Inhibition of Degeneracy by Intense Magnetic Fields - Derivation and Astrophysical Application

Strong magnetic fields inhibit degeneracy in Fermi gases, that is, they postpone degeneracy to higher densities or lower temperatures. We derive this principle, virtually unknown in the physical and astrophysical literature, for the case of an ideal Dirac electron gas. Its possible importance in astrophysics is due to the fact that the equations of state of Fermi gases at given density and temperature can be qualitatively changed by this degeneracy-inhibition by strong fields. All astrophysical work with strong fields up to the present has used the field-free equations of state and the usual MHD approximation: permeability ≈1. Their interest was focussed on the effects of a strong Lorentz force term. We consider an application to hypothetical degenerate stellar objects with arbitrarily strong fields to see what effects the changed equations of state would lead to. One result is that the luminosity-temperature relation of the star is changed: the luminosity is reduced for given mass and interior temperature.