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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]
White dwarfs with hydrogen-poor atmospheres, such as WD J2147–4035, are less affected by CIA and therefore have a yellow to orange color. [80] [77] The white dwarf cooling sequence seen by ESA's Gaia mission. White dwarf core material is a completely ionized plasma – a mixture of nuclei and electrons – that is
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 ...
A quantum Hall state gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow. A quantum spin Hall state is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat. This is a derivation of the Quantum Hall state of matter.
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.
Stars known as white dwarfs have mass comparable to the Sun, but have about a hundredth of its radius. The high densities mean that the electrons are no longer bound to single nuclei and instead form a degenerate electron gas. The number density of electrons in a white dwarf is of the order of 10 36 electrons/m 3. This means their Fermi energy is:
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]