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 9 particles to follow the mass distribution within cubes of side 2h −1 Gpc (τCDM) and 3h −1 Gpc (ΛCDM) with a force resolution better than 10 −4 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 – 13h −1 Mpc for samples with mean separation dc = 30h −1 Mpc to r0 = 22 – 27h −1 Mpc for samples with dc = 100h −1 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
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