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We analyse parallel N-body simulations of three Cold Dark Matter (CDM) universes to study the abundance and clustering of galaxy clusters. The simulations cover a volume comparable to the forthcoming SDSS. We are able to make robust measurements of cluster properties to a redshift larger than unity. We extract halos using two independent, public domain group finders (FOF & HOP) and find consistent results. The correlation function of clusters is in very good agreement with a simple analytic prescription based upon a Lagrangian biasing scheme developed by Mo & White (1996) and the Press-Schechter (PS) formalism for the mass function. The R_0--D_c relation for the open CDM model is in good agreement with the results from the APM Cluster Survey. The SCDM universe shows a robust deviation in the shape and evolution of the mass function when compared with that predicted by the PS formalism. Critical models with a low sigma_8 normalization or small shape parameter Gamma show an excess of massive clusters compared with the PS prediction. When cluster normalized, the SCDM universe at z =1 contains 10 times more clusters with temperatures greater than 7keV, compared with the PS prediction. The agreement between the analytic and N-body mass functions of SCDM can be improved if the value of the delta_c (the extrapolated linear theory threshold for collapse) is revised to be $ delta_c(z) = 1.685[(0.7/sigma_8)(1+z)]^{-0.125}. Our best estimate for the amplitude of fluctuations inferred from the local cluster abundance for SCDM is sigma_{8} = 0.5 pm 0.04. However, the discrepancy between the temperature function predicted in a critical density universe and that observed at z=0.33 (Henry et al. 1998) remains. (abridged)
We compute covariance matrices for many observed estimates of the stellar mass function of galaxies from $z=0$ to $zapprox 4$, and for one estimate of the projected correlation function of galaxies split by stellar mass at $zlesssim 0.5$. All covaria
A large scale SPH+N-body simulation (GADGET) of the concordance LCDM universe is used to investigate orientation and angular momentum of galaxy clusters at z=0 in connection with their recent accretion histories. The basic cluster sample comprises th
Correlation functions and related statistics have been favorite measures of the distributions of extragalactic objects ever since people started analyzing the clustering of the galaxies in the 1930s. I review the evolving reasons for this choice, and
We present measurements of the excess mass-to-light ratio measured aroundMaxBCG galaxy clusters observed in the SDSS. This red sequence cluster sample includes objects from small groups with masses ranging from ~5x10^{12} to ~10^{15} M_{sun}/h. Using
We present a comparison of optical and X-ray properties of galaxy clusters in the northern sky. We determine the recovery rate of X-ray detected clusters in the optical as a function of richness, redshift and X-ray luminosity, showing that the missed