NEW DATA ON RADIO EMISSION FROM THE SUN AND THE GALAXY

G. G. Getmantsev

In the last two or three years several dozen new works have appeared devoted to one of the most interesting problems of astrophysics—the radio emission of the Sun and the Galaxy—which were not included in the two preceding reviews by V. L. Ginzburg1 (cited below as [I] and [II]). Discussion of the data contained in these works constitutes the content of the present article.

In presenting the factual material it proved impossible to avoid references to literature already discussed in [I] or [II]. Below, \([I^{20}]\), for example, denotes a reference to the work listed in the bibliography in [I] under serial number 20, and so on. This procedure makes it possible not to burden the list of cited literature given here with the titles of older sources and, we hope, will not lead to misunderstandings.

1. RADIO EMISSION FROM THE SUN

Numerous studies of the radio emission of the Sun and, in particular, measurements carried out in recent years have revealed three principal sources of radio emission: the solar corona, spots, and eruptions (bursts)[^3][^4][^5]. The contribution to the total observed radio emission of the Sun and the character of the radiation given by each of these sources are different and depend on the frequency at which the observations are made, the index of solar activity, and a number of other causes. The radio emission of the corona, often called the radiation of the “quiet” Sun, is usually interpreted as the thermal radiation of the electron-ion gas forming the corona (see [I]).

The concept of the “quiet” Sun is rather indefinite, since even in periods of minimum solar activity there is always on the Sun some number of spots or pores from which spots, filaments, etc., form, while various dynamic processes

processes in the corona do not cease at all. The radio emission of the “quiet” Sun, by which is meant the thermal emission of the corona and chromosphere in the radio range, is thus an idealization in the sense that it apparently is never observed “in pure form,” i.e., say, without an admixture of the radio emission of spots and eruptions, associated with various dynamical processes in the corona. The intensity of the thermal radio emission of the Sun thus plays the role of a lower limit for the total observed intensity of the radio emission.

At the time when observations of the thermal radio emission of the Sun encounter certain difficulties, connected, as is clear from what has been said, chiefly with the fact that, as a rule, it is rather difficult to separate it, for example, from the much more intense emission of spots, theoretically the question of the thermal radio emission of the Sun has been considered quite thoroughly8, 9, 10, 11. We shall not reproduce these calculations here, taking basically as our point of departure the fact that they are available in8, 12, and shall confine ourselves only to a brief, schematic summary of the principal results.

Fig. 1. Distribution of the electron concentration \(N\ \dfrac{\text{electrons}}{\text{cm}^{3}}\) and of the electron temperature \(T\) in the solar atmosphere7. \(r\) is the radius of the point of observation; \(r_{\odot}\) is the radius of the photosphere.

The thermal radio emission of the solar atmosphere is the bremsstrahlung of electrons moving with thermal velocities in the electrostatic field of ions, and at different wavelengths it comes from different regions (depths) of the solar atmosphere. The distribution of the electron concentration and temperature in the atmosphere of the Sun7 is shown in Fig. 1.

It turns out that for radio waves with wavelength \(\simeq 1\ \text{m}\) and greater, the middle and upper corona is already optically opaque, which, in accordance with Kirchhoff’s law, must therefore emit in this wavelength range approximately as a black body with temperature \(\simeq 10^{6}\) degrees K (see Fig. 1), whereas the temperature of the centimeter and decimeter radiation coming from the lower corona and chromosphere should be of the order of \(10^{4}\)—\(10^{5}\) degrees (see below).

The radio emission of the Sun, propagating in the direction toward the Earth, obviously passes through various regions of the solar

atmosphere on the distance of the radiating region from the center of the solar disk. In this connection, calculations of the distribution of “radio brightness” over the disk of the Sun and their experimental verification are of great interest. Curves of the distribution of “radio brightness” were computed by Martynov[^9], Waldmeier[^11], and Unsöld[^10] for the electron temperature and concentration distribution in the corona usually accepted in astrophysics, close to that presented in Fig. 1. Some of these curves are shown in Fig. 2*). The increase of brightness toward the edges of the disk at decimeter wavelengths ($\lambda = 50$–$60\ \text{cm}$) is explained by the fact that, for rays emerging from the edges of the disk and therefore propagating tangentially to the surface of the Sun, the optical thickness is greater and the radio emission observed is therefore from higher and hotter layers of the corona than for rays emerging from the central regions of the solar disk.

Fig. 2. Theoretically computed distribution of the effective temperature over the solar disk at wavelengths $\lambda = 40$ and $60\ \text{cm}$ and $\lambda = 50\ \text{cm}$.

The magnetic field of the Sun, making the corona anisotropic, should lead to the splitting of the radio emission into “ordinary” and “extraordinary” waves, which are absorbed differently by the corona and differ from one another in their polarization properties[^8,^9],1. According to Martynov’s calculations [[^20]], who assumed the magnetic field at the solar poles to be equal to 50 gauss, the difference in the intensities of the “ordinary” and “extraordinary” waves should have been especially large at a wavelength of $\simeq 50\ \text{cm}$. Owing to the fact that the angle between the polar axis of the Sun and the line of sight of an observer following the Sun changes and, generally speaking, differs from $90^\circ$, the contribution to the observed radio emission from the southern and northern hemispheres of the Sun should be somewhat different. If there is a magnetic field on the Sun $H \simeq 50$ gauss, this latter circumstance should have led, at wavelengths $\simeq 50\ \text{cm}$, to a noticeable difference in the intensities of the circularly polarized components of the radio emission with opposite signs of rotation of the field vectors.

*) Here and below, by the equivalent (or effective) temperature of the Sun is meant the temperature which the Sun would have to possess, with visible dimensions, radiating as a black body, in order to produce radio emission of the required intensity. The intensity of radio emission-

G. G. GETMANTSEV

An experimental study of the distribution of “radio brightness” presents, obviously, great difficulties, since for measurements of this kind it is necessary that the angular width of the receiving antenna’s directivity pattern $\theta$ be considerably smaller than the angular size of the Sun ($\simeq 0.5^\circ$), i.e., that the dimensions of the antenna installation be (for example, at a wavelength $\lambda \simeq 1\ m$) greater than $10^2\ m$.

Another possibility for measurements of this kind, consisting in the observation of radio emission during eclipses, was used by Christiansen and others2 with the aim of verifying the increase of “radio brightness” at the edges of the solar disk predicted by Martin and the expected difference in the intensities of the circularly polarized components of the radio emission. Measurements at a wavelength of $50\ cm$ were carried out simultaneously at three different points in southeastern Australia during the partial solar eclipse of November 1, 1948. Analysis of the time variation of the intensity of the radio emission during the eclipse showed that approximately half of the radio emission comes from regions outside the visible disk of the Sun; however, it was not possible to determine the details of the distribution of “radio brightness” at the limb of the disk. The moments when the intensity decreased abruptly indicated that at that time the Moon was covering a portion of the disk brighter (in radio emission) than the rest of the Sun.

Fig. 3. Position of “radio-bright” regions on the solar disk during the solar eclipse of November 1, 1949, in southeastern Australia: — path of the center of the Moon and --- path of the lunar limb for three observing points. Regions 2, 7, 8 coincide with sunspots, while 3, 4, 5 are close to positions at which groups of spots were present 27 days before the eclipse. Region 1 is the location of a large prominence ($\Pi$). The shaded region was not covered by the Moon at all.

The coordinates of such regions could be determined easily, since the positions of the lunar limb projected onto the solar disk were different and, generally speaking, intersected for all three observing points (Fig. 3). The caption to Fig. 3 makes it unnecessary to give here any explanations regarding the coincidence of regions of the Sun active in radio emission with spots and other

solar formations. As for the intensities of the circularly polarized components of the radio emission, to within the errors of measurement (about 30%) they proved to be equal. This, in the opinion of the authors2, means that the magnetic moment of the Sun is less than \(1.4\cdot 10^{33}\) gauss·\(\text{cm}^3\), i.e. that the magnetic-field strength at the poles is less than 8 gauss. The latter conclusion is especially interesting, since it coincides with the results of estimates of the magnetic moment of the Sun from the data of modern measurements of the deflecting action of the solar magnetic field on cosmic rays[^14].

Only comparatively recently did Stanier[^15] succeed in measuring the distribution of “radio brightness” over the disk of the Sun at a wavelength of 60 cm. The method of measurement he used deserves a few words. The radio emission of the Sun (a period was chosen when there were few spots on the Sun) was received by two antennas operating on one receiver, the distance \(d\) between the antennas being varied in the course of the measurement from zero to \(350\lambda\).

For each definite distance \(d\), the directional diagram of this receiving device consisted, obviously, of a number of separate lobes with an angular size of the order of \(\frac{\lambda}{d}\). Owing to the diurnal rotation of the Earth, the Sun moved in the zone of the multilobe directional pattern of the receiving antennas. It is not difficult to see that the ratio of the maximum readings of the output instrument to the minimum readings must in this case be proportional to the amplitude of the Fourier component of the distribution of radio brightness over the solar disk with an angular period of the order of \(\frac{\lambda}{d}\). Indeed, the harmonic components of the distribution of radio brightness with angular period \(\theta \gg \frac{\lambda}{d}\) (the distribution of radio brightness being represented by a Fourier integral) should not make a noticeable contribution to the variable component of the readings of the output instrument because of averaging over a large number of lobes of the receiving directional diagram. The same may be said of components with \(\theta \ll \frac{\lambda}{d}\), since in this case averaging takes place over the dimensions of one lobe of the directional diagram. From what has been said it should be clear that only components of the distribution with \(\theta\) close to \(\frac{\lambda}{d}\) should cause changes in the readings of the receiver output instrument in connection with the displacement of the Sun, and the magnitude of these changes must be proportional to the modulus of the Fourier component of the radio-brightness distribution with angular period \(\simeq \frac{\lambda}{d}\). The “spectrum” of the distribution of radio brightness (effective temperature) over the solar disk obtained in this way is shown in Fig. 4, a. Then summing the harmo-

components of the distribution with the corresponding phases, the authors succeeded in obtaining the desired distribution of the density of radio-emission sources at \(\lambda = 60\) cm (Fig. 4, b). It turned out that about \(30\%\) of the radiation comes from regions outside the visible disk, and the equivalent temperature of the Sun at this wavelength is \(5.4 \cdot 10^5\) degrees.

Fig. 4. a) The “spectrum” of the distribution of the density of radio-emission sources over the disk of the Sun at \(\lambda = 60\) cm. The different curves represent the results of independent measurements. b) The distribution of the density of sources \((T_{ef})\), obtained as a result of summing the sinusoidal components of figure a.
— · — · — limits of possible errors.

From Fig. 4, b it is clear that there is in fact no increase in brightness toward the edges of the disk, as predicted by Martyn and others (see Fig. 2). On the other hand, it is hardly possible to doubt the correctness of the calculations in \(^{9,10,11}\). The only reasonable explanation of the discrepancy between the results of the calculations and the experiment apparently consists in the fact that the electron temperature in the corona is in reality somewhat lower than that adopted in \(^{9,10,11}\) (\(\simeq 10^6\) degrees), in connection with which the radio emission from the edges of the disk should decrease somewhat, while the radiation coming from the central regions of the disk, on the contrary, should increase owing to an increase

optical opacity of the corona, leading to a displacement of the emitting region into higher (hotter) layers of the corona*).

Measurements of the Sun’s radio emission at wavelengths longer than 1 m over the period from 1944 through 1948 indicate that during this period the effective temperature of the “quiet” Sun, and consequently also the electron temperature in the corona, was \(\simeq 10^6\) degrees. The value \(T_{\text{corona}} = 10^6\) degrees is in good agreement with estimates of the coronal temperature from spectroscopic measurements and with theoretically calculated values of \(T_{\text{corona}}\) (Fig. 1). As far as we know, there are no reliable quantitative data on changes in the coronal temperature over the 11-year cycle of solar activity. This does not mean, however, that such changes are absent or very small; rather, it is evidently connected with the inaccuracy of optical methods for determining \(T_{\text{corona}}\) and, chiefly, with their lack of systematic character. It is possible that the decrease in coronal temperature \((T_{\text{corona}} < 5 \cdot 10^5\) degrees) inferred from a comparison of Fig. 2 and Fig. 4, b is precisely connected with the decrease in solar activity after 1948 (the last maximum of the 11-year cycle of solar activity was in 1948).

Changes in the electron concentration in the corona, as is easy to see, should affect the form of the distribution of “radio brightness” over the solar disk in a way analogous to the influence of changes in the coronal temperature. In other words, a decrease in particle concentration should also lead to a leveling of the distribution of \(T_{ef}\) over the solar disk, i.e. to the distribution shown in Fig. 4, b.

It is still difficult to draw any final conclusions about changes in the temperature and particle concentration in the corona as functions of the phase of the 11-year cycle of solar activity on the basis of the material on solar radio emission published in the literature. By combining data on the distribution of \(T_{ef}\) over the solar disk with data on \(T_{ef}\) of the Sun as a whole, it will probably be possible to obtain more accurate information on the temperature and particle concentration in the corona than that obtained by optical methods of studying the corona.

The presence of spots on the Sun, as was noted long ago ([I], [II]), often leads to a strong increase in radio emission. Using the interference method with two receiving antennas separated by a distance considerable in comparison with the wavelength \(\lambda = 1.7\) m, Ryle and Vonberg\(^3\) measured the angular size and position of sources of intense radio emission, as well as their polarization. It turned out that the sources are regions of the solar disk lying near spots, whose angular diameter is \(< 10'\)

*) The author was able to acquaint himself with works \(^{54,55,56,57,58}\) after the review had been written. Therefore they are not reflected below with sufficient completeness.

and the radio emission of these regions is almost completely circularly polarized. Of the sixteen cases analyzed by the authors, in nine the sign of the polarization corresponded to the “ordinary” wave, in three cases to the “extraordinary” wave, and, finally, in four cases it was not possible to identify the observed polarization with the polarization of one or the other wave*).

In the presence of spots, the equivalent temperature of the Sun reached, at frequencies of 175 Mc/s and 80 Mc/s, values respectively of \(10^8\) and \(10^9\) degrees. At the same time, according to the authors’ evidence\(^{3}\), at frequencies of 200 Mc/s the minimum observed equivalent temperature was \(\sim 10^6\) degrees.

Fig. 5. Dependence of the intensity of the Sun’s radio emission \((A)\) at \(\lambda = 10.7\ \mathrm{cm}\) (relative units) on the number of sunspots \((B)\) (relative numbers).

Interpreting the measurement results of Ryle and Vonberg, Thompson\(^{16}\) points out that: a) the maximum intensity of the radio emission of a spot is usually observed during its passage across the central meridian of the Sun, and b) rapidly developing spots, especially in the early stages of development, as well as spots accompanied by eruptions, give stronger emission.

A close connection between the intensity of radio emission and the number of sunspots is also noted by Covington\(^{17}\). In Fig. 5 the course of the daily intensities of radio emission \((A)\) at \(\lambda = 10.7\ \mathrm{cm}\) for the period February–September 1947 is given, along with the curve of changes in the relative number of spots \((B)\) for the same period of time. In both curves a 27-day period, equal to the time of one rotation of the Sun about its axis, is quite clearly noticeable. The equivalent temperature of the Sun at \(\lambda = 10.7\ \mathrm{cm}\), according to Covington’s measurements, is equal to \(7.9 \cdot 10^4\) degrees.

Observing the radio emission of sunspots at \(\lambda = 25\) and \(54\ \mathrm{cm}\) during the partial eclipse of April 28, 1949, in Paris, the authors\(^{6}\)

*) For a spot whose magnetic field is directed toward the terrestrial observer, the electric vector of the “ordinary” wave rotates counterclockwise, if one looks along the positive direction of propagation of the wave.

came to the conclusion that at these wavelengths the main part of the radio emission comes from the peripheral regions of spots. This interesting result is, however, preliminary and lies at the limit of possible measurement errors.

Whereas at wavelengths of \(\sim 1\) m and longer the presence of spots often leads to an increase in the Sun’s radio emission by \(10^2 \div 10^3\) times, at wavelengths of \(\sim 10\) cm the intensity of the radio emission usually increases only by several times. Taking this into account, Waldmeier\(^{11}\) explains the radio emission of spots at \(\lambda \cong 10\) cm as thermal radiation from coronal condensations—regions of the corona with increased electron concentration \(\left(\text{up to }10^{10}\ \frac{\text{electrons}}{\text{cm}^3}\right)\), lying directly above the spots. The electron concentration in such a condensation is sufficiently large for it to be optically opaque to waves of \(\sim 10\) cm, while the temperature in it is the same as in the higher layers of the corona, i.e. \(\sim 10^6\) degrees. According to Waldmeier’s estimates, the intensity of the radio emission produced by a single coronal condensation can reach up to \(9\%\) of the intensity of the thermal radio emission of the entire corona. During periods when the number of spots on the Sun is large, the radio emission at \(\lambda \cong 10\) cm may therefore increase two- to threefold. The thermal radiation of such condensations cannot, of course, explain the anomalously large radio emission of spots at wavelengths in the meter range.

As already indicated, the intensity of the radio emission of spots in the meter range can reach very large values, an idea of which is given by Table I below (\(\lambda = 4.1\) m) and by the frequency spectrum of the radio emission (Fig. 6)\(^{4}\).

Table I

Let us note that an intensity of \(10^{-22}\ \frac{\text{W}}{\text{m}^2\cdot\text{Hz}}\) at \(\lambda = 4.1\) m is equal to the intensity of the thermal radiation of the entire Sun with an equivalent temperature of \(\sim 10^6\) degrees, i.e. approximately the value observed in the absence of spots.

Sunspot radio emission has a clearly expressed directional character, being concentrated mainly in a cone with an angular aperture of the order of \(40^\circ\), whose axis is perpendicular to the surface of the spot\(^4\). The intensity of sunspot radio emission fluctuates slightly with time\(^ {38}\).

The intensity of the radio emission of eruptions (flares), which sometimes arise in the regions of certain spots and are often accompanied by a sudden interruption of short-wave radio communication (“fade-out”), on the contrary, undergoes considerable fluctuations of the type of sudden “bursts” and peaks\(^4\). “Bursts” of radio emission usually arise several minutes later than the beginning of an eruption, so that it is sometimes very difficult to identify them with one or another eruption. The correlation between radio-emission bursts and flares on the Sun increases, as a rule, with increasing intensity of the flares; moreover, during large eruptions the intensity of radio emission on meter waves reaches very large values

\[ \left(>10^{-19}\ \frac{\mathrm{W}}{\mathrm{m}^{2}\cdot \mathrm{c/s}}\right). \]

Fig. 6. Spectrum of the radio emission of sunspots on November 25, 1947. Unit of intensity — \(10^{-20}\ \dfrac{\mathrm{W}}{\mathrm{m}^{2}\cdot \mathrm{c/s}}\).

With regard to the frequency dependence of the radio emission of eruptions, almost nothing is known, except perhaps that larger “bursts” of radiation correspond to a greater increase in intensity at long wavelengths\(^ {18}\). “Bursts” of radio emission accompanying a “fade-out” usually lag by several minutes relative to the beginning of the “fade-out.” This evidently indicates that the radio emission associated with eruptions arises in the upper layers of the corona, which the agent exciting the radio emission reaches several minutes after the beginning of the flare in the ultraviolet part of the spectrum responsible for the “fade-out”\(^4\), [1].

Recently\(^ {19}\), with the aid of an automatically operating radio interferometer, making it possible in \(\sim 1\) sec to determine the position of the radiating region on the Sun, it has been possible to detect very

an interesting phenomenon—the motion of a source of radio-emission “bursts” that arose as a result of a large eruption at a distance of \(\sim 0.5\) solar radius from the edge of the visible disk. Over a time of about half an hour the source moved through a distance approximately equal to the radius of the Sun and was found at a height of \(\sim 0.5\) radius from the edge of the visible solar disk. On the basis of these data, the mean velocity of the source during the period of observation was

\[ \sim 3\cdot 10^7\ \frac{\text{cm}}{\text{sec}} . \]

As was already indicated in [I] and [II], the radio emission of spots cannot be explained by radiation from electrons rotating with thermal velocities in the magnetic field of a spot \(H\) with the gyromagnetic frequency \(\omega_H=\dfrac{eH}{mc}\). The point is that the electron-ion gas constituting the corona, when a constant magnetic field of the spot is imposed on it, continues to remain in a state of thermodynamic equilibrium (it is assumed that before the magnetic field is imposed the corona, at least locally, was in a state of thermodynamic equilibrium). In such a case the electron-ion gas of the corona cannot, of course, radiate more than a black body at the temperature of the corona. Formally this is manifested in the fact that an increase in the emissive power of the electron gas at the frequency \(\omega_H=\dfrac{eH}{mc}\) must be completely compensated by an increase in the absorptive power of the corona at the same frequency. However, even if one does not take into account the “true,” i.e. collision-related, absorption of radio emission of “gyromagnetic” electrons, this radio emission still cannot leave the corona\(^{20}\). Indeed, an electron rotating in a magnetic field \(H\) with angular frequency \(\omega_H=\dfrac{eH}{mc}\) emits at the frequency \(\nu_H=\dfrac{\omega_H}{2\pi}\) a circularly polarized wave, the direction of rotation of the field vectors in which corresponds to the direction of their rotation in the “extraordinary” wave (for simplicity we confine ourselves to considering only the practically most important case of propagation of radio waves along the lines of force of the magnetic field of the spot). The square of the refractive index for the “extraordinary” wave with frequency \(\nu=\dfrac{\omega}{2\pi}\), propagating in a medium with electron concentration \(N\ \dfrac{\text{electrons}}{\text{cm}^3}\), is, as is known\(^{12}\),

\[ n^2 = 1-\frac{4\pi e^2 N}{m\omega(\omega-\omega_H)} \tag{1} \]

and, consequently, the “extraordinary” wave can propagate, \(n^2>0\), only when \(\dfrac{\omega_H}{\omega}>1\) or

\[ \frac{\omega_H}{\omega}<\left(1-\frac{4\pi e^2N}{m\omega^2}\right). \]

The magnetic field of a spot decreases with increasing distance from the spot. Thus,

if, at some height above a sunspot, an electron rotating in its magnetic field emits radio waves with frequency \(\nu_H=\dfrac{eH}{2\pi mc}\), then, propagating in the direction toward the terrestrial observer, this wave immediately finds itself in a region where \(\dfrac{\omega_H}{\omega}<1\), where \(n^2<0\), i.e., the refractive index is an imaginary quantity and the wave is exponentially damped. In the direction toward the spot, however, this wave, on the contrary, can propagate \(\left(\dfrac{\omega_H}{\omega}>1 \text{ and } n^2>0\right)\).

Another, rather peculiar, attempt to explain the radio emission of spots belongs to Bailey^21. Bailey considered the propagation of radio waves in an ionized gas in the presence of constant magnetic and electric fields and came to the conclusion that, for a certain choice of the magnitudes and directions of these fields, the amplitude of a radio wave propagating in such a medium increases and may, as applied to solar spots, reach the values observed experimentally. There is no need to analyze Bailey’s exposition here, since it is cumbersome, and the final formulas are possibly incorrect. In^22 the considerations developed by Bailey are rejected as completely untenable. Because of the small size of note^22, the grounds for such sharp criticism are not entirely clear.

Several years ago Shklovskii \([1^{19}]\) and Martyn \([1^{21}]\) proposed explaining the radio emission of spots by the radiation of coherently oscillating coronal electrons. Since then, several works have appeared devoted to the question of oscillations in an electron-ion plasma and to methods of exciting these oscillations. We are not able here to present in any detail the content of these works, the discussion of which could be the subject of a separate review, especially since there is as yet no quantitative calculation of plasma oscillations and of the associated radio-emission intensity under the conditions of the solar corona.

Forced oscillations of plasma in discharge tubes are caused by a stream of electrons emerging from the heated cathode of the tube. The only visible mechanism capable of exciting analogous oscillations in the solar corona is likewise reduced to an electron stream, formed in spots, which is modulated in velocities (densities) in certain regions of the corona and then transfers the energy of its translational motion to the oscillatory motion of the plasma (self-excitation of the plasma). Therefore, although oscillations of the coronal plasma are a very probable cause of the occurrence of the powerful radio emission of spots, the calculation of the intensity of forced plasma oscillations cannot ignore the fact that the thermal velocities of electrons in the corona

(at \(T \simeq 10^6\) degrees the arithmetic mean velocity of the particles is of the order of \(10^9\ \frac{cm}{sec}\))—of the order of the velocities of ordered motion acquired by the electrons of the beam exciting the plasma under the action of electric fields existing in spots, during the time between two collisions of electrons with ions. Thermal motion may, therefore, hinder the formation of electron “clots” in the primary unmodulated electron stream that are necessary for exciting the plasma \(^{23}\).

Another possibility for explaining the anomalously large radio emission of spots consists in reducing it to the radiation of relativistic electrons rotating in the magnetic fields of spots. This possibility was pointed out to us by V. L. Ginzburg. A relativistic electron (\(E \gg mc^2\)), moving perpendicular to the lines of force of a magnetic field \(H\), radiates per second, in a unit spectral interval, an energy \(^{42}\)

\[ P(\nu)=16\,\frac{e^3H}{mc^2}\,p\!\left(\frac{\omega}{\omega_1}\right), \tag{2} \]

where \(\nu=\frac{\omega}{2\pi}\) is the radiation frequency, \(\omega_1=\frac{eH}{mc}\left[\frac{E}{mc^2}\right]^2\), and \(p\!\left(\frac{\omega}{\omega_1}\right)\) is a certain function of the ratio \(\frac{\omega}{\omega_1}\) (see \(^{42}\)). The magnetic fields of spots may reach values of \(10^3\) gauss and more in the immediate vicinity of the spot. In the corona, however, at distances from the solar surface of the order of several spot radii, the magnetic field apparently reaches values of \(10\)—\(10^2\) gauss \(^{7}\). Thus, in the corona above a spot (for \(\frac{E}{mc^2}\) greater than, for example, 10) \(\omega_1\) is greater than \(10^{10}\), and \(\frac{\omega}{\omega_1}\ll 1\). In this connection, when estimating the number of relativistic electrons necessary to create radio emission of the required magnitude, one may use the asymptotic expression
\[ p\!\left(\frac{\omega}{\omega_1}\right)=0.256\left[\frac{\omega}{2\omega_1}\right]^{\frac13}, \]
valid for \(\frac{\omega}{\omega_1}\ll 1\), so that from (2), substituting the numerical values of all the constants entering into it, we obtain directly:

\[ P(\nu)=4.35\cdot 10^{-22}H\left(\frac{\omega}{\omega_1}\right)^{\frac13}\ \frac{erg}{sec\cdot cps}. \tag{3} \]

The energy flux from \(N\) radiating electrons at the Earth is equal to:

\[ S=\frac{PN}{4\pi R^2}=\frac{P\pi r^2\Delta hn}{4\pi R^2} =\frac{P}{4}\left(\frac{r}{R}\right)^2\Delta hn\ \frac{erg}{cm^2\cdot sec\cdot cps}, \tag{4} \]

where \(R\) is the distance between the Earth and the Sun, \(r\) is the radius of the radiating region, \(\Delta h\) is the thickness of this region, and \(n\) is the number of relativistic electrons per unit volume. In order to estimate the order of \(n\), it is necessary to compare (4) with the values of \(S\) observed experimentally. It is known that the effective temperature of spots often reaches values \(\sim 10^{12}\) degrees and, consequently, for example for \(\lambda = 3\ m\),

\[ S=\frac{8.7\cdot 10^{-16}}{\lambda^{3}}\left(\frac{r}{R}\right)^{2}T_{ef} \approx 10^{-8}\left(\frac{r}{R}\right)^{2}\frac{erg}{cm^{2}\cdot sec\cdot cps}. \tag{5} \]

Comparing (4) and (5) for \(\omega_{1}=10^{10}\) \((E\simeq 10\ mc^{2}\) and \(H\simeq 10\) gauss), we find

\[ \Delta h\cdot n\sim 10^{13} \]

or, if the depth of the radiating region is \(\Delta h\sim 10^{10}\ cm\) (about one-tenth of the solar radius), then \(n\simeq 10^{3}\ \dfrac{\text{electrons}}{cm^{3}}\). The value \(n=10^{3}\ \dfrac{\text{electrons}}{cm^{3}}\) provides the required intensity of radio emission in the absence of absorption. Allowance for absorption of radio waves in the corona must evidently lead to an increase in the number of relativistic particles required to produce the necessary radio-emission intensity. Assuming, somewhat conditionally, that the radiating region is situated in that layer of the corona where the refractive index for a wave of the given frequency becomes zero in the absence of a magnetic field, and using published data\(^8\) on the absorption of radio waves in the corona (\(T_{\text{corona}}\simeq 10^{6}\) degrees), it is not difficult to establish that taking account of the absorption of radio waves in the meter range compels one to increase \(n\) at most by a factor of \(10^{5}\). Propagating along the lines of force of the magnetic field of a spot, the radio emission of relativistic electrons must be circularly polarized. It can also be shown that, depending on the position of the radiating region in the corona, the sign of the polarization of the radio emission may correspond to either the “ordinary” or the “extraordinary” wave.

The question of the presence in the corona above spots of \(10^{5}\) relativistic electrons per cubic centimeter, with a total electron concentration \(\sim 10^{8}-10^{9}\ \dfrac{\text{electrons}}{cm^{3}}\), is not entirely clear. One of the possible mechanisms capable of accelerating coronal electrons to relativistic energies is the process of acceleration of electrons in an induction electric field arising when the magnetic field of a spot changes. Estimating this effect, Unsöld\(^ {18}\) comes to the conclusion that electrons can thereby be accelerated to energies \(\simeq 10^{10}\ ev\). The induction electric fields arising in the neighborhood of spots and accelerating the charged particles of the corona lead, in the opinion of authors\(^ {20,23,50}\), even to the fact that electron-

temperature of the corona above spots reaches values of \(10^{10}\) degrees and higher, and therefore the radio emission of spots is simply thermal radiation of the corona*).

The determination of what the actual source of the radio emission of spots is could be greatly aided by experimental data on the polarization and spectrum of the radio emission. However, the information available on these questions is not systematic, and this makes it difficult to discuss the reality of one or another mechanism of the radio emission of spots.

As for the polarization and spectrum of the radio emission associated with eruptions, the information about them is still more scanty. Since eruptions (especially large ones) often cause various geophysical phenomena—auroras, magnetic storms, etc.—the radio emission associated with them is apparently due to processes of acceleration and emission of particles in the seat of the eruption. To clarify the processes associated with the radio emission of spots and eruptions, it is also desirable to have more complete information on the distribution function of electron velocities in the corona\(^{24}\).

Finally, we note that works\(^{7,10,18,25,51}\) are of a survey character, with \(^{10,18,25,51}\) containing an extensive bibliographic index of the literature, while \(^{7}\) gives a summary of the basic information on the corona and spots (the distribution of temperatures and electron concentrations in the corona, the magnetic fields of spots, etc.) needed for various calculations connected with the radio emission of the Sun.

2. RADIO EMISSION OF THE GALAXY

Experimental and theoretical works of recent years devoted to the radio emission of the Galaxy introduce much that is new into our ideas about the nature and character of cosmic radio emission. In this connection it seems expedient, before proceeding directly to the analysis of the new data,

*) The magnetic field of a spot \(H\) possesses axial symmetry, and \(E_{\text{ind.}}\) is directed along concentric circles enclosing the magnetic field. By the law of induction, very roughly,

\[ |\varepsilon_{\text{ind.}}|=|E_{\text{ind.}}|\cdot 2\pi r= \]

\[ =\frac{1}{c}\,H(\pi r^2)/\Delta t, \]

where \(r\) is the radius of the spot, \(\Delta t\) is the lifetime of the spot. For \(\Delta t=10\) days \(\simeq 10^6\) sec., \(r=5\cdot 10^9\) cm and \(H=10^2\) gauss, we have \(\varepsilon_{\text{ind.}}\simeq 3\cdot 10^5\) CGSE \(\simeq 10^8\) volts and \(E_{\text{ind.}}\simeq 10^{-4}\) CGSE. In the magnetic field of a spot, under the action of \(E_{\text{ind.}}\), an electron moves perpendicular to \(E_{\text{ind.}}\) and \(H\) with an average drift velocity

\[ \bar v=\frac{cE_{\text{ind.}}}{H}. \]

Since

\[ \frac{E_{\text{ind.}}}{H}\simeq 10^{-6}\ll 1, \]

we have \(\bar v\ll c\). Thus, in the scheme developed, the bulk of the electrons cannot be accelerated to relativistic energies.

to dwell, if only briefly, on the state of the question in the form in which it is presented, for example, in the two preceding reviews [I] and [II].

The radio emission, discovered as early as 1932 and clearly of extraterrestrial origin, was investigated more or less thoroughly in the wavelength range from \(1\) cm to \(31\) m only during the last decade. The generally accepted quantitative characteristic of the intensity of cosmic radio emission, as well as of the radio emission of the Sun, is the so-called effective temperature \(T_{ef}\), defined as the temperature of black-body radiation of the same intensity as that observed experimentally for the given direction. A series of measurements made it possible to compile “radio-astrophotometric” maps, i.e. to find the dependence of \(T_{ef}\) on celestial coordinates. It turned out that the distribution of the intensity of radio emission over directions, at least for waves of the meter range, depends only very weakly on frequency.

Along with the angular distribution of the radio emission, its frequency dependence was also studied. The intensity of the radiation for waves in the range \(3\)—\(7.5\) m decreases with increasing frequency \(\nu\) approximately as \(\nu^{-\alpha}\), where \(\alpha = 0.7\) for strongly emitting regions of the sky and \(\alpha = 0.1\) for weakly emitting regions \([1^{17}]\). In the language of effective temperatures, related to intensity by the Rayleigh–Jeans law, this means that for strongly and weakly emitting regions of the celestial sphere \(T_{ef}\) is proportional, respectively, to \(\nu^{-2.7}\) and \(\nu^{-2.1}\). Finally, let us note that until recently\(^{26}\) there were no indications of the existence of any noticeable extragalactic radio emission.

The explanation of cosmic radio emission and of the principal experimental data relating to it was for a long time based on reducing the radio emission to thermal radiation of an interstellar electron gas with the temperature \(T = 10^4\) degrees accepted in astrophysics. In such an interpretation, the effective temperature \(T_{ef}\) of the radiation reaching the Earth is evidently equal to \(T(1 - e^{-\tau(\lambda)})\), where \(\tau(\lambda)\) is the optical thickness of the Galaxy for the selected direction and wavelength \(\lambda\), and the expression in parentheses is, in essence, the ratio of the absorptive capacity of the Galaxy for this direction to the absorptive capacity of an absolutely black body. Thus, in the thermal mechanism of the origin of radio emission, the effective temperature is always less than the true temperature of the medium, and only when \(\tau \to \infty\) must the observed intensity equal the intensity of black-body radiation with the temperature of the electron gas \(T\).

The Galaxy has the form of a lens with a transverse dimension \(\sim 5 \cdot 10^{22}\) cm and a thickness of the order of one tenth of the transverse dimension. As estimates of the value \(\tau(\lambda > 1\ \text{m})\) show (see [I]) for the direction toward the center of the Galaxy, i.e. for the direction coinciding with its greatest

size, at an electron concentration \(N = 1 \dfrac{\text{electron}}{\text{cm}^{3}}\), \(\tau \simeq 1\). Consequently, the effective temperature of the galactic center must be of the order of \(T = 10^{4}\) degrees, in good agreement with the results of a considerable number of measurements. For other directions, not lying in the plane of the Galaxy, the optical thickness could be less, or even much less, than unity, i.e. \(T_{ef}\) is less and in a number of cases much less than \(10^{4}\) degrees. This, at least qualitatively, explains the firmly established experimental fact that regions of the sky lying near the galactic poles emit considerably less than the region of the Milky Way.

At the present time, however, it has been firmly established that the radio emission of the Galaxy cannot be explained mainly by thermal radiation from interstellar matter. The considerations leading to this conclusion will be set forth below, after we dwell on the new experimental data on cosmic radio emission.

In 1946 Hey and others \([^{16}]\), while investigating radio emission given by one of the secondary maxima lying in the constellation Cygnus, found that the received intensity undergoes noticeable fluctuations similar to those observed in the radio emission of sunspots \({}^{27}\). This suggested the presence in Cygnus of a sufficiently powerful source with angular dimensions small in comparison with the angular width of the directional pattern of the antenna used. It was necessary to investigate the Cygnus region with an installation possessing greater angular resolving power.

Such measurements at frequencies of 65, 85, 100, and 200 Mc were carried out by Bolton and Stanley \({}^{28}\) by means of a method analogous to that already used for measuring the dimensions and position of active radio-emitting regions of the Sun. In Bolton’s installation the role of the second antenna was played by the “reflection” of the real antenna, located on a cliff above the sea. The results of the measurements, given in \({}^{28}\), are as follows: 1) The size of the source proved to be less than \(8'\)—the resolving power of the installation. 2) The coordinates of the source: right ascension \(19^{h}59^{m}49^{s} \pm 10^{s}\), declination \(+41^{\circ}41' \pm 7'\). 3) The radiation of the source can be divided into two components: a constant one and a variable one, consisting of individual “bursts” lasting from several seconds to several minutes. In Fig. 7 a typical record is given of the source’s rising at a frequency of 100 Mc. The constant and variable components of the intensity are separated by a dashed line. 4) Observations at different frequencies showed that the constant component of the intensity of the radio emission has at a frequency of 100 Mc a weakly expressed maximum, whereas the magnitude of the variable component

rapidly increases as the frequency decreases. Already at a frequency of 200 MHz the variable component is absent. 5) Comparatively slow fluctuations of intensity at different frequencies are well correlated in time. As for the power of the source in Cygnus, according to the authors’ calculations^28, for source dimensions \(<8'\) at 100 MHz its effective temperature must be greater than \(4\cdot 10^6\) degrees.

Subsequently Bolton^29, examining a region occupying approximately \(1/4\) of the celestial sphere and enclosed approximately within the coordinates: right ascension \(8^h\), declination \(+40^\circ\); right ascension \(21^h\), declination \(+40^\circ\); right ascension \(4^h\), declination

Fig. 7. Record of the radio emission of the discrete source in Cygnus at rising, at \(\lambda=3\) m.

\(-40^\circ\); right ascension \(17^h\), declination \(-40^\circ\), succeeded in detecting six new discrete sources of radio emission. We do not give here the data relating to these sources, since they have already been reported in Nature^30*).

Measuring, at a frequency of 80 MHz, the polarization of the radio emission coming from the discrete source in Cygnus, Ryle and Smith^31 found it to be naturally polarized. This, apparently, indicates the absence of any appreciable magnetic field in the Cygnus source. In addition, they succeeded in detecting two new discrete sources, the more powerful of which is located in the constellation Cassiopeia and, in the character of its radiation, resembles the source in Cygnus. The intensity of the radio emission of the Cassiopeia source is \(23\cdot 10^{-23}\dfrac{\mathrm{W}}{\mathrm{m}^2\cdot\mathrm{cps}}\), and the magnitude of the variable component is \(6\cdot 10^{-23}\dfrac{\mathrm{W}}{\mathrm{m}^2\cdot\mathrm{cps}}\). At the same time, for the source in Cygnus at a frequency of 80 MHz the corresponding quantities are \(14\cdot 10^{-23}\) and

*) Note^30 is a brief review summary of the principal experimental results presented in^28, ^29, ^31, ^32. Let us also note that in^29 and^30, for the declination of the discrete source in Taurus, an apparently incorrect value \(+28^\circ\) is given, since in another, later article by Bolton^32 this declination is indicated as equal to \(+22^\circ\).

\(20\cdot10^{-23}\) (see below). A less powerful source, located in the constellation Ursa Major, gives an intensity of \(5\cdot10^{-23}\ \dfrac{\mathrm{W}}{\mathrm{m}^2\cdot\mathrm{Hz}}\). The angular dimensions of both sources proved to be less than \(5'\)—the resolving power of the installation.

The discovery of discrete sources of radio emission prompted attempts to identify them with visible celestial objects of one kind or another. For this purpose, as accurate as possible a determination was made of the coordinates of sources located in the constellations Taurus, Virgo, and Centaurus. It turned out that the indicated discrete sources, within the limits of experimental errors, coincide with nebulae. The coordinates of these sources and some data relating to the nebulae identified with them are given in Table II below.

Fig. 8. Curves of relative intensity of radio emission coming from the region of the Great Nebula in the constellation Andromeda. One division on the intensity axis corresponds to \(10^{-25}\dfrac{\mathrm{W}}{\mathrm{m}^2\cdot\mathrm{Hz}}\).

If, for example, Taurus A actually proved to be the nebula N.G.C. 1952, whose dimensions are \(\sim 4'\cdot6'\), then the effective temperature of its envelope would have to reach a value of \(\sim 2\cdot10^6\) degrees. Despite a number of outstanding peculiarities possessed by the “Crab” Nebula, the actual temperature of its envelope is many times less than \(2\cdot10^6\) degrees. The thermal radiation of this nebula therefore cannot explain the intensity of radio emission observed in the experiment. The “Crab” Nebula belongs to the Galaxy. The question of whether the other two nebulae belong to the Galaxy is still unclear.

Recently\(^{26}\) appreciable radio emission was discovered from the Great Nebula (M 31) in the constellation Andromeda, i.e., from an evidently extragalactic object. The radio emission coming from M 31 was detected at a frequency of 158.5 MHz with the aid of a giant parabolic mirror about \(66\ \mathrm{m}\) in size, operating with a very sensitive receiver. In Fig. 8 a series of records is shown

Table II

*) The numbers indicate the serial numbers under which the objects are listed in the most widely used star catalogs of Dreyer and Messier.

cosmic radio emission for various declinations in the interval of right ascensions from \(23^h40^m\) to \(01^h20^m\), obtained with the aid of this apparatus. The curves corresponding to declinations between \(40^\circ18'\) and \(40^\circ52'\) have, at \(00^h40^m\), a noticeable maximum, indicating the presence in this region of a discrete source of radiation. A more detailed analysis of these curves and some other measurements made it possible to draw the following conclusions about the newly discovered discrete source (Table III).

Table III

The coordinates of the newly discovered source almost coincide with the coordinates of the center of the nebula M 31, so that there can hardly be any doubt that this discrete source is in fact the nebula M 31. The comparatively small intensity of the radio emission of the new source explains why earlier attempts \([1^1]\) to detect the radio emission of M 31 ended in failure, and makes it possible to ascribe to the radio emission of M 31 a thermal origin with a source temperature of about 1000 degrees.

One of the interesting and at the same time unresolved questions connected with discrete sources is the question of the origin of the variable component of the radio emission of these sources. As was already noted above, a variable component is present in the sources in Cygnus and Cassiopeia. On the other hand, until recently there existed the conviction that in the radio emission of some other sources (for example, the one located in the constellation Coma Berenices) the variable component is absent \(^{29}\). The main problem is that it is not clear whether fluctuations in the intensity of radio emission are the consequence of some terrestrial (atmospheric) phenomena, or whether they are intrinsic to the radiation incident on the Earth’s atmosphere and are therefore connected, in one way or another, with the mechanism of generation of the radiation in the source. At the same time this question is very important, since if the intensity fluctuations are connected with the source, then, as will be shown below, it becomes possible to make a number of statements about the linear \(^{33}\) and angular dimensions of discrete sources and about the distances to them \(^{34}\).

To clarify the question of the nature of the variable component, a series of measurements was carried out of the radio emission of the sources in Cygnus

and Cassiopeia with the aid of two installations operating independently of one another, the distance between which was varied and reached 160–210 km3. At distances between the receivers of \(<4\) km, a good correlation was observed in the time variation of the radio emission at both receiving points. This correlation was also preserved at greater distances between the receivers (up to 20 km). At distances exceeding 20 km, however, the time variation of the radio emission at one of the observing points bore no resemblance to the variation in the intensity of the radio emission at the other point, except in a few cases when sudden “bursts” of emission were registered at both points, although the distance between them was 210 km. All these facts, in the opinion of the authors[^35], indicate a terrestrial (ionospheric) origin of the fluctuations in the intensity of the radio emission, with the exception of the sudden “bursts,” which undoubtedly represent true changes in the radiating capacity of the discrete sources.

The most convincing proof of the terrestrial (ionospheric) origin of the bulk of the fluctuations in the intensity of radio emission is provided by the results of Ryle’s measurements[^53]. Ryle measured, over the course of several months, at wavelengths of 3.7 and 6.7 m, the radio emission of discrete sources located in the constellations Cygnus, Cassiopeia, Taurus, and Coma Berenices. It was established that the intensity of the radio emission of these sources fluctuates to the same extent for all four sources. This compels one to reject the principal objection to the ionospheric origin of the intensity fluctuations, namely that if fluctuations were indeed absent in the radio emission of the Taurus and Coma Berenices sources, then it would not be possible to ascribe an ionospheric origin to the fluctuations in the intensity of the radio emission of the Cygnus and Cassiopeia sources. Moreover, it turned out that the magnitude of the variable component of the intensity changes strongly over the course of the day, being maximal in the midnight hours (Fig. 9). This again speaks for the terrestrial origin of the intensity fluctuations and makes understandable the fact why earlier[^29] no fluctuations had been detected in the radio emission of the Taurus and Coma Berenices sources. In this connection, the figures given above[^31], characterizing the magnitude of the variable component of the radio-emission intensity of the discrete Cygnus and Cassiopeia sources, are somewhat conditional.

The details of the ionospheric mechanism causing fluctuations in the intensity of the radio emission of discrete sources are still unclear. This question is complicated by the fact that fluctuations of intensity at different wavelengths (3.7 and 6.7 m) often correlate well (Fig. 10)[^35], whereas at such different wavelengths the influence of the iono-

sphere should, it would seem, lead to completely different patterns of intensity fluctuations.

Measuring the frequency dependence of the intensity of cosmic radio emission, Herbstreit and Joyler \(^{37}\) found that for all directions \(I \sim \nu^{-0.41}\).

Fig. 9. Diurnal variation of the amplitude of the variable component of the radio-emission intensity (average for the sources in Cygnus, Cassiopeia, Taurus, and Coma Berenices). Along the ordinate is plotted the value of the variable component of the intensity relative to the mean intensity.

For earlier measurements \([1^{17}]\), however, as has already been indicated, the frequency dependence has a different form for weakly and strongly emitting regions of the sky. There is no contradiction with \(^{37}\) in this, since in \(^{37}\) the measurements were made with an antenna system having a broad directional pattern (a half-wave dipole located at a height of one quarter wavelength above a well-reflecting surface) and therefore collecting radiation from different regions of the sky. Consequently, the exponent 0.41 plays, in a certain sense, the role of an average for different directions.

Fig. 10. Radio-emission intensity of a discrete source in Cassiopeia at wavelengths of 3.7 and 6.7 m, July 4, 1949.

Hey and others \(^{38}\) and Reber \(^{39}\), continuing their earlier work on the study of the directional distribution of cosmic radio emission, present \(^{38,39}\) maps of radio isophotes at frequencies of 64 and 480 Mc/s. The map \(^{38}\) does not differ greatly from that presented earlier \([1^{13}]\) and contains only a greater number of details, in accordance with the fact that the measurements were made with a more “narrowly directed—

...with the antenna device. Reber’s map, while preserving a general similarity to the map he had earlier obtained at the frequency of 160 MHz \([^{11}]\), indicates a considerably greater concentration of radio emission at the frequency 480 MHz in the region of the Milky Way than at the frequency 160 MHz.

It was already stated above that it is impossible to explain the basic level of the Galaxy’s radio emission by thermal radiation of the interstellar medium. The considerations that force one to reject thermal radio emission of the interstellar medium as a possible cause chiefly responsible for the radio emission of the Galaxy seem to us quite convincing and, briefly, are as follows \([^{18,40}]\).

1) Already at frequencies of 20–30 MHz the effective temperature of the sky reaches values of \(10^5\) degrees \([^{123}, II^{8}]\), and even if the optical thickness of the Galaxy is \(\tau \sim 1\) or \(\tau \gg 1\) (which is unlikely), the true temperature of the interstellar gas would have to be no less than \(10^5\) degrees. In astrophysics, however, the value now adopted is \(T = 10^4\) degrees, apparently not exceeded even in the envelopes of planetary nebulae. 2) The concentration of interstellar matter, and hence also the main contribution to the optical thickness of the Galaxy, is especially large near hot stars of classes O and B. The bulk of these stars is concentrated in the plane of the Galaxy. Cosmic radio emission is also concentrated in the galactic plane, but not so strongly as the stars of the indicated types. 3) If cosmic radio emission were indeed the thermal radiation of interstellar electron gas, then there would be a connection between the intensity of the radio emission and the intensity of the hydrogen line \(H_{\alpha}\), since in the first case it is a question of the bremsstrahlung of an electron in the field of a proton, and in the second, of recombination with a proton. However, regions of the sky “bright” in the \(H_{\alpha}\) line are not distinguished in any very significant way with respect to radio emission. 4) The intensity of cosmic radio emission depends on frequency, roughly speaking, as \(\nu^{-0.4}\), which again cannot be explained on the basis of a model of thermal radiation, since if the optical thickness of the Galaxy \(\tau \gg 1\), the intensity, determined by Jeans’ formula, must be proportional to \(\nu^2\). If, however, \(\tau \ll 1\), the effective temperature must be proportional to \(\tau\), and since \(\tau \sim \dfrac{1}{\nu^2}\),\({}^{12}\) as a result the intensity of radio emission should in general not depend on frequency. 5) Thermal radiation of the interstellar medium cannot, of course, explain the fact that discrete sources exist.

Taking all these facts into account, Unsöld \([^{18,40}]\) advanced the hypothesis of the stellar origin of cosmic radio emission.

The main objection \([^{18}]\) encountered by the assumption of the stellar origin of cosmic radio emission consists in the fact that, for example, at a frequency of 64 MHz, averaged over the sky, one visual stellar magnitude corresponds to an intensity...

of radio emission of the order of \(10^{-23}\ \dfrac{\text{W}}{\text{m}^2\cdot\text{cps}}\). For some discrete sources (for example, for the sources in Cygnus and Taurus), which are certainly fainter than the sixth stellar magnitude, one stellar magnitude corresponds to approximately \(10^{-20}\ \dfrac{\text{W}}{\text{m}^2\cdot\text{cps}}\). At the same time, for the Sun (whose brightness on the visual scale is \(-27\)), radiating on average as a body with an effective temperature \(\sim 10^6\) degrees, one stellar magnitude corresponds to a radio-emission intensity \(\sim 10^{-33}\ \dfrac{\text{W}}{\text{m}^2\cdot\text{cps}}\).

At first glance it seems strange that the ratio of the intensity of radio emission to the intensity of visible radiation for stars turns out to be \(10^{10}\), and for discrete sources of radio emission \(10^{13}\) times greater than for the Sun. In the opinion of Unsöld\({}^{18}\), however, there is nothing surprising in this, since it may be assumed that the Sun is a rather weak “radio emitter.” On the other hand, the radio emission of the Sun during large eruptions sometimes increases by a factor of \(10^5\) and more; moreover, this radiation comes from regions above spots, the area of which is \(\sim 10^{-3}\) of the visible surface of the Sun. In addition, astrophotometric observations show that, for example, for stars with a temperature of \(3000^\circ\), the surface area corresponding to a unit of visible light is approximately \(10^3\) times greater than for the Sun.

Thus, the ratio of the intensity of radio emission to the intensity of visible light that interests us, for foci of especially strong solar radio emission, turns out, in order of magnitude, to be equal to its value for stars and, under certain additional assumptions, may be increased by several more orders of magnitude.

The occurrence of eruptions is often accompanied by an increase in the flux of cosmic particles. If cosmic radio emission actually arises in the atmospheres of certain stars, then it is possible that precisely these stars are also sources of primary cosmic rays. The hypothesis of a common source for cosmic radio emission and primary cosmic particles was also advanced in\({}^{33}\). The point of view set forth does not meet, apparently, with general objections, but, on the other hand, there is as yet no direct confirmation of it. It can be confirmed or refuted only by means of a more detailed study of the radio emission of the Galaxy and a comparison of these data with the results of astrophotometric observations.

If, after all, radio emission arises not in stars but in the interstellar medium, then, as was shown, it cannot be explained by the thermal radiation of interstellar electrons and in\({}^{41,42}\) is associated with the braking radiation of relativistic electrons in weak interstellar and circumstellar magnetic fields.

A relativistic electron with energy \(E\), rotating in a magnetic field \(H\), emits a maximum of energy at frequencies close to the frequency

\[ \omega_1=\frac{eH}{mc}\left[\frac{E}{mc^2}\right]^2. \]

In order of magnitude, this energy per unit time in a unit frequency interval is equal to\(^{43}\)

\[ P_{\max}\simeq \frac{e^3H}{mc^2}\simeq 10^{-22}H\, \frac{\text{erg}}{\text{sec}\cdot\text{cycle}}. \tag{6} \]

Since the optical thickness of the Galaxy for waves of the meter range cannot be significantly greater than unity [1], then, without a large error, absorption of radiation may be neglected in obtaining the correct orders of magnitude. In this case the maximum specific intensity of the radiation is evidently equal to

\[ I_\nu \simeq \frac{1}{4\pi}P_{\max}N\cdot R\, \frac{\text{erg}}{\text{cm}^2\cdot\text{sec}\cdot\text{cycle}\cdot\text{sterad}}, \tag{7} \]

where \(N\) is the mean number of particles in \(1\ \text{cm}^3\) over Galactic dimensions in the chosen direction, and \(R\) is the size of the Galaxy in this direction.

The intensity of radio emission at the wavelength \(\lambda=10\ \text{m}\) corresponds to an effective temperature \(T_{ef}\simeq 10^5\) degrees, so that the specific intensity of the radio emission at this wavelength is

\[ I_\nu=\frac{2kT_{ef}}{\lambda^2}\simeq 10^{-17} \frac{\text{erg}}{\text{cm}^2\cdot\text{sec}\cdot\text{cycle}\cdot\text{sterad}}. \tag{8} \]

Taking \(R=10^{22}\ \text{cm}\) and comparing (7) and (8), we find:

\[ H\cdot N\simeq 10^{-16}. \tag{9} \]

According to\(^{43}\), the strength of the interstellar magnetic field is approximately \(10^{-6}\) gauss and, thus,

\[ N\simeq 10^{-10}\frac{\text{electrons}}{\text{cm}^3}. \]

Consequently, the radiation of relativistic electrons with energies \(E\sim 10^9\ \text{eV}\) and concentration

\[ N=10^{-10}\frac{\text{electrons}}{\text{cm}^3}, \]

rotating in a magnetic field \(H\simeq 10^{-6}\) gauss, leads to the observed intensity of cosmic radio emission.

Above, no concrete assumptions were made about the distribution of electrons by energy, for the simple reason that the form of this distribution is not yet known. At the same time, since the frequency spectrum of the radiation of a relativistic electron \(P(\nu,E)\) depends on the energy of the particle, the energy spectrum of relativistic electrons determines the frequency spectrum of cosmic radio emission. It seems to us that the inverse problem is of some interest: from the radio-emission spectrum known from experiment, to determine the energy spectrum of relativistic electrons invoked to explain Galactic radio emission. The numerical calculation we have carried out, taking into account the concrete form of the function \(P(\nu,E)\)\(^{44}\), the details of which it is not expedient to present here, showed that the frequency dependence of the intensity of cosmic radio emission \(\nu^{-0.4\div37}\)

corresponds to the following distribution of cosmic electrons with respect to energies:

\[ dN(E)=kE^{-1.8}\,dE . \tag{10} \]

Here \(dN(E)\) is the number of cosmic electrons in \(1\ \mathrm{cm}^{3}\) possessing energies contained in the interval \(E, E+dE\), and \(k\) is a proportionality coefficient of order \(10^{-2}\). Formula (10) is valid for particle energies of order \(10^{9}\ \mathrm{ev}\). Integrating expression (10) within definite limits, one can find \(N\)—the concentration of relativistic electrons required to produce the observed intensity of radio emission. Such a calculation gives, for \(N\) at \(\lambda \simeq 5\text{–}7\ \mathrm{m}\), the value \(N \simeq 10^{-9}\ \dfrac{\text{electrons}}{\mathrm{cm}^{3}}\), which is 10 times greater than the \(N\) obtained in \(^{42}\). This is connected with the fact that in \(^{42}\), and in the derivation given above, the maximum value of the energy radiated by an electron was used, so that the value \(N \simeq 10^{-10}\ \dfrac{\text{electrons}}{\mathrm{cm}^{3}}\) for \(H \simeq 10^{-6}\) gauss evidently plays the role of a lower bound for the required number of relativistic electrons. Whereas at the boundary of the Earth’s atmosphere the number of cosmic electrons per unit volume is at least \(10^{3}\)—\(10^{4}\) times smaller than is needed to produce the observed radio emission, the value \(N \simeq 10^{-9}\ \dfrac{\text{electrons}}{\mathrm{cm}^{3}}\) with \(E \simeq 10^{9}\ \mathrm{ev}\) and the energy spectrum (10) in interstellar space does not appear impossible.

Leaving aside the question of whether the interstellar medium can be responsible for the basic level of cosmic radio emission over a broad frequency range, one should point out the probability of the existence of appreciable monochromatic radiation from the interstellar medium \(^{34}\). Such radiation at a wavelength of \(21\ \mathrm{cm}\) may, for example, arise owing to transitions between components of the hyperfine structure of the ground state of hydrogen atoms. According to the calculations of I. S. Shklovsky \(^{34}\), the radio emission caused by such transitions may quite well be detected by radio-engineering means ordinarily used for measurements of this kind*).

The observation of monochromatic radio emission of the Galaxy should be of great astrophysical interest.

The question of the nature of the discrete sources of radio emission is unclear. Their angular size is smaller than the resolving power of modern apparatus (several minutes of arc), and the distance to the most powerful sources in the constellations Cygnus and Cassiopeia is greater than \(2\cdot 10^{16}\ \mathrm{cm}\); consequently, they lie beyond the limits of the solar sy-

*) The estimate of the directive-action coefficient \((G_a)\) of the receiving antenna required for observing the monochromatic radio emission of the Galaxy at \(\lambda=21\ \mathrm{cm}\) was made insufficiently correctly in \(^{34}\). In \(^{34}\) it was not taken into account that the angle \(\Omega\) within which the antenna receives radiation, and \(G_a\), are closely related quantities:

systems^33. This refutes the rather improbable, and for a number of other reasons, assumption^45 that the discrete sources are large, faintly luminous comets belonging to the solar system.

The fluctuations of the intensity of the radio emission of discrete sources have already been discussed above. It is undoubted that at least some of them, which appear in the form of sudden “bursts” lasting 10–20 sec, are connected with processes in the source. The origin of these intensity bursts is associated^31, ^33 with a sudden and simultaneous increase in the emissive power of all elements of the source. If this is so, then the linear size of the source must be less than the path traversed by light in a time of the order of the duration of the “burst.” The minimum observed duration of the radio-emission “bursts” for the source in Cygnus is about 10 sec, so that its linear size must be less than \(10^{11}—10^{12}\) cm—the size of main-sequence stars^33.

Assuming that the fluctuations in radio-emission intensity presented in Fig. 10 arose in the source, I. S. Shklovsky used the fact of the near temporal coincidence of individual “pushes” of intensity at different wavelengths to estimate the upper limit of the distance to the discrete source in Cygnus^46. In the constellation Cygnus there is, as it turns out, a large cloud of ionized interstellar gas. If the discrete source were located beyond this cloud, then the delay of the intensity “pushes” at different waves, determined by the difference in the times of group retardation, would reach two minutes. Since in reality (Fig. 10) this delay is less than several seconds, the source of radio emission must be located in front of this cloud, i.e. the distance to it must be \(< 10^{20}\) cm. The discrete source in Cygnus therefore belongs to the Galaxy. A more careful time registration of the radio-emission “bursts” can in principle make it possible to estimate more accurately the distance to the source^46. In practice, however, to lower the upper limit of this distance by an order of magnitude or more at present is apparently difficult. The point is that, according to the data available in the literature, the time constant of the receiving apparatus used for measurements of cosmic radio emission is of the order of one or several seconds. Such, therefore, is also the accuracy with which the arrival time of a radio-emission pulse can be determined.

For lack of space we shall not dwell here on an analysis of the various, often quite vague, hypotheses on the nature of the radio emission of discrete sources. We note only that, in analyzing various mechanisms for the occurrence of radio emission, Ryle^33 rejects coherent oscillations of plasma as a possible cause of the occurrence of radio emission in discrete sources and reduces it to the thermal radiation of medium-sized stars with a temperature \(\simeq 10^{14}\) degrees. Thanks to such a high electronic tem-

temperature, corresponding to particle energies of the order of \(10^{10}\) eV, the discrete sources of radio emission, in Ryle’s opinion, are at the same time sources of primary cosmic rays—a point of view which, as has already been said, is also expressed in \(^{18,40}\).

Ryle’s model is, of course, to a considerable extent speculative. Nothing is yet known about the existence of stars with so high an envelope temperature. The question of the structure of a star whose brightness is less than the 6th magnitude, while the temperature in its atmosphere is \(\sim 10^{14}\) degrees, has not been considered.*)

In this connection, an attempt to explain the radio emission of discrete sources by means of the mechanism considered above, in the case of the Sun and the Galaxy, of emission from relativistic electrons rotating in a magnetic field \(H \sim 10^{-5}\) gauss surrounding some stars \(^{42,49}\), is of particular interest.

Finally, we wish to make one remark concerning fluctuations in the intensity of the radio emission of discrete sources. It has already been said above that at least some of them, appearing in the form of short-term “bursts” of intensity lasting 10–20 sec., are connected with the source of radio emission. It may turn out that these “bursts” are analogous to the chaotic modulation to which the radiation of many real systems consisting of mutually independent emitters is subject. The mean period of modulation (the duration of a “burst”) is then determined, as is known \(^{47}\), by the mean time during which the phase of oscillations of an individual emitter is preserved.

With such an interpretation of the “bursts” of radio-emission intensity of the discrete sources Cygnus and Cassiopeia, it becomes possible to estimate the upper limit of the angular sizes of these sources. Indeed, let the radio-emission intensity at wavelength \(\lambda\) of a system of size \(d\), consisting of many independent emitters, be described for direction 1 by some random function of time \(f_1(t)\), and for direction 2 by the function \(f_2(t)\) (Fig. 11). Then, if the angle \(\alpha\) between directions 1 and 2 is

\[ \ll \frac{\lambda}{2d}, \]

the functions \(f_1(t)\) and \(f_2(t)\) are practically identical. Conversely, for

\[ \alpha \gtrsim \frac{\lambda}{2d} \]

the functions \(f_1(t)\) and \(f_2(t)\), generally speaking, are completely different. The linear size of the discrete source \(d\) is equal to \(\delta R\), where \(\delta\) is the angular diameter of the source, and \(R\) is its distance. If the distance between the observation points is \(l\), then \(\alpha = \dfrac{l}{R}\). In accordance with what has been said, the condition for the existence of correlation between

*) Let us recall that in those regions where most discrete sources are located, there are no stars brighter than the 6th stellar magnitude \(^{18}\).

intensity fluctuations will then be written as follows:

\[ \alpha=\frac{l}{R}\ll \frac{\lambda}{2d}=\frac{\lambda}{2R\delta} \quad \text{or} \quad l\ll \frac{\lambda}{2\delta}. \tag{11} \]

Conversely, if the distance between the receivers is greater than \(l_0 \cong \dfrac{\lambda}{2\delta}\), then, generally speaking, the correlation between the fluctuations must be absent. According to the data of \(^{35}\), \(l_0 \gg 200\ \text{km}\), \(\lambda=6.7\ \text{m}\). Hence the angular diameter of the discrete source in Cygnus is \(\delta \cong \dfrac{\lambda}{2l_0}\ll 4''\). The fundamental question of the angular dimensions of discrete sources can, of course, be finally resolved only by direct measurements, which is especially difficult. Certain possibilities in this direction, however, do exist \(^{48}\). The diffraction pattern arising at the moment when a discrete source is occulted by the Moon would make it possible to attain resolving powers an order of magnitude and more greater than those attainable at present by other methods. According to a rough estimate, the nearest eclipse of the discrete source in Taurus will occur at the end of 1954.

Fig. 11.

The radio-astronomical achievements of recent years testify to the fruitfulness of the application of radio in astronomy. However, despite the existence of already quite extensive and varied material, the nature of the radio emission of the Sun and the Galaxy is in many respects unclear. At the same time, establishing the connection between radio emission and the physical conditions and processes in the Sun, stars, or the interstellar medium is the principal task of radio astronomy. There is no doubt that further investigations of the radio emission of the Sun and the Galaxy will make it possible in the near future to solve this problem.

In conclusion we wish to thank Professor V. L. Ginzburg for discussing the material included in this review and for a number of comments made by him when reading the review in manuscript.

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2. emission is related to the effective temperature $T_{ef}$ by the Rayleigh–Jeans formula
   \[ I=\frac{2\pi k}{\lambda^2}\left[\frac{r}{R}\right]^2\cdot T_{ef} =\frac{1.85\cdot 10^{-21}}{\lambda^2\ (\text{in meters})}\cdot T_{ef}\ \frac{\mathrm{erg}}{\mathrm{m}^2\,\mathrm{sec}}, \]
   where $r=6.95\cdot 10^{10}\ cm$ is the radius of the Sun, and $R=1.495\cdot 10^{13}\ cm$ is the distance to it. ↩↩

3. An account of the principal results of this work is given in [^36]. ↩