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8. Measurement techniques

Three distinct techniques for the measurement of the Sunyaev-Zel'dovich intensity effects in clusters of galaxies are now yielding reliable results. This section reviews single-dish radiometric observations, bolometric observations, and interferometric observations of the effects, emphasizing the weaknesses and strengths of each technique and the types of systematic error from which they suffer. A discussion of the constraints on observation of the non-thermal effect is contained in the discussion of bolometric techniques. No concerted efforts at measuring the polarization Sunyaev-Zel'dovich effects have yet been made, and so only intensity-measuring techniques will be addressed here.

8.1. Single-dish radiometer measurements

The original technique used to detect the Sunyaev-Zel'dovich effects made use of existing radio telescopes on which large tranches of observing time could be obtained. This always meant the older single-dish telescopes, so that the measurements were made using traditional radiometric methods. This is exemplified by the early work of Gull & Northover (1976) using the Chilbolton 25-m telescope, or the more recent work of Uson (1986) on the NRAO 140-foot telescope. These telescopes tend to have beam-sizes of a few arcminutes at microwave frequencies, which is a fairly good match to the angular sizes of the moderately distant clusters of galaxies which X-ray astronomy was then beginning to study. With such large and general-purpose telescopes, it was impossible to make major modifications that would optimize them for observations of the microwave background radiation, and much early work had to cope with difficulties caused by the characteristics of the telescopes through minor changes to the receiver package or careful design of the observing strategy.

The closest clusters of galaxies (at redshifts less than about 0.05) have larger angular sizes, and it is possible to observe the Sunyaev-Zel'dovich effects using smaller telescopes. In such cases is has been possible to rework existing antennas to optimize them for microwave background observations - both of the Sunyaev-Zel'dovich effects and primordial structures (for example, using the OVRO 5.5-m telescope; Myers et al. 1997). This is now leading to a generation of custom-designed telescopes for sensitive measurements of the CMBR: some ground-based and some balloon-based systems should be in use in the near future.

A simple estimate of the sensitivity of a single-dish observation is of interest. A good system might have a noise temperature of about 40 K (including noise from the atmosphere) and a bandwidth of 1 GHz. Then in 1 second, the radiometric accuracy of a simple measurement will be 0.9 mK, and a differenced measurement, between the center of a cluster of galaxies and some reference region of blank sky, would have an error of 1.3 mK. Thus if problems with variations in the atmosphere are ignored, it would appear that a measurement with an accuracy of 10 µK could be made in 4.4 hours.

This observing time estimate is highly optimistic, principally because of emission from the Earth's atmosphere. Sensitive observations with large or small single dishes always use some differencing scheme in order to reduce unwanted signals from the atmosphere (or from the ground, appearing in the sidelobes of the telescope) to below the level of the astronomical signal that is being searched for. Consider, for example, observations at 20 GHz, for which the atmospheric optical depth may be ~ 0.01 in good conditions at a good site. The atmospheric signal will then be of order 3 K, several thousand times larger than the Sunyaev-Zel'dovich effects, and atmospheric signals must be removed to a part in 105 if precise measurements of the Sunyaev-Zel'dovich effects are to be made.

The simplest scheme for removing the atmospheric signal is simply to position-switch the beam of an antenna between the direction of interest (for example the center of some cluster) and a reference direction well away from the cluster. The radiometric signals measured in these two directions are then subtracted. If the atmospheric signal has the same brightness at the cluster center as at the reference position, then it is removed, and the difference signal contains only the astronomical brightness difference between the two positions. Thus the reference position is usually chosen to be offset in azimuth, so that the elevations and atmospheric path lengths of the two beams are as similar as possible.

Of course, the sky in the target and reference directions will be different because of variations in the properties of the atmosphere with position and time, and because of the varying elevation of the target as it is tracked across the sky. Nevertheless, if the target and reference positions are relatively close together, the switching is relatively fast, and many observations are made, it might be expected that sky brightness differences between the target and reference positions would average out with time. The choice of switching angle and speed is made to try to optimize this process, while not spending so much time moving the beams that the efficiency of observation is compromised.

An alternative strategy is to allow the sky to drift through the beam of the telescope or to drive the telescope so that the beam is moved across the position of the target. The time sequence of sky brightnesses produced by such a drift or driven scan is then converted to a scan in position, and fitted as the sum of of a baseline signal (usually taken to be a low-order polynomial function of position) and the Sunyaev-Zel'dovich effect signal associated with the target. Clearly, structures in the atmosphere will cause the baseline shape to vary, but provided that these structures lie on scales larger than the angular scale of the cluster, they can be removed well by this technique. Many scans are needed to average out the atmospheric noise, and this technique is often fairly inefficient, because the telescope observes baseline regions far from the cluster for much of the time.

In practice these techniques are unlikely to be adequate, because of the amplitude of the variations in brightness of the atmosphere with position and time: at most sites the sky noise is a large contribution to the overall effective noise of the observation. Nevertheless, the first reported detection of a Sunyaev-Zel'dovich effect (towards the Coma cluster, by Parijskij 1972) used a simple drift-scanning technique, with a scan length of about 290 arcmin and claimed to have measured an effect of -1.0 ± 0.5 mK.

More usually a higher-order scheme has been employed. At cm wavelengths, it is common for the telescope to be equipped with multiple feeds so that two or more directions on the sky can be observed without moving the telescope. The difference between the signals entering through these two feeds is measured many times per second, to yield an ``instantaneous'' beam-switched sky signal. On a slower timescale the telescope is position-switched, so that the sky patch being observed is moved between one beam and the other. At mm wavelengths it is common for the beam switching to be provided not by two feeds, but by moving the secondary reflector, so that a single beam is moved rapidly between two positions on the sky. This technique would allow complicated differencing strategies, if the position of the secondary could be controlled precisely, but at present only simple schemes are being used. Arrays of feeds and detectors are now in use on some telescopes, and differencing between signals from different elements of these feed arrays also provide the opportunity for new switching strategies (some of which are already being used in bolometer work, see Sec. 8.2).

Table 1. Radiometric measurements of the Sunyaev-Zel'dovich effects

Paper Technique nu theta h theta b theta s
(GHz) (arcmin) (arcmin) (arcmin)

Parijskij 1972 DS 7.5 1.3 x 40 . . . 290
Gull & Northover 1976 BS+PS 10.6 4.5 15.0 . . . *
Lake & Partridge 1977 BS+PS 31.4 3.6 9.0 . . . *
Rudnick 1978 BS+DS 15.0 2.2 17.4 60-120
Birkinshaw et al. 1978a BS+PS 10.6 4.5 15.0 . . . *
Birkinshaw et al. 1978b BS+PS 10.6 4.5 15.0 . . . *
Perrenod & Lada 1979 BS+PS 31.4 3.5 8.0 . . .
Schallwich 1979 BS+DS 10.7 1.2 8.2 15 *
Lake & Partridge 1980 BS+PS 31.4 3.6 9.0 . . .
Birkinshaw et al. 1981a BS+PS 10.7 3.3 14.4 . . . *
Birkinshaw et al. 1981b BS+PS 10.6 4.5 15.0 . . .
Schallwich 1982 BS+DS 10.7 1.2 8.2 15
Andernach et al. 1983 BS+DS 10.7 1.2 3.2, 8.2 15
Lasenby & Davies 1983 BS+PS 5.0 8 x 10 30 . . .
Birkinshaw & Gull 1984 BS+PS 10.7 3.3 20.0 . . .
BS+PS 10.7 3.3 14.4 . . .
BS+PS 20.3 1.8 7.2 . . .
Birkinshaw et al. 1984 BS+PS 20.3 1.8 7.2 . . .
Uson & Wilkinson 1984 BS+PS 19.5 1.8 8.0 . . . *
Uson 1985 BS+PS 19.5 1.8 8.0 . . *
Andernach et al. 1986 BS+DS 10.7 1.18 3.2, 8.2 15
Birkinshaw 1986 BS+PS 10.7 1.78 7.15 . . *
Birkinshaw & Moffet 1986 BS+PS 10.7 1.78 7.15 . . . *
Radford et al. 1986 BS+DS 90 1.3 4.0 10
BS+PS 90 1.2 4.3 . . .
BS+PS 105 1.7 19 . . .
Uson 1986 BS+PS 19.5 1.8 8.0 . . . *
Uson & Wilkinson 1988 BS+PS 19.5 1.8 8.0 . . .
Birkinshaw 1990 BS+PS 20.3 1.78 7.15 . . . *
Klein et al. 1991 BS+DS 24.5 0.65 1.90 6.0
Herbig et al. 1995 BS+PS 32.0 7.35 22.16 . . .
Myers et al. 1997 BS+PS 32.0 7.35 22.16 . . .
Uyaniker et al. 1997 DS 10.6 1.15 . . . 10
Birkinshaw et al. 1998 BS+PS 20.3 1.78 7.15 . . .
Tsuboi et al. 1998 BS+PS 36.0 0.82 6.0 . . .

Note. - The technique codes are BS for beam-switching, PS for position-switching, DS for drift- or driven-scanning. nu is the central frequency of observation. theta h is the FWHM of the telescope. theta b is the beam-switching angle (if beam-switching was used), and theta s is the scan length (for drift or driven scans). * in the final column indicates that the paper contains data that are also included in a later paper in the Table.

Table 1, which reports the critical observing parameters used in all published radiometric observations of the Sunyaev-Zel'dovich effects, indicates the switching scheme that was used. Most measurements have been made using a combination of beam-switching (BS) and position-switching (PS), because this is relatively efficient, with about half the observing time being spent on target. Some observations, including all observations by the Effelsberg group, have used a combination of beam-switching and drift or driven scanning (DS). The critical parameters of these techniques are the telescope beamwidth (the full width to half maximum, FWHM), theta h, the beam-switching angle, theta b, and the angular length of the drift or driven scan, theta s. Some of the papers in Table 1 have been partially or fully superseded by later papers, and are marked *.

Figure 13. A representative beam and position-switching scheme, and background source field: for observations of a point near the center of Abell 665 by the Owens Valley Radio Observatory 40-m telescope. The locations of the on-source beam and reference beams in this symmetrical switching experiment are shown as solid circles. The main beam is first pointed at the center of the cluster with the reference beam to the NW while beam-switched data are accumulated. The position of the main beam is then switched to the SE offset position, with the reference beam pointed at the center of the cluster, and more beam-switched data are accumulated. Finally, the main beam is again pointed at the cluster center. As the observation extends in time, the offset beam locations sweep out arcs about the point being observed, with the location at any one time conveniently described by the parallactic angle, p. Since Abell 665 is circumpolar from the Owens Valley, the reference arcs close about the on-source position: however, the density of observations is higher at some parallactic angles because p is not a linear function of time (see equation 91).

In techniques that use a combination of beam-switching and position switching, the beam and position switching directions need not be the same, and need bear no fixed relationship to any astronomical axes. However, the commonest form of this technique (illustrated in Fig. 13) has the telescope equipped with a twin-beam receiver with the two beams offset in azimuth. Since large antennas are usually altazimuth mounted, it is convenient also to switch in azimuth (and so keep the columns of atmosphere roughly matched between the beams). In any one integration interval (typically some fraction of a second) the output of the differential radiometer is proportional to the brightness differences seen by the two beams (possibly with some offset because of differences in the beam gains, losses, etc.). The configuration used by Readhead et al. (1989) in their observations of primordial anisotropies in the microwave background radiation is typical. In the simplest arrangement, where the two beams (A and B) are pointed towards sky positions 1 and 2, and the signals from the feeds enter a Dicke switch, followed by a low-noise front-end receiver, and then are synchronously detected by a differencing backend, the instantaneous output of the radiometer, DeltaP, was written by Readhead et al. as

Equation 89 (89)

Here G is the gain of the front-end system (a maser in the OVRO 40-m telescope configuration used by Readhead et al.), with an equivalent noise temperature of Tmaser. gA and gb are the back-end gains corresponding to the A and B (main and reference) feeds, and lA and lb are the losses in the feeds, waveguides, and Dicke switch associated with the two channels. These losses are distributed over a number of components, with temperatures ThetaA and ThetaB which range from the cryogenic temperatures of the front-end system to the ambient temperatures of the front of the feeds.

It is clear that the instantaneous difference power between channels A and B may arise from a number of causes other than the sky temperature difference (Tsky1 - Tsky2) which it is desired to measure. In general, the atmospheric signal greatly exceeds the astronomical signal towards any one position on the sky (Tatm1 >> Tsky1) so that small imbalances in the atmospheric signal between the two beams dominate over the astronomical signals that are to be measured. Over long averaging times, and with the same zenith angle coverage in the two beams, it is expected that < Tatm1 - Tatm2 > approx 0. The accuracy with which this is true will depend on the weather patterns at the telescope, the orientation of the beams relative to one another, and so on.

The ground pickup signals through the two beams are likely to be different, since the detailed shapes of the telescope beams are also different. This leads to an imbalance TgndA - TgndB, and an offset signal in the radiometer. The amplitude of this signal is reduced to a minimum by tapering the illumination of the primary antenna, so that as little power as possible arrives at the feed from the ground. Some protection against ground signals is also achieved by operating at elevations for which the expected spillover signal is smallest. However, since the ground covers a large solid angle there are inevitably reflection and diffraction effects that cause offsets from differential ground spillover.

The losses lA and lb in the two channels of the radiometer are reduced to a minimum by keeping the waveguide lengths to a minimum and using the best possible microwave components, but it is impossible to ensure that the losses are equal. Furthermore, the temperatures of the components in which these losses occur depend critically on where they are in the radiometer housing, so that the radiated signals from the components, integ ThetaA dlA and integ ThetaB dlB are likely to be significantly different. Once again, this produces an offset signal between the two sides of the radiometer.

These problems are exacerbated by their time variations. It is likely that the gains and temperatures will drift with time. The receiver parameters are stabilized as well as possible, but are still seen to change slowly. The atmosphere and ground pickup temperatures change more significantly, with varying weather conditions and varying elevations of the observation. Thus simple beam-switched measurements of the Sunyaev-Zel'dovich effect are unlikely to be successful, even after filtering out periods of bad weather and rapid temperature change when the atmospheric signal is unstable.

The level of differencing introduced by position-switching removes many of these effects to first order in time and position on the sky. The standard position-switching technique points one beam (A, the ``main beam'') at the target position for time tau, with the second beam (B, the ``reference beam'') offset in azimuth to some reference position, then switches the reference beam onto the target for time 2 tau, with the main beam offset to a reference position on the opposite side of the target, then switches back for a final time tau with the original beam on the target. If the total cycle time (4tau + s1 + s2, where s1 and s2 are the times spent moving) is small, then the reference positions observed by beams A and B do not change appreciably during a cycle, and the combination

Equation 90 (90)

is a much better measurement of the sky temperature difference between the target and the average of two points to either side of it (offset in azimuth by the beam-switching angle, thetab) than the estimate in (89). This is so even when the move and dwell times in the different pointing directions change slightly, for example because of variations in windage on the telescope. If tau is chosen to be small, then quadratic terms in the time and position variations of contaminating effects in (89) can be made very small, but at the cost of much reduced efficiency 4tau + s1 + s2) in the switching cycle. For observations with the OVRO 40-m telescope made by Readhead et al. (1989) and Birkinshaw et al. (1998), tau was chosen to be about 20 sec, and even large non-linear terms in the telescope properties are expected to be subtracted to an accuracy of a few µ K.

Even at this degree of differencing, it is important to check that the scheme is functioning properly. For this reason, the best work has included either a check of regions of nominally blank sky near the target point, or a further level of differencing involving the subtraction of data from fields leading and following the target field by some interval. A representative method (Herbig et al. 1995) consists of making a few (~ 10) observations using the beam-switching plus position switching technique described above at the target field, referenced to the same number of observations on offset regions before and after the target field, with the time interval arranged so that the telescope moves over the same azimuth and elevation track as the target source. The off-target data may be treated as controls, or may be directly subtracted from the on-target data to provide another level of switching which is likely to reduce the level of differential ground spillover. In either case, rigorous controls of this type necessarily reduce the efficiency of the observations by a factor 2 or 3. Alternatively, observations can be made of closer positions (perhaps even overlapping with the reference fields of the target point), without attempting an exact reproduction of the azimuth and elevation track on any one day, but allowing an equal coverage to build up over a number of days. This was the approach used by Birkinshaw et al. (1998).

The various beam switching schemes that have been used are described in detail in the papers in Table 1 that discuss substantial blocks of measurements. Quantitative estimates of their systematic errors from differential ground spillover, residual atmospheric effects, or receiver drifts, are also usually given. Whichever beam-switching technique is used, it is advisable to use the same technique to observe control fields, far from known X-ray clusters, where the expected measurement is zero. Systematic errors in the technique are then apparent, as is the extra noise in the data caused by primordial structures in the CMBR. It is important to realize that the Sunyaev-Zel'dovich effect plus primordial signal at some point can be measured to more precision than the systematic error on the Sunyaev-Zel'dovich effect that is set by the underlying spectrum of primordial fluctuations. That is, the measurement error is a representation of the reproducibility of the measurement, which is the difference between the brightness of some point relative to a weighted average of adjacent points. Noise from the spectrum of primordial fluctuations must be taken into account if realistic errors on physical parameters of a cluster are to be deduced from measured Sunyaev-Zel'dovich effect data.

A further difficulty encountered with single-dish observations is that of relating the measured signal from the radiometer (in volts, or some equivalent unit) to the brightness temperature of a Sunyaev-Zel'dovich effect on the sky. The opacity of the atmosphere can be corrected using tip measurements, and generally varies little during periods of good weather, so that the principal problem is not one of unknown propagation loss but rather one of calibration. Generally the absolute calibration of a single-dish system is tied to observations of planets, with an internal reference load in the radiometer being related to the signal obtained from a planet. If that planet has solid brightness temperature Tp, then the output signal is proportional to Tp, with a constant of proportionality which depends on the solid angle of the planet, the telescope beam pattern, etc. Thus by measuring the telescope beam pattern and the signal from planets, it is possible to calibrate the internal load. The accuracy of this calibration is only modest because of

1. measurement errors in the planetary signal, from opacity errors in the measurement of the transparency of the atmosphere, pointing errors in the telescope, etc.,
2. uncertainties in the brightness temperature scale of the planets, and in the pattern of brightness across their disks, and
3. variations in the shape of the telescope beam (and hence the gain) over the sky.

Thus, for example, the recent measurements of Myers et al. (1997) are tied to a brightness temperature scale using the measurement of the brightness temperature of Jupiter at 18.5 GHz (Wrixson et al. 1971). This measurement may itself be in error by up to 6 per cent. Difficulties may also arise from changes in the internal reference load, which will cause the calibration to drift with time. Relating this load back to sky temperatures at a later date will introduce another set of ``transfer errors''. Even if these are well controlled, it is clear that radiometric Sunyaev-Zel'dovich effect data contain systematic uncertainties in the brightness scale at the 8 per cent level or worse. This calibration error has a significant effect on the interpretation of the results.

It is important to mention, at this stage, that the differencing schemes described here have the effect of restricting the range of redshifts for which the telescope is useful. If observations are to be made of a cluster of galaxies at low redshift, then the angular size of the cluster's Sunyaev-Zel'dovich effects (which are several times larger than of the cluster's X-ray surface brightness) may be comparable to the beam-switching angle, theta b, and beam-switching reduces the observable signal. Alternatively, if the cluster is at high redshift, then its angular size in the Sunyaev-Zel'dovich effects may be smaller than the telescope FWHM, theta h, and beam dilution will reduce the observable signal. The two effects compete, so that for any telescope and switching scheme, there is some optimum redshift band for observation, and this band depends on the structures of cluster atmospheres and the cosmological model. An example of a calculation of this efficiency factor, defined as the fraction of the central Sunyaev-Zel'dovich effect from a cluster that can be observed with the telescope, is shown in Fig. 14 for the OVRO 40-m telescope. The steep cutoff at small redshift represents the effect of the differencing scheme, while the decrease of the efficiency factor at large z arises from the slow variation of angular size with redshift at z gtapprox 0.5.

Figure 14. The observing efficiency factor, eta , as a function of redshift, for observations of clusters with core radius 300 kpc and beta = 0.67, using the OVRO 40-m telescope at 20 GHz and assuming h100 = 0.5 and q0 = 1/2. eta is defined to be the central effect seen by the telescope divided by the true amplitude of the Sunyaev-Zel'dovich effect, and measures the beam-dilution and beam-switching reductions of the cluster signal. The decrease in eta at z > 0.15 is slow, so that these observations would be sensitive to the Sunyaev-Zel'dovich effects over a wide redshift range.

In dealing with the variations of signal during a tracked observation of a cluster, it is convenient to introduce the concept of parallactic angle, the angle between the vertical circle and the declination axis. An observation at hour angle H of a source at declination delta from a telescope at latitude lambda will occur at parallactic angle

Equation 91 (91)

where the parallactic angle increases from negative values to positive values as time increases (with the parallactic angle being zero at transit; Fig. 13) for sources south of the telescope, and decreases from positive values to negative values for sources north of the telescope. For a symmetrical beam-switching experiment, like that depicted in Fig. 13, the parallactic angle may be taken to lie in -90° to +90°. With more complicated beam-switching schemes, which may be asymmetrical to eliminate higher-order terms in the time or position dependence (e.g., Birkinshaw & Gull 1984), the full range of p may be needed.

The conversion between time and parallactic angle is particularly convenient when it is necessary to keep track of the radio source contamination. Many of the observations listed in Table 1 were made at cm wavelengths, where the atmosphere is relatively benign and large antennas are available for long periods. However, the radio sky is then contaminated by non-thermal sources associated with galaxies (in the target cluster, the foreground, or the background) and quasars, and the effects of these radio sources must be subtracted if the Sunyaev-Zel'dovich effects are to be seen cleanly.

Figure 15. Observing positions and radio sources in the cluster Abell 665. The dark-grey circles represent the FWHMs of the primary pointing positions of the Birkinshaw et al. (1998) Sunyaev-Zel'dovich effect observations in the cluster, while the light-grey areas are the reference arcs traced out by the off-position beams. A VLA 6-cm radio mosaic of the cluster field is shown by contours. Note the appearance of a significant radio source under the pointing position 4 arcmin north of the cluster center. This source appears to be variable, causing significant problems in correcting the data at that location. Other radio sources appear near or within the reference arcs, and cause contamination of some parts of the data.

Figure 15 shows a map of the radio sky near Abell 665. Significant radio source emission can be found in the reference arcs of the observations at many parallactic angles. Such emission causes the measured brightness temperature difference between the center and edge of the cluster to be negative: a fake Sunyaev-Zel'dovich effect is generated. Protection against such fake effects is implicit in the differencing scheme. Sources in the reference arcs affect the Sunyaev-Zel'dovich effect measurements only for the range of parallactic angles that the switching scheme places them in the reference beam. A plot of observational data arranged by parallactic angle therefore shows negative features at parallactic angles corresponding to radio source contamination (e.g., Fig. 16), and data near these parallactic angles can be corrected for the contamination using radio flux density measurements from the VLA, for example.

Figure 16. A comparison of the observed and modeled parallactic angle scans for OVRO 40-m data at a point 7 arcmin south of the nominal center of Abell 665. Two features are seen in the observed data (left). These correspond to bright radio sources which are seen in the reference arcs at parallactic angles near -50° and 40° (position angles +40° and -50° on Figs. 13 and 15). The model of the expected signal based on VLA surveys of the cluster (Moffet & Birkinshaw 1989) shows features of similar amplitude at these parallactic angles, so that moderately good corrections can be made for the sources. The accuracy of these source corrections is questionable because of the extrapolation of the source flux densities to the higher frequency of the Sunyaev-Zel'dovich effect data and the possibility that the sources are variable.

This procedure is further complicated by issues of source variability. At frequencies above 10 GHz where most radiometric observations are made (Table 1), many of the brightest radio sources are variable with timescales of months being typical. Source subtraction based on archival data is therefore unlikely to be good enough for full radiometric accuracy to be recovered. Simultaneous, or near-simultaneous, monitoring of variable sources may then be necessary if accurate source subtraction is to be attempted, and this will always be necessary for variable sources lying in the target locations. Variable sources lying in the reference arcs may also be simply eliminated from consideration by removing data taken at the appropriate parallactic angles: thus in Fig. 16, parallactic angle ranges near -50° and +40° might be eliminated on the basis of variability or of an imprecise knowledge of the contaminating sources. However, sources which are so strongly variable that they appear from below the flux density limit of a radio survey will remain a problem without adequate monitoring of the field.

Despite difficulties with radio source contamination, calibration, and systematic errors introduced by the radiometer or spillover, recent observations of the Sunyaev-Zel'dovich effects using radiometric techniques are yielding significant and highly reliable measurements. The detailed results and critical discussion appear in Sec. 9, but a good example is the measurement of the Sunyaev-Zel'dovich effect of the Coma cluster by Herbig et al. (1995), using the OVRO 5.5-m telescope at 32 GHz. Their result, an antenna temperature effect of -175 ± 21 µK, corresponds to a central Sunyaev-Zel'dovich effect DeltaTT0 + DeltaTK0 = -510 ° 110 µK, and is a convincing measurement of the Sunyaev-Zel'dovich effect from a nearby cluster of galaxies for which particularly good X-ray and optical data exist (e.g., White et al. 1993).

Figure 17. Measurements of changes in the apparent brightness temperature of the microwave background radiation as a function of declination near the clusters CL 0016+16, Abell 665 and Abell 2218 (Birkinshaw et al. 1998). The largest Sunyaev-Zel'dovich effect is seen at the point closest to the X-ray center for each cluster (offset from the scan center in the case of Abell 665), and the apparent angular sizes of the effects are consistent with the predictions of simple models based on the X-ray data. The horizontal lines delimit the range of possible zero levels, and the error bars include both random and systematic components.

For a few clusters, single-dish measurements have been used not only to detect the central decrements, but also to measure the angular sizes of the effects. This is illustrated in Fig. 17 which, for the three clusters CL 0016+16, Abell 665, and Abell 2218 shows the Sunyaev-Zel'dovich effect results of Birkinshaw et al. (1998). The close agreement between the centers of the Sunyaev-Zel'dovich effects and the X-ray images of the clusters is a good indication that the systematic problems of single-dish measurements have been solved, although observing time limitations and the need to check for systematic errors restricts this work to a relatively coarse measurement of the cluster angular structure. Much better results should be obtained using two-dimensional arrays of detectors, as should be available on the Green Bank Telescope when it is completed.

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