2004MNRAS.354..332S

We measure the geometry, topology and morphology of superclusters in mock Sloan Digital Sky Survey (SDSS) catalogues prepared and reported by [Cole et al. (1998)]. The mock catalogues refer to τCDM and ΛCDM flat cosmological models and are populated by galaxies so that these act as biased tracers of mass, conforming with the observed two-point correlation function (TPCF) measured using the APM catalogue on scales between 1 and 10 h^–1Mpc. We compute the Minkowski functionals (hereafter, MFs) for the cosmic density fields using surfgen and use the available 10 realizations of τCDM to study the effect of cosmic variance in estimation of MFs and shapefinders; the statistics derived from MFs, and used to study the sizes and shapes of the superclusters. The MFs and shapefinders are found to be extremely well constrained statistics, useful in assessing the effect of higher-order correlation functions on the clustering of the galaxy distribution. We show that though all the mock catalogues of galaxies have the same TPCF and similar clustering amplitude, the global MFs due to τCDM show systematically lower amplitude compared to those due to ΛCDM. This is an indirect, but detectable effect due to non-zero, higher-order correlation functions, and enables us to distinguish successfully the two models of structure formation. Next we establish that scale-dependent biasing leads to different clustering properties for galaxies as against the dark matter background. Thus, we stress the importance of incorporating a realistic treatment of bias in preparing and analysing the mock catalogues before confronting our models with the observed Universe.

We measure the characteristic thickness, breadth and length of the superclusters using the 10 τCDM realizations. While and, we find the top 10 superclusters to be as long as 90h^–1Mpc, with the longest superclusters identified at percolation to be rare objects with their length as large as 150h^–1Mpc. The longest structures of τCDM are found to be almost twice as long as those in ΛCDM. The dominant morphology of the large superclusters at percolation threshold is found to be filamentary.