Neutron vs electron degeneracy pressure

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Discussion Overview

The discussion explores the differences between neutron degeneracy pressure and electron degeneracy pressure, particularly in the context of supporting dense astronomical objects like neutron stars and white dwarfs. It addresses theoretical aspects, physical principles, and the implications of particle properties on degeneracy pressure.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why neutron degeneracy pressure can support higher density objects compared to electron degeneracy pressure, suggesting that electron degeneracy pressure might be conceptually stronger due to the charge of electrons.
  • Another participant clarifies that electron degeneracy pressure is primarily due to electrons occupying higher energy states rather than electric repulsion, and notes that neutron degeneracy pressure is greater because neutrons have a larger mass, which increases the energy of their states.
  • It is mentioned that at the same density, electron degeneracy pressure is larger, which supports white dwarfs, but if it becomes too large, electron capture can occur, leading to collapse into neutrons, whose degeneracy pressure can increase significantly in a compact object.
  • A participant requests elaboration on why electron degeneracy pressure is larger at the same density, prompting a response that attributes this to the lighter mass of electrons, which affects the pressure equation.
  • The pressure equation is presented, with a participant explaining that it applies to all cold fermions and noting the relationship between mass and pressure at a given density.
  • Another participant discusses the physical implications of particle density and interparticle spacing, explaining how these factors relate to momentum and pressure.
  • Questions are raised about the role of the Pauli exclusion principle in both electron degeneracy pressure and neutron star physics, with affirmations that it is indeed applicable in both contexts.

Areas of Agreement / Disagreement

Participants express differing views on the nature and implications of degeneracy pressures, particularly regarding the comparative strengths and underlying principles. While some points are clarified, no consensus is reached on all aspects of the discussion.

Contextual Notes

Limitations include the dependence on definitions of degeneracy pressure and the specific conditions under which the discussed equations apply. The discussion does not resolve the complexities of the interactions between particle types and their respective pressures.

PeterB
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How is neutron degeneracy pressure able to support a much higher density object such as a neutron star where electron degeneracy pressure only supports a comparatively less dense object such as a white dwarf. Conceptually I would think electron degeneracy pressure to be stronger due to the charge of electrons pushing off another.
 
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As far as I know, electron degeneracy has little if anything to do with the repulsive force from their like electric charges. Instead it is the result of the electrons running out of low energy states to occupy and being forced into higher energy states. This higher energy state requires more energy, and hence takes more pressure to kick the electron up to that state than lower energy states do.

I think the much greater degeneracy pressure of neutrons is due to their much greater mass, which increases the energy of each of their states.

As always, someone correct me if I'm wrong.
 
At the same density electron degeneracy pressure is larger. That's why white dwarfs are supported by it. If the electron degeneracy pressure gets too large then electron capture (proton+electron -> neutron+neutrino) become energetically favorable and the electron degeneracy pressure cannot increase more. If the mass is too large the object collapses. The created neutrons don't have a mechanism where they could disappear, their degeneracy pressure can grow to much larger values in a more compact object.
 
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Can you elaborate on why electron degeneracy pressure is larger for the same density, mfb?
 
Electrons are lighter, their energy states are further apart.
$$P=\frac{(3 \pi^2)^{2/3} \hbar^2}{5 m}\rho^{5/3}$$
This applies separately for each particle type where ##\rho## is the density of free particles of this type and m is their mass. As you can see from the mass in the denominator lighter particles lead to a higher pressure at the same density.
 
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What is the name of this equation and what is the scope of this equation for what it pertains to specifically. Is this for all subatomic particles?
 
It applies to all cold* fermions. I'm not aware of a special name for it. You can find it e.g. on Wikipedia.

*not highly relativistic
 
Physically, what is happening is that if you specify the particle density, you are setting the interparticle spacing. If you also specify that the particles are degenerate, it implies that the interparticle spacing is comparable to the particle deBroglie wavelength, which is inversely proportional to the particle momentum. Hence the momentum is fixed by the interparticle spacing, but that makes the particle speed inversely proportional to the mass. Pressure relates to momentum flux, not just momentum, so when the momentum per particle is fixed by the particle density, lower mass means higher speed which means higher rate of momentum flux which means higher pressure.
 
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Can we say Pauli exclusion principle is evident in electron degeneracy pressure.
Also at neutron star stage ,is there too some principle like Pauli exclusion principle at work?
 
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gianeshwar said:
Can we say Pauli exclusion principle is evident in electron degeneracy pressure.

Yes.

gianeshwar said:
Also at neutron star stage ,is there too some principle like Pauli exclusion principle at work?

Yes. It's called the Pauli Exclusion Principle.
 
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