Stars as Laboratories for Fundamental Physics - MPP Theory Group

Appendix D
Characteristics of Stellar
Plasmas
D.1 Normal Matter
D.1.1
Temperatures and Densities
The material encountered in stars is usually in a state of thermal equilibrium.
In the absence of strong magnetic fields, the plasma is entirely
characterized by its temperature T , mass density ρ, and a set of chemical
composition parameters X, Y , X 12 , etc. which determine the mass
fractions of the elements 1 H, 4 He, 12 C, and so forth. The mass fraction
of all elements heavier than helium (“metals”) is denoted by Z.
The number density of a species with mass fraction X j , atomic
weight A j , and charge Z j e is given by
n j = (ρ/m u ) X j /A j ,
(D.1)
where m u = 1.66×10 −24 g = 0.932 GeV is the atomic mass unit. 99 The
number density of electrons is
n e = ∑ j
Z j n j =
ρ m u
∑
j
X j Z j
A j
= ρ
µ e m u
, (D.2)
where µ e is the “mean molecular weight” per electron, not to be confused
with the electron chemical potential. (Strictly speaking n e =
n e − − n e +, the number density of electrons minus that of positrons.)
99 The proton and neutron mass are 0.9383 and 0.9396 GeV, respectively. An exact
translation between mass and number density thus requires taking nuclear binding
energies into account whence the A j are not exact integers. For the purposes of this
book these differences are negligible.
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