Abundances, masses and weak-lensing mass profiles of galaxy clusters as a function of richness and luminosity in ΛCDM cosmologies

We test the concordance Lambda cold darkmatter (Lambda CDM) cosmology by comparing predictions for the mean properties of galaxy clusters to observations. We use high-resolution N-body simulations of cosmic structure formation and semi-analytic models of galaxy formation to compute the abundance, mean density profile and mass of galaxy clusters as a function of richness and luminosity, and we compare these predictions to observations of clusters in the Sloan Digital Sky Survey (SDSS) maxBCG catalogue. We discuss the scatter in the mass-richness relation, the reconstruction of the cluster mass function from the mass-richness relation and fits to the weak-lensing cluster mass profiles. The impact of cosmological parameters on the predictions is investigated by comparing results from galaxy models based on the Millennium Simulation (MS) and the WMAP1 simulation to those from the WMAP3 simulation. We find that the simulated weak-lensing mass profiles and the observed profiles of the SDSS maxBCG clusters agree well in shape and amplitude. The mass-richness relations in the simulations are close to the observed relation, with differences less than or similar to 30 per cent. The MS and WMAP1 simulations yield cluster abundances similar to those observed, whereas abundances in the WMAP3 simulation are two to three times lower. The differences in cluster abundance, mass and density amplitude between the simulations and the observations can be attributed to differences in the underlying cosmological parameters, in particular the power spectrum normalization sigma(8). Better agreement between predictions and observations should be reached with a normalization 0.722 < sigma(8) < 0.9 (probably closer to the upper value), i.e. between the values underlying the two simulation sets.