ATMOSPHERIC LUMINESCENCE

I. A. Khvostikov

TYPES OF ATMOSPHERIC LUMINESCENCE

In the Earth’s atmosphere there is a constant glow of the gases that make up its composition. The types of glow are manifold. One type of atmospheric luminescence has long been known: these are the auroras, the luminescence of the air at an altitude of 100 km and higher.

As early as M. V. Lomonosov, in his “Discourse on Atmospheric Phenomena Occurring from Electrical Force,” gave a detailed description of the aurora of January 23, 1750, accompanying it with his own drawing, engraved on a copper plate. M. V. Lomonosov was a century and a half ahead of the science of his time in understanding the significance of studies of the high layers of the atmosphere, in particular by studying the corresponding optical phenomena. His interest in auroras was deep and constant. Lomonosov sketched every aurora of any note. He began to write a large work, “An Investigation of the Cause of the Aurora and Other Similar Phenomena” (1763). His views on the origin of auroras, linking the glow of the air with electrical processes in the atmosphere, correctly grasp the main point and are not inferior to the theories of auroras of the second half of the nineteenth century. Only still later, half a century ago, after the discovery of “southern” auroras and the successes of heliophysics and of the doctrine of the Earth’s magnetic field, another important circumstance became clear: the electrical atmospheric processes that excite polar auroras are caused by solar radiation. At present there can scarcely be any doubt that the cause of auroras is corpuscular streams ejected by separate regions of the Sun’s surface. In its time this hypothesis encountered great difficulties: it was even suggested that auroras were excited by powerful short-lived bursts of ultraviolet radiation from the Sun. The theory of corpuscular excitation has overcome the principal difficulties, although to this day it is not entirely complete and indisputable[^1].

Already in the twentieth century several other types of atmospheric glow were discovered. These are the luminosity of the night sky (1919), twilight

luminescence of the atmosphere (1936) and artificially excited fluorescence of the atmosphere (1947).

The four types of glow indicated differ substantially from one another. Hundreds of works are devoted to their study, many of which belong to the pen of outstanding physicists, geophysicists, and astronomers. The results obtained have great scientific and practical significance, in particular for studying the composition of the air at different altitudes, the general structure of the atmosphere, and for understanding a number of remarkable physical phenomena in the upper layers of the atmosphere. A detailed exposition of the factual data may be found elsewhere[^1]. Here we shall attempt to give a general characterization of the present state of the problem of atmospheric luminescence as a whole and to identify those main points to which, in our opinion, special attention should be paid in the further development of this interesting problem.

NIGHT AND TWILIGHT GLOW

Forty-seven years ago Newcomb discovered an “excess” brightness of the night sky[^2]. Knowing the illumination produced on the earth’s surface by a star of a given magnitude, and calculating the number of stars of different magnitudes, one can compute the illumination produced by all the stars and compare it with the actual illumination at night. The latter is several times greater than the illumination that can be explained by starlight. Recently, the successes of stellar statistics have made calculations of starlight quite reliable and fully confirm the existence of the indicated excess of light[^1]. A hypothesis arose concerning the continuous glow of the atmosphere[^3]. A series of discoveries, beginning in 1919, confirmed this hypothesis. In the spectrum of the night sky the green line \(\lambda = 5577\ \text{Å}\) was discovered, the same one that is always present in the spectrum of auroras[^4]. It was soon shown that it is emitted by atomic oxygen in forbidden transitions between two metastable states. This radiation of the night sky, in contrast to auroras, is observed at any moment of every night and at any geographical location. The intensity of the green line, corresponding to the emission of approximately \(10^8\) quanta per 1 sec. in a vertical atmospheric column of cross section \(1\ \text{cm}^2\), is almost the same at all latitudes. Subsequently, other lines of atomic oxygen and numerous bands of molecular nitrogen were found in the spectrum of the night sky[^1]. The terrestrial origin of these lines and bands of radiation is proved by the regular increase of their brightness from the zenith toward the horizon (by a factor of 2–3); for a glow of extra-atmospheric origin there could be no such dependence. From the ratio of brightness at the zenith and at the horizon one can even approximately determine the height of the luminous layer: it is obtained between 50 and 500 km; according to the most rigorously processed measurements of Academician V. G. Fesenkov, it is 250 km for the green line[^5]. From purely theoretical

From theoretical considerations it follows that the layer emitting the oxygen lines is enclosed between altitudes of 130–180 km[^1]. The mechanism of excitation of the night-sky luminosity remains, for the time being, in many respects unclear, as we shall see further on.

In 1936–1937 twilight luminescence of the sky was discovered. At first, in France, the presence of very bright oxygen radiation \(\lambda = 6300\ \text{Å}\) was discovered when the Sun was submerged below the horizon by \(9^\circ\)–\(14^\circ\). But the most remarkable case was discovered by the Soviet physicists M. F. Vuks and V. I. Cherniaev in 1937: a bright flash of the yellow sodium line (the doublet \(D_1 - D_2\)) when the Sun was submerged below the horizon by \(6^\circ\)–\(7^\circ\). During the last 10 years more than fifty papers have been published devoted to the study of this interesting glow[^8]. It has been established that the sodium content is not less than \(10^{10}\)–\(10^{11}\) atoms in a vertical column of air with a cross section of \(1\ \text{cm}^2\), and almost all this amount of sodium is contained in a relatively thin layer of air which extends, apparently, from 50–60 km to 80–85 km above the Earth’s surface. The glow is excited by solar rays and is a resonant fluorescence of sodium vapor[^8].

THE GLOW OF SODIUM IN THE TROPOSPHERE

The study of the atmospheric glows described above—aurorae, the luminosity of the night sky, and twilight glow—has yielded much that is interesting and important for physics, astronomy, and especially for geophysics (the investigation of the composition and structure of the high layers of the atmosphere). But for all the great significance of these results, they all differ in that they are connected with a glow occurring in the atmosphere “by itself,” without the intervention of the experimenter, as a result of which the investigation of the glow is reduced to the observation of “ready-made” phenomena. In the investigations mentioned there is no experiment in the strict sense of the word, but only observation, although at times carried out by means of subtle and refined experimental instruments. Of course, far more far-reaching possibilities would open up if it were possible to excite atmospheric glow at the discretion of the experimenter. From this point of view, a new type of glow of the free atmosphere, which was discovered in 1947 and continues to be studied in 1948 near Moscow, is of fundamental interest.

The search for this glow continued for a number of years and only now has been crowned with success. What is in question is the fluorescence of sodium vapor in the lower layers of the atmosphere.

Where does the sodium observed in the layer 60–80 km come from? Ch. Fabry believes that sodium enters the atmosphere from interstellar space. A number of French authors take the point of view of a meteoric origin of sodium in the stratosphere and ionosphere. Some connect the entry of sodium into the atmosphere with volcanic activity—

ness. But on the basis of a critical analysis of the available data, which is known to the reader from a recently published review in Uspekhi fizicheskikh nauk⁸, it should be considered most probable that the main source of sodium is sea salt, entering the atmosphere together with droplets sprayed by waves. The very small droplets are carried upward from the ocean surface by ascending air currents and evaporate, leaving grains of salt in the air. There can hardly be any doubt that, at least up to a height of 85 km, there is constant mixing of air from different levels; therefore particles of sodium or salt can penetrate up to 85 km. Apparently, the layer 85–120 km, distinguished by a strong temperature inversion, plays the role of a retarding layer, through which exchange of air between the stratosphere and the ionosphere can proceed only very slowly. The brightness of the twilight glow of sodium suddenly decreases by tens of times when the Sun sinks 6°–7° below the horizon, whence it follows that sodium is contained predominantly in a layer bounded above by a height of 80–90 km. This fact in itself suggests that sodium enters the layer 60–80 km from below, and not from above. It is known, for example, that noctilucent clouds appear after strong volcanic eruptions accompanied by the ejection of a large amount of dust-like material to heights of 20–30 km, and the clouds are always recorded at heights of 80–85 km, but above the level of 85 km this volcanic dust never in any way reveals itself.

The glow of stratospheric sodium in twilight becomes noticeable when the Sun sinks below the horizon by an angle \(h_\odot\) not less than 4°–5°, when the Earth’s shadow passes at a height of 50 km. Does the absence of the sodium \(D\)-lines in the spectra of the twilight sky at \(h_\odot < 4^\circ\) mean that sodium is absent in the air layers below 50 km? Many mistakenly think so. But let us suppose that the number of sodium atoms in \(1\ \mathrm{cm}^3\) is the same at heights of 30 km and 50 km. A change in the height of the Earth’s shadow during twilight by 20 km corresponds to a 10-fold change in the brightness of the scattered light of the twilight sky. Consequently, the sodium \(D\)-lines due to sodium luminescence at the level of 30 km will be accompanied by a continuous spectrum of scattered sky light of 10 times greater brightness than, respectively, at the level of 50 km, although the brightness of the \(D\)-lines will change little. But the continuous spectrum is precisely the main obstacle to detecting the \(D\)-lines. It is clear that below 50 km there may also be a considerable quantity of sodium, which, however, remains unnoticed in twilight observations. If sodium comes into the stratosphere from the troposphere, and not from the ionosphere, then one may try to detect it directly in the lower layers of the atmosphere. Such searches, on the advice of S. I. Vavilov, we undertook as early as 1939.

At first we tried to detect sodium by absorption. For this purpose the spectrum of an incandescent lamp was photographed from a distance of 4.5 km.

Once—this was on the shore of the Black Sea near Simeiz—we noticed, against the background of the continuous spectrum of a lamp, an absorption line whose position coincided with the \(D\)-line (with our low-dispersion luminous spectrograph we could not separate the yellow doublet). But a number of other analogous exposures never gave us a repetition of this result. It was clear that, if sodium is present in the lower layers of the air, it is present in such small quantities that detecting it by absorption over a path of \(4.5\ \mathrm{km}\) is extremely difficult.

However, one may try to detect small quantities of sodium not by absorption, but by its fluorescence. For a long time these attempts also remained without result. But in 1947 it finally proved possible to obtain a reliable result. It is now clear that in our earlier experiments the brightness of the exciting beam was insufficient. A sodium lamp of sufficient power inevitably has large dimensions of the luminous volume. To obtain a directed beam, long-focus optics are needed. If, at the same time, the aperture of the optics (lens or mirror) is small, then a negligible fraction of the light emitted by the lamp is used. Only in 1945–1946, when work at the Geophysical Institute of the Academy of Sciences of the USSR on searchlight sounding of the atmosphere was developed, did optics of maximally large dimensions enter into the practice of our investigations. The fluorescence of sodium vapors in the near-ground air was detected by us after, for exciting fluorescence, a beam was used that was produced by a parabolic mirror \(150\ \mathrm{cm}\) across, at the focus of which a high-power sodium lamp was installed.

Our experiments have now proved the frequent presence of sodium vapors not only in the near-ground air, but also in the air up to a height of \(800\text{–}1000\ \mathrm{m}\) above the ground. Experiments on detecting sodium in still higher layers are continuing. The essence of the experiments may be briefly stated as follows.

When the air is illuminated by monochromatic light \(\lambda = 5890\text{–}96\ \mathring{\mathrm A}\) (the yellow sodium doublet), and when the illuminated volume is photographed from the side, the yellow doublet will be obtained in the spectrum even in the absence of sodium vapors: simply as a consequence of scattering. But we have found an excess of brightness in comparison with that which can be produced by scattering alone. It is impossible to find this latter theoretically, since the scattering power of the near-ground air is subject to rapid and large fluctuations. We determine it each time by measurements, for which purpose the air is simultaneously illuminated by the light of the mercury line \(\lambda = 5769\text{–}90\ \mathring{\mathrm A}\). If the brightness of the sodium \(D\)-lines \(B_1\) is due only to scattering in the air, then the brightness \(B_2\) of the \(5769\text{–}90\ \mathring{\mathrm A}\) lines must be related to \(B_1\) by the relation:

\[ \frac{B_1}{B_2}=\left(\frac{5780}{5892}\right)^n, \]

where \(n\), generally speaking, may vary from zero (neutral scattering by large dust particles and droplets in the air) to 4 (Rayleigh scattering by clean air). Thus, \(B_1\)

must always be less than \(B_2\), if there are no other sources of brightness \(B_1\) and \(B_2\), apart from scattering according to the law \(\frac{1}{\lambda^n}\).

The measurements of I. M. Mikhailin and the author showed that on some days \(B_1\) noticeably exceeds \(B_2\). This excess of the brightness \(B_1\), sometimes reaching 50–100% and more, directly indicates the presence in the air of a substance which fluoresces when illuminated by light of \(\lambda = 5890\text{–}96\ \text{\AA}\).

When observed at an angle of \(90^\circ\) to the exciting beam, the scattered light is strongly polarized (up to 90%). As for the resonance fluorescence of sodium vapor, it is known to be only slightly polarized (less than 10%). This provides a good additional means of distinguishing fluorescence from scattered light. Preliminary experiments showed that the greater \(B_1\) is in relation to \(B_2\), the smaller the degree of polarization when the air is illuminated by sodium light. On some days (more precisely, nights) the polarization falls from 90% to 10%.

This phenomenon, new for atmospheric optics—artificially excited fluorescence of air in the free atmosphere—opens up the possibility of carrying out a large program of new investigations of atmospheric processes by optical methods. In particular, one may try to investigate the distribution of sodium with height not only in the troposphere, but also in the stratosphere, and thereby resolve the question of the origin of sodium in the layer of 60–80 km. The corresponding experiments are being carried out at the present time.

THE NATURE OF THE LUMINOSITY OF THE NIGHT SKY

What causes the air at an altitude of 120–250 km to emit light continuously? This question still remains open, although there is no lack of hypotheses on this subject. There are three different views on the nature of the glow: the photochemical theory, the hypothesis of excitation by solar corpuscular streams, and the hypothesis of optical excitation.

According to the photochemical hypothesis, the source of energy for the continuous emission of light by the atmosphere is the energy of dissociation of oxygen molecules and, perhaps, nitrogen. Above 100 km oxygen is practically wholly dissociated. Dissociation occurs during the day as a result of absorption of solar radiation: \(\mathrm{O}_2 + h\nu = \mathrm{O} + \mathrm{O}\). Radiation with wavelength \(\lambda < 1750\ \text{\AA}\) has a dissociating effect. Day and night recombination takes place, which can occur only in triple collisions: \(\mathrm{O} + \mathrm{O} + \mathrm{M} = \mathrm{O}_2 + \mathrm{M}^*\), where \(M\) denotes some third particle ensuring fulfillment of the conservation laws. The dissociation energy, 5.1 eV, is partly transferred to the third particle, which passes into an excited state: \(\mathrm{M} \to \mathrm{M}^*\). Then the excited particle \(\mathrm{M}^*\) spontaneously emits light.

Nitrogen atoms may recombine

\[ \mathrm{N}+\mathrm{N}+\mathrm{M}=\mathrm{N}_2+\mathrm{M}^*, \]

as may also ions

\[ \mathrm{N}+\mathrm{N}^+ + \mathrm{M}=\mathrm{N}_2^+ + \mathrm{M}^* \]

or

\[ \mathrm{N}_2^+ + \mathrm{O}^-=\mathrm{N}_2^*+\mathrm{O}^*, \]

and so forth. The last reaction is accompanied by the release of a large amount of energy, of the order of \(12.5—13.4\) electron-volts, sufficient to excite all the bands of \(\mathrm{N}_2\) and the lines of \(\mathrm{O}\) observed in the spectra of the night-sky luminosity.

The photochemical theory simply and clearly explains the sources of the energy of the night-sky luminosity. It can hardly be doubted that the glow of the atmosphere, excited in the indicated way, takes place constantly, and not only at night but also by day. It would be very interesting to detect and investigate this daytime glow, but attempts of this kind have so far remained fruitless: in the daytime the brightness of the continuous spectrum of sunlight scattered by the atmosphere is too great.

But by the photochemical mechanism alone it is apparently impossible to explain all the properties of the night-sky luminosity.

In recent years more and more facts have been accumulating which testify to the constant presence of irregular and short-lived flashes of brightness of the night sky in individual, arbitrarily chosen parts of it. This already suggests a glow of the auroral type. Flashes are observed at various latitudes, down to those close to the equator. There is no reason to deny the possibility of a constant action of corpuscular solar streams upon the upper layers of the atmosphere at all latitudes. A glow of the auroral type, in a certain sense, may not be the privilege only of the polar regions. One must take into account the intensity of auroras. Bright auroras are observed, as a rule, precisely in the polar regions and rarely at middle latitudes. But could it not be that weak auroras occur all the time, and not only during periods of considerable eruptions on the Sun, accompanied by such perturbations on our planet as magnetic storms, disturbance of radio communication, and so on? And could it not also be that these constant and weak, in contrast to episodic and strong, effects of streams of solar corpuscles on our atmosphere have only a small latitudinal effect and cover almost equally the entire terrestrial globe, and not only its polar and circumpolar regions? It is necessary to take into account how far it is possible to detect weak auroras. The fact is that the contrast sensitivity of the eye under night conditions drops sharply. If the night sky had the same brightness at all its points, then at night “by eye” it would be possible to measure only those auroras whose brightness exceeds the brightness of the night sky by at least \(10—20\%\). But the night sky is a very nonuniform background; the detection of weak bright patches is hindered by bright stars, star clusters, nebulae, dark patches, and so on. In order that, against such a “motley” background, a separate bright patch (an aurora) could be noticed, its brightness must differ from the brightness of the sky background by \(40—60\%\), if the angular dimensions of the patch and the duration of the glow are sufficiently large.

But observation is made still more difficult and complicated if we are dealing with a multitude of short-lived flashes, each of which separately occupies a small area in the sky. If, in sum, all such flashes of aurorae accounted for 30–40% of the total brightness of the sky (and this is already almost the entire brightness of the luminosity of the night sky!), we would not detect them “by eye.” They could be detected not visually, but photoelectrically, since under night conditions the “contrast sensitivity” of a photocell can be made an entire order of magnitude greater than that of the eye.

And indeed, something of this sort can be observed by simple means: a sensitive photocell, onto which the image of a separate portion of the sky is projected, often shows rapid changes in brightness, the amplitude of which increases as the angular dimensions of the sighted portion decrease. It is very important that the intensity of these brightness fluctuations changes from night to night. Sometimes (rarely) nights are “quiet,” and the fluctuations are imperceptible. The study of such fluctuations is of interest not only for elucidating the nature of the luminosity of the night sky, but also for further investigation of the mechanism by which corpuscular and ultraviolet radiation of the Sun acts upon the upper layers of the Earth’s atmosphere (the “Earth–Sun” problem).

From comparing the facts indicated above with data on the properties of the ionosphere (for example, rapidly moving ionic “clouds”) and with possible considerations concerning the ways in which solar radiation acts on the ionospheric layers in which the luminosity of the night sky arises, one may adopt a certain working hypothesis that helps one to imagine better the program of a number of further investigations. In brief, this program is devoted to establishing the existence of constant weak aurorae at all latitudes. Let us imagine motion-picture photography of the night sky through narrow light filters transmitting \(\lambda\lambda = 5577,\ 5892\), and \(6300\ \text{Å}\); these are the wavelengths of the principal emission lines of the night sky of terrestrial origin. It is possible that the films would reveal the presence of aurorae pulsating and rapidly changing their position in the sky. The green and other lines of the night sky may perhaps not be emitted uniformly by the whole sky at all, but arise predominantly from individual unsteady zones of the sky. Here it is appropriate to recall the discussion concerning atomic nitrogen in the upper layers of the atmosphere, recently presented in the pages of Uspekhi Fizicheskikh Nauk.^9 The nitrogen lines 5200 and 3466 Å are present, as was shown several years ago, in the spectra of aurorae, and the line 5200 Å is detected in bright aurorae of temperate latitudes during periods of strong solar eruptions. The greater susceptibility of nitrogen to solar influences may also be due to the probably higher (of the order of 100 km in magnitude) position of the region of nitrogen dissociation above the region of oxygen dissociation: the greater part of the solar (corpuscular and

(short-wave ultraviolet) radiation is absorbed in higher atmospheric layers. If the infrared nitrogen line 10400 Å is indeed present in the spectrum of the night sky, then it is quite possible that it, more than any other, can help to detect constant weak aurorae at all latitudes, and its intensity may prove to be especially fluctuating.

The indicated “cinematography” of the night sky is not feasible if it is understood literally: the sensitivity of photographic materials is more than 3 orders of magnitude below what is necessary. Even if the aurorae under consideration can be recorded by photographs with the required long exposure, the photometric interpretation of the photographs is connected with enormous labor because of the “mottledness” of the night-sky background. In carrying out the indicated program it is necessary to make extensive use of low-inertia photoelectric instruments and to apply other modern methods possessing high sensitivity to light.

If “aurorae” of the indicated type exist, then the glow of the night sky possibly represents a recombination glow (photochemical mechanism), constantly disturbed by flashes of weak aurorae.

PHOTOLUMINESCENCE OF THE SKY

In 1938–1939 it was established that some emission lines of the night-sky glow are partially polarized (degree of polarization of the order of 10%), and that there is a rotation of the plane of polarization corresponding to the motion of the Sun below the horizon10, 11, which suggests purely optical excitation of the glow. What can be the mechanism of this excitation? The general idea was expressed by Academician S. I. Vavilov as early as 1935: it is a strong bending (refraction) of rays of that wavelength for which the refractive index of air has a selectively large value owing to anomalous dispersion. The refraction of such rays could, generally speaking, reach 20°–30°. In this case the rays can illuminate the upper layers of the atmosphere even at night, when the Sun has descended below the horizon by 20°–30°.

A similar effect can be appreciable near resonance lines. Such lines are present in the spectrum of the night sky, and even in relatively large number: 2 lines out of the total of three constantly observed. These are the oxygen line 6300 Å and the sodium line 5892 Å. They have the polarization properties indicated above.

It is noteworthy that subsequently both of these lines were found in the spectra of the twilight sky, and in this case their optical excitation by direct sunlight can hardly be doubted. Moreover, as early as 1939 it was shown for one of these two lines (for 6300 Å) that to explain the peculiar depen-

dependence of the line brightness on the angle of the Sun’s depression below the horizon can be obtained only on the assumption of a mechanism connected with selective refraction in the region of anomalous dispersion[^14]. Recently Elvey and Farnsworth in the USA have carried out careful measurements of the nocturnal variation of the brightness of this line, 6300 Å. The course of the brightness is very peculiar, and the authors mentioned consider it enigmatic. In short, the “enigma” consists in the fact that the brightness of the line, while showing a distinct minimum at midnight (which is natural), increases strongly toward morning; moreover, a considerable increase of brightness takes place long before (by 1 hour or more) the moment of astronomical twilight.

From the point of view of the theory of optical excitation as a result of selective refraction, such a nocturnal course receives a natural interpretation not only qualitatively, but also quantitatively. In general outline the matter is as follows.

It may be assumed that the principal share of the radiation of the 6300 Å line of atomic oxygen must arise in the indicated manner in a thin atmospheric layer at an altitude of 110–130 km. All known data agree that below the level of 100–110 km oxygen is almost undissociated, while above it is practically completely dissociated. Thus the selective refraction of solar rays with wavelength close to 6300 Å, caused by the presence of atomic oxygen in the air, cannot occur below the 100–110 km level. But the refractive index of oxygen depends on the density, which rapidly decreases with height (by a factor of 5–10 for every 20 km). Thus sufficiently strong selective refraction can occur only for rays propagating no more than 20–30 km above the 100–110 km level. Therefore, in a first approximation one may suppose that there exists a sufficiently thin “effective” layer of refraction (Fig. 1), in which the glow also arises. In this case it is easy to calculate the diurnal variation of the brightness of the 6300 Å line.

Fig. 1. Diagram of optical excitation of the red oxygen line at night and in twilight (selective refraction).

If measurements are made by an observer \(A_1\) at some point of the sky, for example at the zenith \(Z_1\), then an increase in the angle of depression of the Sun below the horizon of the observer \(A_1\) is equivalent to the observer himself moving along the earth’s surface successively

at the points \(A_2, A_3,\ldots\). It is easy to see that, for the position of the observer at any of the points \(A_1, A_2, A_3,\ldots\), the path of the solar rays to the “effective” layer, i.e. the path along the segment \(Sk\), remains unchanged, but the path within the “effective” layer changes: the lengths of the path segments \(kZ_1, kZ_2, kZ_3,\ldots\) change. The lengths of these segments, which are arcs of one and the same circle with its center at the center of the Earth, are proportional to the angle of depression of the Sun below the horizon; more precisely, the length of any such segment \(kZ_i\) is linearly related to the angle of depression of the Sun below the horizon \(\varphi_i\): \(kZ_i=m+n\varphi_i\), where \(m\) and \(n\) are constants.

If the luminescence arose only in the indicated “effective” layer, then the theoretical calculation of the expected course of the brightness of the red oxygen line would be extremely simple: the logarithm of the brightness would have to vary linearly with increasing angle of depression of the Sun below the horizon \(\varphi\). Indeed, in this case the decrease in the brightness of the red line with increasing angle would be caused only by the increase in absorption of the exciting solar rays along the path in the “effective” layer, while the absorption increases with increasing path \(kZ\) according to an exponential law. Thus, plotting along the abscissa axis the values of the angles of depression of the Sun below the horizon for different moments of observation, and along the ordinate axis \(\lg \frac{1}{B}\), where \(B\) is the brightness of the 6300 Å line, we would obtain a straight line. The slope of this straight line would give the value of the absorption coefficient of radiation \(\lambda=6300\) Å in the “effective” oxygen layer.

In reality, however, the geometrical picture of the excitation of luminescence must be somewhat more complicated. In fact, the luminescence must arise not only in the effective layer, but also below it and above it. Moreover, solar rays that are refracted more strongly and less strongly than those for which refraction gives a radius of curvature of the trajectory exactly equal to \(R+H_{\mathrm{e}}\) (\(R\) is the radius of the Earth) participate in the excitation of the luminescence. A quite small displacement along the wavelength scale \(\lambda\) in the region of anomalous dispersion is sufficient to obtain a noticeable change in the refractive index \(n\), since in this region the dispersion curve \(n=f(\lambda)\) has a steep course. Rays that are refracted more strongly will have little influence, since they are greatly weakened by absorption in the atmosphere (for them the absorption coefficient is large) and, most importantly, they will quickly pass below the effective layer, where there is no atomic oxygen. Rays that are less refracted are, on the contrary, in a more favorable position with respect to absorption, and therefore it is necessary to take them into account. To calculate their share in the total luminescence, let us simplify the problem by assuming that their refrangibility differs little from that of “ordinary rays,” i.e. rays not experiencing the influence of anomalous dispersion. In this case such rays can illuminate only those layers of the atmosphere which lie above the Earth’s shadow. If the red line were excited only by such rays, then

its brightness \(B\) at any moment of twilight would be determined by the expression

\[ B = C \int_{H_m}^{\infty} I(H)\rho(H)\,dH, \tag{1} \]

where \(\rho(H)\) is the density of atomic oxygen at altitude \(H\), \(I(H)\) is the intensity of solar rays at \(6300\,\text{\AA}\) illuminating the atmospheric layer at altitude \(H\), \(C\) is the brightness of the glow of a layer of atomic oxygen of unit thickness and unit density, illuminated by rays of \(6300\,\text{\AA}\) of unit intensity, and \(H_m\) is the height of the Earth’s shadow.

If we did not take into account phenomena connected with the selective refraction of solar rays, then the intensity \(B\), determined by integral (1), would, as \(H_m\) changed, vary approximately in proportion to the pressure of atomic oxygen, i.e. the brightness of the red line, and consequently also its decrease as the height of the Earth’s shadow increased, would be determined only by the law of the decrease of density with altitude. In reality the decrease of brightness would occur, as the Sun descends, even more rapidly because of the progressively increasing absorption of solar rays in the atmosphere (the influence of the function \(I(H)\)). But calculation shows \(^{14}\) that in fact the brightness of the red line during twilight decreases much more slowly than would correspond to the rate at which air density decreases with altitude.

As the Sun sinks below the horizon, the influence of an additional brightness of the red line of another origin makes itself felt to an ever greater degree. Thus we obtain the following general picture of the phenomenon:

1. At the beginning of twilight, when \(H_m \leq H_{\text{э}}\), the brightness of the red line is determined practically entirely by the excitation of the resonance fluorescence of oxygen by “ordinary” solar rays, i.e. rays not experiencing “selective” refraction due to anomalous dispersion. We shall denote the brightness of the red line excited by such rays by \(B_0\).

2. For \(H_m > H_{\text{э}}\), solar rays traveling along the “effective” layer of refraction (having undergone “selective” refraction) begin to take a noticeable part in exciting the glow. We shall denote the share of the brightness of the red line caused by the action of these rays by \(B_a\).

3. As \(H_m\) increases (i.e. the angle \(\varphi\) of the Sun’s immersion below the horizon), the share \(B_a\) in the total glow \(B_0 + B_a\) increases, while the share \(B_0\) decreases, since \(B_0\) decreases with increasing \(\varphi\) more rapidly than \(B_a\). For large \(\varphi\), the brightness of the red line should be determined almost entirely by the share \(B_a\).

It follows from what has been said that, plotting along the abscissa axis the angle \(\varphi\), and along the ordinate axis \(\lg B\), where \(B\) is the measured brightness of the red line,

we must obtain not a straight line, but a line which, for small \(\varphi\), should descend more steeply; for large \(\varphi\) it should approach a straight line, since, as we have shown, \(\lg B_a\) must be a linear function of \(\varphi\). The indicated graph should deviate from rectilinear form the less, the greater the share of \(B_a\) in the total brightness \(B=B_0+B_a\).

We processed in this way all the published measurements, namely: the curve published in 1939 by Kabanov and Garriga\(^{15}\), and the curves published by Elvey and Farnsworth in 1942.\(^{16}\) The latter curve is an average of many curves measured by these

Fig. 2. Comparison of the data of Kabanov and Garriga (crosses) with the theory of selective refraction (straight line).

Fig. 3. Comparison of the data of Elvey and Farnsworth (evening twilight and beginning of night) with the theory of selective refraction.

authors. In addition, this curve essentially contains two curves: for morning and evening twilight separately.

In all three cases the curves “stabilize” toward midnight, asymptotically approaching a certain constant value. Most likely, the greater part of this midnight brightness corresponds to another mechanism of excitation of the glow, namely the one indicated by the photochemical theory of the luminosity of the night sky. Therefore we subtracted this share of the brightness (which, however, is small) from all brightness values for the different moments of twilight and night.

In the cited works of Kabanov, Garriga, Elvey, and Farnsworth, the zenith distances of the Sun for the individual measured

intensities, but these latter are given as functions of time. Having no data on angles, we therefore plotted \(\lg B\) as a function of time, and not of angles. This, of course, somewhat distorts the course of the curves, but only slightly.

The curves recalculated in this way are presented in Figs. 2–4. In all cases the curves have the form predicted by the theory set forth above.

As was indicated, from the slope of the straight line (i.e., from the derivative \(d\lg B/d\lambda'\)) one can determine the absorption coefficient of the solar rays of wavelength \(\lambda = 6300\) Å by atomic oxygen in the “effective” layer.

The absolute values of the absorption coefficient of atomic oxygen for the 6300 Å line, found from the slopes of the straight lines in Figs. 2–4, agree well, in order of magnitude, with the theoretical values of the absorption coefficient. We shall not dwell here on the details.

The theory set forth requires further verification and refinement. But the facts adduced above, together with the discovered properties of the luminosity of the night sky in the ultraviolet part of the spectrum[^13], on which we shall not dwell here for the sake of brevity, taken together compel one to consider that optical excitation, along with photochemical and electronic excitation, participates in producing the luminosity of the night sky.

For refining the optical mechanism of excitation, it would be interesting to investigate the polarization of the red oxygen and yellow sodium lines during twilight, and to trace the state of polarization continuously until night and during the night. Because of the strong interference produced by the bright scattered light of the twilight sky, such an investigation proves very difficult, but it is possible to carry it out.

Fig. 4. Comparison of Elvey and Farnsworth’s data (end of night and morning twilight) with the theory of selective refraction.

CITED LITERATURE

1. I. A. Khvostikov, The Luminescence of the Night Sky. 2nd ed. Academy of Sciences of the USSR (1948).
2. S. Newcomb, “A rude attempt to determine the total light of all the stars.” Astrophys. Journ., 14, 297–312 (1901).
3. Intema. “On the brightness of the sky and total amount of starlight.” Publications of the Astronomical Observatory at Groningen, No. 22 (1909).

1. V. M. Slipher, On the general auroral illumination of the sky and the wave-length of the chief aurora line. Astrophys. Journ., 49, 266–275 (1919).

2. V. G. Fesenkov, Meteoritic Matter in Interplanetary Space. Publishing House of the Academy of Sciences of the USSR (1947).

3. H. Garrigue, Nouveaux résultats sur la lumière du ciel nocturne. Comptes Rendus, 202, 1807–1809 (1936).

4. V. I. Chernyaev and M. F. Vuks, The spectrum of the sky at twilight. DAN SSSR, 14, 77–79 (1937).

5. I. A. Khvostikov, Sodium in the stratosphere. UFN, 30, issue 3–4, 184–244 (1946).

6. I. A. Khvostikov, Infrared radiation of the night sky and the question of nitrogen dissociation in the ionosphere. UFN, 33, issue 4, 570–600 (1947).

7. I. A. Khvostikov, Polarization of the green line of the night-sky glow. DAN SSSR, 21, No. 7, 326–329 (1938).

8. I. A. Khvostikov, Polarization of emission lines in the spectrum of the night-sky glow. DAN SSSR, 27, No. 9, 217–220 (1940).

9. V. L. Ginzburg, On the polarization of lines in the spectrum of the night-sky glow and in the spectrum of auroras. DAN SSSR, 38, No. 8, 226–269 (1943).

10. I. A. Khvostikov and A. A. Shubin, Polarization of the night-sky glow in the ultraviolet part of the spectrum. DAN SSSR, 27, No. 3, 221–223 (1940).

11. I. A. Khvostikov, Twilight photoluminescence of the Earth’s atmosphere. Izvestiya AN SSSR, geographical and geophysical series, pp. 175–182 (1939).

12. J. Cabannes et H. Garrigue, Un phénomène de photoluminescence dans la haute atmosphère: l’excitation par la lumière solaire de la raie 6300 Å de l’oxygène, Comptes Rendus, 203, 484–487 (1936).

13. C. T. Elvey and A. H. Farnsworth, Spectrophotometric observations of the light of the night sky, Astrophys. Journ., 96, No. 3, 451–467 (1942).