Why is the degeneracy criterion the same for all stars?

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SUMMARY

The degeneracy criterion for stars is fundamentally linked to the Pauli exclusion principle, which asserts that no two fermions can occupy the same quantum state. This principle ensures that the degeneracy pressure in stellar objects is independent of the mass of the electrons involved. Consequently, the equation governing this criterion remains consistent across different types of stars, as it is solely determined by the quantum mechanical properties of fermions rather than their mass.

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Homework Statement
The degeneracy criterion equation is $$\dfrac{T}{\rho^{\frac{2}{3}}}\lt D$$, where $$D=1261 Km^2kg^{-\frac{2}{3}}$$ is a constant. From this equation, why can we say that D is constant for every star?
Relevant Equations
$$\dfrac{T}{\rho^{\frac{2}{3}}}\lt D$$
Is it anything to do with the equation being independent of mass etc.. of the star? or to do with the Pauli exclusion principle? Any help will be much appreciated.
 
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The equation being independent of mass is related to the Pauli exclusion principle, which states that no two fermions (particles with half-integer spin) can occupy the same quantum state. This applies to the electrons in a star, so the equation is independent of the electron mass because they cannot be in the same quantum state.
 

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