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The Current State of the Question of the Nature of the Solar Corona
I. S. Shklovsky.
The term “solar corona” is now understood to mean the uppermost layers of the Sun’s atmosphere. During total solar eclipses these layers are observed as a pearly-white glow surrounding the solar disk covered by the Moon. The lower boundary of the corona may, more or less conventionally, be taken as a distance of \(40''\) from the solar limb (which in linear units corresponds to approximately 30,000 kilometers). It was at precisely this distance that Waldmeier usually observed the corona outside eclipses (see below). On the other hand, the calcium chromosphere can be traced up to 14,000 kilometers. Thus, at a height of 14,000–30,000 kilometers, the transition from the chromosphere to the corona must take place. As will be seen from what follows, in its physical characteristics the corona differs qualitatively from the lower chromosphere. It should be noted that this “intermediate” region of the solar atmosphere, where the chromosphere passes into the corona, has so far been studied comparatively little. Protuberances often rise above the chromosphere by many tens and even hundreds of thousands of kilometers, i.e., they are already located in coronal regions. As for the upper boundary of the corona, it, of course, cannot be established with sufficient sharpness. Individual investigators have succeeded in tracing the corona out to a distance of 4–5 solar radii.
Although, since the time of the first spectroscopic studies of the corona (1869), the latter had been observed for a total duration of only a little more than one hour (the method of observing the corona outside eclipses was developed only in 1930 and is a very valuable supplement to observations of the corona during total eclipses, but by no means replaces them), by 1939 a large number of factual data had accumulated requiring theoretical interpretation. Analysis of these facts forced investigators to attribute to coronal matter properties very different from those of matter in other cosmic objects. Conclusions obtained on the basis of analysis of one group of facts often contradicted conclusions obtained from another group of facts. It may be said without exaggeration that it is difficult in astronomy to find another object which, like the corona, would have posed...
before researchers such a large number of puzzling problems. Substantial progress in the study of the corona was achieved in 1939–1941, and the main part of the present review will be devoted to work done after that time. The introductory part is devoted to a brief (and far from complete) account of the state of the problem of the solar corona by 1939. More complete information covering this period may be found in the excellent review by N. N. Pariiskii[^1].
§ 1. GENERAL INFORMATION ON THE CORONA.
Various investigators have determined the surface brightness of the corona (in photographic rays) as a function of distance—either from the edge of the solar disk, \(h\), or from its center, \(\rho\). By averaging the observed brightness over all directions, a number of empirical laws were obtained for the decrease of brightness with distance, usually either of the form \(I=\dfrac{c_1}{h^{n_1}}\), or \(I=\dfrac{c_2}{\rho^{n_2}}\).
As a result of very carefully performed work, Baumbach[^2] found the mean value of the brightness of the corona, using the results of observations of 10 eclipses covering the period 1905–1927, in the form:
\[ I(\rho)=\frac{0.052}{\rho^{2.5}}+\frac{1.425}{\rho^7}+\frac{2.565}{\rho^{17}}, \tag{1} \]
where \(\rho\) is expressed in fractions of the solar radius, and the brightness at the center of the solar disk is taken equal to \(10^6\). The first term is important for describing the course of the variation of brightness in the outer corona; the third describes the brightness of the parts of the corona closest to the solar surface. A single expression of the form \(\dfrac{c_2}{\rho^{n_2}}\) cannot describe the brightness gradient for the entire corona. Although formula (1) is very important and useful for many calculations connected with the corona (see below), it should not be forgotten that it gives a very averaged value of the quantity \(I(\rho)\). Here there is a double averaging: different investigators averaged \(I\) over all position angles, and Baumbach averaged these mean results. In reality the brightness of the corona (especially that part of it which is closest to the edge of the Sun) depends strongly on the position angle (see below). In addition, the corona is not a stationary formation. Its characteristics change from eclipse to eclipse.
In this connection we note that the illumination produced by the corona on the Earth and, on average, equal to half the illumination produced by the Moon, changes for different eclipses by almost 50%. We also note that the very shape of the corona, as Ganskiy[^3] showed, depends on the phase of solar activity.
The study of the spectral composition of the radiation of the corona served as the basis for dividing it into 2 parts. The spectrum of the so-called
of the inner corona, extending approximately to a distance of up to \(10'\) from the limb of the Sun (which corresponds to \(430\,000\) km), consists of a continuous component, with an energy distribution over wavelengths analogous to the spectrum of the Sun, and a monochromatic component. The latter consists of a large number of emission lines of varying intensity, superposed on the continuous spectrum of the corona from its ultraviolet part to the infrared.
These so-called “coronal” lines are of outstanding interest. Until recently they had not been identified (see below). In contrast to the spectrum of the Sun, the continuous spectrum of the inner corona contains no Fraunhofer lines.
The spectrum of the outer corona (\(h > 10'\)) is very similar to the spectrum of the Sun. There are no emission coronal lines here. On the contrary, Fraunhofer lines are present. Near the boundary of the inner corona the Fraunhofer lines are very weak, i.e. their “residual intensities” are very large. As one moves away from the Sun these residual intensities decrease. At the same time, however, the half-width of the Fraunhofer lines in the outer corona is the same as in the spectrum of the Sun.
In 1905 the founder of modern astrophysics, K. Schwarzschild, put forward his hypothesis concerning the nature of the glow of the corona, now regarded as generally accepted. According to this hypothesis, the mechanism of the corona’s glow is the scattering of photospheric radiation by free electrons. It is known that in the case of Thomson scattering the scattering coefficient does not depend on wavelength. Consequently, the spectral composition of the scattered radiation must be identical to the spectral composition of the radiation being scattered, which is indeed observed.
According to Schwarzschild’s hypothesis, the light of the corona should be partially polarized, and the degree of polarization should not depend on wavelength. Observations unquestionably show that the light of the corona is polarized; however, concerning the dependence of the degree of polarization on wavelength and on distance from the solar disk, different authors obtain very different results. Apparently, the methodology of such observations is still not sufficiently perfected. For more detail on the polarization of the corona, see \(^{1}\).
From the observed surface brightness \(I(\rho)\) one can obtain the volume luminosity (the amount of energy emitted by a unit volume of the corona per unit time) \(J(r)\), where \(r\) is the distance of the volume element of the corona from the center of the Sun. Obviously,
\[ I(\rho)=\int_{-\infty}^{+\infty} J(z)\,dz . \]
The solution of this integral equation of Abel type is the expression:
\[ J(r)=\frac{1}{\pi}\int_r^\infty \frac{\dfrac{\partial I(\rho)}{\partial \rho}} {\sqrt{\rho^2-r^2}}\,d\rho . \]
Baumbach, proceeding from (1), obtained:
\[ J(r)=\frac{0.0304}{r^{3.5}}+\frac{1.452}{r^8}+\frac{4.157}{r^{18}} . \tag{2} \]
Knowing the mechanism of the corona’s radiation—Thomson scattering—one can obtain from (2) the concentration of free electrons \(N_e\) in the corona as a function of \(r\):
\[ J(r)=N_e(r)\cdot\sigma\int\frac{\bar I\,d\omega}{4\pi}, \tag{3} \]
where the Thomson scattering coefficient is \(\sigma=\dfrac{8\pi}{3}\dfrac{e^4}{m^2c^4}\), the scattering being regarded as isotropic; \(\bar I\) is the intensity of the photosphere’s radiation at the point of the corona \(r\). The integration extends over all solid angles. Taking into account the darkening of the solar disk toward the limb, given by the formula \(\bar I=\bar I_0(1-u+u\cos\theta)\), where the “darkening constant” \(u\), according to observations, is equal to 0.4, and \(\theta\) is the angle between the normal to the solar surface and the direction toward the point of the corona \(r\), Baumbach found that
\[
K=\int \bar I\frac{d\omega}{4\pi}
={}^{1}\!/\!_{2}\bar I_0
\left\{(1-u)\left[1-\sqrt{1-\frac{1}{r^2}}\right]\right.
\]
\[
\left.
+{}^{1}\!/\!_{2}u\left[1-r\left(1-\frac{1}{r^2}\right)\log\sqrt{\frac{r+1}{r-1}}\right]\right\}.
\tag{4}
\]
On the basis of (2) and (4) Baumbach found the following approximate expression for \(N_e\):
\[ N_e(r)=10^8\left(\frac{0.36}{r^{3/2}}+\frac{1.55}{r^6}+\frac{2.99}{r^{16}}\right)\ \text{cm}^{-3}. \tag{5} \]
If the darkening of the Sun toward the limb were not taken into account, the value of \(N_e\) in the very inner regions of the corona would be 40% smaller. At the distance \(r=2\), \(N_e\) is 100 times smaller than at the base of the corona. We give the table of values of \(I\), \(J\), and \(N_e\) computed by Baumbach (Table 1).
Schwarzschild explained the absence of Fraunhofer lines in the spectrum of the inner corona by the Doppler effect, which occurs when the radiation of the photosphere is scattered by coronal electrons moving with large thermal velocities. As can be shown, this leads to a “washing out” of the Fraunhofer lines in the scattered light. Indeed, let radiation \(\bar I(\lambda)\), continuously distributed over the spectrum, be incident on free electrons. Let us fix our attention on some wavelength \(\lambda_1\).
Radiation scattered with this wavelength will arise both from slow electrons scattering radiation with a wavelength close to \(\lambda_1\), and from fast electrons scattering radiation
Table 1
| \(r\) | \(h'\) | \(I\) (center of the Sun = \(10^6\)) | \(J\) | \(N_e\) |
|---|---|---|---|---|
| 1,00 | 0′,00 | 4,07 | 5,64 | \(4,58\cdot10^8\) |
| 1,03 | 0,48 | 2,76 | 3,62 | 3,11 |
| 1,06 | 0,96 | 1,95 | 2,39 | 2,29 |
| 1,10 | 1,6 | 1,28 | 1,45 | 1,56 |
| 1,20 | 3,2 | \(5,47\cdot10^{-1}\) | \(5,10\cdot10^{-1}\) | \(7,04\cdot10^7\) |
| 1,3 | 4,8 | 2,84 | 2,27 | 3,84 |
| 1,4 | 6,4 | 1,66 | 1,17 | 2,38 |
| 1,6 | 9,6 | \(7,04\cdot10^{-2}\) | \(4,05\cdot10^{-2}\) | 1,11 |
| 1,8 | 12,8 | 3,56 | 1,72 | \(6,13\cdot10^6\) |
| 2,0 | 16,0 | 2,05 | \(8,38\cdot10^{-3}\) | 3,73 |
| 2,2 | 19,2 | 1,31 | 4,57 | 2,50 |
| 2,4 | 22,4 | \(9,06\cdot10^{-3}\) | 2,75 | 1,79 |
| 2,6 | 25,6 | 6,65 | 1,77 | 1,35 |
| 2,8 | 28,8 | 5,12 | 1,22 | 1,10 |
| 3,0 | 32,0 | 4,07 | \(8,72\cdot10^{-4}\) | \(9,13\cdot10^5\) |
| 3,5 | 40,0 | 2,57 | 4,43 | 6,32 |
| 4,0 | 48,0 | 1,75 | 2,60 | 5,12 |
| 5,0 | 64,0 | \(9,68\cdot10^{-4}\) | 1,13 | 3,81 |
with a wavelength appreciably different from \(\lambda_1\). The intensity of the scattered radiation will be equal to:
\[ I(\lambda_1)=\sigma\cdot N_e\,\frac{1}{\sqrt{\pi}} \int_{-\infty}^{+\infty} e^{-\left(\frac{\lambda-\lambda_1}{\Delta\lambda_D}\right)} \overline{I}(\lambda)\, d\left(\frac{\lambda-\lambda_1}{\Delta\lambda_D}\right), \]
where the Doppler shift is
\[ \Delta\lambda_D= \frac{\sqrt{\dfrac{kT_e}{m}}}{c}. \]
Let us consider the case when \(I(\lambda)\) corresponds to a region of the spectrum containing a strong Fraunhofer line, for example, \(H\) or \(K\) (lines belonging to ionized calcium). In this case, as is known,
\[ \overline{I}(\lambda)=F_0\cdot \frac{1}{1+\dfrac{3}{4}\dfrac{N'_H C_1}{\lambda-\lambda_0}}, \]
where \(F_0\) is the radiation flux of the photosphere in the continuous spectrum in the vicinity of \(\lambda_0\), the “center” of the line; \(N'_H\) is the number of \(Ca^+\) atoms forming the line (in a column of unit cross section), \(C_1=\mathrm{const}\).
Introducing the notations
\[ \frac{\lambda-\lambda_1}{\Delta\lambda_D}=x,\qquad \frac{\lambda_1-\lambda_0}{\Delta\lambda_D}=a,\qquad \frac{\frac{3}{4}N_H C_1}{(\Delta\lambda_D)^2} =\left(\frac{d}{2}\right)^2 \]
and, carrying out the calculations, we obtain:
\[ I(\lambda_1)=F_0\cdot\sigma\cdot N_e\frac{1}{\sqrt{\pi}} \left\{ \int_{-\infty}^{+\infty} e^{-x^2}\,dx - \frac{d^2}{4} \int_{-\infty}^{+\infty} \frac{e^{-x^2}\,dx}{\left(\frac{d}{2}\right)^2+(x-a)^2} \right\}. \tag{6} \]
Assuming, on the basis of observations,
\[ N_H=23.6\cdot10^{18}\ \text{cm}^{-2}\ (\text{cm.}^{4}),\quad \lambda_0=3968\ \text{\AA} \]
and calculating the integral with the aid of existing tables, one can plot the line contour in scattered light. We give the contours of the \(K\) line for two values of the electron temperature of the corona, \(T'_e=168\,000^\circ\left(\frac{d}{2}=\frac{1}{5}\right)\) and \(T''_e=625\,000^\circ\left(\frac{d}{2}=\frac{1}{10}\right)\) (Fig. 1).
Since the \(K\) line is not observed at all in the coronal spectrum, one may conclude that \(T_e\) of the corona is much closer to \(625\,000^\circ\) than to \(168\,000^\circ\). For the first time Grotrian\(^5\), analyzing the blurring of Fraunhofer lines in the inner corona, indicated that its electron temperature is of the order of \(350\,000^\circ\). As will be seen below, this circumstance plays a fundamental role for various processes occurring in the solar corona.
Fig. 1. Theoretical contour of the \(K\) line of the solar-corona spectrum.
a) \(T=168\,000\), b) \(T=625\,000\).
As regards the presence of Fraunhofer lines in the spectrum of the outer corona, the interpretation of this phenomenon is apparently one of the most difficult problems of coronal physics. If one assumes that the mechanism of emission of the outer corona is the same as that of the inner corona, it is necessary to admit that \(T_e\) there is very small, of the order of several tens of degrees! Grotrian\(^6\) believes that Fraunhofer lines in the spectrum of the outer corona arise as a result of scattering of photospheric radiation by dust particles. However, Russell\(^7\) pointed out that the very existence of such dust particles in the vicinity of the Sun is impossible.
For more details on this, see\(^1\). In any case, at the present time this problem is far from being solved.
§ 2. RESULTS OF OBSERVATIONS OF THE CORONA OUTSIDE ECLIPSE AND WITH STANDARD CORONAGRAPHS.
Recently, observations of the corona in the light of various coronal lines (usually \(\lambda = 5303 \,\text{Å}\) and \(\lambda = 6374 \,\text{Å}\)) outside eclipse have been acquiring ever greater importance. This problem was first solved in 1930 by Lyot. His success was due to the careful elimination of scattered light both in the instrument and in the atmosphere (for which the observations were conducted at Pic-du-Midi, in the Pyrenees, at an altitude of about 3000 m). For a description of the details of the construction of Lyot’s coronagraph, see\(^8\). Here we shall speak only about Lyot’s work of 1933–1944. For the results of earlier studies, see\(^9\). In 1939 Lyot used, for observations of the corona, polarization monochromatic filters, consisting of a stack made up of 6 quartz plates alternating with 7 polaroids.
Fig. 2. Monochromatic images of the solar corona obtained by Lyot outside eclipse. Above—in the light of the line \(\lambda = 6374\,\text{Å}\), below—in the light of the line \(\lambda = 5303\,\text{Å}\).
This system transmits 13 bands, with widths from 3 Å in the red part of the spectrum down to 2 Å in the green. The bands are located near the principal chromospheric and coronal lines (\(H_{\alpha}\), \(H_{\beta}\), \(\lambda = 5303\,\text{Å}\), \(D_3\), \(\lambda = 6374\,\text{Å}\), etc.). The entire system is placed in a thermostat. By small changes in temperature, precise coincidence is achieved between the transmission bands of the filter and the monochromatic coronal or chromospheric radiation under investigation. Monochromatic images of the corona revealed a number of interesting details; in particular, it turned out that the distribution of the intensities of the green and red lines in the corona is different. We reproduce photographs of the corona obtained by Lyot in the light of these lines\(^ {10}\) (Fig. 2).
With this filter Lyot for the first time carried out simultaneous cinematographic photography of the corona in the light of the green and red lines and of the \(H_{\alpha}\) line of the chromosphere and prominences. Some exposures were very long—up to 12 hours. The behavior of the coronal lines is very little connected with the behavior of the \(H_{\alpha}\) line, which is interpreted by Lyot in that
in the sense that the corona is almost independent of prominences. During these, rather long, exposures the monochromatic image of the corona changed only slightly. Lyot did not detect motions in the corona, which were observed by a number of authors (in white light!). Thus, Lyot’s results show that the corona must be regarded as a quasi-stationary formation.
Equator
— Intensity of the line $\lambda = 5303\,\text{\AA}$
○–○–○ Intensity of the line $\lambda = 6374\,\text{\AA}$
Fig. 3. Diagrams of the intensity of coronal lines.
This conclusion undoubtedly has fundamental significance for the problem of the corona.
Lyot carried out visual photometry of the red and green coronal lines, whose intensity was compared with the intensity of the corresponding spectral regions of the center of the Sun. In this way absorption in the Earth’s atmosphere was excluded. The photometry pro-
ON THE NATURE OF THE SOLAR CORONA
was plotted for different points of the Sun’s limb. The intensity of the coronal lines differs greatly for different points of the limb. At the solar poles it is equivalent to the intensity of a band of the continuous spectrum of the center of the Sun of width \(2 \cdot 10^{-6}\) Å, while in some regions of the limb it is \(80 \cdot 10^{-6}\) Å. We give the “intensity diagrams” obtained by Lyot\(^{10}\) (Fig. 3).
In 1938 Waldmeier began his major work on studying the corona outside eclipses by Lyot’s method. His observatory is located on Monte Arosa (Switzerland, altitude 2050 m above sea level). The methods and results of his investigations were published in a number of papers\(^{11}\). He studied the distribution of intensity of the green and red coronal lines \(\lambda = 5303\) Å and \(\lambda = 6374\) Å along the solar disk at a distance of \(40''\) from it. His first works contained visual estimates of the brightnesses of coronal lines, expressed on a special scale.
Fig. 4. Coronal contours according to Waldmeier. \(a\)—lines \(\lambda = 5303\) Å, \(b\)—lines \(\lambda = 6374\) Å.
In this way Waldmeier constructed a series of “coronal contours” (see Fig. 4, \(a\) and 4, \(b\)). The dashed line denotes the axis of rotation of the Sun. The distance from the contour to the solar limb is proportional to the intensity of the coronal line for the given position angle. It is clearly seen from the drawings that at the equator there is a minimum of intensity, the principal maxima are in the spot zone (heliographic latitude \(10^\circ\)—\(20^\circ\)), and a secondary maximum is at heliographic latitude \(\pm 60^\circ\). The “coronal contours” are fairly stable: over the course of a day they usually change little. As is evident from the drawings, the “coronal contour” of the red line, generally speaking, does not coincide with the contour of the green line. Usually the intensity of the red line is about \(1/10\) of the intensity of the green, but in some regions of the corona strong deviations from this rule are often observed. Regions where the intensity of the red line is anomalously large Waldmeier calls “red regions”; regions where the green line is anomalously intense are designated by him as “green regions.” Finally, on rare occasions he observed regions where the intensity of the green line was especially strong. These regions of the corona Waldmeier designates as “C-regions.”
By successively observing the corona over a number of days, Waldmeier was the first to construct a synoptic map of the corona, shown in Fig. 5, \(a\) and \(c\). The density of the hatching corresponds to the intensity of the coronal line.
The heliographic coordinates are given in Carrington’s system. In Fig. 5, \(b\) a synoptic map of the solar photosphere is given for this same
time. On it the black regions denote spots, and the hatched regions denote facular fields. A clearly expressed connection between details in the corona and in the photosphere is striking. Above each spot the monochromatic brightness of the corona is enhanced. However, bright coronal regions are encountered beneath which there are no spots at all. The “green region” with coordinates \(5^\circ, -55^\circ\) and the “red” one with coordinates \(310^\circ, +55^\circ\) are clearly visible. In addition, Waldmeier compares synoptic maps of the corona and the chromosphere and finds a close connection between bright coronal regions and such chromospheric formations as bright flocculi. Neither in the photosphere nor in the chromosphere were any formations found that could be connected with the secondary maxima of the intensity of the coronal lines at latitudes \(\pm 60^\circ\).
Fig. 5. Synoptic maps of the solar corona: \(c\)—in the light of the red line \(\lambda = 6374\), \(a\)—in the light of the green line \(\lambda = 5303\) Å,
\(b\)—synoptic map of the photosphere.
In addition to visual observations, Waldmeier carried out careful photographic photometry of the corona in the light of the green line. The results obtained fully confirm the visual observations. He investigated the monochromatic brightness gradient in the inner corona both in the case of the so-called coronal rays and for “normal” coronal regions. It turns out that the intensity of the monochromatic radiation decreases with distance from the solar surface faster than the intensity of the “continuous” radiation. The law of variation of the monochromatic intensity with distance \(\rho\) from the center of the solar disk was found in the form \(I = \mathrm{const.}\,\rho^{-2.4}\) (for a coronal ray). This relation is valid near the limb of the Sun. At distances exceeding \(2'\), the monochromatic intensity is proportional to the “continuous” intensity, in agreement with Grotrian’s results\(^5\). The profiles of the green line obtained by Waldmeier at various distances from the limb have a Doppler character. The half-width of this line decreases from \(0.54\) Å for a distance of \(51''\) to \(0.28\) Å for a distance of \(3'38''\). The corresponding random-
emission velocities of the radiating matter decrease from 37 to 19 kilometers per second.
Waldmeier’s conclusion about the influence of the so-called “C”-regions on geomagnetic disturbances is very interesting. It turns out that, on the average, 6.2 days before a “C”-region is observed on the western limb of the solar disk and 7.4 days after this region is observed on the eastern limb, a magnetic storm usually occurs on Earth. This can be explained by the fact that fast corpuscles are ejected from the “C”-regions, covering the distance from the Sun to the Earth in 0.6 day and producing a magnetic storm.
Thus it is possible that the “C”-regions are those areas of the Sun which are responsible for geomagnetic disturbances.
Observations of the solar eclipse of 1936 by Soviet expeditions, made with standard coronagraphs located along the eclipse belt, initiated a cycle of work on the study of the structure of the corona and of motions within it. Similar observations were repeated in 1941 and 1945. The processing of the observational material carried out by E. Ya. Bugoslavskaya[^12] and S. K. Vsekhsviatsky[^13] gave the following results. The forms of coronal details (in photographic rays of the continuous spectrum) depend on details of the solar surface. The physical characteristics of coronal details (for example, brightness gradient, degree of polarization) depend on the corresponding details of the underlying layers of the solar atmosphere. Prominences, as a rule, are enveloped by arc-shaped and “helmet-shaped” coronal shells. Powerful coronal “rays” emerge from faculae. Near spots these “rays” are deformed. Above large groups of spots there may form shells reaching gigantic dimensions. From the chromosphere into the corona matter is continuously ejected, which either dissipates in the corona or falls back. The study of motions in the solar corona (eclipse of 1936) showed that displacements of the rays generally satisfy the assumption of rotation of the corona. However, peculiar motions are present. The character of the behavior of various details of the corona, in the opinion of E. Ya. Bugoslavskaya, shows that there exists on the Sun a general magnetic field, as well as local fields in active regions.
Of great importance is Waldmeier’s observation of the corona outside eclipse on 21 IX 1941. On that day a total solar eclipse occurred, which, despite wartime conditions, was successfully observed by Soviet astronomers, chiefly in Alma-Ata. Bugoslavskaya[^12] compared her photographs, obtained with a standard coronagraph, with Waldmeier’s results for that day. The comparison showed:
1) The isophotes of the corona in photographic rays of the continuous spectrum have the same flattening as the isophotes for the green line.
2) As in Waldmeier’s observations, the isophotes of the innermost parts of the corona in photographic rays show an equatorial minimum.
3) The near-polar secondary maximum of intensity of the green line corresponds to the boundaries of the polar corona, as they appear in photographic rays.
4) The “ray” structure of the corona in bright lines corresponds to the “ray” structure in the continuous spectrum.
These investigations of coronal details by Soviet scientists are of great importance for the solution of a number of problems. However, in order to obtain conclusions of a physical nature, still more work on the spectrophotometry of coronal details is necessary.
§ 3. THE PROBLEM OF “CORONIUM”
During the eclipse of August 7, 1869, Young, Harkness, and Lockyer independently discovered in the spectrum of the corona an emission line \(\lambda = 5303\) Å. Since then observations during total solar eclipses have considerably increased the list of coronal lines.
Lyot, outside eclipse, discovered five lines in the red and infrared part of the spectrum \(^{14}\). At the present time the number of emission lines undoubtedly present in the spectrum of the inner corona is 24. In addition, many investigators, during various eclipses, observed very weak coronal lines. Their wavelengths were measured very uncertainly. More than once they were not observed. In Table II the wavelengths of these lines are enclosed in parentheses.
Table II
Coronal lines
| \(\lambda\) Å | \(\nu\ \mathrm{cm}^{-1}\) | \(I\) | \(\lambda\) Å | \(\nu\ \mathrm{cm}^{-1}\) | \(I\) | \(\lambda\) Å | \(\nu\ \mathrm{cm}^{-1}\) | \(I\) |
|---|---|---|---|---|---|---|---|---|
| 3328 | 30 039 | 1,0 | 3865 | 25 865 | — | 5116 | 19 541 | 4,3 |
| (3359) | 29 762 | — | (3891) | 25 693 | — | 5302,8 | 18 853 | 100 |
| 3388,1 | 29 506 | 16 | 3986,9 | 25 075 | 0,8 | 5536 | 18 059 | — |
| 3454,1 | 28 942 | 2,3 | 4086,3 | 24 465 | 1,0 | 5694 | 17 557 | 1,2 |
| (3461) | 28 885 | — | (4130) | 24 206 | — | 6374 | 15 683 | 8,1 |
| (3505) | 28 522 | — | (4131,4) | 24 298 | — | 6704,8 | 14 910 | 5,4 |
| (3534) | 28 288 | — | 4231,4 | 23 626 | 2,6 | 7059,6 | 14 961 | 2,2 |
| (3601,0) | 27 762 | 2,1 | (4244,8) | 23 552 | — | 7891,9 | 12 677 | 13 |
| (3626) | 27 571 | — | 4311,0 | 23 190 | — | 8024 | 12 459 | 0,5 |
| (3641) | 27 457 | — | 4359,0 | 22 935 | < 0,8 | 10 746,8 | 9314,4 | 55 |
| 3642,9 | 27 443 | — | (4398) | 22 731 | — | 10 797,9 | 9261,0 | 35 |
| (3648) | 27 404 | — | (4412) | 22 659 | — | |||
| (3651) | 27 382 | — | (4533,4) | 22 054 | — | |||
| 3800,8 | 26 302 | — | 4567 | 21 890 | 1,2 | |||
| 4586 | 21 799 | — | ||||||
| (4722) | 21 172 | — | ||||||
| (4725) | 21 158 | — | ||||||
| (4779) | 20 919 | — | ||||||
| (5073) | 19 706 | — |
In the third column of Table II are given the relative intensities of the coronal lines, the intensity of the green line \(\lambda = 5303\,\text{\AA}\) being taken as 100. The indicated intensities are given on the basis of the results of Grotrian\({}^{5}\) and Lyot\({}^{15}\).
These data have been reduced to the single system of Edlén. It must be pointed out that the relative intensities given can be regarded only as averages, since in different regions of the corona and at different times they may assume quite different values (see above).
A remarkable feature of the coronal lines was the fact that until quite recently they had not been identified. Meanwhile, very much work had been done in this direction. We give, in chronological order, the principal attempts to identify the coronal lines\({}^{16}\): the hypothetical element “coronium” (1911), twice ionized calcium (1922), argon (1929), atomic Raman effect (1930), oxygen (1931—1933), twice excited helium (1930, 1933—1935), hydrogen molecules (1932), negative ions (1934), forbidden lines N II, forbidden lines Fe II (1938) and Fe III (1938).
Since almost all permitted lines of atoms and ions (we have in mind the first two stages of ionization) had by that time been obtained in laboratories, it could be assumed that the coronal lines are associated with some forbidden transitions. But lines connected with such transitions are, as is known, very narrow, whereas the coronal lines have a comparatively large half-width (see above).
In 1939 Grotrian\({}^{17}\) showed that transitions between the components of the multiplets
\(\mathrm{Fe\,X}\;3s^{2}3p^{5}\,{}^{2}P_{1/2} - {}^{2}P_{3/2}\) and
\(\mathrm{Fe\,XI}\;3s^{2}3p^{4}\,{}^{3}P_{1} - {}^{3}P_{2}\), within the limits of experimental error, must give lines which in wavelength coincide with two coronal lines, respectively
\(\lambda = 6374\,\text{\AA}\) and \(\lambda = 7892\,\text{\AA}\). The spectra of these ions had been obtained experimentally by Edlén in a spark discharge with the aid of a vacuum spectrograph of Siegbahn’s design\({}^{18}\). This spectrograph makes it possible to record radiation with wavelength \(\lambda < 200\,\text{\AA}\). Its dispersion is of the order of \(0.3—0.5\,\text{\AA}/\mathrm{mm}\), its resolving power \(0.01\,\text{\AA}\). We give in full the experimental data which led Grotrian to the indicated identification (see Table III).
Edlén, on the basis of unpublished data available to him on the spectra of highly ionized ions, found two more direct coincidences of transitions:
\[ \mathrm{Ca\,XII}\;2s^{2}2p^{5}\,{}^{2}P_{1/2} - {}^{2}P_{1 1/2} \quad \text{and} \quad \mathrm{Ca\,XIII}\;2s^{2}2p^{4}\,{}^{3}P_{1} - {}^{3}P_{2} \]
with the weak coronal lines \(\lambda = 3328\,\text{\AA}\) and \(\lambda = 4086\,\text{\AA}\), respectively.
Since these term differences are determined from measured lines of very small wavelength, they are obtained comparatively inaccurately.
Table III
| Fe X \(3s^2 3p^5\)—\(3s^2 3p^4 4s\) | \(\lambda\,\text{Å}\) | \(\nu\,\text{cm}^{-1}\) | Term difference | \(\nu\) of the corona |
|---|---|---|---|---|
| \({}^{2}P_{1^{1}/_{2}}—{}^{2}P_{1/2}\) | 95.338 | 1 048 900 | 15 714 | 15 683 |
| \({}^{2}P_{1/2}—{}^{2}P_{1/2}\) | 96.788 | 1 033 186 | 15 714 | 15 683 |
| \({}^{2}P_{1^{1}/_{2}}—{}^{2}P_{1^{1}/_{2}}\) | 96.122 | 1 040 345 | 15 660 | 15 683 |
| \({}^{2}P_{1/2}—{}^{2}P_{1^{1}/_{2}}\) | 97.591 | 1 024 685 | 15 660; 15 687 | 15 683 |
| Fe XI \(3s^2 3p^4\)—\(3s^2 3p^3 4s\) | ||||
| \({}^{3}P_{2}—{}^{3}D_{2}\) | 87.025 | 1 149 095 | 12 667 | 12 668 |
| \({}^{3}P_{1}—{}^{3}D_{2}\) | 87.995 | 1 136 428 | 12 667 | 12 668 |
| \({}^{3}P_{2}—{}^{3}S_{1}\) | 89.185 | 1 121 265 | 12 679 | 12 668 |
| \({}^{3}P_{1}—{}^{3}S_{1}\) | 90.205 | 1 108 586 | 12 679; 12 673 | 12 668 |
ones. Therefore Edlén carried out laborious work on obtaining the indicated term differences more accurately by extrapolating the magnitude of the splitting in multiplets of various isoelectronic sequences\({}^{19}\). These sequences included iron ions from Fe X to Fe XIV. The corresponding ground configurations of these ions are: \(3s^2 3p^5\) (Fe X), \(3s^2 3p^4\) (Fe XI), \(3s^2 3p^2\) (Fe XIII), and \(3s^2 3p\) (Fe XIV). The configuration \(3s^2 3p^3\) (Fe XII) was not considered for reasons that will be discussed below. In the case of the configurations \(3s^2 3p^5\) and \(3s^2 3p\), the extrapolation is performed comparatively easily. Here the ground state is the doublet \({}^{2}P_{1^{1}/_{2},\,1/2}\), and its splitting \(\Delta\nu\) varies in the isoelectronic sequences Cl I, A II, … Fe X… and Al I, Si II, …, Fe XIV, …, according to Landé’s formula
\[ \Delta\nu=\frac{R\alpha^2(Z\sigma)^4}{n^3 l(l+1)}, \tag{7} \]
where \(R\) is the Rydberg constant, \(\alpha\) is the fine-structure constant, \(n\) and \(l\) are quantum numbers, \(Z\) is the atomic number of the element, and \(\sigma\) is the screening parameter, which changes little along an isoelectronic sequence.
Sufficiently accurate experimental data for \(\Delta\nu\) in the case of the series \(3s^2 3p\) are available up to Sc IX, and in the case of \(3s^2 3p^5\), up to V VII. Relying on these data, with the aid of relation (7)
Edlén confidently found three more coincidences: Fe XIV \(3s^2 3p\,{}^2P_{1/2}—{}^2P_{3/2}\) with the coronal line \(\lambda=5303\) Å; the same transition in Ni XVI gives a coincidence with the line \(\lambda=3601\) Å; Ni XII \(3s^2 3p^5\,{}^2P_{3/2}—{}^2P_{1/2}\) coincides with the coronal line \(\lambda=4231\) Å.
In the case of the sequences \(3s^2 3p^2\) and \(3s^2 3p^4\), the problem of extrapolation is much more complicated. Here the levels of the ground configuration are arranged in the following order: \({}^3P_0\), \({}^3P_1\), \({}^3P_2\), \({}^1D_2\), \({}^1S_0\), and, respectively: \({}^3P_2\), \({}^3P_1\), \({}^3P_0\), \({}^1D_2\), \({}^1S_0\). The reason for this difficulty is that, in this series of isoelectronic sequences, there is a gradual transition from Russell–Saunders \(LS\) coupling to \(j—j\) coupling. Therefore the basic spectral regularities in this region are determined by the theory of intermediate coupling, developed comparatively recently in the works of Gaudsmith, Shortley, and Robinson (see, for example, the monograph by Shortley and Condon \(^{20}\)). According to this theory, the energy of each component of a multiplet is determined by the principal coupling parameter
\[ \chi=\frac{\zeta}{5F_2}, \]
where \(\zeta\) is the energy of the spin–orbit interaction, and \(F_2\) is the energy of the electrostatic interaction. For example, in the case of the configuration \(3s^2 3p^4\) the term difference is
\[ {}^1D_2-{}^3P_1 = 5F_2 \left( \frac{3}{5} - {}^3/_4\chi + \sqrt{\frac{9}{25}+\frac{3}{10}\chi+\frac{9}{16}\chi^2} \right). \]
In the case of \(LS\)-coupling, \(\chi\to 0\). It turns out that the quantities \(\chi\), \(F_2\), and \(\zeta\) vary with \(Z\) quite regularly (unlike \(\Delta\nu\)), and therefore they are convenient for extrapolation. Up to the elements V VIII \((3s^2 3p^4)\) and Sc VIII \((3s^2 3p^2)\), these quantities were obtained from experimental data according to the measured ratios
\[ R_c=\frac{{}^3P_2-{}^3P_0}{{}^1D_2-{}^3P_2} \quad\text{and}\quad R_L=\frac{{}^3P_2-{}^3P_1}{{}^3P_1-{}^3P_0} \]
and the theory of intermediate coupling.
Subsequently \(\chi\), \(F_2\), and \(\zeta\) were extrapolated, with \(F_2\sim Z\), and \(\zeta\sim (Z-\sigma)^4\). As a result of this work it was possible to identify a number of coronal lines. The transition Fe XIII \(3s^2 3p^2\,{}^3P_2—{}^3P_1\) corresponds to the coronal line \(\lambda=10747\) Å. The transition \({}^3P_1—{}^3P_0\) of the same ion gives the line \(\lambda=10798\) Å. The corresponding transitions in Ni XV give the lines \(\lambda=8024\) Å and \(\lambda=6702\) Å. Finally, the transition Fe XIII \(3s^2 3p^2\,{}^1D_2—{}^3P_2\) is identified with the intense coronal line \(\lambda=3388\) Å. For the configuration \(3s^2 3p^4\) the following coincidences are obtained: Fe XI \(3s^2 3p^4\,{}^1D_2—{}^3P_0 \to\) coronal line \(\lambda=3987\) Å; Fe XI \(3s^2 3p^4\,{}^3P_1—{}^3P_2 \to \lambda=7892\) Å. The corresponding transitions for nickel give coincidences with the coronal lines \(\lambda=3643\) Å and \(\lambda=5116\) Å. The procedure of extrapolation and identification becomes clear upon considering the accompanying graph (Fig. 6).
As soon as Edlén succeeded in identifying 13 lines belonging to the ions Fe X, Fe XI, Fe XIII, Fe XIV, and to isoelectronic Ni ions, the question arose whether lines belonging to other ionization states of Fe and Ni could exist in the spectrum of the corona? In connection with this, Edlén notes that Fe VII lines are present in the spectra of some novae. Since these lines have not been detected in the spectrum of the corona, he concludes that, owing to the prevailing ionization conditions there, one cannot expect in the coronal spectrum lines of the ions Fe VI, Fe III, Fe IV, Fe II. The situation is similar for the lower ionization states of nickel. For Fe VIII and Ni X the splitting of the ground term \({}^2D\) is very small, so that the corresponding transition gives a line of very great wavelength. In Fe IX and Ni XI the ground state is a singlet. Although Fe XII and Ni XIV are undoubtedly present in the corona, their lines cannot be observable. This follows from the attached term scheme of this configuration, borrowed from Swings \(^{21}\) (Fig. 7).
Fig. 6. Multiplet splittings for various isoelectronic sequences. The arrows indicate the coincidences found by Edlén.
The ground configuration of Fe XV, Fe XVI, and Fe XVII and of the corresponding Ni ions is singlet. As for higher ionization states, the following should be noted. In the transition from Fe XVII to Fe XVIII the \(L\)-shell of Fe is “stripped,” and the ionization potential rises sharply. Consequently, there will be extremely few Fe XVIII ions in the corona. Of course, analogous considerations are applicable also to Ni ions.
Investigating the next, second, configuration of Fe XV \(3s\,3p\), Edlén found here two metastable sublevels \({}^3P_0\) and \({}^3P_2\). The forbidden
the transition \(^{3}P_2 — {}^{3}P_1\) gives a line that agrees well in wavelength with the coronal line \(\lambda = 7059\) Å. True, in this case the excitation potential of the initial level is unusually large (31.9 volts), but owing to the prevailing conditions in the corona this circumstance does not lead to difficulties. Nine metastable levels are present in the second configuration Fe IX and Ni XI — \(3s^2 3p^5 3d\), with an excitation potential of the order of 50 V. It is possible that transitions between them may explain some weak, as yet unidentified, coronal lines. For the time being, spectroscopy does not possess the corresponding exact data.
Fig. 7. Scheme of the sublevels of the ground configuration Fe XII and Ni XIV.
A natural question arises: why, in the configuration \(3s^2 3p^k\), are only the ions Fe and Ni responsible for the radiation of coronal lines? For it is clear that, for example, the Co lines corresponding to the Fe and Ni lines, as a rule, lie in the accessible part of the spectrum. According to Edlén, this is explained by the fact that the relative amount of Co and of other elements “neighboring” Co in the corona is small. Edlén assumes that the relative abundance of the elements in the corona is the same as in other cosmic objects, in particular meteorites. For the latter, Goldschmidt\(^{22}\) gives the following data (see Table IV):
Table IV
| \(Z\) | Element | \(\dfrac{n}{n_{\mathrm{Fe}}}\cdot 100\) | \(Z\) | Element | \(\dfrac{n}{n_{\mathrm{Fe}}}\cdot 100\) |
|---|---|---|---|---|---|
| 11 | Na | 5.0 | 18 | A | ? |
| 12 | Mg | 98 | 19 | K | 0.77 |
| 13 | Al | 9.9 | 20 | Ca | 6.4 |
| 14 | Si | 112 | 22 | Ti | 0.53 |
| 15 | P | 0.65 | 24 | Cr | 1.27 |
| 16 | S | 12.8 | 25 | Mn | 0.74 |
| 17 | Cl | 0.6 | 26 | Fe | 100 |
| 27 | Co | 0.39 | |||
| 28 | Ni | 5.2 |
Having made the indicated assumption, Edlén theoretically calculates the intensity of some lines that could be observed
in the corona (the intensity of the green line \(\lambda = 5303\) Å is, as before, taken to be 100). The method of calculation will be discussed below. As is seen from Table V,
Table V
| Transition | \(\lambda\) | \(I\) |
|---|---|---|
| Co XV \(^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) | 4349 Å | 0.4 |
| Mn XIII \(^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) | 6539 | 0.7 |
| S XII \(^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) | 7536 | 2 |
| Cr XII \(^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) | *8159 | 0.6 |
| Co XIV \(^{3}P_{1} - {}^{3}P_{0}\) | 8448 | 0.3 |
all these lines are at the limit of visibility (their intensities are of the order of the intensities of the weakest coronal lines).
In this connection we note that the Indian investigator Kundu erroneously identified the coronal line \(\lambda = 4359\) Å with the line Co XV \(^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) [23]. His error occurred because the corresponding extrapolation was made by him without due care.
Since at the very beginning of his work Edlén identified two coronal lines with certain transitions of Ca XII and Ca XIII ions, it was necessary to carry out an investigation of the configurations \(2s^{2}2p^{k}\), to which the mentioned ions belong.
The extrapolation procedure here is, in the main, analogous to the case of the \(3s^{2}3p^{k}\) configuration.
In addition to those indicated above, the following coincidences were also found: the transition A X \(2s^{2}2p^{5}\,{}^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) corresponds to the coronal line \(\lambda = 5536\) Å; the transition A XIV \(2s^{2}2p^{2}\,{}^{2}P_{1^{1}/_{2}} - {}^{2}P_{1/2}\) corresponds to the line \(\lambda = 4359\) Å (which Kundu erroneously identified). However, Edlén considers the identification of this line somewhat doubtful. The transition Ca XV \(2s^{2}2p^{2}\) corresponds to the line \(\lambda = 5694\) Å. Since the ionization potential of Ca XV is anomalously large (812 volts), Edlén regards this identification also as doubtful. In separate regions of the corona, according to Lyot [9], the intensity of this line, usually amounting to one percent of the intensity of the line \(\lambda = 5303\) Å, at times exceeds the intensity of the latter. Possibly this serves as an indication of an anomalous state of ionization in these coronal regions.
Thus, in all, Edlén identified 19 lines out of 24 whose presence in the corona has been established beyond doubt.
An outstanding merit of Edlén, in addition to the identification of coronal lines, is also the calculation of their transition probabilities and the construction of a preliminary theory of the intensities of coronal lines [19].
Since coronal lines are forbidden by the Laporte rule, it was necessary to calculate the transition probabilities in the case of magnetic-dipole and quadrupole radiation. Let us denote these probabilities respectively by \(A_m\) and \(A_q\).
It is known that \(A_m\) and \(A_q\) exist only for transitions between two even or two odd terms. In addition, there are the following selection rules: for \(A_m\), \(\Delta J = 0, \pm 1\) (except \(0 \to 0\)); for \(A_q\), \(\Delta J = 0, \pm 1, \pm 2\) (except \(0 \to 0\), \({}^{1}/_{2} \to {}^{1}/_{2}\), \(0 \to 1\)).
According to Shortley \(^{24}\) and Pasternack \(^{25}\),
\[ A_m = 2.70 \cdot 10^{-11}\frac{S_m \nu^3}{2J+1}\ \mathrm{sec}^{-1}, \tag{8} \]
\[ A_q = 1.68 \cdot 10^{-22}\frac{S_q \nu^5}{2J+1}\ \mathrm{sec}^{-1}. \tag{8'} \]
\(A_m\) is determined only by the magnetic moments of the ions. For \(LS\)-coupling (transitions of the \({}^{2}P_{1/2,\,3/2}\) configurations \(3s^23p\) and \(3s^23p^5\)),
\[ S_m = \frac{[J^2-(L-S)^2][(S+L+1)^2-J^2]}{4J}, \]
where in the present case \(J=1{}^{1}/_{2}\), \(S={}^{1}/_{2}\), \(L=1\). For the configurations \(p^2\), \(p^3\), \(p^4\), it is obviously necessary to use the theory of intermediate coupling. On the basis of this theory, Shortley, Becker, Aller, and Menzel calculated the quantities \(S_m\) as functions of the intermediate-coupling parameter \(\chi\) \(^{26}\). Edlén uses these investigations for calculating \(A_m\). The quantity \(S_q\) may be represented in the form: \(S_q = C_q \cdot S_q^2\), where \(C_q\) is tabulated in the cited work \(^{26}\). \(S_q\) is determined by the radial eigenfunctions of the corresponding ions. Pasternack \(^{25}\) calculated \(S_q^2\) in the case of hydrogen-like eigenfunctions:
\[ S_q(nl)= \frac{n^2(5n^2+1-3l^2-3l)}{5(Z-\sigma_{nl})^2}. \]
The quantity \((Z-\sigma_{nl})\) is eliminated by Edlén with the aid of the relation: \(F_2 = 315.9(Z-\sigma_{3p})\) (he used this relation in extrapolating the quantities \(F_2\); see above). Finally, for the configurations \(3s^23p^2\) and \(3s^23p^4\) one obtains:
\[ A_q = \frac{5.4 \cdot 10^{-6} C_q \nu^5}{(2J+1)\cdot F_2^4}\ \mathrm{sec}^{-1}, \tag{8''} \]
therefore, knowing \(F_2\) and \(\chi\) (by which \(C_q\) is determined), one can find \(A_q\) for each transition.
In all cases in which \(A_m\) exists, it overwhelmingly exceeds \(A_q\). For different transitions, \(A_m\) varies from a few units to several hundred reciprocal seconds. It is known that for allowed transitions in the visible part of the spectrum \(A_{ik}\) is of the order of \(10^8\ \mathrm{sec}^{-1}\). On the other hand, the transition probability for the nebular line O III, according to Pasternack \(^{25}\), is \(10^{-7}\ \mathrm{sec}^{-1}\). Thus, in “degree of forbid-
in “intensity,” coronal lines occupy, as it were, an intermediate position between permitted and nebular lines. Let us note that, independently of Edlén, the Chinese investigator Kun Huang calculated the transition probabilities of coronal lines[^27]. His results are in excellent agreement with Edlén’s—in all cases (except one) three significant figures coincide!
The emission per unit volume per unit time in a certain forbidden line is determined by the relation
\[ E=\frac{\eta\cdot \nu\cdot A_1}{A_1+A_2+\cdots+B+C}\, \frac{\text{erg}}{\text{sec}\cdot\text{cm}^3}, \tag{9} \]
where \(\eta\) is proportional to the number of excitations of the initial level per unit volume per unit time, \(A_1\) is the transition probability for the given line, \(A_1, A_2\), etc. are the probabilities of transitions from the given level to lower ones, \(B\) is the probability of collisions of the second kind which destroy the metastable state, and \(C\) is the probability of absorption of radiation in which the ion passes into a “higher” state. \(C\) must be very small, since the nearest state \(3s3p^{k+1}\), combining with the ground state \(3s^2 3p^k\), corresponds to radiation with wavelength of the order of \(400\) Å (for Fe ions), and in this region of the spectrum the radiation of the solar photosphere is negligibly small. Edlén estimates the role of collisions of the second kind by means of the following elegant device.
If \(B\) were much greater than \(\sum A_i\), then in a stationary state the “population” of the various levels of any ion would be determined by Boltzmann’s formula, and the parameter \(T\) of this formula would coincide with the electron temperature of the corona \(T_e\), which is very large—of the order of hundreds of thousands of degrees. Therefore the exponential entering into Boltzmann’s formula would differ little from unity; consequently, the intensities of the various lines belonging to a given ion would be proportional to the quantity \((2J+1)\cdot A\cdot \nu\). For example, in the case of Fe XIII the intensities determined by the transitions \({}^1D_2-{}^3P_2\), \({}^3P_2-{}^3P_1\), \({}^3P_1-{}^3P_0\), would be in the ratio \(128:4.6:3.9\), whereas the actual ratio of the intensities of the corresponding lines is \(16:35:55\). The latter quantities, obviously, have nothing in common with the former, which proves the insignificance of the role of collisions of the second kind in the emission of coronal ions.
For the mechanism of excitation of the initial levels of coronal ions Edlén, by analogy with planetary nebulae, takes electron impact. He remarks, however, that since the transition probabilities for coronal lines are \(7\)--\(8\) orders of magnitude greater than for nebular lines, while the electron concentration is \(4\) orders of magnitude greater (in the inner corona \(N_e \simeq 10^8\ \text{cm}^{-3}\), and in typical nebulae \(N_e = 10^4\ \text{cm}^{-3}\)), excitation of the initial levels by absorption of photospheric radiation may play some role. Kun Huang[^27] showed that in most cases the second excitation mechanism
(radiation) is insignificant in comparison with the first. The effective cross section for the excitation of coronal ions by electron impact, strictly speaking, is unknown. Here excitation by slow (thermal) electrons takes place; but, as is known, in this case the Born approximation is not applicable, while exact theoretical calculations are extremely complicated. For want of anything better, Edlén uses the expression for the effective excitation cross sections of nebular O III lines (configuration \(2s^2 2p^2\)), obtained by Hebb and Menzel by the method of partial cross sections[^28]. Then the number of excitations of a certain level per unit volume per unit time will be equal to:
\[ \bar{\eta}=\frac{8.54\cdot 10^{-6}}{T_e^{1/2}}\cdot N_e\cdot \Omega' \cdot (2J+1)e^{-\frac{h\nu}{kT_e}}, \tag{10} \]
where \(\Omega'\) is a dimensionless parameter of order unity.
Of course, this arbitrary assumption is a comparatively weak point in the theory, although Kun-Huang[^27] has shown that it apparently describes the phenomena in the corona satisfactorily.
Using formula (10), Edlén showed that the observed ratios of the intensities of coronal lines can be explained if it is assumed that the relative abundance of iron and nickel in the corona is the same as in meteorites, and \(T_e\) is very large, of the order of \(250\,000—400\,000^\circ\).
We give the final table of the principal characteristics of the identified lines according to Edlén.
Table VI
| \(\lambda\) in Å | Intensity (according to Grotrian) | Intensity (according to Lyot) | Transition | \(A_m\), sec\(^{-1}\) | E.P., volts | I.P., volts |
|---|---|---|---|---|---|---|
| 3328 | 1.0 | — | Ca XII \(2s^2 2p^5\ ^2P_{1/2} — {}^2P_{1\,1/2}\) | 488 | 3.72 | 589 |
| 3388 | 16 | — | Fe XIII \(3s^2 3p^2\ ^1D_2 — {}^3P_2\) | 87 | 5.96 | 325 |
| 3601.0 | 2.1 | — | Ni XVI \(3s^2 3p\ ^2P_{1/2} — {}^2P_{1/2}\) | 193 | 3.44 | 455 |
| 3642.9 | — | — | Ni XIII \(3s^2 3p^4\ ^1D_2 — {}^3P_1\) | 18 | 5.82 | 350 |
| 3985.9 | 0.7 | — | Fe XI \(3s^2 3p^4\ ^1D_2 — {}^3P_1\) | 9.5 | 4.68 | 261 |
| 4086.3 | 1.0 | — | Ca XIII \(2s^2 2p^4\ ^3P_1 — {}^3P_2\) | 319 | 3.03 | 655 |
| 4231.4 | 2.6 | — | Ni XII \(3s^2 3p^5\ ^2P_{1/2} — {}^2P_{1\,1/2}\) | 237 | 2.93 | 318 |
| 4359 | — | — | ?A XIV \(2s^2 2p\ ^2P_{1/2} — {}^2P_{1\,1/2}\) | 108 | 2.84 | 682 |
| 5116.03 | 4.3 | 2.2 | Ni XIII \(3s^2 3p^4\ ^3P_1 — {}^3P_2\) | 157 | 2.42 | 350 |
| 5302.86 | 100 | 100 | Fe XIV \(3s^2 3p\ ^2P_{1/2} — {}^2P_{1\,1/2}\) | 60 | 2.34 | 355 |
| 5536 | — | — | A X \(2s^2 2p^5\ ^2P_{1/2} — {}^2P_{1\,1/2}\) | 106 | 2.24 | 421 |
| 5694.42 | — | 1.2 | ?Ca XV \(2s^2 2p^2\ ^3P_1 — {}^3P_0\) | 95 | 2.18 | 814 |
| 6374.51 | 8.1 | 18 | Fe X \(3s^2 3p^5\ ^2P_{1/2} — {}^2P_{1\,1/2}\) | 69 | 1.94 | 233 |
| 6701.83 | 5.4 | 2.0 | Ni XV \(3s^2 3p^2\ ^3P_1 — {}^3P_0\) | 57 | 1.85 | 422 |
| 7059.62 | — | 2.2 | Fe XV \(3s\,3p\ ^3P_2 — {}^3P_1\) | — | 31.7 | 390 |
| 7891.94 | — | 13 | Fe XI \(3s^2 3p^4\ ^3P_1 — {}^3P_2\) | 44 | 1.57 | 261 |
| 8024.21 | — | 0.5 | Ni XV \(3s^2 3p^2\ ^3P_2 — {}^3P_1\) | 22 | 3.39 | 422 |
| 10 746.80 | — | 55 | Fe XIII \(3s^2 3p^2\ ^3P_1 — {}^3P_0\) | 14 | 1.15 | 325 |
| 10 797.95 | — | 35 | Fe XIII \(3s^2 3p^2\ ^3P_2 — {}^3P_1\) | 9.7 | 2.30 | 325 |
Note. E.P. — excitation potential; I.P. — ionization potential (refers to the preceding stage of ionization).
§ 4. On the Chemical Composition of the Solar Corona.
As a result of a whole series of investigations of the surface brightness of the corona, culminating in the work of Baumbach, values were obtained for the concentration of free electrons in the corona as functions of the coordinates. In the inner corona, as we have seen, \(N_e \simeq 10^8\ \mathrm{cm}^{-3}\).
From the physical point of view the corona must be an ideal plasma. The condition of quasineutrality \(N_e = N_i\) must be satisfied in it with a high degree of accuracy, since the dimensions of the corona are exceptionally large. One uncompensated elementary charge is enough for \(10^{10}\) compensated ones for the resulting volume charge not to escape observation. What, then, is the nature of the ions that compensate the negative charge due to the coronal electrons? Can they be the ions Fe, Ni, etc., considered above? Two works are devoted to this question—those of Kun-Huang \(^{27}\) and I. S. Shklovskii \(^{29}\). The matter reduces to determining the concentration of coronal ions from the observed absolute intensities of coronal lines.
We shall give the main points of Kun-Huang’s work. According to Waldmeier \(^{11}\), the intensity of the line \(\lambda = 5303\ \text{Å}\) at a distance of \(42''\) from the solar limb is equal to the intensity of the corresponding spectral region of the center of the Sun of width \(\delta\lambda = 6.75 \cdot 10^{-5}\ \text{Å}\), i.e. equal to
\[ \frac{2hC^2 \cdot \delta\lambda} {\lambda^5 \left(e^{\frac{h\nu}{kT}} - 1\right)} \qquad (T = 6000^\circ). \]
Then, evidently, the total number of photons emitted by a column of unit cross section (the axis of this column coincides with the line of sight) at the indicated distance from the limb of the Sun will be
\[ N = \frac{\delta\lambda \cdot 2hC^2 \cdot 4\pi} {\lambda^5 \cdot h\nu \left(e^{\frac{h\nu}{kT}} - 1\right)} = 7.1 \cdot 10^{14}\ \mathrm{cm}^{-2}\ \mathrm{sec}^{-1}. \]
Dividing \(N\) by the transition probability for the green line \(A = 60\ \mathrm{sec}^{-1}\), we obtain the number of Fe XIV ions in the initial state \({}^2P_{1/2}\) located in this column.
In order to pass to the volume concentration of Fe XIV ions, Kun-Huang uses Grotrian’s observations \(^{5}\), according to which the intensity of the coronal lines varies with distance in proportion to the intensity of the continuous radiation of the corona. For the intensity of this radiation Kun-Huang applies Turner’s law
\[ I = \mathrm{const}\cdot \rho^{-6}, \]
where \(\rho\) is the distance from the center of the solar disk. Assuming now
\[ N_i = \frac{C'}{r^n} \]
(where \(N_i\) is the concentration of Fe XIV ions in the co-
state \({}^3P_{1,\lambda}\), we shall have:
\[ \frac{N}{A} = \int_{-\infty}^{+\infty} \frac{C'\cdot d(\rho \tg \theta)}{\rho^n \sec^n \theta} = \frac{2C'}{\rho^{\,n-1}} \int_0^{\frac{\pi}{2}} \sec^{\,2-n}\theta\,d\theta = \frac{16}{15}\frac{C'}{\rho^{\,n-1}} . \]
It is clear from this that \(n=7\) and
\[ C'=\frac{N}{A}\frac{15}{16}\rho^{\,n-1}, \]
where \(\rho=7.26\cdot 10^{10}\ \mathrm{cm}\) \((\)this corresponds to an angular distance of \(42''\)\()\).
Knowing the intensities of the coronal lines relative to the line \(\lambda=5303\ \text{\AA}\), Kun-Huang determines the concentrations of the corresponding coronal ions in the initial states. In order to pass to the concentrations of these ions in the ground states, Kun-Huang proceeds as follows. The three obtained values of the concentration of Fe XIII ions in the states \({}^1D_2\), \({}^3P_1\), and \({}^3P_2\) Kun-Huang wishes to represent by the Boltzmann formula. It turns out that for this it is necessary that the electron temperature \(T_e\) be equal to \(20000^\circ\mathrm{C}\). With the temperature “obtained” in this way he determines the concentrations of all ions in the ground state, using the Boltzmann formula. Obviously, in this part of his work Kun-Huang committed a gross error.
Fig. 8.
Already Edlén, analyzing the role of collisions of the second kind in the emission of coronal ions, showed that it is impossible to represent the “populations” of the excited levels of coronal ions by the Boltzmann formula. The values obtained by Kun-Huang for the concentrations of ions in the ground states are therefore incorrect.
Fig. 9. Equivalent width of a coronal line according to Grotrian. \(I_0\) is the intensity of the continuous spectrum of the corona in the vicinity of the line.
In Shklovsky’s work the concentration of coronal ions in the ground state is determined directly. The radiation of a unit volume of the corona in a certain line is determined by formula (9). On the other hand, Grotrian expressed the intensities of coronal lines in equivalent widths of the continuous spectrum of the corona (see Fig. 9).
Since, according to Grotrian, the intensity of the monochromatic radiation of the corona is proportional to the intensity of its continuous radiation (caused by Thomson scattering), for a unit volume of the corona one may write [see formulas (9) and (10)]
\[ E_\lambda = \frac{\eta \cdot \nu \cdot A_1}{A_1 + A_2 + \ldots + B + C} = \frac{8 \cdot 54 \cdot 10^{-6} N_e \Omega' \cdot (2J+1) e^{-\frac{h\nu}{kT}} \cdot N_i} {T^{1/2}\left(\sum A_i + B + C\right)} = \Delta \lambda \cdot \sigma \cdot N_e \int I\,d\omega, \tag{11} \]
where \(\sigma\) is the coefficient of Thomson scattering. The integration extends over all solid angles. \(I_\omega\) is the intensity of the radiation of the solar photosphere in the direction of the corresponding solid angle \(\omega\). The equivalent widths \(\Delta\lambda\) obtained by Grotrian vary from \(27.5\,\text{\AA}\) \((\lambda = 5303\,\text{\AA})\) to \(0.3\,\text{\AA}\) \((\lambda = 4087\,\text{\AA})\). For the distance from the center of the Sun (entering into the expression \(\int I\,d\omega\)) the value \(r = 1.1R_{\odot}\) was adopted.
We give a table of the values of \(N_i\) obtained from formula (11).
Table VII
| ion | \(\lambda\) in Å | \(E_\lambda\), \(\dfrac{\text{erg}}{\text{cm}^3\,\text{sec}}\) | \(N_i\ \text{cm}^{-3}\) |
|---|---|---|---|
| Fe X | 6374 | \(1.3 \cdot 10^{-10}\) | 13 |
| Fe XI | 7892 | 15 | |
| Fe XI | 3986 | \(1.7 \cdot 10^{-10}\) | 5.4 |
| Fe XIII | 10747 | \(6.3 \cdot 10^{-10}\) | 37 |
| Fe XIV | 10798 | \(4.0 \cdot 10^{-10}\) | 40 |
| Fe XIV | 3388 | \(1.8 \cdot 10^{-10}\) | 20 |
| Ni XII | 5303 | \(1.2 \cdot 10^{-10}\) | 105.0 |
| Ni XIII | 4231 | \(4 \cdot 10^{-11}\) | 4.5 |
| Ni XV | 5116 | \(5.2 \cdot 10^{-11}\) | 4.6 |
| Ni XV | 5702 | \(4.3 \cdot 10^{-11}\) | 2.6 |
| Ni XVI | 3601 | \(6.2 \cdot 10^{-11}\) | 1.8 |
As is evident from this table, the relative amount of Ni and Fe in the corona is approximately the same as in meteorites. The values of \(N_i\) for any ion, determined from different lines belonging to it, differ noticeably from one another. Evidently, the main reason here is the inaccuracy of the Menzel-Hebb formula (10). The data of Table VII must be understood as values averaged in space and in time, since the corona is not, generally speaking, a static formation.
In any case, the concentration of Fe and Ni ions in the corona proves to be quite insufficient to neutralize the coronal electrons. The ratio of the concentration of free electrons
and the concentration of iron in the corona of the order of \(10^5\), whereas in the solar atmosphere, according to Strömgren \(^{30}\), the ratio of the concentration of hydrogen to iron is of the order of \(10^4\). Unsöld obtained approximately the same value from an analysis of the atmosphere of the star \(\tau\) Scorpii \(^{31}\). It is therefore natural to assume that the ions neutralizing the coronal electrons are protons. In this case, however, a difficulty arises, since the emission lines of the Balmer series are not observed in the corona. These lines should arise in recombinations of electrons to excited levels and subsequent cascade transitions to the ground state. Assuming that the proton concentration \(N_i = N_e\), Shklovsky \(^{29}\) calculated the equivalent width of various lines of the Balmer series as a function of \(T_e\) and of the distance from the center of the solar disk \(\rho\). It turns out that, if at \(T_e = 20\,000^\circ\) the \(H_\beta\) line would have an equivalent width \(\Delta\lambda = 6.9\,\text{\AA}\) and would, of course, be observable. Even at \(T_e = 320\,000^\circ\) its \(\Delta\lambda = 0.3\,\text{\AA}\)—the same as that of the weak coronal lines in this region of the spectrum. In this connection, however, the following should be noted. As Waldmeier \(^{11}\) and Lyot \(^{32}\) have shown (see above), the emission lines of the corona have profiles determined by the Doppler effect. If the corresponding velocities are of thermal (and not turbulent) origin, then it is clear that the hydrogen lines will have a half-width
\[ \sqrt{\frac{M_{\mathrm{Fe}}}{M_{\mathrm{H}}}} \simeq 7 \]
times greater than the iron lines. Such broad lines, if they are weak (i.e. if \(\Delta\lambda\) is small), may escape observation.
It is evident that the fact that the Balmer lines are not observed in the corona is a new, independent confirmation of the existence in the corona of a very high electron temperature (of the order of hundreds of thousands of degrees).
As for such abundant elements as He, C, N, O, etc., as Edlén \(^{19}\) pointed out, under the conditions existing in the corona they cannot give either forbidden or permitted lines. In summary, it should be said that the chemical composition of the corona apparently does not differ very greatly from the composition of the lower layers of the solar atmosphere, meteorites, nebulae, and the majority of other cosmic objects.
§ 5. RADIATION OF THE SOLAR CORONA BY VERY HARD
RADIATION AND RADIO WAVES.
A necessary consequence of Edlén’s identification of the coronal lines must be the presence in the coronal spectrum of very hard radiation. This question is the subject of a paper by I. S. Shklovsky \(^{33}\). The existence of the indicated radiation can be proved from the following considerations. The coronal line \(\lambda = 7059\,\text{\AA}\) is emitted in transitions between sublevels of the second quantum state of the ion Fe XV (see above). The ground state of this ion is the singlet \(3s^2\,{}^1S_0\). The second
state—the triplet \(3s3p\left\{\begin{array}{l}P_1\\ P_2\\ P_0\end{array}\right.\). The sublevels \(P_0\) and \(P_2\) are metastable.
In the transition \(P_2—P_1\) the line \(\lambda 7059\) Å is emitted. But, finding itself in the state \(P_1\), the Fe XV ion must necessarily pass into the state \(S_0\), emitting thereby the line \(\lambda=424\) Å. The lower limit of the intensity of this line \(I_1\) is determined from the condition that the number of transitions \(P_1—S_0\) is no smaller than the number of transitions \(P_2—P_1\). Then \(\dfrac{I_1}{I_2}=\dfrac{7059}{424}=17\), where \(I_2\) is the intensity of the line \(\lambda=7059\) Å, constituting \(2\%\) of the intensity of the line \(\lambda=5303\) Å. Thus, the intensity of the line \(\lambda=424\) Å is of the same order as the intensity of the brightest, green, coronal line. One more example may be given. The transition Fe XIII \(3s^2 3p^2\,{}^1D_2—{}^3P_2\) gives an intense coronal line \(\lambda=3388\) Å. But from the same level \({}^1D_2\) a transition to the level \({}^3P_1\) of the same configuration is also possible. In this case the line \(\lambda=2580\) Å will be emitted. Let the intensity of the latter line be equal to \(I'_1\), and the intensity of the line \(\lambda=3388\) Å to \(I'_2\); then \(\dfrac{I'_1}{I'_2}=\dfrac{3388}{2580}\dfrac{A_1}{A_2}\), where \(A_1\) and \(A_2\) are the transition probabilities of these lines, calculated by Edlén\({}^{19}\). Hence \(I'_1=1.08\,I'_2\). On the basis of Edlén’s original works on the spectra of strongly ionized elements\({}^{18}\), it is possible, to be sure, to compile a very incomplete list of ultraviolet lines present in the spectrum of the corona.
Table VIII
| Fe X | Fe X | Fe XV | Fe XV | Fe X \({}^2D—{}^2P\) | Fe X \({}^2D—{}^2P\) |
|---|---|---|---|---|---|
| Transition | \(\lambda\) in Å | Transition | \(\lambda\) in Å | \(\{94\ \text{Å}\) \(94.2\) \(95.5\}\) |
\(\{94\ \text{Å}\) \(94.2\) \(95.5\}\) |
| \({}^1S_0—{}^3P_1\) | 1479 | \({}^3P_1—{}^1S_0\) | 424 | Ni XIII \({}^3D_2—{}^3P_2\) | 2124 Å |
| \({}^1D_2—{}^3P_1\) | 2602 | \({}^3D_2—{}^3P_1\) | 228 | Ni XV \({}^1D_2—{}^3P_2\) | 2820 |
| \({}^3S_0—{}^3P_1\) | 90 | \({}^3F_4—{}^3D_3\) | 1250 | Ni XV \({}^1D_2—{}^3P_1\) | 2087 |
| \({}^3D_3—{}^3P_2\) | 87 | \({}^3F_4—{}^3D_3\) | 154 |
The intensity of this hard radiation is, at least, equal to the intensity of the monochromatic radiation of the corona emitted in the accessible part of the spectrum. This circumstance can be explained by the very high electron temperature of the corona. If \(T_e=350\,000^\circ\), then the mean kinetic energy of the free electrons will be equal to 45 volts, which exceeds the resonance potential of Fe ions. Consequently, the number of excitations by electron impact of the levels of the second and even third configurations will be of the same order as the number of excitations of the sublevels of the ground configuration, in transitions between which the observed coronal lines are emitted.
It can be calculated that the intensity of hard coronal radiation exceeds the intensity of the continuous radiation of the photosphere, with wavelength shorter than \(\lambda_0\), by \(10^9\) times if \(\lambda_0 = 504 \,\text{\AA}\), and by \(10^{34}\) times if \(\lambda_0 = 228 \,\text{\AA}\). In this it is assumed that the Sun radiates in the far ultraviolet as an absolutely black body with temperature \(T = 5740^\circ\), while the intensity of the hard radiation of the corona is equal to the intensity of the observed coronal lines. As a consequence of the foregoing, it follows that in these regions of the spectrum \((\lambda < 800 \,\text{\AA})\) the integral spectrum of the Sun must be a line spectrum.
This hard radiation must affect the state of ionization of the lower, chromospheric layers of the solar atmosphere[^33]. Apparently this radiation must also affect the state of the Earth’s ionosphere. However, no work in this direction has yet been done.
Quite recently, the works of Reber[^34], Southworth[^35], and Appleton[^36] have established the presence of radio emission coming from the Sun. Reber investigated radiation with wavelength \(\lambda = 187 \,\text{cm}\) and found that its intensity \(I^* = 3 \cdot 10^{-17}\) CGS, which corresponds approximately to the intensity of thermal radiation at \(T = 3500^\circ\). Southworth investigated the radio emission of the Sun in the range \(1\)—\(10 \,\text{cm}\). He showed that the intensity of this radiation can be represented by the Rayleigh–Jeans formula with \(T = 6000^\circ\). Theoretical analysis of this effect is the subject of the works of V. L. Ginzburg and I. S. Shklovsky[^37]. The latter, analyzing the conditions of absorption of long-wave radiation in the solar atmosphere, showed that, whereas centimeter waves are generated by the chromosphere, radiation in the meter range must be generated chiefly by the outer corona. If the electron temperature of the latter were as high as in the inner corona, the intensity measured by Reber would be tens of times greater. Consequently, it must be assumed that the electron temperature of the outer corona is comparatively low, of the order of \(3500^\circ\). Further investigations in this direction are highly desirable, since they may yield valuable information about the nature of the outer corona. V. L. Ginzburg, too, basically arrived at the same results.
Appleton[^36] points out that at times, chiefly in epochs of maximum sunspot activity, radio observations made it possible to detect radiation from the Sun with wavelengths from 7 to 30 meters. The intensity of this radiation exceeded by \(10^4\) times the corresponding intensity of equilibrium radiation at temperature \(T = 6000^\circ\). Usually this phenomenon preceded strong disturbances in the ionosphere.
I. S. Shklovsky[^37] believes that in this case there occur natural oscillations of the plasma of the outer corona. The basis for this is the coincidence of the frequency of the natural oscillations, determined by Langmuir’s formula[^38]
\[ \omega_L = \sqrt{\frac{4\pi e^2 N_e}{m}} \]
with the observed ...
amplitude frequency. These oscillations can be excited by streams of ions moving through the plasma with superthermal velocities. The calculation performed shows that the magnitude of the flux of these ions required to excite oscillations of the observed intensity lies within reasonable limits.
Thus, radio engineering has provided a new, very powerful method for investigating the upper layers of the solar atmosphere. The future radio service of the Sun, while solving a number of fundamental problems of solar physics, will at the same time apparently also have great practical significance, creating a new methodology for forecasting geomagnetic and ionospheric disturbances.
§ 6. THE NATURE OF THE SOLAR CORONA
The well-known astrophysicist and spectroscopist Swings[^16] recently pointed out that it is necessary to distinguish between the problem of “coronium” and the problem of the corona. If the first problem, thanks to Edlén’s brilliant work, is now essentially solved, the latter is still very far from solution.
The interpretation of the principal observational results encounters serious difficulties. Let us indicate some of them:
1) An anomalously low density gradient in the corona. The density of coronal matter is determined by formula (5). (Since the concentration of the most abundant ions (protons) in the corona must be equal to \(N_e\).) If the corona were in equilibrium under the action of the Sun’s gravitational force and the pressure gradient, then at a coronal temperature of the order of the Sun’s boundary temperature (\(4800^\circ\)) the law of density distribution would be \(\rho = \rho_0 e^{-\alpha(r-1)}\), where \(\alpha = \dfrac{\mu g}{kT} = 4.77 \cdot 10^3\) (the unit of distance being taken as the solar radius). In the inner corona, according to (11), \(\rho = \rho_0 r^{-16}\), whence \(\alpha = \dfrac{16 \lg r}{r - 1} = 6.6\) (\(r = 1.1\)). As we see, the discrepancy is monstrously large.
2) An anomalously high degree of ionization in the corona. It may be said that no object in astrophysics (with the exception of stellar cores) possesses such a degree of ionization. In the atmospheres of ordinary stars, twice-ionized elements are encountered. In some peculiar stars (novae, nova-like stars, Wolf–Rayet stars) still higher stages of ionization are also encountered—N V, O VI, Fe VI, Fe VII. It must be mentioned that two stars have shown emission of coronal lines. These are the nova-like RS Ophiuchi (in 1932 and 1942) and T Pyxidis. However, they emitted these lines for a very short time.
A vivid idea of the degree of ionization in the corona, after Waldmeier[^11], can be formed in the following way.
Let us write Saha’s ionization formula in the form:
\[ \lg \frac{n^*}{n_0} = -\chi \cdot \frac{5040}{T} + \frac{5}{2}\lg T - 0.48 - \lg P_e, \tag{12} \]
where \(\frac{n^*}{n_0}\) is the degree of ionization, \(P_e\) is the electron pressure, \(\chi\) is the ionization potential.
Let us denote the quantity \(\chi \frac{5040}{T}\) by \(\Phi(\chi)\). Then we shall have the following graph (Fig. 10).
According to Waldmeier,\(^{11}\) the observed degree of ionization of the corona can be described by Saha’s formula with \(T = 240\,000^\circ\).
3) The unusually large width of the coronal lines. According to Waldmeier (see above), the Doppler velocities for the line \(\lambda = 5303\ \text{\AA}\) vary within the limits from 37 to 19 km/sec. Lyot obtained approximately the same result. If these velocities are assumed to be thermal in nature, then the kinetic temperature of Fe ions must be equal to \(1.4 \cdot 10^6\) degrees. However, the possibility is not excluded that the Doppler velocities determining the contours of the coronal lines may, partially or completely, have a turbulent character. It is known that in the underlying chromosphere the contours of many lines of the flare spectrum are explained by turbulence. These velocities reach 15 km/sec (see \(^{39}\)).
Fig. 10. Anomalous ionization in the chromosphere and corona (after Unsöld and Waldmeier).
Waldmeier tried to explain the anomalous distribution of densities in the corona by the influence of turbulence. If turbulent velocities are superposed on thermal ones, then
\[ a = \frac{2g}{v_t^2 + v_T^2}, \]
where \(v_t\) is the mean turbulent velocity, which Waldmeier assumed equal to 28 km/sec. Taking the (kinetic) temperature of the corona to be \(4800^\circ\), he obtained \(a = 8.52\), which approximately agrees with the observed value. However, he had made a gross arithmetical error (this was pointed out by A. Deutsch\(^{40}\)). In reality \(a\) comes out equal to 486. This means that the density distribution in the corona cannot be explained by the effect of turbulence.
Alfvén\(^{41}\) assumed that the density distribution in the corona is determined by its exceptionally high kinetic temperature. The condition of equilibrium is written:
\[ \frac{dP}{R_\odot dr} = - \frac{g_\odot N_e m_H}{r^2}; \qquad P = \frac{4}{3} N_e E; \qquad E = \frac{3}{2} kT_e, \tag{13} \]
where \(g_\odot = 2.74 \cdot 10^4\ \text{cm sec}^{-2}\) is the acceleration of gravity at the solar surface, \(m_H = 1.66 \cdot 10^{-24}\ \text{g}\) is the mass of the hydrogen atom (the element most abundant in the corona).
From (13) one can obtain:
\[ \frac{d}{dr}\left(\frac{E}{E_0}\right)+\frac{1}{N_e}\frac{dN_e}{dr}\cdot\frac{E}{E_0}=-\frac{1}{r^2}, \]
\[ E_0=\frac{3}{4}\,g_{\odot}R_{\odot}\cdot m_H=1.49\cdot10^3\ \text{volts}, \]
whence
\[ \frac{E}{E_0}=-\frac{1}{N_e}\int\frac{N_e}{r^2}\,dr. \]
Taking \(N_e\) from (5), Alfvén obtains the following graph for \(\dfrac{E}{E_0}\) (Fig. 11).
As can be seen, \(E\), and consequently also \(T_e\), changes comparatively little in the corona. In the region \(1.2<r<3\), \(E\simeq180\) volts, \(T_e\simeq1.3\cdot10^6\) degrees.
Fig. 11. Electron temperature of the corona as a function of distance from the center of the Sun, determined from the density gradient (according to Alfvén).
In addition to gravitation and the pressure gradient, Alfvén takes into account the force due to the existence in the corona of a nonuniform magnetic field \(H\). Under coronal conditions the radius of curvature of a charged particle moving in the general magnetic field of the Sun is much smaller than the mean free path. Then for the indicated force Alfvén gives the expression\({}^{42}\):
\[ f_m=-\frac{\frac{1}{2}mV_\perp^2}{H}\cdot\frac{dH}{dz}, \]
where \(V_\perp\) is the component of the particle velocity perpendicular to the magnetic field. Allowance for this force leads to a somewhat smaller value of the kinetic temperature required to explain the observed density gradient. Thus, for example,
for \(r = 1.2\), \(T_s = 840\,000^\circ\). Let us note, however, that the data on the magnitude, and still more on the gradient, of the magnetic field in the corona are still very uncertain. The central problem of the inner corona is to determine the reason for the existence in it of atoms ionized to an extremely high degree. At the present time there already exist several theories explaining this phenomenon.
The first attempt to explain Edlén’s discovery belongs to Russell[^43], who suggested that the coronal ions are due to the fall of meteors onto the Sun. The basis for such a supposition was the circumstance that both in the corona and in meteorites the most abundant elements are such as iron and nickel. However, as was indicated above, in reality the most abundant element in the corona is apparently hydrogen. Moreover, as Shakha and Swings[^19] pointed out, if the coronal ions were of meteoritic origin, their velocities would be of the order of \(600\ \mathrm{km/sec}\) (the parabolic velocity at the surface of the Sun is \(622\ \mathrm{km/sec}\)). In reality the velocities of the coronal ions are much smaller—of the order of \(20\)–\(40\ \mathrm{km/sec}\). Braking of the ions (of meteoritic origin) does not explain this discrepancy, since in that case the velocities of the ions should decrease as they approach the solar disk, whereas in reality, according to Waldmeier, they increase. Finally, the clearly expressed connection of the radiation of coronal ions with various formations on the solar surface, established by the work of Waldmeier and Lyot, makes Russell’s hypothesis untenable. For the fall of meteors onto the solar surface is a sporadic phenomenon, in no way connected with phenomena on the solar surface. N. N. Pariiskii pointed out this last circumstance.
A very original theory of the origin of highly ionized atoms in the corona was given by Shakha[^44]. He considers physically absurd the idea of the existence in the corona of a very high temperature. According to Shakha, the corona must in no case be regarded as a stationary or quasi-stationary formation. The corona is thought of as a stream of rapidly moving particles formed in deeper layers of the solar atmosphere. Coronal matter is continuously “renewed.”
Shakha believes that nuclear reactions of certain types occur not only in the interior of the Sun (where they serve as a source of energy), but also in the outer layers of the solar atmosphere. In particular, the presence in the spectrum of the chromosphere of the lines He and He\(^+\) he explains by nuclear reactions with the emission of \(\alpha\)-particles. According to his theory, somewhere at the boundary of the reversing layer and the chromosphere there occur nuclear reactions analogous to the well-known fission of uranium upon neutron capture. Shakha admits the existence, alongside asymmetric binary fission of uranium, of its fission into 3–4 and even a larger number of fragments. He draws attention to the circumstance that the initial velocities of the fragments exceed the velocities of their electrons
in the outer shells. This leads to the fragments, as they begin their path in the chromosphere, losing up to 15 electrons, i.e., becoming strongly ionized.
Saha showed that, in the case of triple and quadruple fission, the fragments, after β-transformations, become stable isotopes of elements from Ca to Ni, moving with kinetic energy of the order of 60 MeV. In this case the atom Fe will correspond to the configuration \(1s^2 2s^2 2p^6 3s\). In calculating the braking of these ions Saha used Bethe’s formula. Basically, the braking will obviously occur on hydrogen, owing to the exceptional abundance of the latter. For complete braking of the fragments, \(6.3 \cdot 10^{21}\ \mathrm{cm}^{-2}\) hydrogen atoms above a square centimeter are needed. On the other hand, the number of hydrogen atoms above 1 square centimeter of the base of the reversing layer, according to Unsöld, is \(1.8 \cdot 10^{22}\ \mathrm{cm}^{-2}\). It follows from this that only those fragments can penetrate into the corona which were “born” in the very upper layers of the reversing layer. In their motion through the solar atmosphere the fragments ionize chromospheric atoms. The electrons torn from the latter enter (with high velocities) the corona. Such is the origin of the coronal electrons.
When the fragments enter the corona, their velocities have time to fall to \(40\ \mathrm{km/sec}\) and then decrease still further (in accordance with Waldmeier’s results). At the same time they capture electrons into various levels, turning into Fe XIV, Fe XIII, etc., whose emission we observe. In principle, in the outer corona further electron captures could lead to the formation of Fe IX ... Fe I; however, as Saha indicates, the probabilities of recombination to the \(3d\) levels are very small. Such, in general outline, is Saha’s theory.
However, as it seems to us, this theory encounters serious difficulties and, apparently, is hardly in accord with reality.
Although the triple and quadruple fissions proposed by Saha have not been observed under laboratory conditions, they are energetically quite possible. Up to now uranium lines in the spectrum of the Sun have not yet been observed, but weak thorium lines have been found. The main difficulty of the theory is hardly not the necessity of assuming that, in the upper layers of the reversing layer, the concentration of free neutrons must be exceptionally large.
Indeed, let \(N_1\) be the concentration of Fe ions in the corona, and \(V_1\) their velocity. Then, according to Saha, the number of fragments entering the corona per unit time is equal to \(4\pi R_\odot^2 N_1 V_1 = Z_1\), where the inner radius of the corona is taken equal to the radius of the Sun \(R_\odot\). On the other hand, the number of uranium fissions in the reversing layer and in the chromosphere for which the fragments enter the corona will be equal to
\[ Z_2 = 4\pi R_\odot^2 \int_{R_1}^{R_2} N_2 n \overline{V\sigma}\, dR, \]
where \(R_1\) is the radius of the top of the reversing layer,
$R_2$ is the inner radius of the corona, $N_2(R)$ is the concentration of uranium, $n(R)$ is the concentration of neutrons, $\overline V$ is their velocity, $\overline \sigma$ is the effective fission cross section. Putting $Z_1=Z_2$, we obtain:
\[ N_1 V_1=\int_{R_1}^{R_2} N_2 \overline V n\overline \sigma\, dR =\bar n\cdot \overline{N}_2\cdot \overline V\overline \sigma\cdot (R_2-R_1), \]
$N_1 \simeq 10^3\ \mathrm{cm}^{-3}$ (see Table VII), $V_1=4\cdot 10^6\ \mathrm{cm/sec}$, $R_2-R_1 \simeq 5\cdot 10^9\ \mathrm{cm}$, $\bar\sigma\simeq 10^{-24}\ \mathrm{cm}^2$.
In the case of fission of $U_{235}$ under the influence of slow (thermal) neutrons, $V \simeq 10^5\ \mathrm{cm/sec}$. If we assume that the concentration of $U_{235}$ in the upper layers of the rotating layer is equal to the concentration of all metals (which is plainly absurd), $\overline N_2=10^9\ \mathrm{cm}^{-3}$. Then $\bar n=10^{11}\ \mathrm{cm}^{-3}$, i.e., approximately equal to the concentration of all atoms in the upper part of the rotating layer! If fission occurs through the capture of fast neutrons, then, under the same assumptions, $\bar n=10^7\ \mathrm{cm}^{-3}$. Of course, such neutron concentrations are absurd.
Against Schach’s theory one may also raise the following objection. If the mean free path of some fast particles is $l$, then the dispersion of this quantity, as a rule, is equal to $1$–$2\%$. (The phenomenon of “range scatter,” “Stragling.”) Consequently, in order to slow down the fragments, in Schach’s case, $6.3\cdot 10^{21}\div 10^{20}$ atoms (ions) of hydrogen per square centimeter are needed. Since above a unit area at the base of the corona there are only $4\cdot 10^{18}$ hydrogen ions, this means that the entire corona lies in the region of range scatter. This would inevitably lead to the extent of the inner corona (where the radiation of coronal lines is observed) being tens of times greater than that observed.
Finally, it is necessary to point out the following circumstance. Schach categorically denies the presence of any stationarity (or quasi-stationarity) in the corona. If the concept of a static corona is untenable, then Schach’s concept represents another extreme. Schach rejects the possibility of the existence of a Maxwellian distribution of velocities among coronal particles. But from general physical considerations it is difficult to imagine an enormous space filled with a large number of corpuscles, interacting in the strongest manner (according to Coulomb’s law), yet without a Maxwellian distribution of velocities. The length of relaxation, determined in any way (see, for example, $^{45}$), is a thousand times smaller than its extent for the corona.
In this connection it is necessary to recall Lyot’s observations, which showed that for sufficiently large space-time intervals the corona may be regarded as a quasi-stationary formation.
The hypothesis concerning the origin of coronal matter, proposed by Menzel $^{46}$, deserves attention. According to this hypothesis, coro-
coronal matter enters the upper layers of the solar atmosphere through a kind of “crevices” on the surface of the Sun from its depths. As Menzel supposes, these “crevices” (“crevices”) are found chiefly in the region of spots, since, according to Waldmeier, the corona is especially bright above spots. Thus, the corona is to some extent analogous to terrestrial volcanoes.
Very close to Menzel’s hypothesis is the theory of the Indian investigators Das and Rao1. These authors, like Menzel, suppose that coronal matter comes from the solar depths, where the conditions of temperature, pressure, and density are such that elements like iron are deprived of their outer electrons. For certain reasons, possibly as a result of jumps in light pressure, equilibrium in these deep layers is disturbed, and a mass of very hot gas begins to rise upward.
If the velocity of such “convection” is small, then the state of the gas (temperature, ionization, etc.) at each level will be determined by the corresponding conditions of local thermodynamic equilibrium. However, if the velocity of convection exceeds a certain critical value, then the degree of ionization of the rising mass of gas will substantially exceed the degree of ionization of the surrounding matter. Eddington2 was the first to point out this circumstance. The method of calculating the “critical velocity” is essentially as follows. Consider two layers \(B\) and \(A\) and a column of matter rising between them. The level \(B\) lies deeper. The temperatures corresponding to these levels are \(T_B\) and \(T_A\). A certain atom, under the conditions prevailing at level \(B\), is ionized \(p\) times, and at level \(A\), \(p - 1\) times. The principal ionizer is radiation. Let \(n_\phi\) be the concentration of photons with frequency \(\nu \geq \nu_0\), where \(\nu_0\) is the ionization frequency of the element under consideration. Then the number of photons passing upward through unit surface of the lower base of the column \(B\) will be equal to \(\frac{1}{4} n_{\phi B} \cdot c\); the number of photons passing through unit surface at the upper base of the column \(A\) in the same direction is equal to \(\frac{1}{4} n_{\phi A} \cdot c\), where \(c\) is the velocity of light. One can determine the number of atoms under consideration \(N\) in a column of unit cross section between \(B\) and \(A\). Evidently, the number of ionizations in this column per unit time is equal to \(\frac{1}{4} c (n_{\phi B} - n_{\phi A})\). The time required for the establishment of ionization equilibrium, in order of magnitude, will be equal to
\[ \frac{4N}{c(n_{\phi B} - n_{\phi A})}, \]
and the “critical velocity” \(V_{\mathrm{cr}}\) is
\[ V_{\mathrm{cr}} = \frac{(n_{\phi B} - n_{\phi A}) \cdot d \cdot c}{4N}, \]
where \(d\) is the distance between \(A\) and \(B\).
Thus, invoking the theory of the internal structure of the Sun (Eddington’s model), Das and Rao calculated that, in order to
for Fe ions to enter the corona, they must begin their ascent from a depth of 26,000 kilometers beneath the photosphere, and the “critical velocity” of convection must exceed 300 kilometers per second.
This velocity seems too great. The turbulent velocities in the chromosphere and corona, according to observations, do not exceed 30–40 km/sec. Further development of this theory is necessary in connection with modern investigations of convection and turbulence in the solar atmosphere.
The next theory of the solar corona belongs to Alfvén3. Unlike Shakh, Dasa, and Rao, Alfvén considers that the fast corpuscles observed in the corona have velocities of a thermal character. Thus it makes sense to speak of the kinetic temperature of the corona.
According to Alfvén, the “heater” of the corona is located in the chromosphere, and in this respect Alfvén’s theory is formally analogous to Shakh’s theory. But the nature of the “heaters” is entirely different in the two theories. In an earlier paper4, Alfvén indicated the possibility of the formation in the solar chromosphere of large potential differences (up to \(10^7\) volts) as a consequence of vortical motions of ionized gases in the magnetic field of spots. This idea had been expressed by many authors before Alfvén, see5. By this mechanism Alfvén explains the forms of prominences. Alfvén assumes that charged particles, passing through such large potential differences, acquire enormous energy and, entering the corona, serve as “heaters” of the latter. Thus the corona is “heated” by prominences.
Alfvén considers the following scheme: in a column of unit cross-section, from the surface of the photosphere to some height \(h\), there is produced each second an amount of energy equal to \(\varepsilon \frac{\mathrm{erg}}{\mathrm{cm}^2\,\mathrm{sec}}\).
The temperature distribution above the surface of the photosphere is sought. Let \(R\) be the distance from some point of the solar atmosphere to the center. For \(R - R_{\odot} < h\), Alfvén writes: \(\varepsilon_1 = \varkappa \frac{dT}{dR}\), where \(\varepsilon_1\) is the energy passing in one second through a square centimeter in the direction toward the solar surface (the coefficient of thermal conductivity
\[ \varkappa = 0.6\, \frac{1}{\pi c^2}\, \frac{K^{3/2}}{m^{1/2}}\, T^{5/2}. \]
Consequently, for \(R - R_{\odot} < h\),
\[ T = \left[ \frac{R - R_{\odot}}{h}\left(T_h^{7/2} - T_1^{7/2}\right) + T_1^{7/2} \right]^{2/7}, \]
where \(T_1\) and \(T_h\) are the temperatures at \(R = R_{\odot}\) and \(R = R_{\odot} + h\). For \(R - R_{\odot} > h\) it is necessary to take into account the curvature of the coronal layers. The corresponding equation is written as
\[ \varepsilon_2 = \varkappa \left(\frac{R}{R_{\odot}+h}\right)^2 \frac{dT}{dR}, \qquad T = T_h \left(\frac{R}{R_{\odot}+h}\right)^{-2/7}. \]
We present the graph of the temperature distribution in the corona according to Alfvén (Fig. 12).
The course of the curve qualitatively coincides with the graph in Fig. 11. In order that \(T_e\) be equal to \(10^6\) degrees, it is necessary that \(\varepsilon=\varepsilon_1+\varepsilon_2=2\cdot 10^5\) erg·cm\(^{-2}\)·sec\(^{-1}\).
This energy amounts to only \(10^{-5}\) of the energy radiated by the Sun. In Alfvén’s theory the very mechanism of formation of fast corpuscles in the chromosphere and prominences is not entirely clear.
Fig. 12. Electron temperature of the corona as a function of distance from the center of the Sun, theoretically calculated by Alfvén.
Undoubtedly, chromospheric matter continuously penetrates into the corona and dissipates in it. This is indicated by direct observations[^12]. However, if very fast corpuscles arise in the chromosphere, it is not clear why its temperature is comparatively low (of the order of \(10000^\circ\)[^51]), and why highly ionized atoms are not observed in it.
If potential differences of the order of \(10^7\) volts can arise in the chromosphere, this still does not mean that charged particles will be accelerated to large energy values. It should not be forgotten that here we are dealing with the motion of charge in a gas. On the basis of the general ideas of the physics of gas discharge, the charges will move with a constant velocity determined by the mobility of the ions: \(u=b\cdot E\) (where \(u\) is the velocity of “drift” of the charges, \(b\) is the mobility, \(E\) is the electric-field strength).
I. S. Shklovskii proposed a theory of the corona very different from all those considered above[^52]. Whereas all the theories discussed seek a “heater” of the corona outside it, Shklovskii believes that the “heater” is localized in the corona itself.
The author regards the corona (and the chromosphere) as a discharge plasma. It is known that the electron temperature of a plasma under terrestrial experimental conditions often reaches many tens of thousands of degrees.
The mechanism of plasma heating is the release of Joule heat, due to the presence in the conducting plasma of a certain macroscopic electric field \(E\). The amount of heat released per unit volume per unit time is \(W=\lambda\cdot E^2\), where \(\lambda\) is the electrical-conductivity coefficient of the ionized gas. The (kinetic) temperature of the plasma of the corona and chromosphere is determined as the solution of the heat-conduction equation:
\[ 2N_e k \frac{\partial T_e}{\partial t} = \chi \Delta T_e + W - E, \]
where \(\Delta\) is the Laplace operator, \(E\) is the amount of energy leaving a unit volume of plasma per unit time. \(E\) is determined by inelastic collisions of electrons with coronal ions, and also by recombinations of electrons with ions. Taking into account all the mechanisms leading to the “cooling” of the plasma of the corona, I. S. Shklovsky showed that, in the stationary case, in order to maintain in the corona a kinetic temperature at the level of \(10^6\) degrees, the electric field in it must be astonishingly small—of the order of \(10^{-9}\ \frac{\text{volt}}{\text{cm}}\).
The physical meaning of this paradoxical result lies in the exceptionally weak capacity of the corona to give off heat into outer space by radiation. This latter property of the corona is due to its negligible density. Meanwhile, the release of Joule heat \(W\) in a strongly ionized gas depends almost not at all on density. This means that one and the same weak electric field has absolutely no effect on the energy balance of the chromosphere and radically affects the energy balance of the corona. The study shows that the plasma of the corona is “isothermal” in the sense that the electron temperature is equal to the ion temperature. The weak vortex electric field in the corona is apparently caused by turbulent motion of coronal matter in the general magnetic field of the Sun or in the field of spots. Variations of the Sun’s magnetic field can also cause the appearance of weak electric fields in the corona. The connection of coronal phenomena with phenomena in the underlying layers of the solar atmosphere possibly has an electromagnetic nature. In addition, the cause of such a connection may be streams of rapidly charged corpuscles breaking out from comparatively deep layers of the solar atmosphere (cf. Waldmeier’s “C” regions).
In another paper\(^53\) Shklovsky investigates the question of the nature of the anomalously high ionization in the corona and shows that the Saha formula cannot be applied to the corona.
Indeed, the Saha formula assumes a state of local thermodynamic equilibrium. If there is a sharp deviation from the state of thermodynamic equilibrium, one must proceed (in the stationary case) from the equation of ionization equilibrium, expressing the equality of the number of ionization acts to the number of recombination acts
(ambipolar diffusion, which plays a decisive role in neutralization processes under gas-discharge conditions, is insignificant for astrophysical objects, and triple collisions, owing to the very low density, may be neglected). In the corona the principal mechanism of ionization is inelastic collision with coronal electrons. In this case the degree of ionization does not depend on the concentration of free electrons (since the number of ionizations and the number of recombinations are proportional to $N_e$). The concentrations of iron in various degrees of ionization in the stationary case are determined as the solution of a certain system of equations. The degree of ionization depends strongly on $T_e$; to explain the observed degree of ionization one must assume $T_e$ of the order of $10^6$ degrees, which is in agreement with the values of $T_e$ found from other characteristics of the corona. In addition to collisions with coronal electrons, collisions with fast heavy corpuscles flying out from the Sun may have some significance for the ionization of coronal matter. The calculations were carried out on the basis of Bethe’s formulas[^54] for ionization by impact and of Stückelberg–Morse[^55] for the capture of electrons by strongly ionized atoms.
Since the corona cannot be regarded as a completely stationary formation, the time required for ionization equilibrium to be established in it was investigated. It was found that this time is of the order of days. In this connection we note that, according to Waldmeier and Lyot, the corona can remain practically unchanged over a number of days. Consequently, in a first approximation the corona may be regarded as a quasi-stationary formation.
CONCLUSION.
In recent years great successes have been achieved in the study of the inner corona. But an enormous number of problems, both experimental and theoretical in character, still await solution. Meanwhile, the study of the nature of the solar corona is not only of great theoretical interest. Apparently, in the corona there are localized regions of the Sun whose radiation (corpuscular and radiative) exerts such a great influence on a number of geophysical processes. Despite the fact that the corona has a negligible mass (the entire mass of the corona amounts to only 0.001 of the mass of the Earth’s atmosphere!), this influence proves possible owing to the exceptional conditions prevailing in it.
Unfortunately, recent years have given almost nothing essential in the knowledge of the nature of the outer corona. Perhaps the greatest “coronal riddle” at the present time is the question of the nature of the Fraunhofer spectrum of the outer corona.
Recently N. N. Pariiskii developed a theory according to which the “Fraunhofer component” of the outer corona (see [^6]) is a phe-
...an apparent one, caused by the diffraction of sunlight at the lunar edge during total eclipses. However, it turned out that the intensity of the light produced by diffraction is too small. The work of N. N. Pariiskii is very valuable, since it undoubtedly proves the coronal nature of the Fraunhofer component.
In this connection let us recall that in the eighteenth century the question of the solar origin of the corona itself was long debated.
Spectroscopic studies of the outer corona must be given an important place during eclipse observations, since it is as yet impossible to observe the outer corona outside an eclipse.
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