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From the quantum statistics of a completely degenerate electron gas (all the lowest quantum states are occupied), the pressure and the density of a white dwarf are calculated in terms of the maximum electron momentum standardized as = /, with pressure = and density =, where
Following the Pauli exclusion principle, there can be only one fermion occupying each quantum state. In a degenerate gas, all quantum states are filled up to the Fermi energy. Most stars are supported against their own gravitation by normal thermal gas pressure, while in white dwarf stars the supporting force comes from the degeneracy pressure ...
Sirius B, which is a white dwarf, can be seen as a faint point of light to the lower left of the much brighter Sirius A. A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: in an Earth sized volume, it packs a mass that is comparable to the Sun.
In white dwarf stars, the positive nuclei are completely ionized – disassociated from the electrons – and closely packed – a million times more dense than the Sun. At this density gravity exerts immense force pulling the nuclei together. This force is balanced by the electron degeneracy pressure keeping the star stable. [4]
The concept of universal wavefunction was introduced by Hugh Everett in his 1956 PhD thesis draft The Theory of the Universal Wave Function. [8] It later received investigation from James Hartle and Stephen Hawking [9] who derived the Hartle–Hawking solution to the Wheeler–deWitt equation to explain the initial conditions of the Big Bang ...
The high mass density of white dwarfs was demonstrated in 1925 by American astronomer Walter Adams when he measured the gravitational redshift of Sirius B as 21 km/s. [18] In 1926, British astrophysicist Ralph Fowler used the new theory of quantum mechanics to show that these stars are supported by electron gas in a degenerate state.
White dwarfs resist gravitational collapse primarily through electron degeneracy pressure, compared to main sequence stars, which resist collapse through thermal pressure. The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction.
Fermi–Dirac statistics was applied in 1926 by Ralph Fowler to describe the collapse of a star to a white dwarf. [8] In 1927 Arnold Sommerfeld applied it to electrons in metals and developed the free electron model, [9] and in 1928 Fowler and Lothar Nordheim applied it to field electron emission from metals. [10]