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4. Limiting Factors and Characteristics of the RATAN  
 

4.1. Theoretical Sensitivity of the Radio Telescope and the Problem of Attaining it in Practice

The 7.6-cm radiometer described above definitely has very good characteristics; the amplifier itself has a noise temperature of approximately 10 K and a bandwidth of 500 MHz. Therefore, the problem of actually obtaining these characteristics in practice was particularly acute. The problem was divided into the "internal" (or engineering) problem of achieving the highest possible sensitivity (lowest possible noise); the problem of actually obtaining this sensitivity from the radio telescope-radiometer system with short integration times; and, finally, the problem of obtaining the maximum possible sensitivity in the essentially unknown field of studying extended regions of the sky at surface brightness levels of 1 mK or flux densities of 1 m Jy.*

In Experiment Cold, we dealt with all of these problems. We shall now list the limiting factors:

(1) receiver noise and front end losses in the radiometer;
(2) the contribution to the antenna noise temperature due to radiation from the ground;
(3) instabilities in the receiver, which lead to variations in the noise temperature or the transmission coefficients;
(4) variations in the contribution of the radiation from the ground and the input waveguide (due to ambient temperature variations, for example);
(5) variations in the atmospheric emission;
(6) the influence of spatial sky noise (from very weak, unresolved sources √ "confusion noise") and low-level interferences from very strong sources (the Sun);
(7) interference from the terrestrial and cosmic activity of humanity; and,
(8) loss of signal (downtime) and various malfunctions in the data recording and data reduction systems.

(4.1)

a

for an effective collecting area of 1000 m². A further reduction in DT_a and DP_min is possible, in principle, if the integration time is increased. These are the kinds of numbers we should aim for.

However, the actual state of affairs is not determined by Eqn (4.1) but by the sum

(4.2)

4.2.3 Atmosphere

The clearest example of the type of interference discussed above is the emission from the atmosphere. With an average atmospheric emission temperature of approximately 2.5 K at 7.6 cm (about 10% of the total system temperature), the dispersion in the atmospheric interference (defined as the root-mean-square deviation from the average over a time interval of 1 hr) in all of the Cold experiments was a factor of 100 greater than the theoretical radiometer sensitivity (averaged over two months of observations). As is well known (Esepkina et al., 1973; Kaidanovskii et al., 1982), when observing sources of small angular diameter (on the order of a few beamwidths in size), an effective filtering method is widely used √ double-beam observations (in which the antenna records the difference in the emission from two adjacent directions √ source and background). In our case, the observations were, by necessity, carried out using a single beam and, because of this, other filtering methods were necessary. Two methods seemed promising:

suppressing the low-frequency fluctuations during the data reduction, and using the correlation between the atmospheric emission at various wavelengths for cleaning. Let us briefly explain these two methods. At Pulkov and the RATAN, a fair amount of experience has been accumulated in studying the fluctuations in the atmospheric emission and suppressing them; this experience has been reviewed by Kaidanovskii et al. (1982). Two important conclusions follow from the measurements of the fluctuations in the emission from a cloudy atmosphere* that have been carried out at the RATAN over the last few years:

(1) The structure function of the atmospheric emission, D(r), increases with t; it is of the form shown in Fig. 4.1(a). The dispersion in the fluctuations increases with increasing scale length; consequently atmospheric noise plays a more important role when studying more

Figure 4.1 (a) An example of the structure function observed at the RATAN-600 for the fluctuations in the radio emission from a cloudy atmosphere. (b) The spectrum of the fluctuations in the atmospheric radio emission corresponding to structure function (a).

extended structures. An increasing structure function corresponds to a fluctuation spectrum which increases rapidly at low frequencies; a sample spectrum W( f ), calculated from observations of a structure function similar to the one in Fig. 4.1(a), is shown in Fig. 4.1(b). The fact that the spectrum has this property means that only one solution is available: to cut off the low frequencies and sacrifice the large spatial scales in the signal down to some scale. It should be noted that although many measurements have been carried out in the process of studying atmospheric fluctuations (Kaidanovskii and Stotskii, 1979), and the spectrum of the atmospheric noise is better known that that of any other source of interference, this determinacy is, in fact, illusory √ the Kolmogorov spectrum is formed too slowly. An observer knows that the atmosphere usually appears on individual diurnal records as a slow drift with quasiperiodic oscillations superposed on it, rather than as an "off-the-shelf" power-law structure function. The statistical properties of the atmospheric noise differ significantly from one segment of a scan to another. Only by accumulating a large number of 24-hour-long scans (on the order of 100 for Experiment Cold) is it possible to even make a rough estimate of the size spectrum for the atmospheric emission.

(2) The fluctuations in the atmospheric emission at different wavelengths are correlated, and the correlation coefficient is very large. This property was first observed at the RATAN by Korol'kov and

Figure 4.2 The radio emission from clouds at 2.1 and 3.9 cm (from observations at the RATAN-600 with the antenna stationary). The correlation of the emission at these two wavelengths is very striking; the intensity of the emission is proportional to l ^-24
 

Figure 4.3 Experiment Cold: (a) correlation of the atmospheric emission at 4 and 8 cm; (A) samples of the scans (65 scans were averaged without selecting with respect to weather conditions); (c) samples of the "cleaning" process, i.e., subtraction of the 4-cm Scan from the 8-cm Scan multiplied by the appropriate factor.

 Timofeeva when the first remarkably similar simultaneous recordings at various wavelengths (Fig. 4.2) were obtained; Ipatov and Bulaenko then demonstrated a rather effective, simple cleaning method. This method was later studied in detail by M. N. Kaidanovskii (1980, 1981). The point is that the spectrum (wavelength dependence) of the atmospheric emission differs from that of most sources; this circumstance (together with the fact that the atmospheric fluctuations are correlated) can be used for cleaning, as long as simultaneous observations are made at several different frequencies. In the cycle of Experiment Cold discussed here, observations were made at wavelengths of 1.35, 2, 3.9, 7.6 (the main wavelength), 8.2, and 31 cm. The observations at the shorter wavelengths (2 and 3.9cm; see Fig. 4.3) were used to remove the effects of the atmosphere from the images at 7.6 cm. When testing the correlation method (Kaidanovskii, 1981), we succeeded in suppressing the fluctuations in the atmospheric emission by approximately a factor of 10 (or somewhat more).*

Vitkovskii has proposed an interesting, simple method of dealing with strong atmospheric interference:

Suppose we have several scans of the same piece of sky which are of various quality (more precisely, with different contributions from atmospheric noise). The best of these scans (assume that it is the first) is then adopted as a reference for which the contribution from atmospheric noise can be neglected to first approximation. Then, all of the remaining records can be made so that they are no worse than the reference scan. In fact, subtracting the first record from the second, we remove the emission from sources, the Galaxy, and the Universe, and the remainder gives.us the contribution of the atmosphere to the second scan (since the contribution to the first is assumed to be zero), and so forth. These atmospheric components can be subtracted from all the records. This method was tested on 22 scans of the section 13^h < a < 14^h of Cold-1. This is successful provided

 

 
4.3. Confusion Noise

The noise-like fluctuations which arise as the antenna pattern moves over a sky filled with faint background sources is called "confusion noise". If the distribution of such sources over the sky is random, the

power at the output of the radio telescope will also vary in a random fashion. These fluctuations are not removed by long integration times, and they are diferent for diferent radio telescopes. If the "number of sources √ flux density" curve (logN√logP, see Fig. 6.5) is known accurately, it is possible to estimate the confusion noise. In order to do this, however, it is necessary to know the shape as well as the eftecive solid angle of the antenna pattern of the radio telescope. This is essential when comparing the RATAN-600 to paraboloids. For the RATAN, the confusion noise becomes progressively smaller (according to the variation in the excess resolution coefficient h (see Section 4.6 for a discussion of the coefficient h)) as each of the following observing modes is used:

√ observing with the plane mirror (which is equivalent to observing on the horizon with any sector (h = 1));
√ observing at rather high elevations using any sector (h < 1);
√ one-dimensional synthesis using the southern sector (h << 1);
√ observing near the zenith with the entire ring (h << 1).

In more complex cases, Scheuer suggests the following relationship:

DP  P₁

where P₁ is the flux density at which the surface density of sources is one radio source per antenna beam. However, if we are interested in sufficiently large regions of the sky, it is possible for high-resolution instruments to overcome confusion noise. We shall discuss this in more detail in the following section.
 

4.4. Elimination of Discrete Sources

Usually, "specialization" of radio telescopes calls for a certain division of labor: aperture synthesis instruments study the discrete sources, while small antennas (including horns and dipoles) study the background emission. However, if the requirements on the accuracy with which the background emissioon is measured are increased, the background from faint (and bright!) radio sources inevitably becomes a limitation for low-resolution telescopes. If the contributions from such radio sources are not taken into account when observing, then, using the log N √ log P curve (for a given wavelength), it is possible to find the limitations on the accuracy with which the surface brightness of extended features can be measured. The calculations carried out by Daneze et al. (1982) using the latest log N √ log P data are shown in Fig. 4.4. The RATAN-600 allows the contributions from interfering sources to be taken into account to first order, down to a level of at least a few millijanskys (in Experiment Cold), i.e., the beam size of the radio telescope is much smaller than the region of background emission being studied. Essentially, the confusion noise can be reduced by at least a factor of 10 on scales of ~10'. See Fig. 6.4 for an illustration of the procedure by which sources were removed using Gaussian analysis. The next step in taking sources into account more carefully consists of complex studies of the same region using aperture synthesis instruments (the discrete sources) and the RATAN-600 (the background with the sources subtracted out); at present, the inability of aperture synthesis instruments to study large regions of the sky is the limitation here. Discussions are currently under way to organize observations of this type in a collaboration between the RATAN and the VLA.

4.5 Sky Surveys Using the RATAN-600

Carrying out surveys of the sky is one of the fundamental branches of astronomy. Without such surveys, our picture of the Universe is incomplete. The catalogs compiled when carrying out a sky survey are the basis for detailed studies by any of the methods available to humanity. The ideal survey would cover the entire sky at the highest sensitivity (and resolution!) available with current radio telescopes. But, since radio astronomers have not been able to develop a radio telescope for an experiment of this type, it is necessary to restrict ourselves to "specialized" surveys: to carry out either a rapid (rough) survey of the entire sky (paraboloids), or extremely deep surveys of very small sections of the sky (VLA). It is clear that the higher the desired sensitivity of the survey, the more difficult it is to survey a large section of the sky. Therefore, the extremely deep VLA surveys have little statistical significance (Keller-man, 1982), and the so-called rapid, "complete" surveys with para-boloids contain only the very strong sources, of which there are, once again, very few (see Kellerman, 1974).

The RATAN-600 occupies an intermediate position with respect to surveys. It is the only radio telescope at which a study of the entire sky with a resolution of 15" √ 1' at wavelengths of 2, 3.5, and 8 cm, and a sensitivity higher than that of the so-called "strong-source surveys" is currently being carried out.

At its most sensitive wavelength, the VLA can make a map of a 1' x 1' region of the sky with an RMS noise level of approximately 0.08 mJy in 8 hr of synthesis. True, 8-hr exposures are also possible at the RATAN, but at present, only in the region near the North Pole. Here, in this limited region, the same flux sensitivity as the VLA can be obtained. However, the struggle for statistically significant material leads to another mode of operation, where a significantly larger section of the sky can be studied in the same amount of observing time (at the price of a loss in sensitivity), and a larger number of sources are detected. That is, one should pay more attention to the relationship between the region surveyed, the sensitivity and the number of sources. The high sensitivity of the VLA (0.08mJy) is achieved through a prolonged synthesis of a very small region. Transforming this to t = 1 s, this corresponds to an RMS of about 1 may; the RATAN-600 has a comparable sensitivity for  t=1s (~ 5mJy), but even when observing with only one sector, the emission (integrated) from a 1' x 10' region (for observations using the plane periscopic refector on the south sector, a 1' x 40' region) is recorded. Because of this, a region which is a factor of 10⁵ larger than at the VLA is surveyed in the course of 8 hrs of observations. It is possible to develop a way of carrying out such a survey in which the number of sources observed is as large as possible. Observations near the equator using the periscopic reflector of the RATAN (with a broad field of view in the vertical direction √ approximately 40') turned out to be almost ideal from this point of view. In this mode, the RATAN-600, together with the high-sensitivity radiometer described in the previous section, has a record-breaking productivity √ several hundred radio sources per day, which is approximately equal to the total number of radio sources which have been observed to date in all centimeter-wavelength surveys.

Thus, we see that there are two methods of increasing the number of sources: increasing the depth to which a small fixed region of the sky is surveyed (increasing the exposure), and actually increasing the area surveyed. It is easy to show that where the log N √ log P curve is steep, the former is more efficient, while for extremely faint surveys, where the slope of the log N √ log P curve is small, the latter is considerably more efficient. This method is widely used at the RATAN-600, and this method was chosen as the basic method for Experiment Cold in particular.
 

4.6. Brightness Temperature Sensitivity

If a radio telescope is attached to a matched load, the source and telescope are in thermodynamic equilibrium: all of the power received by the radio telescope from a distant object of arbitrary shape is reradiated back into space by the radio telescope. If we received radiation from the cosmos from an isotropic background with a temperature of 2.7 K over an angle of 4p sr, the so-called "effective antenna temperature" of the load resistance would be exactly equal to the brightness temperature of the background, i.e., 2.7 K. When studying an object of finite extent, it is necessary to know the shape of the source as well as the complete antenna pattern, i.e. the intensity of the radiation emitted by the radio telescope in all directions (over 4p sr). Only in this case is it possible to calculate the coefficient for the transformation between brightness temperature and antenna temperature. This calculation is based on thermodynamic arguments, since it is necessary to find out how much of the radiation emitted by the radio telescope will not be emitted toward the source of the radio emission. We shall take these losses into account using the two coefficients h₁, and h_{2 ,} where h₁, involves the losses in the antenna system (spillover and scattering from errors in the surface), and h₂, takes the ratio of the solid angles (and the shapes) of the source and antenna pattern into account. Thus, we write the relationship between the brightness temperatures and antenna temperature as

where

A_p is the pattern of the primary horn;
W_f is the solid angle subtended by the secondary mirror ("feed") at the focus;
A_f (w) is the pattern of the secondary mirror;
W_m is the solid angle subtended by the main mirror of the radio telescope at the secondary mirror; and,
e_f  and e_m are the surface errors of the feed and the main mirror of the radio telescope, respectively.

It will be remembered that the aperture efficiency should not be confused with the coefficient h₁, (as was done by Partridge (1980)). Moreover, if the errors in the surface are small, in order to make the beam efficiency approach unity, it is a good idea to decrease the aperture efficiency by decreasing the so-called aperture coefficient, i.e., underilluminating the main mirror. In fact this procedure was carried out in Experiment Cold by "refocusing" the system so that the secondary mirror illuminated a smaller portion of the main mirror than in the normal operating mode. As we have already mentioned, in Experiment Cold, the primary feedhorn was moved away from the focus in such a way that the secondary mirror formed a converging wave with the focus at the main mirror, rather than a plane wave. This led to a small RMS phase error over the aperture, but reduced the losses due to spillover (and decreased the antenna noise).

We shall now attempt to take the relative sizes of the telescope beam and the scales on which we are studying the variations in the 3-degree background into account, i.e., determine the coefficient h₂,. For scales comparable to the size of the horizon at the hydrogen recombination epoch (several degrees), there is no correction: the entire antenna pattern (as well as the error pattern), which lies within the envelope of the pattern of a single element, is contained in a single inhomogeneity, and only the losses which were discussed above need to be taken into account. The situation is completely different when the antenna pattern is comparable to the size of the inhomogeneities being studied. This case is illustrated for a single inhomogeneity in Figs. 4.5(a √ c). The relationship between the antenna temperature and the brightness temperature for each of these three cases is given by

Figure 4.5 The relationship between the antenna temperature and brightness temperature for various ratios of the source size and beam size.

where W_A is the effective solid angle of the antenna pattern within the pattern of a single element of the antenna. Here, we neglect all of the coefficients discussed above, but the values of h₂, are

respectively. These relations are obvious from the same thermodynamic considerations discussed above. Two points still need to be clarified:

First, the quantity f_Ay ,. is not the vertical half-power beamwidth of the actual pattern. The antenna pattern of the RATAN-600 is a function of the elevation at which one is observing. For observations on the horizon, the "aperture" (i.e., as in the shape of the main reflecting surface of the RATAN-600 as it appears to an observer looking from the source) is a rectangle, and both cross-sections through the antenna beam (in azimuth as well as elevation) are Gaussian in form. For observations at intermediate elevations (our case), the aperture is shaped like a curved slit. In this case, the size of the center of the antenna pattern remains almost unchanged in azimuth but becomes much narrower in elevation (see Figs. 4.5 and 3.8). If the width of the antenna pattern is approximately f_Ay = 40' when observing on the horizon, then at the altitude of SS433 (at culmination), the size of the center of the beam in elevation is approximately 10'. However the narrowing of the antenna pattern in elevation occurs through the redistribution of energy over concentric surrounding regions centered on the axis of the antenna pattern. This means that for a roughly circular source, the situation is independent of altitude above the horizon from the viewpoint of thermodynamics. Therefore, without resorting to taking the shape of the antenna pattern into account exactly, we can use the transformation from brightness temperature to antenna temperature for the simple case of a "knife-edge" antenna pattern (i.e., the case of observations on the horizon). Thus, the full width of the antenna pattern at half-power for observations on the horizon (i.e., the size of the antenna pattern of a single element) should be used for f_Ay  in case (b) above.Second, we are studying the statistical anisotropy of the sky, rather than an isolated fluctuation. We should take the fact that the number of inhomogeneities which simultaneously fall within the antenna beam is diferent for cases (a) and (b) into account. It is easy to see that this number n is equal to 1, f_iy/f_Ay  and W_i/W_A respectively. As Bracewell and Conklin showed, taking the number of fluctuations per antenna beam into account leads to the following relationships between theantenna temperature and brightness temperature for cases (a), (b), and (c), respectively:

 

Thus, we must use the following relationships when reducing our data:

(a) for scales comparable with the horizon at the recombination epoch:

                 (4.5)  

(b) in the search for protoclusters (scales of order  f_{Ay, synth}, Fig. 4.5),

           (4.6)  

(c) when extrapolating the observational results to the scales of protogalaxies, globular clusters, and protostars (see Section 8),

      (4.7)

              (4.8)

where D² _synth is the synthesized aperture, and W_synth is the solid angle of the synthesized beam, and S_eff is the effective collecting area. In large synthesis systems, the coefficient h₂ very small, on the order 10^-6 for the VLA and 10^-10 for VLBI; therefore, these systems have very low brightness temperature sensitivity. For the RATAN, the coefficient h₂ , can also be used to characterize the excess resolution obtained in elevation because of the fact that the aperture appears to be curved when observing sources at elevations other than zero (the horizon), as was mentioned above; the value of h₂ , can be determined using Eqn (4.8) and Fig. 3.5;

h₂ =f_Ay,synth / f_Ay0.25

4.7. Conclusion: The Role of the RA TAN in Modern Radio Astronomy

  As became clear in the 1970's, radio astronomers were incapable of building a completely universal instrument whose capabilities exceeded those of any other specialized radio telescope intended for solving a particular astrophysical problem. This can not be overcome by increasing the amount of money spent √ both existing radio telescopes costing 100 million dollars and all of the enormous proposed telescopes costing tens of billions of dollars (such as, for example, the Cyclops project) suffer from this limitation.

Modern radio telescopes have become specialized not only with respect to wavelength region or field of radio astronomy, but even with respect to a model of a typical radio galaxy (see Fig. 4.6). The giant "global" radio telescope networks only see the nuclear sources, which have sizes of ~ 10^-3 arsec and a surface brightness very close to the limit, ~ 10¹² K. They do not detect any of the main body of a radio galaxy (or, perhaps, they may see nothing at all, if the nucleus of the galaxy is not in an active phase. Moreover, they do not see any other objects √ nebulae, H II regions, supernova remnants, main-sequence stars, the Sun, Moon, the planets and their statellites, etc.

The very large VLA-type aperture synthesis instruments only see the integrated emission from the nuclear source and the narrow streams and jets coming out of it, as well as the so-called "hot spots" in the radio components. The extended regions which emit most of the energy are only partially detected, and are sometimes completely invisible. Even the brightest source in the sky, Cas A, all of 4' in size, is completely invisible at the highest resolution of the VLA.

The RATAN-600 can detect the point source in a galaxy nucleus (but only from its integrated emission!) and obtain coarse images of the main body of a radio galaxy, but images of the nuclear source, jets, and hot spots are beyond its reach.

The largest paraboloids in the world are, as a rule, completely incapable of studying the structure of a typical radio galaxy, but they measure the integrated characteristics of radio galaxies very well, and are indispensible for studying the Galaxy, etc. It should be remembered that the bulk of the information on radio source statistics has been obtained using paraboloids at centimeter wavelengths. The fatal characteristic of a completely universal radio telescope is the same as for a person: a generalist knows a little bit about everything, in contrast to a narrow specialist, who knows everything within a very small field. In modern radio astronomy, as in modern society, the era of the Humboldts and Lomonosovs has come to an end. Progress in radio astronomy now occurs through the results obtained using specialized instruments.

In many respects, the RATAN-600 occupies an intermediate position between the large aperture-synthesis systems and the ordinary para-boloids. However, experience has shown that it is difterent from all other radio telescopes in some combinations of parameters; this allows us to use the RATAN-600 for problems which are practically impossible for other radio telescopes. This capability is due to the following characteristics of the RATAN: 

(a) the ability to observe at many frequencies simultaneously √ up to 20 √ 30 points in the region between 1 and 30cm can be obtained practically simultaneously;
(b) a greater degree of freedom from the influence of the atmosphere and background sources (than for paraboloids);
(c) a surface-brightness sensitivity several orders of magnitude higher (than that of large synthesis systems), which, in combination with item
(b) makes the RATAN-600 a unique instrument for studying the background radiation, at least at wavelengths longer than 6cm;
(d) a large "dynamic range" √ the ability to observe faint regions adjacent to bright sources. Large synthesis systems do not have this capability. In combination with the resolution (which is higher than that of paraboloids), this allows faint features to be observed around a significant number of radio galaxies and quasars;
(e) the ability to carry out many observing programs simultaneously at the RATAN-600, i.e., it is possible to carry out 3 √ 4 observing programs simultaneously; this allows problems which require a large amount of observing time (all-sky surveys, averaging over several months, etc.) to be carried out;
(f) a significantly larger "one-day field of view" than for very large (VLA-type) arrays. The VLA has a larger collecting area (than a single sector of the RATAN-600), but the allowed bandwidth is a factor of 10 smaller. Therefore, the RATAN-600 has a similar (and, in practice, higher) flux-density sensitivity for identical integration times. Let us
compare the "field of view" of the VLA in two observing modes:

In the first case, data is collected from a 1' x 1' (10^-5 sr) region in 24 hr, but at high sensitivity. In the second case, the 24-hr field of view is 2p rad x 1'  2 x 10^-3 sr, with a sensitivity similar to that of the RATAN-600 in sky-survey mode. However, in this mode, the RATAN-600 observes a region 2p radian x 40' = 0.8 x 10^-1sr in a 24-hr period, i.e., forty times larger. Therefore, specialization of instruments makes sense: it is efficient to carry out statistical work (but not on objects which are too faint) at the RATAN-600 and extremely deep studies of selected regions using the VLA.

 In the next section, we shall describe how we selected the problems best suited to the capabilities of an almost ideal radiometer.