where
is the “homogeneous depth.” The pressure is then directly proportional to the surface gravity.
INFLUENCE OF PRESSURE ON THE SPECTRUM
Lowered pressure increases the degree of ionization. The tendency of the atoms to lose electrons by thermal ionization should depend solely on their energy supply, and should thus be independent of the pressure. The total absorbing power of the gas will, however, depend on the number of suitable atoms that it contains, not upon their rate of formation. The number of suitable ionized atoms present at any moment in the atmosphere is a function not only of the rate at which ionization proceeds, but also of the rate of recombination. The more readily recombination takes place, the larger is the number of effective neutral atoms, and the smaller the number of effective ionized atoms, when a steady state is attained. The rate of recombination, which depends upon the probability of a suitable encounter between an ionized atom and a free electron, will increase with the pressure—more accurately, with the partial pressure of free electrons.
The higher the pressure, therefore, the greater the number of neutral atoms, and the smaller the number of ionized atoms. This argument explains at once the strength of the neutral (arc) lines in the spectra of stars of low luminosity (high surface gravity), and the predominance of ionized (spark) lines for absolutely bright stars (low surface gravity, resulting chiefly from large radius). Low surface gravity, then, increases the number of ionized atoms present by discouraging recombination.
It should be noted that any tendency to extensive ionization will increase the concentration of free electrons and tend to encourage recombination, thus counteracting the effect of low surface gravity. The effect of an increased concentration of free electrons will not, however, attain the magnitude of the surface gravity effect, since even for the hottest stars examined, three electrons appear to be the largest number that can be thermally removed under reversing layer conditions.
The theoretical effect of lowering the pressure has been discussed by Stewart,[416] who, after alluding to the importance of the surface gravity, suggested that the ultimate lines of neutral atoms easier to ionize than the average should be weakened by low pressure, and that the corresponding enhanced lines should be strengthened. For atoms harder to ionize than the average the reverse should be the case for the two classes of lines. From this standpoint he showed that the absolute magnitude effects might be qualitatively accounted for. The “average ionization potential” was the average for the lines used in the estimates; Stewart adopted the value of six volts for Classes
to