The application of of Fermi Dirac statistics in the white dwarf

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Fermi Dirac statistics are applicable in white dwarf research despite high core temperatures because these temperatures remain significantly lower than the Fermi temperature. While the Fermi energy is often referenced at absolute zero, the relevant condition for applying Fermi Dirac statistics is that the temperature must be much less than the Fermi temperature. This indicates that white dwarfs are highly degenerate, necessitating the use of Fermi Dirac rather than Maxwell-Boltzmann statistics. The approximation of T=0 is useful, but the practical application requires understanding that T must be much lower than T_F. Thus, white dwarfs are considered strongly degenerate systems.
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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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