RADIO ASTRONOMY*)

M. Ryle

CONTENTS

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509
2. First astronomical observations at radio wavelengths . . . . . . . . . 511
3. A chaotic field at radio frequency and its equivalent temperature . . . 513
4. Measurements of weak chaotic fields. Measurements of small values of noise energy at radio frequency (516) . . . . . . . . . . . . . . . . . . 515
5. Observation of a weak source against the background of Galactic radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
   a) “Pencil” beam (522). b) “Interferometric” method (523). c) Detection of discrete sources in the Galaxy (526). d) Measurements of the diameter and position of a source (529).
6. Measurements of polarization . . . . . . . . . . . . . . . . . . . . . 530
7. Experimental investigations of solar radiation . . . . . . . . . . . . 533
   a) Observations at wavelengths shorter than 1 m (534). b) Observations at wavelengths longer than 1 m (539).
8. Experimental investigations of Galactic radiation . . . . . . . . . . 546
   a) General radiation of the Galaxy (546). b) Discovery of discrete sources in the Galaxy (547). c) Distribution of discrete sources (550). d) Polarization of the radiation of discrete sources (553). e) Cause of intensity fluctuations (553).
9. Theory of solar radiation . . . . . . . . . . . . . . . . . . . . . . . 557
   a) Application of magneto-ionic theory to the solar atmosphere (558). b) Models proposed to explain the radio emission of the Sun (561). c) Study of the unperturbed Sun (561). d) Formation of high-energy electrons in the solar atmosphere (564). e) Enhanced radiation of sunspots (566). f) Detailed calculation of the mean energy of an electron maintained by an electric field (571). g) Theory of rapid fluctuations in the radiation of sunspots and associated large disturbances connected with flares in the chromosphere (573).
10. Theory of Galactic radiation . . . . . . . . . . . . . . . . . . . . . 575
    a) Source in the interstellar gas (575). b) Nature of the sources (576). c) Mechanisms of the intense radiation of the sources (577). d) Origin of the total radiation of the Galaxy (579).
11. Future development of radio astronomy . . . . . . . . . . . . . . . . 583
    a) Study of the solar atmosphere (583). b) Study of stellar envelopes (584). c) Origin of cosmic rays (585). d) Structure of the Galaxy (586).
    Cited literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

) M. Ryle, Reports on Progress in Physics 13, 184–246 (1950). On questions of the radio emission of the Sun and the Galaxy, the journal Uspekhi Fizicheskikh Nauk has published the following articles: V. L. Ginzburg, 32, 26–53 (1947), 34, 13–33 (1948); G. G. Getmantsev, 41, 408 (1950), 44, 527–557 (1951). (Translator’s note.)*

1. Introduction

Our knowledge of the Universe has been obtained almost exclusively from observations and measurements of the electromagnetic radiation falling upon the Earth. Until recent years these observations were limited to wavelengths lying in the visible region and close to the visible rays. Although measurement techniques are available for almost 40 octaves of the spectrum, astronomical observations were limited to only 4 octaves.

Measurements of radiation in this narrow range of wavelengths made it possible to draw conclusions about the nature and physical conditions of remote bodies. However, it seemed possible to study only bodies that emit, or cause refraction or absorption of, the radiation received.

Therefore, astronomy in the range of visible wavelengths was for the most part concerned with the study of the denser regions of the Universe. In particular, direct observations of stellar envelopes were usually hindered by the relative weakness of the light they emit, in comparison with the light emitted by the denser and colder regions of a star’s surface. Direct observations of the solar envelope, which are possible during an eclipse of the photosphere by the Moon or with the aid of special instruments, have shown that it has an extremely high temperature, and it seems probable that from direct observations of stellar envelopes astrophysics will obtain information of great importance.

The use of other waves of the electromagnetic spectrum is a means of increasing the possibilities for experimental knowledge of the Universe. Observations on the Earth are, obviously, limited to wavelengths that are little affected by the terrestrial atmosphere. Unfortunately, over a wide range of the electromagnetic spectrum in which measurement techniques have been developed, the atmosphere is completely opaque. The extension of the visible, or near-visible, wavelength range toward shorter wavelengths is limited by regions of atomic absorption. On the long-wavelength side, however, regions of molecular absorption are arranged almost continuously up to wavelengths of the order of 1 cm (Fig. 1).

However, at wavelengths longer than 1 cm the absorption becomes negligibly small, and for observations it is possible to use wavelengths up to 10–20 meters. Beyond this boundary the incoming radiation from outside will in some cases be reflected back by the ionosphere.

The development of high-altitude rocket technology has made it possible to raise recording apparatus above a significant part of the terrestrial atmosphere. In this way observations can be carried out at wavelengths that are very strongly absorbed by the entire atmosphere and, thereby, the possibility appears of extending the range of wavelengths used. Experiments have already been carried out in which the study of the solar spectrum

was extended toward shorter waves down to 2100 Å (Durand, Oberly, and Tousey, 1949)*). Although with further development of rocket apparatus it will apparently be possible to obtain some important results, it is unlikely that such short-term and costly experiments will play the principal role in the development of observational astronomy.

Thus, astronomical observations from the earth’s surface are limited to a frequency region about 4 octaves wide, including the visible part of the spectrum, and to a frequency region about 10 octaves wide at wavelengths between 1 cm and 20 m. Only in the last few years has it become possible to observe the radiation of the Sun and the Galaxy in the radio range.

Before describing the experimental results it is useful to discuss the difference between observations on radio waves and on waves of visible

Fig. 1. Approximate value of the transparency coefficient of the earth’s atmosphere for electromagnetic radiation.

Labels in the figure: γ-rays; X-rays; ultraviolet rays; infrared rays; radio waves. Horizontal axis: wavelength in cm, with marks \(10^{-10}\), \(10^{-8}\), \(10^{-6}\), \(10^{-4}\), \(10^{-2}\), \(1\), \(10^{2}\), \(10^{4}\), \(10^{6}\).

light. From the astrophysical point of view the significance of observations on radio waves lies in the fact that they are strongly absorbed, refracted, and emitted by rarefied ionized gas. These questions will be considered in section 9a), where it will be shown that for waves in the meter range the radiation of the solar corona approaches black-body radiation. Thus, a region which radiates extremely weakly at visible wavelengths approaches a perfect emitter of radio waves. It is therefore clear that the use of radio waves makes it possible to observe regions in which the rarefaction is too great for observation in visible light. The possibility of studying the solar corona on radio waves has already been demonstrated. Direct observations of stellar envelopes carried out in this way will undoubtedly lead astrophysics to important successes.

*) See the review by S. L. Mandelstam, UFN 46, no. 2 (1952). (Translator’s note.)

The experiments carried out have already shown how important a more complete knowledge is of the mechanisms of the phenomena occurring in the solar envelope; the stability of protuberances, the radiation of corpuscular streams, and the intensity of ultraviolet radiation indicate that sources of great energy exist in the Sun’s envelope. It is possible that similar phenomena, but on an even larger scale, occurring on other stars are responsible for the acceleration of cosmic-ray particles, for fluctuations in the light intensity of certain stars, and also for other astrophysical phenomena. This indicates how important direct studies of stellar envelopes are.

On the other hand, at radio wavelengths it is not possible to achieve a resolving power comparable with that which is available at visible wavelengths. In the following sections it will be shown that most of the limitations of radio astronomy are connected with the difficulty of resolving neighboring sources and detecting small sources against the background of the general radiation of the Galaxy.

Recently two reviews on radio astronomy were published (Hey, 1949; Pawsey, 1950). The present article merely supplements them. In it the emphasis is, to some extent, different. The details of experimental investigations are set forth briefly, while the principal limitations of the various experimental methods and certain theoretical interpretations of the present-day data are discussed in greater detail.

It is apparently inevitable that in a review of this type some emphasis is placed on the experimental and theoretical work of the laboratory with which the author is associated (Cavendish). This is especially difficult to avoid when considering the theoretical considerations presented in Sections 9 and 10, where the author attempts to give a coherent explanation of a large body of experimental data.

At the same time, a detailed analysis of theories proposed by other authors is almost impossible, both because of the limited information that can be extracted from the published articles and because of the contradictions that arise in these theories when interpreting the various difficulties indicated in Sections 9 and 10.

2. FIRST ASTRONOMICAL OBSERVATIONS AT RADIO WAVELENGTHS

The first definite proof of the existence of radio emission of extraterrestrial origin was obtained in 1932 by Jansky (1932, 1933), who observed, at a wavelength of 15 m, chaotic noise signals whose intensity varied during the day. Initially he attributed these fluctuations to diurnal variations in the state of the ionosphere. However, after several—

...months it became clear that they have a period equal to a sidereal day.

Thus, the source of the radiation could not be associated with the ionosphere or with the Sun; it had to be located outside the solar system. Further observations showed that the intensity of the radiation was maximal when the antennas were directed toward the center of the Galaxy.

Franz’s subsequent observations (1942) at a wavelength of 10 m confirmed that the radiation arises mainly in the plane of the Galaxy, while calculations showed that some regions of the Galaxy radiate at these wavelengths as if they had a temperature on the order of 100,000°.

Jansky also attempted to detect analogous radiation from the Sun, but without success. The absence of appreciable radio emission from the Sun indicated that the observed radiation of the Galaxy is not a consequence of radio emission from the stars, but is apparently caused by emission from interstellar gas.

Later, Southworth (1945) succeeded in detecting radiation from the Sun at shorter wavelengths between 1 and 10 cm (at which the radiation of the Galaxy is considerably weaker). In these experiments he used antennas with considerably greater resolving power. At the same time, Hey (1946), working at a wavelength of 4 m, detected radiation from the Sun which, during the passage of large sunspots, had for short periods a greater intensity than that of the radiation of the Galaxy. He did not, however, have the possibility of observing radiation from the undisturbed Sun (in the absence of sunspots) because of the screening action of the Galactic background.

From observations at shorter wavelengths, Southworth came to the conclusion that the intensity of the radiation corresponds to emission from a source whose temperature, in order of magnitude, is equal to the temperature of the photosphere predicted by visual observations (6000°). The much greater intensities observed at a wavelength of 4 m during the passage of sunspots could be explained by assuming that the Sun radiates as if it had a temperature of \(10^9\) degrees (Appleton, 1945; Appleton and Hey, 1946).

The first observations of both the Galaxy and the Sun showed that if the signal is fed from the antenna to a loudspeaker or to a cathode-ray tube, it displays many properties of the chaotic noise generated by a heated resistance. It was therefore natural to associate this radiation with the emission of a source having a high temperature.

Before describing later observations, some important questions concerning methods for measuring and interpreting the low-power radio noises received from the Sun and the Galaxy are discussed below.

3. THE CHAOTIC FIELD AT RADIO FREQUENCY AND ITS EQUIVALENT TEMPERATURE

Radio-astronomical observations consist mainly in the fact that, at radio frequency, the energy of chaotic oscillations is measured, which can be taken from an antenna of specified directivity. Methods for measuring very small values of energy at radio frequency are discussed in Section 4; here the question considered is the interpretation of measurement results on the basis of the physical properties of the source emission.

The radiation incident on the antenna may come from a diffuse source occupying a large solid angle in comparison with the angle to which the antenna system is sensitive. However, the source may also subtend a small solid angle of unknown magnitude. Under real conditions the radiation may arrive simultaneously from sources of both types. Therefore methods are needed that would make it possible to distinguish them. Such methods are described in Section 5. Here, however, it is assumed that only one source is involved.

Since the observed radiation is similar to chaotic noise, the received energy is proportional to the passband width of the measuring apparatus, and in order to measure the energy radiated by the source it is necessary to know precisely the bandwidth in which the observations were made. In measurements of chaotic noise this difficulty is overcome by introducing, for the description of noise energy, the concept of “equivalent temperature,” which removes additional difficulties associated with ambiguity in the definition of impedance. The concept of equivalent temperature is a convenient method for describing the energy received by an antenna system placed in a field of chaotic noise.

According to Nyquist (1928), the useful energy that can be extracted from a resistance heated to temperature \(T\) is determined by the expression

\[ k \cdot T \cdot \Delta f, \]

where \(k\) is Boltzmann’s constant and \(\Delta f\) is the frequency band in which the energy is measured. Burdgess (1941, 1946) and Lehman (1946) applied this law to the radiation resistance of an antenna enclosed in an absolutely black shell heated to temperature \(T\), and showed that the energy extracted from the antenna is also equal to \(kT\Delta f\). In such an antenna, connected by means of a transmission line to a resistance, an equilibrium state is established if the temperature of the resistance is equal to that of the shell.

By choosing the temperature of the resistance so that there is no flow of energy in it, one can theoretically measure the temperature of the shell.

Simple thermodynamic considerations show that analogous conditions arise in a directional antenna. In it, up to

an equilibrium state is reached when the temperatures of the enclosure and the resistance are equal. Let the antenna directivity coefficient in the direction \((\theta,\varphi)\) be given by the function \(f(\theta,\varphi)\); then the effective reception angle is

\[ \Omega=\iint f(\theta,\varphi)\cdot\cos\theta\cdot d\theta\cdot d\varphi, \]

and the gain of the antenna relative to an isotropic radiator is equal to

\[ \frac{4\pi}{\Omega}. \]

If the antenna is not enclosed in a casing but is directed at a black body subtending a solid angle greater than the reception angle \(\Omega\), then the equilibrium state occurs if the resistance has the same temperature as the black body. If, however, the black body subtends a solid angle smaller than \(\Omega\), then the corresponding value of the energy will decrease.

These considerations may now be applied to the radio reception of chaotic oscillations from sources in the Galaxy. Initially let us assume that the radiation is received from a diffuse source subtending a solid angle greater than \(\Omega\). If the energy delivered to the receiver corresponds to the power developed in a matched resistance at temperature \(T_A\), then the antenna can be connected to this resistance and, in this way, equilibrium conditions can be achieved. The equivalent temperature \(T_A\) is now a measure of the radiation of the source. Indeed, if in the receiver’s range the source is an absolutely black body, then the equilibrium state is established if \(T_A\) is equal to the temperature of the source.

Thus, comparison of the energy extracted from the antenna with the energy of a heated resistance having the same impedance makes it possible to determine the equivalent temperature of a diffuse source occupying a solid angle larger than the antenna angle \(\Omega\).

If, now, the radiation is received from a source subtending an angle \(\omega\) smaller than the angle \(\Omega\), then the equilibrium state between the antenna and the heated resistance will occur when the energies delivered by the resistance and by the antenna are equal. The energy extracted from the antenna is \(\frac{\omega}{\Omega}\) times less than the energy that would be received from a large source. Therefore, in this case equilibrium between the resistance and the antenna will occur at the same temperature \(T_A\) if the radiation intensity of this source is \(\frac{\Omega}{\omega}\) times greater than the radiation of the large source. For calculating absolutely black radiation at a radio frequency we shall apply the Rayleigh–Jeans law: the emission per unit frequency is proportional to the temperature; therefore the radiation energy of the source corresponds to the emission of an absolutely black radiator whose temperature is

\[ T_S=\frac{\Omega}{\omega}T_A. \]

Thus, by comparing the energy extracted from the antenna with the energy of a heated resistance and knowing the solid angle of reception, one can determine the effective temperature \(T_S\) of a source subtending a smaller angle.

If radiation is received from a small source subtending an unknown angle (as in the case of point sources in the Galaxy), then the effective temperature cannot be determined, and the intensity of the radiation is characterized only by the value of the energy flux at the Earth in the given frequency range. The energy extracted by the antenna from a specified incident flux is determined by its effective area \(A\), the value of which is related to the solid angle of reception by the expression

\[ A=\frac{\lambda^2}{\Omega}, \]

where \(\lambda\) is the wavelength (cm, for example, Smith, 1949).

It is important to note that when the emission of a source is described by the energy flux at the Earth, the polarization of the antenna must be taken into account. If, for measurements of randomly polarized radiation, a linearly or circularly polarized antenna is used, or if a linearly polarized antenna is used to measure circularly polarized radiation, then the measured energy flux is only one half of the total incident flux. This complication does not arise when the emission of a source is described by an equivalent temperature.

Of course, the emission of a diffuse source, or of a discrete source subtending a small but known solid angle, can also be described by the value of the energy flux at the Earth in the given frequency range per unit solid angle. Because of the inconvenience of such a unit, the method of measuring the energy received in the antenna is usually reduced to comparing its value with the energy obtained from a local noise source. In this way the idea of the equivalent temperature of the antenna is introduced. The concept of the equivalent temperature of a source is applied in discussing the radiation of any body. It must be emphasized that this concept is used simply as a convenient unit of radiation, and its introduction by no means implies that the source of the radio emission of the Galaxy necessarily radiates as a black body. This will be clear from the sections in which the various theories of radio emission are discussed.

4. MEASUREMENTS OF WEAK RANDOM FIELDS

Early observations at wavelengths shorter than \(10\) cm showed that the emission of the Sun has the magnitude expected from a source at a temperature of \(6000^\circ\). From the Galaxy, however, no appreciable radiation was detected at these wavelengths. From observations at a wavelength of about \(4\) m it followed that, during periods of noticeable activity of sunspots, the radiation intensity corresponds

emission of a source occupying the same solid angle as the Sun and having a temperature of \(10^9\) degrees. Intense radiation from the Galaxy was also observed at the still longer wavelength of \(10\) m, corresponding to the emission of a source at a temperature of the order of \(10^5\) degrees. At these same longer wavelengths the radiation of the undisturbed Sun was not detected, partly because of the insufficient sensitivity of the receiving devices and partly because of the shielding action of the radiation of the Galaxy, which is especially pronounced when antennas with low resolving power (having a large value of \(\Omega\)) are used.

It is clear that it is necessary to be able to observe the Sun’s radiation at these wavelengths at all times, and not only during periods of increased activity. With the improvement of the sensitivity of receiving devices and with the construction of antennas of high resolving power, it became possible to observe the radiation not only of the undisturbed Sun but even to detect discrete sources of radio waves in the Galaxy.

Below we consider the problem of measuring weak random fields and questions of designing antennas with high resolving power, making it possible to distinguish the radiation of a weak source from the general background of the Galaxy.

Measurement of small values of noise energy at radio frequency

For measuring small values of the energy delivered by an antenna to a system (expressed in terms of the equivalent antenna temperature \(T_A\)), the use of amplifiers is unavoidable; the input of these amplifiers itself creates random noises, the energy of which may considerably exceed the energy of the noises received by the antenna. According to Johnson, the noise energy and the shot effect that are inherent in the input circuit of a receiver are expressed in terms of the equivalent temperature \(T_R\). With the antenna disconnected, random fluctuations about a mean value will be observed at the receiver’s output indicator, depending on the energy supplied to the receiver and associated with \(T_R\). The instantaneous readings of the output indicator may have an arbitrary magnitude; however, their mean value, obtained from a large number \(n\) of instantaneous observations, will differ from the true mean value by an amount proportional to \(\frac{1}{\sqrt{n}}\). If \(B\) is the bandwidth of the circuits preceding the output indicator, then \(B\) independent observations per second can be obtained. If now the time constant of the output indicator is large and corresponds to a bandwidth \(b\), then the indicator will register the mean value of the output over a time equal to \(\frac{1}{b}\) sec. This

means that it effectively registers the average of \(\dfrac{B}{b}\) independent observations. Thus, the readings of the output indicator fluctuate about the true mean value with an amplitude proportional to \(\sqrt{\dfrac{b}{B}}\), and, consequently, the energy of the noise due to the input circuit of the receiver can be determined with an accuracy of \(T_R\sqrt{\dfrac{b}{B}}\).

If an antenna is now connected to the receiver, the readings of the indicator will be randomly scattered about the mean value corresponding to the output temperature \(T_A + T_R\). An increase in the reading of the output instrument will be noticeable if it exceeds the scatter. Therefore the energy received by the antenna will be registered by the instrument if

\[ T_A > T_R\sqrt{\frac{b}{B}}. \]

Consequently, it is possible to detect noise induced in the antenna whose energy is considerably less than the noise energy inherent in the receiving amplifier itself, provided that a broadband amplifier and a narrow-band output indicator are used. Below are given the limiting values of sensitivity that are obtained in this way under practical conditions. It should, however, be pointed out that there are certain important circumstances which limit the minimum value of the energy measured. First, in these experiments it is important to measure the dependence of the radiation intensity of the source on frequency, and this means that the experiment must be carried out using receivers with a comparatively narrow-band input. In addition, limitation of the receiver bandwidth is also required because, in some arrangements, high resolving power is achieved by means of an interference device, while the different components of the oscillations received by a broadband amplifier have different phase values, which complicates the interference pattern. Secondly, the use of narrow-band output indicators is limited by the need to record comparatively rapid changes in the intensity of the received signals. Such changes arise because of fluctuations in the energy of the incident radiation, and also because of changes in the energy picked up from the antenna as it rotates. In practice, values of \(\dfrac{B}{b}\) of the order of \(10^5\)—\(10^7\) are often used, which make it possible to detect energies entering the antenna amounting to approximately one thousandth of the energy of the receiver’s own noise.

In the manner indicated, small values of energy can in theory be detected. In practice, however, the calculation of such a system presents considerable difficulties, partly because in the apparatus

it is necessary to operate for a long time without calibration with an automatically recording output. By connecting a narrow-band filter to the output of a standard receiver, its nonconstancy is reduced to a value corresponding to the required sensitivity. However, the mean value of the amplitude of the output signal is proportional to the gain of the receiver, and, consequently, changes in gain by an amount of the order of \(10^{-3}\) will cause changes in the output reading corresponding to the limiting values of the energy being measured. Changes in the receiver’s own noise (for example, because of deterioration of the first tube) will also cause changes in the output reading. Accurate maintenance of the constancy of gain and of the noise energy of amplifiers with large gain is practically impossible without their periodic calibration.

These difficulties were partly overcome by Dicke (1946), who used the method of periodically replacing the antenna by a resistance heated to room temperature. The switching period was sufficiently short that, in the interval between the two positions of the switch, the parameters of the apparatus could be regarded as unchanged. If the antenna and the auxiliary resistance have equal impedance values at the receiver input, then, at the receiver output during switching, an alternating component of current will appear whose frequency is equal to the switching frequency, and whose amplitude is proportional to the gain of the receiver and to the difference between the equivalent temperature of the antenna and room temperature. Therefore a twofold increase in the output reading will correspond to a doubling of the receiver gain. In the usual system, however, a twofold increase of the output indication may sometimes be caused by a change in the receiver gain of only \(0.1\%\). However, since the reading at the output of the receiving device also depends on the linearity of the receiver and on the characteristic of the detector, the receiver must still be calibrated; moreover, if the receiver is not calibrated with the aid of a standard noise source, it is necessary to know its frequency characteristic.

An alternative method for measuring small values of noise energy was developed (Ryle and Vonberg, 1948), one that does not depend on the gain coefficient and frequency characteristic of the receiver and does not require knowledge of the detector characteristic. This method can be used over a wide range of energy variation without a calibrated gain switch.

In this system, which is shown schematically in Fig. 2, there is a local noise source, which is regulated automatically and continuously so that it is in equilibrium with the antenna. The receiver is alternately connected to the antenna and to the local noise source. If the impedances of the antenna and of the noise source are equal to each other, then the value of the energy entering the receiver is the same in both positions of the switch, provided that

equality of the values of the effective temperature of the noise source and the antenna. These conditions do not depend on the impedance and the level of the intrinsic noise of the receiver itself. If, however, the energy values are not equal, then at the output of the receiver there will appear a variable component of the voltage with a frequency equal to the switching frequency; the amplitude and phase of this component are a measure of the imbalance between the antenna and the noise source. As a result of passing this component and the voltage obtained from the handle of the switch motor through the detector, a direct current arises, whose voltage is proportional to the deviation obtained at the output from the noise generator. This current can be used to regulate the noise source. This operation does not depend

Fig. 2. Diagram of a device for continuous measurement of small values of noise energy.

on the gain of the receiver and on its frequency characteristic, as well as on the characteristic of the detector.

As the noise source a diode was used, the temperature of which was limited. If the anode current \(J\) of this tube is passed through a resistance \(R\) (chosen so that at the receiver input it has the same impedance as the antenna), then the noise energy in the band \(\Delta f\) is equal to

\[ \frac{1}{2} eJR + kT_0 \Delta f, \]

where \(e\) is the electron charge, and \(k\) is Boltzmann’s constant. (The second term represents Johnson noise in the resistance.) This energy is equal to that which can be obtained by heating the resistance to the temperature \(T_0 + T_D\), where \(T_D = \frac{eJR}{2k}\).

Thus, the equivalent temperature of the antenna can be determined from the mean value of the anode current of the diode, using a simple parameter: the resistance of the diode anode circuit.

The operating range of the instrument can be extended if a cable with attenuation is inserted between the noise source and the switch. It can be shown that a resistance whose temperature is \(T\), connected by means of a matched transmission line whose power attenuation coefficient is \(\alpha\), delivers the same energy as a resistance at the temperature

\[ \alpha T + (1-\alpha)T_0, \]

where \(T_0\) is the temperature of the transmission line.

Thus, if an absorbing cable is used at the output of the diode noise source, the effective temperature is given by the expression

\[ \alpha (T_0 + T_D) + (1-\alpha)T_0 = T_0 + \alpha T_D . \]

Therefore the sensitivity of the device is reduced by a factor of \(\alpha\), and the zero level still corresponds to room temperature.

If, however, an antenna whose equivalent temperature is \(T_A\) is connected to the switch by means of a cable whose attenuation coefficient is \(\beta\), then the equilibrium conditions correspond to the equality

\[ \beta T_A + (1-\beta)T_0 = T_0 + \alpha T_D. \]

or

\[ T_A = T_0 + \frac{\alpha}{\beta} T_D. \]

Therefore the anode current can be used directly for recording the energy of the antenna. The zero reading of the curve always corresponds to room temperature, while the scale of its calibration depends on the resistance of the diode anode circuit \(R\) and on the ratio of the attenuation coefficients \(\alpha\) and \(\beta\).

At shorter wavelengths the antenna temperature is sometimes lower than room temperature. The zero reading of the instrument can be shifted by deliberately detuning the antenna; however, then it depends on the noise level of the receiver. Although this is of no significance when using interferometric antennas (see Section 5), such a dependence is often undesirable. An alternative method, eliminating this complication, was used at a wavelength of 60 cm. The roles of the resistance and the antenna were interchanged; the latter acted as the load resistance of the diode. This arrangement could be used to count off an antenna temperature lower than room temperature, since

\[ T_A = T_0 - \frac{\alpha}{\beta} T_D, \]

(Stanier, unpublished.)

The design details of an automatically balancing system and a complete analysis of the effect of antenna impedance detuning and of the system’s susceptibility to rapid changes in antenna temperature have been described by Machin, Ryle, and Vonberg (paper in preparation).

5. OBSERVATIONS OF A WEAK SOURCE AGAINST THE BACKGROUND OF GALACTIC RADIATION

Along with the difficulty encountered in measuring small values of the energy delivered by an antenna, difficulties arise in measuring the intensity of a source having a comparatively small angular diameter, for example one such as the Sun. This difficulty is the result of the screening action of the background of the Galaxy. In most of the wavelength ranges that have been used in radio astronomy, the angle of reception \(\Omega\) is considerably larger than the solid angle \(\omega\) subtended by the Sun. If the emission of the Sun corresponds to absolutely black radiation at temperature \(T_s\), and if it is assumed that the emission of the Galaxy is constant over the entire solid angle of reception and has temperature \(T_g\), then the ratio of the energies received in the antenna from the Sun and from the Galaxy, respectively, is

\[ \frac{\omega T_s}{\Omega T_g}. \]

Therefore the radiation of the Sun cannot be detected until \(T_s\) becomes greater than \(T_g\). For example, the radiation of the undisturbed Sun at a wavelength of \(4\ \text{m}\) corresponds to a temperature \(T_s\) of the order of one million degrees, whereas near the equator of the Galaxy the temperature \(T_g\) is of the order of \(5000^\circ\). If the solid angle of reception of the antenna is equal to one steradian (which corresponds to an effective area of the order of \(20\ \text{m}^2\)), then the component of the energy from the Sun is equal to \(10^{-2}\) of the energy received from the Galaxy. In order for the component of the energy of the Sun to be equal to the component from the Galaxy, it is necessary to use an antenna with an area of \(2000\ \text{m}^2\).

Thus, measurements of the radiation intensity of the undisturbed Sun and, as will be seen below, the detection of discrete sources in the Galaxy are evidently limited by the background radiation of the Galaxy. Let us analyze these limitations in more detail. In doing so, we shall assume that the sensitivity of the receiver is itself limited.

Two types of antennas have been developed for recognizing the background of the Galaxy: in the first, antennas with large radiating surfaces are used, giving so-called “pencil” beams (small \(\Omega\)). In the second method, the interference pattern formed by two separated antennas is used. This provides considerably greater resolving pow—

properties by means of simpler antennas. A spaced antenna system is similar to a Michelson interferometer; many of the advantages inherent in that optical system are likewise used in the radio case.

Both methods are considered first as applied to the radiation of the Sun, and then the more difficult problem of detecting discrete sources in the Galaxy is analyzed.

a) “Pencil” beam

The technique of a “pencil” beam, which is analogous to that in optical astronomy, requires the use of antennas with the largest possible aperture. It has already been indicated that an antenna with an effective radiating surface \(A\) has a radiation pattern with effective solid angle \(\Omega = \dfrac{\lambda^2}{A}\), where \(\lambda\) is the wavelength. (It is useful to point out that the energy received by such an antenna, directed at a distant source, is \(G = \dfrac{4\pi A}{\lambda^2}\) times greater than the energy received by an isotropic antenna. This antenna parameter is important when the detection limit is determined by the maximum possible sensitivity of the receiver. When this limit is set by the background radiation of the Galaxy, however, it is necessary to take into account only the solid angle of reception \(\Omega\).)

In measurements of the intensity of the Sun’s radiation by means of a “pencil” beam, one compares the energy received when the antenna is directed at the Sun with the energy obtained when the antenna is turned away from it by an angle at which the contribution of the Sun may be neglected. In the ideal case this angle corresponds exactly to \(\sqrt{\Omega}\); in practice, however, because the radiation pattern has secondary maxima, the antenna must be turned through a considerably larger angle. Assuming that the energy entering the antenna from the Galaxy is the same in both of its positions, one can determine the component of the energy of the Sun’s radiation. Even in the absence of discrete sources in the Galaxy, it is clear that the accuracy of this method is limited by the variation of the intensity of the Galaxy’s radiation with angle. If the angular variation of the structure of the Galaxy is comparable with the width of the antenna radiation pattern, then the intensity of the Sun’s radiation cannot be measured at all if the energy entering the antenna from it is not comparable in order of magnitude with the energy received from the background of the Galaxy.

At shorter wavelengths (shorter than \(50\ \mathrm{cm}\)) it is easy to obtain beams of small width with a structure of the required size. Since in this range of wavelengths the intensity of the Galaxy’s radiation is relatively

relatively small compared with the intensity of the Sun’s radiation, the “pencil-beam” method becomes a very suitable method for observing solar radiation. At longer wavelengths the difficulties of constructing antennas of sufficiently large dimensions increase considerably—such that the angular width of their radiation pattern is small in comparison with the structure of the Galaxy. For this reason, and also because of the more intense radiation of the Galaxy, it is difficult to associate the small changes obtained when the antenna is rotated through an angle equal to the width of its beam with the radiation of a weak remote source such as the undisturbed Sun. The minimum value of the antenna aperture required for measuring a solar-radiation flux of a given magnitude is difficult to determine, since it depends not only on the intensity of the Galaxy’s radiation but also on the degree of its dependence on the angle of observation in the direction of the Sun. For a typical case, when observations are made of the radiation of the undisturbed Sun at a wavelength of 4 m, \(T_s = 10^6\) degrees and \(T_g = 5000^\circ\), an antenna with an aperture of the order of \(200\ \text{m}^2\) is apparently sufficient. In this case the received energy amounts to \(10^{-1}\) of the radiation energy of the Galaxy, while the change in the background radiation of the Galaxy when the antenna is rotated through the width of its beam (of the order of \(15^\circ\)) will give smaller changes. From this example, however, it is clear that for accurate and prolonged measurements of the intensity of the Sun’s radiation at longer wavelengths (when the position of the Sun relative to the Galaxy changes), it is necessary to use antenna systems of sufficiently large size—namely such that, in the antenna, the component from the Sun is of the same order as that from the total radiation of the Galaxy.

b) Interference method

In this method, interference from two antennas is used to obtain the radiation pattern. Within the limits of the primary radiation pattern of each of the antennas, such a system has a large number of interference maxima and minima. Two types of interferometers have been used: one is based on interference between the radiation of an antenna installed on a high cliff and its reflection from the sea surface (McCready, Pawsey, and Payne-Scott, 1947); the other is based on interference from two identical antennas separated in a direction perpendicular to the wave front (Ryle and Vonberg, 1946, 1948).

When such an interference pattern moves across the sky (for example, as the Earth rotates), the passage of successive maxima past the Sun causes periodic changes in the amplitude of the recorded signal. If the angular spacing between the maxima of the interference pattern is small compared with

compared with the structure of the Galaxy, the radiation of its background does not lead to such periodic changes. When the primary radiation pattern of each of the antennas sweeps across the sky, then, from the Galaxy, a constant or slowly varying run of the curve will be obtained at the receiver output. In order that the variable component of such a record could be used to determine the intensity of the Sun’s radiation, independently of its distribution over the disk, it is important that the minimum obtained because of the Sun be very small. (This requirement is analogous to that which arises with respect to the visibility of fringes in a Michelson interferometer.) Since the outer regions of the Sun also radiate (it will be seen below that even the edge of the corona radiates), the antennas must be separated sufficiently that the distance between maxima amounts to several diameters of the Sun. Figure 3 shows the interference pattern formed by two weakly directional antennas separated by 10 wavelengths (Ryle and Vonberg, 1946). This system was widely used for recording solar radiation at different wavelengths; a typical record obtained at a wavelength of 3.7 m is shown in Fig. 4.

Fig. 3. Radiation pattern of two antennas with an aperture of one wavelength, separated by 10 wavelengths.

The use of an interference system makes it possible to recognize the background of the Galaxy in the same way as with the aid of a “pencil” beam whose angular width is equal to several diameters of the Sun. However, obtaining such a “pencil” beam requires an antenna with an aperture approximately twice the distance between the antennas of the interferometric installation. In the interferometric method the degree of recognition does not depend substantially on the aperture of each of the antennas, so that simple antennas can be used for these measurements. (At shorter wavelengths, at which the possibility of detecting solar radiation is sometimes limited by the sensitivity of the recording receiver, it is important to use antennas with a large effective area. This makes it possible to increase the energy collected by the antenna. At long wavelengths, however, the degree of recognition is determined only by the shielding action of the background of the Galaxy.) Recent experiments in Cambridge (Machin, unpub-

published), in which an interference method with a somewhat modified receiver was used, have shown that at a wavelength of 6.7 m regular observations of solar radiation can be carried out if each of the antennas has an exceptionally small directivity (\(G = 8\)). The energy received in the antenna from the undisturbed Sun amounts in such an arrangement to approximately \(10^{-3}\) of the energy received from the radiation of the Galaxy.

The possibility of using antennas with low directivity is a great advantage, especially at long wavelengths, not only because of their simple construction, but also because over a long period of the day the Sun can be observed without continuously rotating a very complex antenna structure, as must be done when using the “pencil-beam” method.

Other advantages of these antennas are connected with absolute measurements and are, in practice, very important. In Section 4 it has already been noted

Fig. 4. Record obtained at a wavelength of 3.7 m with separated antennas, illustrating the radiation of the undisturbed Sun and the Galaxy.

that small changes in the impedance of the antenna can lead to a displacement of the zero of the recorded curve. These displacements disturb measurements carried out by the “pencil-beam” method, but do not affect the results of measurements carried out by the interference method.

It should be pointed out that in interference measurements there are gaps during the periods when the Sun passes near the minima of the interference pattern. Thus some short-term changes in the intensity of the radiation are missed. It has been established, however, that these gaps have no practical significance.

In Section 5 g), the question of applying the interference method to determine the dimensions and position of the source is considered.

c) Detection of Discrete Sources in the Galaxy

Until now it has been assumed that the radiation background of the Galaxy is homogeneous within angles that are small in comparison with its overall structure. At the present time, however, it is well known that there are sources in the Galaxy whose angular diameters are very small, and that their radiation constitutes a significant fraction of the total radiation of the Galaxy. It is possible that, in reality, all the radiation of the Galaxy is produced by a large number of such sources scattered throughout the Galaxy, and that with existing apparatus only the most intense of them have been found. This possibility is discussed in Section 10; here we consider the question of detecting such sources.

It is obvious that discrete sources of Galactic radiation can substantially affect measurements of solar radiation, since the methods proposed for recognizing it against the Galactic background are based on the assumption that the angular distribution of the latter is constant within angles comparable with the angle subtended by the Sun. In practice, however, it has been found that only two discrete sources produce at the Earth an intensity comparable with the intensity of the undisturbed Sun, and that neither of these sources is located in a direction close to the Sun. Therefore, in solar measurements it is legitimate to regard the Galaxy as a diffuse source whose angular variations of intensity are comparable with the structure of the Galaxy.

Let us apply the considerations given above to the problem of detecting discrete sources in the Galaxy. The angular dimensions of these sources are smaller than the size of the Sun, and the intensities of their radiation may be considerably less than the intensity of the radiation of the Galactic background. It is therefore important to consider the limits of maximum resolvability of these sources obtainable by various methods.

It is clear that, by means of the technique of “pencil” beams, constructing larger and larger antennas, one can considerably increase the detectability of the diffuse radiation of the Galaxy. If the beam width were small in comparison with the angular structure of the Galaxy, then the detection of discrete sources would be limited only by the confusion of different sources. However, up to now, for none of the wavelengths at which the Galaxy has been observed has an antenna of sufficiently large size yet been built which would have a radiation pattern small in comparison with the structure of the Galaxy. If such an antenna is built, then the change in the received energy that will be observed as it moves along a discrete source will be

correspond to its own radiation pattern. The largest number of discrete sources that can be identified in this way naturally depends on the solid angle of reception. In the case of uniformly distributed sources of equal intensity this number is of the order of \(\frac{G}{4}\), where \(G=\frac{4\pi A}{\lambda^2}=\frac{4\pi}{\Omega}\) is the power gain. All antennas that up to the present time have been used for observing discrete sources of the Galaxy had too small values of power gain, so that the angular variability of the structure of the Galaxy was ignored by them. The changes in received energy observed when the antenna was rotated were caused chiefly by fluctuations in the intensity of the “diffuse” radiation of the Galaxy. The number of changes that could have been identified with discrete sources was considerably smaller.

On the other hand, the use of an interference system makes it possible to exclude all intensity changes except those associated with sources having small angular dimensions; moreover, this does not require complicated antennas with large effective cross sections. Such an antenna, recognizing variations of the “diffuse” background, corresponds to an antenna with a “pencil” beam having an aperture twice as large as the distance between the antennas. Thus, by separating sufficiently far apart two antennas having relatively low directivity, one can obtain the required degree of recognition of the background radiation. In Cambridge observations were carried out at a wavelength of \(3.7\) m by means of two antennas, each of which had a solid angle of reception of the order of \(0.05\) steradian (corresponding to a power gain of about 250); the spacing between the antennas was equal to 110 wavelengths (about 400 m). The antenna and its radiation pattern are shown schematically in Fig. 13. With such a system discrete sources were identified whose intensity amounted to \(10^{-5}\) of the background of the Galaxy. (This number corresponds to fluctuations of the total antenna energy by \(10^{-3}\) times.)

The maximum number of discrete sources that can be detected with the aid of an interference system depends on the extent to which the radiation patterns formed by two neighboring sources overlap one another (in the absence of limitations due to the sensitivity of the apparatus). Therefore only \(\frac{G}{4}\) sources can be detected, where \(G\) is the power gain of each of the antennas. (In Section 8 it will be shown that, to some degree, two sources can be recognized even if their radiation patterns overlap one another, since sources having different declinations form interference patterns of different periodicity.)

Thus, the total number of sources that can be detected by an antenna with a “pencil” beam or by means of an interferometric system having the same effective aperture will be approximately the same for very large values of the effective aperture, if the “pencil” radiation pattern is sufficiently small for the recognition of sources against the diffuse background. However, an antenna of sufficiently large size, which would ensure the observation of galactic sources, has not yet been built; and, compared with antennas of small size, an interferometric system has considerable advantages, since it always makes it possible to eliminate the confusion produced by fluctuations in the radiation of the diffuse background. There remains the limitation connected with the possibility of confusing different discrete sources, but with the aid of an interferometric system one can detect

\[ \frac{G}{4} \]

uniformly distributed sources of equal intensity, for all values of the antenna gain \(G\). The advantages of antennas with a “pencil” beam, however, rapidly disappear as \(G\) decreases, since it becomes difficult to distinguish variations connected with the structure of the Galaxy from those caused by genuinely discrete sources.

In addition to the advantages indicated above, an interferometric system has an important application for the precise determination of the position of a source. The accuracies attainable in this case are the same as in the case of a system with a “pencil” beam having an aperture twice as large as the mutual distance between the antennas of the interferometric system. These applications are described in Sections 5 c) and 8 b).

In the preceding discussion it was assumed that the reception of signals does not present great difficulties. In many cases, however, along with the question of recognizability, it is important also to consider the question of the limiting sensitivity of the apparatus. The point is that it is necessary to detect a weak additional signal produced by a discrete source as a “pencil” beam or an interference pattern passes over it. At wavelengths shorter than \(3\) m, the limits of possible signal detection are determined by noises generated in the receiver. At longer wavelengths, however, statistical fluctuations of the received background radiation of the Galaxy form a large “noise level,” and it can be reduced only by statistical averaging. It is clear that the time suitable for such averaging depends on how much the contribution from the discrete source changes as the antenna radiation pattern passes over it. Thus, in all systems with high resolving power in which Earth-based antennas are used, the bandwidth of the receiver output (and hence its sensitivity)

some limit is set, which depends on the angular resolving power of the antenna and on the rate of rotation of the Earth.

These considerations are important when one attempts to determine accurately the positions of weak sources.

d) Measurements of the diameter and position of a source

It has been shown above how great the importance is of determining the positions and sizes of sources of intense solar radiation. Here we shall analyze the question of applying interferometric techniques to these measurements. The question of locating discrete sources in the Galaxy is left until Section 8 b).

It has already been noted that a source whose angular dimensions are small in comparison with the angular distance between the maxima of the interference pattern will give a record with minima falling to zero. If, however, the source subtends an angle comparable with the distance between the maxima, the minimum will not be complete, and the ratio between the maximum and minimum values will make it possible to measure the diameter of the source. This method is analogous to Michelson’s method for measuring the angular diameter of stars; the ratio of maximum to minimum corresponds to the visibility of optical fringes. Both the method of separated antennas and the method of placing a single antenna on a cliff, which is similar to Lloyd’s reflecting interferometer, have been used to determine the sizes of sources of enhanced solar radiation associated with sunspots.

By accurately recording the moment at which the central interference maximum occurs, one can determine the direction to the source accurately. Both types of interferometer have been used for these measurements, and, when the antennas were separated from one another by 100–200 wavelengths, the positions of sources were determined with an accuracy of 1–2 minutes. For antennas spaced at such distances, two adjacent maxima are separated by a quantity of the order of the diameter of the solar disk, so that no difficulties arise in identifying the principal maximum.

Analogous methods have been used to determine the positions of discrete sources in the Galaxy. In this case, however, it was necessary to have an independent method for identifying the principal maximum of the recorded curve. For this purpose two methods were used. In the first, the central maximum is determined from the amplitude of the primary radiation diagram. In the second, two different spacings between the antennas are used, so that the records have different periodicities but the same phase at the central maximum. In Section 8 b) it is described how these methods are used to determine the position of a source, its declination, and the position of the North–South sign.

In many applications of the interferometric method it is important that the observations be confined to the central lobe. For lobes of high order, the value of the phase of the interference pattern

depends on frequency, and since the receiver has a band of finite width, the ratio of the maximum to the minimum of the recorded curve decreases. Therefore the determination of the source diameter at angles noticeably displaced from the center will be erroneous, since the observed ratio of the maximum to the minimum will be interpreted as an apparent increase in the source diameter. This effect is analogous to the case in optics when, at the center of an interference pattern, a white fringe is formed, while at larger angles colored fringes are formed. The visibility of the fringes, measured with an instrument sensitive over a wide range of wavelengths, is maximal at the center and decreases as the angle increases.

This effect becomes quite significant when wide-band receivers are used in order to obtain the greatest possible sensitivity. For example, at a wavelength of \(1.7\ \text{m}\), with a band of \(2\ \text{Mc/s}\) \(\left(\dfrac{\Delta f}{f} \simeq 0.01\right)\), and with antennas separated by 140 wavelengths, such measurements are limited to an angle of only 40 minutes (Ryle and Vonberg, 1948).

A very interesting application of the interferometer with separated antennas is the determination of the distribution of radiation intensity over the disk of the Sun in the absence of sunspots. In such experiments the amplitudes of recorded curves obtained with antennas separated by various distances were determined. Each amplitude value in this case corresponds to one term in the Fourier expansion of the original angular distribution of the source intensity. Assuming that it has circular symmetry, one can calculate the true distribution along the solar disk. This question is considered in more detail in section 7 a).

6. MEASUREMENTS OF POLARIZATION

Chaotic radiation, for example such as the radiation of light from an incandescent solid body, produces a field whose mutually perpendicular components are incoherent. Studies of the radio waves emitted by the Sun have shown, however, that from time to time it is not chaotically polarized, but that a circularly polarized component is observed in it.

In this connection, a comprehensive analysis of the structure of the waves emitted by the Sun and by sources in the Galaxy becomes important. Since the waves may consist of a mixture of elliptically polarized and unpolarized radiation, it is necessary to determine the relative intensities of the chaotic, circularly, and linearly polarized components. The methods used are analogous to the methods of analysis of polarized light; a linearly polarized antenna takes the place of the Nicol prism, and a quarter-wave plate is used both in optical and in radio systems, although more often waves polarized in a circle are detected by means of

of two mutually perpendicular linearly polarized antennas, shifted in phase by a quarter wavelength.

So far no linearly polarized component has yet been detected in radio emission; therefore polarization measurements mainly concern the determination of the ratio of the intensities of the circularly polarized and randomly polarized components.

Two cases should be considered: a) when the intensity of the source radiation is large in comparison with the total intensity of the background radiation, and b) when the intensity of the source radiation is comparable with or less than the intensity of the background radiation.

In the first case, the presence of a linearly polarized component could be detected by rotating a linearly polarized antenna about the normal to the wave front, while observing the change in the strength of reception. When the position of the antenna is changed, randomly or circularly polarized waves will not change the effect at the output; therefore the difference between the maximum and minimum values of the recorded curve will indicate a change in the intensity of the linearly polarized wave. The presence of circularly polarized radiation is determined with the aid of two adjacent linearly polarized antennas whose planes of polarization are mutually perpendicular. If the outputs of both antennas are calibrated so that in one of them the length of the optical path (phase) is additionally increased by half a wavelength, then the system is sensitive to a circularly polarized wave having either left-hand or right-hand rotation. For a wave having the opposite sign of rotation, the effect at the output will be equal to zero. Randomly or circularly polarized waves induce in each of the antennas equal amounts of energy, equal to half the energy induced by a linearly polarized wave of equal energy. Thus, in two alternative cases one can determine the intensity and character of the polarization of the circularly polarized wave, as well as the intensity of the linearly or randomly polarized wave. Of course, by this method it is impossible to distinguish from randomly polarized radiation two circularly polarized waves having equal intensities but opposite signs of rotation.

A shift by a quarter wavelength can be introduced either by spacing the two antennas by a quarter wavelength in the direction of the normal to the wave front, or by means of an additional quarter-wave line inserted into the circuit of one of the antennas. If, within the range of the receiver, the antennas are not tuned exactly to the transmission line, then the introduction of an additional quarter-wave transmission line may lead to inequality of the impedance values of the two antennas at their point of connection. In this case the system does not ensure complete suppression of the undesired component of the circularly polarized wave (having the opposi-

a complex sign of rotation). Therefore a more perfect arrangement is a system of two antennas with lines of equal length but spaced by a quarter wavelength.

At shorter wavelengths the “quarter-wave” plate can be constructed in the form of a waveguide. By placing it in front of the antenna so that its axes make an angle of \(45^\circ\) with the axis of the antenna, one can make the system sensitive to one or another component of circularly polarized waves. In this way Covington (1949) carried out investigations of the state of polarization of solar radiation at a wavelength of \(10.7\) cm.

Fig. 5. Interference polarimeter. View along the normal to the wave front.

Fig. 6. Diagram illustrating two types of curves obtained with an interference polarimeter.

If the radiation of the source under investigation is masked by chaotically polarized radiation of equal or greater intensity, then by the method described it is, naturally, difficult to determine the character of its polarization, chiefly because the small changes in the polar diagram and impedance that arise when the antennas are rotated or switched lead to small changes in the energy received from the Galactic background. Therefore an alternative method of measurement has been developed, eliminating displacement or switching of the antennas. In this system two linearly polarized antennas are arranged on an east—west line; the periodic change in intensity caused by the rotation of the Earth is used in order to distinguish the radiation of the source under investigation from Galactic radiation. In order to establish the presence of a linearly polarized component, it is necessary to observe the amplitude of the interference pattern obtained with parallel antennas as they rotate relative to the normal to the wave front.

If the antennas are now arranged mutually perpendicular (Fig. 5), then the system can be used to determine the intensity of a circularly polarized wave. An incident chaotically polarized wave forms in the antennas two incoherent

components; therefore, a change in the difference of their paths in two antennas, arising from the rotation of the Earth, will not cause changes at the receiver output. Thus, the presence of chaotically polarized radiation is equivalent to an increase in the radiation of the Galactic background. On the other hand, an incident circularly polarized wave excites coherent oscillations in the antennas; therefore, a change in the difference of their paths leads to a periodic change in the amplitude of the record at the receiver output. For a fully polarized wave, the amplitude of this record is equal to the amplitude obtained with parallel antennas; moreover, with another antenna system the recorded curve is shifted in time by a quarter of a period in a direction depending on the sign of rotation of the polarization of the wave. Therefore, comparison of the amplitudes obtained with parallel or mutually perpendicular antennas makes it possible to determine the sign and degree of polarization of the incident wave. Fig. 6 gives a typical record obtained for incompletely polarized radiation of the Sun. It should be noted that a linearly polarized wave whose plane of polarization is located in an intermediate position relative to the planes of the two antennas also gives periodically varying curves, but the phase of the curves is the same for different antennas.

An interferometer with separated antennas was used to study the state of polarization of weak radiation from the Sun (Ryle and Vonberg, 1948) and discrete sources in the Galaxy (Ryle and Smith, 1948). This method, while of great importance for polarization measurements in the presence of a strong unpolarized background, is less convenient for the investigation of short-duration bursts of radiation associated with the activity of sunspots. However, in these cases the radiation intensity is usually sufficiently large, and direct methods can be used for measuring the polarization.

7. EXPERIMENTAL INVESTIGATIONS OF SOLAR RADIATION

Two extensive reviews on the radio emission of the Sun have recently been published (Hey, 1949; Pawsey, 1950), in which the history of these experimental investigations is set forth in detail. Therefore, the present section does not give a complete picture of the experiments, but summarizes only the most important conclusions from these observations.

It is convenient to divide the waves used for solar observations into two ranges: (a) waves shorter than \(1\ m\), extending down to \(1\ cm\), and (b) waves longer than \(1\ m\), reaching at the present time approximately \(7\ m\). Some short-duration phenomena have also been observed at wavelengths of the order of \(20\ m\).

In the range of waves shorter than \(1\ m\) the radiation of the Galactic background is weak, and since in this range, in addition, it is easier to construct antennas

…with considerable directivity, then the radiation of the undisturbed Sun was extensively studied on these waves. At longer wavelengths there is less information about the radiation of the undisturbed Sun, but there are many observational results on its enhanced radiation, which is associated with the activity of sunspots.

Fig. 7 shows approximately the dependence of the energy of the radio emission of the Sun and the Galaxy, entering an antenna (having identical physical parameters), on wavelength. The energies of the radiation of the Sun and the Galaxy obtained experimentally have been recalculated for an antenna with an effective area of \(10\ m^2\).

Fig. 7. Dependence of the energy received by an antenna of area \(10\ m^2\) from the Galaxy and the Sun on wavelength.

For antennas having a smaller area, the relative fraction of the energy received from the Sun, in comparison with the energy of the radiation of the Galaxy, will be smaller. It should, of course, be remembered that the construction of an antenna with such parameters is considerably simpler at long wavelengths; at a wavelength of \(10\ cm\), antennas with an area of the order of \(5\ m^2\) are usually used, whereas at a wavelength of several meters the effective areas may be of the order of \(100\ m^2\).

a) Observations at wavelengths shorter than \(1\ m\)

For the entire range of waves—from \(1\ cm\) to \(1\ m\)—there are as yet no sufficiently complete investigations. However, detailed measurements have been made in the vicinity of \(1\), \(3\), \(10\), and \(50\ cm\). Some observations also took place at a wavelength of \(25\ cm\). Southworth (1945) first detected the radio emission of the Sun at \(1\), \(3\), and \(10\ cm\). He established that this radiation corresponds to a temperature of the Sun differing little from the temperature obtained in visual observations (\(6000^\circ\)).

Subsequent observations at \(1\ cm\) by Dicke and Beringer (1946) during a partial solar eclipse showed that the radiation corresponds to a source having the dimensions of the visible disk and a temperature of the order of \(10\,000^\circ\). Similar observations at a wavelength of \(3\ cm\) were carried out by Sander (1947). Shulkin et al. (1948) found at a wavelength of \(3\ cm\) that during chromospheric eruptions

a sudden and brief flare-up of radiation intensity is observed.

Covington (1947, 1948, 1949) carried out a detailed investigation of solar radiation at a wavelength of 10 cm. He showed that in the absence of sunspots the radiation of the Sun corresponds to 80,000°, while observations during a solar eclipse established that in the vicinity of sunspots the radiation has a considerably higher intensity (corresponding to a temperature of the order of \(1.5 \cdot 10^6\) degrees).

Covington’s regular observations over the course of 8 months at a wavelength of 10 cm showed that the course of the intensity of the Sun’s radiation gives a good correlation with the course of the sunspot number. The enhanced radiation associated with sunspots is circularly polarized. Slight sudden increases in intensity were sometimes observed during periods of chromospheric flares.

In the observations of McCready, Pawsey, and Payne-Scott (1947) at a wavelength of 25 cm it was found that the Sun usually radiates as a body with a temperature of \(2 \cdot 10^5\) degrees; however, Laing and Yabsley (1948) showed that such an intensity at this wavelength is also connected with the radiation of sunspots.

More complete data were obtained at wavelengths of 50–60 cm. Reber (1946, 1948a) showed that the intensity associated with spots varies from day to day (by approximately 15%), but that a short-term increase in emission is sometimes observed. These results were confirmed by the work of Houtgast and Laffineur (1948). In extensive investigations carried out at Cambridge over the course of 9 months, it was found that in the absence of sunspots the temperature of the Sun corresponds to the radiation of a black body subtending an angle of 0.5° and having a temperature of \(5.5 \cdot 10^5\) degrees (Stanier, 1950). From these investigations it was also found that changes in the mean daily values of the intensity reach 100% when large sunspots pass across the disk of the Sun; at the same time, rare radiation bursts, reaching more than 10 times the intensity, are almost entirely associated with chromospheric flares. The enhanced radiation associated with spots is usually slightly circularly polarized (up to 20%); the radiation corresponding to flares, however, is more strongly circularly polarized. The radiation of the undisturbed Sun is not polarized.

In the description given above it was assumed that the radiation of the undisturbed Sun corresponds to uniform emission from a disk having the same diameter as the photosphere (\(\sim 0.5^\circ\)). Some theoretical considerations (see Section 9c) show that at a wavelength of 50–60 cm (and also at shorter wavelengths) the radiation should come chiefly from a narrow ring at the periphery of the Sun. In order to test this theory, and also because, as the solid angle subtended by the source decreases,

increases, it was important to investigate experimentally the distribution of the intensity of the Sun’s radiation at a wavelength of 50 cm. For this purpose two methods were used: in the first of them (Laffineur, Michard, Steinberg, and Zisler, 1949) a partial eclipse of the Sun was used. The results obtained at wavelengths of 25 cm and 50 cm showed that at neither wavelength is there any noticeable enhancement of the emission of the ring.

Similar experiments have recently been carried out by Christiansen, Yabsley, and Mills (1949) at a wavelength of 50 cm. Although they were able to show that a considerable part of the total radiation of the undisturbed Sun corresponds to regions lying near or beyond the edge of its disk, they could not reliably choose between a source whose brightness increases toward the edge and a uniformly radiating source having a radius of the order of \(1.3R_0\), where \(R_0\) is the radius of the photosphere.

Observations based on changes in the received intensity during an eclipse are difficult (with the exception of nearly total eclipses), because the observed change in intensity is not very sensitive to the degree of “brightening” of the edge of the disk.

The second method (Stanier, 1950) makes it possible to measure directly the distribution across the solar disk, and therefore with its aid observations can be made during a period of increased sunspot activity. Measurements in the first case are made more complicated if there are sunspots during the eclipse. Stanier uses an interferometer with separated antennas and determines the amplitudes of the periodic curves recorded at the output and obtained with several antennas separated by different distances.

The directional coefficient of separated antennas in a direction \(\theta\), measured from the central direction, is known to be equal to

\[ 2F(\theta)\left[1+\cos\left(\frac{2\pi d}{\lambda}\sin\theta\right)\right], \]

where \(F(\theta)\) is the directional function of each of the antennas, and \(d\) is the distance between them. For small angles \(\theta\) one may neglect the variation of \(F(\theta)\) due to the primary radiation pattern and take the directional coefficient equal to

\[ a\left\{1+\cos\left(\frac{2\pi d}{\lambda}\theta\right)\right\}. \]

We shall now calculate the energy received from an extended source, which may approximately be represented as a strip parallel to the line joining the antennas and having a distribution \(f(\theta)\).

The energy received by the antenna may be represented as

\[ a\int\left\{1+\cos\left[\frac{2\pi d}{\lambda}(\theta+\theta_1)\right]\right\}f(\theta)\,d\theta, \]

where \(\theta_1\) is the angle made by the center of the source with the central maximum of the interference pattern; the integration extends over the entire source. The last expression can be rewritten in the form:

\[ a \int f(\theta)\,d\theta + a \cdot \cos\left(\frac{2\pi d}{\lambda}\theta_1\right) \int \cos\left(\frac{2\pi d}{\lambda}\theta\right) f(\theta)\,d\theta - \]

\[ {}- a \sin\left(\frac{2\pi d}{\lambda}\theta_1\right) \int \sin\left(\frac{2\pi d}{\lambda}\theta\right) f(\theta)\,d\theta . \]

Let us consider how the energy in the antenna changes when the interference pattern is displaced, as caused by the rotation of the Earth along the source. Omitting the constant component of the energy, we see that the variable component is determined by two terms of the Fourier transform of \(f(\theta)\), having the period \(d/\lambda\). If \(f(\theta)\) is a symmetric function, then the term with \(\sin\left(\frac{2\pi d}{\lambda}\theta\right)\) is equal to zero, and the amplitude of the observed variation of the received energy is proportional to

\[ 2a \int \cos\left(\frac{2\pi d}{\lambda}\theta\right) f(\theta)\,d\theta . \]

Thus each of the measurements carried out with an interferometer with differently spaced antennas gives one term of the Fourier transform of the source radiation-intensity distribution. From several values measured for different \(d\), one can construct the function \(f(\theta)\).

This method is exactly analogous to Michelson’s method for determining the fine structure of spectral lines from the visibility of the interference pattern obtained when the line under investigation is used to illuminate the interferometer. In this way Michelson calculated one term of the Fourier transform of the line-intensity distribution on the wavelength scale. The measured visibility values for different values of the path difference in the interferometer allowed him to calculate the distribution function of the spectral line.

Having thus obtained \(f(\theta)\)—the distribution function of the equivalent (“strip”) source—it is necessary to calculate the intensity distribution of a source possessing circular symmetry (such as the Sun) that leads to the observed “strip” distribution.

Stanier carried out observations at a wavelength of \(60\) cm with antennas spaced by \(365\) wavelengths. His results showed that, out to \(0.7R_0\) (\(R_0\) being the radius of the Sun), the Sun radiates uniformly with

equivalent temperature of \(4.5 \cdot 10^5\) degrees; then its “brightness” gradually falls. The effective temperature is equal, at \(1.1 R_0\), to half its value at the center, and at \(1.5 R_0\) it is less than \(0.5 \cdot 10^5\) degrees (Fig. 8). The total radiation of the solar disk corresponds to a source \(0.5^\circ\) in size at a temperature of \(5.5 \cdot 10^5\) degrees.

Before describing the results of investigations at longer wavelengths, one should briefly summarize the results obtained at wavelengths shorter than \(1\ \mathrm{m}\).

1) In the absence of sunspots the Sun emits radio waves whose intensity corresponds to temperatures of: \(10^4\) degrees at \(\lambda = 1\ \mathrm{cm}\), \(8 \cdot 10^4\) degrees at \(\lambda = 10\ \mathrm{cm}\), \(2 \cdot 10^5\) degrees at \(\lambda = 25\ \mathrm{cm}\), and \(5.5 \cdot 10^5\) degrees at \(\lambda = 60\ \mathrm{cm}\) (see Fig. 9).

Fig. 8. Distribution of the “brightness” of the solar disk at a wavelength of \(60\ \mathrm{cm}\).

Fig. 9. Dependence of the emission of the undisturbed Sun on wavelength.

At all these wavelengths the Sun’s emission is distributed almost uniformly over the entire solar disk; beyond the visible disk the radiation is noticeably weaker, especially at the longer wavelengths.

2) When sunspots are present, the increase in the Sun’s emission as a whole is connected with the area of the spots. The increase in radiation intensity is not especially large and even at long wavelengths rarely reaches 100% of the intensity of the undisturbed Sun. There is reliable evidence that the increase in intensity is caused by regions lying close to sunspots, and that this radiation is circularly polarized.

3) Sometimes sudden, short-term increases in intensity are observed, lasting only a few minutes. The increase is small and rarely amounts to 50% of the normal intensity. There is good agreement between them and chromospheric flares.

b) Observations at wavelengths longer than 1 m

The radio emission of sunspots is of considerably greater importance at wavelengths longer than 1 m. Therefore, although in this range the detection of radio emission from the undisturbed Sun is considerably difficult (partly because of the masking effect of the Galactic background, and also because of the difficulty of constructing highly directional antennas), when sunspots are present at the center of the solar disk the intensity of the radiation increases by more than \(10^4\) times, and in this case the energy received even by a simple antenna greatly exceeds the receiver’s own noise.

Sudden increases in the intensity of a burst of radiation, associated with chromospheric flares, reach values up to 100 times greater within a few seconds.

Very large intensity values associated with sunspots create certain difficulties in determining the contribution of the radiation of the undisturbed Sun. Only as a result of continuous observations carried out over several months is it possible to determine the true minimum of the radiation intensity corresponding to the undisturbed Sun.

Pawsey (1946) was the first to measure the intensity of the undisturbed Sun at longer wavelengths. He established that at a wavelength of \(1.5\ \mathrm{m}\) the emission of the Sun corresponds to a source with an angular diameter of \(0.5^\circ\), having a temperature of one million degrees. Subsequent observations by Ryle and Vonberg (1947) at wavelengths of \(1.7\ \mathrm{m}\) and \(3.7\ \mathrm{m}\), using the interferometer with separated antennas described in Section 5, gave temperature values of \(6 \cdot 10^5\) and \(1.2 \cdot 10^6\) degrees, respectively.

In recent experiments at a wavelength of \(6.7\ \mathrm{m}\) in Cambridge (Machin, unpublished), a value of \(2 \cdot 10^6\) degrees was obtained for the temperature of the undisturbed Sun. The recording curves of the radiation of the undisturbed Sun obtained at Cambridge, respectively at wavelengths of \(60\ \mathrm{cm}\), \(1.7\ \mathrm{m}\), and \(3.7\ \mathrm{m}\), are given in Fig. 10.

There are some indications concerning the distribution of the radiation intensity of the undisturbed Sun at longer wavelengths. In the observations of Khaikin and Chikhachev (1948) during the solar eclipse of 1947, it was found that during the period of total eclipse the radiation intensity amounted to about 40% of its uneclipsed value; however, in these experiments a certain connection was observed between the intensity of the Sun’s radio emission and the activity of prominences, and therefore these results apparently cannot be interpreted as the distribution of the radiation of the undisturbed corona.

When sunspots pass across the solar disk, a considerably greater radiation intensity is observed. The intensity increases by 100 times or more at wavelengths of \(1\text{--}2\ \mathrm{m}\) and до-

reaches up to \(10^4\)-fold at the longer wavelengths. The emission is maximal when sunspots pass through the central meridian; however, because of considerable irregular fluctuations of the intensity, it is difficult to obtain an exact polar diagram of the source radiation. In studying several large groups of sunspots, Appleton and Hey (1946 b), and recently Hey, Parsons, and Phillips (1948 b), came to the conclusion that at a wavelength of \(4\ \mathrm{m}\) the emission decreases significantly when the group of spots is

Fig. 10. Curves of radio emission of the undisturbed Sun, obtained with spaced antennas at wavelengths of \(60\ \mathrm{cm}\), \(1.7\ \mathrm{m}\), and \(3.7\ \mathrm{m}\).

removed from the center by 1–2 days. Similar conclusions were drawn by Allen (1947) for emission at a wavelength of \(1.5\ \mathrm{m}\).

Recently Machin (unpublished) analyzed the results of 12-month investigations of the diurnal variation of the intensity of solar radiation by means of a correlation diagram. This method proved unsuitable for large spots; however, it gave an effective polar diagram of the radiation for an “average” sunspot. From records obtained at wavelengths of \(1.7\ \mathrm{m}\) and \(3.7\ \mathrm{m}\), he concluded that the intensity falls to one half, respectively, at angles of \(\pm 15^\circ\) and \(\pm 7^\circ\) (corresponding to \(\pm 1\) day and \(\pm \tfrac{1}{2}\) day from the time of passage through the central meridian).

Much attention was paid to establishing a connection between the intensity of the radiation and the sizes and type of sunspots. Thus, Pawsey, Payne-Scott, and McCready (1946) came to the conclusion that there is some connection between the intensity at a wavelength of 1.5 m and the total area of sunspots. However, longer observations at several wavelengths did not show any simple dependence between them.

Fig. 11. Curves of the Sun’s radio emission at wavelengths of 60 cm, 1.7 m, and 3.7 m, obtained during the passage of sunspots.

In addition to its high intensity, the radiation of sunspots differs noticeably in its character, as is evident, for example, from the typical record shown in Fig. 11. The rapid fluctuations of intensity that are characteristic of the increasing radiation at wavelengths longer than one meter do not correlate at different wavelengths, such as 1.7 m and 3.7 m (Ryle and Vonberg, 1947). Williams (1948), at a wavelength of 4 m, and Smith (unpublished), at a wavelength of 1.4 m, carried out detailed studies of some such fluctuations. They showed that many rapid outbursts have double intensity and a duration of the order of \(1/2\) sec.

The cause of these fluctuations is still unknown. In order to determine whether they are caused by refraction in the Earth’s atmosphere, McCready, Pawsey, and Payne-Scott (1947) carried out simultaneous observations at a second station, 160 miles away, and found complete agreement between the records at the different stations. It followed from this that these fluctuations arise either from variations in the emission of the source, or from refraction effects in a remote region, such as the atmosphere of the Sun above the source*).

Despite the fact that there are reliable indications establishing a connection between sunspots and the increase of radiation, it was important to find out whether the increase of radiation, as well as sunspot activity, was not due to the influence of a common factor. For these experiments McCready, Pawsey, and Payne-Scott (1947), and also Ryle and Vonberg (1946), used antennas of high resolving power. The experiments showed that relatively small regions situated in the vicinity of a visible group of spots emit intensely.

From measurements of the diameters of these sources it followed that the enhanced radiation indicates a considerably higher temperature than the temperature values adopted above. The intensity of the radiation corresponds, at wavelengths of 1.5–1.7 m, to a temperature of \(10^9\)–\(10^{10}\) degrees, while measurements at a wavelength of 3.7 m gave still larger temperature values.

In addition to the usual rapid fluctuations of intensity associated with the emission of spots, still larger intensity surges are sometimes observed, which many authors describe as “bursts.” Disturbances of this type cause even a 100-fold increase in intensity. Although the structure of these oscillations is different at different wavelengths, the times of their appearance almost coincide with one another. These large and sudden disturbances often coincide with chromospheric eruptions and disturbances in the Earth’s ionosphere and are associated with an increase in the ultraviolet radiation of the Sun. A typical example of such a “burst,” observed at four different wavelengths in Cambridge, is given in Fig. 12.

In observations at several wavelengths it is of interest to determine accurately the times of onset of this effect. Payne-Scott, Yabsley, and Bolton (1947) noted that the effect begins earlier at the shorter wavelengths, as in the example shown in Fig. 12. They therefore suggested that the disturbances are caused by luminous matter ejected by the photosphere and passing gradually through the different layers of the Sun’s atmosphere. It was found, however, that such a time sequence is often not observed; experiments

*) See the note on p. 553 (Translator’s note).

in Cambridge on April 28, 1944, at the same four frequencies as in the case shown in Fig. 12, showed that the sequence of the times of onset of such a disturbance was the reverse. In other experiments an irregular sequence was observed

Fig. 12. Sudden increase in the intensity of the radio emission of the Sun, or so-called radio-emission “bursts,” observed at wavelengths of 60 cm, 1.7 m, 3.7 m, and 6.7 m (February 1, 1949).

of the beginning of this effect; it began at intermediate wavelengths, and then was observed, in different cases, sometimes at longer and sometimes at shorter wavelengths.

From Allen’s discussion (1947) it follows that the connection between the “bursts” of the Sun’s radio emission, the activity of chromospheric eruptions and prominences, and iono-

by spherical storms. There is no doubt that the more considerable bursts are almost always connected with flare activity, but for smaller disturbances this correlation is less well observed; many “bursts” are not accompanied by visible disturbances, while, on the other hand, many flares do not cause a noticeable increase in radio emission. It is possible that the absence of correlation is related to the value of the angle at which radio emission can emerge from some point of the solar corona.

The question of the propagation of radio waves in the solar atmosphere will be considered in more detail in section 9a). It may, however, be noted here that at longer wavelengths radio emission can emerge from regions adjacent to sunspots only within a relatively small solid angle. This theoretical conclusion follows from the fact that the additional radiation caused by sunspots increases noticeably when the group of spots is near the central meridian. It should therefore be supposed that sudden disturbances in regions located near the limb of the Sun will not cause intense radio emission at long wavelengths. The “bursts” at shorter wavelengths of 25 cm and 50 cm observed by Lehaney and Yabsley (1948) (for which the conditions for the emergence of radiation are not so strict), not accompanied by disturbances at 1.5, 3, and 5 m, give additional confirmation of this point of view. Hey, Parsons, and Phillips (1948b), on the other hand, established that very intense “bursts” of radiation at a wavelength of 4 m do not have a noticeably greater correlation with flares appearing near the center of the solar disk. It is possible that the conditions for the emergence of such intense disturbances are modified because of a significant change in the electron concentration in the region of the solar atmosphere close to flares, so that the radiation can emerge from the solar atmosphere at larger angles.

In the range from 1 m to 7 m, extensive studies were made of the state of polarization of the Sun’s radiation (Martin, 1946a; Appleton and Hey, 1946a; Ryle and Vonberg, 1946). It was established that the radiation of the undisturbed Sun is chaotically polarized; however, the radiation associated with sunspots is usually circularly polarized, the sign of rotation being different for different spots. It was found that when the radiation is completely polarized, the rapidly fluctuating component associated with the increasing emission of sunspots is also completely polarized and has the same sign of rotation as the constant component. In those same cases when the radiation is not completely polarized, rapid fluctuations were observed, and the component corresponding to them had both signs of polarization rotation; it is possible that in these cases the radiation came from two sources and each of these radiations was completely polarized.

The state of polarization of the radio emission associated with large outbursts is still not fully known. There are some indications (Pawsey, 1950) that this emission is chaotically polarized, although often shortly after the onset of an outburst the emission has been polarized. In this case the decisive experiment is difficult because of the rapid change in amplitude at the beginning of such a disturbance, and also because of the rarity of these short-lived phenomena.

Although there is still no complete certainty on the question of the state of polarization of the radiation during periods of its very great intensity, there is no doubt that normally increasing radiation coming from sunspots is predominantly circularly polarized. However, the degree of polarization of the radiation is often reduced because of the presence of several sources of radiation. It is natural to associate the circular polarization of the waves with the influence of the magnetic field on the processes of emission and absorption of the sources, especially because of the large magnetic fields arising in the vicinity of a sunspot. In Section 9 a) it will be seen that two radiating regions may exist near sunspots and that both of them emit circularly polarized waves having different senses of rotation.

In order to distinguish these regions, it is necessary to determine the relation between the sign of the polarization and the direction of the magnetic field of the spot (which is determined from visual observations). Early experiments (Ryle and Vonberg, 1948) were not decisive because of the difficulty of identifying the source of radio waves with an individual sunspot, although even then the conclusion was reached that the radiation corresponds to the ordinary component of Appleton’s magneto-ionic theory.

In experiments carried out recently (Stanier, unpublished) on wavelengths of 1.4 m and 3.7 m, using a system of spaced antennas with high resolving power, the position of each radio-wave source was determined separately. However, because of the complex structure of the magnetic field of the group of spots, it is difficult to specify with sufficient certainty the direction of the magnetic field at a point lying high in the corona, where the source of radiation is apparently located. Therefore the results of these experiments cannot yet be regarded as decisive; they provide sufficient grounds for concluding that at wavelengths of 1.4 and 3.7 m the radiation corresponds to the extraordinary wave.

In Section 9 a) it will be shown that this wave corresponds to a source located in the solar atmosphere at a greater height than the source generating the ordinary wave.

It is useful to summarize the results of the investigation of solar radiation between 1 m and 20 m:

1) In the absence of sunspots, the intensity of the Sun’s radio emission corresponds to the emission of a “black” source

with an angular diameter of \(0.5^\circ\), at a temperature of \(6 \cdot 10^5\) degrees at a wavelength of \(1.5\) m, \(10^6\) degrees at a wavelength of \(3.7\) m, and \(2 \cdot 10^6\) degrees at a wavelength of \(6.7\) m (see Fig. 9). At longer wavelengths, the radio emission of the undisturbed Sun has not yet been observed. The radiation is apparently chaotically polarized.

2) In the presence of sunspots, considerably enhanced radiation is observed; at a wavelength of \(1.5\) m the intensity increases up to 100-fold. At longer wavelengths an increase by \(10^4\) times has been observed. This increase in intensity differs substantially in magnitude from the increase in intensity observed at wavelengths shorter than \(1\) m. The enhanced radiation is characterized by rapid fluctuations of intensity; it is usually circularly polarized.

3) The increase in radiation is caused by regions of comparatively small area located in the vicinity of visible sunspots. The emission of these regions corresponds to a temperature exceeding \(10^9\) degrees at a wavelength of \(1.5\) m and \(10^{10}\) degrees at a wavelength of \(3.7\) m. At longer wavelengths, experiments to determine the diameter of these sources have not yet been carried out.

4) In some cases, still larger bursts of radio-emission intensity have been observed for short periods; these often coincided with chromospheric eruptions or other kinds of solar activity. These disturbances are characterized by a sudden onset. Little information is available on the sizes of the sources of this radiation and on the state of its polarization.

8. EXPERIMENTAL STUDIES OF GALACTIC RADIATION

a) General radiation of the Galaxy

The observation that the Galaxy emits radio waves of appreciable intensity was made by Jansky (1932) at a wavelength of \(16\) m. He was unable to detect the radiation of the Sun and therefore suggested that the radiation of the Galaxy is not the summed radiation of stars, from which one should expect a considerably lower radiation intensity than from the Sun. Later observations by Reber (1940, 1944), carried out at a wavelength of \(1.9\) m with an antenna of considerably greater resolving power than Jansky’s, made it possible to obtain a sufficiently detailed distribution of radiation intensity. His results showed that it is chiefly the Milky Way that emits. In addition, he found maxima in the constellations Sagittarius, Cygnus, Cassiopeia, Canis Major, and Puppis. Later observations by Hey, Parsons, and Phillips (1941 a) (in which a special device was used for correcting the measured intensity and preventing errors due to the finite width of the radiation pattern of the antenna system) made it possible to obtain the distribution of intensity at a longer wavelength

at 4.7 m. Their results on the whole well confirmed the known data on the structure of the Galaxy. Their attempts to obtain a more complete agreement with the distribution of various types of stars, however, proved fruitless. The distribution of intensity was also measured by Reber (1948 b) at a wavelength of 60 cm, and here again the energy flux was so small that measurements could be made only near the plane of the Galaxy. It is clear that the general distribution obtained was, on the whole, the same.

The most important feature of these observations is the very great intensity of the radiation. Franz (1942), measuring at a wavelength of 10 m, came to the conclusion that the intensity at this wavelength corresponds to the emission of an extended source whose temperature reaches \(10^5\) degrees. The results of Hey, Parsons, and Phillips (1948 a) at a wavelength of 4.7 m correspond to a temperature of \(1.8 \cdot 10^4\) degrees in the direction of the center of the Galaxy. Thomas and Bardsley (1947) calculated that Reber’s results at a wavelength of 1.9 m correspond to a temperature of \(1.5 \cdot 10^3\) degrees; his measurements at a wavelength of 60 cm give a maximum temperature of \(30^\circ\). At shorter wavelengths the radiation of the Galaxy had not yet been observed.

From these experiments it could be concluded that the radiation of the Galaxy, excluding the shortest wavelengths, corresponds to a temperature varying approximately as the square of the wavelength, and that in the range from 50 cm to 10 m the angular distribution of the intensity in general corresponds to the general structure of the Galaxy. More detailed investigations of the dependence of temperature on wavelength were carried out in the range 1.5–7 m by Moxon (1946). He found that in the direction of maximum intensity the effective temperature varies as \(\lambda^{2.7}\), while in a direction close to the poles of the Galaxy a dependence \(\lambda^{2.1}\) is obtained. These conclusions will be of great importance in discussing the probable sources of the radiation of the Galaxy (Section 10 g)). It is important, however, to take into account the great difficulties that arise when comparing the results of measurements with antennas of different directivity, chiefly because a considerable part of the radiation of the Galaxy, as is now known, corresponds to sources with small angular radii. In other experiments Herlofson and Jolliffe (1948) obtained, at wavelengths of 12 m and 2.7 m with antennas of very small directivity, that the effective temperature is proportional to \(\lambda^{2.4}\).

b) Discovery of discrete sources in the Galaxy

The results of the investigations described in the preceding paragraph may be attributed to the radiation of sources of any type scattered throughout the Galaxy; moreover, as will be shown in Section 10 a), interstellar gas at first seemed a more probable source of radiation than stars. However, in 1946,

Hey, Parsons, and Phillips (1946) observed, at a wavelength of 5 m in the direction of the constellation Cygnus, rapid fluctuations of the radiation lasting several minutes. They believed that these fluctuations were not connected with refraction processes in the Earth’s atmosphere, and pointed out that at least part of the radiation of the Galaxy does not correspond to a diffuse-emitting region. Fluctuations of intensity indicated that the observed radiation was analogous to the radiation of sunspots.

Further measurements with an antenna of greater resolving power were carried out at a wavelength of 3 m (Bolton and Stanley, 1948) and at a wavelength of 3.7 m (Ryle and Smith, 1948). The former investigators used a “Lloyd’s mirror” interferometer, employing an antenna installed on a high cliff overlooking the sea, as had first been done by McCready, Pawsey, and Payne-Scott (1947) to determine the positions of sources of intense radiation from sunspots. By observing the change in the recorded intensity as a “point” source rose above the horizon, they were able to distinguish it against the background of the general radiation of the Galaxy and to compute both its coordinates from the times of its rising and setting. The times of rising and setting give the coordinate measured from east to west, or the right ascension of the source, while the difference of these times determines the coordinate measured from north to south, or the declination.

Fig. 13. Diagram and radiation pattern of a system with separated antennas, used for the detection of discrete sources in the Galaxy.

By this method it was possible to determine, with greater accuracy than Hey, the position of the source in Cygnus. In addition, these measurements showed that the angular diameter of the source is less

resolution of the installation (about 8 minutes), subsequent observations (Bolton, 1948) indicated the existence of several discrete sources of lower intensity*).

Ryle and Smith (1948) used the method of an interferometer with separated antennas, analogous to Michelson’s method for determining the diameter of stars. The antennas were set on an east–west line, and each of them had a narrow radiation pattern in the east–west direction ($\pm 1.5^\circ$) and a broad one in the north–south direction ($\pm 45^\circ$) (see Fig. 13). The resulting radiation pattern consisted of a narrow fan-shaped beam with a spacing between maxima of order $1/2^\circ$. If at the latitude of Cambridge ($52^\circ$ N latitude) the antenna is arranged so as to radiate upward, then the fan extends from the north pole almost to the plane of the equator, falling short of it by only a few degrees.

As the Earth rotates, the antenna radiation pattern thus sweeps across almost the entire northern hemisphere. In the absence of any discrete source of radiation (having an angular diameter less than $1/2^\circ$), the recorded amplitude will remain constant or will undergo small variations when the envelope of the radiation pattern is directed toward different regions of the Galaxy. If, however, the radiation pattern passes over a discrete source of small diameter, the recorded amplitude undergoes periodic variations, since the source is contained within $\pm 1.5^\circ$ of longitude. From the time of observation of the central maximum of the curve one can determine the source’s time of rising. Its declination is determined by using another property of the interferometer with separated antennas. The path difference from a distant source to the two antennas depends on the declination $\delta$ of the source, namely, it is proportional to $\cos \delta$. The periodicity of the recorded curve is given by the expression $t_0 \sec \delta$, where $t_0$ is the periodicity of a source placed on the equator ($t_0$ is the time in which the Earth passes through an angle corresponding to the angular distance between two interference maxima of the antenna system shown in Fig. 13; it is of the order of 2 minutes).

This interferometer has the advantage over Lloyd’s mirror interferometer that, with its aid, measurements can be made during meridian transits under conditions in which the angle of incidence of the radiation on the ionosphere and troposphere is minimal.

*) We note here that G. G. Getmantsev and V. L. Ginzburg [7] proposed using radio emission diffraction by the Moon to refine the determination of the sizes and coordinates of radio-emission sources during their occultations by the Moon. Their estimates show that the resolving power obtainable in these measurements reaches, in a number of cases, only a few seconds, which far exceeds the resolving power of installations currently in use (approximately 5–10′). (Translator’s note.)

Therefore the probability of errors due to refraction in the Earth’s atmosphere is considerably reduced.

Using this system at a wavelength of 3.7 m, Ryle and Smith investigated the source in the constellation Cygnus, and also found another source of still greater intensity in the constellation Cassiopeia. They also detected 28 sources of lower intensity. A typical record on which the emission of these two sources is noticeable is shown in Fig. 14. None of the sources coincides with any visible outstanding star, and the two named intense sources, whose positions were determined with an accuracy of 5—

Fig. 14. Part of a record obtained with an interferometer with separated antennas, revealing intense sources in the constellations Cygnus and Cassiopeia.

10 minutes, cannot be assigned to any star brighter than eighth magnitude.

c) Distribution of discrete sources

In view of the absence of correlation between an intense source of radio emission and visible stars, it is important to verify whether the sources are comparatively local bodies situated within the Solar System. Therefore an attempt was made to measure the distance to the two most intense sources from their parallax. Precise measurements of the distance to the sources in Cygnus and Cassiopeia were carried out at a wavelength of 3.7 m during two periods separated by 6 months (Ryle and Smith, unpublished). Within the accuracy of the measurements it was found that the distance of each of the sources does not change and that it is greater than \(2 \cdot 10^{16}\) cm. Although this distance is considerably smaller than that of the nearest known fixed star (about \(3 \cdot 10^{18}\) cm), this value nevertheless shows that the discrete sources are not within the Solar System, but are apparently located at stellar distances*).

*) Independently, I. S. Shklovsky \(^1\) estimated, by the method he proposed, the distance to the point source in the constellation Cygnus and obtained that it must be less than \(10^{20}\) cm. On this basis he also came

The angular distribution of the sources detected in the northern hemisphere does not show any noticeable concentration near the Milky Way. The total number of sources known at present

Fig. 15. Map of discrete sources detected in the Northern Hemisphere by Bolton and Stanley (circles) and by Ryle and Smith (crosses).

is still insufficient to draw firm conclusions about their distribution. In Fig. 15 is shown

the conclusion that the sources of radio emission are not hot class O stars, and that radio stars possess a luminosity considerably lower than that of the Sun. The method they proposed is based on measuring differences in arrival times, correlated with one another, of “bursts” of radio emission from a source at different wavelengths. It should be noted that, since it has now been shown that the main part of the fluctuations in the intensity of radio emission from sources is caused not by changes occurring in the source itself, but by diffraction of their radiation on irregularities in the ionosphere, this method, like other conclusions based on analysis of changes in the intensity of radio emission, requires further verification. (See the note on p. 553.) (Translator’s note.)

a map illustrating the location of the sources*). If the observed sources are at distances small in comparison with the dimensions of the Galaxy (i.e., if they are at stellar distances), then the angular distribution should be considered more or less uniform.

Proceeding now from the assumption that the observed discrete sources are at stellar distances, and that the remaining sources are similarly distributed throughout the Galaxy, one may attribute the general background radiation of the Galaxy to the radiation of all these stars. This point of view thus does not require any model based on the radiation of interstellar gas.

The emission of discrete sources and of interstellar gas should depend differently on wavelength; therefore an additional experimental test of this hypothesis is possible from a comparison of the distribution of the radiation intensity of discrete sources and of the general background of the Galaxy by wavelength. Studies of both intense sources have been carried out at several wavelengths. Bolton and Stanley (1948) investigated the source in Cygnus at 1.5, 3, 3.5, and 5 m and came to the conclusion that in this wavelength range the intensity has a small maximum at a wavelength of 3 m. For radiation sources in the constellations Cygnus and Cassiopeia, Ryle and Smith (unpublished) obtained at wavelengths 1.4, 3.7, and 6.7 m the following intensity values (in \(10^{-22}\ \frac{\mathrm{W}}{\mathrm{m}^{2}}\)):

	\(1.4\ \mathrm{m}\)	\(3.7\ \mathrm{m}\)	\(6.7\ \mathrm{m}\)
Cygnus . . . . . . . . .	1.3	1.4	1.3
Cassiopeia . . . . . . .	1.8	2.3	2.2

These results may be compared with the results of measurements of the intensity of the general background of the Galaxy (Moxon, 1946; Herbstreit and Johler, 1948). From these experiments it follows that the dependence of the effective temperature on \(\lambda\) varies between \(\lambda^{2.1}\) and \(\lambda^{2.7}\). This shows that the energy flux per unit solid angle depends on \(\lambda\) as \(\lambda^{0.1}\div \lambda^{0.7}\).

Until more accurate measurements over a wide range of wavelengths have been made for a larger number of sources, it will hardly be possible confidently to detect a difference between the intensity distributions obtained as functions of wavelength.

* At present more than 100 sources of radio emission have been discovered in the Galaxy (see, for example, \(^{9}\)). (Translator’s note.)

г) Polarization of the radiation of discrete sources

It is quite natural to draw an analogy between the intense radiation of the discrete sources of Galactic emission and the enhanced radiation of sunspots. From this point of view it is also important to check the polarization of this radiation and to determine whether it is circularly polarized, like the radiation of sunspots. The experiments of Ryle and Smith (1948) at a wavelength of 3.7 m, in which the interference polarimeter described in Section 6 was used, showed that the constant component of the radiation of both sources is not polarized. The same results were obtained at wavelengths of 1.4 and 6.7 m. Measurements of the state of polarization of the variable component of the radiation of the source Cygnus present certain difficulties, since the period of these fluctuations is comparable with the period of the interference pattern. Experiments, however, showed that this component of the radiation too is not polarized. These results made it possible to conclude that the steady radiation of discrete sources indicates the absence of any appreciable magnetic field in the emitting regions. The authors therefore suggested that the mechanism of this emission is apparently similar to the mechanism producing the radiation of the undisturbed Sun.

д) Causes of intensity fluctuations

Following the initial studies (Hey, Parsons, and Phillips, 1946) of random fluctuations in the intensity of the radiation at a wavelength of 5 m arriving from the direction of the constellation Cygnus, it was natural to seek an explanation for these fluctuations based on refraction in the Earth’s atmosphere. However, under existing theories of the structure of the ionosphere and troposphere it is difficult to regard them as responsible for such large fluctuations at such short wavelengths*).

) In later investigations⁴˒⁵, carried out at wavelengths of 6.7 m and 3.7 m, it was established that the character of the irregular variations (fluctuations) of the received intensity of the radio emission of sources in the Galaxy begins to differ noticeably at points separated from one another by distances of 20 km (from observations at a wavelength of 6.7 m) and even 3.9 km (from observations at a wavelength of 3.7 m). This leads to the conclusion that this type of fluctuation is caused mainly by diffraction processes of this radiation in the ionosphere. Subsequently, as a result of prolonged observations (over periods from 6 to 15 months)⁶ at wavelengths of 3.7 and 6.7 m of four radio-emission sources in the Galaxy, it was found that this type of irregular intensity fluctuation is associated with irregular ionization processes in the terrestrial ionosphere, the “fluctuation index” of the radio emission having a diurnal variation with a maximum at approximately 01 h 00 m local time. The authors suppose that the irregular processes in the ionosphere which cause changes in the received intensity of the radio emission of the Galaxy arise as a consequence of additional irregular ionization of the ionosphere (the \(F\) layer and above) under the influence of interstellar matter attracted by the gravitational field of the Sun. (Translator’s note.)*

Further evidence against the refraction mechanism was obtained by Ryle and Smith (1948) from studies of a source in the constellation Cassiopeia. They found, over a period of 2 months (May—June 1948), that the intensity of the latter source remains constant, whereas the intensity of the radiation of the source in Cygnus often fluctuates. Although during the observations the angles of incidence on the ionosphere were in both cases small (corresponding to 12° and 6°), it seemed impossible that atmospheric refraction should affect the radiation of only one source. It was therefore concluded that the fluctuations in the intensity of the Cygnus source are caused by genuine changes in the radiation of the source itself and are possibly analogous to “outbursts” of solar radiation associated with chromospheric flares*).

However, since the origin of fluctuations of the sources of the Galaxy (see Section 10b) is of great importance for the theoretical study of the nature of the sources themselves, further experimental investigations were carried out with the aim of determining whether these fluctuations are connected with changes in the emission of the source or whether they may be attributed to comparatively local processes of refraction.

Experiments of this type were performed by Pawsey and his colleagues (private communication). At a wavelength of 3 m they carried out simultaneous studies of the Cygnus source with receivers installed on two cliffs, one in Australia and the other in New Zealand. Comparison of the recorded curves obtained at the two points showed that, when fluctuations appear, they do not coincide noticeably with one another. This suggests that the fluctuations are caused by refraction in the atmosphere**).

It has already been noted that investigation by means of an interferometer using reflection from the sea surface provides observations of a source low above the horizon. In this case the influence of refraction in the ionosphere and, chiefly, in the troposphere should be greater than in the case when the source is at a great altitude. However, since additional refraction of this type may mask the primary changes in intensity, experiments are also necessary which use a method allowing observation of a source situated high above the horizon.

) Later observations⁶ showed that the relative values of the fluctuations (the “fluctuation index”) of the intensity of the radio emission of different sources have an annual variation. The annual-variation curves obtained for 4 sources showed that in general they coincide with one another, but are shifted relative to one another in time, according to the times of their meridian transit. In the authors’ opinion, this explains the results of Ryle and Smith (1948). (See also the note on p. 553.) (Translator’s note.)*

) See also the note on p. 553. (Translator’s note.)

Two series of such experiments were carried out in England, where the source in Cygnus can be observed at a small angle of incidence (12°) and where additional data can also be obtained by observing the source in Cassiopeia. The first experiment was carried out jointly with Lovell. In this experiment, investigations were made at a wavelength of 3.7 m, simultaneously with two receivers located respectively at Cambridge and Jodrell Bank (the distance between them was 210 km). The source in Cygnus was observed when it was near the meridian. In order to eliminate confusion caused by the interferometer system, simple antennas with considerable directivity were used; the intensity of the Galactic background radiation was measured

Fig. 16. Records obtained from the source in Cygnus with the aid of a simple antenna: a—May 28, 1949, and b—June 4, 1949.

previously with the aid of the interferometer system. In Fig. 16 two typical curves are shown, obtained at Cambridge from the source in Cygnus, respectively on a “quiet” and a “disturbed” day. The dashed line in the figure corresponds to the intensity of the background radiation.

The second experiment was set up at a longer wavelength, 6.7 m, since it could be expected that refraction would have a greater effect at it than at the wavelength 3.7 m. In these experiments two receivers were also used simultaneously—one was in Cambridge, the other was moved to various points, up to distances of the order of 170 km from Cambridge.

In both series of experiments it was established that, although at times a good correlation of the curves obtained at different points was observed on those nights when disturbances appeared, nevertheless a large part of the fluctuations observed at points considerably distant from one another were not similar to each other. It was also esta-

It was found that, at the time when the preceding experiments showed that the source in Cygnus was more active than the source in Cassiopeia, during the period from March to October 1949 frequent considerable fluctuations of the intensity of both sources were observed). From the results of these experiments it thus followed that a large part of the fluctuations of the radiation intensity observed in this period can be ascribed to processes occurring relatively close to the Earth*).

In addition to the type of fluctuations shown in Fig. 16,b) (at a wavelength of 6.7 m), another type of radiation fluctuation was sometimes observed. A large increase in intensity would suddenly appear, lasting 10–20 sec. Cases of this type of disturbance were not connected with the appearance of the first type of disturbance. Moreover, they coincided at two widely separated points (Cambridge—Mullard). Since these phenomena occur too rarely and their duration is very short, it was difficult to identify their direction with any source; however, it seems scarcely probable that they had a terrestrial origin***).

Thus, the modern, still insufficiently complete results of the experiments suggest two mechanisms causing fluctuations of the intensity of discrete sources in the Galaxy:

1) A mechanism based on irregular effects in the terrestrial atmosphere. Records similar to those shown in Fig. 16,b), in which the intensity fluctuates, taking values both greater and less than the normal mean value, indicate that the cause of the fluctuations may be refraction in the ionosphere.

) See the note on p. 553 (Translator’s note*).

) In observations (see 9), carried out over 18 months at a wavelength of 3.7 m with a radio interferometer with separated antennas, the constancy of the intensity of the radio emission of sources in the Galaxy was studied. From consideration of the published 150 records relating to periods when fluctuations in the intensity of radio emission were observed, caused, as the authors suppose, by diffraction phenomena in the ionosphere, the authors came to the conclusion that during this period of time the intensity of the radiation of radio stars was constant: with an accuracy of up to 10% for all radio stars, and with an accuracy of up to 5% for the most intense radio stars. In these observations the radio emission of about 100 radio stars was studied (Translator’s note).

*) It should be pointed out that I. S. Shklovsky⁸ calculated that, in interstellar gas, transitions between components of the hyperfine structure of the ground state of hydrogen atoms may give rise to monochromatic radio emission at a frequency of 1421.3 Mc/s (λ = 21 cm), the half-width of this line being only 4·10⁴ cps. Recently, in experiments carried out at three points (see 10, 11, 12, 13), monochromatic radio emission of the Galaxy at the wavelength λ = 21 cm was discovered. Experimental searches for this line in the radio emission of the Sun proved unsuccessful. (Translator’s note)

In order to obtain further evidence of the influence of ionospheric refraction, Ryle and Smith (unpublished) checked whether the times of these fluctuations (obtained from a series of observations at a wavelength of 3.7 m, lasting nine months) coincided with the times of noticeable ionospheric disturbances. From this analysis no correspondence was found between the periods of fluctuation and the periods of ionospheric or magnetic storms.

In addition, from observations carried out at Cambridge at wavelengths of 3.7 and 6.7 m, it turned out that many disturbances are observed simultaneously at both wavelengths. Therefore, it is unlikely that any theories explaining these phenomena on the basis of a simple mechanism of refraction are correct.

Thus, although, apparently, there can hardly be any doubt that the terrestrial atmosphere sometimes does cause noticeable fluctuations in the intensity of the radiation of discrete sources in the meter-wave range, further experiments are still required in order to find their causes.

2) Changes in the intensity of the source itself. Sudden large changes in intensity, observed simultaneously in two considerably separated receivers, resemble “bursts” of solar radiation. However, since they occur rarely and have a short duration, it is difficult to study them in detail. Further experiments will be required before it will be possible to establish a definite connection between them and solar “bursts.” Both types of fluctuations are of considerable interest for theory. The first because the question of the structure of the ionosphere is associated with it, the second because it makes it possible to draw conclusions concerning the physical extent of the source of radiation.

9. THEORY OF SOLAR RADIATION

The experimental study of the radio emission of the Sun has been carried out by many investigators. The results obtained by them have made it possible to construct a coherent, though incomplete, picture of the phenomena occurring in the range between 1 cm and 10 m. On the other hand, theoretical work has not yet reached a state in which there is complete agreement in theory. For example, there is a discrepancy of particular importance in the theories dealing with the emission of the enhanced radiation of sunspots in the meter-wave range. Many of these disagreements are perhaps connected with the variety of conditions permissible in the solar corona (for which visual observations do not provide the corresponding data). However, some disagreements are of fundamental significance, and their resolution represents one of the most important problems not only of radio astronomy but, in general, of all

astrophysics. This is connected with the fact that, as a result of radio investigations and on the basis of the conclusions drawn from them, it may prove possible to obtain data concerning stellar envelopes, which are lacking in observations by means of the visible spectrum of waves.

In this section an attempt is made to analyze, in general outline, the most important theoretical questions of the radio emission of the Sun. In Section 10 the question is discussed of the applicability of these theories to the calculation of the radiation of discrete sources of the Galaxy.

The results of experimental investigations of the radio emission of the Sun have been summarized earlier in Sections 7a) and 7b). Before discussing possible mechanisms of radio-wave generation, it is important to consider the question of the propagation of radio waves in the solar atmosphere, paying special attention to the conditions necessary for them to be able to emerge beyond the limits of the Sun.

a) Application of magneto-ionic theory to the solar atmosphere

Magneto-ionic theory (Appleton, 1932) was applied to the propagation of radio waves in the solar atmosphere by Saha, Banerji and Guha (1947), by Martyn (1948), and by Ryle (1948). The conclusions obtained in these works are briefly discussed below.

In the absence of an external magnetic field, the refractive index \(\mu\) of a region containing \(N\) electrons in \(1\ \text{cm}^3\) is, for a wave having angular frequency \(\omega\), equal to

\[ \mu^2 = 1 - \frac{4\pi N e^2}{m\omega^2}, \]

where \(e\) and \(m\), respectively, are the charge and mass of the electron. Therefore the propagation of a wave of given frequency is possible in the region where

\[ N < \frac{m\omega^2}{4\pi e^2}. \]

Thus, in this case a wave with angular frequency \(5\cdot 10^8\) (corresponding to a wavelength of \(3.7\ \text{m}\)) cannot propagate in the solar corona at heights less than \(1.5\cdot 10^{10}\ \text{cm}\) above the photosphere (see Fig. 17, a)).

In the case of the presence of a magnetic field, the refractive index has a different form, and for propagation along the direction of the magnetic field is given by the formulas

\[ \mu^2 = 1 - \frac{4\pi N e^2}{m\omega(\omega+\omega_H)} \quad \text{(ordinary wave)} \]

and

\[ \mu^2 = 1 - \frac{4\pi N e^2}{m\omega(\omega-\omega_H)} \quad \text{(extraordinary wave),} \]

where

\[ \omega_H\left(=\frac{eH}{mc^2}\right) \]

is the natural frequency of rotation of the electron in the magnetic field (the gyroscopic frequency). Both waves are circularly polarized in opposite directions (the wave having

the same direction of rotation as a free electron, is known as the extraordinary wave).

It is evident that, for any values of \(\omega_H/\omega\), the ordinary wave can propagate if the inequality

\[ \frac{4\pi Ne^2}{m\omega^2}<1; \]

is satisfied; for large values of \(\omega_H/\omega\), the wave can propagate at larger values of \(N\). Therefore the presence of an intense magnetic field allows the circularly polarized component to propagate in regions that have a high electron density.

Fig. 17. Curves of the dependence of \(\mu^2\) of the solar atmosphere on height at a wavelength of \(3.7\ \mathrm{m}\): \(a\)—without taking the magnetic field into account, \(b\)—above a sunspot with a field of \(3000\) gauss.

On the other hand, the extraordinary wave cannot propagate until the inequalities

\[ \frac{\omega_H}{\omega}>1 \]

or

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

are satisfied. For intermediate values of \(\omega_H/\omega\), this wave cannot propagate.

The influence of the magnetic field can be demonstrated more clearly by applying these expressions to the propagation of a \(3.7\ \mathrm{m}\) wave in the solar atmosphere. Figure 17a shows the curve of the dependence

of \( \mu^2 \) on height in the absence of a magnetic field. It is seen from the figure that the wave can propagate above the photosphere at heights exceeding \(1.5\cdot 10^{10}\) cm. In Fig. 17b the influence is shown of the magnetic field of a unipolar sunspot, which has the form of a dipole placed at a height \(0.1R_0\) below the photosphere (\(R_0\) is the radius of the photosphere) and which produces a magnetic field of 3000 gauss in the photosphere (in this example the change in electron concentration above the sunspot is not taken into account). In this case the ordinary wave can propagate beginning at a height of \(6\cdot 10^8\) cm, whereas the extraordinary wave cannot propagate in the region of heights between \(2.6\cdot 10^{10}\) cm and \(3\cdot 10^{10}\) cm. At a height of \(2.6\cdot 10^{10}\) cm the wave frequency and the gyroscopic frequency are equal to one another (\(\omega_H=\omega\)). From this example it is clear that, in the absence of any appreciable magnetic field, a source whose radiation at a wavelength of 3.7 m can reach the Earth must be located at a height greater than \(1.5\cdot 10^{10}\) cm above the photosphere. Emission from a sunspot, however, may come from a source located above \(6\cdot 10^8\) cm (ordinary wave) or above \(3\cdot 10^{10}\) cm (extraordinary wave).

Besides analyzing the refractive index of the solar atmosphere for a given wave, it is also important to investigate the absorption of the wave. It will be seen below that some theories of the radio emission of the Sun proceed from an “equilibrium” state of the heated electron gas. With the aid of Kirchhoff’s law one can calculate the emission of the Sun, knowing the absorption coefficient and the temperature of the emitting region. (Martyn (1948) considered the question of the applicability of Kirchhoff’s law in the case of the presence of a magnetic field and came to the conclusion that for circular polarization, as occurs in most problems of the solar atmosphere, Kirchhoff’s law is applicable.)

Ryle (1948) showed that under conditions of complete ionization, existing in the solar corona, the absorption of radiation at meter waves is small, except for three regions: one of them is the region where the gyroscopic frequency is equal to the wave frequency; in it, owing to “resonance absorption,” the extraordinary wave is strongly absorbed. Considerable absorption also arises in the region where the refractive index is small; each of the two circularly polarized components undergoes absorption at heights where the values of their refractive indices tend to zero.

The question of the value of the absorption coefficient for different wavelengths passing through the solar atmosphere is discussed below in connection with the problem of emission of the heated solar atmosphere. It should be noted here that a wave approaching normally to the surface, \(\mu=0\), may often be strongly absorbed, whereas the absorption of a wave incident at a large angle

and reflected at a finite value of \(\mu\) (given by Snell’s law), is considerably smaller.

The above outline of the theory of radio-wave propagation in the solar atmosphere*) shows that the generation of radio waves must take place in the solar atmosphere at considerable heights. Investigation of these regions by visual methods is difficult, and information concerning the physical conditions existing in them is, to some extent, limited. For these reasons it is impossible to base the various theories of radio emission on generally accepted data. Studies of radio emission, in themselves, apparently open up the possibility of drawing more exact conclusions concerning the structure of the solar atmosphere than is permitted by observations at visible wavelengths.

b) Models proposed for explaining the radio emission of the Sun

In a recent communication by Ryle (1949a), theories of the radio emission of the Sun are divided into two groups:

1) “Equilibrium” mechanisms, in which the intensity of the radiation tends toward a value corresponding to the mean energy of the thermal motion of the electrons.

2) Non-thermal mechanisms, in which coherent radiation from a large number of electrons is capable of producing radiation of considerably greater intensity than that which corresponds to the mean energy of the thermal motion of the electrons.

Conclusions based on the first group of ideas require knowledge of the mean energy of the thermal motion of the electrons, or of the electron temperature of the emitting region, together with knowledge of the emission power of the region. Theories based on this mechanism must also explain how the very high electron temperatures necessary for producing the observed intensities are maintained.

In the second case a high electron temperature is not required, but a detailed description is needed of the phenomena explaining how coherent radiation from a large number of electrons is maintained.

c) Radiation of the undisturbed Sun

Experimental investigations have shown that at wavelengths of the order of \(3\ \mathrm{cm}\) the undisturbed Sun radiates as though it had a temperature of \(2\cdot 10^{4}\) degrees, while at a wavelength of \(50\ \mathrm{cm}\) it has a temperature of about \(5\cdot 10^{5}\) degrees. At longer wavelengths (up to \(7\ \mathrm{m}\)) the emission gradually increases, so that the temperature reaches \(2\cdot 10^{6}\) degrees (Fig. 9). Experiments have also shown that,

) For more details on the propagation of radio waves in an ionized gas under the influence of a magnetic field, see \(^{14,15}\). (Translator’s note.)*

that at wavelengths of 60 cm and shorter the Sun radiates more or less uniformly over the whole disk; no data have been obtained on the distribution of radiation over the disk at long wavelengths.

Martyn (1948) and Ryle (1948) proposed theories of radio emission based on an “equilibrium” mechanism*). On the basis of thermodynamic considerations they calculated the radiation of a region of given absorptivity. Different methods for calculating the emission of a heated ionized gas were used by Greenstein (1947), Unsöld (1947), and Waldmeier (1948). These authors calculated the total radiation, taking as the starting point individual acts of collision of an electron with an electron and of an electron with a proton (the theory of the “free-free” transition). Martyn (1948) showed that these calculations give the same results when the refractive index does not differ appreciably from unity. However, in the case when the refractive index is small, the theory of the “free-free” transition becomes complicated. Since the most interesting experimental results refer to waves for which the refractive index of the solar corona differs substantially from unity, this theory has not been widely used for them. It has, however, been applied to the calculation of the emission of very short waves, which are absorbed in a region where the refractive index differs only slightly from unity.

The thermodynamic considerations used by Martyn (1948) and Ryle (1948) were also applied to regions in which the refractive index is very small; therefore they were, in particular, applied to determine the emission at long wavelengths, which are appreciably absorbed only in the region where the refractive index is small. Both authors calculated the total absorption in the solar atmosphere for small values of $\mu$ and showed that the absorption in the range 1–10 m is appreciable. They came to the conclusion that the emission of the Sun at these wavelengths can be likened to the radiation of a black body having a temperature equal to the temperature of the electrons located in the region in which $\mu$ is small.

On this basis, measurements of the intensity at different wavelengths should give information about the electron temperature at different levels of the solar atmosphere (as was indicated by Ginzburg, 1946).

Denisse (1949a) raised objections concerning the consideration of the relation between the absorption coefficient and the emissivity of a region in which $\mu$ is small. He asserts,

*) The corresponding theoretical analysis was first carried out by V. L. Ginzburg$^{16,18}$ and I. S. Shklovsky$^{17}$. See also $^{19}$. (Translator’s note.)

that although for \(\mu \simeq 0\) the absorption coefficient increases strongly, the emissivity tends to zero.

This conclusion arises as a result of confusion between the true emissivity and the energy propagating in a region in which \(\mu\) varies continuously from very small values to unity. In the considerations of Martin and Ryle, large values of the absorption and emission coefficients are used; the loss of reflectivity should not be taken into account in the case of the solar corona because of the small gradients of the refractive index.

Martin (1948) extended his treatment of absorption to the case of an obliquely incident wave. In this way he was able to calculate the emission of various regions of the Sun at wavelengths from \(20\ \mathrm{cm}\) to \(30\ \mathrm{m}\). In this treatment it was assumed that the temperature of the corona is \(10^6\) degrees (obtained from the identification of spectra of highly ionized atoms of the corona; Edlén (1942)) and that the temperature of the chromosphere is 30,000 degrees (following from measurements of the profile of the spectral lines of the chromosphere; Redman (1942)). It is further assumed that the temperature changes more rapidly at the boundary between the corona and the chromosphere.

Martin’s results show that at longer wavelengths (greater than \(10\ \mathrm{m}\)) even a normally incident wave is not completely absorbed and is partially reflected. At these wavelengths the emission even from the center of the solar disk is somewhat less than the value expected for a source with a temperature of \(10^6\) degrees. On the other hand, at wavelengths shorter than \(1\ \mathrm{m}\), a normally incident ray, passing through the chromosphere, is not reflected. Therefore the intensity of the radiation from the center of the disk corresponds to the temperature of the chromosphere.

Thus his theory predicts that at wavelengths shorter than \(1\ \mathrm{m}\) the emission from the center of the solar disk should be less than the emission from the limb. Similar results were obtained by Unsöld (1947) and Waldmeier (1948), who based their calculations on the same assumptions concerning the distribution of temperature in the solar atmosphere.

Observations at wavelengths of \(60\ \mathrm{cm}\), \(10\ \mathrm{cm}\), and \(3\ \mathrm{cm}\), however, showed that the Sun radiates as a uniform disk or as a disk with a somewhat darkened limb.

It is possible that the discrepancy between the theoretical considerations of Martin, Unsöld, and Waldmeier and the experimental results is explained by an incorrect assumption made by them concerning the distribution of temperature in the solar atmosphere. It can be shown that the emissivity of the solar atmosphere at wavelengths from \(10\ \mathrm{cm}\) to \(1\ \mathrm{m}\) depends more strongly on the variation of electron temperature and density with height at the boundary between the corona and the chromosphere. Precisely for this

regions the data obtained by means of visual observations are incomplete. It is possible that a deeper understanding of the phenomena that maintain the electron temperature in the corona and chromosphere will make it possible to obtain a more detailed picture of the structure of the boundary region.

Let us now consider a certain mechanism that is capable of maintaining high temperatures in the solar atmosphere. Its role in different regions of the atmosphere is discussed in greater detail in Section 9 d). This mechanism does not require large values of the electron-temperature gradients between the corona and the chromosphere, and it does not yield the phenomenon of the darkened center predicted by Martyn.

d) Formation of high-energy electrons in the solar atmosphere

It has been shown that the radio emission of the Sun is satisfactorily explained by the chaotic motion of electrons, if it is assumed that the electrons of the solar corona have a kinetic energy corresponding to a temperature of \(10^6\) degrees. Under some conditions the radiation intensity approaches the value corresponding to black-body emission at a temperature of \(10^6\) degrees; under other conditions the intensity proves to be smaller either because the absorption is insufficient for the establishment of equilibrium, or because lower regions are emitting, where the electron temperature is lower. In addition to radio observations, the results of visual observations also confirm that the temperature of the corona is of the order of \(10^6\) degrees. Waldmeier (1945) summarized the results of measurements and showed that four independent methods give comparable values of the coronal temperature:

1) The ratio between the pressure gradient in the corona and in the photosphere corresponds to a coronal temperature approximately 1000 times greater than the temperature of the photosphere.

2) Grotrian’s investigations (1931, 1934) of the broadening of lines emitted by the photosphere and scattered by coronal electrons give, for the electron temperature, a value of \(7 \cdot 10^5\) degrees.

3) Observations of a large number of spectral lines whose ionization potential reaches 100 volts (corresponding to thermal energy at \(10^6\) degrees).

4) Measurements of the width of the Fe XIV line give a Doppler broadening corresponding to a temperature of \(2 \cdot 10^6\) degrees.

It is therefore important to discuss the processes that are capable of maintaining in the corona a temperature of \(10^6\) degrees. Ryle (1948) proposed that the high energy of the electrons in the solar atmosphere is maintained by an electric field. Assuming that the observed rotation velocities of sunspots at different latitudes

correspond to the true difference in the velocities of motion of the photospheric material. Alfvén (1937) showed that the presence of a general magnetic field leads to an increase in the difference of potentials between the poles and the equator of the Sun. Assuming that at the poles the field strength is of the order of 50 gauss, one obtains a potential difference of the order of \(5 \cdot 10^8\) volts.

In discussing the action of such a field it should be remembered that charged particles can move in the solar corona only parallel to the magnetic lines of force. If the magnetic axis and the axis of rotation of the Sun coincide, then every magnetic line of force will intersect the Sun at points of equal potential, and such a mechanism will not impart large velocities to the particles of the solar atmosphere. If, however, these axes make a small angle with one another, a potential difference arises already between points lying on a magnetic line of force. For an angle of \(7^\circ\) (a value computed from a study of the corona during periods of low sunspot activity) the potential reaches \(10^6\)—\(10^7\) volts and, in the absence of space-charge phenomena, will lead to a potential gradient of the order of \(10^{-5}\) volts/cm, capable of accelerating charged particles in the chromosphere and corona. The mean energy of the electrons maintained by such a mechanism depends on the distance traversed by the electron in the field before it undergoes an energy loss in a collision. Therefore the electron temperature at different levels of the solar atmosphere depends on the particle density and on the type of collisions that cause the loss of energy. A more detailed analysis of the dependence of the electron temperature on height will be given in Section 9. Ryle (1948) showed that in the undisturbed solar corona, at heights responsible for the emission of metre waves, one should expect the mean energy of the electron to be \(10^2\)—\(10^4\) electron-volts (i.e., that they have a temperature of \(10^6\)—\(10^8\) degrees).

Although much more work is still needed before the theory of the radio emission of the undisturbed Sun can be considered satisfactory, there is already no doubt that the basis of this emission is an “equilibrium” mechanism and that electrons with high energy exist in the solar corona.

So long as the basis for theoretical analysis is provided by data on the corona obtained from difficult visual observations, one cannot expect a more exact agreement between theoretical predictions and experimental results. It is possible that the creation of a more improved technique of radio measurements will ultimately make it possible to obtain more accurate information about the distribution of temperature in the corona than that which follows from observations at visible wavelengths.

d) Enhanced radiation of sunspots

1) Theories based on the phenomenon of equilibrium

Both Kiepenheuer (1946) and Denisse (1947 a, b) indicated that electrons freely rotating in the magnetic field of a sunspot emit waves polarized circularly. The magnetic field of the chromosphere and corona is sufficient for the generation of radio waves of the observed frequency. However, substantial difficulties arise in carrying out these calculations. From Fig. 17, b) it is seen that radiation produced in this way (having the polarization corresponding to the extraordinary wave), before it can escape, must pass through a considerable distance in a region in which the refractive index has an imaginary value. Apart from the possible leakage of an exponentially damped wave, whose intensity tends to zero, no other transfer of energy through such a region of the medium can be expected.

Kiepenheuer (1946) did not take this damping into account at all, while Denisse (1947 a, b) came to the conclusion that, if the gradient of the magnetic field is large, this damping is not of great importance. In addition, Kiepenheuer obtained intensities considerably greater than those that can be expected for a given electron temperature, and did not point to any mechanism that could sustain the motion of a multitude of electrons. His results are based on summing the radiation of electrons located within a considerable thickness, and were obtained without taking the effect of reabsorption into account. From simple thermodynamic considerations it can be seen that neglecting reabsorption is illegitimate and that the radiation intensity cannot exceed the value determined by the electron temperature.

In a later paper, Ryle (1948) examined in rather great detail the possibility of the escape of energy from the region of “resonance absorption,” where the wave frequency is equal to the gyrofrequency. He showed that, whereas the radiation of an electron rotating in the magnetic field of a sunspot propagates freely toward the center of the Sun, the damping of a wave traveling in the opposite direction is very large. He therefore concluded that this mechanism cannot provide the observed intensities. However, he pointed out that the possibility of an energy flux toward the center of the Sun may be significant, since the presence of a flux of momentum in this direction will lead to the appearance of a reverse radiation pressure on electrons situated in the magnetic field. This point of view is considered in Section 11 a).

In addition to the region of resonance absorption, Ryle also indicated two layers of the solar atmosphere above the spot which absorb the passing wave. Each of these layers absorbs one

of the circularly polarized components. They correspond to regions where the refractive index of each of the waves decreases. For example, for a wave of 3.7 m and a spot field of 3000 gauss, these layers are at heights of the order of \(6\cdot 10^8\) cm (ordinary wave) and \(3\cdot 10^{10}\) cm (extraordinary wave) (see Fig. 17b). The total absorption in both regions is large and depends on the number of collisions and the gradient of the refractive index. Each of these regions therefore emits a circularly polarized wave whose intensity corresponds to the electron temperature in that region. Assuming that the temperature of the solar corona increases with height, one may expect that the predominant polarization observed at the Earth’s surface corresponds to the extraordinary wave. However, in order to judge the relative values of the emissivity of each of these regions, it is also necessary to know the values of the angle at which the corresponding sources are visible from the Earth.

An exact theoretical calculation of the intensity of both components is complicated by the absence of sufficiently accurate data on the electron density and temperature above a sunspot, and by the difficulty of determining the effective number of collisions in a completely ionized gas. Martin (1948) noted that the absorption of radio waves is determined by the type of collisions proposed by Chapman and Cowling (1939), for which a considerably larger collision cross section is obtained than for non-ionized hydrogen. Independently, Ginzburg (1944) obtained the same result when discussing the absorption of a radio wave in the Earth’s atmosphere in the presence of a large number of ions.

If this type of collision is adopted, then the absorption of meter waves in both regions considered by Ryle (1948) will be complete for a wave normally incident on the region \(\mu = 0\). From this it may be concluded that each of these regions will emit circularly polarized waves normally to the surface \(\mu = 0\). The intensity of this radiation corresponds to the electron temperature of the region. Machin (unpublished) investigated the dependence of the radiation intensity on direction in order to obtain a polar diagram of a sunspot at different waves. Such a calculation is difficult, since it requires detailed knowledge of the distribution of electron density near the sunspot. However, the preliminary results obtained by him give polar diagrams that agree well with the experimental results.

The state of polarization of the wave received at the Earth depends on the relative intensity of both components. The intensity of each wave is determined by the total effective solid angle subtended by the source and by the electron temperature of the emitting region. The effective solid angle is obtained from a calculation of the emissivity in each small element of the solid angle of a black ...

source. Until the analysis of this question is possible not only for a spot of simple form and until it is possible only to estimate the electron temperature of each of the regions (by the method considered in Section 9 e), it is impossible to examine completely the action of any group of sunspots. This method is made still more complicated by the complexity of the structure of the magnetic field of spots. Therefore, from comparison of the results of calculation with the experimental data, reliable results have not yet been obtained, although both theory and experiment show that the extraordinary wave (corresponding to a source located at a great height) is usually more intense.

Let us now discuss the phenomena that may maintain a high electron temperature in the solar atmosphere near sunspots. Experimental data have shown that meter waves are emitted by small surfaces situated in the neighborhood of sunspots and having a temperature of \(10^8\)—\(10^{10}\) degrees. Various models have been proposed to explain these temperatures (corresponding to a mean electron energy of \(10^4\)—\(10^6\) electron-volts), based on the acceleration of electrons in an electric field.

According to Alfvén (1937), one should expect a potential difference of \(5 \cdot 10^8\) volts between the poles and the equator of the Sun, arising from the influence of the general magnetic field on the nonuniformly rotating matter of the Sun’s surface. It was shown that, in the absence of sunspots, only a small fraction of this potential can be used to accelerate charged particles in the solar atmosphere. However, when the magnetic field of a sunspot is added to the general magnetic field of the Sun, the electric field that accelerates the particles increases greatly. The resultant magnetic field has magnetic lines of force crossing the photosphere at points that differ greatly in latitude, and Ryle (1948) showed that in the atmosphere near a sunspot the electrons are then accelerated by a potential difference of the order of \(10^8\) volts.* The potential gradient may be modified by the presence of space charges, and also by the motion of the photospheric matter in the sunspot. This question is considered in Section 9 ж) in connection with the discussion of the nature of “explosions” and flashes of the chromosphere. Nevertheless, Ryle concluded that at heights exceeding \(10^9\) cm, the mean energy of the electrons of the corona increases, at least, to \(10^6\) electron-volts (which corresponds to an electron temperature of \(10^{10}\) degrees).

* This number was obtained for values of the magnetic field of 50 gauss. Recent observations (Tisse, 1949) have shown that the magnetic field of the Sun is equal to only a few gauss. However, in Section 9 e) it will be seen that the mean free path of an electron in the solar corona is considerably greater than the value previously accepted. Therefore one may expect a similar acceleration of particles in a general field of 1 gauss.

Giovanelli (1947–1948) and Dungey (1947b, 1949b) proposed an alternative mechanism for the formation of an electric field in the solar atmosphere near a sunspot. Considering the process of the growth of the magnetic field in a sunspot, they came to the conclusion that an intense electric field must arise in the neighborhood of the sunspot. For large, rapidly growing spots, electric fields then arise which accelerate electrons to energies of the order of \(10^6\)—\(10^7\) electron-volts.

As shown above, the experimentally observed intense radio emission of sunspots can be explained by the “equilibrium” mechanism if, in the solar atmosphere near sunspots, the electrons have high energy. Visual observations of the motion of matter in the photosphere, as well as studies of the Sun’s magnetic fields, have shown that the electric fields arising in this case have sufficient intensity to maintain the required electron energy.

2) Theories based on coherent radiation of electrons

Since, in order to explain the observed intensity of the radio emission of sunspots at meter wavelengths, very large values of the electron temperature are necessary, some authors have proposed nonthermal mechanisms for this purpose. The production of emission with an intensity greater than that which corresponds to a given electron temperature requires the presence of phenomena that sustain the coherent radiation of many electrons.

Bruck (1946) suggested that electrical discharges in the solar atmosphere, analogous to luminous discharges on Earth, may amplify radio emission. However, Martyn (1947) noted that such phenomena are improbable for highly ionized regions such as the solar atmosphere, where the electrical conductivity is always large.

Martyn (1947) and Shklovsky (1947) proposed that coherent radiation of coronal electrons is produced by a mechanism analogous to plasma oscillations in discharge tubes. Haff (1948, 1949) suggested that the increase in the intensity of the radio emission of the corona is caused by the interaction of electron beams, leading to amplification analogous to the amplification observed in electron tubes. Bailey (1948a, b, 1949) showed that this does not require the presence of moving beams, and that amplification of space charges arises in the presence of the usual drift velocity.

Ryle (1949a) examined these points of view in detail and came to the conclusion that, although the proposed theories give a satisfactory explanation for such phenomena under the scale conditions of a discharge or electron tube, their use under conditions of large-

scales such as exist in the solar corona encounters great difficulties. Thus, although the electron density at different heights of the solar corona has a value sufficient for the generation of the observed waves, it is very difficult to explain both the excitation of these oscillations and the conditions under which radiation escapes from the oscillating region.

In all the proposed theories the excitation of the oscillations depends on the rate of modulation of the electron beams. In the published calculations a detailed analysis is given of a highly simplified case for one or two beams of electrons consisting of electrons having almost the same drift velocities (a case of interest when the application of the theory to the calculation of electron-beam amplifiers is considered). However, the velocities of electrons in the solar atmosphere do not have a narrow range of values, even if they are accelerated by a uniform electric field, since they undergo a large number of collisions in the accelerating region and are deflected through large angles from the original direction.

In Section 9 e) it is shown that in a large part of the solar atmosphere the distribution of electron velocities can probably be similar to the distribution of random motions, to which a considerably smaller value of the drift velocity in the electric field is added. The application of the model proposed by Haeff and Bailey to these conditions encounters very great difficulties, chiefly in the case when a magnetic field is present.

Even if phenomena existed that maintained these oscillations, it is doubtful that the energy thus generated could reach the Earth. This is connected with the fact that the region in which plasma oscillations are generated has, for the plasma frequency, a refractive index equal to zero, so that electromagnetic energy of this frequency cannot pass through it. Energy can be extracted from the oscillating region by the motion of a bound beam of electrons under the small-scale conditions of a discharge tube (as was indicated by Armstrong (1947) and Neal (1949)). However, such a mechanism is impossible in the solar atmosphere, where the electrons must pass through a large number of wavelengths before they reach the region in which the corresponding radiation can propagate. Moreover, since under these conditions there is no uniform drift velocity, the electron beam will not be preserved at all. Apparently, analogous arguments should be used in considering the Haeff and Bailey model, although in their work the question of the escape of the radiation energy is not examined in detail. It should be pointed out that the emission of electromagnetic radiation with respect to a coordinate system moving with the electron beam is completely determined by the conditions for the escape of the radiation from an ordinary stationary plasma.

Until definite data concerning the nature of the enhanced radiation of the Sun are available, much remains unclear in questions connected with the generation of coherent oscillations of high energy. These difficulties arise when applying the theory of plasma oscillations and of the amplification of space charges to the conditions of the solar atmosphere, in which the motion of the electrons has a velocity distribution close to chaotic, and where the gradients of the electron density and of the magnetic field are very small. Although the solar corona has electron densities agreeing, in order of magnitude, with the frequency of the emitted waves, nevertheless both the excitation of coherent oscillations and the question of the escape of radiation from the oscillating region create considerable difficulties in the existing theories.

On the other hand, the generation of radiation by means of an equilibrium mechanism, assuming chaotic motion of the electrons of higher energy, appears possible.

In this theory, different layers of the solar atmosphere absorb radiation of different frequency, and the layers that absorb appreciably also radiate with an intensity corresponding to the value of the electron temperature. The question of maintaining in the corona above a sunspot an average electron energy of \(10^6\) electron-volts (corresponding to an electron temperature of \(10^{10}\) degrees) presents no greater problem than the question of maintaining an average electron energy of 100 electron-volts (corresponding to an electron temperature of \(10^6\) degrees) in the undisturbed corona; this temperature value has been reliably established by visual observations. It should be assumed that the corresponding conditions are created under the influence of the magnetic field of the Sun and of the electric field arising from the nonuniform rotation of the Sun.

e) Detailed calculation of the mean electron energy maintained by an electric field

In considering the equilibrium mechanism proposed for calculating the radio emission of the Sun, it was assumed that the large mean value of the electron energy in the corona is maintained by an electric field. Ryle (1948) assumed that both the normal temperature of the corona and its enhanced value near sunspots are caused by an electric field maintained by the general magnetic field of the Sun in interaction with the nonuniform rotation of the Sun. Giovanelli (1947, 1948) and Denisse (1947 b, 1949 b) assumed that the increased electron temperature near sunspots is caused by an electric field which is maintained during periods of growth of the magnetic field of a sunspot. It is therefore important to examine in detail how an electric field applied to an ionized gas can act on the aver-

new energy of the electron. It is assumed in this treatment that the principal gas in the corona is hydrogen.

It is clear that the electric field will accelerate both electrons and protons, and in a region of sufficiently large dimensions an equilibrium state may be established in which the average energy acquired by a particle moving along the potential gradient becomes equal to the average energy lost in collisions. Therefore the mean energy of the electrons (and protons) that is maintained in a given electric field depends on the collision processes.

For a gas that is not completely ionized (such as in the chromosphere), the electron loses its energy chiefly in inelastic collision with a non-ionized atom, and, for a low degree of ionization, the electron energy cannot greatly exceed the value determined by the effective ionization potential of the gas. For a more strongly ionized gas, inelastic collisions occur less often and the mean electron energy can increase. It is now necessary to consider how electrons lose energy in the case when the gas is completely ionized. It should be noted here that, for gases of the solar atmosphere among which there are heavy atoms, energy loss in inelastic collisions is still possible, since the mean electron energy increases to a value ensuring the formation of multiply ionized atoms. Therefore the presence of heavy atoms leads to a slower transition from the conditions of the incompletely ionized chromosphere to the completely ionized corona.

In a region that may be regarded as completely ionized (consisting of electrons and protons), an electron can lose energy as a result of elastic collisions with electrons, with protons, or as a result of bremsstrahlung. It is clear that before an electron loses an appreciable amount of energy, a large number of collisions will be required; therefore the motion of the particle will approach chaotic motion, while a drift motion in the direction determined by the electric and magnetic fields will be superposed on this motion. Under these conditions there is no need to consider the phenomena of energy exchange in electron–electron collisions, since the mean electron energy is limited by collisions with protons or by radiative loss.

The first of these mechanisms was considered by Giovanelli (1949), who calculated the energy loss from elastic collisions with protons, taking the collision cross section computed by Chapman and Cowling (1939). In the greater part of his calculation Giovanelli assumed that the mean energy of the protons corresponds to their thermal energy at the temperature of the photosphere (6000°). However, as was already indicated above, the protons will also be accelerated by the electric field—

them, and since they cannot lose energy in collisions with other protons or electrons, the mean value of their energy may become significant, and under certain conditions, when rapid changes of the electric field occur, the proton energy can probably reach the electron energy. Waldmeier (1945) actually observed Doppler broadening of the coronal Fe XIV line corresponding to a temperature of \(2\cdot 10^6\) degrees. Therefore it must be concluded that the mean energy of protons (and possibly of all positive ions) is comparable with the energy of electrons. Under these conditions the electron will, on average, not lose energy in elastic collisions, and its mean free path (before appreciable energy loss) will be determined by the smaller cross section associated with radiative losses. Menzel’s calculations (unpublished) have shown that under these conditions the mean energy of an electron in the solar corona is normally limited only by the potential existing in the corona. In stars of larger dimensions, this effect acquires some significance. A given electric field is capable of maintaining a considerably higher electron temperature than the value obtained from Giovanelli’s theory (1949).

The mean free path of protons, which lose little energy by radiation, will be considerably greater, and in such stars protons (or heavy nuclei) can probably have high energies.

ж) Theories of rapid fluctuations of the radiation of sunspots and sudden large increases associated with flares in the chromosphere

Up to now no satisfactory explanation has been proposed for the rapid oscillations in the intensity of radio emission from sunspots. The absence of correlation between fluctuations observed at different wavelengths can readily be explained by the difference in the heights at which the different waves are generated. However, it is very difficult to explain the short periods of these oscillations. Two main causes of these phenomena may be indicated.

1) Refraction of radiation above the region of its generation—fluctuations analogous to the twinkling of stars due to atmospheric irregularities may arise. Simultaneous observations of fluctuations at two widely separated receivers (McCready, Pawsey, and Payne-Scott, 1947) gave identical recording curves and thereby showed that refraction in the Earth’s atmosphere cannot be responsible for the results of these experiments. However, if these phenomena are caused by refraction in the outer layers of the solar corona, then the dimensions of the refraction pattern must be sufficiently large for identical changes of intensity to be obtained at two points on the Earth.

2) Oscillations of the emission of the source itself. These oscillations may be caused by changes in the electron temperature or density (and hence in the radiating power) of the emitting region. Williams’s observations (1948) at a wavelength of 4 m showed that individual bursts of intensity at first rise rapidly and then decay exponentially; this indicates an instantaneous increase of the electron temperature. On the other hand, in some of Smith’s experiments (unpublished) at a wavelength of 1.4 m, bursts (whose mean duration is of the order of 1/2 sec.) of symmetrical form were obtained.

In a later paper (Ryle, 1949a) it is suggested that, although plasma oscillations of electrons can hardly exist in the solar corona, “acoustic” waves of very low frequency may arise there as a result of ion oscillations (such oscillations were considered by Tonks and Langmuir, 1929). The propagation of this type of disturbance through the emitting region may cause oscillations of the electron temperature and density.

Apparently, until more detailed experimental data on the fluctuations of radio emission have been obtained, it will be impossible to draw more definite conclusions about their nature.

The explanation of sudden large increases of intensity associated with chromospheric flares encounters fewer difficulties. Brück (1946), Martin (1947), Giovanelli (1947), and Ryle (1948) suggested that they appear because of sudden electrical discharges in the solar atmosphere.

Martin suggested that turbulent motions of ionized luminous matter near a sunspot lead to large intermittent electric fields. Giovanelli suggested that a change in the electric field is produced when the magnetic field of a sunspot arises. However, Newton (1948), from an analysis of a larger number of strong flares, showed that there is no correspondence between the times of their appearance and the degree of growth of the magnetic field; on the contrary, he established that the largest flares occur during periods of maximum values of the magnetic field, when the rate of its change is minimal. Ryle suggested that the potential difference produced by the non-uniform rotation of the Sun’s surface leads to the appearance of electrical discharges along magnetic lines of force, which, in turn, carry the matter of the photosphere in a sunspot considerably to the side. These motions create a back e.m.f. capable of reducing the potential gradient of the solar atmosphere (in the same way as in an electric motor), and thereby may lower the mean energy of the electrons of the solar atmosphere to values smaller than those expected for the full potential difference. If the motion of the photospheric matter is disturbed, then—

the magnitude of the full potential becomes significant, and at all points along the path of the discharge the energy of the electron gradually increases substantially. The cause of chromospheric flares is considered to be the increasing radiation of visible light, caused by enhanced excitation of the lower regions. In these theories of increased radiation intensity, the rise of luminous matter appearing as a result of the discharge may play a large role (as was proposed by Payne-Scott, Yabsley, and Bolton (1947) to explain the temporary delays of “bursts” observed at different wavelengths). The rise of luminous matter may play a large role both because it can cause a local increase of the electric field and because of an increase in the radiating ability or in the solid angle subtended by the source.

The absence of correlation between “bursts” of radio-wave emission and chromospheric flares may possibly be due to the “polar diagrams of radio waves”; further study of the propagation of radio waves in the solar atmosphere above a sunspot may provide indications for clarifying this question, although their analysis will be very difficult.

10. THEORIES OF RADIATION FROM THE GALAXY

a) Source in the interstellar gas

Early observations of the radio emission of the Galaxy and failures in searches for analogous radiation from the Sun indicated that the emission of the Galaxy cannot be explained by the radiation of a large number of stars similar to the Sun. Calculations later based on studies of the Sun in fact showed that the radiation of the Galaxy is \(10^8\) times greater than what could be expected from such a source as the Sun. It was therefore necessary to conclude that the radiation comes either from stars with emission much greater than that of the Sun, or that it is radiation from the interstellar gas. Observations at visible wavelengths showed that the Sun is a typical star; therefore the early theories proceeded from radiation of the interstellar gas. Thus, Henyey and Keenan (1940), Van de Hulst (1945), Greenstein, Henyey, and Keenan (1946), and Shklovsky (1947) indicated that such an intensity could be expected at various wavelengths because of the radiation of electrons accelerated by the field of other charged particles of interstellar matter (“free-free” transitions); they assumed that the interstellar gas is ionized hydrogen at a temperature of \(10\,000^\circ\). These calculations agree well with observations at wavelengths shorter than 5 meters, but Townes (1947) showed that all the experimental data can be explained only by assuming that the temperature is at least \(10^5\) degrees.

At the same time, Woolley (1947) showed that, excluding the neighborhoods of young stars, the temperature of the interstellar gas, apparently, can reach only a value of the order of 1000°.

Subsequently Unzold (1948) came to the conclusion that the Galaxy is “optically thin,” since the dependence of the intensity of its radiation on direction is almost the same at all wavelengths in the wavelength range shorter than 7.5 m. Thus, complete absorption of a wave traveling a distance equal to the dimensions of the Galaxy is insufficient for an equilibrium to be established between the mean particle energy and the radiation, and the observed intensities can be explained by assuming only an electron temperature equal to at least \(10^5\) degrees, and an electron density of \(1.5\ \text{cm}^3\).

It follows from this that the explanation of the observed data as the result of radiation from interstellar gas encounters substantial difficulties. Therefore the discovery of discrete sources in the Galaxy not only demonstrates the existence of new sources of radiation in the Galaxy, but also suggests that these sources may explain all the radiation observed in the Galaxy. There is not yet a sufficient amount of experimental data that would refute the supposition that all the radiation of the Galaxy comes from discrete sources and that they are scattered everywhere in the Galaxy. Below are considered the theories that have been put forward to explain the radiation of such discrete sources.

b) The nature of the sources

Early observations of the source in the constellation Cygnus showed that the intensity of this powerful source, which has a small angular diameter, changes rapidly. It was therefore natural to conclude that this radiation comes from a star on which phenomena are observed analogous to sunspots and chromospheric eruptions (Hey, Parsons, and Phillips, 1948a).

Further investigations by Ryle and Smith (1948) showed that this radiation is hardly similar to the radiation of sunspots, since it is not circularly polarized. They therefore supposed that the radiation more closely corresponds to the radiation of the undisturbed Sun. The constancy of its mean value from day to day (apart from short-term fluctuations), observed over the course of 18 months from the two most intense sources, also showed that a mechanism similar to sunspot radiation is hardly plausible here *).

In the experiments of Bolton and Stanley (1948) and Ryle and Smith (1948) it was found that the angular diameter of the Cygnus source is less than 6 minutes.

) See the note to p. 556. (Translator’s note.*)

A calculation based on measurements of the parallax and the period of intensity fluctuations showed that its angular diameter is still considerably smaller (Ryle, 1949b). From a recent comparison of fluctuations in observations with two receivers separated from one another by 150–200 km, it follows that the greater part of these fluctuations is caused by refraction phenomena occurring relatively close to the Earth. However, one type of these fluctuations, usually in the form of an isolated burst lasting 20–30 seconds, coincides almost exactly at the two separated receivers. This indicates that, although some local phenomena—still not fully understood—cause fluctuations of the received signals, there is an additional type of fluctuation inherent in the radiation of the source itself. The existence of such short-term bursts of radiation from distant sources is of great importance, since it indicates that the dimensions of the source producing this component of the radiation do not exceed by much the distance traversed by an electromagnetic wave in 20 seconds. Thus, from these experiments it follows that the sources have the dimensions of stars.

In studies of the parallax of the sources Cygnus and Cassiopeia (Ryle and Smith, unpublished) it was found that the sources are at distances exceeding \(2 \cdot 10^{16}\) cm. An analysis carried out by Smith (unpublished), based on data on the relative intensity of the 25 most powerful sources considered below, showed that the distance to the nearest source is apparently comparable with the distance to the nearest visible star (of the order of \(3 \cdot 10^{18}\) cm).

Using the maximum value of the diameter, 20 light-seconds, given above, and the minimum distance of \(2 \cdot 10^{16}\) cm, it can be shown that the intensities observed at 3.7 m correspond to the emission of a source having a temperature of not less than \(10^{12}\) degrees (if it is assumed that the source is at the distance of the nearest known star, then this radiation corresponds to \(10^{14}\) degrees).

c) Mechanisms of the intense radiation of the sources.

It is now necessary to consider whether the various mechanisms proposed for explaining the intense radio emission of the Sun can be used to interpret the powerful radiation of discrete sources of radio emission in the Galaxy. Since none of the sources in the Galaxy has been identified with known visible stars, the only source providing information about their nature is the results of radio observations. Ryle (1949b) carried out such an analysis and showed that the electron density and magnetic field of a source are approximately the same as in the solar corona. He therefore came to the conclusion that the arguments advanced against the theory which assumes that the int–

intense radiation of the Sun is caused by coherent oscillations of a large number of electrons are applicable in the same way to the case of radiation from sources in the Galaxy. From this he concluded that the emission is caused by the chaotic motion of electrons having a mean energy of \(10^{10}\) electron-volts.

Following Alfvén (1937), Ryle then considered what electric fields should be expected in the atmosphere of a star having values of the magnetic field and rotational velocity considerably greater than those of the Sun. He showed that, on stars with a field of 5000 gauss and a surface velocity of \(2 \cdot 10^{7}\) cm/sec (as obtained by Babcock, 1947), the electric field is capable of producing radio emission \(10^{4}\) times more intense than the radiation of the Sun. Because of the nonlinear relation between the electron temperature and the electric field arising in stars whose dimensions exceed those of the Sun (see Section 9e), the intensity of the radio emission may be still greater.

Assuming that other stars, not yet visually observed, have somewhat larger values of rotational velocity and magnetic field than those observed by Babcock, one may conclude that in the regions responsible for the emission of waves of length 3.7 m, the mean electron energy is \(10^{10}\) electron-volts (corresponding to an electron temperature of \(10^{14}\) degrees). This electric field also accelerates protons and other positively charged particles, which acquire large energies, some of them being able to escape from the stellar atmosphere. Below, the supposition is discussed that discrete sources of radio waves are thus also responsible for the origin of cosmic rays (Ryle, 1949b).

The fact that none of the 30 sources observed in the northern hemisphere coincides with a visible star of large magnitude indicates the possibility of the existence of stars of a new type, in which the high temperature of the corona is compatible with a low brightness in the optical part of the spectrum *). The processes assumed to maintain the high temperature of the corona are not connected in this case with thermal sources of energy in the denser regions of the star.

Bolton, Stanley, and Slee (1949) recently proposed an alternative mechanism of radiation of a discrete source, pointing out that one of the sources, within the accuracy of the measurements, coincides with the position of the Crab Nebula. This object apparently consists of an expanding shell of gas ejected in a supernova outburst, and at present subtends an angle of 5 minutes. Assuming that the electron temperature of this body is of the order of \(2 \cdot 10^{6}\) degrees and that all its radiation reaches

) See also the note on p. 550. (Translator’s note.*)

Earth, it turned out that the intensity of the radiation observed at a wavelength of 3 m coincides with the value calculated in this way. However, the theory under consideration does not explain why intensity outbursts are observed simultaneously at two widely separated points. Moreover, it is evident that a theory based on the properties of unusual stellar bodies leads to difficulties in explaining the distribution of the observed sources.

d) Origin of the Continuous Radiation of the Galaxy

The number of sources detected so far has been limited by the sensitivity and resolving power of the apparatus. There is no doubt that improvement of the apparatus will lead to the discovery of a larger number of sources. It is important, however, to establish whether the continuous radiation of the Galaxy is caused by a large number of discrete sources scattered throughout the Galaxy, the nearest of which are resolved at the present time, or whether there is also a contribution made by the radiation of interstellar gas.

From measurements of the radiation intensity at wavelengths of 1.4, 3.7, and 6.7 m for the two principal sources (Ryle and Smith, unpublished), a dependence of intensity on wavelength has been obtained which coincides with the dependence obtained for the general background of the Galaxy. Therefore one may suppose that the background radiation of the Galaxy is the result of the radiation of analogous discrete sources, if the total number of these sources, scattered throughout the entire Galaxy, is sufficiently large.

In the northern hemisphere, as has already been indicated, 30 sources have been detected, the angular distribution of which does not correspond to the general structure of the Galaxy. These results show that the distances to these sources are considerably smaller than the dimensions of the Galaxy. Therefore the total number of sources may be sufficiently large to explain the intensity of the background radiation.

At the same time it has been found that the ratio between the radiation intensities of the most powerful source and the radiation intensity of the entire sky is, in order of magnitude, equal to the ratio of the intensity of the brightest star to the total intensity of the visible stars over the whole sky.

Although this result cannot yet be regarded as decisive, it shows, taking into account chiefly the difficulties that arise in using mechanisms of interstellar-gas radiation, that further analysis of the data obtained is necessary.

Assuming that the entire radiation background is caused by discrete sources, one can calculate their distribution in space by analyzing the ratio of the intensity of each of the known sources to the total integral intensity of the radiation of the entire

of the northern hemisphere. Starting from the available limited amount of experimental data, Smith (unpublished) carried out the following calculation, based on a simple model. He assumed that the Galaxy is spherical (has radius \(R\)) and that sources of identical intensity are uniformly and chaotically distributed in it. If the mean density of the sources is \(\rho\), then the ratio of the energy \(P_n\), received from the \(n\)-th most intense source, to the energy \(P_t\), received from all sources (from the total background of the Galaxy), is equal to

\[ \frac{P_n}{P_t}=R^{-1}(36\pi\rho)^{-1/3} n^{-2/3}. \]

If one now plots \(P_n^{-3/2}\) as a function of \(n\), a straight line is obtained, whose slope makes it possible to find

\[ \frac{R\rho^{1/3}}{P_t}. \]

Since \(P_t\) can be measured, \(\rho\) is determined if \(R\) is known. Before describing the results of this calculation, let us discuss the simplifications made in it.

1) It is clear that in any real model the density of the sources will be a function of distance and direction. However, since only very nearby discrete sources have been detected, it may be assumed that \(\rho\) is constant throughout the region containing the observed sources. On the other hand, the intensity of the background will depend appreciably on the distribution of sources in the Galaxy.

If the density of the source at the point \((r,\theta,\varphi)\) is given as \(\rho_0 f(r,\theta,\varphi)\), where \(\rho_0\) is the density of sources in the vicinity of the solar system, then at the point of observation the intensity of the radiation received from a small element of space is equal to

\[ A\,\frac{\rho_0 f(r,\theta,\varphi)\, r^2 \cos\theta \, d\theta \, d\varphi \, dr}{r^2}, \]

where \(A\) is the emission per unit solid angle from a unit source.

The total received radiation intensity from the whole Galaxy is equal to

\[ A\rho_0 \iiint f(r,\theta,\varphi)\cos\theta\, d\theta\, d\varphi\, dr. \]

This intensity can be equated to the total intensity from a spherical Galaxy of radius \(R\) with a homogeneous density distribution \(\rho_0\), equal to

\[ 4\pi A\rho_0 \int_0^R \frac{r^2 dr}{r^2}=4\pi A\rho_0 R. \]

Thus, if \(f(r,\theta,\varphi)\) is known, \(R\) can be determined from the relation

\[ 4\pi R=\iiint f(r,\theta,\varphi)\cos\theta\, d\theta\, dr\, d\varphi. \]

Experiments have shown that the angular distribution of the intensity of the radiation of the Galactic background fully corresponds to the structure of the Galaxy obtained from optical observations. It is therefore quite legitimate to assume that the intensity distribution of the radio-wave sources coincides with the distribution of visible stars, and, by calculating \(f(r,\theta,\varphi)\) for visible stars, one can determine \(R\).

2) In the preceding discussion it was assumed that all sources are of the same size. The presence of a large range of values of the sizes of the sources modifies the assumed distribution.

Until there is a more complete theory of the emission of discrete sources, it is impossible to predict what range of variation of these values is possible. However, it can be shown that even if there exists a large range of values, such as for visible stars, the mean value of the distance between sources will vary by no more than a factor of order 10. Therefore one can calculate, to order of magnitude, the value of this distance without knowing the range of absolute values of the sizes of the sources.

Fig. 18. The behavior of \(P_n^{-3/2}\) as a function of \(n\) for the 25 most intense sources observed in the Northern Hemisphere (\(P_n\) is the energy value received from the \(n\)-th source, expressed in \(10^{-24}\ \mathrm{watt}/\mathrm{m}^2\,\mathrm{cycles}\)).

In carrying out an analysis of the experimental data it is also important to take into account the limiting value of the solid angle covered by the antenna system. In the observations considered, its coverage was limited to the northern hemisphere. The result of constructing the graph of the dependence of \(P_n^{-3/2}\) on \(n\) for the 25 most intense radio stars observed in the northern hemisphere at the wavelength

3.7 m, is shown in Fig. 18. From the slope of this graph, the measured value \(P_t\), and the approximate value of \(R\), calculated by the method described above (1000 parsecs), it was found that the mean density of the sources is of the order of three per cubic parsec. This density corresponds to a mean distance between sources of the order of 0.7 parsec \((2 \cdot 10^{18}\ \mathrm{cm})\), i.e., to a number comparable with the mean distance between visible stars*).

Despite the fact that the analysis carried out is based on still very limited experimental material, one may nevertheless conclude that the available observations are consistent with the view that the background radiation of the Galaxy is caused by the emission of sources similar to those observed in the constellations Cygnus and Cassiopeia, and that these sources are distributed in the Galaxy with a density comparable to the density of the distribution of visible stars.

The theory of the radiation of the Galaxy as radiation of interstellar gas accounts for only about 1% of the observed intensity. Therefore, the theory of the summation of the radiation of discrete sources is more suitable. It may be hoped that further experimental work will make it possible to obtain more definite conclusions concerning these two mechanisms. One possible way of verifying the existence of radiation from interstellar gas is the precise determination of the angular distribution of intensity at different wavelengths. If the radiation is caused by interstellar gas, then the large values of the effective temperature observed at long wavelengths (10 m) in the direction of the center of the Galaxy can be explained if the optical thickness has an appreciable value at these wavelengths. But then the total absorption through the entire thickness of the Galaxy is too large for the intensity to be directly proportional to the thickness of the interstellar gas. On the other hand, at shorter wavelengths the effective temperature is considerably smaller; this shows that the optical thickness is also small. Therefore the angular variation of the intensity at short wavelengths will be directly determined by the thickness of the interstellar gas in different directions. The angular distribution of intensity at longer wavelengths will depend directly on the thickness of the interstellar gas in those directions where it is small, while in directions close to the center of the Galaxy one should expect a relatively lower intensity. Therefore precise experi—

) In paper ² I. S. Shklovsky estimated the density of radio stars by another method. He also estimated their mass, luminosity, and temperature, and found that the mean density of radio stars is somewhat greater than one per parsec and that they are distributed fairly uniformly in the vicinity of the Sun. Further, I. S. Shklovsky assumes that the mean mass of radio stars must be less than 0.05 of the mass of the Sun and that they occupy an intermediate place between dwarf stars and planets, their surface temperature being 1000–2000 degrees. (Translator’s note.*)

mental comparison of the angular variation of the intensity at the longer wavelength and at the short wavelength may decide the question of whether radiation from interstellar gas exists.

This question can be resolved by measuring the dependence of the intensity on wavelength in two directions: in the direction of the center of the Galaxy and in the direction of its pole. Both experiments are very difficult, since in order to determine accurately the true value of the intensity in the direction of the center of the Galaxy, a high resolving power of the apparatus is required. Likewise, in order to prove that the Galaxy absorbs appreciably, measurements are necessary at least at a wavelength of 10 m. Therefore antennas of large size are required for these experiments.

11. FUTURE DEVELOPMENT OF RADIO ASTRONOMY

a) Study of the solar atmosphere

It has already been pointed out that the development of astronomical observations at radio wavelengths is a consistent method for investigating regions of the universe with a low density of matter. Existing experimental methods have already shown the possibility of studying the structure of the solar corona and, although the theoretical interpretation of these results is still not sufficiently complete, there is no doubt that the acquisition of new data will be of fundamental importance for understanding a number of phenomena.

One of the most important results of existing theories is that each given region of the solar atmosphere emits radio waves in a limited range. Therefore observations at a given wavelength make it possible to draw conclusions concerning the conditions existing in the region whose electron density can be calculated. By carrying out simultaneous observations over a broad range of radio waves, it is therefore possible gradually to construct a complete picture of the temperature distribution at all heights of the solar atmosphere with an accuracy that is in no way comparable with the accuracy of observations in the visible wavelength range. This possibility is the result of the properties of a fully ionized atmosphere in the radio range.

Carrying out these observations under conditions of a disturbed state above sunspots will provide important information about the phenomena involved in the formation of prominences, chromospheric flares, and corpuscular streams.

Investigation of the properties of radiation during the rotation of electrons in a magnetic field shows that energy can propagate only in regions where the magnetic field increases. Above a sunspot, a negative gradient of the magnetic-field strength leads to the emission from each region being directed downward,

i.e., on the photosphere. The back pressure of the radiation on the radiating electrons may reach a value equal to the gravitational attraction of the hydrogen atom (Ryle, 1948). A more detailed analysis of these phenomena and a study of the electric fields that may arise in the neighborhood of sunspots will be able to shed light on questions connected with the cooling of the photosphere in sunspots and with the occurrence of prominences.

b) Study of stellar envelopes

At the present time, radio observations of individual stars are limited by the poor resolving power and sensitivity of the apparatus. Investigations have shown that some objects, none of which is as yet definitely associated with a known visible star, but which have stellar dimensions, are capable of emitting radio waves whose intensity corresponds to a temperature of \(10^{14}\) degrees *).

Theoretical investigations of the intense radio emission of the corona are greatly aided by the results of measurements obtained in the optical region. However, since radio stars are not identified with visible stars, theories describing the nature of the sources are forced to be based only on the results obtained from these same radio observations. Detailed studies of the two principal discrete sources of radio emission in the Galaxy have made it possible to calculate the maximum density of the emitting region—a number was obtained comparable with the value of the density of the solar corona.

Applying the arguments used in theories of the emission of the solar corona, one arrives at the conclusion that the intensity of the radiation of the Galactic sources indicates the existence of a mean electron energy of at least \(10^{10}\) electron-volts.

The existence of mechanisms capable of maintaining such an order of magnitude of the mean electron energy in the atmospheres of stars is important not only because it bears on the question of the origin of cosmic rays, but also in connection with the question of the structure of the atmosphere of visible stars. Although the absence of a correlation between the intensity of the sources and bright visible stars shows that some bodies emit anomalously intense radio waves, calculations based on the total radiation of the Galaxy nevertheless show that these sources are not unusual bodies, but bodies in which

) It must be emphasized that the question of the sizes of discrete sources cannot yet be considered clarified to any extent, since direct measurements show only that the angular size of the most intense sources is less than several minutes. The question of the mechanism of the radiation of the sources is also completely unclear, and the author’s conclusion that what is involved here is the thermal radiation of relativistic electrons is no more than a hypothesis. (Reviewer’s note.*)

the ratio of radio emission to the emission of visible light is simply greater than in known stars. Analogously to what takes place on the Sun, the high temperature in the atmosphere of a star is hardly due to the same mechanism that governs the temperature of the photosphere. A number of difficulties arising in the study of some visible stars may possibly be resolved as a result of clarifying the details of the corresponding mechanism from investigations of the intense radio emission of discrete sources.

c) Origin of cosmic rays

Models for the formation of electric fields in the atmosphere of rotating magnetized bodies have been considered by several authors (Swann, 1933; Alfvén, 1937; Babcock, 1948) in connection with the question of the generation of cosmic rays. These models were also discussed (Ryle, 1949b) in connection with the question of intense radio emission from stellar atmospheres*). It was shown that stars having the characteristics measured in the optical region (Babcock, 1947) are capable of emitting radio waves with an intensity at least \(10^4\) times greater than the intensity of the Sun’s radiation.

Assuming that some stars have magnetic fields and rotational velocities several times larger, it was shown that the observed intense emission of radio waves can be explained as the acceleration of charged particles to cosmic-ray energies. It was therefore suggested that the discrete sources of radio emission in the Galaxy may be responsible for the origin of primary cosmic rays. This possibility for the origin of cosmic rays was also pointed out by Denisse (1949b) and Unsöld (1949).

Observations of heavy particles in the primary radiation (Freier, Lofgren, Ney, and Oppenheimer, 1948) indicate that cosmic rays are formed as a result of the acceleration of charged particles by electric fields, while recent observations by Auger, Dodd, Denisse, and Dolan (1949) convincingly showed that the source of the primary cosmic-ray radiation is in fact located in the Galaxy. In these experiments primary particles of high energy were observed, and it was found that their intensity changes appreciably over sidereal days; these changes agree well with the angular distribution of the intensity of the general background of radio emission from the Galaxy.

) It should be noted that in later works the suggestion was discussed that the radio emission of the Galaxy is the bremsstrahlung of relativistic electrons in interstellar magnetic fields. In this connection V. L. Ginzburg \(^{3}\) came to the conclusion that, under certain conditions, the total radiation of the Galaxy can be fully explained by such a mechanism. On the question of the origin of cosmic rays, see the review by Ya. P. Terletsky \(^{20}\). (Translator’s note).*

d) Structure of the Galaxy

Along with studies of the nature of the sources themselves, important information about the general structure of the Galaxy can be obtained. Because visible waves are absorbed by dust particles, some regions of the Galaxy are inaccessible to observation even with the experimental equipment currently available, which leads to inaccurate mapping of distant regions. Radio waves, however, undergo negligibly small absorption in dust, and even with the resolving power of the apparatus now achieved, accurate measurements of the angular distribution of the intensity of radio emission can yield important information on the structure of the Galaxy. Such attempts have already been made (Hey, Parsons, and Phillips, 1948a; Northcott and Williamson, 1948); however, since in these works the radiation of the principal sources of the Galaxy was not taken into account, they are unlikely to give an accurate distribution of the background of the Galaxy.

In conclusion, it may be said that the available data on the radio emission of the Sun and the Galaxy should be regarded only as preliminary material on this question. The limitations of sensitivity and resolving power of the existing apparatus are not fundamental, and the development of more advanced apparatus will appreciably increase the amount of available data. At the same time, it is to be hoped that, as a result of further theoretical work, the difficulties arising in considering the various processes occurring in regions of low density will be clarified.

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Additional Literature

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