It is possible to predict from the table which lines are likely to appear in the spectra of the coolest stars. The ultimate lines of Al, K, Ca, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Ga, Rb, Sr, Zr, Mo, Ag, In, Ba, La, and Pb fall in the region ordinarily photographed, and Na can be reached in the yellow. All these elements in the neutral state would therefore be anticipated in the spectra of cooler stars, and they are indeed found without exception. The ultimate lines of several elements contained in the list lie in the far ultra-violet, and cannot be detected in stellar spectra. The corresponding neutral elements will therefore not be recorded unless they also give a strong subordinate series in the photographic region. The elements C, O, S, and probably N, all have ultimate lines in the ultra-violet, and possess no subordinate series in the appropriate range of wave-length. Their apparent absence in the neutral state from stellar spectra is therefore fully explained. All of these elements appear in the hotter stars in the once or twice ionized condition. The elements H, Mg, and Si have strong subordinate series in the photographic region—the Balmer series, the “b” group, and the line[364] at 3905, respectively. They are accordingly represented in the cooler stars.
The elements contained in the table and not yet discussed are Be, B, Ne, A, F, and Cl. These elements have not been detected in stellar spectra. In seeking an explanation of their apparent absence, it has been suggested that a low relative abundance of the corresponding atoms may be responsible. Arguments from terrestrial analogy must be applied with caution, but there is reason to suspect that they may here have a legitimate application.[365] It may be suggested that boron, beryllium, neon, and argon are present in the stars in quantities too small to be detected. The halogens are unrepresented, but it is not possible to draw useful inferences until their laboratory spectra are more fully analyzed.
IONIZATION
At the lowest temperatures, then, the ultimate lines will predominate. As the temperature of the absorbing layer is raised, ionization—the complete ejection of the electron from the atom, instead of a displacement from one stationary state to another—will set in, and the tracing of the resulting spectral changes is the salient feature of the Saha theory. “Ionization can be effected in many ways. To expel an electron against the attractive force of the remainder of the molecule, work is required, and the necessary energy may be furnished by X rays or
rays, or by collision with other electrons.... At high temperatures, when the conditions of maximum entropy demands an appreciable amount of ionic dissociation, the requisite energy is drawn from the environment.... The work required to ionize a single molecule, when expressed as the number of volts through which an electron must fall to acquire this energy, is the ionization potential; it may be regarded as the latent heat of evaporation of the electron from the molecule” (Milne).[366]
The analogy between ionization and evaporation illustrates very well the scope of the Saha theory, in which the process is treated as a type of chemical dissociation. Corresponding to each temperature there is a definite state of equilibrium, where the forward and backward velocities of the ionization process are equal—in other words where ionization and recombination are proceeding at the same rate. The method of statistical mechanics has been applied to this problem by Fowler and Milne.[367] Here the analysis will not be reproduced, but the formulae are required in order to illustrate the process of ionization.
The number of atoms which are unionized at any given temperature is given by the expression
where