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10.2. Cluster velocities

Although the Sunyaev-Zel'dovich effects have not revealed much new information about the detailed structures of cluster atmospheres, the kinematic Sunyaev-Zel'dovich effect (Sec. 6) can provide a direct measurement of the peculiar velocity of a cluster of galaxies relative to the Hubble flow - a measurement that cannot be made with comparable accuracy by any other means, and which is of great importance in the study of the formation of structure. Here the Sunyaev-Zel'dovich effect is particularly good, since it could be measured at any redshift provided that the cluster to be observed has a significant electron scattering optical depth (i.e., a well-developed atmosphere), and that the telescope used has high observing efficiency.

The first application of this technique to set useful limits on cluster velocities was made by Holzapfel et al. (1997b), who measured the Sunyaev-Zel'dovich effects from Abell 1689 and 2163 using the SuZIE array detector on the Caltech Submillimeter Observatory. After decomposing the CMBR anisotropy into thermal and kinetic parts, and using an isothermal model for the cluster gas based on the X-ray image of the cluster from ROSAT, Holzapfel et al. find line-of-sight peculiar velocities for the clusters of

Equation 102 (102)
Equation 103 (103)

which only limits cluster peculiar velocities at z approx 0.2 to less than about 2000 km s-1. However, this is not too far (in terms of required observational sensitivity) from the result of Lauer & Postman (1994) that clusters in the local Universe exhibit a bulk velocity of 730 ± 170 km s-1. Small improvements in the accuracy of the measurement of the Sunyaev-Zel'dovich effects should allow useful velocity measurements to be made, although uncertainties at the level of 200 km s-1 may be unavoidable because of the background of primordial anisotropies against which the clusters are observed. Since the kinematic Sunyaev-Zel'dovich effects and the primordial anisotropies have the same spectrum, they can be separated only through their different angular structures - but at present there is no direct evidence about the amplitude of the primordial anisotropies as observed with a cluster-shaped filter on these angular scales.

Transverse velocity components could be measured through higher-order Sunyaev-Zel'dovich effects (see Sec. 7), or through measurements of the Rees-Sciama terms (Birkinshaw 1989), although the latter are more subject to confusion with primordial anisotropies. Even the noisy measurements of the three-dimensional velocity field of clusters as a function of redshift which might be measured in this way are likely to be useful in studies of the formation of large-scale structure in the Universe, and observations of CMBR anisotropies induced by clusters, even though of limited power to measure individual cluster velocity vectors, are likely to prove important for this reason.

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