Clustering of Galaxy Clusters in CDM Universes

We use very large cosmological N–body simulations to obtain accurate predictions for the two-point correlations and power spectra of mass-limited samples of galaxy clusters. We consider two currently popular cold dark matter (CDM) cosmogonies, a critical density model (τCDM) and a flat low density model with a cosmological constant (ΛCDM). Our simulations each use 10 particles to follow the mass distribution within cubes of side 2hGpc (τCDM) and 3hGpc (ΛCDM) with a force resolution better than 10 of the cube side. We investigate how the predicted cluster correlations increase for samples of increasing mass and decreasing abundance. Very similar behaviour is found in the two cases. The correlation length increases from r0 = 12 – 13hMpc for samples with mean separation dc = 30h Mpc to r0 = 22 – 27h Mpc for samples with dc = 100h Mpc. The lower value here corresponds to τCDM and the upper to ΛCDM. The power spectra of these cluster samples are accurately parallel to those of the mass over more than a decade in scale. Both correlation lengths and power spectrum biases can be predicted to better than 10% using the simple model of Sheth, Mo & Tormen (2000). This prediction requires only the linear mass power spectrum and has no adjustable parameters. We compare our predictions with published results for the APM cluster sample. The observed variation of correlation length with richness agrees well with the models, particularly for ΛCDM. The observed power spectrum (for a cluster sample of mean separation dc = 31h Mpc) lies significantly above the predictions of both models.