TWILIGHT MEASUREMENTS OF SODIUM EMISSION IN THE EARTH’S ATMOSPHERE

Ever since V. I. Chernyaev and M. F. Vuks1 discovered a “flash” of the yellow sodium line in the spectrum of the twilight sky, the question of the altitude distribution of sodium in the Earth’s atmosphere has repeatedly been subjected to experimental and theoretical study (see, for example,2).

Bricard and Kastler3 showed that the sodium line at twilight has a small width and weak polarization (\(\sim 9\%\)). This result made it possible to conclude that the twilight glow of sodium is due to resonance scattering of the direct rays of the Sun. Taking into account the attenuation and refraction of the solar rays along their path through the atmosphere, Bricard and Kastler found that sodium must be located in a comparatively thin layer at an altitude of \(75\) km. The same result was also obtained from measurements of the width of the sodium line, which made it possible to estimate the height of the layer using the dependence of line width on temperature and the sharply expressed altitude dependence of temperature at the corresponding levels. Barbier4 estimated the height of the sodium layer at \(70\) km and concluded that at the upper boundary of the layer the sodium concentration decreases exponentially with a height scale \(H = 8\) km.

The use of more refined apparatus and a more thorough theoretical analysis of the method for processing twilight data enabled the authors of the papers reviewed[^5,^6] to introduce further refinements into this question.

The measurements were carried out with a photoelectric spectrometer that provided the required portion of the twilight-sky emission spectrum within one minute. Initially (at zenith distances of the Sun \(Z\) from \(94^\circ .5 \div 96^\circ\) to \(98^\circ .5 \div 99^\circ\)) the spectrometer was directed to the zenith, and then directed at a small angle to the horizon (\(75^\circ \div 85^\circ\)), and observations continued up to \(Z = 102—103^\circ\). (During morning twilight the order of the measurements was reversed.) In this way it was possible to obtain up to 30 spectra at the zenith and 30 spectra near the horizon during a single twilight. The measurements were made with spectral slit widths of 5 Å and 10 Å, as a result of which the doublet was not resolved. To attenuate the relatively strongly polarized background of scattered light, a Polaroid was used. This made it possible to extend the measurements to Earth-shadow heights of about \(20—30\) km; at lower heights the sodium emission line was completely masked by the Fraunhofer absorption line. The presence of the latter was taken into account in determining the intensity of the emission line.

Fig. 1.

The measurement data were processed as follows. The flux of solar radiation scattered by sodium atoms and reaching the Earth’s surface in the direction toward the nadir is equal to

\[ K(z_1)=\int_{-25}^{\infty} J_0 f(x)\sigma n(z)\,dx \quad \text{quanta}/\text{cm}^2\text{ sec steradian}, \]

where \(z\) is the height of the scattering layer (see Fig. 1); \(z_1\) is the height of the Earth’s shadow (without allowing for refraction, \(x=z-z_1\)); \(J_0\) is the intensity of solar radiation outside the atmosphere; \(\sigma\) is the scattering cross section; \(n\) is the concentration of sodium atoms; and \(T(x)\) is a function allowing for the attenuation and refraction of the direct rays of the Sun on their way to the observer’s zenith. In calculating the function \(T(x)\), account was taken, in addition to scattering of light by air and refraction, of ozone absorption, as well as of the angular dimensions of the Sun. The form of this function is shown in Fig. 2.

Next, three different types of height distribution of sodium were assumed (\(A\), \(B\), and \(C\) in Fig. 2). Calculations showed that in all three cases

\[ K(z_1)=J_0\sigma n_c f(y), \]

where \(n_c\) is the concentration of sodium at the height \(z_c\) (Fig. 2), \(y=z_c-z_1\), and \(f(y)\) has a different form for the different assumptions about the height distribution of sodium. The values of \(K(y)\) found in this way were then compared with the observed values of the intensity of the sodium line for different \(z_1\). Observations at the horizon were reduced to the zenith, taking into account the dependence of the apparent brightness of the layer on the angle of observation, which was done by dividing the observed brightness by 3.3.

Fig. 2.

An example of the experimentally obtained dependence \(\lg K(z_1)\) on \(z_1\) is shown in Fig. 3. It is clear from the figure that the zenith and horizon measurement data are in good agreement. The lines show the results of theoretical calculation under different assumptions about the height distribution of sodium. It is evident that assumption \(C\) is completely ruled out, whereas the choice between assumptions \(A\) and \(B\) is difficult owing to the low sensitivity of the method to the form of the distribution. However, the authors point out that the totality of the data argues rather in favor of assumption \(B\) than \(A\). The height of the maximum sodium concentration was determined by finding the value \(z_1\) corresponding to \(y=0\) on the theoretical curve \(K(y)\) best fitting the experimental points (in Fig. 3 these values \(z_1=z_c\)

marked by vertical strokes). The values of the height of the location of the maximum sodium concentration \(z_c\) found in this way are listed in the table.

Results of determining the height of the maximum sodium concentration

Average \(z_c = 84.7 \pm 0.7\) km

The table gives the statistical error \(\pm 0.7\) km. However, systematic errors are also possible. In particular, the transition from model \(B\) to model \(A\) leads to a decrease in the height \(z_c\) by about 5 km. Therefore the authors give, as the final result, the value

\[ z_c = 85 \pm 3\ \text{km}. \]

In the case of model \(B\) it was assumed that the sodium concentration decreases on both sides of the maximum according to an exponential law with a height scale \(H = 7.5\) km. The authors believe that this assumption is valid

Fig. 3.

from 85 km up to heights of the order of 100, and possibly even 115 km, but that downward the sodium concentration in fact falls much more rapidly. The authors did not perform absolute measurements of the brightness of the sodium glow. However, according to Bjerk and Kastler, they estimate the concentration of sodium atoms at the maximum as \(n_c \simeq 10^4\) atoms/cm\(^3\).

Turning to the consideration of chemical equilibrium, and assuming that at such heights triple collisions are practically ineffective, the authors

are limited to two reactions:

\[ \mathrm{NaO} + \mathrm{O} \to \mathrm{Na} + \mathrm{O}_2, \]

\[ \mathrm{Na} + \mathrm{O}_3 \to \mathrm{NaO} + \mathrm{O}_2. \]

This leads them to the conclusion that

\[ \frac{n(\mathrm{Na})}{n(\mathrm{NaO})} \simeq 3 \cdot 10^{-4}\,\frac{n(\mathrm{O})}{n(\mathrm{O}_3)}. \]

Thus sodium should be found predominantly in the atomic state if the ratio of the concentration of atomic oxygen to the concentration of ozone exceeds \(3 \cdot 10^3\). Since the concentration of atomic oxygen increases, while the concentration of ozone decreases, with height, the relative concentration of atomic sodium should increase with increasing altitude. Consequently, the maximum concentration of atomic sodium should be expected at the altitude where

\[ \frac{n(\mathrm{O})}{n(\mathrm{O}_3)} \simeq 3 \cdot 10^3. \]

According to Bates and Nicolet,\(^{7}\) such a ratio between the concentrations of O and \(\mathrm{O}_3\) occurs at an altitude of about 80 km. This is in good agreement with the height, obtained by the authors,\(^{5,6}\) of the location of the maximum concentration of atomic sodium.

Further, proceeding from rocket data on the short-wave radiation of the Sun, the authors\(^{5,6}\) estimate the concentration of atomic sodium and construct dependences of the expected relative intensity of the total sodium glow on the duration of the light part of the day for various values of the recombination coefficient. These dependences are different for morning and evening twilights.

Thus, seasonal and diurnal variations in the intensity of the glow should occur. The expected diurnal effect is most pronounced in the equinox period, but is not large. The seasonal effect at high latitudes is much greater, and the authors suppose that further measurements will make it possible to estimate the recombination coefficient.

As is known, seasonal and diurnal variations are in fact observed.\(^{2}\) However, Bricard and Kastler\(^{3}\) explain them by variations in the water-vapor content, which affect the attenuation of the sodium line by the thickness of the atmosphere. Evidently, further measurements will clarify which of these mechanisms actually takes place.

R.

Cited Literature

1. V. I. Chernyaev and M. F. Vuks, DAN 14, 77 (1937).
2. I. A. Khvostikov, The Glow of the Night Sky, Publishing House of the Academy of Sciences, 1948.
3. J. Bricard et A. Kastler, Ann. Geophys. 1, 59 (1944); 6, 283 (1950); Mem. Soc. Roy. Sci. Liège 12, 87 (1952).
4. D. Barbier, Ann. Geophys. 4, 193 (1948).
5. D. M. Hunten, J. Atm. and Terrestr. Phys. 5, 41 (1954).
6. D. M. Hunten and G. G. Shepherd, J. Atm. and Terrestr. Phys. 5, 57 (1954).
7. D. R. Bates and M. Nicolet, J. Geophys. Res. 55, 301 (1950).