FOOTNOTES:
[58] Eddington, Zeit. f. Phys., 7, 731, 1921.
[59] Pannekoek, B. A. N., 19, 1922.
[60] Milne, Phil. Mag., 47, 217, 1924.
[61] Ap. J., 42, 271, 1915; Princeton Contr. No. 3, 82, 1915.
[62] M. N. R. A. S., 83, 403, 1923.
[63] Ap. J., 59, 197, 1924.
[64] St. John and Babcock, Ap. J., 60, 32, 1924.
[65] M. N. R. A. S., 82, 394, 1922.
[66] King, Ap. J., 41, 110, 1915.
[67] King, Ap. J., 48, 32, 1918.
[68] Saunders, quoted by Russell and Stewart, Ap. J., 59, 197, 1924.
[69] Payne, H. C. 256, 1924.
[70] A. Fowler, M. N. R. A. S., 80, 692, 1920.
[71] Stewart, Ap. J., in press.
[72] Ap. J., 59, 197, 1924.
[75] Shapley, H. B. 805, 1924.
[76] Chapter XIII, p. [p. 188].
[78] Ap. J., 59, 197, 1924.
[79] Eddington, Zeit. f. Phys., 7, 371, 1921.
[80] Russell and Stewart (loc. cit.) show that there are about 0.4 grams of matter above the photosphere per square centimeter of surface.
[81] Phil. Mag., 26, 9, 1913.
[82] Phil. Mag., 37, 456, 1919.
[83] Zeit. f. Phys., 1, 1, 1920.
[84] Wright, Nature, 109, 810, 1920.
[85] Saha, Nature, 114, 155, 1924.
[86] Nicholson, M. N. R. A. S., 85, 253, 1925.
[87] Unpublished.
[88] Ap. J., 59, 197, 1924.
[89] M. N. R. A. S., 83, 403, 1923; 84, 499, 1924.
[90] H. C. 256, 1924.
[91] H. C. 258, 1924.
CHAPTER IV
THE SOURCE AND COMPOSITION OF THE STELLAR SPECTRUM
THE spectrum of a laboratory source offers a somewhat inadequate comparison with the spectrum of a star. Matter can be studied terrestrially in small quantities only, and when a laboratory source is used in obtaining a spectrum, all the contributing material is collected into a very small region. With the stellar source it is quite otherwise. An enormous mass of matter, spread over a very large region, gives rise to the spectrum, and probably widely different physical conditions prevail at the origin of light of different wave-lengths. The present chapter contains a brief survey of the chief components which go to make up the stellar spectrum.
The spectrum of a star nearly always consists of a continuous background, in which the energy distribution corresponds more or less to that of a black body, and of absorption and emission lines and bands. The observed stellar spectrum is the integrated contribution from all parts of the disc, the unlined portion representing radiation that passes undisturbed from the photosphere through the reversing layer, and the light within any individual absorption line coming from the greatest depth in the reversing layer that can be penetrated by light of the corresponding frequency. This depth, which is a function of the monochromatic coefficient of absorption for the wave-length considered, is negligible when compared with the radius of the star.
DESCRIPTIVE DEFINITIONS
The solar atmosphere is probably qualitatively representative of all normal stellar atmospheres. It has been satisfactorily described by Russell and Stewart:[92] “At the top is a deep layer, the chromosphere, in which the gases are held up by radiation pressure, acting on individual atoms. The pressure and density in this layer increase slowly downwards (as gravity somewhat overbalances radiation pressure) and the pressure at its base may be of the order of
, or 0.0001 mm. of mercury. Below this level, gravity is predominant in the equilibrium, and the pressure increases rapidly with depth—the temperature remaining nearly constant, and not far from 5000°, so long as the gases are transparent. This region is the reversing layer. When the pressure reaches 0.01 atmosphere, the general absorption by electron collisions begins to render the gas hazy. This opacity increases greatly with the pressure, and the reversing layer passes, by a fairly rapid transition, into the photosphere, which on the scale on which we have to study it resembles an opaque mass. As soon as the opacity becomes important the temperature rises in accordance with the theory of radiative equilibrium developed by Schwarzschild and Eddington. The observed effective photospheric temperature is a mean value for the layers from which radiation escapes to us.”
The photosphere, as has been stated, is at an extremely small depth compared with the radius of the star. Taking the sun as an example, it is estimated by Russell and Stewart[93] that the reversing layer, which, with the chromosphere, is responsible for all the solar phenomena that can be spectroscopically studied, consists of about four tenths of a gram of matter per square centimeter of surface, and is only a few hundred kilometers in thickness. As this embraces only about
of the mass and
of the volume of the sun, it is clear that the features that can be studied spectroscopically are purely superficial, and that the larger aspects of stellar composition and constitution are left essentially untouched.
THE CONTINUOUS BACKGROUND
The continuous background of the spectrum represents the photosphere—the deepest layers from which we receive light. The energy that produces it is practically the total energy output of the star. While the actual distribution of energy in the spectrum probably conforms, in general, to that of a black body, the observed distribution naturally deviates considerably. But when corrections have been applied for atmospheric absorption, the resulting energy curves so far obtained do not appear to furnish certain evidence of serious deviation from blackness, although several investigators have suggested that their measures lead to this conclusion.[94][95][96]
If it is admitted that the energy distribution in the continuous background is sensibly black, the application of the Planck and Wien formulae furnishes methods of deriving the effective temperatures of stars from the energy distribution and the position of maximum intensity, respectively. The energy curve has therefore been extensively studied, both photographically and photometrically, and our present knowledge of stellar temperatures rests primarily upon work of this nature. The solar spectrum has been the subject of exhaustive photometric researches by Abbot[97] and Wilsing,[98] and the theory of the energy distribution, and its relation to the law of darkening, have been discussed by Lindblad,[99] and by Milne.[100] In a discussion of the solar energy curve, Milne[101] shows that the continuous spectrum can be regarded as that of a black body displaced to the violet, and that the displacement can be ascribed to the distortion of a normal black body curve by the presence of strong absorption.
H. H. Plaskett,[102] in applying the wedge method of spectrophotometry to the same problem, took care to measure continuous background intensities in spectral regions free from absorption lines stronger than 0 per Angstrom, as measured on Rowland’s scale of intensities. In this way he obtained a series of measures which should give a distribution sensibly free from distortion. His result for the solar temperature agrees more nearly with that derived from the solar constant than do the results of previous observers, and therefore the idea that the continuous background approximates to blackness is borne out by observations made with the proper precautions. R. H. Fowler[103] has remarked that “there is no longer any large discrepancy between the solar constant and the color temperatures, and one may hope that further more accurate work will leave them in full agreement.”
The position of maximum intensity governs the color of the star, which is quite unrelated to the colors absorbed and radiated by the atoms in the reversing layer. In some of the Wolf-Rayet stars, apparently at very high temperatures and with atmospheres under special conditions of excitation, the continuous spectrum appears extremely faint, although there seems to be no reason for supposing that this is not merely an effect of contrast with the powerful emission “bands.” The writer believes that long exposures would demonstrate the presence of continuous background for all such stars.[104] In the spectra of some gaseous nebulae, however, no continuous background has as yet been observed,[105] nor would any be expected, if our conception of the tenuity of these bodies is correct, unless they shine partly by pure reflection. (For example, the presence of some reflected starlight is inferred from the existence of a continuous background for the Orion nebula.) The transparency of gaseous nebulae to the light of stars indicates that their general opacity is extremely low, and it is this general opacity that is operative in producing the continuous background of a photosphere.
THE REVERSING LAYER
The reversing layer, comprising the layers above the photosphere, where the general opacity has greatly decreased and selective opacity begins to be appreciable, is responsible for the lines in the spectrum, which form the major part of the material of stellar spectroscopy. When the energy flowing out through the reversing layer in any specified wave-length is less than the energy in the neighboring continuous background, an absorption line is produced in the spectrum.
Roughly speaking, if an atom absorbs the whole of the light of any given frequency that reaches it from below, it will re-emit all the energy so absorbed, and will in general do so in a random direction.[106] The intensity of the absorption line so formed will then be about 50 per cent of the intensity in the neighboring continuous background. This argument is merely illustrative; it must suffice to point out that if pure selective absorption is operative the spectrum will be crossed by lines that are considerably less intense than the background. If, on the other hand, the energy leaving the atmosphere with any wave-length is greater than the energy in the neighboring continuous background, a bright line or “emission” line appears in the spectrum. Actually, of course, it is no more an emission line than is an ordinary Fraunhofer line, for the difference between stellar absorption and emission is merely a matter of contrast with the continuous background. Both kinds of line are “full of light.”
ABSORPTION LINES
The absorption lines vary greatly among themselves and from star to star, both in intensity and in general appearance. The metallic lines, more particularly those of ionized atoms, are often extremely narrow and sharp—a feature difficult to reproduce in the laboratory, and referable to the very low pressures in the stellar atmosphere.[107] Other lines, such as those of the Balmer series of hydrogen, may be of considerable width, and spread out into wings that extend as much as thirty Angstrom units on each side of the center of the line. Many other lines are probably winged, but are not of sufficient strength for the feature to be seen. The form of the wings and the general shape of the line are of high significance, and should ultimately give much information bearing on the structure of the stellar atmosphere.
Although the absorption lines are commonly regarded as “dark,” the foregoing section indicates that they should always have an appreciable intensity even at their centers. Measures of the central intensities of strong absorption lines have been published by various investigators, and the results are not all in agreement. Schwarzschild[108] gives from a single measurement of the
and
lines in the solar spectrum (center of disc) with the Hartmann microphotometer, wings ten Angstrom units in width on either side of the line center, and a weakening of the intensity of the light, from the continuous background to the center of the line, of about two and a half magnitudes. Bottlinger’s curves[109] appear to lead to considerable intensities at the centers of the hydrogen lines in the
stars. Others have suggested that the central intensities are considerably lower. Abbot[110] quotes estimates ranging from one fifth to one tenth of the continuous background for solar lines, and H. H. Plaskett[111] states that the faintest stellar lines have about one tenth the intensity of the continuous background, as measured by his wedge method.[112]
Determinations of central intensity by means of precise photometry have been made by Kohlschütter[113] and by Shapley,[114] objective prism spectra being used in both cases. Kohlschütter gives the results of the analysis of the spectra of twenty-one stars of Classes
and
by means of the Hartmann microphotometer. The darkening from the continuous background to the center of the line is tabulated in his paper for
,
,
,
, and
; it ranges for
from 1.14 magnitudes for a Lyrae to 0.42 magnitudes for
Cygni. The corresponding central intensities are 35 and 68 per cent of the intensity of the continuous background. The method used by Shapley employed a special set of apertures to obtain a graded series of images for a comparison of the central intensity with that of the adjacent background. Although it is not certain that all the very complex photographic and photometric difficulties involved were overcome by this method, its results are presumably entitled to greater weight than any other determinations of central intensity hitherto made. The intensity in the hydrogen absorption lines of Vega was ascertained to be about 25 per cent of that of the background.
SATURATION OF ABSORPTION LINES
The discussion outlined above presupposes that the substance producing the absorption line in the reversing layer is present in quantities great enough to absorb all the light of the appropriate wave-length, subsequently re-emitting it and giving rise to an absorption line with considerable central intensity. If the atom in question is present in quantities too small for complete absorption to take place, the central intensity of the line produced will of course be higher still. Such atoms are designated “unsaturated.” Saturation has been described by Russell[115] as follows:—“For the strong lines ... the absorption in the reversing layer is so great that a large increase in the number of absorbing atoms present alters the strength of the line very little. For the weak components ... absorption under ordinary conditions is incomplete, and the strengthening (in the spectra of sunspots) is noteworthy”—an increase in the amount of available material produces an increase in the strength of the line. The strong components are saturated, the weak ones are not. It should be noted that here there is an excess of atoms for the radiation. “Saturation” is used in another sense when the word is applied to the conditions at the center of a star,[116] where there is an excess of radiation for the atoms present.
EMISSION LINES
The emission lines observed in stellar spectra differ more widely among themselves than do the absorption lines, and theory has so far been less successful in suggesting the physical conditions under which they may arise.[117] The appearance of the bright-line flash spectrum of the sun, from a region that gives no appreciable continuous spectrum, is of interest in comparing emission and absorption lines. It is fairly obvious that if the source of the flash spectrum had the photosphere behind it, the bright line would appear as absorption lines—which is indeed the case when the sun is ordinarily observed. Russell assigns both the Fraunhofer lines and part of the flash spectrum to the same region, namely the upper reversing layer. The high-level flash is, of course, assigned to the lower chromosphere. The difference between absorption and narrow emission is, as was pointed out in an earlier paragraph, purely a matter of contrast. There has, however, been no satisfactory explanation of how the phenomenon displayed by an ordinary emission line can be produced—an atom that re-emits in some wave-length more light than it receives in that wave-length. Some form of “fluorescent” emission would seem to be involved, and the question is evidently an important one for spectrum theory.
The chief types of emission are found in (a) the long period variables at maximum, (b) the emission
stars, (c) the
stars, including the Wolf-Rayet stars. All these stars are apparently very luminous.[118] Emission is also found in some late dwarfs—for example the
and
lines are reversed in the spectrum of 61 Cygni,[119] and doubly reversed in the solar spectrum. Furthermore the spectra of gaseous nebulae are almost entirely composed of emission lines; and completely abnormal types of stars, with spectra partly or wholly composed of emission lines, might also be mentioned, notably the novae,[120]
Carinae,[121] Merrill’s “iron star,”[122] Z Andromedae,[123] and[124] B. D.+11°4673. The conditions under which bright lines appear vary so widely that a single theory is manifestly inadequate to account for the phenomenon in every case.