IT is certain that the conditions of which we see the integrated result in the stellar spectrum are exceedingly complicated. Unfortunately, the superficial portion of the star about which direct observational evidence can be obtained is far less tractable to theory than is the interior. Progress is only made possible by treating at the outset a simplified case, by aiming merely at approximate results, and in particular by limiting the preliminary discussion to the factors which are numerically the most effective. As an introduction to the theory of thermal ionization, the present chapter aims at the reconstruction and interpretation of a stellar spectrum by applying known physical laws under very simple conditions.

The stellar reversing layer may be represented by an optically thin layer of gas, at a pressure of the order of one ten thousandth of an atmosphere; it lies between the observer and a photosphere which radiates as a black body. The observer receives the radiation from both reversing layer and photosphere, which are regarded, in the present descriptive section, as independent. A more complete treatment would take account of the temperature and pressure gradients in the atmosphere of the star, the flux of energy, and the consequent intimate connection between reversing layer and photosphere. Actually they grade imperceptibly one into the other. The photosphere is that level in the atmosphere at which the general opacity cuts off the direct light from the interior;[355] in the case discussed the reversing layer is considered to be optically so thin that the general opacity is negligible. The selective opacity, depending on the natural absorption frequencies of the atoms present in the gas, gives rise to the line absorption spectrum which we are about to consider; the region of sensible general opacity, represented by the photosphere, gives rise to a continuous spectrum corresponding to the continuous background in the star.

THE ABSORPTION OF RADIATION

The light passing through the layer of gas is absorbed, in terms of atomic theory, in the shifting of an electron from one energy level in an atom to some higher level, losing in the process energy of the definite frequency which is associated with that particular atom and energy transfer. The energy levels and possible electron transfers for the hydrogen atom are reproduced in Figures 2 and 3. In Figure 3 the horizontal lines represent the stationary states which can be assumed by the electron, and the arrows denote possible jumps from one stationary state to another. In Figure 2 the electron orbits corresponding to some of the simpler corresponding transitions for the hydrogen atom are represented. Arrows denote transfers from one orbit to another. The designation of the line corresponding to each transfer is appended to the appropriate arrow. It is evident that the occurrence of a given jump requires that there shall be an electron in the stationary state from which the jump originates.

The ultimate lines[356][357] are those which arise from the lowest energy level, and are therefore those most readily absorbed by the normal (undisturbed) atom. In the hydrogen spectrum these comprise the Lyman series,[358] with the first member at 1215.68. The Balmer and Paschen series are both subordinate series, requiring an initial lifting of the electron from the lowest energy level into a two and three (total) quantum orbit, respectively. The absorption of the Lyman line Ly is necessary to a hydrogen atom before it is in a fit condition to absorb any Balmer line, and for the absorption of a Paschen line, an initial absorption of Ly or H is required.

It appears plausible to assume, at least for low partial pressures, that the amount of energy of any frequency that is lost by black-body radiation in passing through the absorbing layer will vary jointly with the supply of energy and the number of atoms which are in a suitable state to absorb that particular frequency. One of the problems that arise is therefore that of determining what fraction of the whole number of atoms of a given kind will be able to absorb. It is to this problem that ionization theory is able to offer a solution.

By choosing the much simplified case of very low pressure and small concentration, the effects of ionization by collision[359] and of nuclear fields are probably eliminated. The remaining factor which may influence the number of absorbing atoms is thermal ionization, and this is actually the numerically important factor, as was first pointed out by Saha.[360] It is of interest to note that Saha’s original treatment contemplated pressures of the order of one atmosphere. Under such conditions the effects of collisions and of nuclear fields are not negligible, and might well have invalidated the theory. Later work has shown conclusively, however, that the pressures in the reversing layer are probably not greater than ,[361][362] and that thermal ionization is the predominant factor under these conditions.

The absorbing layer is to be regarded as consisting of a mixture of all chemical elements, without any assumption as to quantity, so long as the partial pressure of each individual element is low. In other words, no account is taken, at the present stage, of the relative abundances of different kinds of atoms—the total effectiveness of the corresponding elements as absorbers. The changes in the absorption of the black body radiation by a given element with changing temperature will be the same whatever the partial pressure, provided it is low, and it is with these changes that the preliminary schematic discussion is concerned.

LOW TEMPERATURE CONDITIONS

At low temperatures all the elements will tend to be in their normal atomic state, unless they are aggregated into molecules or compounds. At temperatures of 2500°, which is about the lower limit encountered in dealing with stellar spectra, there is evidence of the existence of various oxides (CO, TiO₂, ZrO₂), of “cyanogen,” and of hydrocarbons, but most of the other possible compounds appear either to be dissociated or to be in very low concentration. Probably the normally polyatomic gases such as oxygen, nitrogen, and sulphur, are to some extent present in the molecular state. Even at atmospheric pressure all the metals are vaporized at 2500° excepting tantalum and the platinum metals, which boil at about 2800° under a pressure of 760 mm; at lower pressures the temperature of vaporization is, of course, lower. The metallic molecule appears normally to be monatomic, so that it will give its line spectrum unless it is in combination. The fact that silicon, the most refractory substance, excepting carbon, with which we have to deal, gives its line spectrum in the coolest stars known, indicates that all the elements may be considered to be gaseous in stellar atmospheres.

ULTIMATE LINES

The absorption spectrum given by the reversing layer when it is at a low temperature will consist of the lines given most readily by the atom in its normal state. The energy transfers which move an electron from its normal orbit to another correspond to the “ultimate lines,” and these lines will therefore be especially outstanding in the spectra of the coolest atmospheres. They are of such importance, from theoretical and from practical standpoints, that a list of them is reproduced here. Successive columns of the table give the atomic number and atom, the ionization potential, the wave-lengths of the ultimate lines, and an indication of their observed occurrence in stellar spectra. An asterisk denotes that the line has been observed, and a dash indicates that it has not been recorded.

It may be remarked that the ultimate lines of sodium, potassium, lithium, rubidium, and caesium are in the visible region—a fact which is utilized in the laboratory flame tests used in qualitative analysis.[363] The brilliancy of the flame colors obtained in the Bunsen burner, at the temperature of about 1500°C., is a striking elementary illustration of the readiness with which the atom in its normal state will take up and re-emit the frequency corresponding to the ultimate lines (second pair for K, Rb, Cs).

Notes in this chapter

Note 1 · Stewart, Phys. Rev., 22, 324, 1923.Note 2 · De Gramont, C. R., 171, 1106, 1920.Note 3 · Russell, Pop. Ast., 32, 620, 1924.Note 4 · A. Fowler, Report on Series in Line Spectra, 1922.Note 5 · R. H. Fowler, Phil. Mag., 47, 257, 1924.Note 6 · Proc. Roy. Soc., 99A, 135, 1921.Note 7 · M. N. R. A. S., 83, 403, 1923; ibid., 84, 499, 1924.Note 8 · Russell and Stewart, Ap. J., 59, 197, 1924.Note 9 · Eder and Valenta, Atlas Typischer Spektren, 10, 1911.