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Night Sky Glow
I. A. Khvostikov, Leningrad
Introduction
The glow of the night sky, despite its very low brightness, belongs among the great phenomena of nature. The essence of this phenomenon is as follows.
Approximately 35 years ago an interesting discovery was made: careful measurements of the brightness of the night sky showed that only one quarter of all the light sent to us by the night sky belongs to the stars and nebulae. What, then, accounts for the remaining part of the light?
As a result of many years of painstaking investigations it has been established that the Earth’s atmosphere itself glows. Atoms and molecules of oxygen, molecules of nitrogen, and other gases that make up the Earth’s atmosphere glow. At what altitude this glow is concentrated is still unknown, but apparently this altitude is not less than 100 km. The spectra of the glow of the night sky are in many respects similar to the spectra of auroras, but in many respects they differ essentially from them. We have, as it were, a continuous aurora of the sky, in many respects resembling, but in many respects also distinct from, the auroras.
What is the nature of this phenomenon? What causes the continuous glow of enormous masses of air at an altitude of 100–200 km? A final solution to this question has not yet been given—for the phenomenon itself is too complex, and our knowledge of the physical properties of the upper layers of the atmosphere is too limited. But the intensive research work being carried out in all countries to solve this question has yielded, and continues to yield, interesting and important results that will constitute a substantial contribution to the science of the Earth’s atmosphere.
The present article is an attempt to set forth systematically all the basic material on the glow of the night sky and to illuminate those problems that have arisen as a result of many years of study of this interesting phenomenon.
1. Newcomb. Measurements of Sky Brightness
Although the well-known American astronomer Simon Newcomb never dealt with the question of the intrinsic glow of the sky, the history of this question must undoubtedly begin with him.
In 1901, in the American Astronomical Journal, an article by Newcomb¹ was printed under the title “A Rough Attempt to Determine the Total Light from All the Stars.” In this article Newcomb for the first time poses the following important question: can the light of all the stars that we discover with the naked eye and in the telescope account for the brightness of the night sky observed in reality?
As a result of his own ingenious measurements, Newcomb, unexpectedly for himself, arrives at the conclusion that all the stars that we can detect in the sky are wholly insufficient to account for the true brightness of the night sky. Newcomb suggests that there exists a multitude of stars inaccessible to our observation, to which a large part of the brightness of the night sky must be attributed.
After Newcomb, a whole series of individuals continued his observations of the brightness of the night sky. These include the works of Burns², Towner³, Intema⁴, Fabry⁵. However, the data of different authors proved to be highly contradictory, and although a deficiency of starlight was almost always obtained for explaining the entire brightness of the night sky, nevertheless the magnitude of this deficiency was different for everyone. Ten years of work could not resolve this question, and even in 1910 the suggestion was expressed that the matter came down to the great difficulty of measurements of this kind and to the associated errors of measurement, and that with more precise measurements the brightness of the sky and the starlight would balance each other. Meanwhile, as early as 1901 a work had been published which, had it immediately attracted the attention it deserved, could have directed thought onto the right path. Wichert⁶, working in Göttingen, found that “in our latitudes (the latitude of Göttingen is 51°30′) aurorae are a much more frequent phenomenon than is usually thought.”
Let us recall that in the spectrum of aurorae, which had been intensively studied already at the end of the last century, the brightest part of the spectrum is a very intense green line, which determines, as is known, the greenish color of the entire aurora. This green line Wichert detected during observations in Göttingen.
For his observations Wichert constructed a luminous direct-vision spectroscope. This spectroscope had a focal length of 108 mm with a lens diameter of 27 mm. Thus the relative aperture of the spectroscope was 1 : 4, which for those times was a very large value. Wichert himself calls his spectroscope “unusually luminous.”
With this spectroscope Wichert went out to make observations in the vicinity of Göttingen (so that the lights and dust of the city would not interfere). “The first clear evening,” writes Wichert⁶, “when I was able to use my instrument was 1 November 1901, and I experienced great joy when, at the very first glance in the northern part of the sky, I detected the auroral line (the green line), which was quite clearly visible.” The green line was detected in all parts of the sky except the western part of the horizon, where the city lights interfered.
The conclusion reached by Wichert is that the light of the aurora is observed at the latitude of Göttingen much more often than might have been thought: apparently, every evening. It did not occur to Wichert to compare his observations with Newcomb’s results, set forth above. Nor did Newcomb himself, or all the others who repeated his measurements, make this comparison.
The Dutch scientist Intema[^4] came closest to the truth. Following Newcomb, he measured the brightness of the night sky and calculated the amount of light that all the stars could give. Discussing his results, he ultimately advanced a hypothesis that rightly allows him to be considered the founder of the doctrine of the sky’s intrinsic glow. Intema concludes that “the light of the sky at night consists of two parts, of which one reaches us directly from the stars, while the other arises as the result of certain processes in the atmosphere. This second part, the so-called ‘green light,’ is only partly scattered starlight. It seems probable that the excess of light is wholly or partly caused by continuous aurora.” This hypothesis was put forward by Intema in 1909.
Intema’s hypothesis was received negatively.[^5] But 10 years later it turned out that this hypothesis was correct.
2. Slipher’s Discovery. Rayleigh’s Observations
Over the course of four years, beginning in 1915, the English scientist Slipher made observations, the results of which he decided to publish only in 1919,[^7] when he had finally convinced himself of the reality of the fact he had discovered and had studied it thoroughly.
In June 1915, Slipher, while photographing for several consecutive nights the spectrum of the Milky Way, discovered on the negative a faint line in the yellow-green part of the spectrum. Taking photographic plates of another kind, whose sensitivity was high in this region of the spectrum, he was able to obtain this line in a single night. Measurements of the wavelength showed that this line was the very famous green line that is always present in the spectra of the northern lights. One can easily imagine Slipher’s amazement, if one notes that his observations were made at latitude \(35^\circ 12'\), where up to that time no one had ever observed the aurora.
Slipher began to take photographs every night. His amazement became still greater when it turned out that the green line could be photographed on a high-aperture spectrograph every night. Moreover, the glow was not concentrated in any particular region; every night it filled the whole sky: the spectrograph recorded the green line regardless of which part of the sky it was pointed at.
Slipher understood the true meaning of his discovery. Having studied the literature, he learned of Wichert’s observations and of the measurements of the bright-
bones of the sky, which always gave an excess of light in comparison with the light of all the stars, and of Intemann’s hypothesis. His photographs showed that, indeed, every night the whole sky emits light resembling the light of the aurorae. In 3½ years of photography, Slipher obtained more than 100 photographs, and in each of them there was a green line.
Photographing at the zenith and nearer to the horizon, Slipher noticed that the brightness of the green line turns out to be the greater, the nearer to the horizon the photograph is taken. This could easily be explained on the assumption that somewhere high in the atmosphere there is a layer in which the “continuous aurora,” as Slipher called it (“permanent aurora”), arises.
Having at his disposal a large number of photographs with the green line, Slipher made careful measurements of its wavelength. The measurements gave \(\lambda = 5578.05\) Å.
As for the possibility of ascribing the green line to one or another gas, insurmountable obstacles were immediately encountered here: not one of the gases had a line of such wavelength in its spectrum. The nature of the green line of the aurorae and of the glow of the night sky remained unknown.
Slipher’s discovery at once attracted general attention. Already in the same year 1919, in which Slipher’s work was printed, three papers appeared devoted to the question of the glow of the night sky. The suggestion was made that the excess part of the light of the night sky is caused by the scattering of solar rays by very rarefied gases, which may extend very far beyond the limits of the Earth’s shadow. In connection with this suggestion Rayleigh\(^8\) undertook exceptionally interesting observations, trying to determine the color of the night sky and to compare it with the color of the Sun and the Moon, and also with the color of the daytime sky. The point is that scattered sunlight differs greatly in spectral composition from direct sunlight. The light of the Sun has a maximum of energy at a wavelength of 5550 Å, and on the blue and red sides of this maximum the energy decreases noticeably, as follows for thermal radiation at a temperature of about \(6000^\circ\) K (Fig. 1, curve \(a\)). But when sunlight is scattered by the Earth’s atmosphere, a redistribution of energy over the spectrum occurs. This is due to the fact that not all wavelengths are scattered equally: the scattering coefficient is inversely proportional to the fourth power of the wavelength of the light, owing to which blue rays are scattered more strongly than red ones. As a result, the color of the sky proves to be not whitish-yellow, like the color of the Sun, but blue. In Fig. 1 (curve \(b\)), for comparison, the relative distribution of energy is given
Fig. 1.
in the spectrum of the scattered light of the sky. Here there is no longer a decline of the curve in the blue part; on the contrary, the energy of the blue rays is very great.
Rayleigh set himself the task of determining to what extent the distribution of energy in the light of the night sky corresponds to scattered sunlight.
Rayleigh photographed the sky through specially selected light filters and was able to judge the color of the night sky. He compared these data with the color of the blue daytime sky, and also with the color of the Sun and the Moon.
On the basis of the data obtained, Rayleigh arrives at the following exceptionally important conclusions. The night sky is more yellow, or less blue, than the clear daytime sky. Comparison with direct solar or lunar light shows that the night sky is close to them in color.
Rayleigh also made visual observations. He took two light filters—one blue-green, the other yellow. At night they appeared equally bright. But at twilight the blue filter appeared brighter. This also confirmed the more yellow color of the sky at night.
Rayleigh points out that these results of his contradict the supposition that what occurs is scattering of sunlight by rarefied gases extending very far beyond the limits of the Earth’s shadow. In this latter case the color of the night sky ought to have been just as blue as that of the daytime sky.
3. Observations of the Green Line by the Interference Method
The nature of the green line continued to remain unclear. In attempts to assign this line to the spectrum of one gas or another, the question of the exact value of its wavelength was of especially great importance, as was the question of the structure of the line itself: its width, the presence of several close components (fine structure of the line), and so on. But the solution of such questions is possible only with the use of spectral instruments of high resolving power. However, simple photography on very fast spectrographs required many hours of exposure, and Slipher’s attempt to photograph the green line with a spectrograph of large dispersion required more than 100 hours of exposure over the course of dozens of consecutive nights. With such low intensity it seemed almost impossible to photograph the green line with the aid of an instrument of high resolving power, for example with the aid of an interferometer.
However, the well-known American astronomer Babcock succeeded in solving this problem, and by surprisingly simple means. In carrying out his experiment, Babcock proceeded from the generally known but often overlooked consideration that any increase in dispersion must weaken the brightness only for a continuous, but not for a line, spectrum.
The scheme of Babcock’s experiments was extraordinarily simple9. The entire setup consisted of only two parts: an interference apparatus, for which Babcock used a Fabry–Perot etalon, and a photographic camera with a fast lens. The Fabry–Perot etalon was simply placed under the open sky, directed northward, and behind it was placed the camera lens, focused on a parallel beam of light and producing, in its focal plane, an image of the interference rings, which were then photographed.
Babcock’s very first attempt to photograph the green line with his apparatus, with an exposure of 10 hours on the night of February 25–26, 1922, in Pasadena, was crowned with complete success. Subsequently Babcock continued his experiments at the Mount Wilson Observatory in the USA. He succeeded in obtaining more than a dozen excellent photographs with distinct rings from the green line, quite suitable for accurate measurements (Fig. 2). The first question that had to be resolved was, if possible, a more precise determination of the wavelength of the green line of the sky glow.
Fig. 2.
As a result of a complex statistical treatment of the material obtained, Babcock derived the following value for the wavelength of the green line of the night-sky glow:
\[ \lambda = 5577.350 \pm 0.005\ \text{Å}. \]
Subsequently these data of Babcock’s were confirmed with an accuracy of up to \(0.003\ \text{Å}\) (by the experiments of McLennan14 and the measurements of Cabannes15 using a concave diffraction grating).
Having determined the wavelength, Babcock attempted to measure the width of the green line. The point is that even if the atoms emitted strictly
monochromatic light, then, owing to the thermal motion of the atoms, the light will be perceived as not quite monochromatic (the Doppler effect). The Doppler width of the line \(\Delta\) is determined, as Fabry and Buisson first derived, in the following way:
\[ \Delta = 0.82 \cdot 10^{-6}\lambda \sqrt{\frac{T}{M}} . \]
Here \(\Delta\) is the width of the line whose wavelength is \(\lambda\); \(T\) is the absolute temperature of the radiating gas; \(M\) is the atomic weight.
On the basis of precise measurements of these photographs of interference rings, Babcock was able to determine the width of the green line. It proved to be equal to \(0.035\,\text{\AA}\). If it had been greater, the interference rings would have been less sharp than was actually observed. If we accept this value for \(\Delta\) and suppose, in accordance with the often-expressed assumption, that the temperature in the upper layers of the atmosphere, beginning from a certain altitude, remains approximately constant and equal to \(-55^\circ\text{C}\), or \(218^\circ\text{K}\), then, substituting these numbers into the formula written above, we obtain for the green line \(M = 3.8\). This comes closest to the mass of a helium atom (the atomic weight of helium is 4). For hydrogen (\(M = 1\)) we would have to obtain the width \(\Delta = 0.07\,\text{\AA}\), which is clearly greater than the observed value. To be sure, a decrease of \(\Delta\) under the assumption of hydrogen could be achieved by lowering the assumed temperature \(T\) of the upper layers of the atmosphere. However, to obtain the necessary \(\Delta\), \(T\) (the temperature enters under the square root) would have to be reduced by a factor of 4, i.e. one would have to set \(T = 54^\circ\text{K}\), or \(-219^\circ\text{C}\). If some gas heavier than helium were assumed, then the width of the line would have had to be less than the observed one, and it would be necessary, conversely, to admit very high temperatures for the upper layers of the atmosphere.
The question cannot be decided unambiguously. However, the data obtained in this way are, of course, of enormous interest. The question of identifying the green line by finding the corresponding line in the spectrum of some gas acquires special urgency.
4. THE HYPOTHESIS OF FROZEN NITROGEN AND ITS REFUTATION
In 1923 Vegard[^10] put forward a hypothesis that was destined to play a very prominent role. Proceeding from the large percentage of nitrogen in the air, Vegard supposed that the majority of the lines of the aurora, including the green line, are emitted by nitrogen. However, in the emission spectrum of gaseous nitrogen the corresponding lines are absent. To explain this fact, Vegard advanced the hypothesis that, owing to the very low temperature prevailing at great heights, nitrogen may exist there in a special molecular state in the form of a solid or of a very rarefied gas which, when bombarded by electron rays, emits a number of bands absent from its spectrum under ordinary conditions.
conditions and are precisely the lines of the spectrum of the northern lights. The principal version of this hypothesis assumed that very small particles of solid nitrogen, in the form of frozen nitrogen dust in suspension, are found in layers at an altitude of 100 km and higher (just where a large part of the auroras occurs). Below this altitude there is almost no solid nitrogen dust, because in the lower layers the temperature proves to be higher. For this reason, below 100 km auroras are scarcely observed at all.
Soon the hypothesis of solid nitrogen as the source of the spectrum of the northern lights and of the green line attracted universal attention, because Vegard discovered facts which seemed to be irrefutable proof of the correctness of his hypothesis. It was Vegard who, in the famous low-temperature laboratory of Kamerlingh Onnes in Leiden, carried out a series of experiments with nitrogen at low temperatures under bombardment of the nitrogen by electron beams. The entire part of the experiments directly involving the low-temperature technique was carried out by Kamerlingh Onnes himself. As Vegard soon published, it turned out that at very low temperatures solid nitrogen, when bombarded by electron beams, glows brightly, and in the spectrum of this glow most of the auroral lines are found. It is not difficult to imagine what impression this discovery made on everyone. The old riddle of the northern lights seemed to have been solved.
However, Vegard’s discovery proved to be a mistake.
In America, in Canada, at the University of Toronto, there is another low-temperature laboratory, headed by the well-known physicist McLennan. As soon as Vegard published his hypothesis of solid nitrogen, McLennan undertook to test this hypothesis. His investigations, carried out in 1923–1925 jointly with Shrum, gave substantially different results.
The most important conclusions reached by McLennan and Shrum were as follows: when nitrogen vapors at a temperature of \(-252^\circ\mathrm{C}\) are irradiated with fast and slow electrons, the vapors fluoresce, and the emission spectrum includes three green lines: \(\lambda = 5556\ \text{Å}\), \(\lambda = 5617\ \text{Å}\), and \(\lambda = 5654\ \text{Å}\). One of them Vegard erroneously identified with the green line of the northern lights. In addition to fluorescence, strongly cooled nitrogen also gives a bright phosphorescence containing the line \(\lambda = 5231\ \text{Å}\). Besides nitrogen, similar experiments were also carried out with cooled argon and a number of other gases. In argon there appeared green lines with wavelengths \(\lambda = 5648.3\ \text{Å}\) and \(\lambda = 5607.4\ \text{Å}\).
The authors come to the conclusion that “on the basis of the fact that the lines of the emission spectra of cooled nitrogen and argon, excited to glow by canal rays, do not coincide in wavelength even remotely with the green line \(\lambda = 5577\ \text{Å}\), it must be concluded that the nature of the green line of the polar auroras cannot be connected with the elements nitrogen or argon.”
5. Solution of the Question of the Origin of the Green Line
In 1925, McLennan and Shrum published a paper[^12] in which they succeeded in discovering a new, previously unknown radiation of oxygen in the green part of the spectrum. The new oxygen line, as precise measurements showed, had the wavelength \(\lambda = 5577.35 \pm 0.15\) Å, i.e., one coinciding with complete exactness with the wavelength of the mysterious green line of the polar aurorae and of the night-sky glow.
How did McLennan and Shrum manage to make oxygen emit the green line, which previously had never been studied in laboratory experiments? It turned out that for the appearance in the spectrum of the glow of oxygen, when an electric discharge is passed through it, of the new radiation in the form of a green line, certain very special conditions are required.
Fig. 3.
McLennan and Shrum initially set themselves a purely empirical task. They decided to take a gas mixture, as far as possible, of the same composition as in the upper layers of the atmosphere, and to try to excite this mixture to luminescence by passing an electric discharge through it under various conditions, and to see what the spectrum of this glow would be.
What may be the composition of the atmosphere at very great heights (100 km and higher)? If one assumes that mixing of the atmosphere (at least in the stratosphere) does not occur, then with height the composition of the air should change in the direction of an increase in the relative content of light gases. The decrease in the density of a given gas with height occurs, according to the well-known barometric formula, the faster the heavier the gas, i.e., the greater its molecular weight. Thus at great height, in addition to nitrogen and oxygen, hydrogen and helium should be present in large quantities. When McLennan and Shrum produced an electric discharge in a mixture of oxygen and helium with a high helium content, it turned out that in the radiation of oxygen there appears a green line \(\lambda = 5577.35\) Å. Under the same conditions, but in the absence of helium, the green line disappeared from the oxygen spectrum.
In Fig. 3 is shown a spectrum, photographed by MacLennan and Shrum, containing the green line \(\lambda = 5577\) Å. On the left is the comparison spectrum (the spectrum of an iron arc).
The strengthening of the green line in the presence of an admixture of helium led MacLennan to investigate this phenomenon in greater detail. He studied the dependence of the brightness of the green line on pressure, on the strength of the current through the discharge tube, etc. In addition, he tried using as an admixture not only helium, but also a whole series of other gases[^13]. It turned out that not only neon, but all inert gases, have an intensifying effect. But an effect quite astonishing in its strength was found for argon. It became clear that, in order to obtain the maximum brightness of the green oxygen line, the discharge actually had to be produced not in oxygen with an admixture of argon, but in argon with an admixture of oxygen. At an argon pressure in the discharge tube corresponding to 10 mm of mercury, and at an oxygen pressure of 1 mm, the brightness of the green line proved to be approximately 1000 times greater than under the most favorable conditions in pure oxygen. At the same time, argon exerts such an intensifying effect precisely with respect to the green line \(\lambda = 5577\) Å, having little influence on the intensity of the other lines.
6. Spectra of the Luminescence of the Night Sky
A very long exposure is needed in order to obtain on a plate with the spectrum of the luminescence of the night sky anything besides the green line. Rayleigh was the first to discover in the spectrum of the luminescence of the night sky, besides the green line, still other lines. During the period 1921–1923 he made photographs with a specially built spectrograph with a direct-vision prism and a relative aperture \(f:0.9\). He used exposures of from 100 to 200 hours (from 15 to 30 nights in succession; if one takes into account that usually one can photograph only during the 4th and 1st quarters of the Moon, so that its light does not interfere, then 30 nights can be accumulated only over two months). The dispersion of his spectrograph was negligible: the length of the visible spectrum was only 2.5 mm.
On the photographs obtained, Rayleigh ascertained the presence of a continuous spectrum with two Fraunhofer lines—the solar absorption lines \(H\) and \(K\)[^16]. He also observed two emission bands in the blue part of the spectrum, with wavelengths 4435 and 4210 Å.
At the very same time (winter 1922/1923) Dufay photographed a series of spectra of the luminescence of the night sky with the aid of a spectrograph of relatively large dispersion. This spectrograph, constructed by Fabry and Buisson for the study of the spectra of the Great Nebula in Orion, had two quartz prisms and an objective with relative aperture \(f:3.5\). To obtain traces of blackening, an exposure of 50–100 hours was required. In these photographs, in the region 4800–3100 Å
was found to contain more than 10 emission lines. In addition, in a number of photographs there was undoubtedly a continuous spectrum with Fraunhofer lines[^17].
Two emission bands in the blue part of the spectrum, discovered by Rayleigh, were absent in Dufay’s photographs. However, Slipher, already known to us, who was the first to discover the green line in the spectrum of the night-sky glow, confirmed the presence of two emission bands in the blue part of the spectrum. He found the following wavelengths for them: 4450 and 4180 Å.
Several years later Sommer, photographing spectra of the night-sky glow in Göttingen, found a very large number of lines in the blue-green and violet part of the spectrum[^18]. In the wavelength interval from 5130 to 3578 Å he measured forty bands and emission lines, of which about thirty coincided with lines in the spectrum of aurorae (Table 1), and twenty-two bands were identified with nitrogen bands.
It must be noted, however, that this spectrum, rich in lines and bands, was observed by Sommer on only one night out of the 41 nights during which the photography was carried out. Of the 41 photographs, on 28 there was nothing except the green line, and on 18 photographs there was nothing at all. That single photograph on which so many lines and bands were obtained was taken with the same exposure and under the same conditions as the other forty plates. This points to the inconstancy of the night-sky glow from night to night and, in any case, to the presence of some sort of disturbances.
The spectra of the night-sky glow were studied in great detail by Dufay. During the autumn of 1931 (September—November) Dufay photographed spectra with a spectrograph having two flint prisms with an 11 cm edge. This spectrograph had a “Kinoplasmat” objective with a focal length of 80 mm and a relative aperture of \(f : 1.5\); it gave a spectrum whose length from the red to the near ultraviolet region was 1 cm, which made it possible to measure wavelengths with sufficient accuracy. With exposures from 22 to 85 hours, Dufay obtained a series of good spectra with a large number of lines and bands in the blue-green part of the spectrum[^19]. Using a more luminous spectrograph with lower dispersion (\(f : 1.25\), focal length 25 mm), Dufay could obtain the most intense bands by exposing for only one night (8–9 hours). However, because of the small dispersion, the wavelength measurements were associated with large errors.
Dufay also succeeded in photographing, with a quartz spectrograph, the spectrum in the ultraviolet region. This spectrum was very weak, but in it one can distinguish, in addition to the continuous spectrum with Fraunhofer lines, also a series of emission lines and bands[^20].
Besides Sommer and Dufay, the spectrum of the night-sky glow in the blue-green part was also photographed in India by Ramazan, working with a single-prism spectrograph (February 1932)[^21]. He found the presence of most of those bands and lines which
Table 1
| Night sky | Night sky | Night sky | Polar auroras |
|---|---|---|---|
| Zommer | Dufay * | Ramanathan | Vegard |
| 5 130 | 5 139,0 | ||
| 4 866 (2) | 4 996,0 | ||
| 4 860 | 4 837 (3) | [4 877,4] | |
| 4 780 (1) | [4 779,2] | ||
| 4 709 | 4 708 (1) | 4 708,8 | |
| 4 698,4 | |||
| 4 679 (2) | |||
| 4 650 | 4 651,9 | ||
| 4 615 (1) | |||
| 4 576 (2) | |||
| 4 552 | 4 554 (3) | 4 555 | 4 552,1 |
| 4 512 (1) | |||
| 4 500 (1) | |||
| 4 478 (1) | 4 480,7 | ||
| 4 457 | 4 447 (3) | ||
| 4 422 | 4 421 (5) | 4 430 | 4 423,6 |
| 4 382 (1) | 4 375,8 | ||
| 4 351 (1) | 4 340,1 | ||
| 4 330 (1) | |||
| 4 278 | 4 278 (1) | 4 277,4 | |
| 4 270 | 4 270 (1) | 4 270 | 4 269,4 |
| 4 238 | 4 237 (1) | 4 236,2 | |
| 4 209 | |||
| 4 200 | 4 199,2 | ||
| 4 186 | 4 180 (4) | 4 180 | 4 182,5 |
| 4 116 (3) | 4 142,6 | ||
| 4 100 (2) | 4 090 | ||
| 4 082 (3) | [4 078,2] | ||
| 4 057 | 4 058,5 | ||
| 4 044 (1) | 4 040 | ||
| 4 031 (1) | |||
| 4 020 (1) | |||
| 3 999 | 3 998,5 | ||
| 3 976 | 3 980 (3) | 3 960 | [3 981,3] |
| 3 946 | 3 952 (1) | ||
| 3 941 | 3 941 (1) | 3 941,3 | |
| 3 916 | 3 915 (1) | 3 914,4 |
* Intensities (given in parentheses) were estimated approximately according to a five-point system.
were those of Dufay. Thus it may be stated that the spectra of auroras are similar at very different latitudes (for Dufay—Lyon—latitude 45°,42′; for Ramanathan—Poona, India—18°90′).
THE GLOW OF THE NIGHT SKY
The results of measurements of wavelengths in the spectrum of the glow of the night sky in the interval from 5000 to 3800 Å by Sommer, Dufay, and Ramanathan are given in Table 1. In the last column, for comparison, data for the aurorae (according to Vegard) are given.
Anticipating what follows, we note that a large part of the bands in Table 1 belongs to the nitrogen spectrum. However, the interpretation of a whole series of other lines has met with great difficulties, as will be discussed below.
In Fig. 4 a microphotometric curve is given, taken from one of Dufay’s spectrograms[^22]. On this microphotogram, besides the bright green line 5577 Å, several more lines and bands in the blue part of the spectrum are indicated.
Fig. 4.
We now turn to the long-wavelength region of the spectrum. The study of spectra in the long-wavelength region involves additional difficulties. The fact is that the sensitivity of photographic plates is low in the red part of the spectrum, and even when photographing on panchromatic plates one has to expose for an extremely long time. In addition, the dispersion of the spectrograph in the red part of the spectrum is much smaller than in the blue, which is especially perceptible, since even without this the dispersion of fast spectrographs, owing to the use of short-focus objectives, is negligibly small. For these reasons, for 10 years (until 1929) it was not possible to detect any radiation of the sky in the red-orange part of the spectrum.
But, on the other hand, already in 1921 Rayleigh[^8], observing through filters, established that the light of the night sky is relatively very rich in red light. Rayleigh obtained this conclusion both in the visual and in the photographic study of the composition of the light of the night sky through filters, and, naturally, the question arose that in the red part of the spectrum there must exist radiation of the sky.
And indeed, this radiation was discovered in 1929. It was discovered by Slipher[^23], who found in the orange-red part of the spectrum a whole group of lines with the following wavelengths: 7270, 6870, 6530, 6315, and 5892 Å.
Several years later, two of these lines were also found by Dufay[^20], who, thanks to the great sensitivity of his plates in the green part, found several more weak green lines[^24]. The wavelengths of the lines discovered by Dufay were as follows: 6315, 5892, 5662, 5478, and 5316 Å.
But an especially rich spectrum in this region was obtained by Sommer. In 1932 he published a paper[^25], in which he gave about 30 lines in the wavelength interval from 5200 to 7300 Å. He photographed
on a very fast spectrograph, which was built for photographing the spectra of extragalactic nebulae at the Mount Wilson Observatory.
7. The latest data on the spectra and their interpretation
The basic information on the spectra of the glow of the night sky, set forth in the preceding paragraph, was obtained, approximately, by 1932–1933. It was found that the spectra contain an enormous number of lines and bands (many tens) in all parts of the spectrum. However, the interpretation of the spectra of the glow of the night sky encountered very great difficulties. The attribution of the bright green line \(\lambda = 5577.3\ \text{Å}\) (oxygen atoms, see above) was established beyond doubt; it was quite definitely possible to speak of the presence of the band spectrum of molecular nitrogen. But very many other lines and bands remained unidentified.
In the period 1933–1936 the study of the spectra of the glow of the night sky proceeded at especially rapid strides. Extremely fast spectrographs were built (\(f:1.2\), \(f:0.7\), and \(f:0.55\)—in France; \(f:1\) and \(f:0.57\); glass and quartz-fluorite—in the USSR). A large number of workers became involved in the investigation of the spectra of the glow of the night sky, and as a result a whole series of cardinal questions was resolved. We now turn to the exposition of these latest data. We shall begin with the long-wavelength region of the spectrum: 8000–5000 Å.
Fig. 5.
The first distinctive feature of the spectra in this region, as compared with the spectra in the blue part, consists in the absence of the continuous spectrum always observed in the blue part. This makes plausible the supposition that the continuous spectrum of the glow of the night sky is due to sunlight scattered by the upper layers of the atmosphere and, perhaps, by some interplanetary particles: the scattered light is far more intense in the blue part of the spectrum than in the red.
THE GLOW OF THE NIGHT SKY
A second peculiarity is the great similarity to the spectra of the aurorae, in contrast to the spectra in the blue part. In the blue part of the spectrum of the aurorae there are characteristic bands that are absent in the spectra of the glow of the night sky, which gave rise to suspicions of an extraterrestrial origin of the glow of the night sky. The similarity of the spectra in the long-wavelength part is very convincing evidence that the glow of the night sky, like the polar aurorae, arises in the upper layers of the earth’s atmosphere.
The total number of lines, bands, and distinctive maxima reaches 70 in the region under consideration; moreover, besides Sommer, Kabann discovered especially many of them.^26, ^27 Fig. 5 shows a microphotometric curve taken from one of the spectra obtained by Kabann. On the curve a number of lines and bands are marked in the region 5500–6500 Å.
The principal part of the emission groups in the spectrum of the glow of the night sky in the region 8000–5000 Å belongs to the so-called first positive system of nitrogen bands. In Fig. 6 a scheme of the levels of the nitrogen molecule \(N_2\) is presented. Along the ordinate is plotted the excitation energy, expressed in electron-volts.
Normal state (marked by the letter \(X\)) is the state which, in the modern theory of spectra, is conventionally denoted by the symbol \({}^{1}\Sigma\). An energy of 6.1 eV is required in order to transfer the \(N_2\) molecule into the excited state \({}^{3}\Sigma\) (denoted by the letter \(A\)). This state is metastable. This means that a molecule which has entered this state cannot leave it by itself (the probability of transition from the metastable state to another state is close to zero). The transition will take place only in the case of an external action, for example, collision with another particle.
The next state is the state \({}^{3}\Pi\) with energy 7.4 eV (denoted by the letter \(B\)).
Fig. 6.
Each of the states indicated in Fig. 6 corresponds to an excitation of the electronic level of the nitrogen molecule. In addition, there is also energy of vibrational and rotational motion. This leads to the fact that each of the indicated electronic levels splits into a large number of energy sublevels, and in the corresponding transitions from one electronic state to another the spectra contain not lines (as in the case of atoms), but entire systems of bands.
Upon transition of the nitrogen molecule \(N_2\) from state \(B\) to state
$A$ ($^3\Pi \to {}^3\Sigma$) gives rise to a system of bands which is called the first positive band system. It is precisely these bands that are observed in the spectrum of the night-sky glow, and also in the spectra of aurorae. Most of the transitions occur from the $^3\Pi$ state with vibrational quantum numbers lying in the range of values around 15 and around 7.
Of particular interest is the question of the presence, in the emission spectra of the night sky, of a number of so-called telluric bands, present as absorption bands in the spectrum of scattered daylight. The corresponding data are given in Table 2.
Table 2
| Name of band | Water vapor | Night-sky glow | Aurorae |
|---|---|---|---|
| $a$ | Å 7330–7160 7020–6920 |
Å 7278–7200 6966–6877 |
Å 7243 |
| $C$ | 6600–6430 | 6607–6468 | 6608–6440 |
| $D$ | 6000–5850 | 5990–5861 | 5975–5867 |
According to Sommer’s data, in the spectrum of the night-sky glow there is also a whole series of telluric bands ($A$, $B$, $\alpha$, $\alpha'$ and $\alpha''$), caused by the absorption of oxygen in the Earth’s atmosphere and appearing in the radiation of the night sky. Cabannes also arrives at the same conclusion.
Finally, it was also established that in the spectra of the sky glow there are, in addition to the green line, 2 more red lines emitted by oxygen atoms. As regards the spectroscopic classification of the oxygen lines, it was found that these three oxygen lines are due to transitions between the following levels$^{28}$:
\[ \lambda = 5577\,\text{Å} \ldots\ldots 2p^1S_0 \to 2p^1D_2 \]
\[ \lambda = 6300\,\text{Å} \ldots\ldots 2p^1D_2 \to 2p^3P_2 \]
\[ \lambda = 6363\,\text{Å} \ldots\ldots 2p^1D_2 \to 2p^3P_1 \]
A scheme of the energy levels in the oxygen atom is given in Fig. 7.
Let us pass to the short-wavelength region 5000–3800 Å. Investigations of recent years, especially the works of Dufay and Cabannes$^{29, 30, 31}$, have shown the presence in this region of more than 100 lines and bands. With the exception of a few of them, whose assignment still remains unclear, the large region of lines and bands may be divided into the following groups.
First, several bands of the first negative system of nitrogen (Fig. 6)—wavelengths of maxima: 4708, 4278, 4236, 4199, and
3914 Å—and of the second positive system of nitrogen: 4574, 4059, and 3998 Å. All these bands are very weak; even the 3914 Å band, whose intensity in the spectra of aurorae is extraordinarily great and may even be compared with the intensity of the green line[^28].
Secondly, there are several weak lines from the argon spectrum. In the spectra of the night-sky glow the following lines are present: 4700, 4632, 4592, 4346, 4337, 4301, 4259, 4193, 4181, and 4160 Å.
Thirdly, there is a whole series of lines whose nature is still unknown and which are typical of the spectra of cometary nuclei. Among them the following lines are especially intense: 4719, 4328, 4299, 4052, 4021, 4014, and 4002 Å. According to Baldet’s measurements[^32], in the spectra of cometary nuclei there are lines with wavelengths: 4724, 4329, 4301, 4052, 4021, 4014, and 4002 Å.
All three of the indicated groups of lines and bands by no means exhaust the spectrum of the night-sky glow in the region 5000–3800 Å. Not included here are most of precisely the brightest and most typical lines and bands, among them the two famous blue bands discovered by Rayleigh as early as 1922. These two bands, with maxima at 4220 and 4433 Å, are distinguished in the spectra of the night-sky glow by very great intensity, but they are entirely absent from the spectra of aurorae (these two bands are customarily denoted specially by the symbols \(X_1\) and \(X_2\)).
Fig. 7.
The question of the origin of these bands, which long remained open, has quite recently been the subject of very lively discussion. In 1934 Kaplan[^33] reported that he had succeeded in exciting in the nitrogen glow a new system of bands, to which the two bands \(X_1\) and \(X_2\) belong. Despite certain quantitative discrepancies, these new bands discovered by Kaplan may be regarded as coinciding with the bands that Vegard was able to observe when bombarding, with cathode rays, a solid mixture (at very low temperatures) of nitrogen dioxide and argon[^28]. The Vegard—Kaplan bands were classified by Herzberg: their frequencies in reciprocal centimeters are given by the formula:
\[ \nu = 49\,774.4 + (1446.46\,v' - 13.93\,v'^2) - \]
\[ - (2345.16\,v'' - 14.445\,v''^2). \]
The first bracket shows that the initial state is (Fig. 6) the metastable state \(A\ ({}^{3}\Sigma)\). On the other hand, if in the second bracket we put \(v = 1\), we obtain the number
2331 cm\(^{-1}\), which is the Raman frequency (energy of the vibrational motion) of the nitrogen molecule. Consequently, the final state is the normal state \(X\ ({}^1\Sigma)\) of the nitrogen molecule. The frequency corresponding to \(\nu'=\nu''=0\) shows that the energy of the metastable level \(A\) is equal to 6.1 V instead of the 8.2 V accepted up to now. Owing to this error, which had existed in determining the energy of level \(A\) until now, the wavelengths of the Vegard—Kaplan bands calculated previously were incorrect, and they could not be detected. However, for the Vegard—Kaplan band system to arise, specific conditions are necessary, since the initial state is metastable.
Fig. 8.
Cabannes and Dufay attempted to verify Kaplan’s assumption; they made special measurements of spectrograms of night-sky luminescence and compared them with calculations according to the formula given above. Complete agreement was found. A large number of bands in the spectra of night-sky luminescence proved to be very close in wavelength to the Vegard—Kaplan bands[^31]. True, in order to obtain close agreement, it was necessary to subtract 21 cm\(^{-1}\) from the constant term in Herzberg’s formula. In this case all the principal bands in the spectrum of night-sky luminescence in the interval from 3400 to 5400 Å found an unquestionable interpretation from this point of view. It turned out that in the spectrum of night-sky luminescence all the Vegard—Kaplan bands are present for which the quantum number \(\nu\) of the initial state is close to 2, with \(\nu''=\nu'=10, 11, 12, 13\).
In Fig. 8 a microphotogram from one of the spectra of Dufay and Cabannes is presented. For the principal bands the wavelengths are indicated, and beneath them are given the values of the quantum numbers \(\nu'\) and \(\nu''\) for the transition responsible for the given band.
8. General Characteristic of the Spectra of Sky Luminescence. Comparison with the Spectra of Aurorae
Summarizing the results of 15 years of investigations of the spectra of night-sky luminescence, the following may be said.
Besides the continuous spectrum (in the blue and ultraviolet part of the spectrum) with Fraunhofer absorption lines, more than 200 lines and bands have been found in the radiation. Through prolonged laboratory experiments and calculations it has been established that these lines and bands are emitted by the following gases:
a) Atomic oxygen: the famous bright green line \(\lambda = 5577.3\ \mathring{\mathrm A}\) \((2p^{1}S_{0} \to 2p^{1}D_{2})\) and two red lines \(\lambda = 6300\ \mathring{\mathrm A}\) \((2p^{1}D_{2} \to 2p^{3}P_{2})\), \(\lambda = 6363\ \mathring{\mathrm A}\) \((2p^{1}D_{2} \to 2p^{3}P_{1})\).
b) Several series of the molecular spectrum of nitrogen. In decreasing order of intensity these series may be arranged as follows: Vegard–Kaplan bands \(A \to X\) (Fig. 7); bands of the first and second positive systems; the negative system.
c) Telluric bands of oxygen and water vapor (bands corresponding to the vibrational motion of the water molecule).
d) A large number of lines coincide with lines in the spectra of cometary nuclei. Their nature is unknown.
e) Several lines of the argon spectrum.
There is also a supposition, though a very doubtful one, concerning the presence of lines of nitrogen and helium atoms.
To what extent do the spectra of the night-sky glow correspond to the spectra of aurorae? These spectra are in many respects similar to one another, which is quite natural, since the medium giving rise to the spectra is one and the same in both cases: this medium is the upper layers of the atmosphere. But in many respects these spectra differ from each other. Thus, for example, the negative system of nitrogen bands is very bright in the spectra of aurorae, but in the spectra of the night-sky glow these bands are extremely weak. Just the reverse is the case for the second positive system of nitrogen: it is very bright in the spectra of the night-sky glow and weak in aurorae.
This difference points to a difference in the conditions under which these two luminescences arise. This difference can be characterized as a difference in the degree of excitation. From the scheme of the energy levels of the nitrogen molecule (Fig. 6) it is seen that, for the excitation of one or another series of bands, the following energies are needed:
| Vegard–Kaplan bands | 6.1 eV |
| First positive system of nitrogen | 7.4 eV |
| Second positive system of nitrogen | 11.0 eV |
| Negative system of nitrogen bands | 19.6 eV |
It is remarkable that this series, arranged in order of increasing excitation energy of the nitrogen molecule, at the same time gives the sequence with respect to the intensity of these bands in the spectra of the night-sky glow: the intensity of the bands indicated in the first line is the greatest, and of those indicated in the last line the smallest. The greater the energy of the level that is the initial one for a given system of bands, the smaller the intensity of these bands in the spectra of the night-sky glow.
*
It is even more remarkable that this same series also holds for the spectra of aurorae, but only in exactly the opposite sense: in the spectra of aurorae the Vegard—Kaplan bands are very weak, while the brightness of the negative system of nitrogen bands is especially great. In the spectra of aurorae: the greater the energy of the level that is the initial one for the given bands, the greater their brightness.
9. Attempts to reproduce, under laboratory conditions, the spectra of the night-sky glow
Vegard’s attempt (1923) to identify the green line \(\lambda = 5577 \text{ Å}\), which stands out brightly in the spectra of aurorae and of the night-sky glow, with the glow of solid frozen nitrogen subjected to bombardment by cathode rays deserves mention only for its historical interest. As we already know (§ 4), Vegard’s hypothesis proved to be incorrect: shortly after the publication of Vegard’s work, McLennan and Shrum discovered that the yellow-green radiation of nitrogen at low temperatures, which Vegard had taken for the green line \(\lambda = 5577 \text{ Å}\), in reality consists of three components with quite different wavelengths: \(5556\), \(5619\), and \(5654 \text{ Å}\). Thus the famous hypothesis, according to which the Earth is surrounded by frozen nitrogen, was refuted. As we know, McLennan and his co-workers established that the green line \(5577 \text{ Å}\) belongs to the spectrum of atomic oxygen and appears only in the presence of a large quantity of inert gases.
Beginning in 1928, Kaplan undertook a series of experiments with an electric discharge in an atmosphere of nitrogen mixed with oxygen (the composition of the Earth’s atmosphere). It turned out that the glow of the gas in the discharge tube continues even after the electric current is switched off, i.e. afterglow takes place. The spectrum of this afterglow differed from the spectrum of the gas glow during the passage of the discharge. To isolate the afterglow, Kaplan used a phosphoroscopic apparatus in which the electric current was interrupted at definite time intervals, and at the moment when the current was flowing the glow was blocked; it opened only during the intervals of time when no electric current was passing through the discharge tube. By this method it proved possible to excite the green line \(\lambda = 5577.3 \text{ Å}\) into emission, and for this it was necessary to produce a discharge in nitrogen with a small admixture (several percent) of oxygen[^34]. In 1932 Kaplan was able to “activate” nitrogen,—he obtained the glow of nitrogen in an uncondensed discharge, after the discharge tube had previously been subjected to the action of an electric discharge lasting several days[^35]. Under these conditions he discovered in the afterglow spectrum
at a relatively high gas pressure (several millimeters of mercury) bands of ionized nitrogen molecules (the negative band system) were observed, not accompanied by the appearance of lines of ionized nitrogen atoms, which, on the contrary, are always present when bands of ionized nitrogen molecules are excited at low pressure. Kaplan came to the conclusion that there are metastable molecules \(A\ ({}^{3}\Sigma)\) in the mixture producing the afterglow, which, by electron impacts, are directly excited to the intense glow of the bands of the negative system. In connection with this, Kaplan suggested that the glow of the polar aurorae may be interpreted as the result of an electric discharge in a mixture of nitrogen and oxygen containing a large number of metastable molecules. From this point of view the spectrum of the aurorae may represent the result of a superposition of the afterglow and the glow of the discharge. Kaplan studied the discharge conditions under which there appears a weak glow, resembling in appearance the aurora and containing in its spectrum the bands of the negative system, as well as the first and second positive systems of nitrogen. The character of the spectra obtained by Kaplan in this way did not differ greatly from the spectrum of the aurorae[^36].
Continuing to work by this method, Kaplan obtained in 1934 in the afterglow of nitrogen (the most suitable pressure being \(0.1\) mm) a new band system, which proved identical with the system of bands discovered by Vegard in the spectrum of the luminescence of solid nitrogen. The new band system was, as already indicated above, classified by Herzberg. The level that is the initial one for this band system undoubtedly corresponds to the metastable state which we (Fig. 6) denoted by the symbol \(A\ ({}^{3}\Sigma)\). Consequently, the appearance of this band system is indisputable proof of the existence in activated nitrogen of metastable molecules \(A\). Soon after this Kaplan suggested that a series of bands in the spectrum of the night-sky glow can best be interpreted as an aggregate of bands belonging to the first and second positive systems of nitrogen and also to the new band system \(A \to X\) discovered shortly before. The presence of activated nitrogen makes possible the excitation of a spectrum of this type, which is obtained under the corresponding conditions in the afterglow.
Thus we may regard this part of the radiation of the night sky as being caused by a very weak afterglow in rarefied nitrogen in the upper layers of the atmosphere.
In 1935 Kaplan reported new experiments, as a result of which it was found that the green line and the bands of molecular nitrogen are excited simultaneously under conditions which reproduce (at any rate in principle) the conditions of the night-sky glow. Instead of attempting to separate the glow of the discharge from the afterglow, Kaplan simply photographed the spectrum of the glow of a discharge tube, the electric current in which was periodically interrupted so frequently that the current strength could not reach its maximum value. Under ...
under these conditions a new system of bands \(A \to X\) (the Vegard—Kaplan bands) and the second positive system of nitrogen appear in the radiation spectrum together with the green line.
The entire body of observations clearly showed that the radiation obtained under these conditions resembles, in its properties, the glow of the night sky \(^{37,38}\).
In 1934 Desjardins and Schwegler investigated \(^{39}\) the glow excited by the rotation of mercury drops along the inner wall of a glass vessel containing unpurified inert gases (triboluminescence, i.e., glow due to friction). If the tube contained neon with traces of nitrogen (and possibly also of helium), then the spectrum obtained was very similar to the spectrum of the aurora both with respect to its spectral composition and in the sense of the intensity ratios for the individual components of the spectrum. The spectrum in this case included the principal bands of the negative and second positive systems of nitrogen, as well as several weak lines of unknown origin which, perhaps, might be attributed to ionized nitrogen atoms or to helium atoms. However, in comparison with the glow of the night sky the similarity of the spectra is much less. If, under the same conditions, the glow of argon is excited, then the spectra obtained, in addition to the lines of argon atoms, contain a large number of lines belonging to argon ions; this circumstance gives an idea of the degree of excitation attainable by this method. The same spectra are also obtained without mercury if continuous friction is produced (with the aid of a woolen cloth or cardboard) on the outer wall of a glass vessel rotated by means of an electric motor. A more careful study of the glow spectra of unpurified neon showed the presence of a series of bands which may be the Vegard—Kaplan bands (measured wavelengths: 4540, 4218, 3981, 3845, 3772 Å; calculated: 4535, 4219, 3979, 3844, 3768 Å). With the exception of the last of these bands, all of them, apparently, are present in the spectra of the aurorae (according to Vegard’s data). On spectrograms corresponding to unpurified argon, three bands are also found which are very close to the Vegard—Kaplan bands (measured wavelengths: 4317, 4220, 3981 Å).
On the other hand, in the physics laboratory of the University of Lyon, Bernard investigated the glow obtained when a gas mixture enclosed in a three-electrode vessel was bombarded by electrons \(^{40}\): the gas mixture consisted of argon and very small quantities of nitrogen or air (the total gas pressure in the vessel was between 0.1 and 0.6 mm; the fraction of nitrogen varied from \(10^{-1}\) to \(10^{-5}\) of the total pressure). The glow obtained under these conditions, with an accelerating potential between 15 and 20 V, proves to be very similar in its spectral composition to the glow of the night sky (apart from the excitation of the bright argon lines). Besides the bands of the first and second positive systems of nitrogen, a large number of Vegard—Kaplan bands are obtained in the spectra, some of which
belong to the sequences to which the following differences of quantum numbers correspond: \(\nu' - \nu'' = 10, 11, 12\), and \(13\). Table 3 gives the results of wavelength measurements obtained from these spectrograms. In the same table, for comparison, data calculated by the Herzberg formula are given.
Table 3
| Measured | Calculated | Measured | Calculated | Measured | Calculated |
|---|---|---|---|---|---|
| 5326 | 5327 | 4495 | 4495 | 3885 | 3956 |
| 5060 | 5061 | 4320 | 4320 | 3769 | 3768 |
| 4960 | 4962 | 4219 | 4219 | 3750 | 3753 |
| 4837 | 4838 | 4171 | 4171 | 3683 | 3684 |
| 4718 | 4718 | 4144 | 4147 | 3664 | 3666 |
| 4650 | 4651 | 4072 | 4073 | 3603 | 3603 |
| 4616 | 4614 | 3979 | 3979 | 3582 | 3582 |
| 4605 | 4605 | 3940 | 3940 | 3503 | 3502 |
| 4535 | 4535 | 3884 | 3889 |
The presence in the glow of bands of the first positive system indicates the presence of molecules in the metastable state \(A\ ({}^3\Sigma)\). As the partial pressure of nitrogen decreases, the relative intensity of the Vegard—Kaplan bands increases, while the intensity of the bands of the second positive system, on the contrary, decreases. A decrease in the nitrogen pressure therefore increases the probability of transitions \(A \to X\), corresponding to the emission of the Vegard—Kaplan bands.
10. Measurement of the Brightness of the Sky
In the pole of the world (the Pole Star), the density of stars is the smallest; therefore it is there that the glow of the night sky is usually studied. In this case it is very convenient to take the Pole Star as a brightness standard. Unfortunately, the brightness of the Pole Star varies somewhat with time. The amplitude of these variations, however, is small: Dufay found\(^{22}\) that the brightness changes visually by 0.11 stellar magnitude and photographically by 0.20 stellar magnitude. The period of the brightness oscillations is somewhat more than four days. These brightness variations can be allowed for by the corresponding corrections.
When comparing the brightness of two stars, the result of the comparison depends on the method of comparison. Usually either the eye (visual measurements) or a photographic plate is used for comparison. An ordinary orthochromatic photographic plate is especially sensitive to blue rays and only slightly sensitive in the green part of the spectrum. The human eye is very sensitive in the green part of the spectrum, but very little sensitive to blue rays. Therefore, if two stars have dif-
...spectral composition, then determining their brightness relative to one another gives different results depending on the method of determination. If the given star is rich in blue rays, then its photographic magnitude will be smaller than its visual magnitude (photographically its brightness will be measured as greater). Thus a comparison of the photographic and visual brightness can give an indication of the spectral composition of the radiation.
According to the determinations of the Harvard Observatory, the Pole Star has a visual brightness equal to 2.12 stellar magnitudes, and photographically—2.62 stellar magnitudes.
For the period from 1923 to 1926, Dufay made a large number of determinations of the brightness of the sky by visual and photographic methods. These measurements, made over the course of 120 nights, were carried out for the most part at Montel, and also in Haute-Provence and at the Lyon Observatory. According to Dufay’s measurements, on average 1 square degree of sky near the Pole Star gives an amount of light equivalent to the light from a star whose magnitude is: visually \(\mu = 4.60\) stellar magnitude (35 clear nights), photographically \(\mu = 4.36\) stellar magnitude (55 clear nights).
If the measurements are referred to a star whose magnitude is equal to 1.00, then 1 square degree of sky is equivalent to: 0.036 stars whose visual brightness is equal to 1.00 mag., and 0.045 stars whose photographic brightness is equal to 1.00 mag.
Measurements made by other investigators are collected in Tables 4 (visual measurements) and 5 (photographic measurements).
Table 4
Visual measurements
| Author | Years | Place of observation | \(\mu\) | \(N_1\)* |
|---|---|---|---|---|
| Newcomb | 1901 | Iceland | 4.84 | \(0.029^{1}\) |
| Burns | 1902 | England | 4.28 | \(0.050^{2}\) |
| Intema | 1907/3 | Holland | 3.13 | \(0.140^{4}\) |
| Abbot | 1909/10 | California (Mount Whitney) | 3.81 | \(0.075^{57}\) |
| Van Rhijn | 1913 | Mount Wilson | 3.21 | \(0.130^{58}\) |
| Burns | 1914 | England | 4.81 | \(0.030^{59–60}\) |
One may also point to the measurements of Elvey, made around 1932 with the aid of photoelements \(^{22a}\). He found \(\mu = 4.5\). In the photoelectric measurement, the spectral region used (the spectral sensitivity of the photoelement) was intermediate between photographic and visual measurements.
* \(N_1\) is the number of stars of the first magnitude equivalent to 1 square degree of sky.
Table 5
Photographic measurements
| Author | Years | Place of observation | \(\mu\) | \(N_1\) |
|---|---|---|---|---|
| Taunley . . . . | 1902 | Lick Observatory . . . | 4.06 | 0.063 |
| Intama . . . . | 1908 | Holland . . . | 3.35 | 0.115^4 |
| Fabry . . . . | 1909 | France . . . | 5.09 | 0.023^5 |
| Bourget . . . . | 1917 | ” . . . | 4.48 | 0.041^61 |
| Bauer, Danjon and Jean Langevin . . . . | 1923 | Mont Blanc . . . | 4.27 | 0.049^62 |
| Dufay . . . . | 1923—1926 | Montpellier . . . | 4.36 | 0.045^27 |
Taking Dufay’s figures as the most reliable, one may make the following estimates^41. If it is assumed that the sky has uniform brightness in both hemispheres and if the influence of the Milky Way is neglected, then one may calculate that the sky as a whole has a visual brightness of magnitude 6.9. The light from the entire sky is equivalent to 1460 stars of the first magnitude; it is 200 times weaker than the light of the full Moon.
If these data are translated into the language of ordinary photometric units, one may say that the sky has a brightness approximately equal to \(10^{-8}\) candle per \(1\ \mathrm{cm}^2\). On a horizontal plane such a uniformly luminous sky should give an illumination equal to \(3\cdot 10^{-4}\) lux. Consequently, the illumination from the night sky is the same as from a 25-candle lamp at a distance of \(335\ \mathrm{m}\). If a photographic plate is exposed to the light of the night sky, a noticeable blackening is obtained with an exposure of 1—2 min.
Using the data of stellar statistics, one may calculate that the illumination given by the stars alone would be \(6\cdot 10^{-5}\) lux. This is 5 times less than the true illumination. Thus only 20% of all the light of the night sky belongs to the stars.
11. Observations of skyglow by the extinction method
In 1928 MacLennan, together with his collaborators, discovered the following very important fact^42: the intensity of the green line in the first half of the night does not decrease, as would have been expected, but increases, reaching a maximum around midnight. In the second half of the night the intensity of the green line decreases.
Unfortunately, the observations of MacLennan and his collaborators were of a very qualitative and preliminary character. The photographic method used by them required long exposures, and neither the more exact course of the intensity during the night nor the degree of increase of the intensity toward the middle of the night was established by them.
In order to investigate the question to the end, it was necessary to employ some especially sensitive methods of photometry.
Such a very sensitive method of photometry was successfully applied to the study of the glow of the night sky in 1934. The matter concerns the photometric “extinction method” developed by S. I. Vavilov, which is the most sensitive method among all existing ones.
After some (30–50 min.) stay in darkness, the sensitivity of the eye, as is known, increases greatly: the so-called adaptation of the eye to darkness takes place. If the corresponding calculation is made, it turns out that the eye, adapted to darkness, is capable of receiving a visual impression from exceedingly small quantities of light, to which no physical instrument will respond. Thus, according to measurements by Vavilov and his collaborators, under the corresponding conditions the eye can sense a luminous flux of such low intensity that only 10–20 light quanta enter the eye each second. To photograph such a weak beam an enormous exposure would be needed. The question arises whether the eye cannot be used as an instrument for measuring the brightness of extremely weak beams of light.
The extinction method developed by S. I. Vavilov43 makes it possible to do this. The method uses the existence in the eye of a definite threshold of visual irritation—some minimum of brightness below which the eye “does not see” at all. With the aid of one or another device we shall weaken the investigated beam of light until it ceases to be visible to the eye, i.e. weaken it exactly to the threshold of vision. Suppose that for this the investigated beam had to be weakened \(n\) times. If, in doing so, some other beam, whose intensity is known and equal to \(I\), had to be weakened \(N\) times in order to bring it to the threshold of vision, then the sought intensity \(x\) of the investigated beam will be found from the simple relation
\[ x = \frac{n}{N} I . \]
At the present time this extraordinarily simple and convenient method of measurement has become widely used.
In 1934 a large group of scientific workers set out for the highest mountain of the Caucasus—Elbrus—with the aim of carrying out there a number of observations. The attempt proved very successful, and at present systematic scientific work has been deployed on Elbrus.
Because of the great dustiness of the lower layers of the atmosphere, it is very important to carry out observations of the glow of the night sky from a height of several thousand meters. In connection with this, beginning in 1934, observations of the glow of the night sky by the above-mentioned extinction method have been carried out on Elbrus every summer. First of all, an attempt was made to study more accurately the variations in the intensity of the green line during the night.
The work was carried out independently by two groups of observers (the Physical Institute of the Academy of Sciences of the USSR\(^ {44}\) and the State Optical Institute\(^ {45}\)).
The results obtained in observations of the green line through a monochromator are presented in Fig. 9. A clearly expressed maximum at 1 o’clock at night is distinctly visible.
These measurements prove the existence of the phenomenon mentioned above—a very sharp increase in the brightness of the green line after nightfall. This fact presents enormous difficulties for its theoretical interpretation. If the brightness maximum occurred at midnight, its explanation could be made more naturally, since at midnight the Sun passes through its lowest position below the horizon, and this maximum of brightness would indicate a direct connection between the intensity of the green line and the position of the Sun. However, the maximum occurs not at midnight, but an hour later. After midnight the brightness of the green line continues to increase just as rapidly and by one o’clock at night exceeds the brightness at midnight by several tens of percent. This “delay” indicates the presence of some special processes, as yet unknown to us.
Fig. 9.
We shall have to return to this question later. Is the sharply expressed maximum of brightness at 1 o’clock at night characteristic only of the green line, or is it also inherent in other components of the night-sky glow? The solution of this question is very important for understanding the nature of the glow of the night sky. As early as 1934 the author established\(^ {45}\) that the spectral region accessible when applying the method of extinction by observing through a monochromator extends from 4500 to 6000 Å, embracing almost the entire visible spectrum, with the exception of the extreme red region, where the sensitivity of the eye is already very low.
In connection with this, in the expedition to Elbrus in the summer of 1935, the Optical Institute carried out the corresponding observations\(^ {46}\). At the “Krugozor” of Elbrus, at an altitude of 3000 m above sea level,
a large optical installation was mounted at the seashore, the schematic arrangement of which is shown in Fig. 10.
The monochromator \(M\) is mounted on a large stone foundation. In front of its entrance slit a swing-away prism for total internal reflection \(P\) is fixed. When the prism is placed close up to the slit (this position of the prism is indicated by a dashed line), light from the standard lamp \(E\) enters the monochromator. The standard lamp is a special incandescent lamp rated at 2.5 V
Fig. 10.
and 0.5 A, for which the color temperature was known for different filament currents, i.e., that temperature which an absolutely black body must have in order for its spectral energy distribution to be the same as that of the given lamp. The standard lamp was supplied with current from a storage battery \(B\), and its electrical conditions were regulated by means of a milliammeter \(mA\) and a voltmeter \(V\). The light from the lamp was attenuated the required number of times by a neutral-gray filter \(F\).
If the prism for total internal reflection \(P\) was swung aside, then light entered the monochromator directly from the photometered portion of the sky. Behind the exit slit of the monochromator an objective \(Z_1\) was installed. The eye was positioned so that the objective \(Z_1\) was seen in its entirety, flooded with the light emerging from the monochromator. A neutral-gray wedge \(K\) served to attenuate the light to the threshold of sensitivity of the eye.
The width of the monochromator slits was such that the spectral interval observed simultaneously amounted to 150 Å in the blue part of the spectrum and 300 Å in the yellow part.
With this installation it was possible to measure the energy distribution in the emission spectrum of the night sky in the wavelength region \(4550\)—\(5900\) Å. The measurements could be made so rapidly that in one night it was possible to record 5—7 complete curves. It turned out that
the spectral composition of the night-sky glow changes sharply during the night. A detailed study of these changes has yielded many significant results.
Figure 11 gives curves showing the distribution of energy over the spectrum of the night-sky glow at different hours of the night. Wavelengths in Å are plotted along the abscissa, and along the ordinate—the amount of energy contained in an interval of 1 Å at each given
Fig. 11.
place in the spectrum. The figure shows five curves: for \(22^{h}30'\), \(23^{h}40'\), \(0^{h}55'\), \(1^{h}40'\), and \(2^{h}40'\).
Owing to the wide slits of the monochromator, the resulting picture of the distribution of energy over the spectrum is correspondingly smoothed (averaged). For example, when the monochromator is set to
\[ \lambda = 5600\ \text{Å}, \]
with our slit width an interval of wavelengths of approximately \(300\ \text{Å}\) is passed, and we regard the energy measured in this case as if it were distributed over this entire interval, although in fact in this interval almost all the energy is due to monochromatic radiation—the bright green line \(\lambda = 5577.3\ \text{Å}\). Our curves do not give details of the spectrum, but they show the averaged energy content over the portion of the spectrum transmitted by the slit.
From these curves one can see how much the spectral composition changes during the night. If, for example, one compares the curve for \(21^{h}30'\) (dotted line) and for \(0^{h}55'\) (solid line), then in the green part of the spectrum the first of these two curves has ordinates half as large; but in the blue part this curve not only becomes equal to the second curve, but rises above it.
Let us turn, however, to a more exact quantitative analysis of these curves.
On the basis of the curves in Fig. 11 one can calculate how the intensity of the night-sky glow changes during the night. These calculations give, for \(\lambda = 5600\ \text{Å}\), the following intensities at different
night hours (in arbitrary units):
\[ \begin{array}{rlrl} 22^{h}30'&—3.3; & 1^{h}40'&—6.5;\\ 23^{h}40'&—4.0; & 2^{h}40'&—5.2;\\ 0^{h}55'&—7.1.& \end{array} \]
Thus, in the green part of the spectrum there is already the nocturnal course of intensity known to us: a steep increase in the first half of the night, a maximum at approximately 1 o’clock in the morning, and then a slower decline. But the change during the night in the form of the spectral curves shows that in other parts of the spectrum the nocturnal course is different. And indeed, if we take the corresponding data for the blue part of the spectrum, 4550 Å, the following picture is obtained:
\[ \begin{array}{rlrl} 22^{h}30'&—4.3; & 1^{h}40'&—5.0;\\ 23^{h}40'&—2.4; & 2^{h}40'&—6.6.\\ 0^{h}55'&—3.2;& \end{array} \]
Here there is no increase in intensity at all in the first half of the night; on the contrary, at first the intensity decreases, and then it increases. One gets the impression that the nocturnal course of intensity in the blue part of the spectrum has a minimum at midnight.
Fig. 12.
To verify this conclusion, one may construct, in an analogous way (from the curves of Fig. 11), the nocturnal course of brightness for all wavelengths. The results obtained in this way are presented in Fig. 12.
The curves for \(\lambda = 5600,\ 5450\), and \(5300\) Å all have a well-defined maximum around 1 o’clock in the morning. But for \(\lambda = 5150\) and \(5000\) Å the maximum at 1 o’clock in the morning, although still present, is already very weakly expressed, and, moreover, a dip appears on the curves around
for 24 hours. Finally, for \(\lambda = 4850, 4700\), and \(4550\) Å there is no maximum at 1 a.m. at all, but the dip around midnight is revealed with certainty.
Analysis of these curves shows that there is a superposition of two kinds of glow: one having a minimum of intensity around midnight and predominating in the blue part of the spectrum, and another having a maximum at 1 a.m. and predominating in the green part of the spectrum. The curves in Fig. 12 give a gradual transition from a sharp maximum at 1 a.m. to a minimum at midnight.
As for the glow of the second type, predominating in the green part of the spectrum and having a maximum at 1 a.m., we know the nature of this glow: it is the intrinsic glow, for which (at any rate for the bright green line) an analogous nocturnal course of brightness has been established. But what is the nature of the glow of the first type, having a minimum of brightness around midnight and predominating in the blue-violet part of the spectrum?
Apparently, a plausible interpretation can also be given for this glow. It must be scattered sunlight. Indeed, the scattering of light by gases obeys, as we know, Rayleigh’s law, according to which light is scattered the more intensely the shorter its wavelength (inversely proportional to the fourth power of the wavelength). Because of this, blue-violet rays predominate in scattered light (the blue color of the sky). Moreover, before midnight the Sun sinks lower and lower below the horizon, but after midnight, on the contrary, it rises, approaching the horizon; therefore in the first half of the night the intensity should decrease, and in the second half of the night it should increase. At midnight there should either be no scattered light at all (the Sun is so far below the horizon that the solar rays do not illuminate even the uppermost layers of the atmosphere), or in any case its intensity should have a minimum.
Such an interpretation of the two constituent parts of the light of the night sky seems to us quite plausible. The question arises whether these curves cannot be used to decide what fraction of all the light is scattered light and what fraction is the intrinsic glow of the night sky. An attempt to carry out such a separation was made by us \(^{47}\).
In attempting to separate the curves of Fig. 11 into components for scattered light and the intrinsic glow of the sky, one must remember the presence of yet a third kind of radiation in the night sky—the light of faint stars. The light of the stars, as we know, amounts to approximately 20% of all the light, i.e. to a quite appreciable quantity that must be taken into account. Thus, the problem posed by us requires the division of all the energy of the glow of the night sky into three parts—the light of stars, scattered light, and the intrinsic glow of the sky.
This problem therefore contains three unknowns, for which only their sum is known. In other words, we have only
one equation with three unknowns, and in order to solve the problem it is necessary to make some assumptions that would narrow the range of possible solutions.
As regards the light of the stars, we may quite well assume, with respect to it, that its intensity remains one and the same throughout the whole night. Moreover, we may make the quite plausible assumption that the integral radiation of all the stars corresponds on average, in its color, to the radiation of an absolutely black body with a temperature of \(5500^\circ K\). This directly applies to stars of spectral type \(G\), and, owing to the great prevalence of this class (the majority of nebulae, the Milky Way), it may be extended, without a very large error, to all stellar integral radiation.
As regards scattered light, we can indicate its spectral composition with sufficient accuracy. This spectral composition of scattered light is determined by factors known to us: it depends on the spectral composition of the “source material” for scattering—the solar rays themselves—and also on the law of scattering of light by gases, the law of inverse proportionality to the fourth power of the wavelength (Rayleigh’s law). Since both are known, it is possible to compute the curve of the distribution of energy in scattered light. It is precisely in this way that the blue color of the sky is explained; moreover, the computations, in the main, correspond quite well to the measured values.
Fig. 13.
For our purposes it is best to use the curve computed by King, taking secondary scattering into account \(^{48}\). We considered this curve to be unchanged in form throughout the entire night.
Finally, substantial assistance in the decomposition of the curves of interest to us may be provided by the following circumstance. Green
line of the night-sky glow has a characteristic course of brightness during the night, with a maximum at 1 o’clock at night. The green line predominates in quantity of light throughout the whole green part of the spectrum of the night-sky glow, and therefore, for those curves which will be obtained by separating the intrinsic sky glow from the curves of Fig. 11 in the green part, one may assume, for checking the curves obtained, the same nocturnal course with a maximum at 1 o’clock at night. The curves obtained may be additionally checked by requiring that at 1 o’clock at night the intensity in the green part be 2.5–3 times greater than at 10 o’clock in the evening, and 1.5 times greater than at 3 o’clock in the morning.
The results of the calculations performed are presented in Fig. 13. The separation of the curves was made for three moments: the beginning of night (more precisely, the beginning of the night measurements on Elbrus, which usually could not be started earlier than 10 o’clock in the evening, since before that hour the slopes of Elbrus are almost always shrouded in fog)—10 h. 30 m. in the evening; the approximate moment of maximum intensity of the green line—0 h. 55 m.; and the end of night—2 h. 40 m. in the morning. Each set of three curves, taken together, gives one of the curves of Fig. 11. Of these three curves, one corresponds to the intrinsic glow of the night sky \(L\), the second to the light of the stars \(Ef\), and the third to the scattered light \(D\).
These curves show how different the relative share of each kind of radiation is at different moments of the night.
The area of each curve is proportional to the energy of the given kind of radiation at the given moment of time (in the wavelength interval from 4550 to 5900 Å, for which all the measurements were made). Thus, if the areas of all the curves are measured, one can obtain the percentage composition of the light of the night sky at different hours of the night.
In order to make the quantities thus obtained absolute, we made additional measurements, comparing the energy of the standard light source with which the night-sky glow on Elbrus was compared with that of an absolutely black body maintained at a temperature of \(850^\circ\) K.
The results of the calculations are presented in Table 6. The energy is given in \(\mathrm{erg}/\mathrm{cm}^2\ \mathrm{sec}\), and each number gives the magnitude of the energy falling on \(1\ \mathrm{cm}^2\) in 1 sec for the radiation of the sky in the wavelength interval 4550–5900 Å.
It is seen from Table 6 that the energy of the total radiation of the sky is greater by 40 percent in the second half of the night than in the first, but in general changes comparatively little. As for the separate components, their relative share changes to a very great extent during the night. This becomes especially evident if, taking the energy of the total radiation as 100, the share of the separate components is expressed in percentages. The corresponding data are given in Table 7. From this table it is seen that if at the beginning of the night all three components of the radiation are present in approximately equal amounts, then at 1 o’clock at night the composition of the sky radiation proves to be quite different: more
Table 6
| Hours of night | Energy of total radiation (1) | Including scattered light (1) | Including light of faint stars (1) | Including intrinsic skyglow (1) | Note |
|---|---|---|---|---|---|
| \(22^{h}30'\) | \(1.14\cdot10^{-3}\) | \(0.36\cdot10^{-3}\) | \(0.38\cdot10^{-3}\) | \(0.40\cdot10^{-3}\) | 1) The radiation energy is given in \(\mathrm{erg}/\mathrm{cm}^{2}\cdot\mathrm{sec}\) (see explanation in the text). 2) The separation of the curves was carried out only for the moments of the night: \(10^{h}40'\), \(0^{h}55'\), and \(2^{h}40'\). |
| \(23^{h}40'\) | \(1.17\cdot10^{-3}\) | (2) | (2) | (2) | 1) The radiation energy is given in \(\mathrm{erg}/\mathrm{cm}^{2}\cdot\mathrm{sec}\) (see explanation in the text). 2) The separation of the curves was carried out only for the moments of the night: \(10^{h}40'\), \(0^{h}55'\), and \(2^{h}40'\). |
| \(0^{h}45'\) | \(1.72\cdot10^{-3}\) | \(0.30\cdot10^{-3}\) | \(0.38\cdot10^{-3}\) | \(1.04\cdot10^{-3}\) | 1) The radiation energy is given in \(\mathrm{erg}/\mathrm{cm}^{2}\cdot\mathrm{sec}\) (see explanation in the text). 2) The separation of the curves was carried out only for the moments of the night: \(10^{h}40'\), \(0^{h}55'\), and \(2^{h}40'\). |
| \(1^{h}40'\) | \(1.68\cdot10^{-3}\) | (2) | (2) | (2) | 1) The radiation energy is given in \(\mathrm{erg}/\mathrm{cm}^{2}\cdot\mathrm{sec}\) (see explanation in the text). 2) The separation of the curves was carried out only for the moments of the night: \(10^{h}40'\), \(0^{h}55'\), and \(2^{h}40'\). |
| \(2^{h}40'\) | \(1.63\cdot10^{-3}\) | \(0.49\cdot10^{-3}\) | \(0.38\cdot10^{-3}\) | \(0.76\cdot10^{-3}\) | 1) The radiation energy is given in \(\mathrm{erg}/\mathrm{cm}^{2}\cdot\mathrm{sec}\) (see explanation in the text). 2) The separation of the curves was carried out only for the moments of the night: \(10^{h}40'\), \(0^{h}55'\), and \(2^{h}40'\). |
Table 7
| Hours of night | Total light of the night sky in % | Including scattered light in % | Including light of faint stars in % | Including light of the intrinsic skyglow in % |
|---|---|---|---|---|
| \(22^{h}30'\) | 100 | 32 | 33 | 35 |
| \(0^{h}55'\) | 100 | 18 | 22 | 60 |
| \(2^{h}40'\) | 100 | 30 | 24 | 46 |
half (60%) falls on the intrinsic radiation of the sky, while only 18% remains for scattered light. Toward morning the scattered light becomes more intense, and the weakest turns out to be the light of the stars (24%).
It is of interest to determine the radiation energy of the green line in absolute measure.
We carried out the corresponding measurements\({}^{47}\). In doing so, the following figures were obtained, giving the number of quanta with wavelength \(5577.3\ \text{Å}\) arriving from the sky in 1 sec. on \(1\ \mathrm{cm}^{2}\):
\[ \begin{aligned} 22^{h}30'&—8\cdot10^{7};\\ 0^{h}55'&—20\cdot10^{7};\\ 2^{h}40'&—12\cdot10^{7}. \end{aligned} \]
The absolute value of the energy of the green line was also determined several years ago by Rayleigh\({}^{49}\).
Rayleigh obtained the number \(18\cdot10^{7}\) quanta, i.e. practically coinciding with our data.
12. Study of Polarization
In the summer of 1935, under the direction of the author of these lines, the optical group of the Elbrus expedition of the Academy of Sciences of the USSR carried out a study of the state of polarization of the glow of the night sky from the slopes of Elbrus. The great altitude of the observing site (3000 m above sea level) ensured high transparency of the air in the absence of any air pollution that would make the lower layers (2–3 km) of the atmosphere turbid.
The purpose of the work was as follows. Rayleigh and Dufay had already discovered the presence of a slight polarization of the light of the night sky. If polarization of the glow of the night sky exists, then this must indicate the presence of scattered light. In that case the plane of polarization of the light must at all times rotate following the motion of the Sun. The task was set—to determine the position of the plane of polarization at different hours of the night.
The method by which the observations were carried out was, unlike earlier investigations, not photographic but visual. We have already described the photometric extinction method developed by S. I. Vavilov, which uses the great sensitivity of the eye adapted to darkness. We used this method for measuring polarization.
A doubly refracting crystalline plate gave two mutually perpendicular polarized images of a square aperture that limited the entrance to the tube of the instrument. The aperture was placed at such a distance that its two images were located side by side.
The entire instrument could be rotated around the line of sight. If the light is partially polarized, then the two small squares appear not quite equal in brightness. But by rotating the instrument we can change the brightness of one square relative to the other. When rotated through 90°, the square that had been less bright becomes brighter. By gradually rotating the tube, one can set it so that, even in the presence of any arbitrarily large polarization, both squares will appear perfectly equal in brightness. This will be the case when the direction of the light vibrations makes an angle of 45° with the direction of polarization in each of the squares. By reading from a special divided circle the angle of rotation of the instrument, one can calculate the direction of the light vibrations.
Thus our method made it possible to determine the direction of the plane of polarization of the glow of the night sky at any given moment.
The results of measurements for three moonless nights in July, August, and September 1935 are presented in Fig. 14 (solid curve). Along the abscissa axis are plotted the hours of the night, and along the ordinate axis—the angle formed by the electric vector of the light vibrations of the partially polarized light of the night sky with respect to the plane passing through the line of sight and through the Sun.
The plane of polarization of scattered light must always make \(90^\circ\) with the plane passing through the line of sight and through the Sun. As the Sun moves below the horizon during the night, the plane of polarization must likewise rotate at the same rate: by \(15^\circ\) per hour (the Sun traverses \(360^\circ\) in 24 hours, i.e. \(15^\circ\) per hour).
Fig. 14.
If the angle between the plane of polarization of the light of the night sky and the plane drawn through the line of sight and through the Sun remained equal to \(90^\circ\) throughout the entire night, then the curve in Fig. 14 would have had to be a straight line parallel to the abscissa axis. In fact, however, the curve has a depression, the maximum of which occurs at 1 o’clock at night. At the beginning and at the end of the night the points give an angle of \(90^\circ\), i.e. as is required for scattered light. From 11 o’clock to 1 o’clock at night the plane of polarization turns “too rapidly”—by more than \(15^\circ\) per hour, as a result of which the angle between the direction of the plane of polarization and the plane passing through the Sun becomes less than \(90^\circ\). The plane of polarization “overtakes” the Sun. But after 1 o’clock at night the rotation of the plane of polarization slows down, and by 2 h 30 min in the morning the angle again takes the value \(90^\circ\).
It may be said that the curve in Fig. 14 testifies to the presence of two different phenomena superposed upon one another: first, this curve shows that scattering of light takes place throughout the night, despite the fact that in the middle of the night the Sun is far below the horizon. Owing to this, partial polarization of the light of the night sky is present throughout the night, and the plane of polarization all the time rotates after the Sun.
Superposed on this basic phenomenon, to which the curve in Fig. 14 bears witness, is some other phenomenon of unknown nature, distorting the regular course of the polarization of scattered light and causing the depression in the curve.
The presence of scattered light in the deep night, even at midnight, is a fact of exceptional importance. It testifies
or of the presence in cosmic space, at great distances around the Earth, of some rarefied matter, or else that the terrestrial atmosphere extends much higher than it has hitherto been customary to think, and that still practically appreciable densities of gas exist at the enormous height of 2000–3000 km above the Earth’s surface.
As for the second of the effects mentioned (the dip in the curve), its nature remains unclear to this day.
13. A Note on the Theory of the Glow of the Sky
What is the origin of the radiation sent to us by the night sky? It is clear that in the present case we are dealing with a glow of atmospheric gases, apparently arising at a very great height.
Under laboratory conditions we often observe the glow of gases, for example in a Geissler tube, in which an electric current of high voltage is passed through a rarefied gas (gas pressure less than 1 mm of mercury). But whence, in the Earth’s atmosphere, can there arise continuously acting electric currents of enormous strength and high voltage? This question appears very unclear.
The glow of gases can also arise under quite different circumstances. Many gases begin to shine if they are illuminated by ultraviolet rays. This is the so-called photoluminescence of gases. But whence can ultraviolet rays come in the atmosphere at night? To this question, too, one can give rather a negative answer.
But perhaps the glow of the sky is excited by quite another agent—namely, cosmic rays? It is known that cosmic rays, entering the nuclei of gas molecules, can knock electrons out of the nuclei, possessing certain velocities. These electrons, encountering atoms and molecules of the gas on their way, can, generally speaking, excite them to luminescence. But will the power of cosmic rays suffice to excite the whole glow of the night sky? In a column of air whose base is equal to 1 cm², about \(10^9\) light quanta are emitted in the atmosphere at night every second. Moreover, cosmic rays, if in the final account they do excite luminescence, will give a very small coefficient of light yield, since, besides luminescence, cosmic rays also produce ionization, as well as other phenomena not connected with luminescence. And even that part which produces luminescence will give radiation not only in the visible region of the spectrum, but also in the ultraviolet and X-ray regions, inaccessible to the eye and not reaching the Earth at all owing to intense absorption in the terrestrial atmosphere.
Furthermore, there is a well-established maximum of the intensity of the green line at 1 a.m.; why should cosmic rays, or their action, possess a maximum at 1 a.m.?
Thus we see that any hypothesis concerning the origin of the glow of the night sky at once gives rise to very substantial objections. The question of the nature of the sky’s intrinsic glow still remains open. The reason for this is, first, the difficulty (owing to the low intensity) of experimental study of the glow of the night sky, and hence the absence of a whole series of important data (for example, the question of the variation of intensity during the night for the blue bands and for the red lines in the spectrum of the glow of the night sky); a second reason is the inaccessibility for direct experiments of the layers where the glow of the night sky arises. We do not even know at what altitude this glow arises: perhaps at an altitude of 20 km, but perhaps at an altitude of 100, or even 1000 km. One can only say that it is somewhere “very high.” The physical properties of these high layers are almost unknown to us; it is known only that they differ in many respects from the layers close to the Earth’s surface.
However, many hypotheses have been put forward regarding the nature of the glow of the night sky. Here one may encounter electrical, luminous, chemical, and cosmic excitation of the glow of gases. What actually takes place is at present unknown to anyone; but one of these hypotheses is nevertheless correct—perhaps even all of them are correct, and the glow of the night sky is caused simultaneously by an entire complex of causes differing in nature.
14. Hypothesis of Electronic Excitation of the Glow of the Night Sky
A very widespread view of the nature of the glow of the night sky is the notion according to which the glow of the sky is excited by electrons. This point of view has its adherents among French investigators (Cabannes, Dufay, Desjardins, and others). At the basis of this view lies an assumption put forward in 1932 by Dauvillier[^50].
Dauvillier’s hypothesis regards the common cause of all geocosmic phenomena (aurorae, the glow of the night sky, zodiacal light, magnetic phenomena, ozone formation, and others) as electron radiation from the Sun. From this same point of view Dauvillier explains the solar corona. The electrons that fly out from the Sun have enormous velocities, close to the speed of light (their velocity corresponds to the accelerating action of an electric field of \(10^{10} V\)), and, according to Dauvillier, they account for the greater part of the faculae in regions close to the equatorial plane of the Sun. Their path, which becomes visible owing to the scattering of sunlight, forms the solar corona and the zodiacal light. From this point of view, the zodiacal light is interpreted as the result of the stretching out of the corona into the region of the Earth’s orbit (the zodiacal light, as is known, can be observed in spring shortly after sunset and in autumn before sunrise in the form of a cone of light situated along the zodiacal constellations),
When electrons from the Sun approach the Earth, their trajectories bend around the lines of force of the Earth’s magnetic field. The radii of the orbits in the region of the poles have values of the order of the Earth’s radius. Thus the Earth is surrounded by a spherical “layer,” formed by the intersecting trajectories of electrons, situated at a height approximately equal to the radius of the Earth.
These fast electrons cause ionization of gases and thereby the appearance of secondary electrons possessing much lower velocities. These secondary electrons are regarded as the agent exciting the glow of the night sky. Thus, for example, Kabanov^51, on the basis of the ideas set forth, draws the following picture of the processes occurring in the upper layers of the atmosphere.
According to Kabanov, the energy of the secondary electrons should correspond to approximately 7 eV. These electrons can excite nitrogen molecules, transferring them into the metastable state \(A\) (see the diagram of the energy levels of the nitrogen molecule in Fig. 6), with simultaneous excitation of the vibrational motion of the molecule corresponding to quantum number 2 or 3 (it is precisely these frequencies that occur in the Vegard—Kaplan band system). This requires 6.49 or 6.66 eV. In addition, such a secondary electron can dissociate an oxygen molecule into two normal atoms (5.09 eV) or into two atoms, of which one is normal and the other is at the metastable level \({}^{1}D_{2}\) (7.05 eV; see the diagram of the oxygen levels in Fig. 7). Transitions from these levels account for the emission of the nitrogen bands of the Vegard—Kaplan system and the green oxygen line.
In the emission of the green line \(\lambda = 5577\ \text{Å}\), the oxygen atom passes from one metastable state, \({}^{1}D_{2}\), into another, also metastable state, \({}^{1}S_{0}\).
The energy of the excited nitrogen molecules \(\mathrm{N}_{2}(A)\) and oxygen atoms \(\mathrm{O}({}^{1}S_{0})\) or \(\mathrm{O}({}^{1}D_{2})\) can be transferred by collision to other particles. Since both these states are metastable, the probability that the energy will be given up by collisions to other particles is sufficiently large. Upon collision of an excited nitrogen molecule \(\mathrm{N}_{2}(A_{2})\) or \(\mathrm{N}_{2}(A_{3})\) (the subscript attached to \(A\) indicates that the quantum numbers of the vibrational energy are respectively 2 or 3) with an excited oxygen atom \(\mathrm{O}({}^{1}D_{2})\) or \(\mathrm{O}({}^{1}S_{0})\), the nitrogen molecule can pass to an still higher level \(B\), with a vibrational quantum number of about 18 or about 7 (it is precisely these frequencies that occur in the first positive system of nitrogen bands). Upon collision of an excited oxygen atom with a water molecule, luminescence of the latter may be excited. The energy of the excited oxygen atom is sufficient to excite into luminescence all the bands of the water molecule.
Such is the train of thought set forth in Kabanov’s work^51 (1935). As regards the relationships among the energy levels of various atoms and molecules, they are indisputable, but these relationships are in no way connected with the question of whether it is at all possible to consider that
the glow of the night sky is excited by the electron rays of the Sun. This hypothesis itself, however, meets with a number of objections.
First, observations have shown the absence of any appreciable influence of the latitude of the observing site on the brightness of the glow of the night sky. Even under the equator the brightness of the sky glow is approximately the same as at temperate latitudes (Rayleigh). Meanwhile, the bending of electrons in the magnetic field occurs in such a way that we should have a very large latitudinal effect.
Second, the presence of a maximum in the brightness of the green line of the sky glow at 1 a.m. is now well known. This maximum is very clearly expressed, and it cannot in any way be explained from the point of view of excitation of the glow by electron rays of the Sun. Yet precisely such phenomena as daily variations in the brightness of the glow must first of all prove to be the key to understanding the nature of the glow.
Finally, the initial hypothesis of Dauvillier itself is doubtful. The explanation of a number of geophysical phenomena by corpuscular radiation of the Sun was proposed long ago and by many persons, in particular by Störmer, for explaining the phenomenon of aurorae. Corpuscular radiation apparently plays a definite role in the formation of aurorae. This is indicated at least by the established close connection between magnetic storms, aurorae, sunspots, and other phenomena on the Sun. But if the very character of aurorae corresponds to disturbances occurring from time to time and under special circumstances, then the glow of the night sky, on the contrary, is an established phenomenon. If the factors in question do take part in exciting the glow of the night sky, then it is only in the form of certain disturbances causing those unexpected increases in the brightness of the night sky which occur from time to time. They may create only some part of the sky glow that is subject to disturbances.
From this point of view, the differences in the spectra of aurorae and of the glow of the night sky deserve special attention. In both cases the principal features are lines and bands belonging to nitrogen and oxygen. This is quite natural, since both glows arise in one and the same medium—in the atmosphere, consisting mainly of nitrogen and oxygen. But the character of the spectra is entirely different with respect to the intensity of the components of the spectrum: in the spectra of aurorae, of all the nitrogen bands the weakest are the Vegard—Kaplan bands, and the brightest are the bands of the negative system; in the spectra of the sky glow, on the contrary, the Vegard—Kaplan bands are the most intense, and the bands of the negative system the weakest. The whole character of the spectra proves to be “reversed.” In addition, in the spectrum of the night sky there are dozens of lines entirely absent from the spectrum of aurorae.
Dauvillier’s hypothesis, which underlies the theory under discussion, explains, as indicated above, the zodiacal light as
scattering of sunlight by an electron cloud around the Sun, elongated in the plane of the Earth’s orbit. In this respect, too, certain remarks must be made. For a very long time already (several hundred years) two points of view have been expressed concerning the nature of the zodiacal light. One of them (as also in Dauvillier) holds that the zodiacal light owes its origin to a ring-shaped cloud of rarefied matter around the Sun, while the other supposes that the zodiacal light is connected with the very highest layers of the Earth’s atmosphere. But in the very recent period new data have been obtained which make it possible to conclude that the zodiacal light must be regarded as a phenomenon connected with the Earth’s atmosphere.
Finally, the conception of a powerful corpuscular radiation of the Sun, supposedly reaching the Earth, generally has a number of unclear points. Thus, for example, during the total solar eclipse of August 31, 1932, observations were made with the aim of detecting not only the “light shadow” of the Moon, but also a “corpuscular shadow,” i.e. the occultation of the corpuscular rays of the Sun by the body of the Moon. The observations showed the absence of a corpuscular shadow. In addition, it is unclear in what way corpuscular rays reach the Earth as a powerful beam without being scattered over the enormous path from the Sun into cosmic space (the repulsion of like-charged particles from one another).
All this compels one to approach with very great caution the hypothesis that the glow of the night sky is excited by electron rays from the Sun. If these rays do excite the glow, then, as the presence of a brightness maximum at 1 a.m. shows, they do not account for all the glow, but only some part of it, causing irregular jumps in the general brightness of the night light which occur on certain nights. The main part of the glow, however, by its stability fundamentally differing from the aurorae, which arise in flashes, apparently has another origin, essentially different from the origin of the aurorae.
15. The dissociating action of the Sun’s ultraviolet rays
There is every reason to believe that the energy of the night-sky glow is supplied by the ultraviolet rays of the Sun. These rays produce dissociation and ionization of gases and in this way accumulate their energy in the atmosphere. Let us consider the processes connected with dissociation in somewhat more detail.
In the atmosphere oxygen exists in the molecular state. However, we have seen that the bright green line \(\lambda = 5577.3\ \text{Å}\) belongs to atomic oxygen. This compels us to suppose that in the upper layers of the atmosphere a part of the oxygen molecules is dissociated into atoms. This dissociation may quite well take place, since it necessarily occurs when an oxygen molecule absorbs ultraviolet light with wavelength from 1300 to \(1800\ \text{Å}\).
and, as is known, there is every reason to assume the presence of ultraviolet rays of this wavelength in the spectrum of the Sun.
Moreover, the idea that atomic oxygen is present in the upper layers of the atmosphere is supported by the presence in the atmosphere of triatomic oxygen \(O_3\), i.e. ozone. For the formation of \(O_3\) molecules, apparently, the reaction \(O_2 + O = O_3\) is necessary.
The ultraviolet radiation of the Sun with an even shorter wavelength (less than \(1000\ \mathring{\mathrm A}\)) must produce ionization of molecules. Therefore, in the upper layers of the atmosphere one should also expect the presence of ions. And indeed, the presence of ionized layers in the upper regions of the atmosphere has been established (the Heaviside layer, etc.).
The processes of dissociation and ionization of gases by solar rays occur in such a way that these processes are concentrated in the atmosphere at some definite altitude. The theory of this phenomenon, which is very important for us, was developed by Chapman, and we shall now briefly consider it.
Suppose that the density of the gas whose absorption of rays interests us decreases with altitude according to an exponential law,
\[ \rho = \rho_0 e^{-\frac{h}{H}}, \tag{1} \]
where \(\rho\) is the density of the gas at height \(h\), \(\rho_0\) is that at ground level, and
\[ H = \frac{RT}{gM}. \]
Here \(R\) is the gas constant, \(T\) is the absolute temperature of the gas, \(g\) is the acceleration due to gravity, \(M\) is the molecular weight of the gas*. Let us consider the absorption in the atmosphere of monochromatic radiation from the Sun, whose intensity outside the atmosphere we shall denote by \(I_\infty\). Let a beam of rays with cross section \(1\ \text{cm}^2\) pass through the layer between \(h\) and \(h - dh\) at an angle \(\chi\) to the vertical. The volume of this element will be
\[ \frac{dh}{\cos \chi}, \]
and the mass of gas in this volume
\[ \rho_0 \frac{dh}{\cos \chi} e^{-\frac{h}{H}}. \]
It may be assumed that the amount of light \(dI\) absorbed in each given volume of gas is proportional to three factors: the coefficient
* For \(h = H\) we obtain \(\rho = \frac{\rho_0}{e}\), i.e. \(H\) corresponds to the height of the atmosphere at which the density of the gas has decreased by a factor of \(e\). Therefore \(H\) has received the name of the height of a homogeneous atmosphere.
absorption of light \(A\), the gas density, and the intensity of the light \(I\) arriving at the volume under consideration. On this basis we may write:
\[ dI = AI\rho_0 \frac{dh}{\cos \gamma} e^{-\frac{h}{H}} . \tag{2} \]
The solution of this differential equation gives:
\[ I = I_\infty e^{-\frac{A\rho_0 H\alpha}{\cos \gamma}}, \tag{3} \]
where
\[ \alpha = e^{-\frac{h}{H}} . \]
This result is obtained by integrating from the altitude where the light is just entering the atmosphere (i.e. \(I = I_\infty\)) to the altitude \(h\). Consequently, \(I\) is a measure of the energy absorbed in the penetration of the ray down to the altitude \(h\).
If the energy absorbed in the volume \(\dfrac{dh}{\cos \gamma}\) is equal to \(dI\), then the absorption referred to \(1\ \mathrm{cm}^3\) will be
\[ dI \frac{\cos \gamma}{dh}. \]
On the basis of formula (2) we may write:
\[ dI \frac{\cos \gamma}{dh} = AI\rho_0 e^{-\frac{h}{H}} . \]
For \(I\) we substitute its value from formula (3):
\[ dI \frac{\cos \gamma}{dh} = AI_\infty \rho_0 e^{-\frac{h}{H} - \frac{A\rho_0 H\alpha}{\cos \gamma}} . \]
Let the number of particles dissociated or ionized by radiation whose energy is equal to unity be denoted by \(\beta\). Then in our case we obtain the number of dissociated or ionized particles if we multiply both sides of the last equality by \(\beta\). We denote this number by \(f\):
\[ f = \beta AI_\infty \rho_0 e^{-\frac{h}{H} - \frac{A\rho_0 H\alpha}{\cos \gamma}} . \tag{4} \]
Thus, this is the number of particles arising in \(1\ \mathrm{cm}^3\) in \(1\) sec.
In this formula the ratio \(\dfrac{h}{H}\) enters as a “two-story” exponent for \(e\), since according to our notation
\[ \alpha = e^{\frac{h}{H}}. \]
This circumstance determines the specific dependence on height of the number of particles arising in \(1\ \mathrm{cm}^3\) per 1 sec. For a given \(\chi\) in formula (4), the only variable quantity is \(h\). Let us express this explicitly:
\[ f(h)=Be^{-\frac{h}{H}-Ce^{-\frac{h}{H}}}, \tag{5} \]
where \(B\) and \(C\) are constant quantities, whose values are evident from formula (4).
How will \(f(h)\) vary as a function of height? Let us consider the exponent:
\[ -\frac{h}{H}-Ce^{-\frac{h}{H}} = -\left(\frac{h}{H}+Ce^{-\frac{h}{H}}\right). \]
For very small \(h\), in the parentheses the first term is small, but the second term will have its maximum value: at \(h=0\) it will be equal to \(C\). As \(h\) increases, the second term will decrease, but the first term will increase; however, the increase of the first term will proceed more slowly than the decrease of the second, since the second term has \(h\) in the exponent, whereas the first is a simple factor. Consequently, \(f(h)\) at \(h=0\) will be
\[ f(0)=Be^{-C}, \tag{6} \]
but as \(h\) increases we shall have an increase of \(f(h)\). At \(h=\infty\) we obtain \(f(\infty)=0\). Consequently, as \(h\) increases, \(f(h)\) first increases, but for large \(h\) it decreases, tending to zero at \(h=\infty\). For some intermediate \(h\), the function \(f(h)\) must have a maximum.
What is the magnitude of \(C\)? It is not difficult to calculate that \(C\) is a very large number if \(A\) (the absorption coefficient) is sufficiently large. Consequently, at small heights \(f(h)\) is very small.
At what height does \(f(h)\) have a maximum? To find the maximum it is necessary to set the first derivative equal to zero:
\[ \frac{df}{dh}=0, \]
whence we obtain that
\[ e^{-\frac{h}{H}}=A\rho_0\frac{H}{\cos\chi}, \]
or
\[ h_{\max}=H\ln A\rho_0\frac{H}{\cos\chi}. \tag{7} \]
Thus the dissociating and ionizing action of solar radiation must have a maximum at a certain height, determined by formula (7).
Above this maximum, the absorption of light (and hence also dissociation and ionization) decreases, because the density of the gas decreases. In the lower layers, however, the light arrives already greatly weakened.
Thus the dissociating and ionizing action of the solar rays will be concentrated in a certain layer, whose effective height is determined by formula (7). This, apparently, is how the Kennelly–Heaviside ionized layer arises in the atmosphere at a height of 100 km, a second, higher ionized layer at a height of about 250 km, and also the ozone layer at a height of 25 km.
As for the shape of the layer, it can be calculated from formula (4). In Fig. 15 a curve is given, calculated for $\chi=0$ (the Sun at the zenith) for the equator. Along the abscissa axis is plotted the amount of absorbed light, and along the ordinate axis—the height (the height of a homogeneous atmosphere $H$ is taken as the unit; see above).
Fig. 15.
For air $H=8$ km. If for the thickness of the absorbing layer we take the distance from the maximum to where the curve drops by a factor of $e$, then according to Fig. 15 this should be from 1.2 to $2H$, i.e. 10–15 km.
Let us note that all the above considerations refer to the number of ions formed in $1\ \mathrm{cm}^3$ in 1 sec at one or another height. If one is interested in the question of the number of ions contained in $1\ \mathrm{cm}^3$, then the processes of recombination of atoms and ions must also be taken into account.
16. Photochemical Theory of the Glow of the Night Sky
All solar radiation, beginning with wavelength 2900 Å and shorter, is absorbed in the Earth’s atmosphere, causing dissociation and ionization of atmospheric gases. As a result, enormous energy accumulates in the atmosphere during the day. Is it not from these reserves that the energy for the intrinsic glow of atmospheric gases at night is drawn?
It was precisely this hypothesis that was put forward as early as 1931 by the well-known English geophysicist Chapman[^52]. This Chapman hypothesis belongs, in our opinion, among the most probable hypotheses.
Chapman, in his reasoning, has in mind the emission of the green line $\lambda=5577.3\ \text{Å}$, belonging to the spectrum of atomic oxygen. Chapman believes that energy must accumulate during the day as the energy of dissociation of $\mathrm{O}_2$ molecules into O atoms. This energy can
be transformed into light only through some reaction (for example, recombination), in which the dissociated particle takes part and which presupposes the collision of the dissociated particle with other particles. As a result of this reaction, one of the products must be an excited oxygen atom.
Chapman calls the particles involved in such reactions the producing substance of metastable atoms.
Chapman regards as one of the possible reactions of this type the reaction of combination of two oxygen atoms into an \(O_2\) molecule:
\[ \mathrm{O} + \mathrm{O} = \mathrm{O}_2. \tag{+} \]
The dissociation energy of the \(O_2\) molecule into atoms is approximately \(6.5\ \mathrm{eV}\). It is precisely this energy that must be liberated in reaction \((+)\). This reaction has as its result the formation of only one particle; therefore, in order for the laws of conservation of energy and momentum to be fulfilled, the reaction will take place only in the presence of some third particle, i.e. a triple collision must occur. The third particle may be either \(N_2\), or \(O_2\), or \(O\). The energy released in reaction \((+)\) is more than sufficient to excite an oxygen atom \((4.18\ \mathrm{eV})\). This excited atom will then emit light.
However, the probability of triple collisions is very small, especially under the conditions of a rarefied gas. Chapman considers another possible reaction, occurring between ions:
\[ \mathrm{N}_2^+ + \mathrm{O}^- = \mathrm{N}_2 + \mathrm{O}_{\mathrm{exc}}. \tag{++} \]
The energy released in this reaction is about \(14\ \mathrm{eV}\). It has two particles as its products and therefore does not require triple collisions. In this respect it corresponds to a much greater probability than reaction \((+)\). Moreover, as a result of reaction \((++)\), not only an oxygen atom may be excited, but also a nitrogen molecule, with the emission of almost all the nitrogen bands. Indeed, the following energies are needed to excite the nitrogen molecule:
| Vegard–Kaplan bands | \(6.1\ \mathrm{eV}\) |
| First positive system of nitrogen | \(7.4\ \mathrm{eV}\) |
| Second positive system of nitrogen | \(11.0\ \mathrm{eV}\) |
As for the presence of ions in the atmosphere, they necessarily exist there, being concentrated in the ionized layers of Kennelly–Heaviside, Elias–Appleton, and others.
Chapman’s photochemical hypothesis seems to us the most natural and plausible. It should especially be noted that
From the standpoint of this hypothesis it is possible, as it seems to us, to explain the maximum brightness of the green line of the night-sky glow at 1 o’clock in the morning. We shall now turn to this question.
17. Explanation of the Variations in the Intensity of the Green Line
The presence of a well-defined maximum in the brightness of the green line of the night-sky glow must, undoubtedly, represent a touchstone for any theory of this glow. From this point of view it seems to us that the photochemical theory should be placed first, within the framework of which we conceive an explanation of the nocturnal maximum.
We have seen that throughout the entire first half of the night the brightness of the green line increases steeply, and this increase continues until 1 o’clock in the morning. At 1 o’clock in the morning the brightness of the green line is 2.5—3 times greater than at 9—10 o’clock in the evening.
This phenomenon has the character of a certain “lag.” Some time must pass before the energy stored in the atmosphere can be expended most intensively in the form of the energy of the night-sky glow. This lag amounts to several hours. What may be the causes of so large a lag?
It seems to us that the causes of this lag may lie in the diffusion of active atoms from one layer to another. Indeed, according to all theoretical calculations, the accumulation of oxygen atoms, to whose spectrum the green line belongs, must occur predominantly in a certain definite layer (Fig. 15). In order for the glow of oxygen atoms to arise, it is necessary that some reaction (recombination) occur between an oxygen atom (or ion) and some other particle—for example, reactions of the type (+) and (++), indicated in the preceding section. Thus, for the glow of oxygen atoms to arise, the presence of some other (as Chapman called them, “producing”) particles is obligatory. But there may be very few of these “producing” particles precisely in that layer where atomic oxygen is formed, and the reaction will be able to take place only as oxygen atoms (or ions) penetrate into layers rich in these “producing” particles. In other words, the reaction will take place as oxygen atoms (or ions) diffuse from one layer to another.
Can one, from this point of view, quantitatively explain the increase in the brightness of the green line over the interval of time from 9 o’clock in the evening to 1 o’clock in the morning (i.e., over 4 hours) by a factor of 2.5—3? To answer this question, it is necessary to solve the corresponding diffusion problem. A rigorous solution of such a problem inevitably encounters insurmountable difficulties; but if one does not strive for complete rigor (which is not at all necessary), and confines oneself to determining the order of magnitude, then such a calculation can quite readily be made.
The emission of the green line gives \(2 \cdot 10^8\) quanta per second from an atmospheric column with a base of \(1\ \mathrm{cm}^2\). Over the entire night (approximately \(4 \cdot 10^4\) sec.) about \(8 \cdot 10^{12}\) quanta are emitted. The glow continues throughout the whole night, and, consequently, the supply of atoms at the beginning of the night must be no less than this number. According to Chapman’s estimates, in order to ensure a steady glow for the whole night it is necessary to have at least a 50-fold reserve of atoms—Chapman indicates\(^{52}\) the number \(5 \cdot 10^{14}\) atoms (or ions) in an atmospheric column with a base of \(1\ \mathrm{cm}^2\). We shall proceed from this number.
Let us suppose that the layer containing the main part of the atomic oxygen lies at an altitude \(h = 120\ \mathrm{km}\) (the Kennelly—Heaviside layer). Let the distribution of oxygen in this layer with height be given by some function \(f(h,t)\), depending on height and on time. We shall denote the diffusion coefficient for oxygen by \(D\). The problem is posed as follows.
If the distribution of the absolute concentrations of oxygen (the number of atoms in \(1\ \mathrm{cm}^3\)) at the beginning of the diffusion process \((t = 0)\) is given by the function \(f(h,0)\), then what will be the distribution of the oxygen concentration \(f(h,t)\) after \(t\) sec.?
The exact solution of the corresponding diffusion problem gives the following result:
\[ f(h,t)=\int_{-\infty}^{+\infty} f(h,0)\,\frac{1}{2\sqrt{\pi tD}}\,e^{-\frac{(h_0-h)^2}{4Dt}}\,dh . \]
Here \(h_0\) is the height of the layer from which all heights are measured. If one were to seek the exact solution of the problem posed, then for the function \(f(h,0)\) one would have to substitute the theoretical function (4) from Section 15. But in that case the solution of the problem would become very difficult; moreover, function (4) is in fact distorted by secondary effects not taken into account in its derivation (reverse recombination of the atoms formed, deviation from the barometric formula, nonmonochromaticity of the absorbed radiation). Therefore we shall simply assume—and for an approximate calculation this will be sufficient—that the atomic oxygen formed is collected in a certain layer at altitude \(h_0\), whose thickness, as we saw above (Section 15, Fig. 15), is \(10\text{—}15\ \mathrm{km}\).
We shall consider that noticeable diffusion (for penetration into a layer rich in “producing” particles) has occurred if the oxygen has diffused over a distance not less than the thickness of the layer, i.e. over a distance of \(10\text{—}15\ \mathrm{km}\). In other words, the problem is to determine the number of atoms that will have time to diffuse over a distance of \(10\text{—}15\ \mathrm{km}\) in the given time. Will this number be large enough to affect the intensity of the green line, i.e. will it be comparable with the number \(5 \cdot 10^{14}\) that we have taken as our basis?
As regards the reckoning of time, it is most correct to take it from noon. Indeed, the dissociating and ionizing action of the Sun’s rays depends sharply on the height of the Sun—it is greatest at noon. Therefore one may consider that by the middle of the day the full quantity of atoms and ions has been formed and that the diffusion processes from noon onward are already proceeding fully. We shall assume that in the absorbing layer complete dissociation (or ionization) takes place.
To obtain the answer to our question, let us calculate how many atoms (or ions) diffuse over a distance of 10 km, first from noon to 9 p.m. and, second, from noon to 1 a.m.
In the calculation we take the height of the layer from which diffusion begins to be 120 km, and compute the total pressure at these heights by the barometric formula. The magnitude of the pressure is of essential importance, since the diffusion coefficient depends on it (in inverse proportion).
The solution gave the following results: 1) by 9 p.m., \(10^{15}\) atoms will diffuse over a distance of 10 km; 2) by 1 a.m., \(10^{16}\) atoms will diffuse.
Thus the results of the calculation prove very encouraging in all respects: 1) a purely diffusion effect can account for penetration from the absorbing layer into places where the luminescence of quantities of oxygen sufficient to explain the observed brightness of the green line may occur; 2) a purely diffusion effect can explain the sharp increase in the glow during the night. By 1 a.m. ten times more atoms will have diffused than by 9 p.m.; but, owing to the decrease in the number of particles as a result of recombination, the increase in brightness will be somewhat smaller. This decrease in the total number of particles due to recombination and the slowing of diffusion processes as a consequence of the equalization of concentrations makes understandable a certain weakening of the green line toward the end of the night.
Our calculations were made for an altitude of 120 km. The results will be substantially different if another altitude is taken, mainly because the diffusion coefficient decreases as the pressure increases. These results prove very instructive.
If an analogous calculation is made for \(h_0 = 100\) km, it turns out that by 9 p.m. only \(5 \cdot 10^2\) atoms will diffuse over a distance of 10 km, i.e. an entirely insufficient number. For \(h = 80\) km the calculation shows that by 9 p.m. not a single atom will diffuse over a distance of 10 km. Conversely, for \(h = 140\) km one obtains \(10^{27}\) atoms. For this altitude, by 9 p.m. \(10^{15}\) atoms will diffuse over 15 km. For \(h = 160\) km it is found that by 9 p.m. \(10^{15}\) atoms will have time to diffuse over a distance of 50 km, and for an altitude \(h = 180\) km by 9 p.m. almost complete mixing will already have had time to occur.
These results mean that, if one proceeds from the photochemical theory and takes into account the influence of diffusion, then the height of the luminous layer can be determined quite well. Indeed, in this case the luminous layer cannot be lower than 120 km, since already at 100 km the influence of diffusion will be negligibly small, and the increase in the brightness of the green line will remain unexplained. Above 180 km, on the contrary, complete mixing will occur even before nightfall, and we should have a continuous decrease in the brightness of the green line during the night, which is not the case in reality. Thus it proves possible to indicate the boundaries of the luminous layer.
A calculation of this kind is the first case in which it has proved possible theoretically to approach the question of the height of the luminous layer. For this reason alone, the very idea of taking into account the influence of diffusion deserves every development.
18. Photoluminescence of the Sky. Detection of Luminescence in Twilight
In 1936 a very interesting phenomenon connected with the intrinsic glow of the sky was discovered. Cabannes and Garrigue[^53] detected an intense glow of the sky in twilight.
When the Sun, in twilight, sinks lower and lower below the horizon, the lower layers of air enter the shadow, while the upper layers continue to be illuminated by direct solar rays. As the boundary of the solar rays rises higher and higher, the brightness of the sky decreases (twilight), until night sets in.
The question had long arisen whether atoms of oxygen and other gases are not excited to luminescence by direct solar rays. It is known that gases irradiated by ultraviolet rays can themselves glow (photoluminescence). Does not the sky itself glow even by day, in addition to scattering sunlight?
The presence of such a glow would be a very important fact for understanding many processes taking place in the atmosphere. However, for a long time attempts to detect this glow remained without result. The author of these lines even made, in March 1936, in search of the intrinsic radiation of the sky by day, two flights on substratostats to a height of 9–10 km. It was expected that the bright background of scattered sky light would be so weakened upon rising to a great height (because a considerable part of the air scattering the solar rays would already remain below) that it would be possible to reveal the intrinsic radiation of the sky, which under ordinary conditions is drowned out by the bright scattered light. However, our searches ended without result—the weakening of the scattered light at a height of 10 km was insufficient.
At the same time, in several places the following idea arose: to photograph the spectrum of the sky in twilight, when the brightness of the sky is weakened hundreds of times, but the high layers of air, in which
must, according to all expectations, have concentrated the glow, are still illuminated by the direct rays of the Sun. These observations gave positive results.
Dufay and Garik, photographing the twilight spectrum with high-speed spectrographs, discovered the radiation of the red oxygen line \(\lambda = 6300\), occurring throughout the whole twilight period. They succeeded in obtaining a whole series of spectra during twilight and thereby tracing the change in the brightness of the red oxygen line as a function of the altitude of the illuminated layer. It turned out that the principal part of the radiation is given by layers at an altitude of \(120\)—\(140\) km.
This is in good agreement with our calculations, made for the phenomenon of diffusion in the preceding paragraph.
Independently of Dufay and Garik, the glow of the sky in twilight was also discovered in the USSR by M. F. Vuks and V. I. Chernyaev at Elbrus.
Further study of this interesting phenomenon appears very important, and, beginning in the summer of 1937, it will be carried out systematically at one of the southern observatories in the USSR.
19. Other Possible Hypotheses
We have exhausted the list of more or less substantiated hypotheses concerning the origin of the intrinsic glow of the sky. And only for the sake of completeness shall we mention several more hypotheses which do not yet figure among the current hypotheses, but which nevertheless are of definite interest.
One such possibility consists in the fact that the glow of the night sky may simply be photoluminescence of the sky, i.e. a glow arising under the direct action of solar rays. Such a possibility is almost certainly excluded (the Sun is deep below the horizon), but not completely. First of all, it is unknown to what altitude appreciable quantities of air extend. The supposition that traces of gas exist up to altitudes of several thousand kilometers is not improbable. One of the arguments for this is the presence, established by us throughout the entire night, of polarized scattered sunlight, amounting to not less than \(20\%\) of all the light of the night sky (see the chapter on polarization). To explain the presence of this scattered light, it is necessary to assume that the scattering of light takes place above \(2000\)—\(3000\) km (the boundary of the solar rays at midnight at the latitudes where our observations were made). To explain all the scattered sunlight at night, it is necessary to assume that at altitudes of \(2000\)—\(4000\) km the density of the gas is approximately \(10^5\) mm of mercury (a very good vacuum). The existence of such densities up to an altitude of \(4000\) km is not impossible.
The possibility is not excluded that the same gases which produce the scattering of sunlight themselves glow under the action of solar rays. To explain from this point of view all the brightness of the glow of the night sky, the same quantity is quite sufficient
gas, which must be admitted (without entering into the cause of its appearance) in the highest layers in order to explain the observed quantities of scattered light.
Finally, an entirely different possibility is also not excluded, namely that even in the deep night the Sun’s rays penetrate into the lower layers of the atmosphere as well. The point is that the ordinary laws of refraction of light are sharply violated for light whose wavelength differs little from the wavelength absorbed by the refracting substance. Near absorption lines and bands the refractive index increases sharply—this is the phenomenon of so-called anomalous dispersion. With a large refractive index, the refraction of light in the atmosphere may be much greater than the \(1^\circ\) usually observed. It is enough for the refraction to reach \(3^\circ\). Then, as can be shown, the ray will no longer leave the Earth’s atmosphere: thanks to total internal reflection, it will go around the Earth.
Cosmic rays may also take a certain part in exciting the sky’s own glow. If Regener’s curve for the intensity of cosmic rays at different heights is extrapolated beyond the limits of the atmosphere, then one can calculate the total energy of the cosmic rays absorbed in the atmosphere. This energy is equal to \(3.5 \cdot 10^{-3}\) erg/\(\text{cm}^2 \cdot \text{sec}\). Meanwhile, the total energy of the glow of the night sky is just \(3 \cdot 10^{-3}\) erg/\(\text{cm}^2 \cdot \text{sec}\). Finally, the possibility is not excluded that a vertical motion of electric charges arises at night. Indeed, during the day, under the action of the Sun’s ultraviolet rays, ions are formed in large numbers in the atmosphere. At night these polarized layers may come into motion, tending toward some redistribution with height in order to establish an equilibrium state. These nocturnal electric currents may excite gases to luminescence, just as happens in a Geissler tube. However, this point of view encounters certain quantitative difficulties. To produce the observed brightness of the night sky over the whole celestial vault, this vertical current would have to develop a very large power: calculations give a power of 10 million kW. Such large currents would have to be detected by a whole series of signs; in particular, they would have to be accompanied by noticeable magnetic fields. In reality, however, such magnetic fields are not detected.
Conclusion
Here we conclude the article on the glow of the night sky. If a person who has read this article is left with the impression that the totality of all the material on the glow of the sky, despite the undoubted interest of many discoveries in this field, as a whole nevertheless gives the impression of something raw, at times unsystematized and unfinished, then we shall have to admit that this is indeed the case. A whole series of basic problems here has only just been posed and has by no means been solved. The author does not
wanted to smooth over roughness where it in fact exists. His aim was, on the contrary, to give such a presentation of the material that everything unfinished would appear unfinished, so that it would be clearly evident in precisely which directions the efforts of a researcher wishing to give the problems connected with the glow of the night sky a more fully developed form should first be directed. The complete solution of all these problems is a matter for the future.
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