Abstract
Galaxy clusters are the largest virialized structures in the Universe. They are a valuable cosmological tool. Their rate of formation at each epoch will enable us to test models of modified gravity. Using gravitational lenses, they will place constraints on the distribution of dark matter. In the early days, clusters were discovered optically, but this requires a large number of galaxy spectra, and there is a lot of foreground contamination. The X-ray hot gas detection method has no contamination.
In principle, observation of the Sunyaev-Zeldovich effect in millimetres does not depend on redshift. In practice, clusters become less massive with z, and more difficult to detect. A statistical study of 3, ,000 clusters has determined their characteristic shapes : they are spheroids of revolution (in the first approximation), oblate or prolate in shape. As with elliptical galaxies, these shapes result from mergers between clusters, and are maintained by an anisotropic dispersion of velocities. The dark matter profile corresponds well to an NFW profile (unlike galaxies). as a first step, we can approximate a homogeneous cluster, and propose a beta profile (density to the power -3/2 β). Patterns are all the more regular as they are determined by " stacking " or stacking all clusters of the same mass together. Light and dark matter have similar radial distributions. There are useful scaling relationships between mass, luminosity and temperature, as a function of redshift. Simulations reproduce observations well. The observed baryon fraction tends towards the universal fraction for the most massive clusters. The inner parts of clusters are relaxed, so it's in the outer parts that we're now looking for traces of cluster formation : shell collapse, splashback. Cluster growth rates will be compared with modified gravity models.
