CLUSTER CORRELATIONS IN THE ZELDOVICH APPROXIMATION

We show how to simulate the clustering of rich clusters of galaxies using a technique based on the Zel'dovich approximation. This method reproduces well the spatial distribution of clusters obtainable from full N-body simulations at a fraction of the computational cost. We use an ensemble of large-scale simulations to assess the level and statistical significance of cluster clustering in open, tilted and flat versions of the cold dark matter (CDM) model, as well as in a model comprising a mixture of cold and hot dark matter (CHDM). We find the open and flat CDM models are excluded by the data. The tilted CDM model, with a slight tilt, is in marginal agreement, while a larger tilt produces the right amount of clustering; CHDM is the best of all our models at reproducing the observations of cluster clustering. We find that all our models display a systematically weaker relationship between clustering length and mean cluster separation than that which seems to be implied by observations. We also note that the cluster 'bias factor', defined either by the ratio of cluster correlations to the linear mass correlations or by the ratio of the variance of cluster cell counts to the mass variance, may considerably vary with scale.