93
86 , 87] Configurations of Equilibrium
kept thoroughly mixed by winds and convection currents, but rather to the
serene upper atmosphere in which the lightest elements float to the top while
the heaviest sink downwards under gravity.
Our discussion has applied only to the interior of a star. On approaching
the star’s surface, our equations of radiative equilibrium begin to fail, so that
the discussion gives no information as to the occurrence of convection-currents
near a star’s surface. Solar physics suggests that there may be quite appreci
able convection currents near a star’s surface, but this neither confirms nor
disproves our theoretical result, which has reference only to stellar interiors.
We cannot overlook the possibility that other factors, which our idealised
discussion has ignored, may produce a tendency to establish convection
currents in stellar interiors.
Electric Field.
We have treated atoms and electrons merely as gravitating particles, thus
ignoring the electric field in a star’s interior. The electric forces between
electrons and positively-charged atoms completely outweigh the gravitational
forces, and this causes the charges to arrange themselves so that the positive
and negative charges nearly neutralise one another, leaving only a small
residual field. This, however, provides no justification for neglecting this
residual field altogether.
Just as the molecules of hydrogen and helium have diffused upwards in
the earth’s atmosphere on account of the smallness of their masses, so the
free electrons, having far smaller masses than nuclei and atoms, must diffuse
outwards in a star. As a result, the inner regions of a star must become
positively charged, and the outer regions negatively charged. The process is
held in check by the electric fields which electronic diffusion creates in the
star’s interior, and as soon as the central regions of a star acquire an appreci
able positive charge, the tendency for the free electrons to wander away to
the surface is counteracted, and a state of equilibrium is attained. The
problem is further complicated by the tendency of the free electrons near a
star’s surface to escape from the star altogether, precisely as the hydrogen
molecules have escaped altogether from the earth’s atmosphere. This results
in the star acquiring a positive charge*.
Pannekoek j* and Rosselandf have studied the equilibrium of a star, taking
the electric forces into account. They find that a quite simple solution exists,
such that the inward force on an electron at any point is precisely equal to
the outward force on a positively-charged atom at the same point. Rosseland
has investigated stellar equilibrium on the supposition that this condition
* Jeans, Dynamical Theory of Gases (4th Edn.), p. 348.
t Bull. Ast. Netherlands, xix. (1922), p. 107.
X M.N., R.A.S. lxxxiv. (1924), p. 720.