Cosmology using cluster internal velocity dispersions

We compare the cumulative distribution of internal velocity dispersions of galaxy clusters, N(>sigma_v), for a large observational sample to those obtained from a set of N-body simulations that we run for seven COBE-normalized cosmological scenarios. They are: the standard CDM (SCDM) and a tilted (n = 0.85) CDM (TCDM) model, a cold+hot DM (CHDM) model with Omega_nu = 0.25, two low-density flat CDM (Lambda CDM) models with Omega_0 = 0.3 and 0.5, two open CDM (OCDM) models with Omega_0 = 0.4 and 0.6. The Hubble constant is chosen so that t_0 ~= 13 Gyrs in all the models, while Omega_b = 0.02 h^2 is assumed for the baryon fraction. Clusters identified in the simulations are observed in projection so as to reproduce the main observational biases of the real data set. Clusters in the simulations are analysed by applying the same algorithm for interlopers removal and velocity dispersion estimate as for the reference observational sample. We find that sigma_v for individual model clusters can be largely affected by observational biases, especially for sigma_v <~ 600 km s^-1. The resulting effect of N(>sigma_v) is rather model dependent: models in which clusters had less time to virialize show larger discrepancies between intrinsic (3D) and projected distribution of velocity dispersions. From the comparison with real clusters we find that both SCDM and TCDM largely overproduce clusters. We verified for TCDM that agreement with the observational N(>sigma_v) requires sigma_8 ~= 0.5. As for the CHDM model, it marginally overproduces clusters and requires a somewhat larger sigma_8 value than a purely CDM model in order to produce the same cluster abundance. The LambdaCDM model with Omega_0 = 0.3 agrees with data, while the open model with Omega_0 = 0.4 and 0.6 under-produces and marginally overproduces clusters, respectively.