74
Gaseous Stars
[ch. Ill
diameter 10 -8 cms. are replaced by crowds of free electrons of diameters about
4 x 10 -13 , of nuclei whose diameters are less even than this and of atoms
whose rings of electrons have nearly all been stripped away.
Even at a density of 50,000 times that of water, the electrons and nuclei
are at mean distances apart which are of the order of 10~ 10 cms., and this is
some hundreds of times the probable diameter of both free electrons and
nuclei. If then all atoms were stripped absolutely bare of electrons, so that
stellar matter consisted solely of electrons and bare nuclei, it would seem
reasonable to assume the ordinary gas-laws to hold, even at these monstrously
high densities, at any rate as a first approximation. Anderson* has pointed
out that the electron pressure in stellar interiors is that of a “degenerate”
gasf, so that the pressure can in no case be given exactly by Boyle’s law,
the divergence increasing from one of a few per cent, in ordinary stars to
a factor of about 2 for Kruger B and Sirius B.
We shall, however, find that, although the mean density of Sirius B may
be 50,000, the density in its central regions is probably to be measured in
millions, so that here Boyle’s law can hardly hold, even as an approximation.
Furthermore, the temperatures at the centres of most stars are not adequate
to break the atoms down to their ultimate constituents. Stellar matter
consists in part of free electrons and perhaps some bare nuclei, but these are
mixed with miniature atoms in which some rings of electrons remain to clear
a space about the nucleus, and when such atoms are present it is not obvious
without further investigation whether Boyle’s law will give a valid approxi
mation to the pressure-density relation or not.
For the moment we shall proceed on the supposition that the pressures in
stellar interiors are those given by Boyle’s law, but we shall soon find it
necessary to discard this supposition. For the two reservations just men
tioned prove to be of the utmost importance in stellar physics, and probably
dominate the whole dynamics of stellar interiors.
The Pressure of Radiation.
70. We have been led to picture the far interior of a star as consisting of
a crowd of dissociated electrons, of bare nuclei and of atoms stripped of
electrons almost down to their nuclei. The electrons move about from one
broken atom to another, seldom staying with any one atom for long, since the
majority of the atoms are either completely or almost completely bare of
electrons. As we approach the surface, we come to regions of lower temperatures
where the disintegration is far less complete, and here we find semi-formed
atoms. Finally, close to the surface we come upon ionised atoms from which
only a few of the outer electrons are missing, and possibly fully formed atoms.
In the iH-type stars, the surface layers are so cool that even fully formed
molecules are found, such as those of titanium oxide and magnesium hydride.
* Zeitsch. f. Physik, l. (1928), p. 874. + E. Fermi, Zeitsch. f. Physik, xxxvi. (1926), p. 911.