ABUNDANCE OF MODERATE-REDSHIFT CLUSTERS IN THE COLD PLUS HOT DARK-MATTER MODEL

Using a particle-particle/particle-mesh simulation which accurately tr eats the density evolution of two components of dark matter, we study the evolution of clusters in the cold plus hot dark matter (CHDM) mode l. The mass function, the velocity dispersion function, and the temper ature function of clusters are calculated for four different epochs of z less than or equal to 0.5. We also use the simulation data to test the Press-Schechter expression of the halo abundance as a function of the velocity dispersion sigma(v). The model predictions are in good ag reement with the observational data of local cluster abundances (z = 0 ). We also tentatively compare the model with the GUM and his collabor ators' observation of rich clusters at z approximate to 0.8 and with t he X-ray luminous clusters at z approximate to 0.5 of the Einstein Ext ended Medium Sensitivity Survey. The important feature of the model is the rapid formation of clusters in the near past: the abundances of c lusters of sigma(v) greater than or equal to 700 km s(-1) and of sigma (v) greater than or equal to 1200 km s(-1) at z = 0.5 are only 1/4 and 1/10, respectively, of the present values (z = 0). Ongoing ROSAT and AXAF surveys of distant clusters will provide sensitive tests to the m odel. The abundance of clusters at z approximate to 0.5 would also be a good discriminator between the CHDM model and a low-density flat CDM model, both of which show very similar clustering properties at z = 0 .