White Dwarf Degeneracy

The graph shows the electron occupation index F(E), as a function of the energy in terms of multiples of the (Fermi Energy - rest mass energy), ie. the kinetic energy corresponding to the Fermi Energy. The sliders control the parameters which influence the degree of degeneracy and whether the degeneracy is relativistic - namely: density (ρ, kg/m^3) and temperature (T, in Kelvin) in logarithmic units (i.e. 7 is equivalent to 10^7) and finally the "mean mass per electron" μ_e in atomic mass units. This parameter is 1 for a pure ionised Hydrogen gas and 2 for ionised gases of Carbon or Oxygen. (e.g. for carbon there are 12 mass units and 6 electrons). The degeneracy parameter ((Ef-mc^2)/kT) is shown along with the Fermi energy and the relativity parameter (pf/mc).

A gas of Fermions can be made degenerate either by increasing the Fermi Energy (increasing the number density of Fermions by increasing the density or decreasing μ_e), or by decreasing the temperature. The electrons can only be made more relativistic by increasing the number density of electrons. An arrow indicates which electrons are very relativistic (p>mc).

A "typical white dwarf has interior densities of 10^9 kg/m^3 and T=3X10^6K. You can see that the degeneracy level is high for these parameters and that the electrons are just becoming relativistic.

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The plots are only valid for a degeneracy parameter quite a bit bigger than 1 and use the "Sommerfeld Expansion" to evaluate the chemical potential α .

F(E) = 1/(exp(E-α)/kT + 1)

Rob Jeffries, Created with GeoGebra