EVOLUTION OF CLUSTERS IN A HYBRID HOT DARK MATTER UNIVERSE

The evolution of clusters of galaxies in a cosmological model where the large-scale structure is formed by gravitational instability in a hot dark matter universe with initial adiabatic Harrison-Zel'dovich fluctuations, but with a lower than usual normalization, is analyzed. The normalization of the power spectrum is possibly too low to form galaxies, so that small-scale structures may be formed by some other short-range process. The analysis is based on the statistics of peaks in a random Gaussian field and the spherical infall model. While the typical mass, virial temperature, and X-ray luminosity change little with redshift, the evolution of the co-moving number density of clusters is dramatic. The evolution is especially severe for high values of the Hubble constant and for low values of the present number density of clusters (low normalizations). The distribution of the velocity dispersion is crucially dependent on several parameters which are not well determined by the theory. A model where the Hubble constant is ∼50 km s-1 Mpc-1 and where the rms density fluctuations evolved to the present epoch by linear theory is ∼0.9-1.1 seems to fit low-redshift observations relatively well, although the abundance of clusters with very high velocity dispersions at high redshifts may cause a problem. Future observations of velocity dispersions of clusters at high redshifts, and especially X-ray observations of virial temperatures, will provide strong constraints for this model.