CHAPTER VII
CRITICAL DISCUSSION OF IONIZATION THEORY
THE theory of thermal ionization, of which the preceding chapter contains an illustrative discussion, may be treated from two points of view—the sufficiency of the analytical treatment, and the nature of the underlying physical assumptions. Actually the two questions are merely two different ways of regarding the validity of the theory, but they divide the discussion conveniently into a section dealing with the analytical treatment and a section dealing with the physical assumptions.
The original treatment by Saha[370] was based on the Law of Mass Action, and the application to stellar atmospheres raised questions of a physical rather than of an analytical nature. These questions are fundamental not only to the Saha treatment, but also to the more recent development of the theory, and they will be discussed in the second half of the present chapter. The first half will be devoted to the analytical formulae.
MARGINAL APPEARANCE AND MAXIMUM
Saha’s discussion was based on the observation of “marginal appearance”—the spectral class at which a particular absorption line is at the limit of visibility. The use of this quantity as a criterion for the temperature scale has certain practical drawbacks. Marginal appearance depends directly on relative abundance, since a more abundant element will give visible lines at a lower “fractional concentration,” that is to say, when a smaller fraction of the element is contributing to the lines in question. Further, in estimating the intensities of lines in stellar spectra, difficulty is experienced when the lines are faint, and the spectral class at which they are first or last seen depends on their width and definition, the intensity of the continuous background, the presence of other lines, and the dispersion used. All of these factors are subject to variation, and in particular the intensity distribution in the continuous background changes with the temperature. The statistical theory of Fowler and Milne has, therefore, a great advantage in that it leads to an estimate of the temperature at which a given line attains maximum. A maximum, unlike a marginal appearance, can be determined without ambiguity from homogeneous material, whatever the dispersion. In the cooler stars the estimates may be made difficult by blending, but the uncertainty can generally be removed by examining the maxima of several related lines. Of the observational factors enumerated above as affecting the estimation of marginal appearance, the changing intensity distribution of the continuous background with the temperature is the only one that may prove serious for the method of maxima.
THEORETICAL FORMULAE
The theory developed by Fowler and Milne has been exhaustively discussed by these authors in several papers, and it appears unnecessary to reproduce the analysis in detail. The ionization and excitation curves have been treated diagrammatically in the previous chapter. The detailed formulae follow.
“If
is the ionization potential of the atom,