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Sirius is the brightest star in the earth's night sky, and we can see it every winter. In 1844, German astronomer and mathematician F. Bessel calculated that Sirius should actually be a binary system with a companion star equal to the mass of the sun. However, because the companion star was so weak that it had not been discovered for a long time, it was not until 1862 that the companion star with only 1/1000 brightness of Sirius was photographed, and then its spectrum was obtained. people finally began to know this new celestial body, the white dwarf.

In order to understand the formation of white dwarfs, we should first start with the evolution of small and medium-mass stars after the main sequence stage. Stars with less than 2.3 solar masses are generally called low-mass stars, and 2.3-8 solar masses are called medium-mass stars. As for the classification criteria, it is naturally the evolution and outcome of stars, which we will discuss in detail below.

With the progress of hydrogen fusion in the core of the star and the gradual depletion of fuel, the mass of a core composed mainly of helium increases gradually, it will gradually contract under the action of gravity, and the temperature, pressure and density will also increase. The star slowly enters the red giant stage. After that, the evolution of stars is divided into two situations: first, the core of a medium-mass star is hot enough to reach the ignition temperature of helium, so it begins the 3 α reaction in which helium aggregates into carbon; second, the core temperature of a low-mass star is not high enough to produce helium fusion, which makes the core unable to rely on radiation pressure to compete with gravity, so it enters a state of electron degeneracy and uses electron degeneracy pressure to resist gravitational contraction.

(figure 2: fusion of hydrogen and helium in stars) what is degenerate pressure? We know that in a system made up of fermions, at most one particle is allowed to exist in the same microscopic quantum state (Pauli incompatibility principle). For example, there are at most two electrons (two different spin directions) in each energy level of electron degenerate gas. other electrons will be repulsed, and the repulsive force between fermions is degenerate pressure. In degenerate gases, because the lower energy levels are quickly filled, most particles have much more energy than they do in ordinary gases, and this high energy corresponds to high momentum. therefore, the pressure generated by the momentum exchange of particles is also far higher than that of the normal gas, which can resist stronger gravity and support the greater density of the core. Theoretical calculations show that the degeneracy pressure of electrons is related to density, and at the same density and temperature, the particles with smaller mass are more likely to degenerate, so it is electrons that enter the degeneracy state of the star core first.

Further contraction of the degenerate core will cause its temperature to continue to rise, and for low-mass stars with masses between 0.5 and 2.3 times the sun, the core will eventually reach the fusion temperature of helium, turning on the explosive combustion of helium, or "helium flashover." After that, the degeneracy is released, and as the core helium burns out, they, like medium-mass stars, produce a core made up mainly of carbon and oxygen, by which time stars have reached the last stage of their lives, asymptotic giants (AGB). Similarly, the carbon-oxygen core is followed by electronic degeneracy, which already has the embryonic form of a white dwarf. The huge luminosity and strong winds make its outer shell lose a lot of material, leaving only a separate carbon-oxygen white dwarf star, and the ejected material forms a planetary nebula. For stars with a mass of less than 0.5 times the sun, their core temperature can never cause helium fusion, and the final evolution result is a helium white dwarf star.

(figure 3: evolution of stars with different masses) 2. Structure and characteristics of white dwarfs there is no longer a nuclear reaction inside the white dwarf, but only the ash after the end of the star's life. They are located at the lower left of the Hero diagram, with low luminosity, high temperature and high density. Take Sirius's companion star as an example, its mass is similar to that of the sun, but its radius is similar to that of the earth, its surface temperature is about 27000 K, and its luminosity is only 1AM360 of that of the sun. Although the internal temperature of the white dwarf may be as high as 108 K, the effect of the electron degenerate pressure is still far beyond the thermal pressure, and the thermal conductivity of the degenerate electron is very strong, and the interior of the white dwarf is basically isothermal. In addition to the core, which accounts for most of the total volume, the white dwarf has a thin non-degenerate ideal gas shell. The heat transfer efficiency of this low-temperature shell, which transfers energy by convection and radiation, is obviously lower than that of isothermal nuclei. It effectively prevents the loss of internal energy, which is also the reason for the slow cooling of white dwarfs.

According to the mass-radius relationship of white dwarfs, as their mass increases, the radius decreases to increase the inner density and electron degeneracy pressure to resist the increasing gravitational force, and the electron gas will gradually develop from non-relativistic degeneracy to relativistic degeneracy. However, the radius of white dwarfs cannot be reduced indefinitely, so there is an upper limit for the mass of white dwarfs, that is, the Chandra Seka limit. It is the upper limit of the mass that degenerate electron gas can support, and when it is reached, the star will be compressed into a singularity. The value of this mass limit is only related to the ratio of atomic weight to atomic number. it is obvious that both helium white dwarfs and carbon oxygen white dwarfs have a value of 2, and their mass limits are the same. are about 1.45 times the mass of the sun as we are familiar with.

3. Accretion and explosion of white dwarfs if the white dwarf is a member of a close binary system, when the companion star evolves to the end of life and the outer layer expands to be full of Roche lobe, the matter of the companion star will flow to the white dwarf through the first Lagrangian point and be accreted. The subsequent development of the white dwarf has a lot to do with the accretion rate: if the accretion rate is too low, the accreted hydrogen will fuse out of control on the surface of the white dwarf, and the original accretion material will be re-ejected through the new star explosion. and it is possible to repeat this process to form a recurrent nova; if the accretion rate is too high, the hydrogen-rich envelope will expand rapidly, and the white dwarf will become an asymptotic giant again.

(figure 4: White dwarf accretion companion matter in close binaries) the stable white dwarf accretion process only exists in a very narrow range of accretion rates, and when the mass of the white dwarf increases close to the Chandraseca limit, a thermonuclear explosion will occur. This process releases more heat than the white dwarf needs to maintain its static equilibrium, so the result is devastating. The white dwarf will break to pieces and become an Ia supernova. The predecessor stars of Ia supernovae have roughly the same mass (Chandra Seka limit), so they also have similar luminosity and absolute magnitude after explosion, which is one of the standard candlelight to measure the distance of celestial bodies in astronomy.

(figure 5: Ia-type supernova to the left of galaxy NGC 2525) although white dwarf explosions generally have no remnants, there are exceptions. If the two sub-stars in the binary system are white dwarfs, gravitational wave radiation will cause the system to lose angular momentum, and eventually the two will be close enough to merge. Numerical simulations show that the lower density and mass of the two white dwarfs will completely disintegrate and be absorbed by another white dwarf. If the accretion rate is high, the electron capture reaction of the fusion product after carbon ignition will lead to a drop in pressure, which will cause the star to collapse and eventually evolve into a neutron star.

Reference books

Introduction to Astrophysics, Xiang Shouping, University of Science and Technology of China Press

An introduction to the Evolution of stellar structure, Li Yan, Peking University Press

Author: Cong Yu

Audit: Ishima

APC editorial Department Science Popularization Group

This article comes from the official account of Wechat: APC Science Alliance (ID:apcscience), author: APC Jun

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