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10. The Sunyaev-Zel'dovich effects analysed in terms of cluster properties

The Sunyaev-Zel'dovich effects provide a window on cluster properties which differs significantly from that afforded by optical, X-ray, or conventional radio data. The present section of this review concentrates on these implications of the measurement of the effects for the understanding of cluster properties.

10.1. Cluster gas properties

The original purpose of measuring the Sunyaev-Zel'dovich effects of clusters was to test whether cluster X-ray emission was thermal in origin, or came from non-thermal processes such as inverse-Compton emission from relativistic electrons and the cosmic background radiation (e.g., Harris & Romanishin 1974). This use of the effects was rapidly made moot by the detection of line emission from clusters of galaxies (e.g., Serlemitsos et al. 1977).

Until recently there were few high-sensitivity measurements of the Sunyaev-Zel'dovich effects from clusters, so that little information could be obtained that was not already available from X-ray images and spectra. Thus, for example, the structural information from cluster Sunyaev-Zel'dovich effects based on radiometric data (e.g., Fig. 17) has much lower signal/noise than the X-ray images of those same clusters (e.g., Fig. 2). This is less true with imaging of the quality that should be available from interferometers, but at present interferometers measure only a fraction of the Fourier information needed for a full reconstruction of the microwave background structure generated by clusters of galaxies, and hence model-fitting to these interferometer images is usually based on existing X-ray data (see Sec. 8.3).

The Sunyaev-Zel'dovich effects do differ significantly from the X-ray data in their sensitivity to different properties of the atmospheres. If a cluster is at rest in the Hubble flow, then in the non-relativistic limit the low-frequency, thermal, Sunyaev-Zel'dovich effect from that cluster on a particular line of sight is

Equation 97 (97)

where y is the Comptonization parameter, which depends on the line-of-sight electron density and temperature as

Equation 98 (98)

(62), and is thus proportional to the line-of-sight integral of the electron pressure. By contrast, the X-ray surface brightness on that line of sight depends on these same quantities as

Equation 99 (99)

(63), where Lambda (E, Te) is the X-ray spectral emissivity, which is a function of the energy of the X-ray observation, E, the electron temperature of the gas, Te, the metallicity of the gas, and the redshift, z. The emissivity depends on temperature roughly as Lambda propto Te1/2 if the X-ray pass-band is sufficiently broad, so that the X-ray surface brightness is proportional to the line-of-sight integral of ne2 Te1/2 while the Sunyaev-Zel'dovich effect is proportional to the line-of-sight integral of ne Te. The Sunyaev-Zel'dovich effect and X-ray surface brightness of a cluster of galaxies are then likely to have different angular structures (if we rule out the possibility of coincidences in the density and temperature structures), and the difference between the X-ray and Sunyaev-Zel'dovich effect images should provide information on the runs of temperature and density in the cluster gas.

Once again, this has largely been superseded by improvements in X-ray technology. The newer generation of X-ray observatories provides some spatially-resolved X-ray spectra of clusters of galaxies and hence direct measurements of variations in the thermal structures of clusters. Sunyaev-Zel'dovich effect data could still be an important probe of structure in the outer parts of clusters, since at low densities the Sunyaev-Zel'dovich effect drops off less rapidly (propto ne) than the X-ray surface brightness (propto ne2). This region of the gas distribution might be expected to show the clearest evidence of deviations from the remarkably successful isothermal-beta model, but the current sensitivity of Sunyaev-Zel'dovich effect measurements is too low, relative to the sensitivity of X-ray images and spectra, for useful comparisons to be made. Where the cluster contains a radio source (particularly a radio halo source), the thermal Sunyaev-Zel'dovich effect is of particular interest since it provides a direct measurement of the electron pressure near that radio source, and so can be used to test whether the dynamics of the radio emitting plasma are strongly affected by the external gas pressure.

The remaining area where information about the Sunyaev-Zel'dovich effect provides unique information about the structure of the cluster gas is on the smallest scales, where structures in the X-ray gas are unresolved by X-ray or radio telescopes. In this case, the structures are better described by a (possibly position-dependent) clumping of the gas, and unless the density and temperature changes in the clumps conspire, the Sunyaev-Zel'dovich effect and X-ray surface brightness scale differently. For example, if clumping is isobaric, with the pressure in clumps the same as outside, then the Sunyaev-Zel'dovich effect will show no variations in regions where the gas is strongly clumped, while the X-ray emissivity will increase as ne3/2. No useful results on the clumping of cluster gas have been reported in the literature to date: it is more usual to see clumping referred to as one of the limiting factors in the use of the Sunyaev-Zel'dovich effects to measure the Hubble constant (Sec. 11.1), although clumping in the intracluster medium is also a biasing factor in the use of the X-ray data to determine gas densities and masses from X-ray images and spectra.

A direct use of the thermal Sunyaev-Zel'dovich effect is as a probe of the gas mass enclosed within the telescope beam (Myers et al. 1997). For an isothermal model of the form (64), the surface mass density in gas along a given line of sight is

Equation 100 (100)

where µe is the mean mass of gas per electron, while the thermal Sunyaev-Zel'dovich effect at low frequency is proportional to the Comptonization parameter (eq. 98). Thus the surface mass density in gas can be related to the Sunyaev-Zel'dovich effect (as measured through the Comptonization parameter) as

Equation 101 (101)

if the electron temperature of the gas is constant.

For clusters such as Abell 2218 which have both a rich population of arcs (Sarantini et al. 1996) and a strong Sunyaev-Zel'dovich effect, the measure (101) of the gas surface density could be compared directly with mass estimates produced by the study of gravitational arcs to estimate the fraction of the lensing mass that is contained in gas. Although this study is possible using the X-ray emission from a cluster, X-rays provide a less direct measure of gas mass, being biased by uncertainties in the clumpiness of the gas. The Sunyaev-Zel'dovich effect should be less susceptible to errors of interpretation, and give a clean estimate of the ratio of baryonic and dark matter within the arcs, which relates to the baryon problem in clusters (White & Fabian 1995). To make the best use of this comparison, the Sunyaev-Zel'dovich effect data should be taken with resolutions better than the radii of the gravitational arcs. Unfortunately observations with high brightness temperature sensitivity and angular resolutions of 10 arcsec or better are very difficult, and this limits the utility of this comparison at present.

Myers et al. (1997) show that for three clusters of galaxies, the ratio of baryonic mass to total gravitating mass (here derived not from gravitational lensing, but rather from cluster dynamics) is in the range 0.06 h100-1 to 0.17 h100-1. These values are larger than the baryonic mass fraction (0.013 ± 0.002) h100-2 expected from calculations of big-bang nucleosynthesis if Omega0 = 1 (Smith et al. 1993). As a result, we can infer that the Universe is open, with Omega0 approx 0.2 h100-1, or that clusters show a baryon segregation effect, with excess baryons in their X-ray luminous cores and excess dark matter further out.

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