White Dwarf Electron Fermi Gas and Nuclei Plasma

Here’s a more detailed breakdown:

1. Structure of a White Dwarf

• Electrons: In a white dwarf, the electrons are compressed into a degenerate Fermi gas due to the extreme density. The pressure from this degenerate electron gas is what supports the white dwarf against gravitational collapse.
• Protons and Neutrons: These are still bound together in atomic nuclei, forming ions like $\text{C}^{6+}$, $\text{O}^{8+}$, or $\text{He}^{2+}$, depending on the chemical composition of the white dwarf.

2. Why Protons and Neutrons Stay in Nuclei

• Nuclear Binding Energy: At the densities found in a white dwarf (around $10^6$ to $10^9 \, \text{g/cm}^3$), the nuclear binding energy holding protons and neutrons together in nuclei is much stronger than the forces trying to separate them.
• Temperature: The temperature inside a white dwarf is relatively low compared to nuclear binding energies (a few $10^6 \, \text{K}$, corresponding to $\sim 1 \, \text{keV}$), so there’s not enough thermal energy to break the nuclei apart.
• Electron Degeneracy Pressure: The support mechanism of the white dwarf relies on electrons, not the protons or neutrons. The nuclei are essentially passive contributors to the mass and do not play a direct role in resisting gravity.

3. Composition of Nuclei in a White Dwarf

The specific nuclei present depend on the star’s evolutionary history:

• Helium White Dwarfs: Formed from stars that lost their outer layers before helium burning began. These are rare and typically low-mass white dwarfs.
• Carbon-Oxygen White Dwarfs: The most common type, formed from stars that went through helium burning and produced carbon and oxygen in their cores.
• Oxygen-Neon White Dwarfs: Formed from more massive progenitors, where further fusion created oxygen and neon nuclei.

In all these cases, the protons and neutrons remain tightly bound in nuclei.

4. Why Not a Fermi Gas of Protons and Neutrons?

• Mass Threshold: If the mass of the white dwarf exceeds the Chandrasekhar limit (about $1.4 \, M_\odot$), the electron degeneracy pressure can no longer support the star. At this point, the white dwarf may collapse into a neutron star, where the electrons and protons combine to form neutrons, creating a degenerate neutron Fermi gas.
• Energetic Favorability: In a white dwarf, it is energetically favorable for protons and neutrons to remain bound in nuclei because breaking them apart would require enormous energies that are not available in the white dwarf’s environment.

Conclusion

In a white dwarf, the protons and neutrons are not free particles forming a Fermi gas. Instead, they remain bound together in nuclei, which coexist with the degenerate electron gas that provides the pressure to counteract gravity. Only in more extreme conditions, such as in a neutron star, would the protons and neutrons form their own Fermi gas.