Evolution of clusters of galaxies

Optical searches for galaxy clusters have shown that the abundance of high-velocity dispersion clusters was much as it is today even at redshifts approaching unity, while X-ray surveys show very strong negative evolution. The optical results are compatible with hierarchical theories with spectral index n ~> -1, if self-similar models are used to predict the evolution of the cluster population. There may be a problem with Gaussian initial fluctuation spectra, since Press-Schechter models require an index n ~ - 2 to fit the present epoch temperature function, and these evolve much too rapidly, but this may also just reflect an inaccuracy of this approximation. The X-ray observation is much harder to reconcile with hierarchical models, at least if the present state of the gas is a result of shocks from gravitationally induced motions-since one would then expect very strong positive evolution of the luminosity function-but it can be better understood if the entropy of the gas we now see was the result of some early injection of heat, perhaps at the time of galaxy formation. I construct a simple model in which the gas is initially uniform in entropy and settles roughly adiabatically into the evolving dark matter potential wells as these evolve. The predicted correlations of gross properties of clusters (X-ray luminosity, temperature, etc.) match quite well what is observed. The model shows strong negative evolution of the X-ray luminosity function, but only for the very brightest clusters. This agrees nicely with current observations, and the form of the evolution at lower luminosities can be tested by ROSAT.