THE theory of thermal ionization enables us to make an analysis of the spectrum of the stellar reversing layer by predicting the number of atoms of any given kind that will be effective in absorbing light from the interior of the star, under given conditions, and by comparing the predicted values with the observed intensities of the corresponding absorption lines. The results depend partly on definite physical constants associated with the atoms—the ionization and excitation potentials, and the arrangement of the electrons around the nucleus. The temperature and pressure of the region in which the atom is situated are also required before the theory can be applied. The scale of stellar temperatures was discussed in the preceding chapter, and the present chapter is devoted to a synopsis of the modern views as to pressures in the reversing layer.

Strictly speaking, we cannot refer to “the pressure in the reversing layer,” for, like the temperature, the pressure has a gradient throughout the star. This gradient, as derived from the theory of radiative equilibrium,[58] is steep in the far interior of the star, but towards the outside the rapid fall of pressure begins to decrease, and changes somewhat abruptly to a very small gradient in the photospheric region, where radiation pressure and gravitation are of the same order of magnitude. Outside this layer of transition between the region dominated by radiation pressure and the region dominated by gravitation, the pressure gradient is very shallow, and decreases until, in the tenuous outer regions of the star, there is no appreciable pressure gradient, and atoms are practically floating freely.

The outermost regions of the atmosphere, at these exceedingly low pressures, make little or no contribution to the ordinary stellar spectrum; they can only be studied in the high-level chromosphere by means of the flash spectrum obtained at a total eclipse of the sun. The spectra that are ordinarily examined are from a region that is at an appreciable depth within the star—the depth from which the light of each individual wave-length can penetrate. The “layer” of which we can obtain a spectrum is therefore not at the same depth for all frequencies; it is most deep-seated in regions of continuous background, and nearest to the surface of the star at the centers of strong absorption lines. The pressures from which the different parts of the spectrum originate differ in the same way, and the idea of “pressure in the reversing layer” is not an easy one to define significantly.

For theoretical purposes it is usual to deal with the pressure at a given “optical depth” (a measure of the amount of absorbing matter traversed by the radiation in coming from the level considered). The optical depth is connected with the density , the mass coefficient of absorption for unit density, , and the vertical depth, , in the star, by the relation[59]

The density gradient is thus eliminated. The optical depth is furthermore related to the pressure by the relations where is the value of gravity at the point in question, and whence

In considering the stellar atmosphere we are dealing with a layer so near the surface that the value of g involved is effectively the “surface gravity” for the star. If is constant, a condition probably approximately fulfilled,[60] the pressure at constant optical depth is then directly proportional to the surface gravity, which varies as the product of the mean density and the radius of the star. Some idea of the range in pressure with which we shall be concerned in the stellar atmosphere can therefore be obtained from stars of known mean density and radius.

The data for eight such stars, all of the second type, are contained in Table X, which is adapted from tabulations given by Shapley.[61] Successive columns contain the name of the star, the spectral class, the mean densities of the two components in terms of the solar density, the hypothetical radii of the two components (on the assumption of solar mass) in terms of the sun’s radius, and the product of mean density and radius for each component.

Notes in this chapter

Note 1 · Eddington, Zeit. f. Phys., 7, 731, 1921.Note 2 · Pannekoek, B. A. N., 19, 1922.Note 3 · Milne, Phil. Mag., 47, 217, 1924.Note 4 · Ap. J., 42, 271, 1915; Princeton Contr. No. 3, 82, 1915.