Why is the degeneracy criterion the same for all stars?

[Kayla Martin]

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.

 

[member 553083]

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.