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1.4. Clusters of galaxies and the CMBR

If the CMBR were undisturbed from the epoch of decoupling, where it picks up these ``primordial'' anisotropies from structure formation, to the present, then all perturbations in the background could be interpreted in terms of early processes in the Universe. If there are strong interactions between the epoch of decoupling and the present, then all the perturbations associated with the formation of structure might have been overwritten by later effects (e.g., from a smoothly re-ionized and dense intergalactic medium; Tegmark et al. 1994).

The true appearance of the CMBR lies between these two extremes. Even away from obvious local structures (such as stars and radio sources) there are a number of structures in the Universe that can affect the propagation of radiation. For example, gravitational lenses redistribute radiation from the epoch of recombination. Were this radiation to be isotropic, then there would be no effect from a static lens. However, a lens would affect the detailed pattern of anisotropies that are imposed on the CMBR at recombination, and detailed studies of these anisotropies should take that effect into account, especially on the smallest angular scales (e.g., Blanchard & Schneider 1987; Sasaki 1989; Watanabe & Tomita 1991). Even an isotropic radiation field may pick up anisotropies from lenses, if those lenses are not static. Examples of such effects have been discussed by Rees & Sciama (1968), Dyer (1976), Nottale (1984), Gott (1985), Gurvits & Mitrofanov (1986), and Birkinshaw (1989).

These metric (Rees-Sciama) perturbations of the isotropy of the background radiation tend to be small, of order the gravitational lensing angle implied by the mass (Deltatheta ~ 4 G M / R c2, where M is the object's mass and R its size or the impact parameter) multiplied by a dimensionless measure of the extent to which the lens is non-static. For example, the fractional intensity change is of order Deltatheta (v/c) for a lens moving across the line of sight with velocity v. For even the largest masses (of clusters of galaxies), for which Deltatheta ~ 1 arcmin), and the largest likely velocities (~ 103 km s-1), the fractional intensity change Delta Inu / Inu ltapprox 10-6. It is interesting that redshift and angular effects introduced by spatial and temporal metric variations of a perturbing mass are closely related (Pyne & Birkinshaw 1993), and can be fitted into the same formalism as the Sachs-Wolfe effect (Sachs & Wolfe 1967), which is the dominant source of anisotropy in the microwave background radiation on the angular scale of the COBE experiments.

The most likely sources for metric perturbations of the CMBR are clusters of galaxies, which are the most massive well-differentiated structures in the Universe. However the structures introduced by metric effects associated with clusters of galaxies will be very difficult to see because of the presence of the Sunyaev-Zel'dovich effects, which are also introduced by clusters, but which are far more intense.

The basic physics of the Sunyaev-Zel'dovich effect is simple. Clusters of galaxies have masses that often exceed 3 x 1014 Msmsun, with effective gravitational radii, Reff, of order Mpc. Any gas in hydrostatic equilibrium within a cluster's gravitational potential well must have electron temperature Te given by

Equation 12 (12)

At this temperature, thermal emission from the gas appears in the X-ray part of the spectrum, and is composed of thermal bremsstrahlung and line radiation.

Figure 2. The central region of the ROSAT PSPC X-ray image containing the distant cluster CL 0016+16 (z = 0.5455), showing the extended X-rays produced by the thermal emission of gas in approximate hydrostatic equilibrium in the cluster's potential well. The coordinates are in epoch J2000. The data, extracted from PI bins 0.4-2.4 keV, have been background subtracted, exposure corrected, and adaptively smoothed. The effective spatial resolution of this image is ~ 30" (half-power diameter). Contour levels start at a value of 1.8 x 10-4 counts s-1 arcmin-2 (75 per cent of the average background level) and increase by multiplicative factors of 1.94. The bright X-ray source immediately to the north of the cluster is an AGN, QSO 0015+162, at a redshift z = 0.554. Note the extended source to the southwest which is a poor cluster, RX J0018.3+1618, at a redshift z = 0.5506 (Hughes et al. 1995).

About a quarter of the mass of clusters of galaxies is in the form of distributed gas (e.g., White & Fabian 1995; Elbaz et al. 1995; David et al. 1995; Dell'Antonio et al. 1995). The density of the gas is sufficiently high that clusters of galaxies are luminous X-ray sources (e.g., Figure 2; see the reviews of Forman & Jones 1982; Sarazin 1988), with the bulk of the X-rays being produced as bremsstrahlung rather than line radiation. Electrons in the intracluster gas are not only scattered by ions, but can themselves scatter photons of the CMBR: for these low-energy scatterings the cross-section is the Thomson scattering cross-section, sigmaT, so that the scattering optical depth taue approx ne sigmaT Reff ~ 10-2. In any one scattering the frequency of the photon will be shifted slightly, and up-scattering is more likely. On average a scattering produces a slight mean change of photon energy (Delta nu / nu) approx (kB Te / me c2) ~ 10-2. The overall change in brightness of the microwave background radiation from inverse Compton (Thomson) scattering is therefore about 1 part in 104, a signal which is about ten times larger than the cosmological signal in the microwave background radiation detected by COBE.

The primordial and Sunyaev-Zel'dovich effects are both detectable, and can be distinguished by their different spatial distributions. Sunyaev-Zel'dovich effects are localized: they are seen towards clusters of galaxies, which are large-scale structures visible to redshifts > 0.5 in the optical and X-ray bands. Furthermore, the amplitude of the signal should be related to other observable properties of the clusters. Primordial structures in the CMBR are non-localized: they are not associated with structures seen at other wavebands, and are distributed at random over the entire sky, with almost constant correlation amplitude in different patches of sky.

It is on the Sunyaev-Zel'dovich effects that the present review concentrates. Although the original discussion and detection of the effects were driven by the question of whether cluster X-ray emission arose from the hot gas in cluster potential wells or from non-thermal electrons interacting with magnetic fields or the cosmic background radiation (Sunyaev & Zel'dovich 1972), more recently the effects have been studied for the information that they can provide on cluster structures, on the motions of clusters of galaxies relative to the Hubble flow, and on the Hubble flow itself (and the cosmological constants that characterize it). The last few years have seen many new detections of Sunyaev-Zel'dovich effects from clusters with strong X-ray emission - and the special peculiarity of the Sunyaev-Zel'dovich effects, that they are redshift-independent, and therefore almost as easy to observe at high as at low redshift, has been illustrated by detecting clusters as distant as CL 0016+16, at z = 0.5455, or at even higher redshift.

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