Cluster evolution and microwave source counts

We present the modeled counts for the expected Sunyaev-Zel'dovich microwave sources associated with clusters of galaxies, predicted for experiments with arcminute-scale spatial resolution, assuming self-similar cluster evolution, for different spectra of the primordial density fluctuations and values of the cosmological density parameter Omega. Our simulations show that the source counts should be a powerful test of the evolution of very high redshift clusters. Experiments with 1 - 2 min spatial resolution, with moderate sensitivity but covering a large area of the sky, would be most effective for studying the SZ source population. Recent arcminute-scale radio experiments, the Owens Valley Radio Observatory (OVRO) RING experiment and VLA deep imaging, achieved sensitivity and sky coverage close to that needed for the detection of negative sources associated with very distant clusters. From the absence of cluster detections in these experiments, we rule out, with 90% confidence, models with Omega less than 0.3 and n = +1 as predicting too many bright sources; or there is no hot gas in clusters more distant than z(sub max) = 5 in such models. If the single negative source detected in the RING experiment is a distant cluster, the Omega = 1, n = -2 model also may be ruled out as it predicts too few sources. The new generation of telescopes, including the new SUZIE and Ryle instruments, will soon be able to detect distant clusters. The cluster population in the past has been modeled by scaling the observed present-day sample of X-ray clusters back to high redshifts, an approach which makes the best use of the observed cluster gas parameters, and makes the simulations robust to the assumed evolution at very early epochs. Although the pure self-similar model may be incompatible with the variety of observed evolutionary effects, we show that reasonable modifications to the intracluster gas history in that model, proposed to reconcile the self-similar evolution of cluster mass and the observed evolution of their X-ray luminosity, do not considerably change our microwave predictions made using the pure self-similar model. That is, the results of our simulations are applicable to the wide class of evolutionary models in which the cluster gas mass times gas temperature evolves as the dark mass times cluster virial temperature.