The gravity on the surface of white dwarfs is about 60-70 times greater than on the Sun. If a person weighs 75 kg on Earth, then on the Sun he would weigh 2 tons, and on the surface of a white dwarf his weight would be 120-140 tons. Taking into account the fact that the radii of white dwarfs differ little and their masses are almost the same, we can conclude that the force of gravity on the surface of any white dwarf is approximately the same. There are many white dwarfs in the Universe. At one time they were considered rare, but a careful study of photographic plates obtained at the Mount Palomar Observatory showed that their number exceeds 1,500. Astronomers believe that the frequency of white dwarfs has been constant, at least over the past 5 billion years. Maybe, white dwarfs constitute the most numerous class of objects in the sky.

It was possible to estimate the spatial density of white dwarfs: it turns out that in a sphere with a radius of 30 light years there should be about 100 such stars. The question arises: do all stars become white dwarfs at the end of their evolutionary path? If not, what fraction of the stars go into the white dwarf stage? A major step in solving the problem was taken when astronomers plotted the positions of the central stars of planetary nebulae on a temperature-luminosity diagram. To understand the properties of stars located in the center of planetary nebulae, let's consider these celestial bodies. In photographs, the planetary nebula appears as an extended ellipsoidal mass of gases with a faint but hot star at the center. In reality, this mass is a complex turbulent, concentric shell that expands at speeds of 15-50 km/s. Although these formations look like rings, they are actually shells and the speed of turbulent gas movement in them reaches approximately 120 km/s. It turned out that the diameters of several planetary nebulae, to which it was possible to measure the distance, are about 1 light year, or about 10 trillion kilometers.

Expanding at the above rates, the gas in the shells becomes very rarefied and cannot be excited, and therefore cannot be seen after 100,000 years. Many of the planetary nebulae we see today were born in the last 50,000 years, and their typical age is close to 20,000 years. The central stars of such nebulae are the hottest objects known in nature. Their surface temperature varies from 50,000 to 1 million degrees Celsius. K. Due to unusually high temperatures, most of the star's radiation falls in the far ultraviolet region of the electromagnetic spectrum.

This ultraviolet radiation is absorbed, is transformed and re-emitted by the shell gas in the visible region of the spectrum, which allows us to observe the shell. This means that the shells are significantly brighter than the central stars - which are actually the source of energy - since a huge amount of the star's radiation is in the invisible part of the spectrum. From an analysis of the characteristics of the central stars of planetary nebulae, it follows that the typical value of their mass is in the range of 0.6-1 solar mass. And for the synthesis of heavy elements in the bowels of a star, large masses are needed. The amount of hydrogen in these stars is negligible. However, gas shells are rich in hydrogen and helium.

Some astronomers believe that 50-95% of all white dwarfs did not originate from planetary nebulae. Thus, although some white dwarfs are entirely associated with planetary nebulae, at least half or more of them originated from normal main sequence stars that did not go through the planetary nebula stage. The full picture of white dwarf formation is hazy and uncertain. So many details are missing that, at best, a description of the evolutionary process can only be constructed by logical deductions. Still, the general conclusion is that many stars lose some of their matter on the way to their white dwarf-like finale, and then disappear into the celestial graveyards as black, invisible dwarfs. If the mass of a star is approximately twice the mass of the Sun, then such stars lose stability in the last stages of their evolution. Such stars can explode as supernovae and then shrink to the size of balls with a radius of several kilometers, i.e. turn into neutron stars.