Sodium in the Stratosphere

I. A. Khvostikov

Introduction.—The yellow line in the spectrum of the night sky.—The sodium doublet in the spectrum of the twilight sky.—Interferometric measurements.—Some remarks on observations of sky fluorescence under twilight conditions and on priority of discovery in this field.—Determination of the height and extent of the sodium layer.—On the mechanism of excitation of sodium emission in the stratosphere.—Where does sodium in the high layers of the atmosphere come from?—Absolute measurements of the brightness of the yellow line.—Determination of the amount of sodium in the atmosphere.—The width of the \(D\)-lines of sky radiation and the question of the nature of the glow.—Measurements of the absorption of the sky \(D\)-lines by sodium vapor.—Seasonal variation of the brightness of the yellow line.—On the structure of the high layers of the atmosphere.

1. Introduction

For thirty years now, the study has continued of a remarkable natural phenomenon that has received the name of the glow of the night sky. This phenomenon consists in the following. Careful measurements of the brightness of the night sky have shown that only \(1/4\)—\(1/3\) of all the light sent to us by the night sky belongs to the stars and nebulae. The night sky sends us “too much” light. Where does this excess glow come from?

The work of Newcomb\(^{1}\), Intema\(^{2}\), Slipher\(^{3}\), and others established that the earth’s atmosphere itself emits radiation. The upper layers of the atmosphere are constantly glowing, emitting ultraviolet, visible, and infrared rays. The spectrum of this glow is a line spectrum; it contains lines of oxygen, nitrogen, and other constituent parts of the air. The glow of the night sky is detected always and everywhere: at any point in the sky, at any moment of the night, in any geographic locality.

The systematic study of the spectra of the night-sky glow in the twenties and thirties yielded results of fundamental importance for geophysics. The previously generally accepted theory of the composition of the air at great heights was disproved; according to that theory, the upper part of the atmosphere should consist predominantly of light gases, hydrogen and helium. It was established that the lines of hydrogen and helium are absent from the spectra of the night sky. It was shown that the high layers of the atmosphere consist mainly of nitrogen and oxygen, as do the lower layers.

These data formed the basis of the now existing supposition that the atmosphere is “mixed” at all heights, that air—

...possible only in the presence of powerful vertical motions in the stratosphere; previously it was thought that such motions could not occur, and even now this question, of fundamental importance for atmospheric physics, remains unclear and controversial. It was shown, moreover, that oxygen is present, and even predominates, in the upper layers of the atmosphere not in the molecular state, as in the lower layers, but in the atomic, dissociated state. Subsequently, lines of ionized gases were discovered in the spectra. These results became the starting point for modern theories of the dissociation and ionization of the upper atmospheric layers, so important for the study of the ionosphere, for the “Earth—Sun” problem, and so on.

Deciphering the spectra of the night-sky glow was not always a simple matter. It was necessary to overcome not only technical difficulties arising from the extremely low intensity of this radiation, but often fundamental difficulties were also encountered, as, for example, in deciphering the green line \(\lambda = 5577\ \text{Å}\). In this case it took 10 years of strenuous work by physicists and astronomers in various countries in order, finally, to establish that this line belongs to atomic oxygen. In investigations of similar questions, important and interesting problems arose and were solved; an account of them may be found elsewhere \(^4\).

The study of the glow of the night sky is far from complete. The basic question—concerning the mechanism of excitation of the luminescence of gases in the upper layers of the atmosphere—still remains open. During the day the ultraviolet radiation of the Sun produces dissociation of the upper layers; at night, during recombination of the dissociated particles, excited particles may arise as a result of triple collisions. Are such photochemical processes the source of the energy of the night radiation of the atmosphere? Or perhaps this glow is excited directly at night by electron impact under the action on the atmosphere of the corpuscular radiation of the Sun? Are nuclear reactions, occurring in the upper layers of the atmosphere under the action of cosmic rays, the source of the energy of the radiation of the night sky? Does direct optical excitation of the sky glow by solar rays occur at night? Finally, is the luminescence of the sky a glow of the same type as in a gaseous electric discharge? In the latter case it would be necessary to assume the existence of corresponding electric currents in the ionosphere.

Similar questions have been considered with greater or lesser completeness in numerous works; however, a convincing answer has not yet been obtained \(^5\). The most recent years, during which the study of the glow of the night sky has not ceased, have brought new discoveries and posed a number of new problems. Among the most interesting of these must undoubtedly be included the discovery of sodium vapors in the upper layers of the atmosphere. This question has already for several years attracted the attention of physicists, astronomers, and geophysicists, since it affects...

poses many important problems in the physics of the upper layers of the atmosphere. In the present article an attempt is made to give a systematic account of the results obtained and of those questions which still await their solution.

2. THE YELLOW LINE IN THE SPECTRUM OF THE NIGHT SKY

Slipher, who discovered in 1919 the green line in the spectra of the glow of the night sky3, 10 years later, in 1929, made another discovery6, the great significance of which became clear only 8–10 years later. He found in the spectra of the glow of the night sky a yellow line with wavelength 5892 Å.

The error in determining the wavelength of lines in the yellow and red parts of the spectra of the glow of the night sky is usually very large, of the order of several Å. This is explained by the necessity, when photographing spectra, owing to the low intensity of the glow of the night sky, of using very fast spectrographs with very short-focus camera objectives, and therefore with extremely small linear dispersion. If we tried to photograph the spectrum of the night sky with such a spectrograph as, for example, the fastest model of the Zeiss spectrograph for the Raman effect \((F : 2)\), an exposure of 30–50 hours would be required in order to obtain in the spectrum only a few of the brightest lines.

Special, particularly fast spectrographs constructed in recent times—such as, for example, the spectrographs of the State Optical Institute in Leningrad with an aperture ratio \(F : 0.58\), or the spectrograph of the Paris Institute of Optics with an aperture ratio \(F : 0.7\)—make it possible to reduce the exposure to 1–2 hours. However, the linear dispersion of such spectrographs in the yellow region is from 500 to 1500 Å per 1 mm. It is understandable that under such conditions an exact determination of the wavelength becomes extremely difficult, despite the fact that the technique of processing such small-scale spectra with the passage of time has attained great perfection.

The yellow line discovered by Slipher aroused the liveliest interest for the reason that every new line in the spectra of the glow of the night sky is an important step toward understanding the chemical composition and physical state of the upper layers of the atmosphere, and, in addition, because lines with such a wavelength had never been observed in the well-studied spectra of aurorae. The measurement of the wavelength of the yellow line was repeated many times by various authors at different geographical points.

In 1932 Dufay7,8 found for the new yellow line the wavelength \(\lambda = 5892.5\) Å. In the same year Sommer9 determined \(\lambda = 5887\) Å. Almost the same value, \(\lambda = 5888\) Å, was found in 1934 by Cabannes10 at the Pic du Midi Observatory in France, and in 1934–1935 Vegard and Tönsberg11,12 in Norway found at first \(\lambda = 5885\) Å, and later \(\lambda = 5892.6\) Å,

In 1938 Cabannes and Dufay\(^ {13}\) found \(\lambda = 5894\) Å; in Fig. 1 their spectrogram of the glow of the night sky is reproduced. After what has been said above about the small dispersion of the spectrographs used, there is no need to be surprised at such considerable discrepancies in the determination of the wavelength of the yellow line, but it is clear that with such uncertainty the question of identifying the line can be resolved only conjecturally.

In 1935 Vegard and Tonsberg obtained the first indications of certain peculiarities in the structure of the yellow line: from an analysis of the spectrograms they concluded that the width of the line is considerably greater than is the case for simple atomic lines, and that, possibly, this line has a fine structure\(^ {12}\). Later Cabannes and Dufay came to the same conclusion\(^ {13}\).

Fig. 1. Yellow line \(\lambda = 5894\) Å in the spectrum of the glow of the night sky (Cabannes and Dufay, 1938).

In 1937 the question of the yellow line became sufficiently definite in the sense that the atmospheric origin of the new glow was proved. This result was obtained by Garrigue, who, photographing the spectrum of the glow of the night sky simultaneously at the zenith and at the horizon, showed that the yellow line at the horizon is 2–3 times more intense than at the zenith\(^ {14}\). Such a result shows, of course, that the radiation arises not beyond the limits of the earth’s atmosphere: the source of the radiation is the atmosphere itself.

But what substance emits the yellow line \(\lambda = 5890\) Å?

For a number of years this question remained open. Various conjectures were put forward concerning the nature of the new yellow line. As always in such cases, close values were sought in tables of wavelengths of emission spectra of various substances, guided only by the plausibility of the assumption that one or another substance is present in the atmosphere. Attention was also drawn to the fact that the obtained values of the wavelength of the new line are close to the wavelengths of the yellow sodium doublet (Dufay\(^8\), 1933), but, apart from the general uncertainty of such comparisons, which commit one to nothing, references to sodium were especially restrained because the presence of sodium vapor as a constant constituent of the atmosphere had never before revealed itself in any way; the hypothesis of sodium, having at that time

too scanty an experimental basis, inevitably seemed far too far-reaching. Much more boldly they wrote about water vapor in the high layers of the atmosphere as a possible source of new atmospheric radiation[^9]. Indeed, in the spectra of water vapor we find close values of wavelengths, and, on the other hand, the presence of water vapor in the air may occur even up to comparatively great heights.

It should be noted, however, that if the very great altitude which had tacitly to be assumed in this case for the moisture-containing layers of the atmosphere created certain theoretical difficulties, then, on the other hand, it also increased the interest of the problem. The point is that, although at that time (and to a large extent even now) the altitude of those atmospheric layers whose radiation creates the glow of the night sky had not been determined with any confidence, many indirect data nevertheless indicated that this altitude was very great, more than 100 km. But it had formerly been considered that water vapor is absent at such great heights, since, originating at the water surface of the terrestrial globe, it easily, owing to the turbulent mixing of the air, spreads to the upper limits of the troposphere, then penetrates, albeit with difficulty, through the tropopause into the lower layers of the stratosphere, but cannot rise into the higher layers of the atmosphere. If an analysis of the spectra of the night sky proved the presence of water vapor up to heights on the order of 100 km, then this, in addition to the tempting possibility of explaining the appearance of the mysterious noctilucent clouds at an altitude of 82 km*, would compel a radical reconsideration of existing views on the possibility of vertical air currents between the lower and upper layers of the stratosphere and between the ionosphere and the stratosphere.

The question remained in this uncertain, speculative state until 1937–1938, when quite unexpectedly its further development took an entirely different direction. The chief result that determined everything that followed was obtained by means of twilight observations.

3. THE SODIUM DOUBLET IN THE SPECTRUM OF THE TWILIGHT SKY

In the summer of 1936, on the slopes of Elbrus, in the Caucasus, at an altitude of 3100 m, new high-luminosity spectrographs, brought there from Leningrad, were installed for photographing the spectra of the glow of the night sky. The exceptional purity and transparency of the high-mountain air made this region very suitable for carrying out various optical observations, undertaken on the initiative and under the general direction of

* The tropopause is the boundary layer of air separating the troposphere from the stratosphere. It is characterized by a peculiar temperature regime, which hampers the circulation of air between the troposphere and the stratosphere.

Acad. S. I. Vavilov by staff members of several research institutes for the purpose of studying the atmosphere by optical methods.

In August, the participants in this work, M. F. Vuks and V. I. Chernyaev, using spectrographs \(F:0.58\) and \(F:1\), made at the State Optical Institute and making it possible to obtain spectra of very high quality (the design of the optical system of the spectrographs belongs to Prof. G. G. Slyusarev), obtained several spectra of the scattered light of the twilight sky at various immersions of the sun below the horizon and, in some of them, against the background of the continuous spectrum of the scattered light of the sky, discovered an intense line in the yellow part of the spectrum. Careful measurement of the spectrograms, carried out in the autumn of the same year at the State Optical Institute, showed that this yellow line is “the very same” line which, for a number of years previously, had been found in the spectra of the glow of the night sky: its wavelength proved to be \(\lambda = 5890\ \text{Å}\).

The result obtained could not but appear surprising, if one takes into account the conditions under which the line was photographed. The line was found against the background of the bright continuous spectrum of the twilight sky with an exposure of only 6 minutes, whereas to obtain this same line in spectra of the night sky a many-hour exposure had always been required. A count showed that the brightness of this line under twilight conditions is approximately 100 times greater than its brightness under nighttime conditions. Such a strong “flash” of the yellow line under twilight conditions was an entirely new fact in the study of this enigmatic radiation of the earth’s atmosphere.

Fig. 2. Record of the spectrum of the twilight sky with the yellow line \(\lambda = 5890\ \text{Å}\) (V. I. Chernyaev and M. F. Vuks, 1936).

In Fig. 2 is reproduced a microphotogram of one of the spectra obtained by M. F. Vuks and V. I. Chernyaev: the emission line of the indicated wavelength is clearly visible on it. The work of M. F. Vuks and V. I. Chernyaev, reporting the indicated discovery, was published1 at the beginning of 1937.

More than a year later, in 1938, a note appeared by the French investigator Bernard[^16], in which he reported the same results. Soon he also reported, simultaneously in several journals[^18],[^19],[^20], on his interferometric measurements, which showed that the yellow line of the sky is a doublet, the structure of which indicates its belonging to the radiation of sodium (the \(D_1\) and \(D_2\) lines of sodium). Quite simultaneously there appeared communications on the same subject by the well-known French physicists and astronomers Cabannes, Dufay, and Gauzit2,3, and then in the pages of the Astrophysical Journal and Comptes Rendus there followed an energetic dispute over priority among the three named authors on the one hand

from one side ^17,21,24 and by Bernard from the other ^22,23. Both simultaneously carried out (and published) interferometric measurements, but even before that Bernard had observed a “flash” of the yellow line in twilight, regarding precisely this discovery as especially significant. The dispute between them continued also in 1939, and in 1940 Vegard also entered this discussion, asserting his rights to the discovery of the twilight flash of the yellow line ^25. Later (§ 5) we shall consider what Vegard’s claims were based on.

This many-sided dispute over priority is noteworthy in that all the named authors make no mention at all of the work of V. I. Chernyaev and M. F. Vuks ^15, to whom alone this right to the discovery belongs. Let us note that the work of V. I. Chernyaev and M. F. Vuks was published in the Reports of the Academy of Sciences of the USSR in two languages: Russian and English ^15.

Observations of one or another glow of the sky during twilight have, in contrast to daytime and nighttime observations, the special feature that they make it possible to judge directly the altitude of the atmospheric layers in which the glow arises. The maximum brightness of the yellow line of the twilight sky is observed when the sun is submerged below the horizon by 6–8°. At this time the Earth’s shadow passes through the atmosphere at an altitude of 50–70 km and, consequently, the lower layers are no longer illuminated by direct sunlight. After 8–10°, when the Earth’s shadow rises above 70–90 km, the brightness of the yellow line rapidly decreases. Taking into account this and what was said earlier about the great brightness of the yellow line during the period of the twilight “flash” (in comparison with nighttime), one may consider that the discovered properties of the twilight “flash” of the yellow line permit the following conclusions:

1. The terrestrial origin of the “yellow” line is definitively confirmed;
2. The greater part of the luminous substance is located, apparently, in a comparatively thin layer at an altitude of 60–80 km;
3. The glow belongs to atomic sodium;
4. The excitation of the glow is connected with the action of solar rays; it is possible that we are dealing with optical resonance.

Thus, in the stratosphere, at an altitude of 60–80 km, sodium vapor is present as a constituent of the air. This most interesting discovery completed the first stage of investigations of the yellow line of the sky, which lasted 9 years—from 1929 to 1938.

4. INTERFEROMETRIC MEASUREMENTS

The large error in determining the wavelength of the yellow line of the sky was caused, as we have seen above, by the necessity of using spectrographs with very short-focus objectives and therefore possessing insignificant linear dispersion. The use of spectrographs of the “normal” type, with sufficiently high resolving power, proves impossible because of the lack of light.

From this point of view, the application of interference methods for the precise determination of the wavelength of the yellow line of the sky initially might have seemed even less feasible because of the same lack of light. Bernard obtained a very fast interference apparatus by making use of the elegant method previously employed by Fabry in his well-known work on the precise determination of the wavelength of the green line of the night-sky glow[^26].

Bernard’s apparatus (see Fig. 3) consists of a Fabry–Perot etalon, behind which there is a fast objective; in the principal focal plane of the objective a photographic plate is placed. The objective is covered with an orange light filter, whose transmission drops off steeply at 5750 Å. Photographic plates were chosen whose sensitivity falls sharply to zero in the orange part of the spectrum. Under these conditions the sensitivity of the instrument is limited to a narrow region, approximately from 5800 Å to 6000 Å, whereby such a considerable weakening of the scattered sky light is achieved, which, as is known, possesses a continuous spectrum, that the interference rings of the yellow line are clearly visible in the photograph against the continuous background of the general blackening of the plate caused by the action of the continuous spectrum. In photographing, the apparatus is directed immediately toward the region of the sky that interests us.

Fig. 3. Diagram of the apparatus for obtaining interference rings from the \(D\) line of the sky. 1 — filter; 2 — Fabry–Perot etalon; 3 — fast objective; 4 — photographic plate.

Fig. 4. Interference rings from the yellow line of the twilight sky (Bernard, 1938). (a) Etalon 0.15 mm, lines \(D_1\) and \(D_2\) are separated; (b) etalon 0.30 mm, lines \(D_1\) and \(D_2\) merge.

Figure 4 shows two photographs of the interference rings of the yellow line of the sky, obtained by Bernard when photographing the twilight sky at the zenith[^19]. Plane-parallel glass plates, suitably metal-coated, with thicknesses of 0.15 mm (photograph a) and 0.30 mm (photograph b), served as the Fabry–Perot etalon.

b). Each photograph is divided into two halves, distinguishable on the print by eye: on the left half are rings from a laboratory source of the sodium \(D\)-lines (an alcohol burner with a solution of Na); these are control rings, while on the right half is a photograph of the twilight sky at the zenith.

In photograph \(a\) the rings are visible separately for the sodium lines \(D_1\) and \(D_2\); in photograph \(b\), with a plate thickness of \(0.30\) mm, the rings merge. The photographs confirm the complete identity of the rings of the yellow doublet of sodium vapors and of the doublet of the yellow radiation of the sky. From the photographs one can determine the ratio of the intensities of the line \(D_1\), \(\lambda = 5896\) Å, and the line \(D_2\), \(\lambda = 5890\) Å. According to Bernard’s measurements it is equal to \(2:1\), i.e. it coincides with the theoretical value for sodium vapors.

Fig. 5. Interference rings of the yellow line of the night sky. Etalon 0.15 mm (Bernard, 1938).

Using this same setup, Bernard obtained interference rings from the yellow line of the night-sky glow[^19]. Under night conditions a much longer exposure was required—more than 10 hours, instead of about 10 minutes in twilight photography. Bernard’s night photograph, obtained with a standard plate of \(0.30\) mm, is reproduced in Fig. 5. Under night conditions the rings are less sharp, but here too their identity with the rings of the sodium \(D\)-lines is unquestionable.

Similar results were obtained at the same time by Cabannes, Dufay, and Gauzit, who also used a Fabry–Perot etalon of equally small thickness23[^24].

In 1940 Vegard and Tønsberg made the justified, though somewhat formal, observation that the interference photographs of Bernard, Cabannes, Dufay, and Gauzit are not a fully rigorous, final proof that the yellow radiation of the sky belongs to sodium vapors[^25]. If the interference experiments showed the presence of a fine structure (doublet) of the yellow radiation, coinciding in the wavelength difference of the doublet and in the intensity ratio of its components with the Na doublet, there still remains the exact determination of the absolute value of the wavelengths of the doublet. This latter could not be done from the previously obtained spectrograms taken on low-dispersion (high-aperture) spectrographs (there the error amounts to several Å; see § 2), but it is possible to an even lesser degree with the Fabry–Perot etalons used by the French authors, whose thickness was only fractions of a millimeter. Such a small thickness is convenient for resolving a doublet with a wavelength difference on the order of 6 Å, which is why it was chosen; but as the thickness of the etalon decreases, the sharpness of the interference rings decreases, and an exact determination of their diameters becomes impossible. Therefore the error in determining the wavelength in this case will be measured in tens of Å.

Vegard and Tønsberg succeeded in obtaining at Tromsø two spectrograms of twilight light on a large glass spectrograph with a dispersion of 99 Å/mm at the yellow line, on which the components \(D_1\) and \(D_2\) were obtained separately (see Fig. 6). These authors reported that “as a comparison spectrum the \(D_1\) and \(D_2\) sodium lines were used, and with a microscope comparator no difference was detected between this doublet and the twilight doublet. Both doublets also coincide with respect to the intensities of the components” (emphasized by Vegard and Tønsberg).

Only these measurements of theirs do the authors named consider final proof that the yellow doublet of the sky radiation belongs to sodium vapor, as is evident from their following concluding remark^25: “These results, together with the interferometric observations, definitively prove that the yellow twilight line is the \(D_1D_2\) sodium doublet.”

The twilight spectrograms obtained by Vegard and Tønsberg (see the microphotogram in Fig. 6) require some clarification. The point is that, although the authors state directly that their spectrograms were obtained during twilight (“...we obtained at Tromsö two spectrograms of twilight giving separation of two components of the yellow line”), in fact, as can be shown, their photographs are not twilight at all, but represent typical spectra of the glow of the night sky. It is necessary to point out this inaccuracy, made by two well-known investigators of the glow of the night sky and of auroras, since it is connected with essential considerations of a general character, which will be examined in the following paragraph.

Fig. 6. Regressogram of the spectrum of the night sky with the resolved sodium doublet 5890—5896 Å (Tønsberg and Vegard, 1940).

Additional indications of the presence of atomic sodium in the atmosphere were given in 1938 by Dejardin, who discovered among the lines of the night-sky-glow spectrum such lines as could with a known probability be ascribed to the sodium spectrum^31. The point is that, among three hundred lines of different intensity found in the spectra of the night-sky glow in the region 3000—8000 Å, many lines remained unidentified. The presence of atomic sodium in the atmosphere was established, as we know, only in 1938. Immediately after the publication of the interferometric measurements of Bernard, Cabannes, Dufay, and Gauzit, which proved the belonging of the yellow line

radiation of the twilight and night sky to the spectrum of atomic sodium, Dejardin undertook a general revision of the unidentified lines of the night-sky spectrum in order to determine whether there were sodium lines among them. The attempt led to a positive result, as is seen from Table 1, which brings together the results of Dejardin’s comparisons31.

Table 1

Comparison of the lines of the spectrum of atomic sodium with unidentified lines of the night-sky spectrum
(after Dejardin)

Sodium	Night sky, \(\lambda\)	Night sky, intensity	Sodium	Night sky, \(\lambda\)	Night sky, intensity
\(^{1}S—^{3}P\) \(3302—3303\) Å	\(3303\) Å	3	\(^{2}P—4P\) \(5533—5527\) Å	\(5532\) Å	0
\(^{2}P—3S\) \(6161—6154\) Å	\(6166\) Å	0	\(^{2}P—5P\) \(4918—4914\) Å	\(4916\) Å	?
\(^{2}P—4S\) \(5154—5149\) Å	\(5153\) Å	0	\(^{2}P—6P\) \(4633—4629\) Å	\(4632\) Å	?
\(^{2}P—5S\) \(4752—4748\) Å	\(4759\) Å	1	\(^{2}P—7P\) \(4472\) ?	\(4472\) Å	1
\(^{2}P—6S\) \(4545—4542\) Å	\(4545\) Å	?	\(^{2}P—8P\) \(4372\) ?	\(4370\) Å	3
\(^{2}P—4D\) \(5688—5683\) Å	\(5680\) Å	1
\(^{2}P—3P\) \(7520\) Å (calculated)

5. SOME REMARKS ON OBSERVATIONS OF SKY FLUORESCENCE UNDER TWILIGHT CONDITIONS AND ON THE PRIORITY OF DISCOVERIES IN THIS FIELD

Optical observations during twilight—observations of the kind that led to the discovery of sodium vapor in the stratosphere—have two important features: they make it possible to obtain directly important information about the altitude of those atmospheric layers in which the radiation under study arises (this possibility is absent in daytime and nighttime observations); in addition, in twilight observations we are certain that the observed phenomena are caused by the direct action of the sun’s rays (and this possibility is not fully present in daytime and nighttime observations). It is clear what significance these circumstances have for elucidating the nature of the phenomena. And it is no accident, of course, that over the last decade many prominent geophysicists, physicists, and astronomers have increasingly turned to twilight investigations. In this direction two main paths have taken shape: one of them is connected with a comprehensive study of the scattered light of the sky during twilight; the second became possible after the twilight fluorescence of the sky had been discovered, and is connected with a systematic investigation of this fluorescence.

SODIUM IN THE STRATOSPHERE

The supposition that the gases forming the Earth’s atmosphere can fluoresce under the action of the Sun’s rays (not necessarily only of light) has been expressed repeatedly on various occasions (for example, in connection with the question of the blue color of the daytime sky). Attempts were made more than once to detect this fluorescence. We can now understand why such attempts had always previously failed, although this fluorescence does exist: it is too weak to be detected by day, in the presence of the bright scattered light of the sky. This fluorescence (at least some of its types) arises only in separate, and moreover high, layers of the air. Only at the appropriate moments of twilight, when the lower, “unnecessary” layers of the atmosphere have already been immersed in shadow and therefore the sky background is already less bright, while the fluorescence itself is still intense—as against the background of the continuous spectrum of the scattered light of the sky we can detect fluorescence lines. But the Earth’s shadow rises rapidly during twilight; layers of air that have only just been illuminated by the Sun’s rays are, after a short time, immersed in shadow; the phenomenon proceeds rapidly, and an enormous light-gathering power of optical instruments is required in order to record everything necessary in time. In the mid-1930s, modern high-aperture spectrographs were realized, and soon after this the fluorescence of the sky, long anticipated and long sought, was finally discovered. It was discovered as the fluorescence of the twilight sky. A most interesting example of such fluorescence is the radiation of the sodium D-lines, which is the subject of the present article.

When a phenomenon that had long and repeatedly been anticipated and discussed in connection with many other important questions is finally discovered, this is, of course, always interesting and important. This determines the great general significance of the discovery and deciphering of the yellow radiation of the sky. On this, too, may be based the legitimate feeling of satisfaction among those who made this discovery. It is therefore understandable with what polemical ardor Bernard, Cabannes, Dufay, Gozi, and Vegard discussed (see § 3) the question of priority; it remains only to note the annoying factual inaccuracies that occurred in this discussion.

It is not the circumstances connected with priority—although the question of priority is important in itself—but the possibility of better understanding the essence of the phenomena under consideration that makes it expedient to analyze certain points relating to the history of the discovery of the fluorescence of the sky. It should be pointed out, first, that the twilight fluorescence of the sky (and hence the fluorescence of the sky in general) was discovered by Garrig27 in 1936 in the form of red oxygen radiation of the sky, \(\lambda = 6300\) Å. This remarkable discovery by Garrig and the subsequent work in this direction undoubtedly deserve much more attention than is usually given to them and, in any case, are of serious importance for a better understanding of the questions to which this article is devoted.

As early as the end of the 1920s and the beginning of the 1930s, as a result of many years of work it was established that three lines in the spectra of the night-sky glow, \(\lambda = 5577.3\) Å, \(\lambda = 6300\) Å and \(\lambda = 6363\) Å, which for a long time had not received a correct interpretation, belong to atomic oxygen. The 6300 line is among the brightest not only in the spectra of the night-sky glow, but also in the spectra of aurorae. A detailed account of the question of the lines of atomic oxygen may be found elsewhere \(^{4}\).

The discovery and study of these lines proved the presence in the upper layers of the atmosphere of a large amount of dissociated oxygen. Moreover, neither in the spectra of aurorae nor in the spectra of the night-sky glow have bands of molecular oxygen been found, which apparently indicates complete dissociation of oxygen in the upper layers of the atmosphere. These facts are among the most important in the whole physics of the upper atmospheric layers.

Let us note in passing that analysis of the sky spectra did not reveal the presence of dissociated (atomic) nitrogen (under the action of the sun’s ultraviolet rays the molecules \(N_2\) are ionized more readily than they dissociate). The presence of the ions \(N_2^+\), \(O^+\), and \(O^-\) has been established.

In 1936 Garrig discovered the line \(\lambda = 6300\) Å in the spectrum of the twilight sky \(^{27}\). Each time the sun is at a depth of \(9^\circ\) below the horizon (at this moment the brightness of the sky is already hundreds of thousands of times less than by day), a red line becomes noticeable in the sky spectrum, standing out against the background of the continuous spectrum of scattered light. As the sun sinks further, the brightness of the red line decreases slowly and very smoothly. According to measurements by Cabannes and Garrig \(^{28}\), if this glow is regarded as resonance radiation of oxygen, the maximum content of atomic oxygen occurs at an altitude of 115 km.

The initial interpretations of the mechanism of the oxygen glow during twilight proved, as was pointed out later \(^{29}\), to be internally contradictory; subsequently a theory of the phenomenon was given which was in good agreement with the experimental data and was based on consideration of those specific features of the refraction of light in the atmosphere which must occur for frequencies close to the absorption frequency (resonance frequency) of oxygen atoms as a consequence of anomalous dispersion \(^{29}\).

In the same year, fluorescence of sodium vapor was discovered, which, as we already know, can be observed under identical conditions: it is necessary to begin photographing the spectra of the twilight sky only when the sun has descended below the horizon by a certain angle, at which a ray 60 km above the Earth’s surface is immersed in the Earth’s shadow (\(6^\circ\)). At this time the brightness of the sky is approximately \(3 \cdot 10^4\) times less than by day.

Who first observed the twilight glow of sodium? Three works on this question had been published before the reports mentioned in § 3 by Bernard, Cabannes, Dufay and Gauzit: Koorrie and Edwards \(^{30}\)

in 1936, Vuks and Chernyaeva1 in 1936; Vegard and Tønsberg5 in 1937.

When, in 1938, the first publications by Bernard, Cabannes, Dufay and Gauzit appeared, and in the course of 1938–1939 a fierce discussion flared up among them about priority (see § 3), none of them mentioned these predecessors of theirs. An exception, however, was the work of Currie and Edwards, but only insofar as Cabannes, Dufay and Gauzit, referring to an earlier publication by Currie and Edwards, thereby rejected Bernard’s right to priority2, 3. The work of Currie and Edwards was published4 in 1936.

What, then, did Currie and Edwards observe?

Their observations were made during the international polar year of 1932–1933 in Canada at latitude 63°20′. They photographed spectra of auroras almost every night in the period from December 1932 to April 1933 and in the second half of August 1933. In all, 693 spectrograms were taken under different conditions: during evening and morning twilight, during continuous twilight in spring (white nights), at night with and without the moon, and during cloudy nights. Their main result is that 2 lines in the yellow-red part of the spectrum of auroras become more intense when there is moonlight or twilight illumination of the sky.

Fig. 7. One of the spectrograms of the night-sky glow, taken at Chesterfield (Canada) by Currie and Edwards.

What are these lines? Let us give the floor to the authors (see4, p. 271):

“Influence of moonlight and twilight illumination on red radiation. Two emissions in the red part of the spectrum are of special interest, since both the frequency of their appearance and their intensity increase during periods of moonlight and twilight illumination. Although their wavelengths could be determined only very approximately because of the small dispersion of the spectrograph in the red part of the spectrum, nevertheless, on the basis of the measurements of Vegard and Tønsberg, Cabannes and others of the wavelengths of lines in this part of the spectrum, it is possible with sufficient confidence to identify the emissions we studied.

The first of them is a broad band with a well-defined short-wave boundary at 6300 Å. The long-wave boundary of this band is diffuse and changes its position from time to time... The other radiation has the form of a broad diffuse band extending approximately from 6000 Å to 5800 Å, with a mean wavelength of 5940 Å.”

We shall also refer to one of the spectrograms of Currie and Edwards, taken as an example from their work^30 (see Fig. 7). Finally, let us note that in the work of Currie and Edwards there is nowhere any indication that they identify their band at 5940 Å with the yellow line 5893 Å, repeatedly observed in spectra of the night sky.

Under these circumstances, the assertion of Cabannes, Dufay, and Gauzit^17, ^21, ^24 that Currie and Edwards were the first to observe a twilight “flash” of the yellow line \(\lambda = 5893\) Å seems strange. Only polemical fervor can explain their statement that Bernard, in 1938, supposedly discovered what had already been discovered by Currie and Edwards several years before him: the increase in brightness of the yellow line of the sky under the action of twilight illumination.

On this point Bernard published, in French^22 and English^23, a detailed analysis of the results obtained by Currie and Edwards in their work. Bernard’s conclusions seem to us convincing and interesting. In particular, from the appearance of the spectra published by Currie and Edwards^30, Bernard concluded that they had mistakenly taken a blurred band in the orange part of the spectrum (5940 Å), caused by the maximum sensitivity of the photographic plates used (Ilford Soft Gradation) and by the action of the continuous spectrum of moonlight, for a band of sky radiation. “The very broad band,” writes Bernard^22, “which is visible in the orange part of the spectrum corresponds very precisely to a fairly well-pronounced maximum of sensitivity of the ‘Ilford Soft Gradation’ plates, and it is extremely probable that it represents simply a portion of the continuous spectrum of moonlight. It is possible to reproduce exactly the general appearance of Currie and Edwards’s spectrograms by photographing, on ‘Ilford Soft Gradation’ plates, the continuous spectrum of a carbon arc.”

Referring the reader for further details to Bernard’s papers^22, ^23, we shall give only his general conclusion: “It is highly probable that Currie and Edwards never observed the radiation of atmospheric sodium; that on which they fixed their attention was, at times, bands of aurorae near 6000 Å, while in other cases it was a narrow region of the continuous lunar or twilight spectrum in the region of the maximum sensitivity of the photographic plates. In their memoir I have found no indications and no assumptions that could lead me to the conclusion that they discovered the twilight effect for the yellow line \(\lambda = 5893\).”

Let us turn to Vegard’s assertions that he was the first to observe the yellow line in spectra of the twilight sky. This statement was made in 1940 in a note published in Nature in the following form^25: “Spectra of twilight giving the yellow line were obtained by Vegard in Oslo on January 13, 1936, and in Tromsø in February of the same year^32... In 1937 Bernard, working at the observatory in Tromsø, carried out a further systematic study of the increase in brightness of the yellow line in spectra of twilight^16, ^18, ^20.”

It is first necessary to make one general remark about the peculiarities of the sky glow at those geographical points (Norway) where Vegard carried out his observations over the course of many years. In these northern latitudes auroras are regularly observed; very prolonged twilights, lasting for months, also occur there. Therefore, at the indicated points optical phenomena of three different types often take place simultaneously: the glow of the night sky, auroras, and twilight. In certain respects such conditions should be considered favorable, since the phenomena indicated, complementing and intensifying one another, create a great variety of processes and make it easier to observe their different forms and combinations. But at the same time such conditions can make it difficult to interpret the phenomena themselves. The three indicated types of atmospheric glow—night, twilight, and auroral—have profoundly individual characteristics; they are phenomena, generally speaking, of different character and origin. To have the possibility of observing these types of sky glow separately is, in a number of cases, very desirable. Such a possibility is difficult at the latitudes of Norway, and Vegard himself, with all his enormous experience, undoubtedly became, at least once, a victim of confusion: he took a typical spectrum of the night sky to be the spectrum of the twilight sky. In the work by Vegard and Tönsberg cited above[^25], they present a microphotogram of a spectrum with the resolved sodium lines \(D_1 — D_2\). We have already reproduced this microphotogram in § 4 (see Fig. 6). Vegard and Tönsberg assert that this is a spectrum of the twilight sky, but in our view it is a typical spectrum of the glow of the night sky. In fact, the spectrum of the twilight sky has its own specific appearance: it is, first of all, the spectrum of the scattered light of the sky, on which only under special conditions can two lines of sky emission be distinguished: the red oxygen line \(\lambda = 6300 \text{ Å}\) and the yellow sodium line \(\lambda = 5893 \text{ Å}\). In its general structure this is the spectrum of the solar rays, with all the proper sharp and weak Fraunhofer lines. The oblique passage of the solar rays through the terrestrial atmosphere under conditions of twilight illumination of the sky leads to an enhancement of lines and bands of absorption of terrestrial origin. In the yellow part of the spectrum, which is of special interest to us in the context of the present article, the light of the twilight sky acquires a characteristic spectral structure.

Fig. 8. Ozone absorption band in the visible region of the spectrum (Chappuis band).

owing to the absorption of solar rays by ozone. In Fig. 8 a curve is given showing the magnitude of the ozone absorption coefficient in the Chappuis band (according to A. Vassy \(^{33,34}\)). This band has two principal absorption maxima at \(\lambda = 5750\,\text{\AA}\) and \(\lambda = 6010\,\text{\AA}\), and between them an absorption minimum at \(\lambda = 5872\,\text{\AA}\). The absorption of solar rays by ozone during the oblique passage of the solar rays through the atmosphere is so great that, against the background of the continuous spectrum of the scattered light of the twilight sky, a bright contrasting band (an absorption band) is always visible in the yellow-orange part of the spectrum; in the middle of this bright band, with sufficiently accurate exposures, one may notice a narrow dark band at \(\lambda = 5860\,\text{\AA}\). In Fig. 9 spectrograms of the twilight sky are reproduced (spectra 1—8 in the left photograph and 1—10 in the right); for comparison, in the right photograph the spectrum of the night sky is given: in the green-red region it is a line spectrum without signs of a continuous spectrum.

Fig. 9. Spectrograms of the twilight sky (1—8 and 1—10), taken successively at various submersions of the Sun below the horizon. At the top (\(N\)) are spectra of the glow of the night sky. (Brickard and Kastler, 1944).

A fine description of the characteristic general appearance of the spectrum of the twilight sky was given as early as 1935 by Götz \(^{35}\). A typical microphotogram of the twilight sky, on which, moreover, the yellow sodium line is visible, may be seen in Fig. 2, where it is reproduced from the work of V. I. Chernyaev and M. F. Vuksa \(^{15}\).

The microphotogram presented by Vegard-Tonsberg \(^{25}\) (Fig. 6), as its very appearance indicates, belongs to a line spectrum without signs of a background; consequently, it cannot belong to the twilight sky. Nor can it be a microphotogram of the spectrum of aurorae, which is likewise a line spectrum, because in aurorae, as is well known, the yellow sodium line never occurs. It is a microphotogram of the spectrum of the glow of the night sky.

If, as Vegard indicates (see above), Bernard did indeed for the first time observe an intensification of the yellow line in twilight while working in Norway, then he acted correctly in publishing the first report of these observations only after he had confirmed these results by observations in the French Alps and at the Lyons Observatory^19.

Such are some remarks on the substance of Vegard’s results. As for the formal side of the matter connected with his claim to priority^25, it is enough to point out that the work of V. I. Chernyaev and M. F. Vuks already known to us was published half a year earlier^15 than Vegard’s communication^32.

The circumstances indicated prove beyond doubt that the right to the discovery of the bright “flash” of the yellow line in the spectrum of the twilight sky, about which there has been so much dispute abroad, belongs to M. F. Vuks and V. I. Chernyaev.

6. DETERMINATION OF THE HEIGHT AND EXTENT OF THE SODIUM LAYER

A characteristic feature of the sodium glow of the twilight sky is its short duration. According to Bernard’s determinations, the intensity of the yellow line decreases by a factor of 100 within several minutes. Knowing the moment of time when the brightness of the sodium radiation becomes small (assumes its nocturnal value) and calculating the depth of the Sun’s immersion below the horizon, and from it—the height of the Earth’s shadow for this moment, one can determine the height of the upper boundary of the sodium layer. It was precisely in this way that Bernard, as early as 1938, obtained a height of 60 km. The rapid fading of the glow indicates a small thickness of that layer of air in which appreciable quantities of sodium vapor are contained.

Fig. 10. On the calculation of the height of the luminous layer at night.

In the same year, 1938, at the height of the discussion about priority, Cabannes, Dufay, and Gauzit pointed out that the height of 60 km obtained by Bernard from twilight observations is not confirmed by their nocturnal determinations of the height of the luminous sodium layer. Using Harrig’s measurements^14, who determined the ratio of the intensity of the yellow line in spectra of the glow of the night sky at the zenith and near the horizon, they obtained a height of 130 km. The idea of such calculations is as follows.

Let ЗЗ (Fig. 10) be the surface of the Earth, and let \(AB\) and \(CD\) be two air layers of equal thickness, bounded by concentric surfaces parallel to the Earth’s surface. The layers are at different heights. When sighting toward the zenith \(Z\), the line of sight intersects equal thicknesses in both layers: \(AB = CD\) or \(AB:CD = 1\). Let us now sight in the direction \(H\), close to the horizon; the line of sight

intersects our layer along the segments \(AB'\) and \(C'D'\); moreover, obviously, \(C'D' : AB' < 1\), and this ratio will decrease as the height \(h\) of the layer \(CD\) increases. If one assumes that the luminous substance uniformly fills such an atmospheric layer bounded by concentric surfaces, and that the brightness of the glow is proportional to the thickness \(CD\), or, respectively, \(C'D'\), then we come to the conclusion that the brightness of the glow should increase with distance from the zenith, and this increase will occur the more slowly the higher the layer \(CD\) is situated. Knowing the actual change in the brightness of the glow from the zenith to the horizon, one can compute the height of the luminous layer \(h\).

Harrig, measuring the ratio \(B_H/B_z\) of the brightness of the yellow line when sighting the spectrograph at an angle of \(10^\circ\) to the horizon to its brightness in the zenith, found\(^{14}\) that this ratio varies from 2 to 3. Taking the mean of this ratio to be 2.8, Cabannes, Dufay, and Gauzit\(^{21}\) found \(h = 130\) km.

Fig. 11. Determination of the boundary of the luminous sodium layer from twilight observations.

Desjardins and Bernard subjected this determination to substantial criticism\(^{36}\). They pointed out that the value \(B_H/B_z = 3\) corresponds to a height \(h = 90\) km, while the value \(B_H/B_z = 2\) corresponds to a height \(h = 400\) km, so that by such a method the height can be determined only very roughly. Furthermore, even if one admits that the sodium glow layer is thin and homogeneous, the error of determination becomes very appreciable when sighting at an angle of less than \(20^\circ\) to the horizon, since in this direction the line of sight intersects the sodium layer very obliquely. Finally, the intensity of various kinds of atmospheric radiations generally passes through a maximum precisely near the direction \(10^\circ\) above the horizon. All this makes the formula used by Cabannes, Dufay, and Gauzit very inaccurate.

Let us return to the determination of the height of the luminous sodium layer from twilight observations. If \(33\) is the Earth’s surface (Fig. 11), \(KS\) is the direction of that solar ray tangent to the Earth’s surface at point \(K\), which determines the boundary of the Earth’s shadow at the moment of appearance of the sodium lines in the spectrum of the sky at the zenith \(Z\) of the observer \(A\), then the height \(h\), which we easily determine from geometrical conditions, may be provisionally taken as the lower boundary of the Na layer.

We say “provisionally,” because, although this circumstance has hitherto remained unnoted, the absence of a noticeable Na line in the spectra of the sky at a smaller depth of the Sun’s immersion below the horizon can by no means be proof of the absence of Na vapor in the lower layers of the air. In fact, let us suppose that in lower

in the lower layers there are sodium vapors in the same quantity as at an altitude of 60 km, where we record the most noticeable brightness of their glow. If the Earth’s shadow moves from an altitude of 50 km to an altitude of 30 km (at our latitudes this will occur in 5–10 minutes), then the brightness of the sky will increase approximately 10-fold as a result of the rapid change in the density (scattering power) of the air with altitude. The brightness of the sodium-vapor glow will change insignificantly, and the yellow line will no longer be detected on the spectrogram, since the photograph would now have to be taken with an exposure 10 times smaller.

Thus, the altitude \(h_1\) should be regarded only as a conventional lower boundary of the layer containing sodium vapors.

Fig. 12. Change in the brightness of the yellow line of the twilight sky with time (Bernard, 1938).

Fig. 13. Height of the Earth’s shadow for the same moments as in Fig. 12. The upper curve is without taking account of the refraction of the Sun’s rays in the atmosphere; the lower, with refraction taken into account.

According to Bernard’s determinations, the brightness of the yellow line, at first changing slowly, then decreases very rapidly: by approximately a factor of 100 in several minutes (Fig. 12). Knowing the moment at which the bright yellow “flash” of the twilight sky ends, one can determine the upper boundary of the sodium layer \(h_2\) (Fig. 11). In one of his papers Bernard gives a curve, computed by him, of the height of the Earth’s shadow (Fig. 13) for different moments of measurement of the brightness of the yellow line, taking into account the atmospheric refraction of the Sun’s rays (curve 2) and without taking it into account (curve 1). The time plotted on the graph (Fig. 13) refers to the same day of measurements as on the brightness curve (Fig. 12). The moment of the end of the “flash,” \(15^{\mathrm h}51^{\mathrm m}\), corresponds to an altitude \(h_2 = 60\) km.

Carroll and Stille\(^{37}\), using Bernard’s data, determined the thickness of the sodium layer as only 9 km.

In his calculations Bernard did not take into account the attenuation of the ray \(KS\) (Fig. 11) along its path through the atmosphere. Meanwhile it is known that,

that the attenuation of rays passing through the lower layers of the atmosphere from the Sun, which is at the horizon, is extremely great. Thus, for example, according to the photometric data of Abney and Müller, who measured the brightness of the Sun at different zenith distances, for rays \(\lambda = 0.59\,\mu\) the Sun observed at the horizon has only \(1‰\) of its full brightness[^38].

Under twilight conditions (Fig. 11) the near-ground rays of the Sun \(KS\) pass twice through the indicated thickness of the atmosphere, and the attenuation reaches a value of \(10^6\).

Thus the rays of the Sun passing through the lower layers of air in fact do not take part in the twilight illumination of the sky at the zenith (the screening action of the troposphere). If one excludes from the calculation the rays that have passed through the lower opaque layers of air, then the calculated heights \(h_1\) and \(h_2\) increase.

It was precisely such refinements that Kario and Stille wished to make. Unfortunately, this was done by them too simplistically[^37]. There has long existed V. G. Fesenkov’s theory, which strictly takes into account the attenuating action of the lower layers of air on the solar rays coming from below the horizon and illuminating the zenith during twilight[^39]. Kario and Stille did not use V. G. Fesenkov’s results. After detailed, but in places overly primitive, reasoning they simply concluded that the troposphere is opaque up to a height of \(8\) km, while absorption in the higher layers may be neglected. As a result, proceeding from Bernard’s experimental data, they obtained \(h_1 = 69\) km and \(h_2 = 78\) km. With German methodicalness they calculate the error of their determination of these heights as equal to \(\Delta h = \pm 1.2\) km, although, as is not difficult to see, the error of their results is much greater owing to the inaccurate allowance for the attenuating action of the atmosphere on the solar rays.

Fig. 14. Vertical distribution of ozone (\(\varepsilon\)—thickness in cm of the reduced layer of ozone, referred to 1 km of air).

It would have been possible to obtain far more accurate results by making use of the above-mentioned theory of V. G. Fesenkov[^39]. We shall not do this, since in 1944 Brikar and Kastler carried out the necessary calculations with sufficient accuracy, taking into account, moreover, the absorption of solar rays by atmospheric ozone that is significant for the phenomena under consideration[^40].

In Fig. 8 we have already given the curve of ozone absorption of light in the Chappuis band. This curve shows that the \(D\)-line of Na, although falling in the interval between the two principal maxima of the Chappuis band, nevertheless corresponds to a place where absorption is large.

Calculating the weakening of solar rays on their path through the atmosphere, Brikar and Kastler, taking into account weakening due to scattering, assumed that:

1. The scattering of light is purely molecular (an ideal atmosphere).
2. The distribution of air density $\rho$ with height $h$ is that of an isothermal atmosphere, i.e. they simply took $\rho_h=\rho_0 e^{-ah}$, where $a$ is a constant.
3. The weakening coefficient $a$ $(I=I_0\cdot 10^{-al})$, calculated by the Rayleigh–Cabannes formula for $\lambda=0.59\,\mu$, is equal to $a=0.0038\ \mathrm{km}^{-1}$ for air at height $h=0$.

Calculating absorption by atmospheric ozone, they assumed that

1. The total amount in the atmosphere corresponds to an ozone layer of thickness $2.7\ \mathrm{mm}$ under normal conditions.
2. The distribution of ozone with height is as shown in Fig. 14.
3. The coefficient of absorption of light by ozone is that obtained in the laboratory measurements of A. Vassy at $18^\circ\mathrm{C}$ (Fig. 8); moreover, for the mean temperature of atmospheric ozone, $-50^\circ\mathrm{C}$, the ozone absorption coefficient is greater by $\Delta a=0.007$, so that:

\[ \begin{aligned} \text{for } \lambda_D &= 5890\,\text{\AA} \quad \text{at } 18^\circ\mathrm{C}\ a=0.058 \text{ and at} \\ &\qquad -50^\circ\mathrm{C}\ a=0.065,\\ \lambda_M &= 6010\,\text{\AA} \quad »\ 18^\circ\mathrm{C}\ a=0.068 \text{ and at} \\ &\qquad -50^\circ\mathrm{C}\ a=0.075,\\ \lambda_m &= 5872\,\text{\AA} \quad »\ 18^\circ\mathrm{C}\ a=0.0575 \text{ and at} \\ &\qquad -50^\circ\mathrm{C}\ a=0.0645, \end{aligned} \]

where $\lambda_M$ and $\lambda_m$ are the wavelengths of the principal maximum and minimum of the Chappuis band curve (see Fig. 8).

Table 2

Weakening of the solar ray illuminating the zenith of the sky during twilight

Least distance of the incident solar rays from the Earth’s surface $y$	Thickness of air traversed by the solar ray, reduced to normal conditions	Thickness of ozone traversed by the solar ray, reduced to normal conditions	Weakening due to molecular scattering	Weakening by ozone	Total weakening $I/I_0$	$\log_{10}\dfrac{I}{I_0}$
$0\ \mathrm{km}$	$568\ \mathrm{km}$	$8.2\ \mathrm{cm}$	$0.0072$	$0.297$	$0.0021$	$0.32-2$
$10\ \mathrm{km}$	$162\ \mathrm{km}$	$8.5\ \mathrm{cm}$	$0.245$	$0.280$	$0.069$	$0.84-1$
$20\ \mathrm{km}$	$47\ \mathrm{km}$	$9.1\ \mathrm{cm}$	$0.67$	$0.256$	$0.17$	$0.23$
$30\ \mathrm{km}$	$13.4\ \mathrm{km}$	$4.4\ \mathrm{cm}$	$0.89$	$0.518$	$0.46$	$0.66$
$40\ \mathrm{km}$	$4.0\ \mathrm{km}$	—	$0.96$	$0.95$	$0.90$	$0.95$

Since both the density of the air and the concentration of ozone vary with altitude, the transparency of the atmosphere for a horizontal ray also changes with altitude. Brikard and Kastler^40 calculated the attenuation for atmospheric layers every 10 km. Their results are given in Table 2. The quantity \(I/I_0\), which determines the transparency of the atmosphere for rays of the Sun coming from below the horizon and illuminating the sky at the observer’s zenith, is presented in Fig. 15 as a function of the altitude \(y\). The lower 15–20 km of air are very little transparent for light of \(\lambda = 0.59\,\mu\); only from an altitude of 25–30 km does the atmospheric attenuation of the light become small. In reality, the attenuation by the lower layers is still greater because of the absorption of light by water vapor and aerosol particles (water droplets, dust particles, ice crystals). At the same time, however, there is, of course, no sharp boundary between a transparent and an opaque atmosphere, as was assumed in their calculations by Carpio and Still^37; the transparency changes very rapidly with altitude over a large interval: 20–25 km. From this point of view, the result obtained by Carpio and Still—that the thickness of the sodium layer may amount to 9 km—should be regarded as illusory. Even if all the sodium were concentrated in an infinitely thin layer, the noticeable decrease in the intensity of the yellow line would occur over a comparatively large interval of time, corresponding to a change in the altitude of the Earth’s shadow by tens of km, as follows from the course of atmospheric transparency (Fig. 15). Moreover, from this point of view the rapid extinction of the yellow line (by a factor of 100 in several minutes), which was obtained from Bernard’s observations^20 (see Fig. 12), appears atypical. Vuks and Chernyaev, who were the first to observe the sodium line in twilight light, did not find such a rapid decrease. According to the data of Brikard and Kastler, obtained in the period 1940–1944, there is likewise no such rapid fall in the brightness of the yellow line. These authors write^40: “Bernard reported that the intensity of the yellow line remains almost unchanged for twenty minutes during twilight, and then suddenly falls, in scarcely 1 minute, by almost a factor of 100. A qualitative examination of our photographs and our first photometric measurements unanimously indicate that during evening twilight the line weakens gradually, and during morning twilight it increases progressively.”

Fig. 15. Attenuation of a ray of \(\lambda = 0.59\,\mu\), passing at different altitude \(y\) above the Earth’s level under conditions of twilight illumination of the sky (attenuation of the ray due to molecular scattering and absorption by ozone).

Having data on the transparency of the atmosphere for \(\lambda = 0.59\,\mu\) for layers of air at different heights (Table 2), one can calculate the theoretical variation of the brightness of the yellow line as a function of the zenith distance of the Sun \(Z_{\odot}\), assuming that sodium is concentrated in a thin layer at some specified height \(h\). For different \(h\), of course, different brightness variations will be obtained. Bricaud and Kastler\({}^{40}\) calculated three curves for \(h = 80\) km (60 km), \(h = 90\) km (75 km), and \(h = 100\) km (100 km); in parentheses are indicated the heights with allowance for the refraction of the solar rays on their path through the atmosphere.

These three curves are shown in Fig. 16, where along the abscissa are plotted the zenith distances of the Sun \(Z_{\odot}\), and along the ordinate—the logarithms of brightness \(\lg I\). The values indicated near the curves, \(y = 0\) km, \(y = 10\) km, \(y = 20\) km, \(y = 30\) km, and \(y = 40\) km, refer to points on the curves marked by the corresponding arrows, and explain details of the results of the calculations. For example, if a thin sodium layer is considered to be located at a height \(h = 90\) km (75 km), then its cross-section at \(Z_{\odot} = 99^{\circ}.12\) is excited, as is determined by the geometrical picture of the phenomenon, by a solar ray passing at the closest distance from the earth \(y = 10\) km. If the sodium layer is assumed to be at a greater height, \(h = 100\) km, then at the same moment it is illuminated by a ray passing higher, \(y = 20\) km, and therefore less attenuated, as a result of which the brightness of the yellow line has a correspondingly greater value.

Fig. 16. Theoretical variation of the brightness of the yellow line of the twilight sky with change in the zenith distance of the Sun \(Z_{\odot}\) under different assumptions concerning the height of the sodium layer.

Bricaud and Kastler\({}^{40}\) consider that, purely qualitatively, the curve for \(h = 90\) km (75 km) is closest to the actual data on the change in brightness of the yellow line in the twilight sky.

It is interesting to note that in the interval of \(Z_{\odot}\) from \(96^{\circ}30'\) to \(97^{\circ}\) the intensity of the yellow line hardly changes. Thus, the brightness of the \(D\)-line in the daytime sky may be assumed to be approximately equal to its brightness at \(Z_{\odot} = 96^{\circ}30'\). From this one can draw conclusions about the conditions under which the yellow line could be observed in the spectrum of the daytime sky.

In the following paragraph we shall see that the question of the height of the sodium layer can be treated somewhat differently from the way it was done above, taking into account a possible mechanism of excitation of the \(D\)-lines.

7. On the Mechanism of Excitation of the Sodium Glow in the Stratosphere

The regular dependence of the brightness of the \(D\)-lines on the zenith distance of the Sun during twilight makes it very probable to suppose that, in the present case, we are dealing with optical resonance. In this case the height of the luminous Na layer can be calculated in the same way as was set forth in the preceding paragraph.

Where can sodium vapor come from in the upper layers of the atmosphere? Bernard was the first to point out that the source of sodium in the atmosphere may be droplets of seawater, scattered by waves and carried from the ocean surface by the wind[^41]. Evaporating, these droplets give the finest particles of NaCl, some of which rise into the higher layers of the atmosphere owing to the vertical mixing of the air. Sodium vapor is formed by evaporation from the surface of grains of common salt.

It is quite unclear whether solid NaCl particles can rise in the atmosphere to a height of many tens of km. But if one admits the presence of NaCl at the corresponding heights, then the formation of Na atoms can occur, for example, by photodissociation of NaCl molecules by the ultraviolet rays of the Sun. The products of photodissociation may be excited Na atoms, which then spontaneously emit light.

Thus, another mechanism is possible for the glow of Na in the atmosphere, one not connected with resonance fluorescence. The possibility of exciting the twilight glow of the atmosphere by preliminary photodissociation by solar rays was first indicated by Götz[^42] (in 1935) in connection with the red twilight emission of the sky \(\lambda = 6300\ \text{Å}\). But the short-wavelength ultraviolet radiation of the Sun, capable of causing dissociation, is absorbed entirely either by \(O_2\) molecules or by \(O_3\) molecules (this will be considered in more detail below). In this case the height of the layer of the atmosphere opaque to the Sun’s rays responsible for the Na glow is considerably increased, and the height of the luminous sodium vapors calculated from twilight data likewise correspondingly increases. Götz[^43] pointed out that in this way one can reconcile the twilight heights found by Bernard (if they are appropriately corrected) with the nighttime heights found by Cabannes, Dufay, and Gauzit from Garrigue’s measurements (see § 6).

Vegard came to the same conclusion in 1940 on the basis of a study of a large number of spectrograms obtained by him in Oslo[^44]. We quote verbatim Vegard’s very brief communication on this question. “With the aid of a small high-speed spectrograph we photographed spectra of the twilight sky, partly at the zenith and partly near the horizon. If we suppose, following Bernard, that the radiation of the yellow line is determined by the shadow of the Earth formed by the visible rays of the Sun, then observations at the horizon give, for the height …”

effective emitting layer than that obtained from spectra taken at the zenith ($45$ km).

It may be supposed, however, that the yellow line is excited by some strong radiation absorbed in the atmosphere—possibly by the Sun’s ultraviolet rays—and that the atmosphere below a certain height $H_s$ acts as a screen for the exciting solar rays; then this screening height can be found from the condition that spectra taken both at the zenith and near the horizon must give one and the same upper height $H_u$ for the radiation of the yellow line*).

Observations in Oslo gave, for the effective screening height, $H_s = 55$ km, and for the upper limit of effective excitation, $H_u = 115$ km.

It is interesting to note that the screening height coincides precisely with the region of relatively large ozone concentration.

Having obtained a height of $115$ km for the Na glow, Vegard especially emphasizes that, thus, according to the Oslo observations, the layer emitting the yellow line is situated in the lower part of the region of auroral luminosity. (As is known, the height of auroras, owing to the local character of their luminosity in the sky, can be determined by baseline observations—simultaneously from two stations; it has been established that the lower edge of auroras does not descend below approximately $90$ km.)

It should be noted that in the spectra of auroras proper the yellow line $0.59\,\mu$ has never been observed.

Let us summarize the preliminary results of the determination of the height $h$ of the layer emitting the sodium $D$-lines.

Regarding the twilight glow as resonance fluorescence of Na vapors excited by sunlight, Bernard found $h = 60$ km; Carno and Stille found $h = 69$ km and a layer thickness of $9$ km ($h_1 = 69$ km, $h_2 = 78$ km); Brikart and Kastler found $h = 90$ km (or $75$ km, allowing for refraction). Vegard obtained $h = 115$ km, considering that the glow is excited by the Sun’s ultraviolet rays. From observations of the spectra of the night-sky glow, Cabannes, Dufay, and Gauzit found $h = 130$ km.

As we already know, the intensity of the $D$-lines in twilight light and in night-sky spectra differs by at least two orders of magnitude. Moreover, whereas in twilight the brightness of the yellow line changes rapidly in accordance with the change in the Sun’s zenith distance, at night, on the contrary, no appreciable changes in the brightness of the yellow line occur. Finally, different heights are obtained for the luminous layers at night ($130$ km) and during twilight ($60$–$115$ km). All this makes it quite probable that the mechanism exciting the Na glow at night and during twilight is different. For the nocturnal radiation, excitation by electron impact is possible,

*) Emphasized by Vegard.

and also by collisions of the second kind. The foremost authority on questions of the physics of the upper layers of the atmosphere, Chapman, considers^45 the excitation of luminescence by electron impact unlikely and assumes that excitation occurs by collisions of the second kind.

The presence in the upper layers of the atmosphere of oxygen in the form of O or O\(_3\) determines the occurrence of reactions that limit the lifetime of free Na atoms, namely,

\[ \mathrm{Na} + \mathrm{O} + \mathrm{M} = \mathrm{NaO} + \mathrm{M} \tag{1} \]

and

\[ \mathrm{Na} + \mathrm{O}_3 = \mathrm{NaO} + \mathrm{O}_2, \tag{2} \]

where M denotes a third body, usually N\(_2\) or O (the first reaction is evidently possible only in triple collisions). The restoration of Na atoms takes place owing to the reaction

\[ \mathrm{NaO} + \mathrm{O} = \mathrm{Na} + \mathrm{O}_2. \tag{3} \]

As a result of reaction (3), an excited Na atom is obtained. In this reaction the Na atoms act, as it were, as an intermediary in the recombination of oxygen: \(\mathrm{O} + \mathrm{O} = \mathrm{O}_2\).

The enormous energy stored by the atmosphere during the day through absorption of the Sun’s ultraviolet radiation, which causes the dissociation of oxygen, is partly preserved throughout the night and can serve as a source of energy emitted by the atmosphere in the form of luminescence (the glow of the night sky). The direct process of recombination \(\mathrm{O} + \mathrm{O} = \mathrm{O}_2\) is possible only in triple collisions, the probability of which decreases with height in proportion to the air density. Reaction (3) occurs in ordinary double collisions and may serve, in Chapman’s opinion, as the cause of the sodium glow at night.

Sodium can also give compounds with nitrogen: Na\(_3\)N and NaN\(_3\). But from the spectra of the glow of the night sky and of auroras it is known that in the upper layers of the atmosphere there are no nitrogen atoms N, but only N\(_2\) molecules; consequently, reactions of sodium with nitrogen are impossible.

Finally, one should also point out a completely different view, expressed by Cabannes, Dufay, and Gauzit concerning the excitation of the \(D\)-lines in the spectra of the night sky.^24 Sodium is a constituent of meteoric matter. When a meteor flies through the atmosphere, which, as is known, occurs at a speed of tens of km/sec, favorable conditions are created for the evaporation of sodium and its subsequent intense glow. Accordingly, the authors mentioned believe^21 that the glow of sodium may be “radiation accompanying the fall of meteors; in this case each sodium atom may undergo excitation followed by emission eight thousand times before it finally leaves the game.” By their estimate, meteors can deliver up to 2500 sodium atoms per 1 sec. per 1 cm\(^2\).

On this point Chapman writes^45: “Although meteors may be an important source of atmospheric sodium, there is nevertheless no particular reason to suppose that sodium glows only during the fall of meteors.”

We shall have to return to the question of the meteoric origin of sodium in § 8.

Thus, five different possible mechanisms have been indicated for exciting the glow of the sodium \(D\)-lines in the upper layers of the atmosphere:

1. Resonance glow, excited by the rays of the Sun (visible spectrum).
2. Photodissociation of NaCl molecules by the ultraviolet rays of the Sun, with the formation of excited Na atoms.
3. Excitation by electron impacts.
4. Excitation by impacts of the second kind.
5. Luminescence of the products of meteor evaporation during their flight through the upper layers of the atmosphere.

8. WHENCE COMES SODIUM IN THE UPPER LAYERS OF THE ATMOSPHERE

When Dufay, in 1933, first “uttered” the word sodium in connection with the yellow line in the spectra of the night-sky glow[^8], he, of course, had no factual data that would allow him to suppose that sodium vapor is a constituent part of the air of the Earth’s atmosphere. He then pointed out that the radiation of the \(D\)-lines might belong to interstellar sodium. However, the bright flash of the yellow line in the twilight sky at certain zenith distances of the Sun, discovered in 1936 by M. F. Vukos and V. I. Chernyaev1, clearly indicates the presence of sodium atoms as part of the Earth’s atmosphere.

Various hypotheses have been advanced concerning the origin of sodium in the atmosphere, and all of them may be divided into two main groups: some assume that sodium enters the upper layers of the atmosphere from outer space; others consider its origin to be terrestrial.

In 1938 Fabry indicated[^46] that the source of sodium in the atmosphere may be interstellar sodium. In order to form a clearer judgment of the grounds for such a hypothesis, it is necessary to recall, at least briefly, those data which characterize the presence of matter in interstellar space.

The light of all celestial bodies has a continuous spectrum with a greater or lesser number of absorption lines arising as a result of absorption along the path of the rays. In the case of observations of stars, this path consists of three parts: the propagation of light through the atmosphere of the star, lasting tenths of a second; the path through interstellar space, lasting centuries; and the path through the Earth’s atmosphere (thousandths of a second). The Doppler effect makes it possible, without particular difficulty, to separate absorption in stellar atmospheres from that in the Earth’s atmosphere. The magnitude of the radial velocity of the star determines the identical displacement of all absorption lines of stellar origin. If

in the spectrum of a star there are lines whose Doppler shift clearly differs from the shift of all the other lines, then we may suspect that these lines, if they are not telluric, are caused by the absorption of light by interstellar matter. Individual groups of stellar lines may even give different and variable values of radial velocity, as, for example, in the case of spectroscopic binaries, and nevertheless lines of interstellar origin will differ from them by an unchanging Doppler shift, different in magnitude from that of the other lines. They also differ in appearance, being narrow and sharp, whereas stellar lines are usually diffuse.

The first such stationary lines in the spectrum of a star with variable radial velocity were discovered by Hartmann in 1904 in the spectrum of $\delta$ Orionis, whose large velocity oscillations had been discovered as early as 1900 by Deslandres. The velocities measured from the hydrogen lines varied within the limits from $+133$ to $-66\ \text{km/sec}$; the lines of ionized calcium $\mathrm{Ca}^{+}$ (the lines $H$ and $K$) gave a constant velocity of $+16\ \text{km/sec}$. Moreover, the calcium lines were narrow and sharp, while the lines of the Balmer series were broad and diffuse. This indicated the existence, in the space between the star and us, of “clouds of ionized calcium.”

Even earlier, in 1901, in Nova Persei, features were found which had to be explained in the same way. While almost all the lines showed very large changes in wavelength, the line $K$ was narrow, of unchanging appearance, and indicated a constant velocity of $+7\ \text{km/sec}$. Subsequently many other stellar spectra were discovered that had calcium lines independent of the star. Spectroscopic binaries, possessing large changes in radial velocity, are especially revealing. For example, in 1909 Slipher reported on $\beta$ Scorpii, whose radial-velocity oscillations amount to $240\ \text{km/sec}$, but whose line $K$ is narrow and stable. All this proved the presence of ionized calcium throughout all space. Later it was shown that in the spectra of stars more distant from us the $\mathrm{Ca}^{+}$ lines are expressed more strongly.

For 15 years the $\mathrm{Ca}^{+}$ lines were the only ones whose interstellar origin seemed beyond doubt. In 1919 Heger (Miss Heger) established the presence of the neutral sodium lines, the doublet 5890 and 5896. Later Adams and Dunham discovered the ultraviolet sodium lines 3302.38 Å and 3302.98 Å (the second doublet of the principal series; see the diagram of sodium levels in Fig. 17). They also discovered lines of ionized titanium. Dunham discovered the neutral potassium line 7699.01 Å (one of the lines of the first doublet of the principal series, the other component of which is masked by the telluric band $A$). Finally, lines have been discovered which cannot be identified. These lines have a different character from those indicated earlier: they are broad.

Probably each of them is the head of an unresolved band. This kind of line suggests molecular spectra; attempts at identification were made, but so far without definite results. A rather improbable hypothesis was put forward concerning microscopic crystals which, at the very low temperature of cosmic space (according to calculations, a black body placed in interstellar space would have a temperature of 3° K), possess absorption bands similar to those indicated above (Vegard).

As for Na and Ca atoms, according to measurements they are distributed uniformly throughout the whole galaxy—the intensity of the lines in the spectra of different stars increases in a regular manner with the distance to the stars[^46]. The distribution in space of Na atoms is approximately the same as that of Ca⁺. The absolute magnitude of the absorption by sodium appears to be somewhat greater than that by Ca⁺. Their velocities relative to the Sun are small; they are smaller than those of many stars. The total number of Na atoms is extremely small. The absorption of light by interstellar sodium is approximately the same as that of a layer of Na vapor 0.01 mm thick at atmospheric pressure. If this layer is imagined as expanding along a cylinder of unit cross-section until its thickness reaches several thousand parsecs, then one may form a visual judgment of the concentration of sodium atoms in interstellar space. From dynamical considerations one can estimate the upper limit of the density of interstellar matter: it is obtained as equal to \(10^{-24}\ \text{g}/\text{cm}^3\). In the composition of this matter, which contains various elements, the fraction of sodium should not be large. On the basis of these data, one may try to make a rough estimate of the amount of sodium which could have accumulated in the terrestrial atmosphere through chance encounters of the Earth with Na atoms during its motion in cosmic space.

Fig. 17. Scheme of sodium levels.

Taking the density of interstellar sodium to be \(10^{-26}\ \text{g}/\text{cm}^3\), we obtain \(10^{11}\) Na atoms per \(1\ \text{km}^3\). The cross-sectional area of the Earth (with the atmosphere) is approximately \(10^8\ \text{km}^2\), and the length of the Earth’s or—

to be \(10^9\) km. Thus, in one year the Earth will encounter on its path \(10^{28}\) atoms of Na. Taking the lifetime of the Earth (after the appearance of the atmosphere) to be \(10^8\) years, we obtain in all \(10^{36}\) atoms, or \(10^{19}\) atoms over each \(\mathrm{cm}^2\) of the Earth’s surface. Of course, it is possible that only a small part of this amount of sodium is retained in the atmosphere. In § 9, where we shall consider the question of absolute measurements of the intensity of the sodium \(D\)-lines in the night and twilight sky, it will be shown that, generally speaking, quantities of sodium of this order are sufficient to explain the observed brightness of the glow.

Another hypothesis, assuming an extraterrestrial origin of sodium in the atmosphere, was put forward by Cabannes, Dufay, and Gauzit, who believe that sodium in the stratosphere cannot be of terrestrial origin, since it seems improbable that sodium itself or substances containing sodium (for example, NaCl) could penetrate from the troposphere to heights of the order of 100 km. In their opinion, sodium in the high layers of the atmosphere originates from meteors and cosmic dust, which continually fly into the atmosphere\(^{21,24}\).

Objections to such an assumption were expressed by Bernard. Here is what Dufay and Bernard write on this matter\(^{36}\).

“Cabannes, Dufay, and Gauzit consider that the yellow line of the night-sky glow may arise as a glow accompanying the fall of meteors and cosmic dust. This hypothesis, already expressed earlier by one of us\(^{31}\), encounters the absence of sodium lines in the spectra of aurorae. In other words, it is a fact that excitation of this line does not occur precisely at those heights where a large number of meteors already die out. On the other hand, this hypothesis hardly permits a simple explanation of the circumstance that twilight glow is bounded above by a height of 60 km. Finally, it should be pointed out that stony meteors, containing MgO in large proportion and sometimes CaO and \(\mathrm{Al_2O_3}\), are relatively poor in alkali metals.”

Let us note that the absence of sodium lines in the spectra of aurorae also creates difficulties for Fabry’s hypothesis concerning the occurrence of sodium in the atmosphere from interstellar sodium.

According to Bernard, the terrestrial origin of atmospheric sodium is more probable\(^{41}\). He points to the possibility of penetration into the upper layers of the atmosphere by particles of salt of marine origin. These particles, being very hygroscopic, may, on their way through the atmosphere, serve as condensation nuclei for the so-called nacreous clouds observed by Størmer between 20 and 30 km.

Dufay and Bernard\(^{36}\) also indicate another possible way for sodium to enter the atmosphere with particles of terrestrial origin, namely, by volcanic activity. In particular, during strong volcanic eruptions, highly comminuted matter may be ejected into the atmosphere directly to heights of 10 to 30 km. As a result, a very high “roof” of extremely fine dust may form over a large part of the terrestrial globe, which considerably

SODIUM IN THE STRATOSPHERE

increases the absorption of light by the atmosphere for long periods of time.

Dejardin and Bernard36 refer to the fact that, as is known (chiefly from the systematic observations of the Smithsonian Institution Astrophysical Observatory47), between 1883 and 1914 four long-lasting disturbances—lasting from 2 to 5 years—of atmospheric transparency and of the intensity of the Sun’s rays were observed, each beginning with a phase of intense volcanic activity. It is permissible to think that, even apart from such exceptional periods, volcanic activity may be a constant source of dusting of the atmosphere. But the products of eruptions usually contain appreciable quantities of substances containing alkali metals. The blocks ejected during eruptions contain on average 3.8% \(Na_2O\). Molecules of \(Na_2O\) may dissociate in the upper layers of the atmosphere as a result of collisions of the second kind with metastable excited nitrogen molecules, whose presence in the upper layers of the atmosphere is known from the spectra of the night-sky glow.

An entirely new suggestion concerning the origin of sodium was made in 1940 by Vegard44. He considers it possible that sodium is present in the corpuscular radiation of the Sun and enters the atmosphere as a result of eruptions on the Sun. “It is possible,” writes Vegard44, “that, in addition to the previously discovered hydrogen showers, there are sodium showers in the atmosphere, likewise coming from the Sun.”

In this connection one should dwell on Vegard’s very interesting 1939 report on his discovery of hydrogen lines in the spectra of aurorae. This discovery of Vegard’s has a direct bearing on two important problems concerning the structure of the high layers of the atmosphere: the presence of light gases in the composition of the upper layers of air, and the origin of the so-called noctilucent clouds at an altitude of 82 km.

Until comparatively recently it was considered beyond doubt that the composition of the air changes at great heights in the direction of an increase in the percentage content of light gases. According to the generally known formulas of static equilibrium of the atmosphere, the decrease of gas density with height should occur in the atmosphere the more rapidly the greater the molecular weight of the given gas, and it was believed that the high layers of air consist predominantly of hydrogen. But when the deciphering of the lines in the spectra of aurorae and of the night sky was for the most part completed, it turned out that hydrogen lines are not detected. It turned out that there is no hydrogen in the composition of the upper layers of the atmosphere. Special photographs of spectra were taken with enormous exposures, when even the weak lines of auroral spectra were overexposed, but there was not a trace of hydrogen lines.

At the same time, however, certain circumstances indicated the possibility of the presence of hydrogen in the high layers of the atmosphere, even if in small quantities. Vegard himself, who perhaps more than others

engaged in searches for hydrogen lines in the spectra of auroras, in 1933 proposed the presence of hydrogen in the upper layers of the atmosphere in connection with an explanation of the occurrence of noctilucent clouds.^48 These clouds, which are sometimes observed at night, are located, according to baseline measurements, at so great an altitude—82 km—that it is difficult to admit the possibility of penetration into these layers by water vapor from the troposphere. On the other hand, the constancy of the altitude of noctilucent clouds is striking: measurements always give, with great accuracy, one and the same altitude, 80–85 km. The presence in the upper layers of the atmosphere of dissociated (atomic) oxygen served as the basis for Vegard’s supposition that molecules of $\mathrm{H_2O}$ may be formed by the combination of O atoms with hydrogen existing at those altitudes, if not always, then at least from time to time, during periods of increased solar activity.

Fig. 18. Registration record of the spectrum of auroras, on which hydrogen lines were discovered for the first time ($H_\alpha$—$\lambda = 6563$ Å and $H_\beta$—$\lambda = 4861$ Å). Taken by Vegard from Oslo on October 18, 1939.

In this connection Vegard, with remarkable persistence, continued to “hunt” for the hydrogen lines. It was advantageous to photograph auroral spectra soon after strong eruptions on the Sun.

Such times of observation do not present special difficulties in practice, since strong eruptions on the Sun, accompanied by the intrusion of powerful corpuscular radiation from the Sun into the Earth’s atmosphere, are known to produce bright auroras (and, in addition, magnetic storms and disturbances of radio communication).

On October 18, 1939, Vegard^49 obtained in Oslo the spectrum of an aurora (arc), a microphotogram of which is reproduced in Fig. 18. In addition to the most intense oxygen lines $\lambda = 5577$ Å and $\lambda = 6300$ Å and other characteristic components of auroral spectra, the microphotogram clearly shows the line $\lambda = 6560$ Å, which within the errors of measurement coincides with the hydrogen line $H_\alpha$ ($\lambda = 6563$ Å), and another line, 4860 Å, which corresponds to the hydrogen line $H_\beta$ ($\lambda = 4861$ Å).

This discovery makes Vegard’s supposition quite plausible: that hydrogen, at times, during periods of increased solar activity, appears in the upper layers of the atmosphere, arriving there from the Sun. Hydrogen is not preserved for long; it combines with oxygen (in the form of O atoms or ozone molecules), forming molecules of water vapor.

The hypothesis stated above, due to Vegard, on the solar origin of sodium in the atmosphere is analogous to what was said about hydrogen. “It is possible,” writes Vegard \(^{49}\), “that, in addition to the hydrogen lines previously detected, there are also sodium lines in the atmosphere, likewise coming from the Sun. The hydrogen lines, together with sodium and atmospheric oxygen, may be the cause of noctilucent clouds.”

9. ABSOLUTE MEASUREMENTS OF THE BRIGHTNESS OF THE YELLOW LINE

Absolute measurements were carried out both for the yellow line of the night sky (Cabannes–Dufay–Gauzit \(^{21,24}\), 1938) and for the yellow line of the twilight sky (Brikard–Kastler \(^{40}\), 1943). The most interesting question that one could try to resolve on the basis of the results of absolute brightness measurements consists in determining the amount of atomic sodium in the atmosphere. From this point of view the twilight measurements are especially important. As we saw in § 7, for the nocturnal glow of sodium three different excitation mechanisms were indicated: electron impacts, collisions of the second kind, and emission during the flight of meteors. In none of these cases do we know either the luminous efficiency of the emission or the intensity of the exciting factor, and determination of the absolute number of Na atoms participating in the process is impossible.

The situation is different for the twilight glow of sodium. True, here too two different modes of excitation are possible (both under the action of sunlight): optical resonance and photodissociation with the production of excited Na atoms. But for one of them (resonance emission) both the luminous efficiency and the intensity of the exciting solar rays may be regarded as sufficiently reliably known. Thus, only in this case can we directly estimate the number of Na atoms participating in the atmospheric emission. Moreover, recently obtained data make it certain that the excitation of the twilight glow of sodium occurs by optical resonance (see § 12).

Brikard and Kastler \(^{40}\) photographed on one and the same spectrogram, with an unchanged arrangement of the apparatus, the spectrum of the twilight sky and the spectrum of a Philips sodium lamp (Philips Philora lamp), under a fixed power-supply regime. To obtain the required weakening of the light from this lamp, it was placed inside a light-tight chamber with a round aperture of 2 mm, through which a white diffusing surface was illuminated (paper with an albedo of 0.8 and a magnesium screen with an albedo of 0.99) at a distance of 2.37 m. The illuminance of the white surface, as measured with a standard lamp, under these conditions (for the white paper) proved to be \(E = 3.72 \cdot 10^{-6}\) phot, which corresponds to a brightness

\[ B = 0.8 \frac{E}{\pi} = 0.96 \cdot 10^{-6}\ \text{candles}/\text{cm}^2 . \]

When this screen was photographed with an exposure of 2 minutes, numerous spectrograms gave a \(D\)-line 4 times more intense than the same line in the twilight spectrum (at a zenith distance of \(6^\circ 30'—7^\circ\)) with the same exposure.

In comparing intensities under these conditions there is one difficulty: the yellow line in the spectrum of the twilight sky is obtained against the background of a bright continuous spectrum, whereas from the sodium lamp an isolated line is obtained, without background. Brücker and Kastler\(^{40}\) drew attention to this. They report that “we studied the effect of a variable continuous background on the blackening of the \(D\) line of a Philora lamp,” but they give no further data on this rather delicate experimental question.

Fig. 19. Comparison of the brightness of the \(D\)-line of the twilight sky with the brightness of the \(D\)-line of a sodium lamp. \(A\)—recording microphotogram of the sky spectrum; \(B\)—the same for a sodium lamp; \(C\)—the same for a sodium lamp \(+\) continuous spectrum.

Brücker and Kastler illustrate the results of their photographs with the microphotograms reproduced in Fig. 19. Here \(A\) is a microphotogram of the spectrum of the twilight sky on 29 October 1943, exposure 2 minutes; \(B\) is a microphotogram of the spectrum of a Philora lamp, exposure 2 minutes; \(C\) is a Philora lamp \(+\) continuous spectrum, exposure 2 minutes.

From these measurements it follows that the brightness of the yellow twilight sodium line is equal to

\[ B = 0.24 \cdot 10^{-6}\ \text{candles}/\text{cm}^2,\ \text{or photons}/\text{steradian}. \]

For the wavelength \(\lambda = 0.59\,\mu\), a brightness of \(10^{-6}\ \text{candles}/\text{cm}^2\) corresponds to an emissive power of

\[ 2 \cdot 10^{-2}\ \frac{\text{erg}}{\text{sec}\cdot\text{cm}\cdot\text{steradian}} . \]

Thus, the energy brightness of the yellow line is

\[ B' = 0.48 \cdot 10^{-2}\ \text{erg}/\text{sec}\cdot\text{cm}^2\cdot\text{steradian}. \]

This brightness corresponds to the moment of maximum intensity of the yellow line in the twilight sky (the Sun’s depression below the horizon from \(6^\circ 30'\) to \(7^\circ\)). With time the brightness, as is known, rapidly decreases.

For the brightness of the yellow line in the spectra of the night-sky glow, Cabannes, Dufay, and Gauzit obtained \(^{21,24}\)

\[ B_n = 5.2 \cdot 10^{-6}\ \text{erg}/\text{sec}\cdot \text{cm}^2 \cdot \text{steradian}, \]

which is almost a thousand times smaller than the twilight value.

The measured brightness of the yellow line in the twilight sky corresponds to from \(1\) to \(2 \cdot 10^{10}\) transitions \(^{2}P \to {}^{2}S\) (see the scheme of the levels of Na atoms, Fig. 17). This quantity was measured in a region of the sky at an altitude of \(22^\circ\) above the horizon. Assuming that at the zenith the brightness is 2 times smaller and that the ratio of the intensities \(D_2 : D_1\) is equal to 2, Brückner and Kastler finally obtained:

\[ B_1 = 0.8 \cdot 10^{-3}\ \text{erg}/\text{sec}\cdot \text{cm}^2 \cdot \text{steradian}\quad \text{for the line } D_1, \]

\[ B_2 = 1.6 \cdot 10^{-3}\ \text{erg}/\text{sec}\cdot \text{cm}^2 \cdot \text{steradian}\quad \text{for the line } D_2. \]

We now have sufficient data to determine the number of sodium atoms participating in the radiation of the yellow line during twilight.

10. DETERMINATION OF THE AMOUNT OF SODIUM IN THE ATMOSPHERE

The brightness of resonance luminescence is proportional to the intensity of the exciting light. To determine the amount of atmospheric sodium from the already known brightness of its glow, it is necessary to know the intensity of the solar rays of wavelength \(\lambda = 0.59\,\mu\), illuminating the high layers of air during twilight.

According to Unsöld \(^{50}\), the emissive power of the Sun in the wavelength interval \(\Delta\lambda = 1\ \text{cm}\) in the region \(\lambda = 0.59\,\mu\) is

\[ F_\lambda = 27 \cdot 10^{14}\ \text{erg}/\text{sec}\cdot \text{cm}^3. \]

At the Earth–Sun distance, the extra-atmospheric value of the energy illumination is

\[ E_\lambda = F_\lambda \cdot \omega = \pi F_\lambda \left(\frac{R}{\rho}\right)^2 = 1.92 \cdot 10^{10}\ \text{erg}/\text{sec}\cdot \text{cm}^3 \]

for the interval \(\Delta\lambda = 1\ \text{cm}\). Here \(\omega\) is the solid angle under which we see the Sun, \(R\) is the radius of the Sun, and \(\rho\) is the radius of the Earth’s orbit.

These data refer to the continuous spectrum of the Sun in the region \(\lambda = 0.59\,\mu\). Speaking of resonance excitation of the \(D\)-lines by solar rays, we must also take into account that within the width of these lines the intensity of the solar radiation is much smaller, since we are dealing precisely with Fraunhofer lines, caused by absorption in the solar atmosphere. The data necessary for introducing the corresponding corrections are found in Allen’s work \(^{51}\).

Determination of the intensity of the solar radiation at the center of the Fraunhofer lines \(D_1\) and \(D_2\) may contain a large error owing to the influence of light scattered inside the spectrograph (reflection

on the surfaces of the lenses and prisms). At the center of absorption lines the light intensity is less than \(1/10\) of the intensity of the adjacent regions of the continuous spectrum, and therefore the effect of parasitic light can be especially noticeable. To introduce

Table 3

Intensity at the center of the sodium \(D\)-lines and their width at the center and at the edge of the solar disk (according to Allen’s measurements)

Line	Observed intensity at the center /%/%/	Corrected intensity at the center /%/%/	Width /m Å/
\(D_1\) /5896 Å/ center . . . . .	14.3	7.2	560
\(D_1\) /5896 Å/ edge . . . . .	15.0	6.0	530
\(D_2\) /5890 Å/ center . . . . .	11.6	6.6	770
\(D_2\) /5890 Å/ edge . . . . .	12.6	6.0	740

Table 4

Full width of the sodium \(D\)-lines at various values of the relative intensity \(r\) (according to Allen’s data)

\(r\)	\(D_1\) (5896 Å), center of Sun, Å	\(D_1\) (5896 Å), edge of Sun, Å	\(D_2\) (5890 Å), center of Sun, Å	\(D_2\) (5890 Å), edge of Sun, Å
0.10	0.08	0.08	0.10	0.10
0.20	0.16	0.14	0.20	0.19
0.30	0.23	0.20	0.30	0.27
0.40	0.31	0.26	0.41	0.35
0.50	0.39	0.33	0.52	0.45
0.60	0.48	0.43	0.67	0.59
0.70	0.62	0.57	0.87	0.80
0.80	0.82	0.80	1.15	1.12
0.85	0.98	0.97	1.38	1.38
0.90	1.23	1.23	1.70	1.75
0.95	1.73	1.73	2.4	2.5
0.98	2.5	2.5	3.5	3.7

the necessary corrections, Allen\(^{51}\) photographed the spectrum of the Sun with the same spectrograph immediately after sunrise in order to obtain the absorption lines of water vapor, namely \(\lambda\lambda\) 5900.048 Å, 5919.059 Å, and 5919.647 Å, with respect to which it is known that at the center of the line they produce complete absorption (with the ray passing almost horizontally through the atmosphere). The exposure was made with a 3-prism spectrograph, dispersion 1.5 Å/mm. The ratio of the intensity at the center of the \(D_1\) and \(D_2\) lines to the intensity of the adjacent continuous spectrum of the Sun was measured, as well as the width of both absorption lines at the center and at the edge of the solar

disc. The results are given in Table 3, where the observed and corrected intensities at the center of the lines are also given. It is seen from the table that the instrumental correction for the line \(D_1\) is almost \(1 \frac{1}{2}\) times greater than for the line \(D_2\), which is due to its smaller width. (Using, for verification, the three above-mentioned water-vapor absorption lines, Allen found a dependence of the magnitude of the instrumental correction on the line width.)

The contour of the Fraunhofer lines \(D_1\) and \(D_2\) is determined by the values of the full width of the lines for different values of the ratio \(r\) of the intensity at a given place in the line to the intensity of the adjacent continuous spectrum (Table 4).

On the basis of these data on the radiation of the Sun within the lines \(D_1\) and \(D_2\), and taking into account that the width of the spectral interval responsible for the excitation of the resonance glow of sodium vapor amounts to hundredths of an Å, we may take for the relative intensity of the radiation of the Sun at the center of the \(D\) lines the value \(0.07\). Consequently, for the extra-atmospheric energy illumination produced by the solar rays in the spectral region of interest to us, we obtain the value

\[ E_\lambda = 0.07 \cdot 1.92 \cdot 10^{10} = 1.34 \cdot 10^9 \ \mathrm{erg/sec \cdot cm^3} \]

for the interval \(\Delta \lambda = 1\ \mathrm{cm}\).

If \(N\) is the total number of sodium atoms in a unit volume, and \(\Delta N\) is the number of atoms excited by our radiation in 1 sec, then, as is known,

\[ \frac{\Delta N}{N} = b \cdot E_\nu, \]

where \(E_\nu\) is the spectral illumination per unit frequency produced by the exciting radiation, and \(b\) is the probability of excitation (Einstein coefficient), with

\[ b = \frac{1}{\tau} \cdot \frac{g_2}{g_1} \cdot \frac{c^2}{8\pi h\nu^3}. \]

Here \(\tau\) denotes the lifetime of the excited state, \(g_2/g_1\) is the ratio of the statistical weights of the upper and lower levels corresponding to the given spectral transition, \(c\) is the speed of light, \(h\) is Planck’s constant, and \(\nu\) is the light frequency.

The radiant flux corresponding to the radiation of a unit volume is equal to

\[ W = h\nu \cdot \Delta N, \]

and the luminous intensity of a unit volume in energy units is

\[ I = \frac{W}{4\pi} = \frac{h\nu}{4\pi}\Delta N. \]

Finally, the brightness of a layer of thickness \(l\) is equal to

\[ B = I \cdot l = \frac{h\nu}{4\pi}\Delta N \cdot l = \frac{h\nu}{4\pi} b \cdot E_\nu \cdot N \cdot l. \]

Since the identical equality \(E_\nu\cdot|\Delta \nu|=E_\lambda\cdot|\Delta \lambda|\) holds, we may write

\[ E_\nu=E_\lambda\cdot\left|\frac{d\lambda}{d\nu}\right|=E_\lambda\cdot\frac{\lambda^2}{c} \]

and

\[ B=\frac{h\nu}{4\pi}\cdot b\cdot E_\lambda\cdot\frac{\lambda^2}{c}\cdot N\cdot l =\frac{1}{\tau}\frac{g_2}{g_1}\cdot\frac{\lambda^4}{32\pi^2c}\cdot E_\lambda\cdot N\cdot l. \]

We can rewrite the last expression in the form

\[ B=K\cdot E_\lambda\cdot N\cdot l, \]

where \(K\) is a coefficient whose numerical value we can now calculate:

\[ K=\frac{1}{\tau}\cdot\frac{g_2}{g_1}\cdot\frac{\lambda^4}{32\pi^2c}. \]

The lifetime \(\tau\) of sodium atoms in the excited state \({}^2P\) (see Fig. 17) is well known\({}^{52}\) and is equal to \(\tau=1.6\cdot10^{-8}\) sec.; \(g_2/g_1=1\) for the line \(D_1\), and \(g_2/g_1=2\) for the line \(D_2\); for the totality of the two components \(\sum g_2/g_1=3\); consequently,

\[ K=2.36\cdot10^{-22}\ CGS. \]

(In the work of Brikard and Kastler\({}^{40}\), \(K=0.93\cdot10^{-21}\ CGS\) is erroneously indicated.)

For the zenith, the brightness of the \(D\)-lines is equal to \(B=0.24\cdot10^{-2}\ CGS\), whence

\[ Nl=\frac{0.24\cdot10^{-2}}{2.36\cdot10^{-22}\ 1.34\cdot10^9} =0.8\cdot10^{10}\ \text{atoms}/\text{cm}^2. \]

This is the number of sodium atoms in a vertical column of air with cross section \(1\ \text{cm}^2\) participating in the emission of the yellow line \(\lambda=0.59\ \mu\) during twilight. This amount is equivalent to a layer of sodium vapor \(1\ \text{cm}\) thick at a density equal to the density of saturated Na vapor at \(115^\circ\)C.

Brikard and Kastler\({}^{40}\) rightly point out that the value they obtained, \(0.8\cdot10^{10}\) atoms/\(\text{cm}^2\), is only a lower limit, since two factors have not been taken into account:

1. Attenuation of the solar rays along their path through the atmosphere. On this account the number of Na atoms, in the opinion of the authors cited, may increase to \(10^{10}\).

2. Reabsorption of the resonance radiation in the sodium layer itself. The calculations of Brikard and Kastler, which they do not reproduce but report only the final results, lead these authors to the conclusion that reabsorption becomes noticeable only when \(Nl>10^{11}\). Assuming that the temperature of the layer containing sodium vapor is approximately \(150^\circ\)C (whereby large variations of temperature have little effect on the results) and, apparently, assuming that the contour of the \(D\) lines is deter—

is determined by the Doppler effect (see the following paragraph), they calculated the fraction \(A\) of absorbed light for different values of \(Nl\), separately for \(D_1\) and \(D_2\). Their results are given in Table 5.

Table 5

Fraction of absorbed light of the sodium \(D\)-lines as a result of self-absorption in the emitting layer of sodium vapor (according to Brickar and Kastler)

\(Nl \cdot 10^{-11}\)	1	2	4	8
\(A_{D_1}\)	0.156	0.274	0.442	0.62
\(A_{D_2}\)	0.274	0.442	0.62
\(D_2/D_1\)	1.72	1.54	1.36

Since the \(D_2\) line is absorbed more strongly than the \(D_1\) line, the effect of reabsorption influences the intensity ratio of the \(D_2/D_1\) lines. Taking the “theoretical” value of this ratio to be 2 (the grounds for using the term “theoretical” value only in quotation marks under the conditions of atmospheric radiation of the \(D\)-lines will be given below), one can calculate the value of the intensity ratio \(D_2/D_1\), taking into account the distorting influence of self-absorption. The results of the calculations, given in the last row of Table 5, show that reabsorption leads to an equalization of the intensities of the \(D\)-lines.

Concerning the actual intensity ratio \(D_2/D_1\) in atmospheric radiation, we know only from qualitative estimates of the intensities of interference rings, on the basis of which Bernard \(^{18,19,20}\) and Cabannes–Dufay–Gauzit \(^{21}\) reported that “the intensity ratio \(D_2/D_1\) is close to the theoretical value 2.”

In this connection it should be recalled that the theoretical value 2 is obtained only in the case when the intensity of the exciting light is the same for both \(D\)-lines. However, photometry of the Fraunhofer \(D\)-lines in the solar spectrum, carried out by Allen (see Tables 3 and 4), indicates a certain difference between them. In addition, as we shall see later, in the wavelength region of the \(D\)-lines there is absorption by water vapor, which is variable (depending on the state of the atmosphere). Brickar and Kastler calculated the theoretical value of the intensity ratio \(D_2/D_1\) under conditions of resonant radiation of atmospheric sodium and found it to be 2.5.

Table 5 shows that for values of \(Nl\) of about \(10^{11}\), absorption by sodium atoms of the beam of solar rays exciting the luminescence becomes noticeable, since this beam crosses the sodium layer obliquely before it can enter the targeted region of the sky.

If observations give, for the actual intensity ratio \(D_2/D_1\), a value of 2, close to the theoretical one, this indicates

that self-absorption plays no appreciable role either in the incident beam of exciting solar rays or in the beam of luminescence on its path to the observer. But for final conclusions of this kind it is necessary to have the results of exact measurements of the intensity ratio \(D_2/D_1\). Still, it seems plausible to assume that the number \(Nl\) can hardly reach the value \(10^{11}\). The value \(Nl = 10^{10}\) may be accepted as close to reality, with sufficient confidence in the correctness of the order of magnitude. The only question that remains open is that of possible quenching of the resonance fluorescence of sodium vapor. This factor has so far not been taken into account in studies of the luminescence of sodium, but facts known from laboratory experiments on quenching the luminescence of sodium vapor by foreign gases indicate the possibility of a large influence of this factor \(^{52, 53, 56, 57}\).

11. WIDTH OF THE \(D\)-LINES OF SKY RADIATION AND THE QUESTION OF THE NATURE OF THE LUMINESCENCE

In 1939 Frank and Rieke \(^{58}\) considered the process of photodissociation of NaCl molecules with the formation of excited Na atoms and showed that if the luminescence of atmospheric sodium arises in this way (photodissociation of NaCl molecules by the ultraviolet rays of the Sun), then there should be a considerable broadening of the \(D\)-lines. Let us examine this question somewhat more closely, but note in passing that Frank (James Franck) and Rieke consider \(^{58}\) “the most probable” source of sodium in the atmosphere to be the process of NaCl evaporation from seawater, although the mechanism of NaCl dissociation at altitudes above 60 km is rather doubtful \(^{41, 59, 60}\).

Under laboratory conditions it has been possible to observe resonance luminescence of alkali metals upon illumination of alkali-halide compounds by ultraviolet rays \(^{61}\). This process includes photodissociation into a normal halogen atom and an excited alkali-metal atom. Under such conditions, radiation of the \(D\)-lines of free Na atoms is observed at concentrations that do not produce measurable absorption (we deal with similar concentrations under atmospheric conditions). The absorption spectrum of alkali-halide molecules is continuous, with several absorption maxima. The first two maxima (from the long-wavelength side) correspond to dissociation of the molecule into a normal atom of the alkali metal, and into a normal and an excited atom of the halogen. The subsequent maxima refer to dissociation with formation of a normal halogen atom and an atom of the alkali metal in the first, second, etc., excited state. For example, for CsJ six maxima have been established, the frequencies of which correspond to iodine atoms \(^{2}P_{1/2} — {}^{2}P_{3/2}\) and cesium \(2P—1S\), \(3D—1S\), \(2S—1S\) and \(3P—1S\).

For NaCl only the first two maxima have been observed (at 2370 Å and 2320 Å). The maximum corresponding to the \(P\)-state of sodium lies beyond the region studied under laboratory conditions, apparently near 1700 Å, as may be calculated by adding 16,950,

Fig. 20. Absorption spectrum of oxygen \(O_2\) and ozone \(O_3\) in the ultraviolet region.

Fig. 21. Potential curves of the NaCl molecule. Along the abscissa axis is the distance between the nuclei; along the ordinate axis, energy in electron-volts.

the wave number of the \(D\)-line, to the wave number 42,190, corresponding to the first absorption maximum of NaCl at \(\lambda = 2370\) Å. The absorption region should extend 200–300 Å toward longer wavelengths.

Thus, the region of the spectrum associated with the photodissociation of NaCl with the production of excited sodium atoms lies precisely in the “atmospheric window” formed by the absorption of ozone and the absorption of molecular oxygen (see Fig. 20).

Figure 21 shows the potential curves for NaCl (the abscissa gives the distance between the nuclei, and the ordinate gives the energy in electron-volts). From these curves it can be seen that the photodissociation of NaCl molecules under discussion is associated with an excess energy of the order of 1 \(eV\) (\(a\) in Fig. 21). At the moment when Na and Cl atoms are formed in photodissociation, mutual repulsive forces arise between the atoms, and the atoms fly apart, acquiring excess kinetic energy. The large magnitude of the excess energy (of the order of 1 \(eV\)) should lead to a considerable broadening of the \(D\)-lines. Such a result for NaCl molecules is conjectural, but for other alkali-halide molecules it has been observed under laboratory conditions\(^{54,55}\) (for example, for NaJ).

Further consideration of the question shows that the broadening of the \(D\)-lines may be an extremely important indication for judging the mechanism of excitation of atmospheric sodium luminescence. The point is that, in the case of excitation of the yellow sodium atmospheric radiation by collisions of the second kind (see § 7), an excess energy of the order of

$1/10\ eV$, which should lead to a much smaller, but still quite appreciable, broadening[^45],[^65]. Finally, in optical resonance the lines should be narrow. Thus, measurement of the width of the $D$-lines in the radiation of the sky could make it possible to determine which of the three processes is responsible for the glow:

1. Photodissociation—very large broadening (excess energy of the order of $1\ eV$).

2. Collisions of the 2nd kind—large broadening (excess energy of the order of $1/10\ eV$).

3. Optical resonance—narrow lines (thermal energy—Doppler broadening—of the order of $1/100\ eV$).

But how could one measure the width of the $D$-lines in the spectrum of the sky, if in photographing spectra one has to use spectrographs of extremely small dispersion, on which the very determination of the wavelength of a line is possible only with an error of several Å?

As early as 1938 Kastler pointed out a simple and effective method for studying the structure (width) of the $D$-lines in the radiation of the sky by measuring its absorption in a cuvette containing sodium vapor, the temperature and density of which are varied in the desired manner[^66]. In 1939, Franck and Rieke[^58] pointed to this same method for testing the considerations set forth above concerning the broadening of the $D$-lines in the excitation of the glow of atmospheric sodium by photodissociation of NaCl molecules. Soon after this, Cario and Stille announced that they were carrying out similar measurements, but they never reported any results[^66].

In 1940 Kastler published the first results of such measurements[^67]. Subsequently he continued these investigations jointly with Bricard. Their results, published in 1944, proved to be very important and interesting[^40].

We now turn to the description of these experiments.

12. MEASUREMENTS OF THE ABSORPTION OF THE SKY $D$-LINES BY SODIUM VAPORS

For their experiments Bricard and Kastler[^40] used the famous French high-luminosity spectrograph constructed by Cojan. This is a single-prism spectrograph $F:0.7$; the prism, made of dense flint glass $n_D = 1.6803$, with an angle of $60^\circ$, has very large dimensions: 12 cm in height. The camera objective has the same large aperture, $F:0.7$, so that the dispersion of the spectrograph is comparatively large: $650\ \text{Å}/\text{mm}$ in the yellow region. The spectrograph was installed at the Pic du Midi observatory at an altitude of $2900\ m$. Spectra of the twilight sky were photographed both at sunset and at sunrise at a point in the sky near the Pole of the World, at an altitude of $22^\circ$ above the horizon in the direction northward. The spectra were photographed with exposures ranging from fractions of a minute to several minutes.

In front of the slit of the spectrograph there was mounted a cuvette $C_1$ with plane-parallel windows at a distance $e$ from one another (Fig. 22),

containing sodium vapor in an amount sufficient for partial absorption of the sky’s \(D\)-line.

Let \(I_0\) denote the intensity of the rays entering cuvette \(C_1\), and \(I\) the intensity of the emerging rays. The ratio \(R = \dfrac{I}{I_0}\) Brikard and Kastler call the reduction factor, and the expression

\[ A = \frac{I_0 - I}{I_0} = 1 - R \]

the absorption fraction.

To determine \(R\) and \(A\), it is necessary to know the quantities \(I\) and \(I_0\), for the measurement of which one must exclude the intensity \(i\) of the continuous background of the sky spectrum, which changes the blackening produced by the line on the spectrogram. Owing to the rapid change in the brightness of the sky during twilight, all determinations must be made simultaneously, taking photographs on one and the same plate. The background intensity \(i\) must be known exactly for the same place where the \(D\) line is located. For this purpose the sky spectrum was photographed simultaneously through a second cuvette \(C_2\), in which the sodium vapor elasticity was sufficient to guarantee complete absorption of the \(D\)-lines. Altogether, on each plate three spectra were photographed simultaneously:

a) The sky spectrum through cuvette \(C_1\), in which the \(D\)-line is absorbed only partially; the blackening corresponds to the sum of the intensities \(I + i\).

Fig. 22. Cuvette with sodium vapor for experiments on absorption of the sky’s \(D\)-lines.

b) The sky spectrum through a control cuvette \(C\), made of two plates (windows) identical to those of cuvette \(C_1\), but without sodium vapor (to take account of the weakening of the rays due to reflection at the plate surfaces at the entrance and exit of cuvettes \(C_1\) and \(C_2\)); the blackening corresponds to the sum of the intensities \(I_0 + i\).

c) The sky spectrum through cuvette \(C_2\), producing complete absorption of the \(D\)-line; the blackening corresponds only to the intensity of the continuous spectrum \(i\).

The arrangement of the three cuvettes was such that their images, produced by a lens, were located on the slit of the spectrograph as shown in Fig. 23. The electric furnaces surrounding the cuvettes and serving to maintain the required temperature of the sodium vapor had windings with opposite turns (Fig. 24), to eliminate the magnetic field that might alter the absorption properties of sodium vapor because of the Zeeman effect. The general appearance of Brikard and Kastler’s setup is shown in a photograph (Fig. 25). In cuvettes \(C_1\) and \(C_2\) the sodium-vapor elasticity was set by the temperature \(\theta_1\) and \(\theta_2\) of their bulbs, while cuvette \(C_1\) itself (see Fig. 22) had a higher temperature \(\theta_0\), in order to prevent deposition of sodium on the win—

as cuvettes. From time to time, control photographs of the sky were taken, during which the cuvettes were not heated (the elasticity of the sodium vapor is practically equal to zero); this was done in order to

Fig. 23. Diagram of the arrangement of the cuvettes relative to the slit of the spectrograph.

Fig. 24. Diagram of the furnace winding.

make sure that the installation was operating properly and that, in all three simultaneously photographed spectra, the brightness of the $D$-line was the same.

Fig. 25. General view of Brikner and Kastler’s installation for experiments on absorption of the sky’s $D$-lines by sodium vapor (1944).

In Fig. 26 are reproduced microphotograms of one of the triplets of simultaneous spectra of the twilight sky, taken in the evening of March 20, 1944. The blackening for the $D$ line on the middle microphotogram (the empty cuvette $C$) is somewhat greater than on the upper one (cuvette $C_1$); on the lower microphotogram there is no $D$ line (cuvette $C_2$ with complete absorp-

tion). Fig. 27 shows microphotograms of an analogous set of three control spectra, taken in the morning of March 21, 1944. In this case all cuvettes remained unheated: the blackening for the line \(D\) is the same in all three spectra.

Fig. 26. Recording photogram of sky spectra, taken simultaneously through cuvettes with different sodium vapor densities.

Fig. 27. Recording photogram of control spectra, taken simultaneously through 3 cold cuvettes.

Before proceeding to present the results obtained, let us consider the theory of the method. It is possible to calculate theoretically the absorption of resonance radiation of monatomic vapors as the radiation passes through a layer of the same vapors, taking the contour of the absorption and emission lines to be purely Dopplerian\(^{40,52}\).

Let \(K_\nu\) denote the absorption coefficient corresponding to the emitting atoms. The radiation intensity \(i_\nu\), according to Kirchhoff’s law, is proportional to \(K_\nu\)

\[ i_\nu = c \cdot K_\nu . \]

The total radiation intensity is equal to

\[ I_0 = \int_0^\infty i_\nu\, d\nu = c \int_0^\infty K_\nu\, d\nu . \]

Let \(k_\nu\) denote the absorption coefficient corresponding to the temperature of the absorbing layer, and let \(l\) be the thickness of this layer. Inten-

the intensity of rays in the spectral interval \(d\nu\) that have passed through the layer is, by definition, \(i_\nu e^{-k_\nu l} d\nu\), and the total intensity of the rays after passing through the layer will be

\[ I=\int_0^\infty i_\nu e^{-k_\nu l}d\nu =c\int_0^\infty K_\nu e^{-k_\nu l}d\nu . \]

The reduction factor

\[ R=\frac{\text{intensity of the transmitted light}}{\text{intensity of the incident light}} \]

will be equal to

\[ R=\frac{I}{I_0}= \frac{\displaystyle \int_0^\infty K_\nu e^{-k_\nu l}\,d\nu} {\displaystyle \int_0^\infty K_\nu d\nu}. \]

The fraction of absorbed light is determined by the relation

\[ A=\frac{I_0-I}{I_0}= \frac{\displaystyle \int_0^\infty K_\nu\left(1-e^{-k_\nu l}\right)d\nu} {\displaystyle \int_0^\infty K_\nu d\nu}. \]

Taking the line contour to be purely Doppler, we may write for \(K_\nu\) and \(k_\nu\)

\[ K_\nu=K_0 e^{-\left[\frac{\beta(\nu-\nu_0)}{\sqrt{T_e}}\right]^2}, \]

\[ k_\nu=k_0 e^{-\left[\frac{\beta(\nu-\nu_0)}{\sqrt{T_a}}\right]^2}, \]

where \(K_0\) and \(k_0\) are the absorption coefficients at the center of the emission and absorption lines, \(T_e\) is the absolute temperature of the emitting vapors, \(T_a\) is the absolute temperature of the absorbing vapors, and

\[ \beta=\lambda\sqrt{\frac{M}{2R}}, \]

where \(\lambda\) is the wavelength of light, \(M\) is the mass of the atom, and \(R\) is the universal gas constant.

Putting

\[ a=\sqrt{\frac{T_e}{T_a}} \quad\text{and}\quad \omega=\frac{\beta(\nu-\nu_0)}{\sqrt{T_a}}, \]

one can rewrite the expression for \(A\) in the form

\[ A_\alpha = \frac{\displaystyle \int_{-\infty}^{+\infty} e^{-\left(\frac{\omega}{\alpha}\right)^2} \left(1 - e^{-k_0 l e^{-\omega^2}}\right)\, d\nu} {\displaystyle \int_{-\infty}^{+\infty} e^{-\left(\frac{\omega}{\alpha}\right)^2}\, d\omega}. \]

\(A_\alpha\) is a function of \(a = \sqrt{\dfrac{T_e}{T_a}}\) and of \(k_0 l\).

Tables of numerical values of this function are given in the book by Mitchell and Zemansky\({}^{52}\) for \(a\) from 0 to 3 and \(k_0 l\) from 0 to 4.5. The absorption coefficient \(k_0\) at the center of the line is given by the expression

\[ k_0 = \frac{2 e^2 \lambda}{mc}\,\frac{Nf}{q}, \]

where \(e\) and \(m\) are the charge and mass of the electron, \(c\) is the speed of light, \(\lambda\) is the wavelength of the light, so that for the sodium \(D\)-line

\[ \frac{2e^2 \lambda}{mc} = 0.99 \cdot 10^{-6}; \]

\(N\) is the number of atoms in \(1\ \mathrm{cm}^3\) of the absorbing vapors; it is determined from the pressure and temperature of the vapors; \(q\) is the root-mean-square velocity of the thermal motion of the atoms, depending on the temperature of the absorbing vapors:

\[ q = \sqrt{\frac{8}{\pi}\frac{RT_0}{M}} = 3.04 \cdot 10^7 \sqrt{T_0}. \]

The quantity \(f\) is the “oscillator strength.” It is related to the lifetime of the excited state by the relation

\[ f\tau = \frac{mc}{8\pi^2 e^2}\frac{g_2}{g_1}\lambda^2 = 1.51\,\frac{g_2}{g_1}\lambda_0^2 . \]

The formula for \(A_\alpha\) should be applied separately for each of the two lines \(D_1\) and \(D_2\). The “oscillator strength” is equal to

\[ f_1 = 0.33 \quad \text{for the component } D_1 \left(\frac{g_2}{g_1} = 1\right), \]

\[ f_2 = 2f_1 = 0.67 \quad \text{for the component } D_2 \left(\frac{g_2}{g_1} = 2\right). \]

Therefore \((k_0 l)_{D_2} = 2(k_0 l)_{D_1}\).

For the final calculations of the absorption of light by a layer of sodium vapor, produced by the totality of both \(D\)-lines, it is necessary to know the initial ratio of their intensities. Brikar and Kastler\({}^{40}\) took the theoretical value

\[ \frac{D_2}{D_1} = 2. \]

Strictly speaking, measurements of absorption must be accompanied by a direct measurement

intensities \(\dfrac{D_2}{D_1}\) in the light of the sky; this could have been done by simultaneously photographing the interference rings (it is impossible to separate the \(D\)-lines by photographing with a spectrograph in twilight light, since the spectrograph required for this, with large linear dispersion, would inevitably have insufficient luminosity).

The absence of such control measurements of the intensity ratio \(\dfrac{D_2}{D_1}\) makes the results obtained by Brik and Kastler only preliminary. In addition, the theory set forth above assumes each of the lines \(D_1\) and \(D_2\) to be simple. Meanwhile it is known that sodium atoms possess nuclear spin \(3/2\), and therefore each of the two \(D\)-lines has a hyperfine\(^{68}\) structure and consists of two components, the distance between which is of the order of the Doppler width: it is equal to \(0.02\,\text{\AA}\). As a result the components overlap one another and partially absorb one another, so that the exact calculation of the function \(A_\alpha\) is very complicated. But in fact the problem is simplified on the basis of the results of Zedén’s\(^{63}\) exact experimental investigation of the reabsorption of the resonance line \(D\) by sodium vapor under laboratory conditions. This author showed that everything takes place as though the hyperfine structure of the \(D\)-lines did not exist, but instead of the “true” values \(f\) there act “effective” values \(f'\):

\[ f'_1=\frac{4}{5}f_1=0.267 \quad \text{for } D_1, \]

\[ f'_2=\frac{4}{5}f_2=0.532 \quad \text{for } D_2. \]

It remains to determine \(N\) as a function of the pressure of sodium vapor. According to kinetic theory \(N=\dfrac{p}{kT}\), where the pressure \(p\) is expressed in bars and \(k=1.38\cdot 10^{-16}\) is Boltzmann’s constant. Data on the pressure of sodium vapor have been collected and discussed in the work of Thiele\(^{62}\). But there we do not find results of direct measurements for temperatures below \(182^\circ\text{C}\). Measurements at lower temperatures were performed by Edmondson and Egerton\(^{69}\), and also by Rodebush and DeVries\(^{70}\). These results may be represented by the formula

\[ \log p=-\frac{5400.0}{T}+7.5510 \ \text{mm Hg}. \]

The fraction of \(\mathrm{Na}_2\) molecules at temperatures below \(200^\circ\text{C}\) is less than \(0.1\%\) and is negligible.

The results of the calculations are collected in Table 6.

Table 6

Saturated vapor pressure of sodium and its density as a function of temperature

Temperature in °C	Absolute temperature in °K	$p$ in mm Hg	$N$	Temperature in °C	Absolute temperature in °K	$p$ in mm Hg	$N$
127	400	$1.125\cdot 10^{-6}$	$2.73\cdot 10^{10}$	162	435	$1.371\cdot 10^{-5}$	$3.06\cdot 10^{11}$
132	405	1.648	3.95	167	440	1.897	3.96
137	410	2.399	5.67	172	445	2.606	5.68
142	415	3.460	8.10	177	450	3.556	7.65
147	420	4.943	$1.14\cdot 10^{11}$	182	455	4.820	$1.03\cdot 10^{12}$
152	425	6.998	1.60	187	460	6.486	1.37
157	430	9.840	2.22	192	465	8.670	1.81
				197	470	$1.151\cdot 10^{-4}$	2.38

Such are the experimental conditions and theoretical assumptions under which the investigations of the absorption of the sky’s $D$-lines by sodium vapor were carried out. Owing to the fact that the resonance radiation of sodium vapor has for a long time been a favorite object of investigation by physicists, we possess, for this radiation, unusually complete data, which make it possible, in applying them to the atmospheric radiation of sodium, to provide a sufficiently rigorous quantitative aspect of the investigations.

The initial result, obtained by Brikar and Kastler$^{40}$, is as follows: the absorption of the $D$-lines emitted by the twilight sky is practically complete for a thickness of the absorbing layer of sodium vapor of 10 mm and a vapor temperature of 180°C. Under these conditions the reduction factor $R=\dfrac{I}{I_0}$ is undoubtedly less than 0.1. From this one may conclude as to the upper limit of the “half-width” of the $D$-lines of the sky radiation: it is less than the “half-width” caused by the Doppler effect at a temperature of 1000°K and is 0.03 Å. The $D$-lines of the sky radiation are so narrow that the hypothesis of optical resonance appears very plausible.

Subsequent measurements by Brikar and Kastler made it possible to refine this result considerably. They reduced the elasticity of the vapors in the absorbing cell $C_1$, which is achieved by lowering the temperature $\theta_1$ of the cell projection (see Fig. 22); in this case only partial absorption of light takes place, which permits a more accurate determination of the residual intensity.

Table 7 gives the results of processing a series of photographs obtained by Brikar and Kastler in January 1944 when photographing during morning twilight$^{40}$. The photographs are arranged in order

of the increase in temperature \(\theta_1\). Let us recall that \(\theta_1\) is the temperature of the arm of the absorbing cuvette \(C_1\) (see Fig. 22), \(\theta_0\) is the temperature of the cuvette \(C_1\) itself, and \(\theta_2\) is the temperature of the arm of cuvette \(C_2\), ensuring complete absorption of the sky \(D\)-line.

Table 7

Measurement of the reduction factor \(R=\dfrac{I}{I_0}\) in the absorption of the sky \(D\)-lines as a function of the vapor pressure (temperature) of the absorbing sodium vapors (according to Brikar and Kastler)

Date of photograph	Temperature \(\theta_0\)	Temperature \(\theta_2\)	Temperature \(\theta_1\)	Spectrum No.	Exposure	\(R\)
31.1.44	224°C	213°C	145.5°C	No. 1	17.5 min.	0.54
31.1.44	224°C	213°C	145.5°C	No. 2	2.5 min.	0.54
31.1.44	224°C	213°C	145.5°C	Average		0.54
30.1.44	217	212	151	No. 1	17.5 min.	0.52
30.1.44	217	212	151	No. 2	2.5 min.	0.45
30.1.44	217	212	151	No. 3	1.5 min.	0.55
30.1.44	217	212	151	No. 4	1.5 min.	0.48
30.1.44	217	212	151	Average		0.50
27.1.44	220	210	152.5	No. 1	17.5 min.	0.47
27.1.44	220	210	152.5	No. 2	1.5 min.	0.44
27.1.44	220	210	152.5	Average		0.455
19.1.44	226	208	156	No. 1	10 min.	0.39
19.1.44	226	208	156	No. 2	2.5 min.	0.42
19.1.44	226	208	156	No. 3	1.5 min.	0.40
19.1.44	226	208	156	Average		0.403
28.1.44	223	210	160.5	No. 1	17.5 min.	0.21
28.1.44	223	210	160.5	No. 2	2.5 min.	0.21
28.1.44	223	210	160.5	Average		0.21

These results indicate a regular increase of the reduction factor \(R\) with increasing temperature \(\theta_1\), which regulates the pressure of the absorbing vapors. Brikar and Kastler point out that the best photographs are those of 30.1.44 and 19.1.44 (the remaining photographs are somewhat underexposed). On the basis of these two photographs one may derive the most reliable data:

\[ \begin{aligned} 30.1.44\quad \theta_1 &= 156^\circ\mathrm{C} \qquad & k_0 l &= 0.77 \qquad & R &= 0.403,\\ 19.1.44\quad \theta_1 &= 151^\circ\mathrm{C} \qquad & k_0 l &= 0.57 \qquad & R &= 0.500. \end{aligned} \]

Calculations according to the formulas given above yield, for

\[ a=\sqrt{\frac{T_e}{T_a}}, \]

a value of about \(0.7\). Since \(T_a=273+\theta_0=480^\circ\mathrm{K}\), it follows that

\[ T_e=240^\circ\mathrm{K}. \]

Thus, the lines of sodium emission from the sky during morning twilight prove to be very narrow; their half-width corresponds to Doppler broadening of the line at a temperature of the emitting atoms of the order of 240°K.

How reliable is this determination of the temperature of the sodium-emitting layer? Bricard and Kastler answer this question as follows:

“It is difficult to determine the accuracy of the measurements, which must be checked by subsequent measurements with variation of the absorption conditions.

At an altitude of 74 km the temperature has a value of the order of 240 ± 50°K.”

By the method described, Bricard and Kastler obtained another result of fundamental significance, although this result is as yet based on a small amount of observational material: they measured the absorption of the yellow line of the glow of the night sky (photographs of January 27–28 and 29–30, 1944). It was established that in the night radiation of the yellow line there are 2 parts, of which one is strongly absorbed (the reduction factor has a value of the same order as for twilight radiation), while the other remains unabsorbed at a sodium-vapor pressure in the cell corresponding to a side-arm temperature of 210°C. The intensities of both parts are approximately the same. This result indicates the presence of two different mechanisms of excitation of the night radiation, which Bricard and Kastler propose to be as follows:

1. Multiple scattering of the resonant twilight radiation of the sky coming from below the horizon on the side of the Sun (strongly absorbed radiation).

2. Excitation of sodium atoms by impacts of the second kind (a broad line, weakly absorbed).

13. SEASONAL VARIATION OF THE BRIGHTNESS OF THE YELLOW LINE. CONNECTION WITH THE IONOSPHERE

As early as 1937, Harrig^14, investigating the glow of the night sky, stated that the yellow line of the night sky was intense in the winter of 1936/37, by the summer of 1937 became very weak, and was not detected at all in July. Bricard and Kastler noticed an analogous annual variation for the twilight yellow line^40. From November 1942 to April 1943 they observed a distinct yellow line in the spectra of morning and evening twilight when the Sun was depressed below the horizon from 6°30′ to 10°. From the beginning of April the brightness of the yellow line began to decrease, above all at smaller depressions of the Sun; and on April 15 traces of the line could be noticed only on spectrograms corresponding to a depression of the Sun from 8 to 10° (usually the yellow line has its greatest brightness precisely when the Sun is depressed from 6°30′ to 8°). In the night sky the yellow line during this period

at that time was still intense. In June and July the yellow line was absent, and in the night and twilight sky it appeared in mid-August in the night sky and at twilight when the Sun was depressed by \(8—10^\circ\). At the beginning of October the yellow line was observed on all spectrograms; its intensity increased in November.

In connection with such seasonal changes in the brightness of the yellow line, Bricaud and Kastler point out[^40] the presence of analogous changes in the intensity of radio-wave reflection from layer \(D\), as was reported already in 1939 by Budden, Ratcliffe, and Wilkes[^71].

Beginning in 1935, these authors systematically investigated the reflection of radioelectric signals (wavelength \(18.8\ \text{km}\)) sent by the transmitter of the British Post Office, installed at Rugby. Over the course of 4 years they observed a lowering of the reflecting layer in winter and an increase of reflection in November. The amplitude of the reflected wave underwent so great an enhancement in November of each year that Budden, Ratcliffe, and Wilkes even introduced[^71] the special term “November effect.” In Fig. 28 we reproduce these authors’ data on the seasonal variation of the amplitude of the reflected wave (at noon) for the period 1935–1938. The amplitudes of the reflected wave are given in fractions of the amplitude of the ground ray[^71]. Indeed, the coincidence is striking between the periods indicated above of enhancement and weakening of the brightness of the yellow line of the sky and the periods of enhancement and weakening of the reflected radio waves.

Fig. 28. Seasonal variation of the amplitude of radio waves of wavelength \(18.8\ \text{km}\), reflected from layer \(D\) (in fractions of the amplitude of the ground ray). According to Budden, Ratcliffe, and Wilkes, 1939.

The measured[^71] heights of reflection varied within the limits from 55 to \(75\ \text{km}\).

In this connection, the suggestion put forward in 1941 by Juo and Vassy\({}^{72,73}\), concerning the identity of the ionospheric layer \(D\) and the layer emitting the sodium \(D\)-line at twilight, deserves attention.

Brichard and Kastler\({}^{40}\) further point out that in winter the brightness of the yellow line of the twilight sky is far less constant than in the night sky. The nocturnal brightness of the yellow line is in no way connected with its brightness during the twilight of the preceding evening or the following morning. In addition, they noted the influence of meteorological factors on the brightness of the yellow line. With a moist westerly wind the brightness is usually reduced, even if at the time of photographing the sky is perfectly clear; in dry cold periods (northerly wind) the brightness increases, owing to which it was sometimes possible to photograph the yellow line even under a cloudy sky. This effect, when compared with the seasonal variations, indicates that a high content of water vapor in the atmosphere is not very favorable for observations of the yellow line. Possibly absorption of the yellow line by water vapor takes place; in the absorption spectrum of the latter we find wavelengths close to the wavelength of the \(D\)-lines.

These wavelengths, obtained from the well-known measurements of the solar spectrum by Rowland, are found in the fundamental work of John, Moore, Adams, and Babcock\({}^{74}\), and their identification with the vibration-rotation spectra of the \(\mathrm{H_2O}\) molecule is given by Fredenhagen and Mecke\({}^{64}\).

Table 8

Absorption spectrum of water vapor near the sodium \(D\)-lines

\(\lambda\)	\(I\)	\(\Delta\lambda\) relative to \(D_2\)	\(\lambda\)	\(I\)	\(\Delta\lambda\) relative to \(D_1\)
5888.708 Å	2	\(-1.269\) Å	5894.950 Å	0	\(-0.994\) Å
5889.091 »	\(-1\)	\(-0.886\) »	5895.148 »	0	\(-0.796\) »
5889.643 »	3	\(-0.334\) »	5896.423 »	0	\(+0.479\) »
5889.888 »	2	\(-0.089\) »	5896.498 »	1	\(+0.554\) »
5890.213 »	0	\(+0.336\) »	5896.835 »	2	\(+0.891\) »
5890.738 »	\(-1\)	\(+0.761\) »
5891.186 »	1	\(+1.209\) »

The American authors cited give the following wavelength values for the sodium \(D\)-lines: \(\lambda = 5895.944\) Å for \(D_1\) and \(\lambda = 5889.977\) Å for \(D_2\). These values differ by \(+0.012\) Å from the wavelengths previously given by Kayser.

Table 8 gives the wavelengths \(\lambda\) of the absorption spectrum of the \(\mathrm{H_2O}\) molecule that are close to the \(D\)-lines. The indicated gradations of intensity \(I\) are taken from Rowland’s measurements. In addition, the wavelength differences \(\Delta\lambda\) relative to the \(D\)-lines are given.

Because of the great length of the path traversed in the atmosphere by both the light emitted by the luminous atmospheric layer (observations

Bricard and Kastler, as already indicated, were taken at a point in the sky \(22^\circ\) above the horizon \(^{40}\), so that, with sunlight exciting optical resonance, the width of the absorption bands of water vapor corresponding to this large path may be considerable and may reach a value of \(0.5\ \text{\AA}\), as is evidenced by measurements of the widths of telluric bands of water vapor carried out by Allen \(^{51}\). With a high content of water vapor in the atmosphere, the \(\mathrm{H_2O}\) absorption bands may overlap the \(D\)-lines and cause their noticeable weakening.

Absorption by atmospheric moisture should have a stronger effect on the \(D_2\) line, near which especially close intense bands of water vapor are located (\(\Delta\lambda = 0.089\ \text{\AA}\) and \(0.334\ \text{\AA}\), see Table 8). The \(D_2\) line gives \(^{2}/_{3}\) of the intensity of the yellow line of the sky. It would be desirable to measure systematically the value of the ratio \(D_2/D_1\) under different meteorological conditions and in different seasons. Such measurements, easily performed with a Fabry and Perot standard of thickness \(0.15\ \mathrm{mm}\), would make it possible to clarify the role of absorption by water vapor in the observed changes in the brightness of the yellow line.

A. and E. Vassy proposed another explanation of these seasonal fluctuations of brightness \(^{75}\): at the beginning of November the Earth crosses the swarm of Leonids, the most significant meteor swarm, which may cause an enrichment with sodium of the upper layers of the atmosphere. To determine which of the two indicated explanations of the seasonal variations corresponds to reality, one could make simultaneous measurements in the southern and northern hemispheres of the Earth.

A rigorous determination of changes in the intensity of emission lines in the spectrum of the night sky is associated with a number of difficulties. The best method for such measurements was proposed in 1940 by Academician G. A. Shajn and P. F. Shajn \(^{76}\). By this method, beginning in 1940, measurements have been made of changes in the intensities of three radiation lines of the night sky: the oxygen lines \(\lambda = 5577.3\ \text{\AA}\) and \(6300.0—6354.1\ \text{\AA}\), and the sodium line \(D\). The measurements, begun in 1940 at the Simeiz Observatory in Crimea, were continued in 1942–1944 by V. F. Gaze at the Abastumani Astrophysical Observatory (Mount Kanobili, Georgia), and now are again being continued by her at the restored Simeiz Observatory. These data, not yet published, will be very important for resolving the questions indicated above.

Unfortunately, the method of G. A. and P. F. Shajn is applicable only under night-time conditions \(^{76}\) and cannot be used to investigate changes in the brightness of the yellow line of the twilight sky.

14. ON THE STRUCTURE OF THE UPPER LAYERS OF THE ATMOSPHERE

The results of the investigation of the yellow line of the spectrum of the twilight and night sky, set forth in the present review, prove the presence of sodium in the upper layers of the atmosphere. The number of sodium atoms has been determined with sufficient confidence. The height of the layer containing sodium hardly differs significantly from \(70—80\ \mathrm{km}\). It has been convincingly proved that

the emission of the \(D\)-lines under conditions of twilight illumination of the atmosphere is excited by optical resonance, but the nocturnal emission of these lines obviously cannot be wholly explained by optical resonance and, apparently, is connected with the excitation of luminescence by collisions of the second kind. Indications have been obtained of a possible connection between the sodium contained in the high layers of the air and many important phenomena occurring in the atmosphere, but there is still insufficient clarity on the question of the origin of atmospheric sodium. In order to form a more definite idea of what the role of the sodium layer may be in the general picture of the physical processes taking place in the atmosphere, we shall, in conclusion of the present essay, briefly consider certain data on the properties of the high layers of the air[^77][^78].

We have already discussed the question of the chemical composition of the air at great heights in the preceding paragraphs. This question is of great importance for the problem of atmospheric sodium, namely, for judging the possibility that sodium penetrates into the high layers of the atmosphere from the troposphere. Does there or does there not exist a powerful turbulent exchange between the troposphere and the high layers of the stratosphere? Many considerations speak of the impossibility of such motions. But in that case there would occur a diffusive separation of light and heavy gases and, with height, the percentage content of light gases would have to increase. Direct chemical investigations of the composition of the air in the stratosphere were carried out (in the USSR, England, the USA, and Germany) up to a height of almost 30 km (up to 22 km with the aid of stratospheric balloons, higher with the aid of sounding balloons). Principal attention was devoted to determining the ratio helium/oxygen: helium as a representative of the light gases, oxygen of the heavy ones. Up to a height of 20 km this ratio remains strictly unchanged and only at heights greater than 20 km begins to increase very slightly and irregularly. This reveals some effect of diffusive separation of the gases, but it is overlain by the more powerful action of vertical mixing, which equalizes the composition of the air. Meanwhile, beginning from heights of the order of 20 km, the conditions for diffusive separation of light and heavy gases become favorable (large diffusion coefficient).

The spectral data already known to us, characterizing the emission of the high layers of the atmosphere (aurorae and the glow of the night sky), confirm this conclusion, testifying that even at heights of 100 km and more the composition of the atmosphere is nitrogen–oxygen. All this, generally speaking, makes the supposition that sodium or, more probably, sodium compounds (\(\mathrm{NaCl}\)) penetrate from the troposphere into the high layers of the atmosphere not contradictory to other known facts.

Interesting and important information has been obtained on the temperature of the high layers of the atmosphere. It is known that the stratosphere, within the limits accessible to radiosondes (usually not above 25 km, occasionally up to 30 km or a little more), is distinguished by great constancy of temperature. Over Europe

the temperature of the stratosphere usually does not exceed 220–230°K. However, anomalies in the propagation of sound waves had long been observed, forcing one to assume an increase in air temperature at great heights. In strong explosions, in addition to the main zone of audibility immediately surrounding the point of explosion, there is also a secondary zone of anomalous audibility, separated from the main zone by a rather wide zone of silence[^77] (the width of the zone of silence is several tens of kilometers, and sometimes more than 100 km). This indicates a bending of the trajectories of sound waves downward, with their subsequent return to the Earth. In the region where the waves return, there must be an increase in the wave velocity \(v\) with height \(h\) (a positive value of the gradient \(\dfrac{dv}{dh}\)). According to Laplace’s formula,

\[ v=\sqrt{\frac{\gamma RT}{M}}, \]

where \(R\) is the gas constant, \(\gamma\) is the ratio of specific heats, \(M\) is the molecular weight, and \(T\) is the absolute temperature. The observed phenomena can be explained by positive values of the gradient \(\dfrac{dT}{dh}\). The theory of the question makes it possible, from observational data, to compute the height of return of the waves \(h_0\) and the air temperature at this height \(T_0\).

Usually \(h_0\) is somewhat more than 40 km, only rarely reaching values of 50 and 60 km. From such observations one obtains a temperature of about 280°K at a height of 40 km, 310°K at a height of 45 km, and 435°K at a height of 50 km.

Information on the temperature of still higher layers has been obtained on the basis of data on air density. In this respect the greatest importance belongs to the enormous “excess” of density at heights of about 100 km, obtained by various methods. Let us first consider the calculations of Lindemann and Dobson[^79], based on data on the heights of ignition and extinction of meteors.

Baseline measurements have established that the ignition of meteors occurs at heights of 60–160 km (most often at heights of 100–140 km), and their extinction at heights of 30–115 km. A meteoric particle enters the Earth’s atmosphere with enormous velocity (also determined by baseline observations), in a few seconds is heated by friction in the air to the boiling temperature, and, emitting bright light during this time, completely evaporates in a few seconds, sometimes leaving a luminous trail. Making certain assumptions about the mechanism of heating and luminescence of the meteoric particle, Lindemann and Dobson[^79] derived formulas that make it possible to compute the air density both at the height of the meteor’s flare-up and at the height of its extinction. Figure 29 gives the results of their calculations for a large number of meteor observations. On this curve, circles denote the density at the height of ignition of the meteor, and dots the density at the height of extinction.

The change in air density \(\rho\) with height in the case of hydrostatic equilibrium of the atmosphere is determined by the well-known barometric formula

\[ \rho=\rho_0 e^{-\frac{Mg}{RT}h}, \]

where \(g\) is the acceleration due to gravity. If the stratosphere is considered mixed (\(M\) does not depend on height) and isothermal (\(T\) does not depend on height), then the distribution of density with height is obtained as shown by the dashed curve in Fig. 29. We see that at an altitude of \(100\) km meteor observations give a density hundreds of times greater than that which should exist for an isothermal stratosphere. Since an increase in \(T\) slows the decrease of density with height (decreases the absolute value of the gradient \(\frac{d\rho}{dh}\)), the indicated discrepancy could be removed by assuming that at altitudes somewhat less than \(100\) km the temperature increases with height.

Fig. 29. Air density at great altitudes according to meteor (circles and dots) and twilight (solid line) observations. The dashed line is the theoretical isothermal atmosphere.

Let us note that the results of the meteor calculations of Lindemann and Dobson are in good agreement with the density determinations by the twilight method, the theory of which was developed by V. G. Fesenkov\({}^{39,80}\) and N. M. Shtau­de\({}^{81}\). In the same Fig. 29 the course of the density according to twilight observations\({}^{82}\) is shown by the solid line.

Finally, the temperatures of the air layers of interest to us may be judged from the reflection of radio waves. Without going into details, we point out that\({}^{78}\):

1) For layer \(E\) (height of the order of \(110\)—\(115\) km) a temperature of \(385^\circ\)K is obtained.

2) Beginning at an altitude of approximately \(90\) km, a sharp increase in temperature takes place.

3) For an altitude of \(75\) km (according to observations of the reflection of long radio waves \(\lambda = 18.8\) km, which we have already mentioned in connection with changes

... by Bälden, Ratcliffe, and Wilkes^71) a very low temperature is obtained: only 200° K.

On the basis of all these data one may suppose the following temperature regime in the region of interest to us: at an altitude of 40–60 km the temperature increases with height, but after 60 km it falls again, reaching at an altitude of 75 km a minimum value of 200° K; from an altitude of 85–90 km a rapid increase in temperature begins, which reaches a value of 385° K in the region of the ionized layer \(E\).

All that has been said provides grounds for forming a certain judgment about what has so far remained the least clear question—the mechanism by which sodium or its compounds (NaCl) enter the upper layers of the atmosphere.

Particles of NaCl salt are undoubtedly present in the troposphere, entering it through the evaporation of the smallest droplets sprayed from the surface of the ocean. These particles, as condensation nuclei, play a major role in the processes of condensation of water vapor in the atmosphere. The presence of NaCl in rainwater has been established by chemical analysis. By turbulent mixing of the air these particles penetrate into the upper layers of the atmosphere (up to 80–85 km). True, on their way they must “break through” the temperature inversion in the tropopause and, perhaps, one more temperature inversion at an altitude of 40–50 km. But the absence of diffusive separation of heavy and light gases indicates the possibility of vertical turbulent exchange sufficiently energetic to ensure such penetration of NaCl particles. At an altitude of 85–90 km, however, these particles encounter so powerful a temperature inversion, and the intensity of turbulent motions is so weakened, that the particles can no longer “break through” this inversion (except by ordinary diffusion), and therefore they accumulate at an altitude of 80–85 km and form a luminous layer emitting the \(D\)-lines under the action of the Sun’s rays. In this case the sodium layer should be rather sharply bounded above. But we know that twilight observations indicate precisely the presence of such a distinct boundary of the layer emitting the \(D\)-lines. The height of this layer, according to twilight observations, is obtained either as 80–90 km, if one starts from the assumption of optical resonance, or as 115 km in the case of excitation of the glow by photodissociation of NaCl molecules by the ultraviolet rays of the Sun. Considering, on the basis of the temperature data, that NaCl particles cannot rise above 80–90 km, we would have to suppose that the twilight glow of sodium vapors must be resonance radiation: from measurements of the width of the \(D\)-lines of the twilight sky (see §§ 11 and 12) we know that this is in fact the case.

NaCl particles, owing to their great hygroscopicity, are especially active condensation nuclei. Noctilucent clouds at an altitude of 82 km may owe their origin to the process of condensation on these nuclei. The striking constancy of the height of noctilucent clouds (82 km) and the very magnitude of this height^83 are ob-

would receive in this case a clear explanation as the result of a sharp limitation of the upward spread of NaCl particles owing to the sharp temperature inversion at these heights.

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