# Degeneracy pressure

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• gianeshwar

#### gianeshwar

TL;DR Summary
Waves due to degeneracy pressure.
Is degeneracy pressure created due to Pauli exclusion principle able to create some waves?
Also at neutron star stage similarly are there waves created may be of higher energy?
Can we talk of some harmonic motions in these stages?

Summary:: Waves due to degeneracy pressure.

Is degeneracy pressure created due to Pauli exclusion principle able to create some waves?
Also at neutron star stage similarly are there waves created may be of higher energy?
Can we talk of some harmonic motions in these stages?
Neutron-star oscillations seem to be mostly theoretical.

Degeneracy pressure is completely normal gas pressure, in every mechanical sense-- the distinctions that give it its name are purely thermodynamic, meaning they relate to temperature. But waves are also mechanical, so "degeneracy pressure" has the same relationship with waves as any type of gas pressure, as long as we are not considering energy transport (which would bring in T). If we do wish to bring in energy transport, we notice that a fully degenerate gas has T=0, and compression does not change degeneracy (only heat transport does), so the T would stay 0 as a wave goes by. Ironically, this does not mean they would act like "isothermal sound waves," it means they would not suffer heat transport, so would act like "adiabatic sound waves." This means that pressure waves in degenerate gas are the same as adiabatic waves in an ideal gas, and would travel at the "adiabatic sound speed," which is the square root of dP/d\rho, where P is proportional to \rho to the 5/2 power. Hence the sound speed would be the square root of 5/2 times the pressure divided by the mass density, which is purely a function of density (a cute fact-- sound waves in a neutron star would depend only on density, as long as there are not complicating components to the neutron star like strings and free quarks and gluons and all that). Beyond that, it's a purely mechanical effect, so has no other relation to degeneracy or the thermodynamics of the gas.

The key point is, gas pressure always comes from the kinetic energy density of the particles (more correctly the stress-energy tensor, but let's keep it simple), and if the particles have no internal degrees of freedom to hold kinetic energy, and are nonrelativistic, their gas pressure always equals 2/3 of their kinetic energy density. This is a purely mechanical consequence of kinetic energy and its relation to momentum flux, so is just as true for "degeneracy pressure" as "ideal gas pressure." The distinctions in those two phrases mean nothing beyond a different temperature behavior in the two cases (the T is way lower at given density and pressure if one is talking about degenerate rather than ideal gas). Hence, we should not say that "degeneracy pressure is created by the PEP", we should say that if you take a given gas pressure, and also assert that you have a PEP playing a key role, you will find the T is way lower than if the PEP was not important.

The phrase "degeneracy pressure" causes all kinds of misconceptions for this reason. But degeneracy pressure simply means that you have reached a state where kT is way below the kinetic energy per particle, and you can calculate the P when T reaches zero (given the density). You then can call that "degeneracy pressure" if you like, but it is more clear to just call it the pressure that is there by the time the gas goes fully degenerate. Since that takes too long to say, we have instead the unfortunate phrase "degeneracy pressure," which is a bit like "centrifugal force"-- it is useful once you know what it is, but leads to a lot of misconceptions before you get there.

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alantheastronomer and topsquark