Annu. Rev. Astron. Astrophys. 2002. 40: 643-680
Copyright © 2002 by . All rights reserved

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The Sunyaev-Zel'dovich Effect (SZE) offers a unique and powerful observational tool for cosmology. Recently, there has been considerable progress in detecting and imaging the SZE. Efforts over the first two decades after the SZE was first proposed in 1970 (Sunyaev & Zel'dovich, 1970, 1972) yielded few reliable detections. Over the last decade, new detectors and observing techniques have allowed high quality detections and images of the effect for more than 50 clusters with redshifts as high as one. The next generation of SZE instruments that are now being built or planned will be orders of magnitude more efficient. Entering the fourth decade of SZE observations, we are now in position to exploit fully the power of the SZE, by obtaining detailed images of a set of clusters to understand the intra-cluster medium (ICM), by obtaining large SZE samples of clusters to determine statistically robust estimates of the cosmological parameters and, most importantly, by conducting large untargeted SZE surveys to probe the high redshift universe. These surveys will provide a direct view of the growth of large scale structure and will provide large catalogs of clusters that extend past z ~ 2 with remarkably uniform selection functions.

The physics of the SZE has been covered well in previous reviews (Birkinshaw, 1999, Rephaeli, 1995, Sunyaev & Zel'dovich, 1980a), with Birkinshaw (1999) and Carlstrom et al (2000) providing recent reviews of the observations. In this review, we look to the near future, using recent observations as a guide to what we can expect.

The SZE is best known for allowing the determination of cosmological parameters when combined with other observational diagnostics of clusters of galaxies such as X-ray emission from the intracluster gas, weak and strong lensing by the cluster potential, and optical galaxy velocity dispersion measurements. For example, cluster distances have been determined from the analysis of SZE and X-ray data, providing independent estimates of the Hubble constant. A large homogeneous sample of galaxy clusters extending to high redshift should allow a precise measure of this number, as well as a measure of the angular diameter distance relation to high redshift where it is highly sensitive to cosmological parameters. Similarly, the SZE and X-ray measurements will allow tight constraints on cluster gas mass fractions which can be used to estimate OmegaM assuming the composition of clusters represents a fair sample of the universal composition. The observed redshift dependence of the gas mass fraction can also be used to constrain cosmological parameters as well as test speculative theories of dark matter decay.

The most unique and powerful cosmological tool provided by the exploitation of the SZE will likely be the direct measurement of the evolution of the number density of galaxy clusters by deep, large scale SZE surveys. The redshift evolution of the cluster density is critically dependent on the underlying cosmology, and in principle can be used to determine the equation of state of the dark energy. SZE observations are particularly well suited for deep surveys because the important parameter that sets the detection limit for such a survey is the mass of the cluster; SZE surveys will be able to detect all clusters above a mass limit independent of the redshift of the clusters. This remarkable property of SZE surveys is due to the fact that the SZE is a distortion of the cosmic microwave background (CMB) spectrum. While the CMB suffers cosmological dimming with redshift, the ratio of the magnitude of the SZE to the CMB does not; it is a direct, redshift independent measurement of the ICM column density weighted by temperature, i.e., the pressure integrated along the line of sight. The total SZE flux detected will be proportional to the total temperature-weighted mass (total integrated pressure) and, of course, inversely proportional to the square of the angular diameter distance. Adopting a reasonable cosmology and accounting for the increase in the universal matter density with redshift, the mass limit for a given SZE survey flux sensitivity is not expected to change more than a factor of ~ 2 - 3 for any clusters with z > 0.05.

SZE surveys therefore offer an ideal tool for determining the cluster density evolution. Analyses of even a modest survey covering ~ 10 square degrees will provide interesting constraints on the matter density of the universe. The precision with which cosmological constraints can be extracted from much larger surveys, however, will be limited by systematics due to our insufficient understanding of the structure of clusters, their gas properties and evolution.

Insights into the structure of clusters will be provided by high resolution SZE observations, especially when combined with other measurements of the clusters. Fortunately, many of the cluster properties derived directly from observational data can be determined in several different ways. For example, the gas mass fraction can be determined by various combinations of SZE, X-ray, and lensing observations. The electron temperature, a direct measure of a cluster's mass, can be measured directly through X-ray spectroscopy, or determined through the analysis of various combinations of X-ray, SZE, and lensing observations. Several of the desired properties of clusters are therefore over-constrained by observation, providing critical insights to our understanding of clusters, and critical tests of current models for the formation and evolution of galaxy clusters. With improved sensitivity, better angular resolution, and sources out to z ~ 2, the next generation of SZE observations will provide a good view of galaxy cluster structure and evolution. This will allow, in principle, the dependence of the cluster yields from large SZE surveys on the underlying cosmology to be separated from the dependence of the yields on cluster structure and evolution.

We outline the properties of the SZE in the next section and provide an overview of the current state of the observations in Section 3. This is followed in Section 4 by predictions for the expected yields of upcoming SZE surveys. In Section 5, we provide an overview of the cosmological tests which will be possible with catalogs of SZE-selected clusters. This is followed by a discussion of backgrounds, foregrounds, contaminants, and theoretical uncertainties that could adversely affect cosmological studies with the SZE and a discussion of observations which could reduce or eliminate these concerns. Throughout the paper, h is used to parametrize the Hubble constant by H0 = 100h km s-1 Mpc-1, and OmegaM and OmegaLambda are the matter density and vacuum energy density, respectively, in units of the critical density.

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