The Discussion of the White Dwarfs

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White Dwarfs
06.04.2020
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Introduction

The white dwarfs represent one of the fascinating object classes in the history of astronomy. These celestial objects have properties, which are extremely different from the ones that humanity deals with on the Earth. Thus, it is noteworthy to discuss the white dwarfs’ internal physics and the hypothesis concerning their mass, emission reasons, and origin.

Discovery and Study of the First White Dwarf

The history of the white dwarfs’ discovery 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 was not straight but had the wavy character. The proper motion of the star did not occur along the straight line. Its trajectory shifted from side to side. In 1844, ten years after the first observations of Sirius, Bessel concluded that there was another star close to Sirius, which being invisible caused the gravitational effect on Sirius (Benningfield, 2011). One could reveal that by fluctuations in the movement of Sirius. Still more interesting was the fact that even if the dark component actually existed, the circulation period of both stars around their common center of gravity was approximately 50 years.

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Another important event happened in Cambridge, Massachusetts (USA) in 1862. Alvan Clark, the biggest telescope builder in the United States, was entrusted by the University of Mississippi to design the telescope with a lens diameter of 18.5 inches, which had to become the largest telescope in the world (Benningfield, 2011). After Clark had completed the processing of the telescope lens, it was necessary to check whether the required accuracy of its surface form was procured. For this purpose, the researchers installed the lens into the mobile tube and directed to Sirius, which was the brightest star and, thus, the best object to test the lenses and identify any flaws. Having fixed the position of the telescope tube, Alvan Clark observed a faint “ghost,” which appeared on the eastern edge of the field of view of the telescope in the glare of Sirius. The image of Sirius was distorted and one could assume that the “ghost” was the outcome of the lens defect, which the designer should eliminate before putting the lens in operation (Benningfield, 2011). However, a faint star that emerged in the telescope’s field of view was the component of Sirius predicted by Bessel, while the construction of the lens was perfect.

Thus, Sirius became the subject of general interest and numerous studies, because the physical characteristics of the binary system intrigued the astronomers. Taking into account the characteristics of the movement of Sirius, its distance from the Earth and the amplitude of deviations from the rectilinear motion, the astronomers managed to determine the features of both stars, named as Sirius A (the bright star) and Sirius B (the faint one) (SSQ, n.d.). The total mass of both stars was 3.4 times bigger than the mass of the Sun. The researchers found out that the distance between the stars was almost 20 times greater than the one between the Sun and the Earth. According to the measured orbit parameters, the Sirius A weight made 2.02 the Sun’s masses, and the mass of Sirius B contained 98% of the Sun’s mass (SSQ, n.d.). After the astronomers had determined the luminosity of both stars, they found out that Sirius A was almost 10,000 times brighter than Sirius B. On the bases of the absolute size of Sirius A one can measure that it shined approximately 35.5 times stronger than the Sun. Thus, the luminosity of the Sun exceeds by 300 times the luminosity of Sirius B (SSQ, n.d.).

The luminosity of any star depends on its surface temperature and its size (the diameter). The proximity of the second component of the binary system to the brighter Sirius obscured the determination of its spectrum, which is required to measure the temperature of the star. In 1915, using all technical means accessible in the largest observatory of that time in Mount Wilson (USA), the researchers obtained the photos of the Sirius’ spectrum. That led to an unexpected discovery: the Sirius B temperature was 25,000 C, whereas the Sun had a temperature of 6000 C (Holberg, 2007). Thus, the “faint” satellite actually turned out to be hotter than the Sun. It meant that the luminosity of a surface unit was higher as well. In fact, a simple calculation shows that every square centimeter of its surface emits four times more energy than a square centimeter of the surface of the Sun. Hence, the surface of the satellite has to be 300 * 104 times smaller than the surface of the Sun and the diameter of Sirius B should be approximately 40,000 km. However, the mass of this star is 98% of the mass of the Sun (Holberg, 2007). This means that a huge amount of the material is “packaged” in an extremely small volume. In other words, the star is enormously dense. Conducting the simple arithmetic operations one can determine that the density of the satellite is 100,000 times greater than the density of water. The cubic centimeter of the star’s substance in the Earth would weigh 100 kg, and 0.5 liters of this material – about 50 tons (Holberg, 2007).

Physical Processes inside the White Dwarfs

It is vital to be aware of the compression method, which allows one cubic centimeter of the substance to weight up to 100 kg. When due to high pressure the substance is compressed to the high densities, like in the white dwarfs, one should operate with the so-called degenerate pressure (NASA, 2010). It occurs in the highly compressed substance inside the star. The compression itself causes the degenerate pressure rather than the high temperatures do. Due to the strong contraction, the atoms are so tightly packed that the electron shells start to penetrate into one another (NASA, 2010). The gravitational compression of the white dwarf is happening for a long time. Thus, the electron shells keep penetrating into each other until the distance between their cores equals the order of the radius of the smallest electron shell. The internal electron shells constitute the impervious barrier, which prevents further compression. When the maximum compression emerges, the electrons are no more connected to separate cores and move freely around them. The process of the electrons separating from the core occurs in result of the ionization with the pressure. When the ionization is complete, the electron cloud will move through the lattice of heavier cores. Therefore, the substance of the white dwarf star acquires certain physical properties, which are typical for metals (NASA, 2010). The energy in this material transfers to the surface with the help of electrons, just as the heat spreads through the iron rod, heated at one edge.

The electron gas shows extraordinary properties as well. While the electrons are compressing, their speed is increasing. According to the fundamental physical principle, two electrons, which occupy the same phase volume unit, will never have equal energy (Chen, n.d.). Therefore, in order not to occupy the same volume unit, they have to move at tremendous speeds. The smallest size of the allowable volume depends on the electron velocity range. However, on average, the lower the velocity of the electron is, the higher is the minimum volume, which it can occupy. In other words, the fastest electrons hold the least volumes. Thus, the velocities of the electrons inside the white dwarfs are extremely high (Chen, n.d.). Their corresponding internal temperature has the order of millions of degrees. However, the temperature of the entire electrons ensemble remains low in general.

The astrophysicists have concluded that the gas atoms of the ordinary white dwarf constitute densely packed lattice of the heavy nucleus, through which the degenerate electron gas moves. Close to the surface of the star, the degeneration weakens, and the atoms on the surface are not completely ionized therefore a portion of the substance stays in the normal gaseous state (NASA, 2010).

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Knowing the physical characteristics of the white dwarfs, one can construct their visual model. The white dwarfs have the atmosphere. The analysis of the dwarfs’ spectrum leads to the conclusion that the thickness of the atmosphere makes only a few hundred meters. In their atmosphere, the astronomers have detected a variety of familiar chemical elements (Koester, 2008). There are two types of white dwarfs – the cold and hot ones. In the atmospheres of the hot white dwarfs, the color of which is close to white, one can observe the reserve of hydrogen, although it probably does not exceed 0.05%. The researchers have detected hydrogen, helium, calcium, iron, carbon monoxide and even titanium in the spectrum of these stars. The atmospheres of the cool white dwarfs are composed of helium. Here hydrogen atom is one in a million. The temperatures of the white dwarfs’ surface vary from 3,000 K of the cold stars up to 50,000 K of the hot ones (Koester, 2008). Under the atmosphere of the white dwarf, there is a region of the non-degenerate substance, which contains a small number of free electrons. The thickness of this layer of Sirius B makes about 160 km and is about 1% of the star’s radius (Koester, 2008). This layer may change over time. However, the diameter of the white dwarf remains constant.

The White Dwarf Size

Typically, the size of the star does not reduce after reaching the state of the white dwarf. White dwarfs behave like a cannon kernel, heated to the high temperature (Holberg, 2007). The kernel can change the temperature of the radiating energy, but its dimensions remain unchanged. The researchers assume that the final diameter of the white dwarf depends on their mass. The white dwarfs with the greatest masses have the smallest radiuses. Theoretically, if the mass of the white dwarf exceeds 1.2 times the mass of the Sun, its radius will be infinitely small. However, the degenerate pressure of the electron gas prevents the star from further compression, and although the temperature varies from the millions of degrees in the star’s core to a few thousand degrees at the surface, the white dwarf’s diameter remains unchanged (Holberg, 2007). Eventually, the star becomes a dark body with the same diameter, which it has had while entering the stage of the white dwarf.

The Emission Reasons of the White Dwarfs

The thermonuclear reactions are impossible within the white dwarfs (Mestel, 1952). Inside the white dwarf, there is no hydrogen, which would support this mechanism of energy generation. The only form of energy, which the white dwarf disposes of, is the thermal energy. The cores of the atoms stay in the random motion, as they are scattered with the degenerate electron gas (Mestel, 1952). Eventually, the motion of the atom cores keeps slowing down which is equivalent to the cooling process. The electron gas, which is not similar to any known gas on the Earth, has exceptional thermal conductivity, and the electrons conduct the thermal energy through the atmosphere to the surface where this energy is radiated into space. The astronomers compare the cooling process of the hot white dwarf with the cooling of the iron rod, removed from the fire. First, the white dwarf cools down rapidly, but after the temperature decreases inside, the cooling process slows down. They have estimated that during the first few hundred millions of years the white dwarf luminosity falls by 1% of the Sun’s luminosity (Mestel, 1952). Eventually, the white dwarf must disappear or transform into the black dwarf, but this process may require trillions of years, and, according to some researches, the age of the universe is doubtfully big enough for the appearance of the black dwarfs at all. The other researchers believe that in the initial phase, when the white dwarf is quite hot, the cooling rate is low. When the surface temperature falls to the Sun’s one, the cooling rate increases and fading occurs extremely quickly. When the bowels of the white dwarf are cool enough, they harden.

Features of the White Dwarfs

Scientists have not identified the masses of the white dwarfs precisely enough. They managed to set them reliably for the binary systems’ components, as in the Sirius case. However, only some white dwarfs are the components of the binary stars. In the most well-studied cases, the masses of the white dwarfs, which were measured with an accuracy of over 10%, were less than the mass of the Sun and were approximately half the mass of the Sun. In theory, the limit mass of the completely degenerate and not rotating star should be 1.2 times more than the mass of the Sun (Redd, 2013). However, if the stars revolve, their masses will possibly be several times greater than that of the Sun.

The gravity force on the surface of the white dwarf is approximately 60-70 times greater than on the surface of the Sun (Redd, 2013). If a person weighs about 75 kg on the Earth, then he would weigh 2 tons in the Sun, and on the surface of the white dwarf, this weight transforms to 120-140 tons. Considering the fact that the radiuses of the white dwarfs do not differ a lot, and their masses are almost identical, one can conclude that the gravity force on the surface of any white dwarf is roughly similar.

There are many white dwarfs in the universe. Once the researchers considered them to be the great rarity, but the careful study of photographic plates obtained in the observatories all over the world showed that their number exceeds 1,500 (Redd, 2013). The astronomers believe that the frequency of the occurrence of the white dwarfs has been constant, at least during the last 5 billion years. Probably, the white dwarfs constitute one of the most abundant classes of celestial objects. The white dwarfs are actually the corpses of many low-mass stars. In the Milky Way, they make 10% of all stars. The spatial density of the white dwarfs near the Sun is about 0.005 per cubic parsec. It means that within 20 parsecs (about 65 light-years) from the Sun, one should find about 170 white dwarfs. The scientists have found more than a hundred of them (Redd, 2013). Within 13 parsecs, all white dwarfs have been discovered.

Some astronomers believe that the white dwarfs emerged from the planetary nebulae (Redd, 2016). However, at least half of them or even more descended from the normal main-sequence stars, without passing through the stage of the planetary nebula. Unfortunately, the completed picture of the white dwarfs formation is vague and quite uncertain. The tremendous amount of details is still absent, thus, one can build the description of the evolutionary process only with the help of logical reasoning.

Conclusion

The French mathematician Bessel played a crucial role in the study of the first white dwarf (Sirius B) in the 19th century. He supposed that there was a less bright celestial object close to Sirius, which was later confirmed by astronomers, who worked with the telescope designed by Alvan Clark. The mass of Sirius B is 98% of the Sun’s mass. Sirius B is almost 10,000 times fainter than Sirius A. Its temperature is around 25,000 C, whereas the Sun has a temperature of 6000 C. With a relatively small diameter (40,000 km), the star is enormously dense. Its density is about 100,000 times greater than the density of water.

The compression of the star substance creates the so-called degenerate pressure. Due to the strong contraction, the atoms are so tightly packed that the electron shells start to penetrate into one another. The electron shells keep penetrating into each other until the distance between their cores equals the radius of the smallest electron shell. The internal electron shells constitute the impervious barrier, which prevents further compression. When the maximum compression emerges, the electrons are not connected to the separate cores anymore and move freely around them, forming the degenerate electron gas. The velocities of the electrons inside the white dwarfs are extremely high. Their corresponding internal temperature reaches millions of degrees. However, the entire electrons ensemble temperature remains low in general.

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Close to the surface of the white draft, the degeneration weakens, and the atoms on the surface are not completely ionized, so that portion of the substance stays in the normal gaseous state, constituting the atmosphere of the star. The spectrum of the hot white dwarfs’ atmospheres includes hydrogen, helium, calcium, iron, carbon monoxide and even titanium. The atmospheres of the cold white dwarfs are composed of helium with a quite small concentration of hydrogen. The temperatures of the white dwarfs’ surface vary from 3,000 K of the cold stars up to 50,000 K of the hot ones. The upper layer of the white dwarf may change over time. However, the diameter of the star remains constant, thus, one can compare the white dwarf with the cooling metal rod. The thermonuclear reactions are impossible within the white dwarfs. The only form of energy, which the white dwarf disposes of, is the thermal energy that dissipates into space from the surface of the star. There are different hypotheses concerning the cooling process of the star as well the origin of the white dwarfs, with more than 100 white dwarfs located within 20 parsecs of the Sun. Some astronomers believe that the white dwarfs emerged from the planetary nebulae. However, at least half of them or even more descended from the normal main-sequence stars, without passing through the stage of the planetary nebula. Thus, there are still too many unresolved issues concerning the white dwarfs, due to the lack of evidence.

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