1.3. Single-dish problems
Single-dish observations can potentially provide rapid detections of SZ effects, particularly if the telescope is equipped with a radiometer array, but the technique faces three generic problems: of cluster selection, calibration, and confusion.
1.3.1. Cluster selection
While beam- and position-switching have the advantage of removing the atmosphere and ground signals to good accuracy, they introduce a selection effect because of the range of angular sizes of SZ effects that can be observed efficiently. SZ effects of small angular size fill only a small fraction of the beam, and so produce only a relatively small signal. SZ effects of large angular size fill not only the target beam, but also the reference beams, so that there is little difference in the brightnesses of the sky in the reference and target beams, so only a small detectable signal. Between these limits there is some angular size, and hence some redshift, for which a given telescope and switching system are most sensitive (Fig. 2).
Figure 2. The observing efficiency factor, , as a function of redshift, for observations of clusters with an isothermal model atmosphere (eq. 25) with core radius 300 kpc and = 0.67 by a telescope with a Gaussian beam of 108 arcsec FWHM. The decrease of is slow at large redshift, and so this observing configuration provides an effective means of detecting clusters at z > 0.05 is their intrinsic shape does not evolve.
The selection imposed by this variation of observing efficiency with redshift is relatively simple, and the change of efficiency with redshift is usually slow beyond some redshift of highest sensitivity, so that this is rarely a major problem.
A crucial requirement is that of precise calibration of the brightness scale. Such absolute measurements are essential if the thermal SZ effect is to be used to estimate the value of the Hubble constant, or if the spectrum from a cluster is to be used to separate the thermal and kinematic effects and so to measure the cluster's peculiar radial velocity (Sec. 2.5).
Calibration of radio telescopes is usually performed by reference to a set of unresolved radio sources with known flux densities. Absolute measurements of flux densities are possible for only a few extremely bright radio sources, and only sparse flux density measurements have been made. These sources are too bright and too extended to serve as useful calibrators for single-dish (or interferometric) SZ observations. Thus it is necessary to transfer these absolutely-calibrated flux densities to a network of unresolved, non-variable, secondary calibrators. The interpolation or extrapolation of these known flux densities to the precise frequency of any given SZ effect measurement requires an assumption about the shapes of the sources' spectra. The spectra are generally assumed to be low-order power-laws in log S - log space, but the sparseness of the absolute measurements can make the calibrators' flux densities somewhat uncertain. The combination of this uncertainty and the difficulties of the original absolute calibration are such that the flux density scale in normal use may contain systematic errors at the 5% level.
An alternative is to calibrate the flux density scale using planets, again making some assumption about the types of spectra that they provide, and taking proper account of emission from their atmospheres and surfaces and the variations in brightness across their disks. This is not an entirely straightforward process, and includes issues of polarization effects, the convolution of the brightness distribution of the planet with the shape of the beam, etc., but provides probably the best calibration of the flux density scale for a telescope, with perhaps 3% systematic errors.
If studies of the spectrum of the SZ effect are to be undertaken, then the bandpass in which a given observation is made needs to be well known. In certain frequency ranges the thermal and kinematic SZ effects have relatively steep spectra, and errors in the knowledge of the bandpass can lead to errors in separating the thermal and kinematic components.
It is not enough to make a single calibration of the flux density sensitivity of an antenna, and then to transfer this calibration to an internal noise source that can be used for frequent checks of the system gain. The shapes of large radio telescopes often vary as they move to different parts of the sky, with a corresponding change in their gain, and the measurement of this changing gain is also important if any flux density measurement is to be accurate at the level of a few per cent.
The beamshape of the telescope must also be well known to interpret the results being obtained. This may be a complicated process: for a single dish equipped with a receiver array, the different off-axis angles of the receiver feeds will mean that each beamshape must be independently measured. Each of the beams will also have different polarization characteristics. Both of these properties will change with telescope elevation.
Finally, a continuing, real-time calibration of the data is essential. At cm and mm wavelengths the opacity of the atmosphere changes with time, and a varying optical depth can change the effective sensitivity of the system. To some extent the optical depth can be monitored from the atmospheric brightness (which is reflected in the noise of the measurements), but at the few per cent level it is essential to obtain opacity measurements based on sky dips or independent sky monitoring.
Observations of any structure on the sky are liable to be confused by other foreground or background structures, and the problems of confusion are greater at low angular resolutions and low radio frequencies than at higher resolutions and higher frequencies. Since most SZ effects have arcminute angular scales, the effects of confusion can often be significant and must be taken into account in interpreting the results.
The most basic confusing signal is that of primordial structure in the MBR. Such signals have a different spectrum from the thermal SZ effects, and so in principle this source of confusion could be removed if sufficiently sensitive data are available at two or more frequencies, and if the relative calibration of the data is good enough. In making this separation, the kinematic SZ effect is also removed since it has the same spectrum as primordial fluctuations in the MBR. MBR confusion is most important at large angular scales, but is likely to be ~ 10 µK at the arcminute scales which are of most interest for searches for high-redshift clusters.
Non-thermal radio sources such as quasars and radio galaxies (and star-forming objects, particularly at mm wavelengths) also make an important contribution to the confusion level. The pattern of confusion can be distorted by the gravitational lensing of the cluster, and so can cause a variation in the confusing signal with angle from the cluster centre that mimics the angular structure of the SZ effects. A large fraction of the background radio source population is of steep spectrum, and so these problems can be minimized by observing at short cm wavelengths, or long mm wavelengths. However, a significant fraction of the radio source population is then variable, causing the confusion to change with time and adding further systematic error.
Another possible approach to the reduction of confusion is to detect the confusing sources using a high-resolution interferometer map, and then to remove their flux densities from the SZ effect data collected by the single-dish observations. This approach may run into difficulties by missing resolved radio emission, but such emission usually has a steep spectrum and so is minimized by working at high frequencies. Clusters with strong radio sources are generally so badly contaminated by their emission that no SZ effect measurements are possible. A more significant limitation is the need for frequent interferometric monitoring to deal with variable radio sources, which form a significant fraction of the confusing population at cm wavelengths.