ON THE MEASUREMENT OF ANGULAR DIAMETERS OF DISCRETE SOURCES OF COSMIC RADIO EMISSION

Since 1946, when the first discrete sources of cosmic radio emission were discovered, more than two hundred discrete sources have already been found. Until now, however, the nature of the radio emission of these peculiar celestial objects remains unclear. In order to elucidate the true mechanism responsible for the radio emission of discrete sources, the latter must first of all be identified with one or another visible celestial object. It is obvious that this problem reduces to as precise a determination as possible of the coordinates and angular dimensions of the sources. In recent years several attempts have been made to measure the angular diameters of some of the most prominent discrete sources. These measurements proved unsuccessful in the sense that, because of the relatively low angular resolving power of the radio interferometers used—of the order of several arcminutes at meter wavelengths—even for the most powerful sources, lying in the constellations Cassiopeia, Cygnus, and Taurus, only an upper limit to the angular dimensions was found.

Recently Mills¹ and Smith², who worked with specially constructed radio interferometers, succeeded in measuring the angular diameter of several of the largest sources.

The radio interferometers used in¹˒² are based on the modulation method of measuring the radio emission of discrete sources, first described and used by Ryle³. The operating principle of the modulation radio interferometer proposed by Ryle is as follows. Two antennas (see Fig. a), separated by a distance considerable in comparison with the wavelength of the received radio emission, work into a common receiver. The directional pattern of such an antenna system consists of a multitude of separate lobes, the width of the central lobes of the pattern being of the order of

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

where \(d\) is the distance between the antennas. If the electrical lengths \(l_1\) and \(l_2\) of the cable sections connecting the receiver with the left and right antennas of the interferometer are equal, then at \(\theta = 0\), obviously, there must be a maximum of the directional pattern. Conversely, if

\[ |l_1 - l_2| = \frac{\lambda}{2}, \]

then at \(\theta = 0\) there must be a minimum of the pattern. A special switch periodically, with a frequency of several tens of hertz, inserts a cable section of length

\[ \frac{\lambda}{2} \]

into one of the arms of the interferometer. From what has just been said it follows that the receiving directional pattern …

will, with the same frequency, be periodically shifted by half of one of its lobes, so that the maxima of the radiation pattern will be replaced by minima and vice versa over a time equal to the half-period of modulation. As a result, the signal from a “point” source (i.e., from a source whose angular width is \(\ll \frac{\lambda}{d}\)) located in the zone of the receiving directional pattern, arriving from the antenna device of the interferometer into the receiver, proves to be amplitude-modulated at this same frequency, i.e., at the frequency at which the “phase switch” operates. The input

Schematics of radio interferometers used for measuring the angular dimensions of radio-emitting cosmic objects:
1 — phase switch, 2 — high-frequency amplifier, 3 — square-law detector, 4 — low-frequency amplifier, 5 — balanced detector, 6 — recorder, \(МП\) — modulation receiver, 7 — high-frequency splitter, 8 — delay line, \(П\) — receiver, 9 — converter, 10 — auxiliary transmitter for phase control, \(\Phi_1\) and \(\Phi_2\) — band-pass filters, 11 — correlator.

high-frequency amplification stage of the receiver equally amplifies both the useful (modulated) signal and the internal noise connected to it. After the square-law detector following the amplifier, the alternating current of the modulation frequency, whose amplitude is proportional to the intensity of the received radio emission, is amplified by a low-frequency narrow-band amplifier and then passes into the “balanced detector.” The magnitude of the constant current produced by the balanced detector, which turns out to be proportional to the intensity of the useful signal entering the antenna, is recorded by a self-recording galvanometer. The sign of the current (and consequently the sign of the deflections of the recorder pen) is deter-

is a sign of the phase difference of the low-frequency signals (one of which is auxiliary and is fed to the “balanced detector” directly from the “phase switch”), supplied to the “balanced detector,” i.e., depends ultimately on the position of the radio-emission source relative to the lobes of the directional pattern of the antenna device.

When the radio-emission source is displaced in the zone of the lobes of the directional characteristic (for example, because of the diurnal rotation of the Earth), the recorder pen describes a wavy line. The maximum deviations of the recorder correspond to the case when, during the operation of the “phase switch,” the source alternately falls into the maxima and into the minima of the directional pattern. Conversely, in the case when the source is located in that part of one of the lobes of the pattern which, when the entire pattern is shifted in space by half the lobe width, is answered by the point symmetric to it in the same or in the adjacent lobe, the recorder deflections must be minimal (not equal to zero only because of fluctuations caused by the noise of the apparatus or because of the presence of other radio-emission sources, say, the total radio emission of the Galaxy*).

Up to now it has been assumed that the radio emission comes from a source whose angular dimensions are much smaller than the width of the lobe of the directional pattern (a “point” source). An elementary calculation shows that, if the finiteness of the angular dimensions of a source having the form of a uniformly luminous rectangular strip of width \(2\Delta\theta\) is taken into account, the interference pattern recorded on the recorder tape will have the same character as for a “point” source of the same intensity; however, the amplitude of the variable component of the record in the second case will be

\[ \frac{\sin\left(\frac{2\pi d}{\lambda}\Delta\theta\right)} {\frac{2\pi d}{\lambda}\Delta\theta} \]

smaller than for a “point” source**).

Knowing the ratio of the amplitudes of the variable components of the recorder records obtained for two different distances between the interferometer antennas, it is evidently possible to find the angular width of the source \(2\Delta\theta\).

In comparison with the interferometers previously used for measuring the coordinates and angular dimensions of discrete radio-emission sources, the modulation interferometer described has a number of undoubted advantages: 1) Its use makes it possible practically almost completely to exclude the total radio emission of the Galaxy, which, when measuring the radio emission of discrete sources, is an undesirable (interfering) background. The output instruments of the receiving installation in this case record only the intensity of that Fourier component of the angular distribution of the intensity of cosmic radio emission over the sky whose angular period is of the order

\[ \frac{\lambda}{d}. \]

In practice,

\[ \frac{\lambda}{d} \]

is usually \(\lessgtr 10^{-2}\). The intensity of the Fourier component of the distribution of radio-emission density (even in the region of the Milky Way, where the “radio brightness” changes most sharply and capriciously) at wavelengths

*) It is customary to say that in this case the source (target) is in the “equosignal zone.”

**) For a source in the form of a circular, uniformly luminous disk this factor should be replaced by

\[ \frac{I_1\left(\frac{2\pi d}{\lambda}\Delta\theta\right)} {\frac{2\pi d}{\lambda}\Delta\theta}, \]

where \(I_1\) is the first Bessel function.

of the meter range, at which discrete sources are usually observed, is, as a rule, much less than the intensity of the source and can be further reduced by increasing the distance between the antennas of the interferometer. 2) An important advantage of the modulation interferometer is its high sensitivity, which makes it possible to detect with its aid very weak sources whose radio-emission intensity is only \(10^{-3}\) of the noise level of the receiving apparatus (modulation gain). 3) To compensate for the attenuation undergone by the signal in the cable sections connecting the antennas and the receiver, in interferometers fairly high-gain auxiliary amplifiers are used, installed directly at the output of the interferometer antennas. It is significant that the difference in the amplification coefficients of these auxiliary amplifiers, placed in the left and right halves of the modulation interferometer, practically does not affect the amplitude of the variable component of the recorder trace, i.e., ultimately, the accuracy of measuring the angular dimensions of radio-emitting objects. In addition, as has already been noted, according to Ryle the angular size of a source must be found from the ratios of the amplitudes of the recorder traces corresponding to two different values of the distance \(d\) between the antennas of the interferometer. It turns out that this ratio depends only on the value of the angular size of the radiating object and does not depend on the coefficients of directional action of the interferometer antennas, owing to which it is possible to use antennas with different directivity coefficients. According to Ryle, who with the aid of the modulation interferometer described measured the coordinates of discrete sources of cosmic radio emission and the angular dimensions of radio-emitting sunspots at wavelengths of 1.4, 3.7, 6, 7 and 8 m, the angular resolving power of such a device can comparatively easily be brought to \(0.15 \dfrac{\lambda}{d}\).

The main structural difference between Smith’s modulation radio interferometer (see Fig. 6), used by him to measure the angular diameters of the two most powerful discrete sources in the constellations Cygnus and Cassiopeia, and Ryle’s interferometer described above consists only in the fact that it uses three receiving antennas, the two outer antennas being fixed, while the middle one can move between them and operate in a pair with either the left or the right antenna[^2]. The directivity coefficients (d.c.) of antennas \(A_1\) and \(A_2\) are equal and should not change during the measurement process, which, however, is not difficult to achieve, since antennas \(A_1\) and \(A_2\) are fixed. The d.c. of the movable antenna \(A_3\) is arbitrary with respect to the d.c. of antennas \(A_1\) and \(A_2\). The three antennas in the combinations \(A_1—A_3\) and \(A_2—A_3\), together with the modulation receiver, form two interferometers with corresponding baselines \(d_1\) and \(d_2\). If, at some fixed position of \(A_3\), one records the radio emission of a discrete source with the aid of both interferometers and takes the ratio of the amplitudes of the recorder traces corresponding to the baselines \(d_1\) and \(d_2\), then, as already indicated, the latter does not depend on the value of the d.c. of antenna \(A_3\), but is determined only by the diameter of the source.

With the aid of the interferometer described, Smith measured the angular diameters of discrete sources in Cassiopeia and Cygnus at \(\lambda = 3.7\) and \(1.43\) m, but he succeeded in making measurements only at \(\lambda = 1.43\) m. The distance \(d = d_1 + d_2\) between the outer antennas of the interferometer was \(430\lambda\). The angular width of the central lobes of the directional pattern was then \(8'\). The measurements showed that the angular diameter of the sources in Cassiopeia and Cygnus is appreciable. For the source in Cassiopeia, \(5.55' \pm 0.2'\) was found, and for the source in Cygnus, \(3.6' \pm 0.3'\). These figures are, of course, conditional, since they were obtained on the assumption that the sources are circular uniformly luminous disks. More definite data on their dimensions can in this case be obtained only with detailed knowledge of their shape and of the distribution of surface radio brightness.

An extremely important circumstance, shedding light on the question of the nature of discrete sources of cosmic radio emission, is that at the place where the source in Cassiopeia is located there has been found a gaseous nebula of approximately circular form with an angular diameter of \(\sim 5'\), having a complex fibrous structure. The latter indicates that the discrete sources of radio emission are apparently connected with nebulae.

Mills, on the basis of the results of his measurements, a brief description of which is given below, also comes to the conclusion that discrete sources are connected with nebulae. A simplified diagram of the interferometer with which Mills experimented is given in Fig. 6. As in Smith’s interferometer, the apparatus described has three antennas. Registration of the radio emission is carried out simultaneously by two completely identical receivers. The apparatus as a whole consists of two simultaneously operating interferometers with baselines \(d_1 = 60\) and \(d_2 = 270\) m. The measurements were made at \(\lambda = 3\) m. The angular spacing of the interference lobes corresponding to the baselines \(d_1\) and \(d_2\) is equal, respectively, to \(3^\circ\) and \(40'\).

Knowing the ratio of the amplitudes of the recordings of the interference patterns when a source passes through the many-lobed diagrams corresponding to the larger and smaller baselines of the interferometer, one can, as follows from what was said above, determine the angular diameter of the source. Having measured, as accurately as possible, the coordinates of six discrete sources, Mills identified four of the strongest of them, located in the constellations Cygnus, Taurus, Centaurus, and Virgo, with nebulae. The source in Cygnus, as it turned out, is located near a weak extragalactic nebula with coordinates \(\alpha = 19^h 57^m 44.6^s\) and \(\delta = 44^\circ 35.7'\). As for the sources in Taurus, Centaurus, and Virgo, as was already reported in УФН4, they were identified by Bolton and Stanley with the nebulae M1 (the “Crab” nebula), N. G. C. 5128, and N. G. C. 4486. The results of Mills’s measurements confirm this conclusion (the coordinates of these sources were measured by him with an accuracy of \(1 \div 2'\)). The angular resolving power of Mills’s radio interferometer in determining the angular dimensions of a source was small (of the order of \(10'\)). In this connection he succeeded in measuring angular diameters only for the two largest sources, located in the constellations Centaurus and Puppis (\(\sim 20'\)).

The works being reviewed\(^{1,2}\) are, so far as we know, the first works whose authors succeeded in measuring the angular dimensions of certain discrete sources and thereby proving that these objects are nebulae and not stars. Quite recently there appeared three new short and, at the same time, very interesting communications belonging to different authors and united by the common title “Angular dimensions of discrete radio-emission sources.”\(^{5}\) This article contains new data on the dimensions of some discrete sources, their form, and the distribution of “surface radio brightness.”

In Cambridge, Smith, at \(\lambda = 1.43\) m, made measurements of the distribution of “radio brightness” in the discrete sources Cassiopeia and Cygnus, using for this purpose the modular radio interferometer described above (Fig. 6), already used in \(^{2}\). By changing, in the course of the measurements, the distance between the antennas of the interferometer from zero to \(400\lambda\), he obtained the dependence of the amplitude of the Fourier component \(A(\omega)\) of the distribution of “radio brightness” on the distance between the antennas or, what is the same thing, on the angle characterizing the period and the cyclic frequency \(\omega\) corresponding to the harmonic component of the distribution. The required angular distribution of “radio brightness” \(I(\theta)\) is, obviously, Fourier-conjugate to \(A(\omega)\), so that

\[ I(\theta) = \int_{0}^{\infty} A(\omega)\cos(\omega\theta + \varphi_\omega)\,d\omega, \]

where \(\varphi_\omega\) is the phase of the corresponding harmonic component corresponding to the frequency \(\omega\). For a number of reasons the authors\(^5\) were unable to find \(\varphi_\omega\). If, however, one assumes that \(I(\theta)\) is a symmetric function of \(\theta\), then \(\varphi_\omega = 0\), and \(I(\theta)\) can be constructed knowing only \(A(\omega)\). The spectra \(A(\omega)\) found by Smith proved to be close to those which should have been obtained under the assumption that the sources in Cygnus and Cassiopeia are “uniformly luminous” disks with diameters of 3.5′ and 5.5′, respectively. The latter, as follows from what was set forth above, agrees with the results obtained earlier.\(^2\)

In the second note Mills reports the results of measurements of the angular sizes of four discrete sources at \(\lambda = 3\) m, carried out in Sydney. The scheme of the interferometer he used is shown in Fig. 2.

An interesting and important feature of this device is that it has no electric cable connecting the antennas. The connection between the interferometer antennas is effected by wireless retransmission of the high-frequency signal received by one of the antennas, with the aid of an auxiliary transmitter-converter, to a receiver located in the immediate vicinity of the other antenna and connected to it through a delay circuit which delays the signal by a time equal to the time of propagation of the signal in free space between the antennas of the interference device. The absence of a connecting cable makes it possible to increase the distance between the antennas almost without limit. In the experiment described this distance was brought up to 10 km, which corresponded to the width of the interference lobe

\[ \frac{\lambda}{d} \sim 0.1'. \]

Mills, like Smith, determined the spectrum of the angular distribution of the intensity of radio emission, and then found the distribution itself and calculated the effective sizes of the sources, the values of which are given in the table below.* Mills points out that the discrepancy between the value of the radio diameter of the source in Centaurus (\(\sim 20'\)) given in\(^1\) and the value given in the table (6′) is due to the fact that in the table, in accordance with the definition of “effective size,” the diameter of the brightest central part of the source is given.

In exactly the same way one may try to explain the discrepancy between the tabulated value of the diameter of the source in Cygnus (\(\sim 1'\)) and the number appearing in Smith (3.5′).\(^2\) In addition, a similar discrepancy between the values of the radio diameter may also be connected with the fact that the sources in Cygnus and Centaurus do not possess circular symmetry, and in\(^1,2\) and\(^5\) their sizes in different directions are discussed. With respect to the source in Cygnus, the latter is confirmed by the observational materials of Brown et al. cited in\(^5\). Observing at \(\lambda = 2.4\) m the sources in the constellations Cygnus and Cassiopeia at different times of day, i.e. for different positions of the plane of polarization of the receiving antenna of the interferometer, these authors found that the source in Cassiopeia

* The “effective angular size” is defined in this case as the angle between the half-values of the surface radio brightness.

has an approximately circular shape, whereas the source in Cygnus resembles an ellipse with an axial ratio of \(\sim 4\). The radio diameter of the source in Cassiopeia turned out to be \(4'\), and the greatest dimension of the source in the constellation Cygnus \(2'10''\). The scheme of the radio interferometer with which these results were obtained is shown in Fig. 6. As in the Michelson interferometer just described (Fig. 2), it has no cable connecting the antennas. The interferometer described differs advantageously from the Michelson interferometer in that the radio link between its antennas is used as a means for transmitting the low-frequency components (of the order of several thousand hertz) of the spectrum of the radio emission under investigation. The principle of operation of the interferometer is, in brief, as follows. The radio emission arriving at antennas \(A_1\) and \(A_2\) is received by two independent, but completely identical, receivers. At the output of the band-pass filters \(\Phi_1\) and \(\Phi_2\), whose pass band extends from \(10^3\) to \(2 \times 10^3\) Hz, there exist random time-dependent voltages \(V_1(t)\) and \(V_2(t)\), corresponding to a narrow (of the order of \(10^3\) Hz) portion of the spectrum entering the receiving antennas. In the case when antennas \(A_1\) and \(A_2\) are located side by side, the functions \(V_1(t)\) and \(V_2(t)\), obviously, must be identical. As the distance \(d\) between the antennas is increased, the correlation between \(V_1(t)\) and \(V_2(t)\) decreases, and at

\[ d=\frac{\lambda}{\theta}, \]

where \(\theta\) is the angular width of an equivalent source with constant “surface radio brightness,” it disappears completely. The latter, as is easy to show, means that the path-length differences between rays drawn from the “centers of gravity” of the two halves of the source to the points where the interferometer antennas are located differ by

\[ \frac{\lambda}{2}. \]

As a result, since different parts of the source oscillate completely independently, there is no correlation between the signals arriving at antennas \(A_1\) and \(A_2\), and consequently between \(V_1\) and \(V_2\), in this case (it is sometimes said that the “condition of coherence” is violated). The device described is more reliable in operation and permits measurements with greater accuracy than can be done by means of the Michelson interferometer, the principal source of errors in which is the instability of the phase of the high-frequency signal retransmitted from one of the antennas to the receiver.

The faint peculiar nebula identified with the discrete source in Cygnus is extragalactic. The brightest part of the nebula, with a size of \(\sim 3\frac{1}{4}'\), is surrounded by a more rarefied envelope with a diameter of \(\sim 2'\). The gaseous nebula in Cassiopeia has, as already noted, an approximately circular form. The diameters of the nebula and of its bright central part are respectively \(5'\) and \(1.5'\). Apparently the nebula N. G. C. 5128, identified with the source in Centaurus, is also an extragalactic object. This source, as indicated above, has considerable angular dimensions. The latter is reflected, in particular, in the character of the fluctuations of the intensity of the radio emission associated with the diffraction of the radio emission on ionospheric inhomogeneities. For the source in Centaurus these fluctuations are noticeably smaller than for other discrete sources having a smaller angular diameter[^1].

The nebula M1, which is the result of the supernova outburst of 1054 and with which the source in Taurus is associated, is an object of our Galaxy.

The coordinates of the center of the source differ slightly from the coordinates of the center of the nebula. The radio diameter of the source (\(\sim 4'\)) is approximately equal to the visible dimensions of the nebula (\(\sim 4 \div 5'\)).

The works whose contents have been set forth above, of course, do not exhaust the question of the angular dimensions of discrete sources, if only because at the present time angular diameters have been measured only for a few of the most outstanding sources. Nevertheless, already now

it is clear that the hypotheses concerning the connection of discrete sources with objects of stellar type are apparently untenable. The discrete sources of cosmic radio emission are not “radio stars,” but rather “radio nebulae.” Since this is so, the possibility is eliminated of reducing all, or in any case the greater part, of the observed cosmic radio emission to the aggregate emission of discrete sources, since otherwise it would be necessary to assume that the number of “radio nebulae” in the Galaxy is at least an order of magnitude greater than the number of nebulae found in it. This means that, in addition to the radio emission of discrete sources, there must exist a general radio emission of the Galaxy, for which the interstellar medium is responsible.

Not being able to discuss in detail the question of the nature of cosmic radio emission, we shall merely point out that the most probable mechanism responsible both for the radio emission of discrete sources and for the general radio emission of the Galaxy is the mechanism of bremsstrahlung radiation of relativistic electrons moving in weak interstellar and circumstellar magnetic fields \(H \sim 10^{-4} \div 10^{-6}\) gauss\(^7\).

G. G.

References

1. B. Y. Mills, Austr. Journ. Sci. Res. 5, 456 (1952).
2. F. G. Smith, Proc. Phys. Soc. 65, 971 (1952).
3. M. Ryle, Proc. Roy. Soc. 211A, 351 (1952).
4. G. G. Getmantsev, UFN 44, 527 (1951).
5. R. H. Brown, R. C. Jennison and M. K. Das Gupta, B. Y. Mills, F. G. Smith, Nature 170, 1061 (1952).
6. I. S. Shklovskii, Astronomicheskii Zhurnal 29, 418 (1952).
7. V. L. Ginzburg, DAN 76, 377 (1951).