Stars as Laboratories for Fundamental Physics - MPP Theory Group

Characteristics of Stellar Plasmas 593
D.1.2
Relativistic Conditions for Electrons
The nuclei in normal stellar matter are always nonrelativistic; relativistic
corrections begin to be important only in neutron stars. The electrons,
on the other hand, tend to be at least partially relativistic. Even
at the center of the Sun at a temperature of 1.3 keV, a typical thermal
electron velocity is about 9% of the speed of light. In Fig. D.2 contours
for the thermal average ⟨v 2 ⟩ 1/2 are shown in the ρ-T -plane. The loci of
the stellar models of Fig. D.1 are also indicated. For low-mass stars, the
electrons are mildly relativistic, although a nonrelativistic treatment is
often enough as a first approximation.
Fig. D.2. Contours for ⟨v 2 ⟩ 1/2 , the average thermal velocity of electrons.
The loci of the stellar models of Fig. D.1 are also indicated.
D.1.3
Electron Degeneracy
The phase-space occupation numbers of fermions in thermal equilibrium
are characterized by a Fermi-Dirac distribution
f p =
1
e (Ep−µ)/T + 1 ,
(D.4)
where E p is the energy of the momentum mode p. If dispersion effects
can be ignored, E 2 p = m 2 + p 2 with the fermion vacuum mass m. The
(relativistic) chemical potential is denoted by µ; for electrons it should
not be confused with the mean molecular weight µ e . The distribution