Comparison of clustering properties of observed objects and dark matter   halos on different mass and spatial scales
  We investigate the large-scale distribution of galaxy clusters taken from several X-ray catalogs. Different statistics of clustering like the conditional correlation function (CCF) and the minimal spanning tree (MST) as well as void statistics were used. Clusters show two distinct regimes of clustering: 1) on scales of superclusters (~40/h Mpc) the CCF is represented by a power law; 2) on larger scales a gradual transition to homogeneity (~100/h Mpc) is observed. We also present the correlation analysis of the galaxy distribution taken from DR6 SDSS main galaxy database. In case of galaxies the limiting scales of the different clustering regimes are 1)10-15/h Mpc; 2) 40-50/h Mpc. The differences in the characteristic scales and scaling exponents of the cluster and galaxy distribution can be naturally explained within the theory of biased structure formation. We compared the density contrasts of inhomogeneities in the cluster and galaxy distributions in the SDSS region. The estimation of the relative cluster-galaxy bias gives the value b = 5 +/- 2. The distribution of real clusters is compared to that of simulated (model) clusters (the MareNostrum Universe simulations). We selected a cluster sample from 500/h Mpc simulation box with WMAP3 cosmological parameters and sigma_8 = 0.8. We found a general agreement between the distribution of observed and simulated clusters. The differences are mainly due to the presences of the Shapley supercluster in the observed sample. On the basis of SDSS galaxy sample we study properties of the power law behavior showed by the CCF on small scales. We show that this phenomenon is quite complex, with significant scatter in scaling properties, and characterized by a non-trivial dependence on galaxy properties and environment. 
A.V. Tikhonov, A.I. Kopylov, S. Gottlober, G. Yepes