The application of of Fermi Dirac statistics in the white dwarf

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SUMMARY

The discussion centers on the application of Fermi-Dirac statistics in white dwarf research, specifically addressing the conditions under which these statistics are applicable. It is established that while the core temperature of a white dwarf is significantly high, it remains low compared to the Fermi temperature (T_F), allowing for the use of Fermi-Dirac statistics to calculate electron degeneracy. The approximation T=0 is clarified as being more accurately represented by T< PREREQUISITES

  • Understanding of Fermi-Dirac statistics
  • Knowledge of white dwarf astrophysics
  • Familiarity with concepts of electron degeneracy
  • Basic grasp of thermodynamic temperature scales
NEXT STEPS
  • Study the implications of Fermi temperature (T_F) in astrophysical contexts
  • Explore the differences between Fermi-Dirac and Maxwell-Boltzmann statistics
  • Research electron degeneracy pressure in stellar objects
  • Examine the thermal properties of white dwarfs and their evolutionary stages
USEFUL FOR

Astronomers, astrophysicists, and students studying stellar evolution, particularly those focused on the properties and behaviors of white dwarfs and electron degeneracy phenomena.

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hi guys, I wonder if I have fully understood the Fermi Dirac statistics properly, but I have a question on it regarding its application in the white dwarf research. I read the Fermi energy is applicable for T=0, now if the core of a white dwarf is too hot then how can we apply the Fermi Dirac statistics there to calculate the electron degeneracy ?

can you please explain me ?
regards
 
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The temperature of a white dwarf is certainly very hot compared to our regular every day standards, but it is low compared to the Fermi temperature ##T_F\equiv \epsilon_F/k## and so a white dwarf is highly degenerate and we *must* use the Fermi Dirac statistics and not Maxwell-Boltzmann statistics.

T=0 is used only as an approximation, it should really read ##T<<T_F## for practical applications. This of course means that the object of interest is not, strictly speaking, totally degenerate, but it is strongly degenerate.
 
thanks a lot, now it makes sense
 

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