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As far as i understand, electron degeneracy pressure relies upon the confined electrons having a lot of kinetic energy, which causes them to push 'outwards', counteracting gravitational pressure in a white dwarf.

Shouldn't this kinetic energy slowly decrease as the white dwarf cools into a brown then black dwarf? If so, wouldn't the star collapse when the pressure decreases enough?

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    $\begingroup$ en.wikipedia.org/wiki/Degenerate_matter says: The key feature is that this degeneracy pressure does not depend on the temperature but only on the density of the fermions. Degeneracy pressure keeps dense stars in equilibrium, independent of the thermal structure of the star. $\endgroup$
    – PM 2Ring
    Commented Jun 6, 2019 at 0:40

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The degeneracy pressure is the pressure exerted by a fermion gas even at zero temperature. The existence of a (potentially very large) pressure even at $T=0$ is counterintuitive and it represents a fundamentally quantum-mechanical effect.

The Pauli Exclusion Principle means that no two identical electrons can be in the same quantum state. If you imagine adding electrons one at a time to a finite region, with each electron falling into the lowest available energy state, you will soon need to be putting electrons into a states with substantial amounts of momentum, because the the low-lying states are already filled. So, even at $T=0$, many of the electrons in a dense electron gas are whizzing around at fairly high speed. It is the kinetic action of these moving electrons that is responsible for the degeneracy pressure.

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  • $\begingroup$ I am almost certain that at T=0, the electrons will not be wizzing around at high speeds. You can satisfy the Pauli exclusion principal simply by stacking the electrons in space so they have different potentials. $\endgroup$
    – user400188
    Commented Jun 6, 2019 at 7:22
  • $\begingroup$ Temperature is defined as either a function of kinetic energy or as dU/dS. For it to be zero you either need zero kinetic energy or for the rate of change of the systems energy to be constant. This will not be the case if the electrons are moving and able to exchanging energy with the rest of the star. $\endgroup$
    – user400188
    Commented Jun 6, 2019 at 7:25
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    $\begingroup$ @user400188 then you would be incorrect. Temperature is not defined in terms of kinetic energy and the electrons in a white dwarf are effectively "cold". Temperature plays almost no role in determining their kinetic energy. You canot move your electrons around in space because they are confined by the gravitational potential of the star. $\endgroup$
    – ProfRob
    Commented Dec 1, 2021 at 21:03
  • $\begingroup$ @ProfRob Hi, I mentioned that temperature is defined as a function of kinetic energy $\textit{or}$ as $dU/dS$. Also I didn’t mention that electrons were moving around in space, in fact I stated they were $\textit{not}$ wizzing around (I think you missed the “not” on your first reading). (edit to comment: for a moment I thought I had misused $T=dU/dS$, but it’s correct in this setting). $\endgroup$
    – user400188
    Commented Dec 1, 2021 at 23:11
  • $\begingroup$ Further, degenerate electrons cannot exchange energy with the rest of the star, or at least they cannot reduce their energy. $\endgroup$
    – ProfRob
    Commented Dec 1, 2021 at 23:47

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