THE ORIGIN OF THE HYDROXYL SYSTEM IN NIGHT-SKY EMISSION

V. I. Krasovskii

1. INTRODUCTION

The emission radiation of the night sky, and in particular the most intense hydroxyl radiation, points to a number of very important and interesting processes in the upper atmosphere. Despite major advances in the study of night-sky radiation and twilight flashes, many uncertainties still remain, and it is difficult to construct a definitive theory of these processes. A number of reviews have already been devoted to this question[^1],[^2]. In recent years, however, additional material has accumulated concerning many very important problems in the physics of the upper atmosphere. The present review is devoted to an exposition of the current state of our ideas about night-sky radiation, especially hydroxyl radiation.

Variations in the intensity of night-sky radiation and twilight flashes make it possible to express interesting judgments about the nature of such phenomena[^3],[^4]. The latter can be explained by changes in the density and temperature of the upper atmosphere, which are most closely connected with tidal-thermal oscillations that determine their diurnal course. Mixing of the upper atmosphere between different latitudes, as well as the well-known annual variation of the mean daily ultraviolet radiation at different latitudes, explain the seasonal variations. Only nighttime interruptions in the illumination of the terrestrial atmosphere remain unnoticeable because of the large time constant of recombination processes. Oscillations of the density and temperature of the upper atmosphere simultaneously cause changes in the intensity of night-sky emissions and in the recombination rate of atmospheric ions, on which the electron density depends. Tidal and wind motions also change the strength of currents induced in the ionosphere. All these circumstances open broad possibilities for explaining positive or negative correlations between emissions of the upper atmosphere, on the one hand, and ionization of the upper atmosphere, variations of the terrestrial magnetic field, and telluric currents, on the other.

At present, however, the more essential question is that of variations in the intensity of upper-atmosphere emissions as a function of solar activity. Apparently, it may be asserted with very considerable certainty that, at least at low and middle latitudes, no clear or, in any case, at all substantial correlation is observed between the intensity of individual emissions of night-sky radiation and solar activity.

Such a conclusion with regard to the 5577 and 5893 Å emissions may be drawn on the basis of Roach’s work[^5]. An analogous conclusion concerning the emissions

hydroxyl and 6300 Å follows from the old works of Rayleigh and Jones⁶, in which wide-band light filters transmitting red radiation were used, where, as has now been established, the hydroxyl and 6300 Å emissions are commensurable. Further consideration reduces mainly to revealing the consequences that would occur if such a circumstance actually existed. It goes without saying that great caution must be exercised in transferring an analogous conclusion to the polar regions. It is quite possible that the upper atmosphere above them undergoes substantial chemical transformations as a result of the intense action of the corpuscular radiation of the Sun, perhaps more effective than ultraviolet. But to resolve this question the observational material that is still lacking is necessary.

The independence of the emissions in low and middle latitudes from solar activity indicates that the ultraviolet radiation of the Sun responsible for these emissions, in contrast to ionizing radiation, does not change at all or, in any case, does not change significantly with solar activity. In the search for the true mechanisms of the night-sky radiation, this circumstance makes it possible to reject a mechanism of excitation connected, to one degree or another, with ionization of the upper atmosphere. As yet it is impossible to point to any processes that could compensate for the effect of variations of ionizing radiation during the solar-activity cycle.

At present two hypotheses have been proposed to explain the hydroxyl radiation of the night sky. Both hypotheses proceed from the assumption that this radiation arises in one of the elementary reactions in the process of recombination of atomic oxygen of the upper atmosphere, dissociated by comparatively soft ultraviolet \((\lambda\lambda > 1200\ \text{Å})\). According to Bates, Nicolet, and Herzberg, it is the ozone–hydrogen reaction⁷. Krasovskii assumes that the hydroxyl radiation arises in the reaction of newly formed vibrationally excited oxygen molecules with hydrogen atoms⁸,⁹. In both hypotheses it is assumed that atomic hydrogen is regenerated again in reactions of deactivated hydroxyl with atomic oxygen. A choice between the hypotheses could be made if the exact height of the layers emitting the hydroxyl emission were known. However, determinations of this height from the ratio of intensities at different zenith distances are extremely contradictory and unreliable¹⁰. If this emission arose at heights of the order of 70–80 km, this would unambiguously indicate the ozone–hydrogen reaction. On the other hand, if this radiation arose at a height of 90–100 km, this would unambiguously indicate the oxygen–hydrogen reaction. At present it is known that the region of practically complete dissociation of atomic oxygen is located definitely above 100 km¹¹. But as a result of mixing of the upper atmosphere, recombination of atomic oxygen into molecular oxygen proceeds most intensively in lower layers, where the number of triple collisions is much greater than in the region above 100 km, and where atomic oxygen enters as a consequence of intense mixing. If it were established that the hydroxyl radiation arises throughout the entire height region between 70 and 110 km, this would testify that both proposed mechanisms of its excitation are operating.

The rotational temperature of the hydroxyl bands, as well as the data on the temperature in the upper atmosphere within the limits of the existing errors and scatter, more or less satisfactorily admit both points of view. At present it is still very difficult to use

justification of the large power of hydroxyl radiation for choosing one hypothesis or another by comparing this radiation with the hard ultraviolet radiation absorbed in one or another region of the upper atmosphere and ultimately transformed into hydroxyl radiation. The point is that it is still not possible, from the observed intensity of the infrared radiation of hydroxyl in the near infrared region of the spectrum, to calculate exactly the total power of hydroxyl radiation. Apparently, for the time being one can only assert that the number of newly formed hydroxyl molecules does not exceed \(10^{13}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\), but is not less than \(10^{11}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\). For schematic calculations the value \(10^{12}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\) is usually used; however, this value is somewhat arbitrary. The reason for this is both the inaccurate information on the power of hydroxyl radiation in the near infrared region of the spectrum and the lack of complete certainty that Scholz’s formula permits, from these data, calculation of the total intensity of hydroxyl radiation with an accuracy substantially greater than the indicated orders of magnitude\(^{12,13,14}\). It must be noted once again that the argument concerning limiting excitation of hydroxyl up to the 9th vibrational level also cannot serve as a means for a final choice between one or another point of view. From the standpoint of the oxygen-hydrogen hypothesis it is quite possible to explain such limiting excitation\(^{8,9,15}\). However, such an interpretation is no longer the only one. It is not without interest to recall the investigation of Norrish, who showed that the reaction of chlorine dioxide molecules with atomic oxygen leads to the formation of an excited molecule not with the limiting excitation up to the maximum energy liberated in this reaction, but only up to a considerably smaller value\(^{16}\). Norrish’s investigation shows that in a reaction between a triatomic molecule and an atom the energy liberated is not at all concentrated in some definite final product, but is distributed, according to a law still unknown to us, between both particles formed. Taking this circumstance into account, one cannot assert that in the case of the ozone-hydrogen reaction all the energy is concentrated in hydroxyl, just as one cannot assert that the excitation energy in the reaction of ozone with atomic oxygen is localized in any one of the oxygen molecules formed. Norrish’s investigations are very favorable to the assumption of a large preservation of the vibrational excitation of the oxygen molecule in the ground state. A final resolution of the question is also hampered by the absence of exact information on the deactivation of vibrationally excited molecules, including hydroxyl, in collisions. The ozone-hydrogen hypothesis is not favored by the circumstance that it is applied to lower layers of the atmosphere, where the role of deactivating collisions is incomparably greater than in the upper, less dense regions.

Determination of the altitude of certain emission radiations of the upper atmosphere by means of rockets apparently indicates the possibility that hydroxyl radiation of the upper atmosphere may also arise in the region around \(100\ \mathrm{km}\)\(^{17,18,19}\). In the region around \(5200\)—\(5300\ \text{\AA}\), where the investigations were conducted, there are the hydroxyl bands 6—0 and 9—2. In addition, the sodium emission recorded in these experiments is strongly blended with the hydroxyl band 8—2. Taking into account the great width of the light filters used, there can hardly be complete certainty that hydroxyl emission, with an intensity approaching the measured values, was absent around \(5200\)—\(5300\) and \(5589\ \text{\AA}\). The rocket experiments in any case show that in this region of the spectrum below \(80\ \mathrm{km}\) substantial emission is absent. A final conclusion

it is necessary to postpone until a further experiment with the determination of the height of occurrence of purely hydroxyl emission.

Regardless of what this conclusion may be, at the present time it makes sense to examine another circumstance, possibly no less significant, which may serve as an additional basis for clarifying the details of chemical transformations in the upper atmosphere. The table gives a list of all elementary reactions of dissociation

Table

and recombination of oxygen at all levels, beginning from 30 km and higher. Until very recently, in studies of ozone formation under laboratory conditions and in the upper atmosphere, reactions 10 and 11 were completely ignored. However, such neglect appears insufficiently justified. Indeed, if vibrational excitation of an ozone molecule can persist for $10^4$–$10^5$ collisions, then neglect of reactions 10 and 11, both in a laboratory experiment and in the upper atmosphere, is inadmissible. There is no doubt that failure to take these reactions into account under laboratory conditions leads to an underestimation of reaction 4 and an overestimation of the role of reaction 12 in comparison with reaction 4, since the ozone formed as a result of the latter will rapidly be converted into molecular oxygen. Thus, a simplified estimate of the rate constants of the various elementary reactions indicated in the table, based on neglecting processes 10 and 11, can be regarded only as yielding certain effective values. Their use will lead to a qualitatively correct result in determining the distribution of ozone in the upper atmosphere in the daytime, when reactions 1, 3, 6, and 7 occur. However, at night, when there is no hard ultraviolet radiation from the Sun leading to the process of ozone formation, and consequently when the processes 1, 3, 6, and 7 fall out of the cycle, the effective values of the coefficients of reactions 4 and 12 indicated above cannot be used. In this case it is necessary to pass from the effective values to the true ones, and the true rate of process 4 will be higher than the true rate of process 12. At night, with the cessation of hard ultraviolet illumination in the lower part of the upper atmosphere, there will begin

rapid conversion of atomic oxygen into ozone and molecular oxygen owing to reactions 4, 10, and 11.

Krasovskii used a value of the rate constant of reaction 4 based on its determination by comparing the rate of reaction 4 with the rate of formation of carbon dioxide in triple collisions involving a carbon monoxide molecule and atomic oxygen\({}^{15}\). This was done in the work of Epikoloian and Nalbandian\({}^{20}\), from which it follows that the rate constant of reaction 4 is determined by a value of about \(10^{-33}\cdot T^{1/2}\ \mathrm{cm^6\,sec^{-1}}\), and not \(5\cdot 10^{-36}\cdot T^{1/2}\ \mathrm{cm^6\,sec^{-1}}\), which was used by Bates and Nicolet\({}^{7}\). It is quite evident that at the present time it is necessary to carry out new laboratory determinations of the rate constants of reactions 4 and 12, taking account of reactions 4, 5, 10, and 11. This will be of great significance not only for the final choice of the mechanism of excitation of hydroxyl radiation of the night sky, but also, in general, for a more exact theory of the process of ozone formation in the upper atmosphere.

A careful consideration of the processes giving rise to all known emissions of the night sky shows that the most acceptable mechanism is a common simultaneous mechanism for their excitation. As will be shown below, all observed emissions are, to one degree or another, connected with the most powerful hydroxyl radiation. Consideration of the processes of excitation of these emissions may serve as an additional means for choosing the most satisfactory hypothesis for hydroxyl excitation.

2. DISCUSSION OF THE NATURE OF HYDROXYL EMISSION

Recently a number of critical remarks have been made in the literature concerning the existing hypotheses on the hydroxyl emission of the night sky. Below a brief account is given of the details of the discussion that has developed on this subject. As was already indicated above, according to Bates and Nicolet\({}^{7}\) and Herzberg\({}^{21}\), vibrationally excited hydroxyl \(\mathrm{OH}^*\) appears in the reaction\({}^{*)}\)

\[ \mathrm{O_3}+\mathrm{H}\to \mathrm{OH}^*+\mathrm{O_2}. \tag{1} \]

Krasovskii\({}^{8,9}\) points to the reaction

\[ \mathrm{O_2^*}+\mathrm{H}\to \mathrm{OH}^*+\mathrm{O}, \tag{2} \]

where the vibrationally excited molecules \(\mathrm{O_2^*}\) are formed in the zone of effective recombination of oxygen. Bates and Masevich\({}^{22}\) object to Krasovskii’s considerations regarding the mechanism of excitation of \(\mathrm{OH}^*\). We shall first examine these objections and in conclusion touch upon several other circumstances neglected by Bates and Masevich.

The \(\mathrm{O_3}\)-hypothesis

The exact value of the excitation energy of the 10th vibrational level of \(\mathrm{OH}\) in the ground state is equal to \(80.6\ \mathrm{kcal/mole}\). On the other hand, according to Gaydon\({}^{23}\), the heats of formation of \(\mathrm{O_2}\), \(\mathrm{O_3}\), and \(\mathrm{OH}\) are equal to \(117.2\), \(140.6\), and \(101\ \mathrm{kcal/mole}\), respectively, whence it follows that the heat effect of reaction (1) is \(77.6\ \mathrm{kcal/mole}\), i.e., \(3\ \mathrm{kcal/mole}\) less than the excitation energy of the 10th vibrational level of \(\mathrm{OH}\). If the activation energy of reaction (1) is \(3\ \mathrm{kcal/mole}\), then excitation of this level is inevitable. In their latest work Bates and Masevich give new data taken from Brix and Herzberg\({}^{24}\): \(118.0\), \(142.4\), and \(104\ \mathrm{kcal/mole}\) for \(\mathrm{O_2}\), \(\mathrm{O_3}\), and \(\mathrm{OH}\)

\({}^{*)}\) The sign \(*\) at the upper right of the molecular symbol denotes that this molecule is in an excited state.

respectively. In this case the thermal effect of reaction (1) will amount to 76.4 kcal/mole, which is 4.2 kcal/mole less than the excitation energy of the 10th vibrational level of OH. Even if the activation energy of (1) is equal to 3 kcal/mole, the 10th level will inevitably be excited and its population will be appreciable, since at a temperature of 260°K (the rotational temperature of the hydroxyl bands in the radiation of the night sky) the number of molecules with energy exceeding 4.2 kcal/mole will be related to the number of molecules with energy exceeding 3 kcal/mole as 1 : 8.5. It must also not be overlooked that the experimental data do not make it possible to obtain an exact value and only indicate that the activation energy of (1) is probably less than 5 kcal/mole (see, for example, ^25). The activation energy of reaction (1) can hardly be substantially less than the activation energy of the reaction

\[ \mathrm{O}_3+\mathrm{O}\to \mathrm{O}_2^*+\mathrm{O}_2^*, \tag{3} \]

which (see below), according to Schumacher ^26, lies in the range from 4 to 6 kcal/mole. Therefore the value 3 kcal/mole, adopted by Bates and Nicolet ^7, is somewhat arbitrary.

Thus, so far there are no indisputable arguments that reaction (1) guarantees excitation of the 10th vibrational level of OH. In reality, in the radiation of the night sky no OH bands are observed in transitions from the 10th and higher vibrational levels. According to Krasovskii ^8,9,15 this occurs because of the reactions (if the hydroxyl radiation originates in denser layers at an altitude of about 75 km):

\[ \mathrm{OH}^*(v\geq 10)+\mathrm{O}_2\to \mathrm{O}_3+\mathrm{H} \tag{4} \]

and

\[ \mathrm{OH}^*(v\geq 10)+\mathrm{N}_2\to \mathrm{N}_2\mathrm{O}+\mathrm{H}. \tag{5} \]

Bates and Masevich agree that this circumstance does not make it possible to judge the nature of the primary excitation of OH. Hence it inevitably follows that the emission spectrum of a mixture of \(\mathrm{O}_3\) and H in the presence of \(\mathrm{O}_2\) or \(\mathrm{N}_2\) also will not contain OH bands with excitation at the 10th and higher levels. Therefore the experiment of McKinley, Garvin, and Boudart ^27, from the description of which it cannot be concluded that \(\mathrm{O}_2\) molecules were absent from the reaction medium, cannot serve as a basis for choosing between reactions (1), on the one hand, and (4) and (5), on the other. The argument about the 9th vibrational level is insufficient to prove that reaction (1) serves as the source of excitation of OH*. For this, other, more convincing arguments are needed.

Bates and Masevich do not agree with Krasovskii’s supposition that \(n(\mathrm{O})\)* decreases by half in 50 sec and 10 min at altitudes of 70 and 80 km, respectively. According to their estimates, the rate constant \(K\) of the reaction

\[ \mathrm{O}+\mathrm{O}_2+\mathrm{M}\to \mathrm{O}_3+\mathrm{M} \tag{6} \]

is equal to \(5\cdot 10^{-36}\cdot T^{1/2}\ \mathrm{cm}^6\mathrm{sec}^{-1}\). This value of \(K_6\) (the subscript indicates the reaction number) was taken by Bates and Nicolet ^7 with reference to Eucken and Patat ^28. However, as has already been said, Krasovskii used another value,

\[ K_6=10^{-33}\cdot T^{1/2}\mathrm{cm}^6\mathrm{sec}^{-1}, \]

recommended recently by Yenikolopyan and Nalbandyan ^20. These authors proceed from the fact that the rate constant of the reaction

\[ \mathrm{CO}+\mathrm{O}+\mathrm{M}\to \mathrm{CO}_2+\mathrm{M} \tag{7} \]

\[ \text{*) } n(x)\text{ denotes the concentration of molecules or atoms of species }x,\text{ and }F(x^*)\text{ is the number of newly formed vibrationally excited molecules }x^*\text{ in }1\ \mathrm{cm}^3\text{ in }1\ \mathrm{sec}. \]

40 times smaller than \(K_6\), and that \(K_7=2.5\cdot10^{-35}\cdot T^{1/2}\ \text{cm}^6\text{sec}^{-1}\). In the old work of Eucken and Patat \(^{28}\) the ratio \(K_6/K_3\) is determined. The absolute value of \(K_6\) depends on the absolute value of \(K_3\). With the extreme values of the activation energy \(\varepsilon_3\), from 4 to 6 kcal/mole, indicated by Schumacher \(^{26}\), the quantity \(K_6\) may lie between

\[ 5\cdot10^{-34}\cdot T^{1/2}\ \text{cm}^6\text{sec}^{-1} \quad\text{and}\quad 10^{-35}\cdot T^{1/2}\ \text{cm}^6\text{sec}^{-1}* \]

The value of \(K_6\) used by Krasovsky is somewhat larger than this maximum limit. The value of \(K_6\) according to Bates and Nicolet \(^{7}\), taken by Eucken and Patat, although it is very favorable for the \(\mathrm{O}_3\)-hypothesis, is nevertheless hardly definitively established.

Most of the known data correspond better to the value \(K_6=10^{-33}\cdot T^{1/2}\text{cm}^6\text{sec}^{-1}\) than to \(K_6=5\cdot10^{-36}\cdot T^{1/2}\ \text{cm}^6\text{sec}^{-1}\). For illustration we cite some excerpts from the book by V. N. Kondrat’ev, Elementary Chemical Processes \(^{29}\).

“According to the measurements of Farkas and Sachs \(^{30}\), the process \(\mathrm{H}+\mathrm{O}_2+\mathrm{M}\to\mathrm{HO}_2+\mathrm{M}\) has a rate approximately 500 times smaller than the rate of the process of recombination of H atoms, i.e. the process \(\mathrm{H}+\mathrm{H}+\mathrm{M}\to\mathrm{H}_2+\mathrm{M}\). Since recombination of H atoms takes place practically at every triple collision, we must conclude that the probability of the process \(\mathrm{H}+\mathrm{O}_2+\mathrm{M}\to\mathrm{HO}_2+\mathrm{M}\) is about \(1/500\). Let us add that this quantity remains practically unchanged for \(\mathrm{M}=\mathrm{H}_2,\ \mathrm{O}_2,\ \mathrm{N}_2,\ \mathrm{Ar}\).” (p. 87)

“Turning to the experimental data, we shall point first of all to the work of Schumacher \(^{26}\), who showed that in this case (the mixture \(\mathrm{O}+\mathrm{O}_2\)) the formation of ozone is connected with a triple collision: \(\mathrm{O}+\mathrm{O}_2+\mathrm{M}\to\mathrm{O}_3+\mathrm{M}\), whose efficiency is equal to unity. The destruction of ozone is due to the process \(\mathrm{O}+\mathrm{O}_3\to\mathrm{O}_2+\mathrm{O}_2\), proceeding at room temperature with probability \(5\cdot10^{-4}\).” (pp. 90–91)

Thus, the rate constants of reactions (6), and also

\[ \mathrm{H}+\mathrm{H}+\mathrm{M}\to\mathrm{H}_2+\mathrm{M} \tag{8} \]

and

\[ \mathrm{H}+\mathrm{O}_2+\mathrm{M}\to\mathrm{HO}_2+\mathrm{M} \tag{8a} \]

are connected with one another by the relation \(K_6\sim K_8\sim500K_{8a}\). The values adopted by Bates and Nicolet \(^{7}\) are as follows: \(K_6=5\cdot10^{-36}\), \(K_8=6\cdot10^{-34}\), and \(K_{8a}=6\cdot10^{-37}\ \text{cm}^6\text{sec}^{-1}\). If \(\exp(-\varepsilon_3/RT)=5\cdot10^{-4}\), then \(\varepsilon_3\sim4.5\) kcal/mole, which, according to Eucken and Patat \(^{28}\), would correspond to \(K_6\sim2\cdot10^{-34}T^{1/2}\ \text{cm}^6\text{sec}^{-1}\). The value of \(K_6\) recommended by Yenikolopyan and Nalbandyan \(^{20}\) makes it possible to regard reaction (6) as more effective than the reaction

\[ \mathrm{O}+\mathrm{O}+\mathrm{M}\to\mathrm{O}_2+\mathrm{M}, \tag{9} \]

which, according to Bates and Nicolet \(^{7}\), has \(K_9\sim5\cdot10^{-34}\ \text{cm}^6\text{sec}^{-1}\).

Thus it becomes clear that it is necessary to substantiate a more exact value of \(K_6\). If \(K_6=5\cdot10^{-36}\ \text{cm}^6\text{sec}^{-1}\), then the \(\mathrm{O}_3\)-hypothesis will not be in difficulty because of the rapid exhaustion of the supplies of atomic oxygen. However, there is still no certainty that precisely this value of \(K_6\) is impeccable.

Shklovsky \(^{12}\), in estimating the upper limit of the content of the OH radical in the Earth’s atmosphere, took the strength of its oscillator to be equal to unity**).

\[ \underline{\phantom{xxxxxxxxxxxxxxxx}} \]

*) Since \(K_6/K_3=aT^{1/2}/bT^{1/2}\exp(-\varepsilon_3/RT)\), \(T=260^\circ\mathrm{K}\) and \(b\sim1.5\cdot10^{-11}\). The value \(K_6/K_3\) is taken from Jansson, Parkes, Goussev, and Vatanabe \(^{31}\).

**) This explanation was given to me by I. S. Shklovsky.

At an oscillator strength of \(10^{-3}\), the maximum possible OH content will be greater than \(10^{12}\) OH molecules \(\text{cm}^{-2}\). In this case the non-observability of OH bands in the absorption of the Earth’s atmosphere cannot be used as an argument against the \(\mathrm{O}_3\) hypothesis.

Bates and Masevich believe that the results of rocket investigations by Johnson, Purcell, Tousey, and Watanabe\({}^{31}\) indicate that at an altitude of about 75 km, where Bates and Nicolet\({}^{7}\) assume the most intense excitation of OH, \(10^6\) photodissociations occur in \(1\ \text{cm}^3\) per second, which are sufficient to maintain approximately the same number of elementary processes in \(1\ \text{cm}^3\) per second. If \(K_6 = 5 \cdot 10^{-36}\, T^{1/2}\ \text{cm}^6\text{sec}^{-1}\), then, as Bates and Nicolet\({}^{7}\) indicate, at an altitude of about 75 km \(n(\mathrm{O})\) will be an order of magnitude greater than \(n(\mathrm{H})\). Under these conditions process (3) will be more intense than (1), since \(K_1\) and \(K_3\) have values differing little from one another. Thus the number of \(\mathrm{O}_3\) molecules consumed in process (1) will be less than the total number of newly formed molecules and single acts of photodissociation of \(\mathrm{O}_2\), and, consequently, \(F(\mathrm{OH}^*)\) will not be able to reach \(10^6\ \text{cm}^{-3}\text{sec}^{-1}\). The lower the altitude, the more significant becomes the deactivation of vibrationally excited molecules in collisions. However, Bates and Masevich completely ignore this process in the case of collisions of \(\mathrm{OH}^*\) with other molecules at an altitude of about 75 km, although they themselves attach exceptional importance to it in substantiating the supposedly complete ineffectiveness of process (2) in the higher layers of the atmosphere, where the number of collisions is smaller. Bates and Masevich, following Hips and Herzberg\({}^{13}\), assume that the mean lifetime of \(\mathrm{OH}^*\) under deactivation by radiation has the value \(10^{-2}\) sec. In this case the frequency of OH collisions at an altitude of 75 km reaches \(5 \cdot 10^5\ \text{sec}^{-1}\). The photodissociating radiation that was used in the calculation in the work of Johnson, Purcell, Tousey, and Watanabe\({}^{31}\) corresponds to a higher effective solar temperature than \(4500^\circ\mathrm{K}\), i.e., the temperature that Bates and Masevich use in estimating the effectiveness of process (2). It is more appropriate to compare (1) and (2) at the same temperature. Thus \(F(\mathrm{OH}^*)\) must be considerably less than \(10^6\ \text{cm}^{-3}\text{sec}^{-1}\), which, apparently, will be sufficient for hydroxyl radiation of the observed intensity.

All the remarks made refer to a quiet, unmixed atmosphere and to that variant of the \(\mathrm{O}_3\) hypothesis in which the constants of elementary processes adopted by Bates and Nicolet\({}^{7}\) are used. In reality, both of these may not be the case. It should be noted that the \(\mathrm{O}_3\) hypothesis will be favored by vertical mixing of the atmosphere, which can bring large masses of \(\mathrm{O}_3\), H, \(\mathrm{O}_2\), and O into contact and thereby increase \(F(\mathrm{OH}^*)\). However, quantitative estimates of this process are as yet lacking.

\(\mathrm{O}_2^*\)-hypothesis

Bates and Masevich believe that every collision of \(\mathrm{O}_2^*\) with O necessarily leads to a decrease in the vibrational quantum number of \(\mathrm{O}_2^*\) or to an exchange reaction with the formation of a new \(\mathrm{O}_2^*\) molecule with a smaller vibrational quantum number. This cannot be accepted. As a counterweight to this, let us cite an assessment of the results of the study of the deactivation of vibrational excitation of molecules in the ground state from V. N. Kondrat’ev’s book Elementary Chemical Processes\({}^{20}\) (p. 44):

“The entire body of experimental and theoretical data relating to processes of exchange of vibrational and translational energy can be summarized in the following propositions:”

1. In a single collision practically only one vibrational quantum is transferred.

2. The probability of quantum transfer \(\left(\gamma_v^{v-1}\right)\), calculated per collision, depends little on the magnitude of the quantum and is of the order of magnitude, varying, depending on the nature of the colliding molecules, within the limits from \(10^{-4}\) to \(10^{-2}\) (at room temperature).

3. The probability \(\gamma\) is a function of temperature and, as a rule, increases rapidly with increasing temperature.

4. For not very large \(v\) (the number of the vibrational level) the probability of quantum transfer \(\left(\gamma_v^{v-1}\right)\) is proportional to \(v\), or \(\gamma_v^{v-1}=v\cdot\gamma_1^0\).”

The above-cited work of Norrish \(^{16}\) also indicates good conservation of vibrational excitation in oxygen molecules in the ground state. In light of this, Kondrat’ev’s data are more likely to be too high than too low.

It must also be noted that every exchange reaction \( \mathrm{O}_2^*[v=v_n]\) with O need not necessarily be accompanied by a decrease in the vibrational quantum number. But such a reaction without a change in quantum number may be disregarded, since \(n\left(\mathrm{O}_2^*[v=v_n]\right)\) does not change in such a transformation.

In the deactivation of \(\mathrm{O}_2^*\) three processes compete:

a)

\[ \mathrm{O}_2^*[v=v_n]+\mathrm{H}\to \mathrm{OH}^*[v=v_k]+\mathrm{O}; \tag{10} \]

b) at small \(v_n\)

\[ \mathrm{O}_2^*[v=v_n]+\mathrm{M}\to \mathrm{O}_2^*[v=v_{n-1}]+\mathrm{M}, \tag{11} \]

where this process is understood to include deactivation both in collisions and in exchange reactions of \(\mathrm{O}_2^*\) with O; and

c) at large \(v_n\)

\[ \mathrm{O}^*[v=v_n]+\mathrm{O}_2\to \mathrm{O}_3+\mathrm{O}, \tag{12} \]

or

\[ \mathrm{O}_2^*[v=v_n]+\mathrm{N}_2\to \mathrm{N}_2\mathrm{O}+\mathrm{O}. \tag{12a} \]

In \(\mathrm{O}_2^*\) molecules the distance between vibrational levels is \(\alpha\) times smaller than in \(\mathrm{OH}^*\), and \(\alpha\sim 2\div 3\). Therefore the production of OH with \(v=v_k\) will occur approximately at the \(\alpha\)-levels of \(\mathrm{O}_2^*\). Thus,

\[ F\left(\mathrm{OH}^*[v=v_k]\right)=n\left(\mathrm{O}_2^*[v=v_n]\right)n(\mathrm{H})K_{10}\cdot\alpha, \tag{13} \]

but

\[ n\left(\mathrm{O}_2^*[v=v_n]\right)= \frac{F\left(\mathrm{O}_2^*[v=v_n]\right)} {n(\mathrm{H})K_{10}+n(\mathrm{M})K_{11}+n(\mathrm{O}_2;\mathrm{N}_2)K_{12}}. \tag{14} \]

Taking this into account, (13) may be rewritten as

\[ F\left(\mathrm{OH}^*[v=v_k]\right)= F\left(\mathrm{O}_2^*[v=v_n]\right) \frac{\alpha} {1+\dfrac{n(\mathrm{M})}{n(\mathrm{H})}\cdot\dfrac{K_{13}}{K_{10}} +\dfrac{n(\mathrm{O}_2;\mathrm{N}_2)}{n(\mathrm{H})}\cdot\dfrac{K_{12}}{K_{10}}}. \tag{15} \]

The total yield of excited molecules in a column of the atmosphere with base \(1\ \mathrm{cm}^2\) will be \(\sum F\left(\mathrm{OH}^*[v=v_k]\right)\) and \(\sum F\left(\mathrm{O}_2^*[v=v_n]\right)\). If in the zone of effective recombination of oxygen \(\alpha\), \(K_{10}\), \(K_{11}\), \(K_{12}\), \(n(\mathrm{H})\), \(n(\mathrm{M})\), \(n(\mathrm{O}_2)\) and \(n(\mathrm{N}_2)\)

remain approximately constant with altitude, then

\[ \sum F(\mathrm{OH}^*[v=v_k]) \sim \sum F(\mathrm{O}_2^*[v=v_n]) \frac{\alpha}{ 1+\dfrac{n(\mathrm{M})}{n(\mathrm{H})}\cdot\dfrac{K_{11}}{K_{10}} +\dfrac{n(\mathrm{O}_2;\mathrm{N}_2)}{n(\mathrm{H})}\cdot\dfrac{K_{12}}{K_{10}} }. \tag{16} \]

If reactions (10) and (12) occur at every gas-kinetic collision, and the probability (11), calculated per one gas-kinetic collision, is equal to \(\gamma\), then for small \(v\), \(K_{11}/K_{10}\sim\gamma\) and \(K_{12}/K_{10}\sim 0\), while for large \(v\), \(K_{12}/K_{10}\sim 1\).

As an example, let us consider the case of relatively small \(v\), when \(K_{12}/K_{10}\sim 0\), i.e. when process (12) may be neglected. In this case

\[ \sum F(\mathrm{OH}^*[v=v_k]) \sim \sum F(\mathrm{O}_2^*[v=v_n])\cdot \frac{\alpha}{ 1+\dfrac{n(\mathrm{M})}{n(\mathrm{H})}\cdot\dfrac{K_{11}}{K_{10}} }. \tag{17} \]

For \(F(\mathrm{O}_2^*[v=v_n])\sim 5\cdot 10^{11}\ \mathrm{cm}^{-2}\mathrm{sec}^{-1}\) (i.e. at an effective solar temperature of \(4500^\circ\mathrm{K}\)),*) \(n(\mathrm{M})/n(\mathrm{H})\sim 10^4\), \(K_{11}/K_{10}\sim 3\cdot 10^{-3}\), and \(\alpha\sim 3\),

\[ \sum F(\mathrm{OH}^*[v=v_k])\sim 5\cdot 10^{10}\ \mathrm{cm}^{-2}\mathrm{sec}^{-1}. \]

For still smaller \(v_n\), when \(\gamma\) decreases, tending to \(10^{-4}\), or for a smaller value of \(n(\mathrm{M})/n(\mathrm{H})\), it is possible that

\[ \sum F(\mathrm{OH}^*[v=v_k]) \sim \sum F(\mathrm{O}_2^*[v=v_n]), \]

i.e. an almost complete conversion of the energy released in the recombination of oxygen into molecules into the energy of hydroxyl radiation in the upper atmosphere.

In those cases when, for \(\mathrm{O}_2^*[v=v'_n]\), process (10) with formation of \(\mathrm{OH}^*[v=v'_k]\) becomes possible,

\[ \frac{n(\mathrm{O}_2;\mathrm{N}_2)}{n(\mathrm{H})}\cdot\frac{K_{12}}{K_{10}} > 1+\frac{n(\mathrm{M})}{n(\mathrm{H})}\cdot\frac{K_{11}}{K_{10}}. \tag{18} \]

Therefore

\[ \sum F(\mathrm{OH}^*[v=v'_k]) \sim \sum F(\mathrm{O}_2^*[v=v'_k])\,\alpha\, \frac{n(\mathrm{H})}{n(\mathrm{O}_2;\mathrm{N}_2)}\cdot\frac{K_{10}}{K_{12}}. \tag{19} \]

Thus, if

\[ \sum F(\mathrm{O}_2^*[v=v'_n]) \sim \sum F(\mathrm{O}_2^*[v=v_n]) \]

and taking into account that

\[ 1+\frac{n(\mathrm{M})}{n(\mathrm{H})}\cdot\frac{K_{11}}{K_{10}} \sim \frac{n(\mathrm{M})}{n(\mathrm{H})}\cdot\frac{K_{11}}{K_{10}}, \]

*) The formation of \(\mathrm{O}\) and \(\mathrm{O}_2^*\) is associated not only with absorption in the Runge-Schumann continuum. These products may also form additionally at an altitude of about 100 km due to absorption in the Runge-Schumann bands. Here are the processes leading to the additional formation of \(\mathrm{O}\) and \(\mathrm{O}_2^*\):

\[ \mathrm{O}_2+h\nu\to(\mathrm{O}_2+h\nu);\qquad (\mathrm{O}_2+h\nu)+\mathrm{O}_2\to \mathrm{O}_3^*+\mathrm{O}; \]

\[ \mathrm{O}_3^*+\mathrm{O}\to \mathrm{O}_2^*+\mathrm{O}_2^*. \]

will take place

\[ \frac{\sum F(\mathrm{OH}^*[v=v'_k])}{\sum F(\mathrm{OH}^*[v=v_k])} \sim \frac{n(\mathrm{O}_3;\mathrm{N}_2)}{n(\mathrm{M})}\cdot \frac{K_{12}}{K_{11}} . \tag{20} \]

Since \(n(\mathrm{O}_2;\ \mathrm{N}_2)/n(\mathrm{M})\sim 1\), and \(K_{12}/K_{11}\sim 1/\gamma\), relation (20) may be written as

\[ \frac{\sum F(\mathrm{OH}^*[v=v_k])}{\sum F(\mathrm{OH}^*[v=v'_k])} \sim \frac{1}{\gamma}, \tag{21} \]

i.e., there is a practically complete break in the population of the high vibrational levels of \(\mathrm{OH}^*\), beginning with the \(v'_k\)-level. This break is a natural consequence of the assumption made above that \(\gamma \ll 10^{-2}\), which in turn determines the effectiveness of process (2).

Process (18) becomes possible when the excitation energy of \(\mathrm{O}_2^*\) reaches a value \(U\) equal to the sum of the heat effect and the activation energy of reaction (10). The heat effect (12) is equal to 93.8 and 93.6 kcal/mole according to Gaydon \(^{23}\) and Briks and Herzberg \(^{24}\), respectively, and the activation energy is \(\sim 4.5\) kcal/mole. Consequently, \(U\) is equal to \(\sim 98.3\) and 98.1 kcal/mole according to Gaydon \(^{23}\) and Briks and Herzberg \(^{24}\), respectively. According to the data of Curry and Herzberg \(^{32}\), this excitation corresponds to \(v\sim 28\). Molecules of \(\mathrm{O}_2^*\) with such and even somewhat smaller*) excitation in reaction with H could ensure the limiting excitation of hydroxyl up to 82.1 and 81.0 kcal/mole according to Gaydon \(^{23}\) and Briks and Herzberg \(^{24}\), respectively, i.e., up to the 10th vibrational level. However, since, owing to process (18), \(n(\mathrm{O}_2^*)\) with such excitation is insignificant, \(\mathrm{OH}^*[v>10]\) are practically not observed in the emission of the upper atmosphere.

The higher up, the fewer deactivating collisions there are, which favors the \(\mathrm{O}_2^*\)-hypothesis in comparison with the \(\mathrm{O}_3\)-hypothesis, applicable to lower layers, where there are more collisions.

Contrary to the remarks of Bates and Masevich, Krasovskii never considered that in the region of effective recombination of \(\mathrm{O}_2\) the break in the population of the high \(\mathrm{OH}^*\) levels is associated with processes (4) and (5). The reason for the indicated break lies in the high efficiency of processes (12), due to the fact that \(\mathrm{O}_2^*\) molecules, unlike \(\mathrm{OH}^*\), are not capable of being deactivated by radiation.

All the foregoing shows that the estimates of the \(\mathrm{O}_2^*\)-hypothesis made by Bates and Masevich are based on the most unfavorable limiting conditions, the existence of which in reality is not necessary.

3. ATOMIC HYDROGEN IN THE UPPER ATMOSPHERE

In all the proposed mechanisms of hydroxyl excitation, one of the initial products is atomic hydrogen, which competes with atomic oxygen in the destruction of excited or unexcited molecules (of oxygen or ozone, respectively). It is therefore natural to expect variations in the intensity of hydroxyl radiation when the concentration of atomic hydrogen changes. If the relative hydrogen content

*) Since some deficiency of energy may be compensated at the expense of the thermal energy of the molecules.

in the atmosphere continuously and at the same time is always in a dissociated state, then there are no grounds for variations in the intensity of hydroxyl radiation. However, at an altitude of about 75 km, where, according to the ozone–hydrogen hypothesis, the occurrence of hydroxyl radiation is assumed, hydrogen is certainly not in a state of complete dissociation, and therefore variations of its concentration should be expected as a function of variations in the intensity of \(HL_{\alpha}\) radiation, which, according to the assumptions of Bates and Nicolet, leads to the dissociation of water vapor. If there is no other means of complete dissociation of water vapor and molecular hydrogen near this altitude under circumstances independent of solar activity, with the exception of the action of \(L_{\alpha}\) radiation, then variations in the intensity of hydroxyl radiation as a function of solar activity are inevitable. If hydroxyl radiation increased its intensity with increasing solar activity, then it could be asserted with a high degree of certainty that it is associated with the ozone–hydrogen reaction.

At great altitudes hydrogen is undoubtedly completely dissociated. Variations in the intensity of \(L_{\alpha}\) radiation will in this case affect oscillations of the lower boundary of the zone of complete dissociation of molecular hydrogen compounds. Therefore, if hydroxyl radiation originates above this threshold, it will not depend on \(L_{\alpha}\) radiation, even if the dissociation of molecular hydrogen compounds is produced by this radiation. It should be noted, however, that dissociation of molecular hydrogen compounds is possible not only as a result of the action of \(L_{\alpha}\) radiation, but also as a consequence of reactions with excited oxygen atoms in the states \({}^{1}D\) and \({}^{1}S\), which are undoubtedly present at altitudes of about 100 km and below[^33]. The independence of hydroxyl radiation from solar activity is more in harmony with the oxygen–hydrogen hypothesis than with the ozone–hydrogen one.

4. THE ROLE OF HYDROXYL IN NIGHT-SKY EMISSIONS

Emission [OI] 5577 Å.

It is usually considered that the emission of atomic oxygen [OI] 5577 Å is easily explained by the formation of excited oxygen atoms in triple collisions involving three oxygen atoms[^19]. If such a process actually operates, then the zone of maximum intensity of [OI] 5577 Å radiation should coincide with the maximum concentration of atomic oxygen, or lie somewhat above it, since some deactivation will occur in collisions of excited states \(O({}^{1}S)\). At present, rocket experiments have established that the zone of maximum concentration of atomic oxygen is situated above 100 km[^11]. However, by means of the same rocket experiments it has been shown that the zone of the most intense generation of [OI] 5577 Å radiation is located at an altitude of 96 km[^17],[^18],[^19], which is certainly below the zone of maximum concentration of atomic oxygen. This is a substantial argument against the view that such emission of atomic oxygen is due to triple collisions involving three oxygen atoms.

It seems to us that a more probable reaction for the excitation of the oxygen emission [OI] 5577 Å is the reaction of vibrationally excited oxygen or hydroxyl molecules with some other atoms or molecules, as a result of which atomic oxygen is liberated. Such atoms or molecules may, for example, be atoms of oxy-

ORIGIN OF THE HYDROXYL SYSTEM IN THE RADIATION OF THE NIGHT SKY

oxygen or hydrogen. However, since the most probable limiting vibrational excitation in the newly formed oxygen and hydroxyl molecules is certainly less than the dissociation threshold, which is assumed in order to explain the excitation of hydroxyl only up to the 9th vibrational level, as a result of the process indicated above one cannot expect the appearance of oxygen atoms with excitation exceeding the state \(O({}^{1}D)\)*.

To explain the appearance of oxygen atoms in the \({}^{1}S\) state, it is necessary that atoms or molecules reacting with vibrationally excited oxygen and hydroxyl molecules lead to the formation of a new molecule with a bond whose energy exceeds the dissociation energy of the initial product. In the case of vibrationally excited oxygen molecules, nitrogen atoms or carbon monoxide molecules may satisfy this requirement, and in the case of a vibrationally excited hydroxyl molecule—unexcited hydroxyl molecules**).

Atomic nitrogen must be excluded from such possible initial products, since the formation of atomic nitrogen in the upper atmosphere can be associated only with ionizing radiation, which varies with changes in solar activity\(^{3,4}\), and this would undoubtedly lead to a corresponding variation in the intensity of the emission of atomic oxygen, if it arises in the reaction of vibrationally excited oxygen molecules with nitrogen atoms. In the upper atmosphere, in the region where oxygen radiation arises, one cannot allow a concentration of atomic nitrogen even remotely comparable with the concentration of atomic oxygen, since otherwise a significant fraction of the newly formed vibrationally excited oxygen molecules would go into the formation of nitrogen oxide at the expense of consuming the potential reserves of the dissociation energy of oxygen, which are evidently scarcely sufficient to maintain hydroxyl radiation at the observed level. Moreover, the appearance of nitrogen oxide, most importantly, would be accompanied by the appearance in the visible region of the spectrum of an intense continuum, which is not actually observed (see below). It is not without interest to note that the concentrations permissible in the upper atmosphere of vibrationally excited oxygen molecules \((10^{6} \div 10^{7}\,O_{2}^{*}\ \mathrm{cm}^{-3})\) and hydroxyl \((10^{4} \div 10^{6}\,OH\ \mathrm{cm}^{-3})\), as well as possible concentrations of carbon monoxide \((10^{6} \div 10^{7}\,CO\ \mathrm{cm}^{-3})\) and unexcited hydroxyl (up to \(10^{8}\,OH\ \mathrm{cm}^{-3}\))*** are quite sufficient to explain the intensity of oxygen emission at the observed level \((\sim 2\cdot 10^{8}\,h\nu\ \mathrm{cm}^{-2}\mathrm{sec}^{-1})\), taking into account that the rate constant of a reaction involving an excited initial product is of the order of \(10^{-10}\ \mathrm{cm}^{3}\mathrm{sec}^{-1}\), and that the height of the homogeneous atmosphere is approximately \(10^{6}\ \mathrm{cm}\).

Oxygen emission \([OI]\ 6300\ \text{Å}\)

All the reactions just discussed are sufficient to excite the nighttime oxygen emission \([OI]\ 6300\ \text{Å}\). Moreover, as already noted, atomic oxygen in the \({}^{1}D\) state may be formed even in reactions of vibrationally excited oxygen molecules

*) These reactions are: \(O_{2}^{*}+O \to O_{2}^{*}+O({}^{1}D)\), \(O_{2}^{*}+H \to OH^{*}+O({}^{1}D)\), \(OH^{*}+O \to OH^{*}+O({}^{1}D)\), and \(OH^{*}+H \to H_{2}^{*}+O({}^{1}D)\).

**) The following reactions are meant: \(O_{2}^{*}+N \to NO+O^{*}\), \(O_{2}^{*}+CO \to CO_{2}+O^{*}\), and \(OH^{*}+OH \to H_{2}O+O^{*}\).

***) As was indicated in Section 2, the nonobservability of hydroxyl bands in absorption in the Earth’s atmosphere indicates that the upper limit of the OH content is \(10^{14}\,OH\ \mathrm{cm}^{-1}\) for a height of the homogeneous atmosphere of the order of \(10^{6}\ \mathrm{cm}\).\(^{15,22}\)

and hydroxyl with atomic oxygen or hydrogen, respectively. The twilight flash of the oxygen emission at 6300 Å is explained without particular difficulty either by resonance fluorescence of atomic oxygen, or by photodissociation of molecular oxygen by ultraviolet light, in which one oxygen atom is formed in the excited state \({}^{1}D\). From this point of view, however, the constantly observed enhancement of this emission during 2–3 evening hours, not observed in the morning, remains unclear. A possible explanation of this phenomenon is discussed somewhat below.

NaI Emission

The NaI emission, both in the twilight flash and at night, undergoes substantial changes during the year, with the intensity minimum occurring in summer. Such intensity variations are very difficult to explain by changes in the influx of micrometeorites, which always contain sodium, since it is known that in the summer months there is not a minimum, but a maximum of the daily meteor streams[^35]. It has been suggested that in summer, when solar radiation acts on the Earth’s atmosphere for a longer time, conditions are created for increased ionization of atomic sodium, and therefore the variation in the intensity of the sodium emission is due to a change during the year in the concentration of atomic neutral sodium[^36]. Since its ionization potential is not large and the corresponding radiation does not undergo substantial variations during the cycle of solar activity, it is indeed possible to assume the effectiveness of such a mechanism for regulating the emission.

If we assume that in the region below 100 km sodium is found mainly, for example, in the form of monoxide, then atomic sodium may be formed in the reaction:

\[ \mathrm{NaO} + \mathrm{O}({}^{1}D;\,{}^{1}S) \to \mathrm{Na}^{*} + \mathrm{O}_{2}. \tag{22} \]

On the other hand, atomic sodium in reactions with vibrationally excited molecules of oxygen or hydroxyl may again be converted into monoxide

\[ \mathrm{Na} + \mathrm{O}_{2}^{*} \to \mathrm{NaO} + \mathrm{O}, \tag{23} \]

\[ \mathrm{Na} + \mathrm{OH}^{*} \to \mathrm{NaO} + \mathrm{H}. \tag{24} \]

In this case atomic sodium can exist in significant concentrations only in regions where excited oxygen atoms in the states \({}^{1}D\) and \({}^{1}S\) are present. Since reactions involving sufficiently excited products take place practically at each collision of the initial products, the equilibrium concentration of atomic sodium, when reactions (22), (23), and (24) are operative, is represented as

\[ \frac{n(\mathrm{Na})}{n(\mathrm{NaO})} \sim \frac{n(\mathrm{O}^{*})}{n(\mathrm{O}_{2}^{*};\,\mathrm{OH}^{*})}. \tag{25} \]

A relative change in the concentration of excited oxygen molecules and atoms, or of excited hydroxyl molecules, will also cause a variation in the concentration of atomic sodium and, consequently, in its emission.

Continuum

At present there is still no fully exhaustive information on the continuum. In some older materials, based on observations of sky radiation with the aid of filters with broad transmission, by—

apparently, there are indications of a correlation of the radiation in the blue and green regions of the visible spectrum with solar activity\(^6\). However, these assumptions must be treated with some caution, since there is no certainty that bright emissions of low-latitude aurorae, belonging to \([OI]\) and \(N_2^+\), were not superimposed on the radiation of the night sky.

To explain the continuum, Krasovskii, as early as the beginning of 1951, suggested that it arises in the radiative combination of nitric oxide molecules and oxygen atoms into nitrogen dioxide\(^ {33}\). Much later, other authors also pointed to such a mechanism\(^ {37,38}\).

Nitric oxide can appear in the upper atmosphere as a result of various processes. In principle, it can arise even in reactions newly formed in the reaction of strongly excited oxygen molecules with unexcited nitrogen molecules. Nitric oxide can also appear during the penetration of meteorites into the upper atmosphere. In this case it is formed owing to the high temperature in the meteor trail, and also because of the reaction of atmospheric molecules reflected from the meteor with molecules of the stationary medium. There is no doubt about the reality of these processes, since at the velocities possessed by meteorites the activation energy necessary for “air combustion” is fully provided. It is quite possible that the formation of the sporadic \(E\) layer is connected not with direct ionization during the fall of meteors, but with the appearance in the zone of fall of micrometeorites of large concentrations of nitric oxide, subsequently ionized by solar ultraviolet. Further, nitric oxide can arise in the photodissociation of a nitrous oxide molecule by hard ultraviolet. And, finally, it can be formed in triple collisions with the participation of nitrogen and oxygen atoms. Apparently, the most effective method of dissociation of atmospheric molecular nitrogen is the dissociative recombination of ionospheric ions containing nitrogen atoms\(^ {34}\). In the region of the \(F\) layers, where the density is too low, recombination by means of triple collisions is practically impossible. Therefore the process leading to the restoration of nitrogen molecules can take place only in lower layers, where atomic nitrogen can penetrate as a result of atmospheric mixing. However, in triple collisions, because of the very large concentration of atomic oxygen, it will be only nitric oxide molecules, and not nitrogen molecules, that will be formed most effectively.

In order that a large concentration of nitric oxide molecules should not arise in the upper atmosphere, a mechanism is necessary which ensures the destruction of nitric oxide molecules and converts their nitrogen into molecules. The only possible such process is the reaction of newly formed vibrationally excited nitric oxide with atomic nitrogen. In this case the equilibrium concentration of excited nitric oxide*) is determined from the relation

\[ J = H \cdot n(\mathrm{NO}^*) n(\mathrm{N}) \cdot K_5, \tag{26} \]

where \(J\) is the number of nitrogen molecules per \(1 \text{ cm}^2\) of the earth’s surface, dissociating during 1 sec. in processes connected with ionization of the upper atmosphere [simultaneously \(J\) is the number of nitrogen molecules formed in higher layers during 1 sec. above \(1 \text{ cm}^2\) of the earth’s surface in the general equilibrium process for the entire upper atmosphere]; \(H\) is the height of a homogeneous atmosphere and \(K_5\) is the rate constant of the reaction, to which there corresponds an effective cross section close to the gas-kinetic one, since it is assumed that the process proceeds with the participation of sufficiently excited

*) Vibrational excitation in the ground state is meant.

product. To ensure this, it is necessary that the newly formed vibrationally excited nitric oxide molecule retain its excitation until collision with a nitrogen atom. This, apparently, will be possible if the ratio of the concentration of atomic nitrogen to the total number of particles of the medium in the reaction zone is not less than \(10^{-4} \div 10^{-5}\). If \(J \sim 10^8\) ion pairs \(\mathrm{cm}^{-2}\,\mathrm{sec}^{-1}\), \(K_2 \sim 10^{-10}\ \mathrm{cm}^3\,\mathrm{sec}^{-1}\) (it is borne in mind that one of the initial products possesses excitation sufficient for the activation energy) and \(n(\mathrm{N}) \sim 10^8\ \mathrm{N}\,\mathrm{cm}^{-3}\), then \(n(\mathrm{NO}^*) \sim 10^4\ \mathrm{NO}^*\,\mathrm{cm}^{-3}\), which does not seem impossible.

The situation is more serious with unexcited nitric oxide molecules, which may be formed both upon deactivation of excited molecules and directly, as final products of various reactions. At present it is possible to indicate only one process of destruction of unexcited nitric oxide molecules by means of their reaction with excited oxygen atoms, mainly in the state \({}^1D\)*). In the daytime, during dissociation of molecular oxygen, one of the two newly formed oxygen atoms appears in the excited state \({}^1D\). If the number of dissociations is estimated approximately as \(10^{12}\) pairs of O \(\mathrm{cm}^{-2}\,\mathrm{sec}^{-1}\), then at the height of the homogeneous atmosphere of order \(10^6\ \mathrm{cm}\) the concentration of \(\mathrm{O}({}^1D)\) may reach \(10^6\) excited atoms in \(1\ \mathrm{cm}^3\). In this case, bearing in mind that the rate constant of reaction with some excited initial product is characterized by a value of order \(10^{-10}\ \mathrm{cm}^3\,\mathrm{sec}^{-1}\), the mean lifetime of an unexcited oxide molecule may be estimated approximately as \(10^4\ \mathrm{sec}\). Thus, in the daytime, in the region of most intense dissociation of molecular oxygen, nitric oxide will disappear with the formation of atomic nitrogen. At night this process will be less intense, since the concentration of \(\mathrm{O}({}^1D;\ {}^1S)\) at this time is insignificant. One may try to estimate approximately the upper limit of the nitric oxide content in the very upper layers of the atmosphere, assuming that atomic nitrogen is formed in the dissociative recombination of molecules containing nitrogen, the intensity of which does not exceed \(10^9\) events \(\mathrm{cm}^{-2}\,\mathrm{sec}^{-1}\), and that as a result of each recombination no more than one molecule of unexcited nitric oxide is formed, since under equilibrium conditions the total number of newly formed molecules is certainly less than \(10^9\ \mathrm{NO}\,\mathrm{cm}^{-2}\,\mathrm{sec}^{-1}\), because, besides unexcited final products, excited ones will also appear, as discussed in the preceding paragraph. Thus, beginning with the zone of effective dissociation of oxygen and above, there will be contained no more than \(10^{13}\ \mathrm{NO}\,\mathrm{cm}^{-2}\), or \(10^{-7}\ \mathrm{NO}\,\mathrm{cm}^{-3}\), at the height of the homogeneous atmosphere near \(10^6\ \mathrm{cm}\).

Now let us estimate the maximum possible concentration of nitric oxide in the upper atmosphere at night from the assumed intensity of the continuum:

\[ \nu = H n(\mathrm{NO}) n(\mathrm{O}) \cdot K_6, \tag{27} \]

where \(\nu\) is the number of continuum quanta \(\mathrm{cm}^{-2}\,\mathrm{sec}^{-1}\), \(H\) is the thickness of the layer, which we shall take approximately equal to the height of the homogeneous atmosphere, and \(K_6\) is the rate constant of the indicated process, approximately estimated as \(10^{-18}\ \mathrm{cm}^3\,\mathrm{sec}^{-1}\). If we leave aside certain, apparently sometimes observed, anomalously large values, then the magnitude \(\nu\) may be estimated as no more than \(10^9\,h\nu\,\mathrm{cm}^{-2}\,\mathrm{sec}^{-1}\). Therefore there can be no more than \(10^9\ \mathrm{NO}\) in the zone where there is \(10^{12}\ \mathrm{O}\,\mathrm{cm}^{-3}\). In the region around \(100\ \mathrm{km}\), these conditions correspond to too high a relative concentra-

*) The reaction \(\mathrm{NO}+\mathrm{O}^* \to \mathrm{N}+\mathrm{O}_2^*\) is meant.

of NO, which seems unlikely. However, neither the place where the continuum arises nor its very existence can yet be considered definitively established. The estimate made in the preceding paragraphs of the content of nitric oxide in the very upper layers, beginning with the zone of effective dissociation of molecular oxygen, most likely indicates that, if the continuum mentioned above does in fact exist, then it arises in a lower layer of the terrestrial atmosphere.

For a final solution of the question of the nature of the continuum and of the mechanisms of dissociation of atmospheric nitrogen and formation of nitric oxide, and also for establishing the dependence of the continuum on solar activity, additional observations are necessary. In conclusion we note that investigation of the continuum may shed additional light on the nature of the ionospheric layer \(D\). Indeed, it is assumed that this layer is formed as a result of ionization of nitric oxide molecules by \(H L_\alpha\) radiation. For this process to be effective, a nitrogen concentration of the order of \(10^{12}\ \mathrm{NO}\ \mathrm{cm}^{-3}\) is necessary. On the other hand, in the light of existing ideas about the process of ozone formation, the concentration of atomic oxygen in this region is estimated at a value of the order of \(10^{11}\ \mathrm{O}\ \mathrm{cm}^{-3}\). Using the relation given above for estimating the intensity of the continuum, we come to the conclusion that at night in the region of the \(D\) layer, at such concentrations of nitric oxide and atomic oxygen, a very intense continuum should be formed, exceeding the observed one by several orders of magnitude, and which in fact is not observed. This means that in the region of the \(D\) layer either there is no nitric oxide concentration assumed to be sufficient for formation of the \(D\) layer, or the concentration of atomic oxygen at night is substantially less than \(10^{11}\ \mathrm{O}\ \mathrm{cm}^{-3}\). It is quite possible that the latter circumstance is valid, indicating a large value of the rate constant of the reaction of formation of ozone and molecular oxygen in reactions (4), (10), and (11) (see the table in section 1). As was already noted above, this should lead to rapid conversion of atomic oxygen into molecules of ozone and oxygen with the onset of evening twilight.

It is quite possible that the enhancement of the [OI] 6300 Å emission observed during the first twilight hours is closely connected with the process of rapid recombination of oxygen under nighttime conditions in the lower layers of the upper atmosphere below 80–90 km. Here is a cycle of reactions that can explain the evening anomaly of the intensity of [OI] 6300 Å:

\[ \mathrm{NO} + \mathrm{O} \to \mathrm{NO}_2 + h\nu, \tag{28} \]

\[ \mathrm{NO}_2 + \mathrm{O} \to \mathrm{NO} + \mathrm{O}_2^{*}, \tag{29} \]

\[ \mathrm{O}_2^{*} + \mathrm{O} \to \mathrm{O}_2 + \mathrm{O}({}^{1}D). \tag{30} \]

It goes without saying that process (29) may also give a certain evening enhancement of the emission \(\mathrm{O}_2\ ({}^{1}\Sigma \to {}^{3}\Sigma)\), as, for example, Meinel pointed out\(^{39}\). In this case, the nonobservability of an evening enhancement of the hydroxyl emission may indicate that, in the indicated reaction zone, the concentration of atomic hydrogen is insignificant.

From the point of view of the oxygen-hydrogen hypothesis of excitation of hydroxyl radiation, it cannot be admitted that, in the zone of its occurrence, the concentration of atomic nitrogen exceeds the concentration of atomic hydrogen. Otherwise, the overwhelming part of the energy of dissociation of atmospheric oxygen would have to be converted not into hydroxyl radiation, but into radiation of the nitric oxide molecule. Thus, to ensure the effectiveness of the oxygen-hydrogen process, it is neces-

so that the ratio of the concentration of atomic hydrogen to the total number of particles of the medium in the upper atmosphere exceeds the value \(10^{-4} \div 10^{-5}\). Fulfillment of this condition is also necessary in order that the hydroxyl radiation not correlate with solar activity, during the maximum of which the concentration of atomic nitrogen will increase because of the intensification of ionization processes in the upper atmosphere.

Emission of \(O_2\)

At present, apparently, no new questions arise in connection with the emissions of molecular oxygen. These emissions may arise in various recombinations of oxygen atoms into molecules. It is quite possible that molecular oxygen in the \({}^{1}\Sigma\) state also arises in the ozone-hydrogen reaction \(^{1,2}\). The nonobservability of this radiation \(O_2({}^{1}\Sigma - {}^{3}\Sigma)\) under laboratory conditions in a mixture of ozone with atomic hydrogen \(^{27}\) still does not mean that it will not arise in the upper atmosphere. In the limited volume of a laboratory apparatus the metastable state \(O_2({}^{1}\Sigma)\) may be strongly quenched in collisions with the walls. In the upper atmosphere there are more favorable conditions for the prolonged existence of this state. For further judgments, more detailed information is needed on the emissions of molecular oxygen, including correlations of the intensities of different emissions of the night sky.

CONCLUSION

A review of the present state of the question of the nature of emissions of the upper atmosphere makes it possible to identify unclear circumstances that hinder the development of a final theory. Below is a list of what appear to be the most essential areas of investigation.

It is most important to determine exact values of the probabilities of deactivation in collisions of excited states of atoms and molecules and, in particular, of vibrationally excited oxygen and hydroxyl molecules in the ground state. No less essential is it to establish definitively also the probability of deactivation by radiation of vibrationally excited hydroxyl in the ground state. Thus, for example, according to Shklovsky \(^{12,14}\), this time is of the order of \(10^{-4}\ \mathrm{sec}^{-1}\), while according to Heaps and Herzberg \(^{13}\) it is of the order of \(10^{-2}\ \mathrm{sec}\).

It may be noted that an increase in the concentration of atomic hydrogen would favor both hypotheses. In this connection, one may note a certain arbitrariness of the assumption concerning the tropospheric origin of hydrogen in the upper atmosphere \(^{7}\). It is hardly possible to reject completely the cosmic origin of hydrogen at great altitudes. Therefore an increased concentration of hydrogen in the upper atmosphere also cannot be considered excluded. However, the question of the degree of its dissociation at an altitude of about \(75\ \mathrm{km}\) requires further study.

The critical remarks of Bates and Masevich concerning the oxygen-hydrogen hypothesis are based on the selection of, to a considerable extent, arbitrary values of the constants of elementary processes. These constants were chosen by Bates and Masevich in such a way that they proved most favorable for the \(O_3\)-hypothesis and least favorable for the \(O_2^{*}\)-hypothesis. However, values of the constants can be chosen that lead to opposite results. Taking this situation into account, we do not yet see grounds for rejecting the \(O_2^{*}\)-hypothesis in favor of the \(O_3\)-hypothesis. The final solution is connected with the refinement of the initial values of the rate coefficients of reactions and of other information, the uncertainty and some arbitrariness of which

becomes clear as a result of acquaintance with the above review. Determination of the exact altitude at which the hydroxyl emission arises can most reliably decide the fate of one or another hypothesis of the origin of the hydroxyl emission. Apparently, a clear interrelation of all emissions of the upper atmosphere is becoming evident. Therefore, the most promising course is a joint investigation of all these phenomena.

References

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2. V. I. Krasovskii, UFN 54, 469 (1954).
3. V. I. Krasovskii, Izv. AN SSSR, geophys. ser., 5 (1957).
4. V. I. Krasovsky, Mém. Soc. R. Sc. Liège, 4S, 18, 58 (1956).
5. F. E. Roach, Ann. Géophysique 11, 222 (1955).
6. Royleigh, Jones. Proc. Roy. Soc. A 151, 22 (1935).
7. D. R. Bates and M. Nicolet, J. Geophys. Res. 55, 301 (1950).
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