Evolution of Clusters in Cold plus Hot Dark Matter Models

We use N-body simulations to study evolution of galaxy clusters over the redshift interval 0 z 0.5 in cosmological models with a mixture of cold and hot dark matter (CHDM). Four di erent techniques are utilized: the cluster-cluster correlation function, axial ratios and quadrupoles of the dark matter distribution in individual clusters, and virial properties. We nd that the correlation function for clusters of the same mass limit was larger and steeper at high redshifts. The slope increases from 1.8 at z = 0 to 2.1 at z = 0:5. Comoving correlation length rc scales with the mass limit M within comoving radius 1:5h Mpc and the redshift z as rc 20(1 + z)(M=M ) , where M = 3 10 h M . When the correlation length is normalized to the mean cluster separation dc, it remains almost constant: rc (0.45 { 0.5)dc. For small masses of clusters (M < 2 10 h M ) there is an indication that rc goes slightly above the relation with the constant of proportionality being 0:55 0:6. Anisotropy of density distribution in a cluster shows no change over redshift with axial ratios remaining constant around 1.2. In other words, clusters at present are as elongated as they were at the epoch of their rst appearance. While the anisotropy of clusters does not change with time, the density pro le shows visible evolution: the slope of density pro le changes from 3:5 at z = 0:5 to 2:5 at the present. We nd that the core of a cluster remains essentially the same over time, but the density of the outlying regions increases noticeably. The virial relation M v is a good approximation, but there is a large fraction of clusters with peculiar velocities greater than given by this relation, and clusters with the same rms velocities have smaller masses in the past, a factor of 2 at z = 0:5. Subject headings: cosmology: theory|dark matter|large-scale structure of the universe|galaxies: clustering|methods: numerical