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How Degenerate Stars Came to be Known as White Dwarfs
Abstract
Sirius B is widely regarded as the first white dwarf to have been ``discovered", in 1862. Arguably, this honor belongs to 40 Eridani B, whose subluminous nature was recognized in 1910. Sirius B joined 40 Eridani B in the lower left hand corner of the H-R diagram in 1915; only after Walter Adams obtained the first spectra of the famous companion of Sirius. The term ``white dwarf" was coined in 1922 by Willem Luyten and subsequently popularized by Arthur Eddington in 1924.
... After that, the people of Kea, incited by Aristaeus, made sacrifices to the constellation of Canis Major and to Sirius; in order to remember his beneficence, they honored Aristaeus as 'Aristaeus Apollo' and pictured his head on the one side of their coins, while on the other side they depicted Sirius crowned with rays (Wendel, 1935: 168.8-12). Indeed, ancient coins retrieved from the island and dating to the third century BC feature dogs or stars with emanating rays, highlighting Sirius' importance (Holberg, 2005). From then on, the islanders of Kea used to predict from the first appearance of Sirius (its heliacal rising) whether the following year would be healthy or not: if it rose clear, it would portend good fortune; if it was misty or faint then it foretold (or emanated) pestilence. ...
... The white dwarf star has been investigated for many years, and it was named first in 1922 (Holberg, 2005). It usually has a very high density with mass similar to our Sun, but the volume is small like the Earth. ...
In this research, first considering the electron–electron interaction in the high-density Fermi electron gas at T = 0 K, this interaction causes the pressure 2/137 time less than the original value. However, the pressure of the Fermi electron gas should have something to do with temperature. Then, we estimate the temperature effect using statistical mechanics and find that the complicated form of the pressure p depends on temperature at the given particle number N and volume V . According to this, the central density–mass ( ρ c - M ), central density–radius ( ρ c - R ), and mass–radius ( M - R ) relations of the white dwarf star are obtained by considering the equation of state (EOS). Traditional formula gives the problematic mass–radius relation R ∝ M − 1 / 3 for the low-density white dwarf stars because it leads to R →∞ and p →0 when M →0. We correct this relation and obtain two reasonable relations in the relativistic and nonrelativistic regions. In our EOS calculations, the central density is divided into the high-, middle-, and low-density regions. All three relations are almost unchanged until 10 ⁸ K in the high-density region. The temperature effect mainly affects the middle- and low-density regions, and it becomes explicitly above 10 ⁷ K. Our calculations can explain Sloan Digital Sky Survey observations where some white dwarf stars with a radius of more than 8 × 10 ³ km have larger mass than the predictions by the relativistic EOS at T = 0 K. This result tells us that the temperature effect is important for the low and middle central-density white dwarf star and also useful to estimate the inner temperature of a white dwarf star.
... The white dwarf star has been investigated many years and it was named first in 1922 [1]. It usually has very high density with the mass similar to our sun but the volume small like Earth. ...
In this research, first considering the electron-electron interaction in the high-density Fermi electron gas at T=0 K, this interaction causes the pressure 2/137 time less than the original value. However, the pressure of the Fermi electron gas should have something to do with temperature. Then we estimate the temperature effect using statistical mechanics and find the complicated form of the pressure P depends on temperature at the given particle number N and volume V. According to this, the central density-mass (ρc-M), central density-radius (ρc-R), and mass-radius (M-R) relations of the white dwarf star are obtained by considering the equation of state (EOS). Traditional formula gives the problematic mass-radius relation R∝M^((-1)⁄3) for the low-density white dwarf stars because it leads to R→∞ and P→0 when M→0. We correct this relation and obtain two reasonable relations in the relativistic and nonrelativistic regions. In our EOS calculations, the central density is divided into the high-, middle-, and low-density regions. All three relations are almost unchanged until 10^8 K in the high-density region. The temperature effect mainly affects the middle- and low-density regions and it becomes explicitly above 10^7 K. Our calculations can explain Sloan Digital Sky Survey observations where some white dwarf stars with a radius more than 8x10^3 km have larger mass than the predictions by the relativistic EOS at T=0 K. This result tells us that the temperature effect is important for the low and middle central-density white dwarf star and also useful to estimate the inner temperature of a white dwarf star.
... The white dwarf star is thought to be the type of the low to medium mass stars in the final evolution stage and it was named first in 1922 [1]. Its density is usually very high with the mass similar to our sun but the radius as small as Earth. ...
The explanation for the pressure against gravity in the white dwarf star is based on the ideally degenerate Fermi electron gas at the temperature of absolute zero. It predicts the upper mass limit of the white dwarf star is 1.44 Mʘ. However, more conditions have to be considered like temperature and charges. In this research, first we use the grand partition function in statistical mechanics to build the expressions of the electron gas pressure and the particle number depending on temperature. At 10^7 K, there is about 1.50x10^(-4) of total electrons exceeding the Fermi energy. Because some of this Fermi electron gas are the relativistic electrons, then we consider that some of them can escape the gravity resulting in a positively charged star. These rest positive charges produce the strong repulsive force and the pressure to against gravity. Furthermore, due to the quantum effect, some electrons can tunnel the potential barrier even their energy is less than the maximal potential. By theoretical analysis, it is possible to be a positively charged star with 2.708x10^20 C as long as the attraction force is strong enough. The increases pressure is almost the same as that of the Fermi electron gas.
... The unusual faintness of white dwarfs was first recognised in 1910 [14]. The name white dwarf was coined by Willem Luyten in 1922 [15]. Now it is well known from the nuclear structure studies that the kind of isotopes of He, C, O, Mg, Ne, and so on present in white dwarfs are all bosons. ...
The aim of this paper is to calculate the analytical form of the equation of state for dilute relativistic plasma. We obtained the excess free energy and pressure in the form of a convergent series expansion in terms of the thermal parameter
... После тога, народ Кее, подстакнут од Аристеја, приносио је жртве сазвежђу Canis Major и Сиријусу; у знак сећања на њихово доброчинство, Аристеја су славили као "Аристеја Аполона" и стављали његову главу на на једну страну свог новца, док је на другој био представљен Сиријус крунисан зрацима (Scholia in Apollonium Rhodium vetera, у C. Wendel (уредник), Берлин 1935, 168.8-12). Заиста, на старом новцу нађеном на острву -из трећег века пре н.е.представљени су пас или звезде са зрацима, што подвлачи значај Сиријуса (Holberg, 2005). Од тада па надаље, острвљани са Кее предвиђали су на основу прве појаве Сиријуса (његовог хелијакалног изласка) да ли ће година бити здрава или не: ако је јасно ружичаст, то ће донети добру срећу, ако је магличаст или слаб, то претсказује кужност. ...
... After that, the people of Kea, incited by Aristaeus, made sacrifices to the constellation of Canis Major and to Sirius; in order to remember his beneficence, they honored Aristaeus as 'Aristaeus Apollo' and pictured his head on the one side of their coins, while on the other side they depicted Sirius crowned with rays (Wendel, 1935: 168.8-12). Indeed, ancient coins retrieved from the island and dating to the third century BC feature dogs or stars with emanating rays, highlighting Sirius' importance (Holberg, 2005). From then on, the islanders of Kea used to predict from the first appearance of Sirius (its heliacal rising) whether the following year would be healthy or not: if it rose clear, it would portend good fortune; if it was misty or faint then it foretold (or emanated) pestilence. ...
The brightest star of the night sky, is Sirius, Alpha Canis Majoris (CMa). Due to its intense brightness, Sirius had one of the dominant positions in ancient mythology, legends and traditions. In this paper the references of the many ancient classical Greek and Roman authors and poets who wrote about Sirius are examined, and the problem of its 'red' color reported in some of these references is discussed.
... After that, the people of Kea, incited by Aristaeus, made sacrifices to the constellation of Canis Major and to Sirius; in order to remember his beneficence, they honored Aristaeus as 'Aristaeus Apollo' and pictured his head on the one side of their coins, while on the other side they depicted Sirius crowned with rays (Wendel, 1935: 168.8-12). Indeed, ancient coins retrieved from the island and dating to the third century BC feature dogs or stars with emanating rays, highlighting Sirius' importance (Holberg, 2005). From then on, the islanders of Kea used to predict from the first appearance of Sirius (its heliacal rising) whether the following year would be healthy or not: if it rose clear, it would portend good fortune; if it was misty or faint then it foretold (or emanated) pestilence. ...
The brightest star of the night sky, is Sirius, Alpha Canis Majoris (CMa). Due to its intense brightness, Sirius had one of the dominant positions in ancient mythology, legends and traditions. In this paper the references of the many ancient classical Greek and Roman authors and poets who wrote about Sirius are examined, and the problem of its 'red' color reported in some of these references is discussed.
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