Cluster correlation functions in N-body simulations

The correlation function of galaxy clusters has frequently been used as a test of cosmological models. A number of assumptions are implicit in the comparison of theoretical expectations to data. Here we use an ensemble of ten large N-body simulations of the standard cold dark matter cosmology to investigate how cluster selection criteria and other uncertain factors influence the cluster correlation function. Our study is restricted to the idealized case where clusters are identified in the three dimensional mass distribution of the simulations. We consider the effects of varying the definition of a cluster, the mean number density (or equivalently the threshold richness or luminosity) in a catalogue, and the assumed normalization of the cosmological model; we also examine the importance of redshift space distortions. We implement five different group-finding algorithms and construct cluster catalogues defined by mass, velocity dispersion or a measure of X-ray luminosity. We find that different cluster catalogues yield correlation functions which can differ from one another by substantially more than the statistical errors in any one determination. For example, at a fixed number density of clusters, the characteristic clustering length can vary by up to a factor of ∼ 1.5, depending on the precise procedure employed to identify and select clusters. For a given cluster selection criteria, the correlation length typically varies by ∼ 20% in catalogues spanning the range of intercluster separations covered by the APM and Abell (richness class ∼ >1) catalogues. Distortions produced by peculiar velocities in redshift space enhance the correlation function at large separations and lead to a larger clustering length in redshift space than in real space. The sensitivity of the cluster correlation function to various uncertain model assumptions substantially weakens previous conclusions based on the comparison of model predictions with real data. For example, some of our standard cold dark matter cluster catalogues agree better with published cluster clustering data (particularly on small and intermediate scales) than catalogues constructed from similar simulations by Bahcall & Cen and Croft & Efstathiou. Detailed modelling of cluster selection procedures including, for example, the effects of selecting from projected galaxy catalogues is required before the cluster correlation function can be regarded as a high precision constraint on cosmological models.