RADIO EMISSION OF THE SUN AND THE GALAXY

V. L. Ginzburg

INTRODUCTION

In recent years (1944–1946) the emission of the Sun in the radio-frequency range has been discovered and has begun to be intensively studied^{1–12, 40}. At the same time, interest has increased in the radio emission of the Galaxy, discovered somewhat earlier^{13–17, 1}. In a number of works the question of radio emission has also been subjected to theoretical analysis^{18–24}. The investigation of the radio emission of the Sun and of cosmic space is of great astrophysical and, to a certain extent, also geophysical and radio-engineering interest. This is quite understandable, since here we are dealing with a substantial extension of the region of the spectrum of electromagnetic waves used in astronomy. Moreover, the information obtained by work in the radio-frequency region by no means duplicates the results that can be extracted from observations in infrared, visible, or ultraviolet rays. The point is that, for example, the optical radiation of the Sun is determined by its photosphere, which has a temperature \(T_{\odot}=6000^\circ\). However, the radio emission of the Sun will by no means, generally speaking, correspond to the radiation of a black body with the temperature of the photosphere. This is explained by the fact that the solar corona and chromosphere, transparent to light, are already completely opaque to meter radio waves; as a result, the radio emission of the Sun in the case of sufficiently long waves will be determined by the corona, and not by the photosphere or chromosphere. Thus the study of the radio emission of the Sun is a method for studying the corona, and moreover a method quite suitable outside eclipses.

According to modern views, the inner corona has a temperature much higher than that of the photosphere, reaching a million degrees (see, for example,^{25})*). From what has been said above it is clear that the thermal radio emission coming from the corona must correspond to this same high temperature, and not to a temperature of \(\sim 6000^\circ\)^{18–20}.

*) What is meant is the temperature of the electrons and ions; thermal radiation in the infrared, visible, and ultraviolet regions is not in equilibrium with the particles and corresponds to a temperature of the order of the photospheric temperature.

The study of the radio emission of the Galaxy, in turn, makes it possible to draw certain conclusions about the temperature and concentration of electrons in interstellar space.

The geophysical and radio-engineering interest in studying the radio emission of the Sun and of world space is connected with the generally known dependence between solar activity, which is sharply reflected in radio emission, and geophysical phenomena and, above all, phenomena determining the propagation of radio waves. In addition, “cosmic noises” in radio equipment are important for determining its sensitivity with respect to terrestrial radio signals.

In the present review, in §§ 1—3 the experimental material available in the literature concerning the radio emission of the Sun and the Galaxy is compared (the literature that had appeared in Moscow up to March 1947 was used). Further, in § 4 a theoretical consideration of the question and a discussion of the observational results are carried out.

§ 1. METHOD OF OBSERVATION

Let us first dwell on the experimental possibilities of investigating radio emission from extraterrestrial sources. Let the energy flux (Poynting vector) from such a source on the Earth be equal to \(S\,\Delta f\), where \(\Delta f\) is the frequency interval under consideration. Then the mean square of the electromotive force in the antenna \(\overline{e_a^2}\) is equal to \({}^{26}\):

\[ \overline{e_a^2}=\frac{\lambda^2}{2\pi}D_a^2 R_a S\,\Delta f, \tag{1} \]

where \(\lambda\) is the wavelength, \(R_a\) is the radiation resistance of the antenna, and \(\dfrac{\lambda^2}{2\pi}D_a^2\) is its “detection area.” The antenna, as is known, delivers maximum power to the receiver if its input resistance is \(R=R_a\); in this case the power received by the receiver is equal to

\[ P=\frac{\overline{e_a^2}}{4R_a}=\frac{\lambda^2}{8\pi}D_a^2 S\,\Delta f. \tag{2} \]

From (2) it is clear that the quantity \(\dfrac{\lambda^2}{8\pi}D_a^2\) is simply the area with which the receiver collects the flux of incident radiation. For a half-wave dipole \(D_a^2 \simeq 3\), and thus, instead of (2), one may write:

\[ P\simeq \frac{3\lambda^2}{8\pi}G_a S\,\Delta f\simeq \frac{\lambda^2}{8}G_a S\,\Delta f, \tag{3} \]

where \(G_a\) is the power gain of the antenna under consideration in comparison with a half-wave dipole (“power gain over a half-wave dipole”; see \(^{7,11,27}\)). If the antenna consists of a large number of dipoles, then very roughly \(^{26}\):

\[ G_a\sim \frac{2\cdot \text{antenna area}}{\lambda^2}. \tag{4} \]

On meter and longer waves usually \(G_a \sim 2\)—\(10\); in the centimeter range \(G_a\) is considerably higher, owing to the possibility of achieving a sharp directivity of the antennas or, in other words, the possibility of using an antenna (mirror) with an area considerably larger than \(\lambda^2\). In the meter range the maximum attainable value of \(G_a\) can hardly exceed \(100\)—\(200\) (at \(\theta G_a \sim 100\)).

The possibility of receiving weak radio signals is limited by noise in the receiver and in the antenna; these noises, as is known\(^{26, 28}\), are due to thermal fluctuations in conductors and to the shot effect in radio tubes. In the antenna itself, with resistance \(R_a\), the mean square of the voltage due to fluctuational thermal noise is equal to\(^{26, 28}\):

\[ \overline{e_{an}^{2}}=4R_a kT_a\,\Delta f, \tag{5} \]

where \(T_a\) is the temperature of the antenna, \(k=1.38\cdot 10^{-16}\) is Boltzmann’s constant, and \(\Delta f\) is the frequency band that interests us. The “noise power” delivered by the antenna to a receiver with a matched input resistance is equal to:

\[ P_{na}=kT_a\,\Delta f. \tag{6} \]

However, the receiver itself is not noiseless, which raises the noise level above the value (6). This increase is taken into account by introducing the noise coefficient \(N\) (or \(F\), see \(^{26}\)), indicating by how many times the power due to noise exceeds the value (6). Thus, it may be considered that the noise power obtained from the antenna, with allowance for the noise of the receiver itself, is equal to:

\[ P_n=NkT_a\,\Delta f. \tag{7} \]

The coefficient \(N\) is determined experimentally. For the meter range usually \(N\sim 3\)—\(10\); for centimeter receivers \(N\sim 10\)—\(15\).

It is obvious that the possibilities of radio observations are characterized by the ratio:

\[ \frac{P}{P_n}=\frac{\lambda^2G_aS}{8NkT_a}. \tag{8} \]

In order to form an idea of what the ratio (8) is in the case of interest to us, let us introduce a certain “standard” power of the Sun’s radio emission, choosing as such a “standard” the thermal radiation of the solar photosphere, i.e., the radiation flux at the Earth from a black body having temperature \(T=T_\odot=6000^\circ\), radius equal to the apparent radius of the Sun \(r=r_\odot\simeq 7\cdot 10^{10}\ \text{cm}\), and situated at a distance from the Earth equal to the distance from the Earth to the Sun \((R\simeq 1.5\cdot 10^{13}\ \text{cm})\). In the radio region, for a body with such a temperature, one may use for the density of black-body radiation the Rayleigh–Jeans formula

\[ u=\frac{8\pi f^2}{c^3}\,kT\,\Delta f. \tag{9} \]

From a unit surface of a black body there emerges in all directions a flux \(S\Delta f=\dfrac{c}{4}u\). Hence it is clear that the flux of radiation from our “standard” at the Earth is equal to:

\[ S_{\odot}=\frac{2\pi kT_{\odot}}{\lambda^2}\left(\frac{r_{\odot}}{R}\right)^2 =\frac{1.11\cdot 10^{-16}}{\lambda^2}\frac{\mathrm{erg}}{\mathrm{cm}^2\cdot \mathrm{sec}\cdot \mathrm{cycle}} =\frac{1.11\cdot 10^{-17}}{\lambda^2\;(\text{in meters})}\frac{\mathrm{watt}}{\mathrm{m}^2\cdot \mathrm{megacycle}}. \tag{10} \]

If the receiver is at room temperature, i.e. \(T_a\simeq 300^\circ\), then, according to (7), the noise power divided by \(\Delta f\) is equal to:

\[ \frac{P_n}{\Delta f}\simeq 4\cdot 10^{-14}N\frac{\mathrm{erg}}{\mathrm{sec}\cdot \mathrm{cycle}} =4\cdot 10^{-15}N\frac{\mathrm{watt}}{\mathrm{megacycle}}. \tag{11} \]

The ratio (8) in the case (10)—(11) is equal to

\[ \frac{P_{\odot}}{P_n}\simeq 3\cdot 10^{-4}\frac{G_a}{N}. \tag{12} \]

Taking for \(N\) the value 10 and assuming that a signal can be noted when its power exceeds \(\sim 5\%\) of the noise power,* we see that the chosen standard radiation will be noticed if

\[ G_i>\sim 2000. \tag{13} \]

Thus, under these conditions, in the meter range the radiation of the Sun with \(T=6000^\circ\) cannot be noticeable.

Let now the radio waves be emitted by the corona, and let the region responsible for the radiation have temperature \(T\) and radius \(r=\eta r_{\odot}\). Then, analogously to (10),

\[ S=\frac{2\pi kT}{\lambda^2}\left(\frac{r_{\odot}}{R}\right)^2\eta^2 =\frac{1.11\cdot 10^{-17}}{\lambda^2\;(\text{in meters})}\frac{T}{T_{\odot}}\eta^2 \frac{\mathrm{watt}}{\mathrm{m}^2\cdot \mathrm{megacycle}} \tag{14} \]

and the power, divided by \(\Delta f\), according to (3) and (14), is equal to*):

\[ \frac{P}{\Delta f}\simeq 0.8kT\left(\frac{r_{\odot}}{R}\right)^2\eta^2G_a \simeq 1.4\cdot 10^{-17}\left(\frac{T}{T_{\odot}}\right)\eta^2G_a \frac{\mathrm{watt}}{\mathrm{megacycle}}. \tag{15} \]

For what follows it is convenient to introduce the effective temperature of the emitter \(T_{ef}\) and its ratio to \(T_{\odot}\):

\[ T_{ef}=T\eta^2=\frac{P}{P_{\odot}};\qquad V=\frac{T_{ef}}{T_{\odot}}. \tag{16} \]

Measuring experimentally \(P\) for the Sun and knowing \(G_a\) (this quantity may be measured or calculated), according to (15), the temperature \(T_{ef}\) or \(V\) is determined.

\[ \overline{\phantom{xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx}} \]

*) Appleton and Hey\(^9\), instead of (7), write \(P_n=(N-1)kT_a\Delta f\), i.e. they take into account, for comparison with the signal, only the noise of the receiver without the antenna. Of course, this difference plays no role. Further, instead of the factor 0.8 in\(^9\) there appears the value 0.41. The reason for this difference has remained unclear to us; perhaps it consists in another definition of \(G_a\). This question is essential only in absolute measurements and calibration of the receiver.

According to (8), (12), (16), and under the condition that \(N\sim 10\) and the minimum perceptible ratio is \(\dfrac{P}{P_n}\sim 5\%\), we see that the radiation can be detected if

\[ V \gtrsim \frac{2\cdot 10^3}{G_a}. \tag{17} \]

For \(\lambda \gtrsim 1\,m\), \(G_a \lesssim 100\), and thus the radiation of the Sun can be detected if

\[ \begin{gathered} T_{ef} \gtrsim 10^5{}^\circ \quad \text{or}\\ V \gtrsim 20 . \end{gathered} \tag{18} \]

However, if, as is still possible, the minimum perceptible value \(P/P_n\sim 1\%\), \(N=5\), and \(G=100\), then \(T_{ef}\gtrsim \sim 10^4\) degrees.

At centimeter wavelengths the factor \(G_a\) may be greater than a thousand, and thus temperatures on the order of \(T_\odot=6000^\circ\) and even considerably lower can be measured.

Fig. 1. Antenna device (mirror) with a diameter of about \(9\,m\), used in an installation for investigating the radiation of the Galaxy and the Sun at wavelength \(\lambda=1.87\,cm\).

A photograph of the installation (a mirror antenna), used\(^1\) for studying the radio emission of the Galaxy and the Sun at \(\lambda=1.87\,m\), is shown in Fig. 1.

From the author’s data, it may be concluded that he estimates the limiting accuracy of his instrument as corresponding to \(V\sim 3\)—4. The area of the mirror is \(\sim 65\,m^2\), and according to the approximate formula (4), \(G_a\sim 40\). Therefore, according to (17), \(V_{\min}\sim 50\). This discrepancy is not serious, since the accuracy of formula (4) does not allow one to exclude the value \(G_a\sim 100\), and, moreover, the author\(^1\) believes that he can detect a ratio \(P/P_n\) smaller than \(5\%\), as was assumed above. In \(^8\) the minimum perceptible value of \(\dfrac{P}{P_n}\) was of the order of \(1\%\).

Fig. 2. Change in the noise level with time. The maximum corresponds to the conditions under which the mirror is directed toward the center of the Galaxy.

Fig. 3. The same as in Fig. 2, during the period when the direction toward the Sun was close to the direction toward the center of the Galaxy. One maximum is from the Sun, the other from the center of the Galaxy.

A record of the noise level in the receiver as a function of time¹ is shown in Figs. 2 and 3 (\(\lambda = 1.87\ \mathrm{m}\)). In Fig. 2 the maximum corresponds to conditions in which the mirror is directed toward the center of the Galaxy (see § 3), while in Fig. 3 one of the maxima corresponds to the center of the Galaxy and the other to the Sun. The displacement of the maximum from the Sun in Fig. 3 is caused by the change in the position of the Sun relative to the center of the Galaxy.

§ 2. RADIATION OF THE SUN

Experimental investigation of the radio emission of the Sun has shown that this radiation can be detected over the entire range studied, from \(1.25\ \mathrm{cm}\) to 12 meters. At the same time, on meter waves only sporadic radiation is usually observed, arising during periods of increased solar activity (large spots, faculae). This sporadic radiation sometimes reaches enormous magnitude—

Table I

Radio Emission of the Sun

*) The author became acquainted with this work after writing the review; therefore it did not receive full treatment below.

corresponds to a value of \(V\) up to \(1.3\cdot 10^8\), i.e. a value of \(T_{ef}\) up to \(2\cdot 10^{12}\) degrees (see\(^ {11}\), \(\lambda=4.14\) m)! It was precisely the presence of such bursts with \(V>10^4\) that made it possible to detect the radio emission of the Sun at meter wavelengths with simple antennas, for which \(G_a\lesssim 10\). Of course, such sporadic radio emission cannot be thermal in character and is connected with disturbances in the corona.

We shall discuss the question of the nature of the radiation in § 4; for the moment we shall give a summary of all the available data (see Table 1).

At \(\lambda=1.25\) cm, measurements\(^ {10}\) were also carried out during a partial solar eclipse, and the course of the radio intensity with time coincided with the course of the intensity in the optical region. The value

Fig. 4. Radio emission of the Sun at \(\lambda=1.5\) m in October 1945. On the lower curve—the area of the visible disk of the Sun covered by spots.

\(T_{ef}\sim 2000^\circ\) for \(\lambda=1.25\) cm in\(^2\) was obtained, apparently, as a result of failing to take into account the very substantial absorption of radio waves in this region in the atmosphere\(^ {10,39}\). In general, the influence of the atmosphere for wavelengths \(\lambda<\sim 5\) cm is substantial and must be taken into account. The increase of the “radio diameter” of the Sun in comparison with the optical diameter (the diameter of the photosphere), which was observed in\(^2\) and is maximal for \(\lambda=1.25\) cm, may have been caused precisely by the influence of the atmosphere.

Measurements\(^ {40}\) at 62 cm, carried out daily over the course of several months, lead to the value \(T_{ef}\sim 10^6{}^\circ\). The “radio diameter” of the Sun was of the order of \(0^\circ.5\), i.e. the effective value of \(\eta\) is small. With the passage of time (on different days) the diameter did not change (accuracy \(0^\circ.1\)). On 21 November 1946 sharp “bursts” of radio emission were observed.

Measurements at the wavelength \(\lambda=1.5\) m showed that the intensity of radio emission is closely connected with solar activity, as a measure of which one may choose the area of sunspots. This connection is clear from Figs. 4\(^5\) and 8\(^9\), and was also noted in works\(^ {3,4,11}\). A gigantic “burst”

radio emission, visible in Fig. 6^11, coincides with the appearance of the bright eruption that arose on July 25, 1946 at 16 h 00 min and reached maximum brightness at 16 h 27 min. The “burst” lasted from 16 h 24 min to 16 h 27 min. In case^9 the maximum intensity \((V\) up to \(10^5)\) was reached during the period February 5–8, 1946,

Fig. 5. Histogram showing the daily distribution of the radiation intensity with \(\lambda = 1.5\) m (increases lasting only a few seconds are not taken into account).
a) Daily, October 5, 1945–December 12, 1945, and January 1, 1946–March 15, 1946.
b) Sunny days, March–May 1946.

which coincided with the period when a giant spot with an area equal to \(5000 \cdot 10^{-6}\) of the disk surface was passing through the central meridian of the Sun (see Fig. 9). On February 7 a strong magnetic storm also began, lasting 36 hours (change of the horizontal component up to \(500\gamma\)). During this same period faculae were observed and the Dellinger effect occurred (fade-out).

According to^9, the radio emission of the Sun sometimes appears a few minutes before sunrise and continues to be observed for several minutes after sunset. This effect is evidently connected with refraction in the ionosphere. The influence of the ionosphere also manifests itself in the daytime for waves longer than \(\sim 10\) m.

The distribution of the intensity of the radio emission over the spectrum^9 is shown in Fig. 10, and in Fig. 11 this distribution is compared with the thermal spectrum corresponding to a temperature of the Sun of \(6000^\circ\) (and \(\eta = 1\)) for the entire frequency region. The values of the radio-emission flux in Fig. 11 are given for the period of maximum solar activity.

During such periods of maxima, radio emission is undoubtedly caused by various dynamic processes in the corona and thus has, to a certain degree, a sporadic character. The question arises: what is the radio emission of the “quiet” Sun? Of course, the concept of the “quiet” Sun is very conditional, but by it one may, say, understand the Sun during periods of minimum solar activity and absence of spots. The question posed cannot be considered clarified; however, there are certain indications that at \(\lambda = 1.5\) m and \(\lambda = 1.87\) m the effective temperature is not lower than \((3 \div 10)\cdot 10^5\) degrees*). This is seen, for example, from the histogram presented,

*) The same is indicated by measurements^40.

Fig. 6. Solar radio emission at \(\lambda = 4.14\ \mathrm{m}\); July 25, 1946.

Fig. 7. Solar radio emission at \(\lambda = 4.14\ \mathrm{m}\); August 2, 1946.
The time scale is stretched compared with Fig. 6.

Fig. 8. Comparison of relative magnitudes:
a) radio emission,
b) absorption of radio waves in the ionospheric \(D\)-layer,
c) ratio of the area of sunspots to the area of the visible disk.

Fig. 9. Photograph of the Sun, February 5, 1946.

in Fig. 5. The value \(S=0.25\cdot 10^{-18}\ \dfrac{\text{watt}}{m^2\,\text{megacycle}}\) corresponds to \(T_{ef}=3\cdot 10^5\) degrees, and at the same time a smaller flux from the Sun was never observed, although the apparatus apparently fully permitted such a flux to be detected (otherwise the author’s assertions would have been meaningless).

The observations\(^1\) refer to a “quiet” period and therefore testify in the same direction. Let us note that Reber himself\(^1\) does not indicate the value of \(T_{ef}\). Eppleton\(^3\), and after him a number of authors, took this value to be equal to \(6000^\circ\), which, however, is erroneous. The point is that Reber measured chiefly the radiation of the Galaxy, which is not sharply directional in character, and related the radiation intensity to 1 square degree by dividing the entire intensity captured by the instrument by the solid angle in which the antenna received the incoming radiation; this angle was apparently \(\sim 50\) square degrees. The Sun is seen under an angle of \(\sim 0.5\) square degree, and therefore, in order to obtain the intensity from the Sun per square degree, the measured total intensity must be multiplied by 2, and not divided by 50. Hence it follows that the intensity of the Sun’s radiation will be obtained from Reber’s value\(^1\)

Fig. 10. Spectrum of the radio emission of the Sun. The symbols ×, □, and △ correspond to different observers.

Fig. 11. Comparison of the spectrum of the radio emission of the Sun with the spectrum of a black body with \(T=6000^\circ\).

\[ S=10\cdot 10^{-18}\ \frac{\text{watt}}{m^2\cdot\text{megacycle}\cdot\text{sq. deg.}}. \]

by multiplication by \(\sim 50\), which gives \(T_{ef}\sim 10^6{}^\circ\), as is also adopted in Table 1.

Special measurements\(^6,{}^7,{}^8\) led to the discovery

of a very interesting circumstance—the circular polarization of the Sun’s radio emission. During the passage of a large group of spots across the meridian on July 26, 1946, at wavelength $\lambda = 1.5\,m$, it turned out that the radiation polarized circularly to the right was 7 times more intense than the radiation polarized circularly to the left (see Fig. 12$^{6}$). Five days later, on the contrary, the left-polarized radiation was 5 times more intense than the right-polarized.

Of great interest is the determination of the distribution of the brightness of the radio emission over the solar disk and in the region of spots. Unfortunately,

Fig. 12. Polarization of the Sun’s radio emission at
$\lambda = 1.5\,m$; July 26, 1946.
$a)$ right circular polarization, $b)$ antenna not directed at the Sun, $c)$ left circular polarization.

the solution of this question is very difficult, since, if one does not speak of the centimeter and decimeter ranges, it is practically impossible to construct antennas with a directivity of less than $0.5$ degrees. Some success, apparently, may be achieved by using the interference of two antennas$^{8}$ located at a distance of several wavelengths—in this case a multi-lobed directivity pattern is obtained, and the solution of the individual lobes may be very small. A more direct and reliable method, proposed by the late Academician N. D. Papaleksi, consists in carrying out observations of radio emission during eclipses. In this connection, the Brazilian expedition of the Academy of Sciences of the USSR for the observation of the total solar eclipse of May 20, 1947, on the initiative of Academician N. D. Papaleksi, included such measurements in the plan of its work.

§ 3. RADIATION OF THE GALAXY

As early as 1932–1933, Jansky$^{13}$ discovered at the wavelength $14.6\,m$ that rather intense radio emission reaches the Earth from cosmic space. This radiation is maximal in the direction

toward the center of the Galaxy and in general is great in the region of the Milky Way. This result was later confirmed in a number of works carried out at wavelengths of 1.5 m and longer\(^{14–17}\). There are still no direct indications of the existence of radio emission of extragalactic origin.

It is natural to characterize the intensity of the radio emission of the Galaxy by a certain effective temperature \(T_{ef}\), defined as the temperature \(T\) of black-body radiation of the same intensity as that observed experimentally in the given direction. As is known, the flux of black-body radiation with temperature \(T\) in the solid angle \(\Delta \Omega\) is equal to:

\[ S \Delta f = K \Delta f \Delta \Omega = \frac{c}{4\pi} u \Delta \Omega = \frac{2 f^2}{c^2} k T \Delta \Omega \Delta f = \frac{2}{\lambda^2} k T \Delta \Omega \Delta f, \]

\[ K = \frac{2.76 \cdot 10^{-17}}{\lambda^2\ \text{(in meters)}} \cdot T\, \frac{\text{watt}}{\text{m}^2 \cdot \text{megacycle} \cdot \text{steradian}} \simeq \]

\[ \simeq \frac{6.6 \cdot 10^{-21}}{\lambda^2\ \text{(in meters)}} \cdot T\, \frac{\text{watt}}{\text{m}^2 \cdot \text{megacycle} \cdot \text{square degree}} \simeq \]

\[ \simeq \frac{8.4 \cdot 10^{-17}}{\lambda^2\ \text{(in meters)}}\, \frac{\text{watt}}{\text{m}^2 \cdot \text{megacycle} \cdot \text{square degree}} . \]

Table II gives the measured values of \(K\) and \(T_{ef}\).

Table II

Radio emission of the Galaxy (at maximum)

The measurements of Reber\(^{1}\) and Hey et al.\(^{15}\) appear to be reliable. The measurements of Jansky\(^{13}\) hardly allow confident conclusions to be drawn. Moxon’s measurements\(^{17}\) for \(\lambda = 1.5\) m and \(\lambda = 3.3\) m contradict the measurements\(^{1,15}\) and apparently contain a substantial error.

Radio isophotes (lines of equal values of \(K\)) of the Galaxy are presented in Figs. 13 and 14. According to Reber’s data\(^{1}\) (Fig. 13), the principal maximum of radiation is located in Sagittarius (the direction toward the center of the Galaxy), with secondary maxima in Cygnus, Cassiopeia, Canis Minor, and Corvus. The main mi-

Fig. 13. Lines of equal intensity of the radio emission of the Galaxy (“radio isophotes”) in units of

\[ 10^{-22}\, \frac{\text{watt}}{\text{cm}^{2}\cdot\text{megacycle}\cdot\text{square degree}}; \qquad \lambda = 1.87\,\text{m}, \]

a b

minimum lies in Perseus. At the minimum the intensity of the radio emission is approximately 50 times smaller than at the maximum. Extragalactic objects (the nebula in the constellation Andromeda, etc.) have not given any noticeable radiation.

Fig. 14. Lines of equal intensity of the radio emission of the Galaxy; cylindrical projection; the dashed line denotes the galactic equator. Intensity in units of
\[ 1.1\cdot 10^{-21}\, \frac{\text{watt}}{m^{2}\cdot \text{Hz}\cdot \text{steradian}}; \qquad \lambda = 4.7\ \text{m}. \]

have not yielded (in¹) a minimum value \(K\) that can be detected,

\[ K_{\min}\sim 2\cdot 10^{-19}\, \frac{\text{watt}}{m^{2}\cdot \text{megahertz}\cdot \text{square degree}}. \]

Hey et al.¹⁶ discovered fluctuations in the intensity of radio emission in the direction of Cygnus. Since the diameter of the Sun is \(\sim 0^\circ.5\), from Tables I and II it is clear that, for example, at \(\lambda = 1.87\ \text{m}\), for the Sun

\[ K_{\odot}=2S_{\odot}\simeq 6\cdot 10^{-18} \]

[\(T_{\odot}=6000\); see (10)], while for the Galaxy

\[ K\simeq 1.12\cdot 10^{-17}. \]

Fig. 15. Frequency dependence of the effective temperature of the radiation of the Galaxy. The upper curve is the maximum intensity (center of the Galaxy); the lower curve is the minimum intensity.

If, as is usually the case, the directivity of the antenna is considerably greater than \(0^\circ.5\), it is clear from this that the radiation of the Sun with \(T\sim T_{\odot}\), during the period when the Sun is in a region close to the center of the Galaxy, cannot be noticed (in the meter range).

For waves longer than \(10\div 15\) meters, the influence of the ionosphere should begin to make itself felt. If for a given wavelength the ionosphere is already completely opaque, then the apparatus described can in principle be used to measure the temperature of the ionosphere. In this case it is essential that the ionosphere absorb the radio waves and not reflect them without absorption. For example, in the region.

gyro-magnetic frequency (for \(H=0.5\) gauss, \(\lambda_H=214\) m), absorption is very strong, and thus the thermal radio emission emitted by the ionosphere may have an effective temperature equal to the temperature of the corresponding region of the ionosphere.

§ 4. THEORY AND DISCUSSION OF THE OBSERVATIONAL RESULTS

For the interpretation of observations of the radio emission of the Sun and the Galaxy, it is necessary first of all to know what the optical thickness of the solar corona and of interstellar gas is for radio waves of various wavelengths.

The solar corona is, as is known, a practically completely ionized gas. The concentration of electrons in the corona is determined by Baumbach’s empirical formula (see \(^{29}\)):

\[ N=10^8\left(0.036\,\eta^{-1.5}+1.55\,\eta^{-6}+2.99\eta^{-16}\right)\ \text{cm}^{-3}, \tag{19} \]

where \(\eta=\dfrac{r}{r_\odot}\), \(r\) is the distance from the center of the Sun and \(r_\odot\) is the radius of the photosphere.

The values of \(N\) are given in Table III (see \(^{25}\)). The value \(\eta=1.00\) in Table III corresponds to the base of the corona \((r-r_\odot\sim 15000\ \text{km},\ \eta\sim 1.02)\). The concentrations given for the outer corona \((\eta>1.6)\) are valid only if the scattering of light in this region is caused by electrons and not, say, by cosmic dust \(^{25,29}\).

Table III

Electron concentration in the corona according to Baumbach’s formula

Since the concentration of ions of all elements, except hydrogen, in the corona is very small \(^{25}\) in comparison with \(N\), it follows from the condition of quasineutrality of the corona that the concentration of protons in the corona is approximately equal to \(N\).

To determine the optical thickness of the corona \(\tau\), it is necessary to consider the propagation in it of radio waves \(^{18}\). We shall regard these waves, with cyclic frequency \(\omega\), as plane waves. The refractive and absorption indices \(n\)

and \(k\) and the absorption coefficient \(\chi\) for an ionized gas are thus \({}^{30}\):

\[ n^{2}=1-\frac{4\pi e^{2}N}{m\omega^{2}} =1-3.19\cdot 10^{9}\frac{N}{\omega^{2}}, \tag{20} \]

\[ k=\frac{\nu}{2\omega}\cdot\frac{1-n^{2}}{n},\qquad \chi=\frac{2k\omega}{c} =\frac{\nu}{c}\cdot\frac{1-n^{2}}{n} =\frac{4\pi e^{2}N\nu}{mc\omega\sqrt{1-\dfrac{4\pi e^{2}N}{m\omega^{2}}}} . \tag{21} \]

Here \(\nu\) is the effective number of electron collisions, and it has already been taken into account that, under the conditions of interest to us, \(\omega\gg \nu\) (see below). The attenuation, as the Sun is approached, of the intensity of a radio wave incident from outside upon the corona and propagating along the radius is determined by the expression

\[ S=S_{0}e^{-\tau(\eta)}, \]

\[ \tau(\eta)=\int_{r}^{\infty}\chi\,dr =\frac{2\omega}{c}\int_{r}^{\infty}k(r)\,dr =\frac{2\omega}{c}\,r_{\odot}\int_{\eta}^{\infty}k(\eta)\,d\eta = \]

\[ =\frac{r_{\odot}}{c}\int_{\eta}^{\infty} \frac{\nu(1-n^{2})}{n}\,d\eta . \tag{22} \]

Here \(\tau\), by definition, is the optical thickness (this generally accepted term is, of course, not especially suitable as applied to radio waves, but we shall retain it). Obviously, \(\tau\) can be defined analogously for nonradial directions.

In the case of the corona it is necessary to take into account only collisions of electrons with ions, and the latter may be regarded as singly charged (protons), with concentration \(N\). In this case \({}^{31}\):

\[ \nu\simeq \pi\frac{e^{2}}{(kT)^{2}} \ln\left(\frac{kT}{e^{2}N^{1/3}}\right)\cdot N\cdot \overline{V} = \frac{5.5\,N}{T^{3/2}} \ln\frac{600\,T}{N^{1/3}}, \tag{23} \]

where

\[ \overline{V}=\sqrt{\frac{8kT}{\pi m}} \]

is the arithmetic mean velocity of the electrons, under the assumption of a Maxwellian distribution law with temperature \(T\); formula (23) is correct to within a factor close to unity.

The formulas given fully take into account the absorption of radio waves by the electron gas (for scattering, see below). The calculation is carried out within the framework of classical theory, which in the present case (free electrons) is entirely correct. The quantum calculation of absorption is equivalent to calculating the so-called “free—free” absorption associated with transitions of electrons from some states of the continuous spectrum to others*).

* ) Therefore summing the classical and “free—free” absorption \({}^{19}\) constitutes double counting of one and the same effect.

The values of \(n\) and \(\nu\) in the corona at temperatures of 6000 and 600 000 degrees are given in Table IV (the values of \(N\) from Table III were used).

Table IV

Values of \(n\) and \(\nu\) in the corona

For \(\lambda=3.76\ \mathrm{m}\) \((\omega=5\cdot10^{8})\) the refractive index becomes zero at \(\eta=1.185\). For \(\lambda=1.5\ \mathrm{m}\), \(n=0\) at \(N\simeq5\cdot10^{8}\), i.e. at the base of the corona; for \(\lambda=5\ \mathrm{m}\), \(n=0\) at \(N\simeq4.4\cdot10^{7}\) \((\eta=1.28)\), and for \(\lambda=15\ \mathrm{m}\), \(n=0\) at \(N\simeq5\cdot10^{6}\) \((\eta\sim1.75)\). For \(\lambda=4.7\ \mathrm{cm}\), \(n=0\) at \(N\simeq5\cdot10^{11}\), i.e. at the base of the chromosphere.

Table V gives the values of \(\tau(\eta)\) for the same waves as in Table IV, under the assumption that the entire corona has either the temperature \(6\cdot10^{3}\), or the temperature \(6\cdot10^{5}\). The graphs of \(\tau(\eta)\) are also given in Fig. 16.

Table V

Optical thickness of the corona \(\tau\)

According to other data\(^{19}\), which we reduced by half for the reason indicated in the note on the preceding page, at \(T=350\,000^\circ\) \(\tau\) for \(\eta=1.05\) is equal to \(0.62\cdot10^{-4}\) at \(\lambda=1\ \mathrm{cm}\), \(0.006\) at \(\lambda=10\ \mathrm{cm}\), and \(2.25\) at \(\lambda=1.87\ \mathrm{m}\).

Let us note that in calculating \(\tau\) with allowance for the region where \(n\sim 0\), i.e., for wavelengths for which reflection from the region \(n\sim 0\) may be appreciable (this reflection is, evidently, analogous to the reflection of radio signals from the ionosphere), one must use the following formula (see \(^{31,32}\)):

\[ \tau = \int_{r(0)}^{\infty} \chi\,dr + \frac{V^2}{c n^2(0)} \left(\frac{4\pi\sigma(0)}{\omega}\right)^{2/3} = \int_{r(0)}^{\infty} \chi\,dr + \frac{V^2[\nu(0)]^{2/3}}{3\omega^2 n^2(0)} = \]

\[ = \int_{r(0)}^{\infty} \chi\,dr + \Delta\tau, \tag{24} \]

where the values of the conductivity \(\sigma=\dfrac{e^2\nu N}{m\omega^2}\), \(\nu\), \(\left(\dfrac{dn^2}{dr}\right)\equiv n^{2\prime}(0)\), and \(r\) are taken at \(n(\omega)=0\), which is conventionally indicated by choosing the argument of these quantities equal to zero (for example, \(\nu(0)\)). Formula (24) differs from the one usually used by the term \(\Delta\tau\), which takes into account deviations from the approximation of geometrical optics in the region \(n\sim 0^{32,31}\). For example, for \(\nu=100\), \(\omega=5\cdot 10^8\) (\(\lambda=3.76\) m) and \(n^{2\prime}(0)\sim 10^{-10}\), \(\Delta\tau\sim 0.4\), i.e., this correction is substantial. The reflection coefficient (in intensity) of radio waves from the solar atmosphere for normal (radial) incidence of the wave is evidently equal to

\[ R=e^{-2\tau}, \tag{25} \]

where \(\tau\) is determined by formula (24).

The number of collisions \(\nu\) and, consequently, \(\tau\), strongly depend on the temperature. Therefore, in order to calculate \(\tau\) in the corona it is necessary to know the temperature distribution in it. For the inner (\(r<1.6\)) corona, apparently, a reasonable value is \(T\sim(3\div 6)\cdot 10^5{}^\circ\). If the scattering of light in the outer corona is due to electrons alone (their concentration in this case is indicated in Table III), then the electron temperature must be \(\ll 6000^\circ{}^{29,25}\), which seems improbable. At the same time, to explain the scattering

Fig. 16. Optical thickness \(\tau\) of the corona in the region of radio frequencies.

1. \(\lambda=4.7\) cm, \(T=6\cdot 10^3\)
2. \(\lambda=18.8\) cm, \(T=6\cdot 10^3\)
3. \(\lambda=94\) cm, \(T=6\cdot 10^3\)
4. \(\lambda=3.86\) cm, \(T=6\cdot 10^5\)
5. \(\lambda=3.86\) cm, \(T=6\cdot 10^5\)

light in the outer corona by cosmic dust is apparently not easy. The problem of the outer corona is now the most acute and unclear question in the physics of the solar atmosphere. The study of the radio emission of the Sun can undoubtedly contribute to the solution of this problem (see also below).

The data presented and Table IV make one think that, practically, the coefficient of reflection of radio waves of all ranges from the Sun is apparently equal to zero, i.e. the waves reach the region of reflection (where \(n\sim 0\)) already very much weakened [see also (24).] At the same time, this conclusion can in no way be regarded as final until the nature of the outer corona and the temperature variation throughout the corona have been clarified*).

In a state of thermal equilibrium, as is clear from Kirchhoff’s theorem, the regions of the corona for which \(\tau\sim 1\) are responsible for thermal radiation. If the absorption of the incident waves is complete, i.e. \(R=0\), then the intensity of the radiation is that for a black body with temperature \(T\), equal to the temperature of the corresponding region with \(\tau\sim 1\). If, however, \(R\ne 0\), then the intensity is smaller by a factor \(1-R\) in comparison with the intensity of black radiation with a temperature equal to the temperature of the region where reflection of the radio waves occurs, i.e. in (16) \(T_{ef}=(1-R)T\eta^2\).

From Table V one may conclude that thermal centimeter waves are emitted by the chromosphere, whose temperature is \(\sim 6000—20000^\circ\) (\(T\) depends on \(\eta\)). The results of the corresponding measurements \(^{2,10}\) (see Table I) agree fully with this conclusion. Waves longer than a meter or, perhaps, approximately from \(50\) cm (see \(^{40}\)) to \(10—10—15\) m must be emitted by the hot inner corona. If this hot radiation of the inner corona is not absorbed by the very cold outer corona, then at the Earth in the meter range there should be observed thermal radiation of the Sun with \(T\sim(3\div 6)\cdot 10^5{}^\circ\) and \(T_{ef}=T\eta^2\sim(3\div 20)\cdot 10^5{}^\circ\).

As is clear from what was said in § 2, such thermal (regular) radiation is apparently indeed observed. Further experimental investigation of this question is very important.

However, not only the emergence of hot thermal radiation, but also the definitely occurring sporadic radio emission at meter waves, testify that the outer corona cannot be very cold (if the concentration of electrons in it is as in Table III, i.e. the scattering of light is determined by electrons). Indeed, even at \(T=600^\circ\) the absorption is greater than at \(T=6000^\circ\) by \(\sim 30\) times [since \(\chi\sim \nu \sim \dfrac{1}{T^{3/2}}\); see (23)] and, thus, the values of \(\tau\) given in Table V for \(\eta=2.0\) must also be increased by \(\sim 30\) times. As a result the values of \(\tau\) will be enormous. Even

* The question of the coefficient of reflection from the Sun, in addition to its connection with the radio emission of the Sun (see below), is of fundamental importance in discussing the possibilities of “radar sounding” of the Sun from the Earth, which were discussed by Acad. N. D. Papaleksi (see \(^{18}\)) in connection with his calculations of “radar sounding” of the Moon \(^{38}\).

if in the outer corona \(T\sim 6000^\circ\), then for \(\eta \geq 2.0\) waves with \(\lambda > \sim 1.5\) m will be absorbed by it completely (see Table V, and also \(^{19}\)).

Thus, at least during periods of intense sporadic radio emission, the temperature of the outer corona must be considerably higher than \(6000^\circ\). If, however, the fact of the existence of regular radio emission in the meter range with \(T_{ef}\sim 10^6\) is finally established, then it will be possible to regard it as proven that, if the outer corona is an electron plasma, then in it \(T>6000^\circ\). In conjunction with the known arguments \(^{29,25}\), according to which at such a temperature the Fraunhofer lines in the outer corona would not be sharp, as is found experimentally, it follows that the scattering of light in the outer corona is determined not by electrons, or, more precisely, is not connected with electrons in any appreciable part.

Above we did not take into account the magnetic field of the Sun, whose intensity for the quiet Sun at its surface is apparently \(\sim 25\text{--}50\) gauss, while near large spots it reaches values up to \(\sim 4000\) gauss.

When the influence of the magnetic field is taken into account, the solar atmosphere becomes doubly refracting (just as the ionosphere under the influence of the earth’s magnetic field). In this case two different waves can propagate in the gas, which, generally speaking, are elliptically polarized and for which \(^{33}\)

\[ (n_{1,2}-ik_{1,2})^2 = \tag{26} \]

\[ 1-\frac{2v(1-v)} {2\left(1-i\frac{\gamma}{\omega}\right)\left(1-v-i\frac{\gamma}{\omega}\right)-u\sin^2\alpha \pm \sqrt{u^2\sin^4\alpha+4u\left(1-v-i\frac{\gamma}{\omega}\right)^2\cos^2\alpha}}, \]

where

\[ v=\frac{4\pi e^2N}{m\omega^2},\quad u=\frac{\omega_H^2}{\omega^2},\quad \omega_H=\frac{eH}{mc}, \]

\(\alpha\) is the angle between the external magnetic field \(\mathbf H\) and the normal to the wave, and the indices 1 and 2, corresponding to the signs \(-\) and \(+\) at the root in (26), refer to the “extraordinary” and “ordinary” waves.

The number of collisions \(\gamma\) in (26), except for the case when \(\omega\sim\omega_H\), is determined by expression (23). For not too large absorption, approximately, and in the absence of absorption, exactly:

\[ n^2_{1,2}=1-\frac{2v(1-v)} {2(1-v)-u\sin^2\alpha \pm \sqrt{u^2\sin^4\alpha+4u(1-v)^2\cos^2\alpha}}. \tag{27} \]

Expression (27) vanishes for the “ordinary” wave at the point

\[ v_{20}=\frac{4\pi e^2N_{20}}{m\omega^2}=1 \tag{28} \]

and for the “extraordinary” wave at the points

\[ v_{10\pm}=\frac{4\pi e^2N_{10\pm}}{m\omega^2}=1\pm\sqrt{u}=1\pm\frac{\omega_H}{\omega}. \tag{29} \]

Formula (28) coincides with that obtained without taking into account the influence of the magnetic field [see (20)], i.e. the points where \(n=0\), determined above for various \(\lambda\), retain their position for the “ordinary” wave when the field is not taken into account.

If

\[ U=\frac{\omega_H^2}{\omega^2}<1, \tag{33} \]

then \(n_1^2=0\) for the point \(v_{10-}=1-\dfrac{\omega_H}{\omega}\), i.e. at a concentration smaller than that corresponding to the point \(v_{20}\). In this case the “extraordinary” wave can be emitted only from greater distances from the photosphere than the “ordinary” wave. The second root \(v_{10+}\) plays no role here, since it corresponds to a point of the corona or chromosphere closer to the photosphere. If, however,

\[ U>1, \tag{31} \]

then the root \(v_{10-}\) does not exist \((v>0)\), and the role is played by the point \(v_{10+}\), lying deeper (i.e. closer to the photosphere) than the point \(v_{20}\). The absorption of both waves is also different, but we have not yet carried out the corresponding calculations as applied to the corona. However, since absorption occurs mainly in the region close to the points \(n_{1,2}^2=0\), it is clear that the influence of double refraction will be manifested in the fact that the radio emission of the “ordinary” and “extraordinary” waves will come from different depths and therefore may correspond to different temperatures*). Hence it follows that the radio emission of the Sun may be circularly, or more precisely elliptically, polarized, which is in fact observed experimentally\(^{6,7}\). The values of \(\omega_H\) and \(\lambda_H=\dfrac{2\pi c}{\omega_H}\) in various fields of interest from the point of view of the Sun are as follows (see Table VI):

Table VI

Values of \(\omega_H\) and \(\lambda_H\)

*) This circumstance was also noted by Martyn\(^{6}\) and by Shakh\(^{34}\). We note, incidentally, that Shakh’s theory of radio emission of the corona, set forth in another article\(^{35}\), like his theory of the corona\(^{36}\), is completely untenable (with regard to \(^{36}\) see 18, 25). It is enough to say that Shakh connects\(^{35}\) the radio emission of the corona with the radiation of the magnetic moments of nuclei (!?).

In the meter range, in the field of spots, case (31) takes place, and “extraordinary” radiation can “break through” outward from the deep layers34. It should be borne in mind, however, that the field decreases with distance from the photosphere and apparently decreases rapidly. Moreover, at different points of the photosphere the direction and magnitude even of a regular field are quite different. These circumstances must be connected with the great complication of the entire observed picture of radio emission.

Calculations of the thermal radiation of the Sun were also carried out by Martyn, but his detailed article has not yet appeared, and in a rather

Fig. 17. Effective temperature of the Sun in the radio region. The solid curve is for the “ordinary” wave, the dotted curve for the “extraordinary” one.

brief communication20 only the results of the calculations are given. The obtained spectrum of radio emission is shown in Fig. 17. The increase in intensity from short waves to long waves is explained by the displacement of the radiating region into the hotter layers of the chromosphere and corona (the form of the function \(T_\eta\), chosen by the author20, is unknown). The fall in intensity in Fig. 17 for \(\lambda > 2\ \text{m}\) is explained by taking account of the reflection coefficient (see above), which, according to the author20, is not equal to zero (the effective temperature in Fig. 17 contains the factor \(1 - R\)). As is clear from what has been said above, this result is hardly correct (see also Fig. 10). Without being acquainted with the formulas used to obtain the results20, it is impossible to determine what is involved here. Martyn20 also considered the distribution of the brightness of radio emission over the disk (Fig. 18). Above we considered only propagation of waves along the radius, i.e. radiation, observed from the Earth, coming from the central regions of the disk. For rays coming from peripheral regions, \(\tau\) is larger and therefore the radiation comes from higher, hotter layers. As a result, the region at the edge of the disk is brighter at decimeter wavelengths than the central regions. At meter wavelengths, according to20, this effect of increased brightness

is masked by the influence of the reflection coefficient, which leads to a “darkening” of the edges of the disk (see Fig. 18).

The indicated effects can in principle be observed during eclipses or with sufficiently sharply directed antennas, which for \(\lambda \sim 20\)—\(40\) cm apparently still does not exceed the bounds of what is possible.

Fig. 18. Distribution of “radio brightness” over the solar disk at various wavelengths (\(r/r_0=1\) at the edge of the disk).

Sporadic “bursts” of radio emission associated with solar activity, as has already been pointed out several times, cannot be explained as thermal radiation. It has been suggested \(^{37}\) that this radiation represents the radiation of electrons rotating in the magnetic field of spots with frequency

\[ \omega_H=\frac{eH}{mc}. \]

Such a point of view, however, is based on a misunderstanding, since if there is thermal equilibrium, then the magnetic field will not lead to any increase in the radiation—the reabsorption and other processes will lead to complete compensation of the “additional” radiation associated with rotation (an analogous criticism is also contained in \(^{21}\)).

Another assumption about the nature of irregular radiation \(^{19,21}\), on the contrary, appears quite possible. The point is that oscillations are possible in an electronic plasma, characterized by the frequency \(\omega_0\):

\[ \omega_0^2=\frac{4\pi e^2N}{m}=3.19\cdot10^9\cdot N;\qquad \lambda_0=\frac{2\pi c}{\omega_0}=\frac{3.34\cdot10^6}{\sqrt{N}}\ \text{cm}. \tag{32} \]

The frequency \(\omega_0\) is equal to the frequency at which, for the given \(N\), \(n^2=0\) [see (20)] and, as is clear from (32) and the preceding discussion, corresponds to the range of interest to us. Plasma oscillations can be excited by streams of electrons ejected by active regions of the Sun \(^{19}\), which emphasizes the connection of the corresponding radio emission with solar activity. The calculation of the intensity of the radiation caused by the oscillations is very complicated and requires knowledge of the dimensions of the oscillating regions, the flux of exciting particles, etc.

If the principal role in the sporadic radiation is played by radiation associated with plasma oscillations—and this is evidently so—then there arise

some additional difficulties with separating out the thermal radiation of the Sun (however, these difficulties exist for any mechanism of irregular radiation). Indeed, even in the quietest periods of solar activity its surface is still very “nonequilibrium,” and, for example, the electron streams exciting oscillations hardly disappear completely. As a result, there can be no certainty that the radiation of the “quiet” Sun is of a purely thermal character. The solution of this question will require prolonged comprehensive observations of radio emission and solar activity, as well as a number of orientational calculations of the radiation associated with oscillations and of the efficiency of its generation.

Let us turn to the consideration of the radio emission of the Galaxy.

As indicated in § 3 (see Table II), the radio emission of the Galaxy at its maximum (the direction toward the center of the Galaxy) is equivalent to thermal radiation with \(T_{ef} \simeq 10\,000^\circ\) \((\lambda = 4.7\ \text{m})\) and \(T_{ef} \simeq 6000^\circ\) \((\lambda = 1.87\ \text{m})\). Such an intensity cannot be explained by the radiation of stellar atmospheres. The same applies to radiation from cosmic dust. On the contrary, a quite acceptable explanation consists in the assumption that the radio emission of the Galaxy is due to interstellar gas or, more precisely, to interstellar electrons \(^{14, 23}\). The electron temperature in this case is just \(\sim 10\,000^\circ\) (see \(^{23, 19, 38}\)). Thus, the thermal radiation of interstellar electrons can explain the results of the most reliable measurements \(^{1, 15}\), provided only that in the direction toward the center of the Galaxy the optical thickness \(\tau\) for absorption due to electrons is greater than unity. For an estimate we shall take as the mean concentration of interstellar electrons \(^{23}\) the value

\[ N = 1\ \frac{\text{electron}}{\text{cm}^3},\quad T = 10^4{}^\circ \quad \text{and} \quad r = 5 \cdot 10^{22}\ \text{cm} \]

(the radius of the Galaxy). Then, according to (23) and (21):

\[ \begin{aligned} \gamma &\simeq 8.6 \cdot 10^{-5};\quad \varkappa \simeq 5.7 \cdot 10^{-23};\quad \tau \simeq 2.8;\quad (\lambda = 4.7\ \text{m}) \\ \varkappa &\simeq 9.0 \cdot 10^{-24};\quad \tau \simeq 0.45;\quad (\lambda = 1.87\ \text{m}) \end{aligned} \tag{33} \]

Since \(T_{ef}=T(1-e^{-\tau})\), for \(T=10^4\), for \(\lambda=4.7\) m \(T_{ef}\cong 10^4\), and for \(\lambda=1.87\) \(T_{ef}\cong 8500^\circ\), which, given the great roughness of the estimate, may be regarded as in complete agreement with experiment.

Analogous calculations\({}^{23}\), taking account of “free—free” absorption, lead to similar results (see Fig. 19). If one trusts Jansky’s data\({}^{13}\), then, according to\({}^{23}\) (see Fig. 19), for \(\lambda=14.6\) m, \(T_{ef}\sim 150\,000^\circ\). The question of \(T_{ef}\) at various waves, and especially at long ones, requires further experimental investigation.

Let us note that in the case of interstellar gas, owing to the smallness of \(N\), the “absorption” due to scattering of light by electrons also becomes appreciable. In this case, as is known,

\[ \varkappa_p=\frac{8\pi}{3}\left(\frac{e^2}{mc^2}\right)^2 N=6.57\cdot 10^{-25}\cdot N. \tag{34} \]

Taking, as above, \(N=1\) and \(r=5\cdot 10^{22}\), for all waves, owing to scattering alone, we obtain the value \(\tau_p\cong 0.033\). For waves \(\lambda\cong 50\) cm, \(\tau_p=\tau\), where \(\tau\) is the value connected with collisions. Thus, for \(\lambda<\sim 30\) cm, \(T_{ef}\cong T(1-e^{-\tau_p})\cong 0.033\,T\cong 330^\circ\). At centimeter waves, such radiation from the center of the Galaxy should be quite noticeable\({}^{10}\).

CONCLUSION

The observations carried out up to the present time of the radio emission of the Sun and the Galaxy and their analysis, which have been discussed above, have quite definitely revealed the great astrophysical, as well as geophysical and radio-engineering, interest of “radio astronomy” or “radio astrophysics,” as this new field of investigation may be called. Here, as in the case of the development of “radio spectroscopy” of molecules\({}^{39}\), we have an example of how the development of radar technology has expanded the field of application of radio methods to the solution of various scientific problems. It may be thought that in the very near future apparatus for observing cosmic radio emission, i.e. “radio telescopes,” will take their place in observatories and at ionospheric stations. Radio investigations (incidentally, considerably less dependent on meteorological conditions than optical observations) will prove a very valuable supplement to ordinary astronomical methods, first of all for the study of the solar atmosphere and of interstellar gas in the Galaxy, and later perhaps also beyond its limits.

CITED LITERATURE

1. G. Reber, Astrophys. Journ. 100, 279 (1944).
2. G. C. Southworth, Journ. Frankl. Inst. 239, 285 (1945); Errata. Journ. Frankl. Inst. 241, март, (1946) and Phys. Abstr. A 49, 268 (1946).
3. F. V. Appleton, Nature 156, 534 (1945).
4. J. S. Hey, F. J. M. Stratton, Nature 157, 47 (1946).
5. J. L. Pawsey, R. Rayne-Scott a. L. L. McCready, Nature 157, 158 (1946).

1. D. F. Martyn, Nature 158, 308 (1946).
2. E. V. Appleton and J. S. Hey, Nature 158, 339 (1946).
3. M. Ryle and D. D. Vonberg, Nature 158, 339 (1945).
4. E. V. Appleton and J. S. Hey, Phil. Mag., 37, 73 (1946).
5. R. H. Dicke and R. Beringer, Astrophys. Journ., 103, 237 (1946).
6. A. C. B. Lovell and C. J. Banwell, Nature 158, 517 (1946).
7. J. L. Pawsey, Nature 158, 633 (1946).
8. K. G. Jansky, Proc. I. R. E. 20, 1920 (1932); 21, 1387 (1933); 23, 1158 (1935); 25, 1517 (1937).
9. G. Reber, Astrophys. Journ. 91, 621 (1940); Proc. I. R. E. 28, 68 (1940).
10. J. S. Hey, S. J. Parsons and J. W. Phillips, Nature 157, 295 (1946).
11. J. S. Hey, S. J. Parsons and J. W. Phillips, Nature 158, 234 (1946).
12. L. A. Moxon, Nature 158, 758 (1946).
13. V. L. Ginzburg, DAN 52, 491 (1946).
14. I. S. Shklovsky, Astronomical Journal 23, 333 (1946).
15. D. F. Martyn, Nature 158, 632 (1946).
16. D. F. Martyn, Nature 159, 26 (1947).
17. F. L. Whipple and J. L. Greenstein, Proc. Nat. Acad. Sci. Amer. 23, 177 (1937).
18. L. G. Henyey and P. C. Keenon, Astrophys. Journ. 91, 625 (1940).
19. J. L. Greenstein, L. G. Henyey and P. C. Keenon, Nature 157, 805 (1946).
20. I. S. Shklovsky, UFN 30, 65 (1946).
21. E. V. Gerold and D. Molter, On reception at ultra-high frequencies. Gosenergoizdat (1945).
22. R. Clayton, D. Houldin, L. Lamont and V. Villaw, Radio measurements on decimeter and centimeter waves, § 10, “Sov. Radio” (1947).
23. V. L. Granovsky, Electrical Fluctuations, ch. IV, ONTI (1936).
24. A. Unsöld, Physik der Sternatmosphären (1938).
25. V. L. Ginzburg, UFN 28, 155 (1946).
26. V. L. Ginzburg, Journ. of Phys. 8, 253 (1944).
27. Ya. L. Alpert and V. L. Ginzburg, Izv. AN SSSR (physical series) 8, 42 (1944).
28. N. D. Papaleksi, UFN 29, 250 (1946).
29. M. N. Saha, Nature 158, 549 (1946).
30. M. N. Saha, Nature 158, 717 (1946).
31. M. N. Saha, Proc. Inst. Sci. India 8, 99 (1942).
32. K. O. Kiepenheuer, Nature 158, 340 (1946).
33. V. Ambartsumian, Theoretical Astrophysics, ch. VIII, ONTI (1939).
34. V. L. Ginzburg, Radiospectroscopy of Molecules, UFN 31, issue 3 (1947).
35. G. Reber, Nature 158, 945 (1946).