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While degeneracy pressure usually dominates at extremely high densities, it is the ratio between degenerate pressure and thermal pressure which determines degeneracy. Given a sufficiently drastic increase in temperature (such as during a red giant star's helium flash ), matter can become non-degenerate without reducing its density.
Using the Fermi gas as a model, it is possible to calculate the Chandrasekhar limit, i.e. the maximum mass any star may acquire (without significant thermally generated pressure) before collapsing into a black hole or a neutron star. The latter, is a star mainly composed of neutrons, where the collapse is also avoided by neutron degeneracy ...
This is the pressure that prevents a white dwarf star from collapsing. A star exceeding this limit and without significant thermally generated pressure will continue to collapse to form either a neutron star or black hole, because the degeneracy pressure provided by the electrons is weaker than the inward pull of gravity.
Astronomy provides a spectacular demonstration of the effect of the Pauli principle, in the form of white dwarf and neutron stars. In both bodies, the atomic structure is disrupted by extreme pressure, but the stars are held in hydrostatic equilibrium by degeneracy pressure, also known as Fermi pressure.
In the nonrelativistic case, electron degeneracy pressure gives rise to an equation of state of the form P = K 1 ρ 5/3, where P is the pressure, ρ is the mass density, and K 1 is a constant. Solving the hydrostatic equation leads to a model white dwarf that is a polytrope of index 3 / 2 – and therefore has radius inversely ...
In a star less massive than the limit, the gravitational compression is balanced by short-range repulsive neutron–neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse. [12]: 74 If its mass is above the limit, the star will collapse to some denser form.
White dwarfs, in which gravity is opposed by electron degeneracy pressure [4] Neutron stars, in which gravity is opposed by neutron degeneracy pressure and short-range repulsive neutron–neutron interactions mediated by the strong force; Black hole, in which there is no force strong enough to resist gravitational collapse
They therefore provide neutron degeneracy pressure to support a neutron star against collapse. In addition, repulsive neutron-neutron interactions [ citation needed ] provide additional pressure. Like the Chandrasekhar limit for white dwarfs, there is a limiting mass for neutron stars: the Tolman–Oppenheimer–Volkoff limit , where these ...