New Data on the Radio Emission of the Sun and the Galaxy

V. L. Ginzburg

Although the previous review on the radio emission of the Sun and the Galaxy1 was written in March 1947, by the present time, in November of the same year, there already exists a whole series of new and interesting materials on this subject.2–8 This alone makes clear the great attention now being paid—and quite deservedly so—to the new branch of astronomy: radio astrophysics. Below we shall consider the new works that have appeared, and also clarify and additionally discuss a number of questions touched upon in article1 (below cited as I; all notations also are as in I).

1. Observations During Eclipses

Even at centimeter wavelengths the directional pattern of a receiving antenna device usually has a width of several degrees. Therefore the antenna receives at once all the radio emission of the Sun and its atmosphere, and it proves impossible to localize the sources of this radiation more accurately. The construction of antenna devices with a very sharp directivity, substantially smaller than the angular dimensions of the Sun, equal to \(1/2^\circ\), is possible in principle, but in practice is far from simple. Therefore observations of the radio emission of the Sun during solar eclipses are of great importance. In this case the Moon evidently plays the role of a screen, covering or uncovering various portions of the solar surface and corona, as well as prominences.

In Denisse and Beringer’s work,9 already mentioned in I, observations were carried out at \(\lambda = 1.25\) cm during the partial eclipse of July 9, 1945; moreover, the course of the radio intensity \((T_{ef} = 10\,000^\circ)\) proved to coincide with the course of the intensity in the optical region. At \(\lambda = 1.25\) cm the radiation, generally speaking, comes from the chromosphere. Therefore there is no reason to expect differences in the general course of the intensity in the radio and optical regions. In addition, measurements at this wavelength can hardly be especially accurate because of absorption of the radiation by water vapor in the atmosphere, which is a variable quantity. As for local disturbances from regions

near spots or faculae, it must be noted that the authors were not interested in this question and do not discuss it in their report.

During the partial eclipse of July 9, 1945, observations³ were also carried out at a wavelength of 3.2 cm, but rain interfered with them to a considerable extent and they did not yield clear results. We note only that outside the eclipse, according to the author’s data³, the flux of solar radiation is equal to \(S = 4 \cdot 10^{-8}\) watt/cm²·megacycle, which corresponds to an effective temperature \(T_{ef}=22\,000^\circ\) [see I, (14)].

In Canada, during the partial eclipse of November 23, 1946, Covington² carried out very interesting measurements at \(\lambda = 10.7\) cm (frequency

Fig. 1. Change in radio intensity during the eclipse of November 23, 1946 (curve \(A\)). Curve \(B\)—the covered part of the solar disk.

2800 megacycles). The change in radio intensity during the eclipse is shown in Fig. 1 (curve \(A\)). Curve \(B\) in the same figure gives the time course of the covering of the solar disk by the Moon, i.e. the covered part of the visible disk (in percent). From curve \(A\) it is seen that even outside the eclipse the intensity of the radio emission is not constant (fluctuations \(\sim 7\%\) before the eclipse and an increase of intensity by \(\sim 15\%\) after the eclipse). At long wavelengths (the meter range) the presence of continuous jumps of radio emission has been firmly established (see § 2). With regard to 10 cm as well, from the data presented it apparently follows that similar fluctuations are present, since, according to the author’s data², the instrumental fluctuations in his receiver amounted to \(\sim 1\%\). Three minutes before the first visible contact, a quite definite decrease in intensity began to be observed, i.e. the radio eclipse began 3 minutes earlier than the visible one. It follows from this that the distance of the edge of the region active for radio emission from the photosphere is equal to \(0.05 r_\odot\) (\(\eta = 1.05\)). The more detailed course of the intensity in the time interval near the first contact is clear from Table I.

Table I

The effective temperature of the Sun, according to³, is equal to 56,000°. However, this figure by itself says little, since the same total radiation intensity may be due both to thermal radiation from the lower part of the corona and to radiation from individual active regions. That such regions exist follows directly from two facts.

From Table 1 it is seen that during the three minutes before contact the radiation intensity fell by 8%. The area covered by the Moon during this time is also known. Hence it follows³ that the equivalent temperature*) of the active region covered in 3 minutes is \(3 \cdot 10^6\) degrees. Here, for example, the occultation of a prominence might have taken place. From curve \(A\) in Fig. 1 one can also clearly see the influence of a large group of spots, which began to be covered by the Moon at 11 h 39 m and began to be uncovered at 12 h 57 m (Fig. 2). As is seen from Fig. 1, at the time when the spots were covered, the intensity was approximately 20–25% lower than when the group of spots was open. The area of this latter group was \(\sim 2.2\%\) of the visible area of the disk. The equivalent temperature of this active region is \(1.5 \cdot 10^6\) degrees. From what has been said it is clear how much can be yielded by observations during eclipses. At the same time it is evident that a total eclipse is of particular interest, as is work in the meter range, where the activity of the Sun manifests itself more sharply.

Fig. 2. Positions of the lunar shadow at the moments of occultation and uncovering of the group of spots.

Similar observations, on the initiative of the late Academician N. D. Papaleksi, were carried out⁷ by a Soviet expedition in Brazil during the total eclipse of May 20, 1947. The work, directed by S. E. Khaikin, was conducted from aboard the steamship “Griboedov” in the Bay of Bahia. The antenna consisted of 96 dipoles and thus had \(G_a \sim 100\); the receiver noise factor was \(N = 6\); measurements were made at wavelength \(\lambda = 1.5\) m. The “aperture angle” of the antenna, i.e., the angle between the directions in which the energy received by the antenna falls to half the maximum value, was equal to

*) Here and in analogous cases below, by the equivalent temperature is understood the temperature that an active region would have to possess in order, radiating as a black body, to produce the observed intensity of radio emission. Of course, in the case of a nonthermal mechanism of radiation there is no basis for considering this temperature the true temperature of the region under consideration.

approximately \(8^\circ\). Therefore, during prolonged observations of the Sun’s radio emission, the antenna had to be turned continuously so that the direction toward the Sun coincided, to an accuracy of \(\sim 1^\circ\), with the direction of maximum receiving intensity. In the experiment this rotation of the cumbersome antenna was carried out by turning the entire motor vessel with the aid of special anchors and cables run to the shore. The accuracy of rotation through the required angles was monitored and proved to be quite sufficient. The results of the measurements are presented

Fig. 3. Change in radio intensity during the total eclipse of 20 May 1947 (curve \(I\)). Curve \(II\)—covered part of the visible disk (course of the optical eclipse). Curve \(III\)—course of the “eclipse” of prominences and filaments.

in Fig. 3 (curve \(I\)); curve \(II\) in this figure represents the course of the optical eclipse. We see that the radio emission does not fall below \(40\%\) of the total radiation intensity of the uneclipsed Sun. Hence it is clear that, for radio waves, the eclipse is not total but annular. If it is assumed that the radio emission comes uniformly from some sphere of radius \(r=\eta r_{\odot}\), then, neglecting the change in brightness toward the edges of the disk (i.e. assuming Lambert’s law), one may say that during the total phase of the optical eclipse \(\sim 60\%\) of the emitting sphere is covered. It follows from this that \(\eta=1.3\). However, this value, though of a reasonable order of magnitude (see I), is only indicative, since from the strong asymmetry of curve \(I\) it is clear that the sources of radio emission are distributed nonuniformly. Namely, from the curve it is evident that the side of the emitting surface which was covered later radiated more intensely than the other side. This conclusion is consistent with the picture of the distribution of sunspots on the day of the eclipse—the greater part of the spots was concentrated in that part of the disk which was covered later. However, it is hardly possible to establish a quantitative relation between the area of the covered spots and the course of the radio intensity, since during the total optical eclipse all

spots were covered, and the intensity of the radio emission was \(\sim 40\%\) of the initial value. Therefore E. I. Mogilevsky carried out a comparison of the course of the radio intensity with the course of the eclipse of the prominences and filaments, by calculating the effective area (the product of area by brightness) of all prominences and filaments visible at each moment of the eclipse (i.e. not covered by the Moon) (see curve III in Fig. 3; the total effective area outside eclipse is taken as unity). Curve III turned out to follow curve I very closely, which indicates a connection between the radio emission and the prominences. The circumstance that prominences may play an essential role in the mechanism of excitation of radio emission was briefly indicated by Martyn\(^ {10}\) (see also, in this connection, \(^{11,12}\)).

From the data presented, which exhaust the materials known to us obtained from observations during eclipses, it is clear how much such observations can yield, especially if they are carried out at different wavelengths simultaneously.

In connection with observations during eclipses it should be noted that, in localizing on the Sun regions active in radio emission, one must keep in mind the possible influence of refraction of radio waves in the solar atmosphere and their diffraction by the lunar limb.

Since for radio waves the refractive index in the corona is \(n<1\), it is clear that the solar atmosphere acts as a scattering optical system. Therefore radio emission which appears to us to come from a point at a distance \(\eta_1\) from the center of the Sun in fact comes from a point with \(\eta_2 \geq \eta_1\). Quantitative calculations of this effect, i.e. of refraction, have not been made, but it is immediately clear that it may be very large, provided only that the radio waves reach regions where \(n\) is appreciably less than unity. Allowance for refraction is also necessary in calculating the distribution of the brightness of radio emission over the solar disk. If, as Martyn asserts (see I, § 3 and reference I\(^ {20}\)), for waves of the meter range reflection from the corona is already substantial, then refraction must play a very large role. Clarifying this whole range of questions is, for us, one of the most urgent and important tasks in the theoretical analysis of solar radio emission.

Fig. 4. Diffraction at the lunar limb.

During an eclipse, when the Moon covers the Sun, diffraction occurs at the edge of the lunar disk. Therefore, even if a given active region on the Sun is already covered by the Moon for a terrestrial observer, some part of the radiation nevertheless still reaches the observer. To estimate this effect one may use the known formulae for diffraction by the edge of a screen (the role of the screen is played by the Moon; see the schematic Fig. 4). The diffraction pattern is determined

with parameter

\[ W=d\sqrt{\frac{\pi}{D\lambda}} . \tag{1} \]

where \(D \simeq 4\cdot 10^{10}\) cm is the distance from the Earth to the Moon and \(d\) is the distance from the edge of the geometrical shadow. The intensity of the radiation \(I\) coming from the point \(Q\) on the Sun is determined by the well-known formula, given in optics courses, containing Fresnel integrals that depend on the parameter \(W\). If \(W=1\), \(I/I_0=0.04\), where \(I_0\) is the intensity in the absence of a screen; for \(W=4\), \(I/I_0=2\cdot 10^{-3}\). For \(W=1\) and \(\lambda=1.5\) m, \(d=14\) km and \(\theta=\dfrac{d}{D}=\sqrt{\dfrac{\lambda}{\pi D}}=4\cdot 10^{-5}\). It follows from this that a point on the Sun is smeared out to dimensions \(l\sim \theta R\sim 6\cdot 10^8\) (\(R\) is the distance from the Sun to the Earth, equal to \(1.5\cdot 10^{13}\) cm). In other words, because of diffraction, during an eclipse we can localize regions on the Sun with an accuracy only up to distances of order \(l\sim \sqrt{\dfrac{\lambda}{\pi D}}\,R\); for centimeter waves the ratio \(l/r_{\odot}\sim 0.001\), and in the meter range \(l/r_{\odot}\sim 0.01\), i.e. this ratio is small enough that one may say that diffraction, from the point of view of localization of active regions, is practically insignificant. At the same time, if the diffraction pattern is observed specially, it is possible to estimate the dimensions of the region emitting radio waves, which is very interesting. These observations must obviously be made in the region \(PA\) (see Fig. 4), where the intensity of the radiation coming from the point \(Q\) has maxima and minima (recall that in the first maximum \(I=1.36 I_0\)). Since the width of the first Fresnel zone \(d_0=\sqrt{\lambda D}\sim 2\cdot 10^6\) cm \(=20\) km (for \(\lambda\sim 1\) m) is substantially greater than the height of the lunar mountains, the presence of the latter can hardly have any noticeable effect on the diffraction pattern. At the same time, in view of the fact that \(d_0\) is much smaller than the radius of the Moon \(\rho\simeq 1.7\cdot 10^8\), the difference between the diffraction pattern and that which occurs for a rectilinear screen also should not be substantial. The only exception may be the very center of the lunar shadow, since at the center of a circular screen, as is known, there is an illuminated spot. However, the brightness of this spot is determined by the brightness of a source lying exactly on the axis of the screen. Therefore, and also for a number of other reasons, observation of such a “radio spot” during eclipses is hardly possible.

2. OBSERVATIONS OF THE RADIO EMISSION OF THE SUN AT DIFFERENT FREQUENCIES

The intensity of the radio emission of the Sun, especially in the meter range, undergoes strong fluctuations all the time. This fact is already visible in Figures 6 and 7 in I, and also in Fig. 3 of the present article. In the latter case two high “bursts” of radio emission

…before and after the eclipse cannot be explained by instability of the apparatus and, thus, belong to the radiation of the Sun itself; the same, apparently, also applies to most of the other oscillations visible on curve I of Fig. 3*). The time course of the intensity of radio emission at various frequencies has been studied in greater detail in papers\(^{4,5}\).

Ryle and Vonberg\(^{4}\) made measurements simultaneously at wavelengths of 1.7 m and 3.75 m (frequencies of 175 and 80 megacycles). During periods of increased

Fig. 5. Solar radio emission at two frequencies (January 22, 1947).

solar activity, the radiation is characterized by the presence of short “flashes” or “bursts,” lasting from one to 20 seconds; the intensity during the “bursts” reaches values 5 times greater than the mean intensity. Bursts of this type at the two frequencies occur independently (correlation is almost absent). A typical curve of the variation of intensity with time is presented in Fig. 5 (the change in the mean intensity visible in this figure is explained by the use of two antennas; see I, § 2 and I, reference\(^{8}\)). Sometimes, however, considerably larger bursts appear, with intensities 20–100 times greater than the mean intensity; these bursts may last many minutes and are usually observed at both frequencies. Many such large bursts coincide with other manifestations of solar activity (eruptions, the Dellinger effect, or “fade-out”). Similar results were obtained by Payne-Scott et al.\(^{5}\), who worked

*) Observations during eclipses may, however, be complicated by diffraction. The symmetrical position of both bursts in Fig. 3 somehow suggests this idea. However, diffraction would seemingly have to produce a substantially smaller effect. It is not yet possible to draw a final conclusion here.

on waves of 1.5 m, 4 m, and 5 m, and sometimes also on waves of 3 m and 10 m (frequencies, respectively, 200, 75, 60, 100, and 30 megahertz). The absence of coincidences between ordinary bursts indicates that they are caused by independent disturbances arising in different regions of the solar atmosphere. The latter is quite understandable, since different frequencies come from different depths (see I). In the case of large bursts, the presence of correlation is connected with the fact that the disturbance affects a considerable region of the solar corona, encompassing the places of generation of radiation of various frequencies. In accordance with this, correlation is more often observed only for a pair of nearby frequencies^5. In addition, correlated bursts at frequencies of 200, 75, 60, and 30 megahertz turn out to follow one another in the same sequence as the indicated frequencies. The delay time fluctuates strongly, but for 60 bursts observed at frequencies of 75 and 60 megahertz, the delay time most often encountered is 2 seconds. A time of the same order is observed between bursts at 200 and 75 megahertz and between bursts at 60 and 30 megahertz. The difference in the arrival times of bursts of different frequencies may be due to two causes—the different propagation times of radio waves of different frequencies, coming from different places, and the nonsimultaneity of excitation of these radio waves. The group delay time of radio waves in the corona (ionized gas), if the influence of the magnetic field of the Sun and sunspots is neglected, is equal to (for simplicity we consider propagation along the radius):

\[ t=\int \frac{dr}{cn(\omega,r)},\qquad n=1-3.19\cdot 10^9\frac{N}{\omega^2}, \tag{2} \]

since the group velocity in this case is equal to \(cn\) (see, for example,^18).

Higher frequencies, generally speaking, must be generated at higher electron densities, i.e. from regions closer to the photosphere (see I). Thus, if all frequencies were excited simultaneously and the velocity of the radio waves were equal to \(c\), the bursts would have to arrive in sequence, beginning with the bursts at frequency 30 megahertz and ending with the bursts at frequency 200 megahertz. The presence in (2) of the factor \(n(\omega)\) can in principle change such a sequence, but this is improbable and may be regarded as excluded if the radiation of frequency \(\omega\) is generated in a region where \(n(\omega)\) is still close to unity, which apparently occurs in the meter range (see I). In the latter case the delay of bursts at frequency 75 megahertz compared with bursts at frequency 60 megahertz should have been of order

\[ \Delta t\sim \frac{0.1R_{\odot}}{c}\sim 0.2 \text{ seconds}. \]

In the experiment, however, bursts at frequency 75 megahertz precede bursts at frequency 60 megahertz by \(\sim 2\) seconds. It follows from this that the delay of the bursts is due to the nonsimultaneity of excitation of radiation of different frequencies, the exciting agent or exciting disturbance being

propagates with a velocity

\[ v \sim \frac{0.1\,r_{\odot}}{2} \sim 3\cdot 10^9 \ \text{cm/sec}, \]

where we have rather arbitrarily assumed that the regions responsible for the radiation at frequencies of 75 and 60 megahertz are separated from one another by a distance of \(\sim 0.1\,r_{\odot}=7\cdot 10^9\) cm. The order of magnitude is thus obtained correctly; the value \(v\sim 3\cdot 10^9\) is rather an upper limit to the velocity of the exciting agent, which is thus of the order of \(10^9\) cm/sec. In the case of electrons this velocity corresponds to an energy

Fig. 6. Giant “burst” of radio emission on March 8, 1947.

\(\sim 400\) eV, and in the case of protons to an energy \(\sim 800\,000\) eV; hence it follows that the influence of protons is apparently excluded.

In the case of bursts of extremely high intensity, delays of several minutes are observed, and again the bursts arrive in the sequence: 200, 75, 60 Mc/s. The most striking example of such giant bursts, observed on 8/III 1947, is presented in Fig. 6. The appearance of these bursts coincided with an eruption on the Sun and a “fade-out” (cessation of radio communication on short waves). The observations were carried out\(^5\) at frequencies of 200, 100, and 60 Mc/s, with the delay between the first two frequencies equal to 2 minutes and between the second and third frequencies 4 minutes. Let us note that the intensity at the frequency 60 Mc/s (\(\lambda=5\) m) during the burst was for some time greater than \(10^{-9}\) watt/m\(^2\)·Mc/s, which corresponds to an effective temperature

\[ T_{ef} > 1.5\cdot 10^{13} \]

degrees.

If, for orientation, we assume that radiation of a given frequency comes from the region where, for this frequency, \(n(\omega)=0\), then it is possible to determine the velocity of the disturbance causing the bursts (see Table II).

Of course, to suppose that the radiation comes from a region where \(n=0\) is without foundation, and, on the contrary, it more likely comes from higher layers (see I). However, the order of magnitude obtained in this case will be correct, and thus, in the case under consideration the agent velocity is \(v \sim 5 \cdot 10^7\ \text{cm/sec}\), which corresponds, for protons, to an energy of \(\sim 2000\ \text{eV}\). This velocity is of the order of the velocity of motion of matter in prominences and of the presumed velocity of neutral

Table II

particles of solar origin reaching the Earth. Thus the largest disturbances are apparently excited by prominences, by matter ejected during eruptions, etc.; weaker disturbances are probably excited by electron streams.

In the figure: ordinate—effective temperature; upper curve—\(80\) MHz; lower curve—\(175\) MHz; dates—December 1946, January 1947, February, March, April.

Fig. 7. Change in the mean daily intensity of radiation in the period from December 1946 to April 1947.

Ryle and Vonberg\(^4\) also carried out observations of the day-to-day change in the mean intensity of radio emission at frequencies of 80 and 175 MHz. Figure 7 presents the change in intensity over the period

from December 14, 1946 to April 22, 1947, the mean intensity over 4 daytime hours being expressed on the scale of effective temperatures. In this figure the 27-day period of solar activity is, it would seem, indistinctly expressed. This period, however, stands out clearly if one plots on the graph the ratio of the effective temperatures at the two frequencies \(T_{80}/T_{175}\) (Fig. 8). In Fig. 8 the fluctuations are also considerable, but still substantially smaller than in Fig. 7, which indicates the existence of a connection between the variations with time of the intensity at the two frequencies. The ratio \(T_{80}/T_{175}\) is on the average close to the ratio

\[ \frac{\lambda_{80}^{2}}{\lambda_{175}^{2}} = 4.8, \]

but often differs noticeably from it. The authors believe\(^{4}\) that their results, presented in Figs. 7 and 8, make probable the assumption that the directivity pattern of solar radiation is different at different frequencies. In this case the change in effective temperature may be due both to a change in the temperature of the source and to a change in the angular distribution of the radiation. At present we see no particular grounds for such assumptions.

Fig. 8. Ratio \(T_{80}/T_{175}\) of the effective radiation temperatures at frequencies of 80 and 175 megahertz.

Hey and others,\(^{6}\) working at a wavelength of 12 m, observed the radio emission of the Sun and the Galaxy. A wave of 12 m is already noticeably absorbed by the ionospheric \(D\)-layer, as a result of which, during ultraviolet flares on the Sun, which cause an increase of ionization in the \(D\)-layer, it begins to be absorbed more strongly. This absorption can be noticed from the decrease in the radio emission of the Galaxy reaching the Earth. The situation is, of course, complicated if the ultraviolet flare is associated with a “burst” of solar radio emission. However, as experience shows, these phenomena are sometimes separated. Thus, on August 1, 1947, at 15 h 16 min, a strong “fade-out” began, accompanied by a magnetic storm and caused by an ultraviolet flare on the Sun*). Nevertheless,

* Unfortunately, the authors do not give direct data on this flare, and since sometimes a “fade-out” is not accompanied by a visible flare, there is no complete clarity here.

the radio emission of the Sun at a wavelength of 12 m, which under normal conditions was negligible in comparison with the radiation of the Galaxy, did not appear. At the same time, the radiation of the Galaxy began to weaken because of absorption in the \(D\)-layer as early as 15 h 16.8 m (Fig. 9). In this case no bursts of radio emission from the Sun were noticed at shorter wavelengths either. On the contrary, on June 14, 1947, a “fade-out” was also observed, beginning at 10 h 36 m. At a wavelength of 5 m a burst of radio emission was observed and began at 10 h 40 m, while at 12 m absorption of the radiation

Fig. 9. Radiation of the Sun and the Galaxy on August 1, 1947.

of the Galaxy began at 10 h 36.2 m, and a burst of radio emission was observed at 10 h 39.2 m (Fig. 10). Thus observations of the radio emission of the Galaxy can be used to detect absorption in the \(D\)-layer if the solar radiation is relatively weak or if a flare (burst) of this radiation is delayed in time in comparison with the ultraviolet flare. Such a delay is explained by the fact that the ultraviolet disturbance comes from the lower layers of the solar atmosphere, whereas radio emission at wavelengths \(\sim 10\) m comes from rather high layers of the corona, which are reached by the disturbance not at once. In the example cited (June 14), the delay is equal to 3 minutes, which corresponds to a disturbance velocity

\[ v \approx \frac{5 \cdot 10^{10}}{3 \cdot 60} = 2.7 \cdot 10^8 = 2700 \text{ km/sec} \]

(it has been assumed that the ultraviolet radiation comes from regions lying no higher than the beginning or lower layers of the corona, while the radiation at the wavelength 12 m comes from a region where \(\eta(\omega) = 0\); for \(\lambda = 12\) m, \(n = 0\) when \(\eta = 1.7\)). Of course, if the beginning of absorption in the \(D\)-layer, in its

in turn, was delayed relative to the ultraviolet flare, about which we have no data, then the velocity \(v\) will be less than that given. The impulses at wavelengths 12 and 5 m (see above) have the order expected, but, in view of the absence of any details here, nothing can yet be said.

It seems to us that establishing a temporal correlation between impulses of radio emission and disturbances observed by ordinary astronomical methods on the Sun (prominences, eruptions, etc.) is of special interest.

Fig. 10. Radiation of the Sun and Galaxy on June 14, 1947.

In conclusion we note that, as estimates show, nonlinear phenomena of the Luxembourg–Gorky effect type cannot be significant in the corona (for details see the author’s article “On the Theory of the Luxembourg–Gorky Effect,” appearing in Izv. AN SSSR, physical series).

3. RADIATION OF THE GALAXY

No new experimental data on the radiation of the Galaxy have appeared; however, Townes’s article\(^8\), devoted to the interpretation of old measurements, contains a number of additional details obtained by this author privately from a number of experimenters.

For calculating the optical depth \(\tau\), Townes uses the following expression for the absorption coefficient (notation coinciding with that adopted in I has been introduced):

\[ \chi=-\frac{32\pi^{2}e^{6}N^{2}}{3\sqrt{2\pi}(kTm)^{3/2}c\omega^{2}} \ln\left(\frac{(2kT)^{3/2}}{2.115\,\omega e^{3}m^{1/2}}\right). \tag{3} \]

Here the inequalities are assumed to be satisfied

\[ \frac{kT}{2e^{2}N^{1/3}}\simeq \frac{300T}{N^{1/3}}\gg 1,\quad \omega\gg \sqrt{\frac{kT}{m}}\,N^{1/3}. \tag{4} \]

If, however,

\[ \omega\ll \sqrt{\frac{kT}{m}}\,N^{1/3}, \tag{5} \]

then, instead of formula (3), the author gives the following:

\[ \chi=\frac{32\pi^{2}e^{6}N^{2}}{3\sqrt{2\pi}(kTm)^{3/2}c\omega^{2}} \ln\left(\frac{0.61\,kT}{e^{2}N^{1/3}}\right). \tag{6} \]

In I, as is evident from formulas (I,21) and (I,23) and from the fact that \(n\simeq 1\), we used the expression

\[ \chi=-\frac{16\pi^{3}e^{6}N^{2}}{\sqrt{2\pi}(kTm)^{3/2}c\omega^{2}} \ln\left(\frac{kT}{e^{2}N^{1/3}}\right) =\frac{0.59N^{2}}{T^{3/2}\omega^{2}}\ln\left(\frac{600T}{N^{1/3}}\right). \tag{7} \]

As is clear from the derivation of the expression for the number of collisions (see I\(^{31}\)), formula (7) is obtained if the Debye radius

\[ D=\left(\frac{kT}{4\pi e^{2}N}\right)^{1/2} \]

is taken as the maximum value for the collision parameter \(\rho_m\). More precisely, in this case an additional factor \(0.68\), which was omitted, appears under the logarithm in (7)\(*\). Formula (6), on the other hand, with the replacement under the logarithm of the factor \(0.61\) by \(2\), is obtained if one takes \(\rho_m=N^{-1/3}\). Since, in the cases of interest to us, the first of inequalities (4) is always certainly fulfilled, the presence of a small factor under the logarithm in (6) and (7) is completely inessential, and these formulas differ only by the presence in (6) of the factor \(2/3\). In view of the fact that the use for \(\rho_m\) of the value \(D\), and not of the quantity \(N^{-1/3}\), seems more correct, formula (7) must nevertheless be preferred in comparison with expression (6). The condition of applicability of these formulas is in fact inequality (5), better with \(N^{-1/3}\) replaced by \(D\), which means that during the period of oscillation

\[ T_0=\frac{2\pi}{\omega} \]

the electron has time to travel a distance considerably greater than \(D\) (or \(N^{-1/3}\));

\(*\) In paper I\(^{31}\), because of a misprint, the value \(0.86\) is given instead of \(0.68\). It should be noted that in the case where the electron temperature is equal to the ion temperature, and not much higher than it, for \(D\) one must take the expression \(D=(kT/8\pi e^{2}N)^{1/2}\).

the latter is clear, since inequality (5) can be written in the form
\(\dfrac{2\pi D}{\bar v T_0}\ll 1\), where \(\bar v\simeq \sqrt{\dfrac{kT}{m}}\) is the mean velocity of the electrons. In the other limiting case, when the second of inequalities (4) is satisfied, formula (3) is obtained if for \(\rho_m\) one takes a value of the order

\[ \sqrt{\frac{kT}{m}}\,\frac{1}{\omega}\simeq \frac{\bar v T_0}{2\pi}. \]

We have not examined the question of how reliable such a choice is. This question has no practical significance, since the difference between formulas (3) and (6) appears in expressions under the logarithm, which in the cases of interest to us differ from one another comparatively little. Therefore Townes\(^{8}\) uses formula (3) also where it is necessary to use formula (6), indicating that the error thereby introduced is very small. This is also immediately clear from (6), (7), and (8).

The effective radiation temperature of the Galaxy is equal to (see I § 3):

\[ T_e=T(1-e^{-xl})= T\left[ 1-e^{-10^{-24}\frac{4\pi^2 N^2}{T^{3/2}\omega^2} \left(19.7-\ln\frac{\omega}{2\pi T^{3/2}}\right)l} \right], \tag{8} \]

where \(T\) is the temperature of the interstellar electron gas and \(l\) is the path traversed by the ray in the given direction.

Taking \(T=10^4\) degrees, \(l=60\,000\) light-years \(\simeq 6\cdot 10^{22}\ \text{cm}\), and \(N=1\), one can see that \(xl=1\) for \(\omega=6\cdot 10^8\) \((\lambda=3\ \text{m})\).

Let us note that the statement made in I concerning the necessity at high frequencies of taking into account the scattering of radio waves by electrons is erroneous. Owing to scattering, the absorption of radiation increases only because of the lengthening of the path of the radiation before it leaves the system (in the present case, the Galaxy). Since, however, the scattering is small, this lengthening is not substantial and in a first approximation may be neglected. Thus \(T_{ef}\) is determined by formula (8) also at high frequencies.

Further, in \(^{8}\) the assertion is made that the experimental determination of \(T_{ef}\) must be carried out from the following considerations. If the antenna is in a space with temperature \(T_{ef}\), then, with a matched receiver input, it receives the power \(P=kT_{ef}\Delta f\), where \(\Delta f\) is the width of the frequency band. Hence, knowing \(P\), one can immediately find \(T_{ef}\). However, such a method is valid only if the radiation comes from all directions, which by no means occurs in experiment. Thus, for example, under normal incidence of radiation on a half-wave dipole, the receiver obtains, as is shown in the following paragraph, the power

\[ P\simeq \frac{\lambda^2}{15.4}\,S\Delta f; \]

if we consider thermal radiation in a solid angle \(d\Omega\) close to the normal, then

\[ P\simeq \frac{\lambda^2}{15.4}\cdot \frac{2}{\lambda^2}\,kT_{ef}\,d\Omega\,\Delta f. \]

If, however, the direction of the flux makes an angle \(\varphi\) with the axis of the dipole, then \(P\) is multiplied by \(\sin^2\varphi\). In the case of radiation incident from all directions, as a result of integration over \(d\Omega\) we obtain \(P\simeq kT_{ef}\Delta f\), where the approximate character of the equality is due to the inaccuracy of the initial formula

for \(P\) (instead of the factor 15.4 there should stand some slowly varying function \(\varphi\)). For multipole antennas or antennas with reflectors the situation is, of course, more complicated. But from what has been said it is clear that the antenna always receives a smaller power than the power, expressed in the eighth power, \(P=kT_{ef}\Delta f\). It would not be appropriate to discuss here in greater detail the processing of the material carried out by Townes. We shall therefore give the final table, accompanying it with a few comments.

Table III

In Table III the references “private communication” refer to data obtained by Townes directly from the authors; references of the type \(^{18}\) refer to the bibliography in I, while reference \(^{14}\) is given at the end of the present article. The minimum experimental values of \(T_{ef}\) were obtained by Townes with the aid of the formula \(P=kT_{ef}\Delta f\). The probable values (column 5) were obtained by us in the same way as in I. In columns 6 and 7 are given the values of \(T_{ef}\) calculated from formula (8) for \(T_{ef}=10^{4}\), \(l=6\cdot10^{22}\) and \(N=0.63\) (variant \(a\)) and for \(T=1.5\cdot10^{5}\), \(l=6\cdot10^{22}\), \(N=1.1\) (variant \(b\)). The concentrations have been selected here so that, at the corresponding temperature, the calculated values of \(T_{ef}\) should coincide with Townes’s experimental value for \(\lambda=1.87\ \text{m}\). The principal result of Table III, which was also indicated in I\(^{23}\) and in I, is that for long waves \(T_{ef}\gg10^{4}\). On the basis of a whole series of considerations, however, the values of \(T_{ef}\) for long waves appear unreliable. Further experimental work is necessary here, and first of all at wavelengths \(\sim10\ \text{m}\), where refraction and absorption in the ionosphere and absorption in layer \(D\) are less noticeable than at longer waves—

waves. Measurements at \(\lambda=12\ \mathrm{m}\) were carried out by Hey et al.\({}^{6}\), but the value of \(T_{ef}\) has not yet been published. If, in fact, at long wavelengths \(T_{ef}\gg 10000^\circ\), then this conclusion would be very interesting, since it would mean, evidently, that \(T\gg 10000^\circ\) as well. Meanwhile, in astrophysics the value \(T=10000^\circ\) is now adopted. If \(T_{ef}\gg 10^4\) and at the same time other astrophysical data can be considered as decisively contradicting the assumption that the temperature of interstellar electrons is also \(\gg 10^4\), then other sources of the radio emission of the Galaxy will have to be sought. In this connection it must be borne in mind that, for example, radiation with \(\lambda=30\ \mathrm{m}\) is absorbed by a factor \(e\) over a distance of only \(\sim 5\cdot 10^{20}\ \mathrm{cm}\), i.e. along a path of \(\sim 1/_{100}\) of the dimensions of the Galaxy (this figure refers to the values \(N=1\) and \(T=10^4\)). Therefore the sources of radiation must be located at a relatively small distance from the Earth. In favor of the assumption of the existence of discrete sources of radiation in the Galaxy are the fluctuations in the intensity of the galactic radio emission discovered by Hey et al. (see I\({}^{16}\)).

4. SOME REMARKS

It seems advisable also to make here several remarks and to correct some errors and misprints contained in review I. First of all we shall dwell on the determination of the effective temperature of radio emission from the measurement of the power at the output of the receiver. Let a radio wave be incident on a half-wave dipole \(\left(\text{the length of the dipole } l=\dfrac{\lambda}{2}\right)\), the electric field of which is directed along the axis of the dipole and is equal to \(E_0\). Then the electromotive force \(e_a\) induced in the dipole is equal to \(e_a=\dfrac{\lambda}{\pi}E_0\), since the effective height of such a dipole is \(\lambda/\pi\) (see, for example, \({}^{16}\)). Further, the maximum power delivered by the antenna to the receiver \(P\) is equal to \(\dfrac{e_a^2}{4R_a}\), where \(R_a=73.3\) ohms \(=8.15\cdot 10^{-11}\) CGSE is the radiation resistance of the dipole. Thus for a half-wave dipole

\[ P=\frac{\lambda^2 E_0^2}{4\pi^2 R_a}. \]

If the radiation is not polarized and has a continuous spectrum, then

\[ E_0^2=\frac{2\pi}{c}S\Delta f \]

and

\[ \frac{P}{\Delta f} = \frac{\lambda^2}{2R_a\pi c}\,S \simeq \frac{\lambda^2 S}{15.4}, \]

where \(S\) is the radiation energy flux (the Poynting vector) and \(\Delta f\) is the transmitted frequency band. In the case of the radio emission of the Sun,

\[ S=\frac{2\pi kT}{\lambda^2}\left(\frac{r_\odot}{R}\right)^2\eta^2, \]

and we finally obtain:

\[ \frac{P}{\Delta f} = \frac{kT}{R_a c}\left(\frac{r_\odot}{R}\right)^2\eta^2 = 0.41\,kT\left(\frac{r_\odot}{R}\right)^2\eta^2 = 0.41\,k\left(\frac{r_\odot}{R}\right)^2T_{ef} = \]

\[ = 1.23\cdot 10^{-22}T_{ef}\ \frac{\mathrm{watt}}{\mathrm{megacycle}}. \tag{9} \]

V. L. GINZBURG

In the case of a complex antenna it is customary to characterize it by a factor \(G_a\), showing how much greater the maximum power is that it can deliver to the receiver in comparison with a half-wave dipole. Hence, by definition, in the case of any antenna:

\[ \frac{P}{\Delta f}=0.41\,kT\left(\frac{r_{\odot}}{R}\right)^2\eta^2G_a =1.23\cdot 10^{-22}G_aT_{ef}\, \frac{\text{watt}}{\text{megacycle}} . \tag{10} \]

Formula (10), which coincides with that given by Appleton and Hey (see \(1^\circ\)), differs from formula [1, (15)] only by replacing the factor \(\sim 0.8\) by 0.41, which is connected with the fact that in I polarization was not taken into account; in other words, it was not taken into account that the antenna receives only that half of the radio-radiation flux which corresponds to the field directed along the axis of the antenna dipoles*). For a multidipole antenna \(G_a\) is, in order of magnitude, equal to the number of dipoles.

The noise power in the receiver according to [1, (11)] is equal to (the receiver temperature \(T_a\) is taken as \(\simeq 300^\circ\) abs):

\[ \frac{P_n}{\Delta f}=kT_aN=4\cdot 10^{-15}N\, \frac{\text{watt}}{\text{megacycle}} . \tag{11} \]

Specifying the minimum measurable excess of radio radiation over the noise, from (10) and (11) one can at once obtain the smallest value of \(T_{ef}\) that can be detected by the given apparatus.

As was already noted in I, until recently the question of the nature of the outer solar corona remained unclear. The problem here consisted in the fact that, on the one hand, radiation attributable to the outer corona, as follows from the experimental data (the presence of Fraunhofer lines), must be due to scattering on dust (i.e. on cosmic particles). On the other hand, the presence of dust at small distances from the Sun (\(\eta\simeq 1.5\)) seems almost impossible because of its sublimation. A way out of these contradictions was apparently correctly indicated recently by Holstom \(^{16}\).

*) In formula [1, (15)], in addition, there is a misprint: instead of \(10^{-8}\) there stands the value \(10^{-17}\). Among other misprints we note the following: on p. 37 of I it is said that the Sun is visible at an angle of \(0.5\) square degrees, whereas it should be \(0.25\) square degrees; accordingly, six lines below, instead of the number 2 there should stand 4. On p. 39 it should be

\[ K=\frac{8.4\cdot 10^{-21}}{\lambda^3(\text{in meters})}\, \frac{\text{watt}}{\text{megacycle}\cdot \text{square degree}} . \]

On p. 41 it should be \(K\odot=4S\odot\simeq 12\cdot 10^{-18}\) instead of \(K\odot=2S\odot\). In the last of formulas [1, (21)] the denominator has \(\omega\) instead of the required \(\omega^2\), and in formula [1, (23)] there stands \(e^2\) instead of the required \(e^4\). In formula [1, (24)], in the denominator in the third term of the equality there should be \(3\cdot 10^{10}\omega^{1/2}\) instead of \(3\omega^3\), and in the second term \(n^2\). Further, in the example: \(\Delta\tau=0.02\), not \(0.4\).

NEW DATA ON THE RADIO EMISSION OF THE SUN AND THE GALAXY

The point is that if the cosmic particles scattering the light are sufficiently large (substantially larger than the wavelength of the light), then the indicatrix of the light scattered by them has a sharp maximum in the direction of the incident radiation. Therefore, even if such particles are found only at a considerable distance from the Sun \((\eta = \eta_0 \gg 1)\), the visible surface brightness of the light scattered by them will increase on approaching the Sun, as is found experimentally (in the case of isotropic scattering the surface brightness would have a maximum at a distance from the Sun equal to the distance \(\eta_0\), beginning from which the cloud of particles extends). This explanation is apparently correct, and in any case the fact that the outer corona is connected with scattering by dust is beyond doubt. The presence of an insignificant amount of dust can have no noticeable influence on radio waves, and thus for us only the electron density in the corona is of interest. The latter is usually calculated from measurements of the brightness of the corona without separating out scattering by dust. As a result, what is obtained is not the true electron density, but an effective one. To obtain the true density it is necessary to isolate the scattering by electrons, which leads to a change in the values of \(N\) given in I in Table III.

The new values of the electron concentration in the corona, obtained in \(^{16}\), and compared for convenience with the old values, are given

Table IV

in Table IV. The values for which it is already difficult to vouch are placed in parentheses. It should also be recalled that the discussion concerns mean values of \(N\), since the corona is not static, and \(N\) changes rather strongly depending on the cycle of solar activity, etc.

The change in the concentration \(N\) will not noticeably affect the calculations whose results are given in I, since waves shorter than \(\sim 5\) m are mainly absorbed in the inner corona \((\eta < 1.6)\), where all the

corrections are relatively small. On the contrary, for longer waves the changes in \(N\) may be quite substantial.

In this connection we note that the formulas (21) given in I for \(n\) and the absorption index

\[ k=\frac{\nu}{2\omega}\,\frac{1-n^2}{n} \]

are valid only for not too small \(n\). In the general case\({}^{18}\):

\[ \left. \begin{gathered} k=\sqrt{-\frac{\varepsilon}{2}+\sqrt{\left(\frac{\varepsilon}{2}\right)^2+\left(\frac{2\pi\sigma}{\omega}\right)^2}};\qquad x=\frac{2k\omega}{c};\\[6pt] \varepsilon=1-\frac{4\pi e^2N}{m\omega^2}=1-3.19\cdot10^9\,\frac{N}{\omega^2};\\[6pt] \sigma=\frac{e^2\nu N}{m\omega^2}=\frac{1-\varepsilon}{4\pi}\,\nu,\qquad n=\sqrt{\frac{\varepsilon}{2}+\sqrt{\left(\frac{\varepsilon}{2}\right)^2+\left(\frac{2\pi\sigma}{\omega}\right)^2}}. \end{gathered} \right\} \tag{12} \]

where \(k\) is the absorption coefficient, \(n\) is the refractive index, \(\sigma\) is the conductivity, \(\varepsilon\) is the dielectric constant, and \(\nu\) is the effective number of collisions; in the expressions for \(\varepsilon\) and \(\sigma\) only the fact that \(\omega^2\gg\nu^2\) has been taken into account. The formulas [I, (21)] apply if

\[ \varepsilon \gg \frac{4\pi\sigma}{\omega}=\frac{1-\varepsilon}{\omega}\,\nu; \]

this inequality is only strengthened if it is written in the form \(\varepsilon\gg\nu/\omega\). Under coronal conditions \(\nu<10^5\), and even for \(\lambda\sim5\ \mathrm{m}\) (\(\omega\sim10^8\)), \(\nu/\omega<10^{-3}\). Thus we see that the use of formulas (12) instead of [I, (21)] may be necessary only in the most exceptional cases.

On the question of the origin of the sporadic radio emission of the Sun, two explanations have been proposed: Kiepenheuer\({}^{17}\) advanced the assertion that the source of the radiation is electrons rotating in the magnetic field of sunspots. On the other hand, Shklovskii and Martyn\({}^{18}\) drew attention to the possibility of exciting in the corona oscillations of the type of oscillations of a gas-discharge plasma; these oscillations may lead to intense radio emission. As was indicated in I, Kiepenheuer’s theory is erroneous, since the presence of a magnetic field does not disturb thermal equilibrium and Kirchhoff’s theorem remains valid. It follows from this that a gas cannot emit more than a black body with a temperature equal to the temperature of the gas. Here, however, the following apparent contradiction arises. Let us consider some relatively small volume of gas with a Maxwellian distribution of electrons over velocities and with an optical thickness which is very small for radio waves. Now place the gas in a magnetic field \(H\); then the electrons, rotating in spirals, emit waves with frequency

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

and, for a sufficiently large volume of gas, the intensity of the radiation considerably exceeds the intensity of thermal radiation. At the same time, since the optical thickness of the gas is small, it seems that the processes of reabsorption cannot in any way greatly diminish the in-

intensity of the radiation and ensure the validity of Kirchhoff’s theorem. The answer to this “paradox” consists in the fact that the absorption of radio waves by the gas in a field changes greatly, and from the fact that the optical thickness without taking the field into account was small, it by no means follows that it will be small in the field as well. On the contrary, precisely the emitted frequency

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

is absorbed most strongly, just as the frequency of the resonance radiation of atoms is at the same time the frequency of maximum absorption. Therefore, as a result of reabsorption, the validity of Kirchhoff’s theorem will be ensured. Additional radiation connected with the magnetic field could in principle occur only if the electrons did not have a Maxwellian velocity distribution, for which there are no special grounds. As for the explanation of radio emission by the excitation of plasma oscillations, it meets with no general objections, but as yet a sufficiently complete analysis of the question has not been carried out here. Let us note that, as was indicated by I. M. Gordon (private communication), eruptions on the Sun may have an indirect effect on radio emission in a certain sense—namely, they may lead to the heating of individual regions of the corona and, consequently, to a decrease in the absorption of radio waves [see I, (23)]; as a result, radiation, say of waves of length \(\sim 5\) m, may come from lower and hotter layers of the corona than before the eruption, etc.

The data presented above clearly show how fruitful the application of radio observations in astrophysics has proved to be. It is therefore difficult to doubt that in the near future we shall witness an expansion of investigations in this field and new achievements.

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