THE ULTRAVIOLET AND X-RAY SPECTRUM OF THE SUN

K. Jager*)

INTRODUCTION

In the present article the energy distribution in the ultraviolet and X-ray regions of the solar spectrum is calculated. At the end of the article the results of these calculations are compared with observations.

For such calculations it is necessary to know the structure of the solar atmosphere, the inhomogeneities of structure and density existing in its outer layers, the physical processes responsible for the emission and absorption of energy, and also the values of the corresponding emission and absorption coefficients, which are determined by the chemical composition of the solar atmosphere.

As is known, the solar atmosphere consists of three parts: the photosphere—a layer 400 km thick, situated directly beneath the surface of the Sun; the chromosphere—a layer 10,000–14,000 km thick, situated directly above the surface of the Sun; and the corona, extending from a height of about 10,000 km above the surface of the Sun to heights of several million kilometers. The structure of the solar atmosphere is determined by a number of functions: \(T(h)\), \(N(h)\), and \(N_e(h)\), where \(T\) is the temperature, \(N\) is the number of particles in \(1\ \mathrm{cm}^3\), \(N_e\) is the electron concentration, and \(h\) is the height above the surface of the Sun, measured from the limb in the radial direction. The limb of the Sun is defined as the point of inflection of the curve representing the dependence of the radiation intensity of the solar disk on the distance from its center.

Inhomogeneities of temperature and density in the outer layers of the Sun may in some cases substantially affect the magnitude of the intensity of the outgoing radiation. In the ultraviolet part of the spectrum this effect is especially strong. Deviations from thermodynamic equilibrium, which are significant everywhere except in the photosphere, must also be taken into account.

STRUCTURE OF THE SOLAR ATMOSPHERE

Structure of the photosphere. The results of various recent determinations of the temperature in the solar photosphere are shown in Fig. 1. The temperature is given as a function of the monochromatic optical depth \(\tau_0\) for radiation of wavelength \(\lambda = 5000\ \text{Å}\). The optical depth \(\tau_0\) is determined by the formula

\[ \tau_0 = \int_0^h x_0(h)\rho(h)\,dh, \]

*) C. de Jager, Annales géophysiques 11, No. 3, 330–352 (1955). Report at a meeting of the Special Committee for the International Geophysical Year in September 1954 in Rome. Translated from English by E. V. Kononovich.

where \(h\) is the geometrical depth in the photosphere, measured perpendicular to the surface; \(\varkappa\) is the absorption coefficient of continuous monochromatic radiation, calculated per 1 g of matter; the subscript “0” means that the absorption coefficient has been calculated for radiation with wavelength \(\lambda = 5000\) Å; \(\rho\) is the density of matter in the photosphere. The geometrical depth, which is almost proportional to the logarithm of the optical depth, is also indicated in Fig. 1. The relation between them is taken from Minnaert’s photospheric model.^1 The solid line in Fig. 1 depicts the temperature distribution obtained by Feautrier^2 for layers with optical depth greater than 2 (i.e., for depths greater than

Fig. 1. Chromosphere models obtained from observations. The two limiting cases in Böhm’s three-component model are denoted by “Б”.

350 km). This temperature distribution was obtained on the basis of a study of the profiles of the magnesium \(PD\)-lines and of their variation from the center to the limb of the solar disk. The dotted line gives the temperature variation in the interval of optical depths between 0.01 and 8.0, obtained and extrapolated by Jäger.^3 In the interval between 0.1 and 1.6 this temperature variation coincides with Jäger’s model V (Table 34 of the above-mentioned work), which was derived from the observed variation in the intensity of continuous radiation from the center of the Sun to its limb. For optical depths greater than 1.4 and less than 0.1, the dotted line coincides with the temperature distribution in Jäger’s model VII from work.^3 It was obtained on the basis of a study of the profiles of the hydrogen absorption lines in the spectrum of the Sun. In this latter model, the temperature of the very

of the uppermost and lowest layers of the photosphere is determined more accurately than in the model obtained from the continuous spectrum. Böhm-Vitense^4 obtained a model of the photosphere, very similar to Yager’s model, from an analogous combination of the results of observations of continuous radiation and observations of the cores of hydrogen and strong metallic lines (the dashed line in Fig. 1).

Prister’s model^5 applies only to the outer layers of the photosphere (optical depth less than 0.2). It was obtained on the basis of measurements from the center to the limb of the wings of the sodium \(D\)-lines in the solar spectrum. This model coincides with the model previously proposed by Böhm-Vitense.

The fifth model, used in constructing Fig. 1, was obtained by Pagel^6 on the basis of a study of the center-to-limb variation of some infrared iron lines. It gives the temperature variation for optical depths from 2.0 to 0.002. It is easy to see that all the models are in good agreement with one another for optical depths greater than 0.1, but for the outer parts of the photosphere there are considerable discrepancies, up to temperature differences of \(700^\circ\) for the level with optical depth 0.02. These discrepancies can be explained by two causes. First, measuring the continuous radiation of the Sun near the limb, i.e. in the region where the radiation practically comes from layers lying above the layer with optical depth 0.10, is a very difficult task. The layers of the photosphere whose optical depth is less than 0.02 lie at a distance of \(2 \cdot 10^{-4}\) solar radii from the limb. Consequently, the temperature distribution in these, the outermost, parts of the photosphere must be obtained from other sources, such as, for example, the profiles or equivalent widths of Fraunhofer lines. Böhm^7 showed that in these outer layers of the solar atmosphere the deviations from thermodynamic equilibrium are very significant. This explains why the determination of temperatures by different methods leads to large discrepancies. Another reason for the discrepancies in the temperature determinations is the inhomogeneity of the distribution of temperature and density in the photosphere, associated with turbulence and convection. For a level situated at one and the same optical depth, the temperature may differ, according to Yager^8, by \(800\)—\(1000^\circ\). For a level with the same geometrical depth these differences may double. However, the latest determinations show that these preliminary estimates are too high. Böhm^7, investigating strong and some weak iron lines and the sodium \(D\)-lines, obtained smaller temperature discrepancies. He adopts a “three-component” model, according to which the photosphere consists of columns of three kinds: 50% of them have a mean temperature corresponding to blackbody radiation with Planck function \(B(h)\), equal to the radiation observed at height \(h\); in 25% of them the temperature corresponds to the Planck function \(0.4B(h)\), and in the remaining 25%—to the Planck function \(1.6B(h)\). These temperature inhomogeneities occur throughout the photosphere. Some Fraunhofer lines may be formed chiefly in cold gas masses, while others scatter the radiation of hot masses more strongly; this can partly explain the discrepancies between those models for which Fraunhofer lines were used.

The temperature of the limb of the Sun is defined as the temperature at the point of inflection of the curve of the distribution of solar intensity with height (at the point with \(\tau_0 = 0.002\), where \(\tau_0\) is measured in the direction of the solar radius). It can be found from the models given in Fig. 1 and has a value of about \(4000^\circ\), whereas the temperature inhomogeneities near the limb, according to Böhm, have magnitudes from \(+400\) to \(-800^\circ\).

Structure of the transition region from the photosphere to the chromosphere. In the present article the transition region from the photosphere to the chromosphere is defined as that part of the solar atmosphere which is still appreciably

thus scatters the continuous photospheric radiation near the solar limb. Its upper layers lie at a height of about 500 km. The structure of these parts of the solar atmosphere can be found on the basis of the following sources:

a) the curve of the energy distribution in the ultraviolet spectrum of the Sun;

b) the “profile,” i.e., the distribution of the radiation intensity with height, near the very limb of the Sun;

c) the intensities of the lines of the flare spectrum that belong to the very lowest layers of the chromosphere.

It is very difficult to obtain all these data. An exact “profile” of the limb can be found only during total solar eclipses, and as yet there are no absolute measurements. All observations give relative intensity values, which greatly reduces their quality. The ultraviolet spectrum of the Sun can be measured only from observations with the aid of rocket techniques, the results of which strongly depend on temperature inhomogeneities. Finally, too much reliance cannot be placed on observations of the flare spectrum. The intensities of the lines in the spectrum of the lower layers of the chromosphere depend strongly on deviations from thermodynamic equilibrium. Moreover, it is difficult to obtain the “pure” spectrum of the chromosphere, consisting only of radiation from a strip of the chromosphere several hundred kilometers thick. Nevertheless, Ety, Pecker, and Thomas^9 succeeded in obtaining a model of the lower chromosphere from the continuous flare spectrum beyond the Balmer series limit; according to this model, when the height changes from 100 to 500 km the temperature increases from 5000 to 6000°. Although it is difficult to explain the difference of about 1000° between this latter result and the limb temperature of about 4000° obtained from photospheric observations, a simple explanation may still be that the observations of Ety, Pecker, and Thomas refer to hot elements of the lower chromosphere. It is difficult to find another explanation: one may try to reconcile both results by assuming that the temperature is 4000° at \(h = 0\), and that at a height of 500 km the temperature is already 5500–6000°. However, this assumption is clearly incorrect, because such a sharp increase of temperature is incompatible with the observed intensity gradient near the solar limb. This sharp increase of temperature would reduce the intensity gradient in comparison with the observed one and, in addition, would shift the position of the solar limb upward into the chromosphere by an amount of from 200 to 500 km in comparison with the actually observed position. As an example, we note that in Yager’s chromospheric models^3, with a temperature equal to 8000° at a height of 1000 km, the limb of the Sun should be situated at a height of about 600 km. Consequently, we must attach greater weight to the low temperature values and assume its mean value to be about 4000° at the height \(h = 0\) km. If this temperature value is assumed, then the turbulent state of the very upper layers of the solar atmosphere can be found from the intensity gradient near the solar limb. Yager^10 obtained the following values for the radial component of the field of turbulent velocities:

\[ \xi_0 = 10.5\ \text{km/sec}, \]
if the temperature is constant in the interval of heights from 0 to 500 km;

\[ \xi_0 = 6\ \text{km/sec}, \]
if the temperature rises from 4000 to 4400° in the same interval of heights.

On the basis of the study of the flare spectrum^11, ^12 it may be concluded that the latter value of \(\xi_0\) is more probable than the former; hence we find that the temperature is about 4500° at a height of 500 km.

Structure of the chromosphere. It is possible that the process of increase of turbulent velocities with height continues in the upper parts of the chromosphere. The chromosphere, with its observed irregularities, is often compared with a burning steppe or forest consisting of elongated protrusions, so

called “spicules.” Although spicules are visible only at heights exceeding 5000 km, there is nevertheless no reason to believe that they are not present in large numbers at lower heights as well. The study of hydrogen spectroheliograms makes it possible to suppose the presence of an enormous number of spicules whose kinetic energy is less than the energy of the observed spicules, and which occupy a considerable part (possibly half) of the solar surface at heights of the order of several thousand kilometers above the limb.

Up to now many authors have confined themselves to a model of a homogeneous chromosphere. The best models obtained from observations are collected in the present section (with the exception of models obtained on the basis of ionospheric data, such as, for example, the Woolley and Allen model of 1950). The aim of the present investigation is to calculate the distribution of energy in the ultraviolet spectrum of the Sun exclusively from solar data, in order to make it possible to study independently the problem of the origin of the ionospheric layers. Therefore, models obtained on the basis of ionospheric data are excluded from consideration.

Fig. 2. Models of the chromosphere and corona obtained from observations.

The first chromospheric model used in the present section is Piddington’s model, published several years ago^13. When it is compared with Jaeger’s model^3, large discrepancies become apparent. Nevertheless, both these models explain the observed distribution of energy in the radio emission of the Sun. The difference between them lies in the way the results of optical observations are used. It is evident that a chromospheric model must be based not only on radio observations, but also on the complete and critical use of optical measurements. Both models have recently been replaced by more refined ones. In Fig. 2 are shown the distributions of temperature with height in the chromosphere according to Piddington’s model, according to the two alternative models of Athay, Pecker, and Thomas^9 and, finally, according to Wolter’s model^14. In Wolter’s model the inhomogeneities of the chromo-

sphere, and the temperature distribution with height in the spicules and in the space between them is specified. According to Wolter, over the entire chromosphere the spicules occupy about 2% of the solar surface. It is assumed that they are hotter than the cold matter between them. As we have already noted, it is possible that the relative number of spicules at low heights is considerably greater than in the upper layers of the chromosphere. Therefore, in the lower chromosphere Wolter’s model apparently should be refined. At present, however, we regard this model as the best one*). It should be noted that Wolter’s model is in fact based on non-eclipse observations of three kinds. Namely, the structure and distribution of the spicules were studied from a photograph of the solar limb obtained by Lyot with the aid of an interference-polarization Hα filter; subsequent photometry and standardization were carried out from a photograph of the spectrum in the region of the hydrogen Hα line, obtained by Yager outside eclipse; finally, the model was calculated with the aid of radio observations. Wolter’s results clearly show that the importance of non-eclipse observations for obtaining a model of the chromosphere is increasing more and more. Without in the least denying the value of observations of the chromosphere during solar eclipses, we believe that reliable non-eclipse observations, despite the great difficulties, should yield good results. In this connection we note the excellent observations of chromospheric spicules recently made by Michard^15 with the spectrograph at Arcetri.

Comparing the chromospheric models shown in Fig. 2, one may notice that they all have a common character: an extended region of low temperature, followed by a sharp rise of temperature at a height of about 10,000 km. In some cases, however, large discrepancies occur between the different models. They are especially large in the height interval between 3000 and 10,000 km. Therefore the calculation of the ultraviolet spectrum of the Sun will encounter great difficulties in that wavelength region which is emitted by the solar layers lying at these heights.

Solar corona. According to radio observations the mean temperature of the inner corona should be of the order of \(7\cdot 10^5\)—\(8\cdot 10^5\) degrees. Doppler profiles of coronal emission lines indicate higher temperature values. However, these profiles are certainly distorted by turbulent motions. Moreover, in the corona there evidently occur considerable temperature fluctuations. Often at one and the same point of the corona the emission line of nine-times ionized iron Fe X (the red coronal line) is observed with the same intensity as the line of thirteen-times ionized iron Fe XIV (the green line). The corresponding excitation potentials of these lines are 233 eV and 355 eV. In the coronal spectrum there are also lines belonging to intermediate stages of ionization. The presence of such different ionization stages cannot be explained by one and the same temperature. Therefore Shklovsky^16 suggested that the corona consists of a mixture of regions of two kinds—cold and hot. Since the corona is optically thin, both kinds of regions can be observed together in one and the same direction; according to Shklovsky’s supposition, the temperatures of both regions should respectively be \(5.5\cdot 10^5\) and \(1.2\cdot 10^6\) degrees. A test of the existence of both temperature regions is a direct comparison of the observed widths of the Fe XIV and Fe X lines. The first line should be broader, since it corresponds to the higher kinetic temperature. Pecker’s observations,

) Since the publication of Yager’s work, a new two-component model of the chromosphere has been proposed (Athay, Thomas, Menzel, Astrophys. J. 123, No. 2, 285 (1956)), based on the results of observations of the total solar eclipse of 1954 in Khartoum. In contrast to Wolter, the authors believe that the spicules are colder than the surrounding matter. Translator’s note.*

Billings and Roberts^17 do not agree with Shklovsky’s assumption, since they found that the half-widths of the Fe X and Fe XIV lines indicate nearly the same kinetic temperature \((3.5 \cdot 10^6 — 6 \cdot 10^6\) degrees). The authors believe that the simultaneous presence of lines with such different ionization potentials is unclear from the standpoint of the theory of ionization of the corona (see also the following section).

In addition to temperature fluctuations, density fluctuations also occur in the corona. A considerable increase in the electron concentration occurs in coronal condensations. The magnitude of the “normal” fluctuations can be found by studying the intensity of the radio emission of the quiet Sun. In addition, these fluctuations manifest themselves in the strong scattering of radio waves by point radio sources located in the corona. Independently, Shklovsky and Pikel’ner^18 and Royle^19 found that \(\overline{N_e^2}/\overline{N_e}^{\,2}\)*) can reach a value of 2 or 3.

The ionization state of the corona. The ionization of the corona cannot be determined by the Saha formula, since the corona is not in a state of thermodynamic equilibrium. There is no detailed balance between the processes of ionization and recombination (Shklovsky^16, Elwert^20; we follow Elwert’s results). Coronal atoms are ionized by electron impact. The number of ionization events per unit volume is equal to \(n_i n_e S_{12}\), where \(S_{12}\) is the probability of collision of an electron with an ion, and \(n_i\) and \(n_e\) are, respectively, the concentration of ions in the \(i\)-th stage of ionization and the concentration of electrons. The reverse processes are recombinations with the emission of light quanta. The number of recombinations per unit volume is equal to \(n_{i+1} n_e Q_{21}\), where \(Q_{21}\) is the effective recombination cross section. Another possible mechanism of ionization is photoionization by photospheric radiation, which has a temperature of \(5.7 \cdot 10^3\) degrees. This mechanism plays an insignificant role, especially in the short-wavelength region of the spectrum. The intensity of the coronal radiation is too small to cause appreciable photoionization. Recombination by means of collisions of the second kind is negligible because of the low density in the corona. Therefore the number of ionization events by electron impact may be equated to the number of recombinations. Hence:

\[ \frac{n_{i+1}}{n_i} = \frac{S_{12}}{Q_{21}} . \tag{1} \]

Since \(S\) and \(Q\) depend only on the temperature, the ratio of the populations of levels of different stages of ionization depends only on the temperature, and not on the electron concentration. Relation (1) was calculated by Biermann^21, Shklovsky^16, and later in more detail by Elwert^20,22. In Table I of the last of the cited works, ion concentrations are calculated for three temperature values and for a large number of ionization stages of nine elements. As an example, Fig. 3 gives the relative concentrations of iron ions in different stages of ionization, according to Elwert’s calculations for two temperature values: \(6 \cdot 10^5\) and \(10^6\) degrees. For comparison, the same figure also gives curves obtained on the basis of Shklovsky’s results. The clear difference between the two results, especially for the smaller temperature value, is due to the difference in the adopted values of the effective cross sections for the processes of ionization and recombination. Effective recombination cross sections are usually calculated on the basis of the assumption that the ion under consideration is hydrogen-like. However, this can lead to serious errors. Werner^23, using the intensities of the Fe XIV lines, made a new determination of the coronal temperature with the aid of more accurate values of the effective cross sections for recombination to the ground level, calculated from Hartree wave functions. The equality between

) \(\overline{N_e^2}/\overline{N_e}^{\,2}\) is the ratio of the mean squares of the electron concentrations for two regions located at equal distances from the center of the solar corona.
Transl. note.*

the number of recombinations and the number of excitations by collisions leads to a temperature of \(2\cdot 10^6\) degrees, which is higher than the value of \(1\cdot 10^6\) degrees obtained on the basis of the former data. This new value of the temperature, based on only one ionization state, cannot be regarded as very reliable. However, the result indicates that the true value of the temperature may be higher than the average value of \(7\cdot 10^5—8\cdot 10^5\) degrees accepted by many authors. Thus the discrepancy is partly reduced between the low temperature of the corona obtained on the basis of the study of the degree of ionization and its high temperature determined from the density gradient and the widths of lines. Nevertheless, a more accurate calculation of the various effective cross sections needed for studying ionization equilibrium in the corona is highly desirable. Fig. 3 clearly shows that the presence of two observed maxima in the population of different stages of ionization of iron in the corona cannot be explained by only a single value of the temperature. This served as the basis for Shklovsky’s hypothesis that the corona consists of regions of two types (hot and cold). There are indications that the hot regions vary more strongly in extent and intensity than the cold ones; therefore the corona may be regarded as a “cold” mass of gas with local increases of temperature and density.

Fig. 3. Ionization of iron in the corona according to Shklovsky and Elwert.

CALCULATION OF THE ULTRAVIOLET AND X-RAY SPECTRUM

Calculation of the spectrum of the Sun in the near ultraviolet region. Radiation with wavelength greater than 1600 Å practically emerges only from the photosphere and from the regions transitional between the photosphere and the chromosphere. The model of these parts of the solar atmosphere is well known, and the values of the continuous absorption coefficient have been calculated by Vitense \(^{24}\). In Fig. 4 the dependence of the continuous absorption coefficient on wavelength is shown under the assumption that the temperature is equal to 4200 degrees, and the electron pressure

constitutes 0.1 bar. Similar values of temperature and electron pressure probably occur near the solar limb and in the lower chromosphere. From Fig. 4 it is seen that the coefficient of continuous absorption increases very strongly toward shorter wavelengths. This means that radiation with a wavelength of about 1200 Å must originate from higher layers. The total radiation of the Sun (integrated over the whole disk) is calculated by the following formula:

\[ I_\lambda=\int_{0}^{\infty} B_\lambda(\tau_\lambda)K_2(\tau_\lambda)\,d\tau. \tag{2} \]

Here \(B_\lambda\) is the Planck function, and \(K_2\) is the exponential integral of the second kind.

On the basis of the photospheric model obtained by averaging the curves in Fig. 1, the author has calculated, by formula (2), the energy distribution in the ultraviolet spectrum of the Sun in the wavelength interval between 2000 Å and 3000 Å. In doing so, values of the absorption coefficients found by Vitense were used. The energy distribution obtained on the basis of these calculations in the continuous spectrum of the Sun, together with the curve representing

Fig. 4. Coefficient of continuous absorption for a temperature of 4200 degrees and an electron pressure of 0.1 bar (after Vitense).

Fig. 5. Observed (solid line) and calculated (dashed line) energy distribution in the near ultraviolet region of the solar spectrum (the ordinate gives the energy in \(\mathrm{erg\ cm^{-2}\ sec^{-1}\ \mathring A^{-1}}\) at the distance of the Earth).

the observations, are shown in Fig. 5. In this connection the results of observations by Johnson, Purcell, and Tousey \(^{25}\) were used. There is fairly good agreement between the two curves in the wavelength region exceeding 2600 Å, especially since the relative uncertainty of the data should be taken into account. Nevertheless, the differences between observations and calculations are considerably larger than in the case of the visible region of the spectrum. For radiation with wavelength less than 2600 Å these discrepancies increase. For a wavelength of 2300 Å the assumed radiation temperature is 4500 degrees, whereas the observations give temperature values of about 5000 degrees. The observed radiation in this region of the spectrum is 5 times greater—

is less than the value obtained from calculations. This discrepancy is explained by temperature inhomogeneities in the photosphere. Böhm quite properly introduced temperature inhomogeneities in such a way that their mean radiation is almost equal to the radiation of an absolutely black body with the corresponding mean temperature. However, this assumption, valid for the visible region of the spectrum, is no longer valid for the ultraviolet. Temperature inhomogeneities of the order of 500 degrees can increase the radiation with a wavelength of about 2200 Å by a factor of 5 (Yeger \(^{10}\)).

Attention should be paid to the depression of the observed continuous spectrum in the wavelength region around 2800 Å, caused by the strong magnesium lines between 2800 Å and 2850 Å, and also to the depression around 2500 Å, caused by the continuous absorption of magnesium in this region of the spectrum.

The continuous spectrum in the wavelength region 1040–1350 Å. Although the first photographs of the continuous spectrum of the Sun in the wavelength region 1100–1300 Å are already available (for example, the observations of Johnson, Purcell, and Tousey \(^{25}\)), for accurate photometry it is still necessary to use data obtained with photon counters. Table I gives the results of observations used in the present work (Tousey, Purcell, and Watanabe \(^{26}\); Byram, Chubb, Friedman, and Kiehl \(^{27}\)).

Table I

The radiation intensity of \(1\ \mathrm{cm}^2\) of the surface of the Sun will be obtained if the data from Table I are multiplied by \(4.60 \cdot 10^4\). First let us calculate the radiation temperature corresponding to the results of these observations. Suppose that in the wavelength interval under consideration the Sun radiates as an absolutely black body. Then the temperature is determined from the equation

\[ 1.18 \cdot 10^{-5} \int_{\lambda_1}^{\lambda_2} \frac{\lambda^{-5}\, d\lambda}{e^{\frac{1.43}{\lambda T}} - 1} = \text{observed intensity of radiation from the surface of the Sun.} \]

For the data from Table I, by this formula we find the following values of the radiation temperature:

\[ \begin{aligned} \text{for } \lambda\lambda\ 1040\text{–}1240\ \text{Å}\quad & T_R = 5500^\circ \pm 100^\circ,\\ 1165\text{–}1265\ \text{Å}\quad & T_R < 4800^\circ,\\ 1280\text{–}1340\ \text{Å}\quad & T_R = 5050^\circ \pm 100^\circ . \end{aligned} \]

The second value seems to us the more probable. The results are shown in Fig. 6, where the mean error is indicated by the width of the hatched bands. The breaks in the curves are entirely arbitrary and indicate only the limits of the wavelength regions to which the measurements refer. They are a consequence of our

working hypothesis, namely that in each of these spectral regions the energy distribution can be represented by a Planck curve; but this assumption seems to us incorrect.

The results obtained show the enormous importance of observations of the ultraviolet spectrum of the Sun, which expand our knowledge of the structure of the chromosphere. In principle, they make it possible to determine with sufficient accuracy the dependence of temperature on height in the lower chromosphere. As is known, most of the radiation reaches us from layers situated at such a height as corresponds to an optical depth equal to unity. It therefore remains to find the geometrical height above the limb of the Sun for which the optical depth in the wavelength interval under consideration is equal to unity.

Temperature and density in the lower chromosphere. The optical depth for radiation in the continuous spectrum with wavelength \(\lambda\) is approximately equal to:

Fig. 6. Energy distribution in the ultraviolet spectrum of the Sun.

\[ \tau_\lambda = \chi_\lambda N_M H_M; \tag{3} \]

where \(\chi_\lambda\) is the coefficient of continuous absorption, calculated per atom; \(N_M\) is the number of neutral atoms of the given element in \(1\ \mathrm{cm}^3\), and \(H_M\) is the height of a homogeneous chromosphere for these atoms. Let us assume that the coefficient of continuous absorption is due to recombinations between electrons and neutral or ionized atoms. Its value in the wavelength region between 1050–1300 Å is determined chiefly by the absorption of magnesium, silicon, and iron. According to Vitense \(^{24}\), the absorption coefficient may be calculated on the assumption that the atomic levels are hydrogen-like. Let us assume that only the ground level of the atom plays a noticeable role and that all the atoms under consideration are in one stage of ionization. Then \(\chi_\lambda\)—the total absorption coefficient per atom—is determined by the following Kramers formula:

\[ \chi_\lambda = \frac{64\pi^4}{3\sqrt{3}}\cdot \frac{(Z+s)^4 m e^{10}}{c h^3}\, \frac{1}{\nu^3}. \tag{4} \]

Here \(c\) is the speed of light, \(m_e\) the electron mass, and \(h\) Planck’s constant. The factor \((Z+s)^4\) has been introduced in order to take into account the difference of the given atom from the hydrogen atom:

\[ (Z+s)^4 = \frac{E_{iM}^{2}}{E_{iH}^{2}}, \]

where \(E_{iM}\) is the ionization energy from the ground level of the metal atom, and \(E_{iH}\) is the ionization energy of hydrogen. Using formulas (3) and (4), the author carried out a calculation for the wavelength 1260 Å, for which the temperature value was taken as

4600 degrees. For \(H_M\), according to Van de Hulst (Table 7, \(^{28}\)), the value \(5 \cdot 10^7\) cm is adopted. Having calculated \(\varkappa_\lambda\) from formula (4), we put \(\tau_\lambda = 1\) in formula (3). Since the relative abundance of the element under consideration and hydrogen \(A_M\) in the solar atmosphere is known, we obtain from formula (3)

\[ N_H=\frac{1}{\varkappa_\lambda A_M H_M}=\frac{2\cdot 10^{-8}}{\varkappa_\lambda A_M}. \tag{5} \]

Now, if the density distribution in the chromosphere is known (for example, from a chromospheric model), one can find the relation between temperature and geometrical depth. The following abundances of magnesium, silicon, and iron relative to hydrogen are adopted (from Yager’s review \(^{29}\)):

\[ A_{\mathrm{Mg}}=N_{\mathrm{Mg}}/N_H=5.25\cdot 10^{-5}, \]

\[ A_{\mathrm{Si}}=N_{\mathrm{Si}}/N_H=1.86\cdot 10^{-5}, \]

\[ A_{\mathrm{Fe}}=N_{\mathrm{Fe}}/N_H=5.9\cdot 10^{-5}. \]

Using the calculated values of \(\varkappa_\lambda\), we find \(\varkappa_\lambda A_M = 8\cdot 10^{-21}\). To this value of true absorption it is necessary to add the coefficient of Rayleigh scattering by free electrons \(\sigma_R\). The resulting sum (called, at Menzel’s suggestion, the “extinction coefficient”) plays a large role in determining the level from which the observed radiation originates. A rough estimate (see also Witte’s graphs) shows that \(\sigma_R\) is about \(0.5\varkappa_\lambda\). Therefore we shall take \(\varkappa_\lambda A_M+(\sigma_R)_\lambda=10^{-20}\). Then from formula (5) \(N_H=2\cdot 10^{12}\), which corresponds to a height of about \(1000\) km above the surface of the Sun.

Intensity and contour of the \(L_\alpha\) line. The only strong emission line with wavelength greater than \(912\) Å that can be expected in the spectrum of the Sun is the first line of the Lyman series of hydrogen, \(L_\alpha\), with wavelength \(1215\) Å. Observations (Byram, Chubb, Friedman, and Geylar \(^{27}\)*) give, for the total radiation in this line at the boundary of the Earth’s atmosphere, the value \(0.10 \pm 0.02\) erg cm\(^{-2}\) sec\(^{-1}\). This corresponds to radiation from the surface of the Sun of \(4.6\cdot 10^3 \pm 0.9\cdot 10^3\) erg cm\(^{-2}\) sec\(^{-1}\). The same authors conclude that the width of the line must be less than \(1\) Å. This follows from the fact that the absorption coefficient of the Earth’s atmosphere in the frequency region of the \(L_\alpha\) line increases by at least \(200\%\) when shifted by \(1\) Å to either side from the center of the line. The \(L_\alpha\) line must be narrower than \(1\) Å, since observations at different altitudes reveal a linear dependence of the logarithm of the intensity on the residual path of the ray in air.

In discussing the results of these observations we shall follow the considerations of Goldberg \(^{30}\). Suppose that the profile of the \(L_\alpha\) line is Doppler with a width of \(1\) Å. Then the maximum intensity in the line, equal to \(4.3\cdot 10^3\) erg cm\(^{-2}\) sec\(^{-1}\)/Å or \(4.3\cdot 10^{11}\) erg cm\(^{-3}\) sec\(^{-1}\), corresponds to the radiation of chromospheric layers for which the optical depth corresponding to the center of the line is unity. Such radiation is given by an absolutely black body with a temperature of about 6400 degrees. The uncertainty in this result is due mainly to ignorance of the profile of the \(L_\alpha\) line, which may give an error in the intensity of the core of the line by a factor of 1.5, corresponding to an error in the temperature value \(\Delta T = 150\) degrees. The optical

* More recent data on the radiation of the \(L_\alpha\) line: E. T. Byram, T. A. Chubb, H. Friedman and J. E. Kupperian, Astrophys. J. 124, No. 2, 480 (1956). Translator’s note.

the depth \(\tau_{\nu_0}\) for the center of the line is determined by the integral

\[ \tau_{\nu_0}=\int_{\infty}^{h} N_1\alpha_0\,dx, \]

where \(N_1\) is the number of hydrogen atoms in the ground state in \(1\ \mathrm{cm}^3\); \(\alpha_0\) is the absorption coefficient, calculated per 1 hydrogen atom for the frequency corresponding to the center of the \(L_\alpha\) line, determined by the expression

\[ \alpha_0=\frac{\sqrt{\pi}\,e^2}{mc^2}\lambda^2\cdot f\frac{1}{\Delta\lambda_D}, \]

\[ \Delta\lambda_D=\frac{\lambda}{c}\cdot\sqrt{2RT}=4.2\cdot 10^{-10}\ \mathrm{cm} \]

for a kinetic temperature of \(6.4\cdot 10^3\) degrees; the oscillator strength is \(f=0.46\).

Consequently, \(\alpha_0=5.2\cdot 10^{-14}\ \mathrm{cm}^2\). An optical depth \(\tau_0=1.0\) is reached under the condition that

\[ \int_{0}^{x} N_1\,dx=1.9\cdot 10^{13}. \]

The distribution of hydrogen atoms in the ground state with height, i.e. the function \(N_1(x)\), is known from Wolter’s model, which takes into account the detailed structure of the upper chromosphere. Wolter kindly communicated to us unpublished values of \(\lg N_1\), which he obtained for his model. We give his data (Table II).

Table II

From numerical integration of this model we obtain that

\[ \int_{+\infty}^{h} N_1(x)\,dx=1.9\cdot 10^{13} \]

for the height \(h=9600\ \mathrm{km}\). At this height, in Wolter’s model, the temperature is already about 35,000 degrees. On the other hand, we have found that, according to observations of the \(L_\alpha\) line, the temperature at this level must be about 6400 degrees, although in higher layers it may increase considerably. At the same time, it is very difficult to modify Wolter’s model so that it agrees with observations of the \(L_\alpha\) line. The point is that at a temperature of 6400 degrees at a height of 10,000 km the degree of ionization of hydrogen must be considerably smaller than at a temperature

35,000 degrees, and, consequently, the concentration of hydrogen atoms in the ground state must be considerably greater.

The explanation of this difficulty lies in the fact that the treatment carried out above is too greatly simplified. The \(L_{\alpha}\) line is formed by pure scattering, and the local electron temperature cannot be equated to the radiation temperature of this line. An analysis of the \(L_{\alpha}\) line carried out by Giovanelli\(^{31}\) showed that, under the conditions occurring in the upper chromosphere, the radiation temperature must lie between 5000 and 6200 degrees, which is in good agreement with the observations.

Let us turn to the consideration of the profile of the \(L_{\alpha}\) line. The absorption coefficient, calculated per atom at a distance of \(0.5\,\text{\AA}\) from the center of the line, is \(1.65\cdot 10^{-18}\,\text{cm}^{-2}\) (Goldberg\(^{30}\)). At this wavelength the optical depth equal to unity is reached at the point where

\[ \int_{+\infty}^{h} N_1\,dx = 6.1\cdot 10^{17}, \]

which is \(3\cdot 10^{4}\) times greater than the value of this integral calculated for the center of the line. Combining the models of Wolter and van de Hulst (for the lower layers of the chromosphere), we obtain that this point lies at a height of \(4500\,\text{km}\) above the surface of the Sun. If half the half-width of the line is \(0.5\,\text{\AA}\), then this means that at such a distance from the center of the line the intensity is half as large as at the center. This corresponds to a radiation temperature of 6150 degrees. Thus the temperature at a height of \(4500\,\text{km}\) is approximately equal to 6150 degrees. The temperature value of 4500 degrees obtained by Goldberg appears to us to be erroneous.

Radiation in the spectral region with wavelengths 910–1050 Å. In this region of the spectrum there are as yet no accurate measurements suitable for treatment. Tousey, Purcell, and Watanabe\(^{26}\) suppose that the radiation intensity in this spectral region is 10–100 times greater than the radiation of an absolutely black body at a temperature of 6000 degrees. This corresponds to a radiation temperature of \(7000 \pm 400\) degrees. These data may be treated in the same way as was done in Section 9. The continuous absorption is due to carbon (absorption edge near \(1040\,\text{\AA}\)). It is approximately one order of magnitude greater than the absorption in the spectral region near \(1250\,\text{\AA}\), which is caused chiefly by the greater abundance of carbon in comparison with metals. However, the effective value of the absorption coefficient in this wavelength region is considerably greater than the continuous absorption of carbon, owing to the presence of numerous strong lines of the Lyman series (\(L_{\beta}=1030\,\text{\AA}\), \(L_{\gamma}=970\,\text{\AA}\), etc.). The total absorption coefficient of these lines is known. We shall assume that their influence is uniformly distributed over the entire spectral region of width \(140\,\text{\AA}\), and thus compute a kind of “mean” absorption coefficient. The total absorption coefficient within a spectral band of width \(140\,\text{\AA}\) for the entire Lyman series, excluding \(L_{\alpha}\), calculated per hydrogen atom, is equal to

\[ (\chi_{\lambda})_{\text{eff}} = \frac{1}{1.4\cdot 10^{6}}\, \frac{\pi e^{2}}{m e^{2}}\, \lambda^{2} \sum_{n=2}^{\infty} f_{1,n} = 3.5\cdot 10^{-17}\,\text{cm}^{2}. \]

With this value of \((\chi_{\lambda})\) we find from equation (5): \(\lg N_{\mathrm H}=8.7\) at the level where the optical depth equal to unity is reached. This value occurs at a height of \(5000\,\text{km}\); therefore the temperature is approximately equal to 7000 degrees for a height of about \(5000\,\text{km}\).

It follows from this section that the study of the ultraviolet spectrum of the Sun in principle makes it possible to construct a model of the lower chromosphere, which

appears just as plausible as other models obtained from studies of line intensities and from other sources. For a theoretical calculation of the Sun’s ultraviolet spectrum, however, our knowledge of the chromosphere is not sufficiently precise.

The continuous spectrum beyond the limit of the Lyman series, emitted by the chromosphere. As yet we do not have published data on measurements of the intensity of the Sun’s continuous spectrum beyond the limit of the Lyman series. For completeness of exposition, we shall present a method for the theoretical determination of this radiation, following van de Hulst (\(^{28}\), p. 246). As in all the other cases considered in the preceding sections, the principal matter is to determine the region for which the optical depth is equal to unity. The temperature of this region determines the intensity of the corresponding radiation. The optical depth is \(\tau = \varkappa N_1 H_1\), where \(\varkappa = 6.3 \cdot 10^{-18}\ \mathrm{cm}^2\); \(N_1\) is the concentration of neutral hydrogen atoms; \(H_1\) is the height scale for neutral hydrogen. The value of \(\tau\) can be calculated for any given model of the chromosphere, but in this respect the various models published up to now are not independent. As an example let us take Wolter’s model. It is constructed in such a way that \(\tau = 1\) for the level where the temperature is about 6300 degrees. This was done in order to obtain a total Lyman radiation of about \(4 \cdot 10^3\ \mathrm{erg}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\), necessary for explaining ionospheric observations. A sharp increase of temperature in the layers lying above the layer with a temperature of 6000 degrees was admitted in order to reduce the radiation contributed to the Lyman continuum by the overlying layers. An analogous procedure was carried out by Piddington \(^{13,32}\). In his first model the optical depth equal to unity is reached at a height of \(7.5 \cdot 10^3\ \mathrm{km}\) above the surface of the Sun. Here the temperature is of the order of \(10^4\) degrees, which gives a flux of ultraviolet radiation equal to \(10^8\ \mathrm{erg}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\). This value seems too large to be consistent with ionospheric data. Therefore Piddington in 1953 proposed a new model*) with a discontinuity in the temperature distribution at a height of 8000 km, where the temperature changes abruptly from 8000 degrees to 14500 degrees.

From both the geophysical and the astrophysical point of view, it would be very important to determine from observations the intensity of radiation in the continuous spectrum beyond the limit of the Lyman series.

Continuous radiation of the corona. In the preceding section we saw what difficulties are involved in calculating radiation in the spectral region \(800\text{--}2000\ \text{\AA}\). These difficulties are due chiefly to the limited nature of our knowledge of the structure of the chromosphere. Since the corona has been studied better, more is also known about the radiation of this part of the solar atmosphere. The problem of coronal radiation in the region of the X-ray spectrum has been investigated by various authors (Kiepenheuer \(^{33}\), Woolley and Allen \(^{34}\), Shklovsky \(^{15}\)), but the most detailed study was carried out by Elwert \(^{20,22}\). Since the corona is optically thin in the wavelength interval under consideration, its continuous spectrum cannot be calculated on the simple assumption that it radiates as an absolutely black body. It is therefore necessary to study the elementary processes that lead to the emission of energy. There are two possible sources of radiation: photorecombination of electrons with ions, and free-free transitions of electrons in the fields of atomic nuclei. Elwert made a calculation for temperature values \(7 \cdot 10^5\) and \(10^6\) degrees. Fig. 7 shows Elwert’s results for a temperature of \(10^6\) degrees. A separate curve is given for radiation due to recombinations of hydrogen alone. The total intensity of the continuous radiation of the corona is of the order of \(10^3\ \mathrm{erg}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}\). In this case the fraction of energy falling on the free-

) J. H. Piddington, Astrophys. J. 119, 531 (1954). Translator’s note.*

bound-free transitions, of the same order as recombination radiation.

Elwert noted the curious fact that the curve of coronal radiation has the same form as Planck’s function for a temperature of \(10^6\) degrees. Both curves have a maximum at approximately the same wavelength, but the intensity of the coronal radiation is many orders of magnitude smaller than the Planckian one. This means that, for a very rough investigation of the continuous spectrum, it is sufficient to regard the corona as optically thin and radiating according to Planck’s law as a gray body (i.e., with an absorption coefficient independent of wavelength). Comparing the two curves shown in Fig. 7, one can determine the optical thickness of the corona, which proves to be of the order of \(4\cdot 10^{-17}\).

Fig. 7. Solid line—the energy distribution in the X-ray region of the spectrum according to Elwert (the inhomogeneity factor \(Q\) is taken equal to 2); dashed line—radiation due to recombinations alone; dotted line—radiation of an absolutely black body with a temperature of \(10^6\) degrees, multiplied by \(4\cdot 10^{-17}\).

Elwert’s results were obtained under the assumption that the corona is isothermal and has no density fluctuations. If density fluctuations are present, with inhomogeneity factor \(\overline{N_e^2}/\overline{N_e}^{\,2}=Q\), the emitted energy must be multiplied by this factor \(Q\). According to the investigations of Shklovsky and Pikel’ner\(^{18}\) and Royle\(^{19}\), the multiplier \(Q\) for the curve in Fig. 7 is taken to be equal to 2.

Monochromatic radiation of the corona. Emission in the continuous spectrum is not the most important part of the corona’s radiation. Its monochromatic intensity, as Elwert showed, is considerably greater. Calculation of the line spectrum of the corona is a difficult problem, since the wavelengths of possible coronal lines are not known exactly. They were determined only on the basis of a critical study of the energy levels of multiply ionized elements. It is also necessary to determine the mechanism of radiation in the lines. Recombination of ions with electrons leads to the formation of excited levels; since the probability of collisions of the second kind is small, transitions from these levels will almost always be accompanied by radiation. This is one of the possible mechanisms

monochromatic radiation. Another mechanism is the excitation of ions by collisions with electrons. A detailed study shows that this latter mechanism is the most important. In general, the energy differences between the various levels are so considerable that only the first level, situated above the ground state, can be excited. In calculating the line spectrum it was found that, for monochromatic radiation, the corona is not optically thin. The profiles of the coronal lines are determined by the Doppler effect and have a width on the average of about \(0.01\) Å. Using the known values of the oscillator strengths and a model of the corona, one can calculate its monochromatic radiation. Elwert reports detailed results for three temperature values: \(6\cdot 10^5\), \(7\cdot 10^5\), and \(10^6\) degrees (Figs. 6, 7, and 8 of the cited work). Although the intensity of each

Fig. 8. Continuous (hatched) and monochromatic radiation of the corona (according to Elwert). The monochromatic radiation has been summed over wavelength intervals of 10, 20, 50, and 100 Å.

Fig. 9. The same as in Fig. 8, but on a logarithmic intensity scale. The monochromatic radiation has been summed over wavelength intervals of 10–20 Å. The points show observational results.

line changes as a function of temperature, nevertheless the total monochromatic radiation of the corona remains constant within certain limits. It is of the order of \(2.5\cdot 10^3 Q\) erg cm\(^{-2}\) sec\(^{-1}\). This corresponds to an energy flux equal to \(6\cdot 10^{-2} Q\) erg sec\(^{-1}\), passing through \(1\) cm\(^2\) located at the boundary of the Earth’s atmosphere. Monochromatic radiation leads to the result that, as the temperature increases, the maximum of the total radiation of the corona shifts toward shorter wavelengths. At a temperature of \(6\cdot 10^5\) degrees the radiation maximum lies in the wavelength region 80–90 Å, while at a temperature of \(10^6\) degrees it shifts to 60 Å. A comparison of the continuous and monochromatic radiation of the corona is given in Fig. 8, where the monochromatic radiation has been summed over wavelength intervals of 10–20 Å. The same has been done for the continuous radiation shorter than 100 Å; for longer wavelengths the summation intervals have been increased. From Fig. 8 it is clearly seen that the intensity of the monochromatic radiation is greater than that of the continuous radiation.

Comparison with observations. Variable component of hard X-ray radiation. In Fig. 9, on a logarithmic...

the curve from Fig. 8 is reproduced on a logarithmic scale. Here, for comparison, are also plotted the results of observations by Friedman, Lichtman, and Byram ^35 and by Byram, Chubb, and Friedman ^36, ^37, ^38. They were obtained under different conditions and show considerable scatter. However, these discrepancies can be explained only partly by instrumental effects; the main cause is the variability of solar radiation, especially in the hard X-ray region of the spectrum. Apparently, the smallest observed intensities correspond to the radiation of the quiet corona, while the larger ones pertain to the radiation of the corona during a period of increased solar activity. If this is correct, then Elwert’s calculations are in agreement with the observations for radiation with wavelength greater than 20 Å (see Fig. 9). A discrepancy remains for very short wavelengths. This may mean either that some mechanism of emission of X-rays in the spectral region between 8 and 15 Å has not been taken into account, or that the layers of the corona responsible for this radiation in fact contain many small condensations with high temperature, or, finally, that the observations were made when the Sun was not quite quiet. We believe that the second and third assumptions are more correct. Dr. Elwert has set forth his point of view on the variable component of the Sun’s hard X-ray radiation and has kindly permitted it to be published. He writes:

“Although I have not yet carried out detailed calculations relating to the theory of the variable component of X-radiation, it is nevertheless clear that local increases of temperature, which have already been mentioned together with local density fluctuations in order to explain the slowly varying component of radio emission, may also lead to an increase in the intensity of hard X-radiation with wavelength less than 20 Å. The intensity in this spectral region increases rapidly with increasing temperature.

Fig. 10. Intensity of the Sun’s X-radiation for different distances from the center of the disk (after Shklovsky).

Waldmeier and Müller proposed that the temperature in coronal condensations is close to \(6 \cdot 10^6\) degrees, while Piddington and Minnett even admit a temperature of \(10^7\) degrees. However, on the basis of the arguments set forth below, I do not think it necessary to postulate a temperature of \(10^7\) degrees. The maximum of the intensity of continuous radiation on the wavelength scale lies, as was already mentioned in my article, approximately at the same wavelength as the maximum of the radiation of an absolutely black body, i.e., in agreement with Wien’s displacement law. The difference is only in the smaller intensity. The intensity maximum calculated from Wien’s law for a temperature of \(10^7\) degrees is found near the wavelength 3 Å. The wavelengths of monochromatic radiation are naturally somewhat larger: at a temperature of \(10^6\) degrees the maximum of continuous radiation is located near 30 Å, and that of monochromatic radiation near 60 Å. If one assumes the same ratio of the positions of the radiation maxima also for a temperature of \(10^7\) degrees, then line radiation at this temperature will have a maximum near 6 Å. However, this value seems too small, especially since in this case the continuous radiation is also emitted in a more short-wavelength region of the spectrum. Of course, in these calculations it is necessary to take into account the presence of coronal condensations and their electron density. In addition, for a more detailed discussion of the dependence of the distribution of the emitted energy on wavelength

waves, the degree of ionization and the population of the excited levels must be known. However, such a consideration appears premature, since the initial temperature of \(10^7\) degrees was adopted more or less arbitrarily. For further investigation, calculations of the distribution of intensities for temperatures in the interval \(10^6\)—\(10^7\) degrees would be very interesting. We hope to carry out these calculations in the near future.”

In the region of intermediate wavelengths \((20\ \text{\AA}<\lambda<80\ \text{\AA})\) there are sometimes excesses of the observations over the calculations by a factor of 10. Apparently, in order to explain them, one should first consider not temperature fluctuations, but changes in the optical depth of the corona. In this connection it is useful to note that the greater part of the X-radiation comes from regions of the corona situated near the edge of the solar disk. In Fig. 10 the intensity of the X-radiation is presented as a function of distance from the center of the solar disk, according to the calculations of Shklovskii \(^{16}\).

Fig. 11a. Proposed energy distribution in the ultraviolet and X-ray spectrum of the Sun. Solid lines show observations. Dotted lines give calculations or interpolations.

CONCLUSION

The proposed spectrum of the Sun for wavelengths shorter than 3000 Å. The results of the present article are summarized in Fig. 11a, which shows the proposed spectrum of the Sun in the wavelength region shorter than 3000 Å. This curve is based primarily on observations; the results of theoretical calculations have been used for interpolations between them. Variations of the radiation are expected and observed only for wavelengths shorter than, say, 500 Å. It does not seem possible that the intensity of the \(L_\alpha\) line or of the Lyman continuum spectrum varies by more than a factor of 2*). In Fig. 11b, according to the data of Nicolet \(^{39}\), the total number of quanta passing in 1 second through an area of \(1\ \text{cm}^2\), located outside the Earth’s atmosphere, and having energies greater than the value of the abscissa, is shown.

Fig. 11b. Total number of quanta with energy greater than \(h\nu/c\).

) The intensity of the radiation of the \(L_\alpha\) line according to rocket observations made at the end of 1955 (see the footnote to p. 654) increased, in comparison with the data used in the present article, by a factor of 10–100. This is apparently connected with the new cycle of solar activity. Editor’s note.*

References

1. M. Minnaert, Ch. 3 of The Sun (ed. G. P. Kuiper), Univ. of Chicago Press, 1953.
2. H. H. Voigt, Zeits. f. Astrophys. 27, 82 (1950).
3. C. de Jager, Recherches Obs. Utrecht 13 (1), (1952).
4. E. Böhm-Vitense, Zeits. f. Astrophys. 34, 209 (1954).
5. W. Priester, Zeits. f. Astrophys. 32, 200 (1953).
6. B. E. J. Pagel, M. N. R. A. S. 115, 493 (1955).
7. K. H. Böhm, Zeits. f. Astrophys. 35, 179 (1954).
8. C. de Jager, Nature 173, 680 (1954).
9. R. G. Athay, D. H. Menzel, J. C. Pecker, R. M. Thomas, Astrophys. J. suppl. series 1, 505 (1955).
10. H. Hubent, C. de Jager, B. A. N. 13, 43 (1956).
11. E. Böhm-Vitense, Zeits. f. Astrophys. 36, 145 (1955).
12. R. O. Redman, Z. Suemoto, M. N. R. A. S. 114, 524 (1955).
13. J. H. Piddington, Proc. Roy. Soc. London, A 203, 417 (1950).
14. L. Woltjer, B. A. N. 12, 165 (1954).
15. R. Michard, The Observatory 74, 209 (1954).
16. I. S. Shklovskii, Izv. Krymsk. astrof. obs. 6, 109 (1950).
17. Ch. Pecker, O. E. Billings, W. O. Roberts, Astrophys. J. 120, 509 (1954).
18. I. S. Shklovskii, S. B. Pikelner, Izv. Krymsk. astrof. obs. 6, 29 (1950).
19. A. Reule, Zeits. f Naturforschung 7a, 234 (1952).
20. G. Elwert, Zeits. f. Naturforschung 7a, 432 (1952); (Mitt. Tübingen, 4).
21. L. Biermann; Naturwiss. 34, 87 (1947).
22. G. Elwert, Zeits. f. Naturforschung 9a, 637 (1954); (Mitt. Tübingen, 8).
23. A. Werner, Austr. J of Phys. 7, 25 (1954).
24. E. Vitense, Zeits. f. Astrophys. 28, 81 (1950).
25. E. S. Johnson, J. D. Purcell, R. Tousey, Bull. Phys. Soc. 29 (4), (1954).
26. R. Tousey, J. D. Purzell, K. Watanabe, Phys. Rev. 83, 792 (1951).
27. E. T. Byram, T. Chubb, Friedmann, N. Gallar, Phys. Rev. 91, 1278 (1953).
28. H. C. van de Hulst, Ch. 5 of The Sun (ed. G. B. Kuiper), Univ. of Chicago Press, 1953.
29. C. de Jager, In colloquium on stellare classification C. N. R. S., Paris, 1955.
30. Goldberg, Astrophys. J. 120, 185 (1954).
31. R. G. Giovanelli, Austr. J. of Phys. 1, 305 (1948).
32. J. H. Piddington, Astrophys. J. 119, 53 (1954).
33. K. O. Kiepenheuer, Ann d’Astrophys. 8, 210 (1935).
34. R. v. d. R. Woolley, C. W. Allen, M. N. R. A. S. 108, 292 (1948).
35. H. Friedman, S. M. Lichtman, E. T. Byram, Phys. Rev. 83, 1025 (1951).
36. E. T. Byram, T. Chubb, H. Friedman, Rocket exploration of the upper atmosphere. Pergamon Press Ltd., 1954.
37. E. T. Byram, T. Chubb, H. Friedman, Phys. Rev. 92, 1066 (1954).
38. E. T. Byram, T. Chubb, H. Griedman, Bull. Amer. Phys. Soc. (1954).
39. M. Nicolet, Int. Ass. Terr. Magn. Oslo, Doa. 48, 1948—1951.
40. H. Kristenson, Ssokcholm. Ann. 17 (1951).