Two cosmological models for clusters of galaxies

Abstract

We investigate the properties of clusters of galaxies in two cosmological models using N-body simulations and the Press--Schecter (PS) theory. In the first model, the initial power spectrum of density fluctuations is in the form P(k) ∝ k−2 at wavelengths λ <120 h−1 Mpc. In the second model, the initial linear power spectrum of density fluctuations contains a feature (bump) at wavelengths λ~30–60, h−1 Mpc, which correspond to the scale of superclusters of galaxies. We examine the mass function, peculiar velocities, the power spectrum and the correlation function of clusters in both models for different values of the density parameter Ο0 and σ8 (the rms fluctuation on the 8, h−1Mpc scale). The results are compared with observations. We find that in many aspects the power spectrum of density fluctuations in model (2) fits the observed data better than the simple power-law model (1). In the first model, the mass function and peculiar velocities of clusters are consistent with observations only if Ο0<0.6. In the second model, the permitted region in the (Ο0, σ8) plane is larger. In this model, the power spectrum of clusters is in good agreement with the observed power spectrum of the APM clusters. This model predicts that there is a bump in the correlation function of clusters at separations r ~20–35, h−1 Mpc. In the future, accurate measurements of the cluster correlation function at these distances can serve as a discriminating test for this model. We examine the linear theory predictions for the peculiar velocities of peaks in the Gaussian field and compare these to the peculiar velocities of clusters in N-body simulations. We determine the clusters as the maxima of the density field smoothed on the scale R ~1.5, h−1 Mpc, and define their peculiar velocities using the same smoothing scale as for the density field. The numerical results show that in this case the rms peculiar velocities of clusters increase with cluster richness. The rms peculiar velocity of small clusters is similar to the linear theory expectations, while the rms peculiar velocity of rich clusters is higher than that predicted in the linear theory (~18 per cent for clusters with a mean intercluster separation dcl=30 h−1 Mpc).