Morphology of Mock SDSS Catalogues

We measure the geometry, topology and morphology of the superclusters in mock SDSS catalogues prepared by Cole et al.(1998). The mock catalogues refer to $\tau$CDM and $\L$CDM {\em flat} cosmological models and are populated by galaxies so that these act as biased tracers of mass, conforming with the correlation function measured using APM catalogue. We compute the Minkowski Functionals (MFs) for the cosmic density fields using SURFGEN (Sheth et al.2003) and use the available 10 realizations of $\tau$CDM to study the effect of cosmic variance in estimation of MFs and Shapefinders, which we find to be extremely well constrained statistics. Although all the mock catalogues of galaxies have the same two-point correlation function and similar clustering amplitude, the global MFs due to $\tau$CDM show systematically lower amplitude compared to those due to $\L$CDM; an indirect, but detectable effect due to nonzero, higher order correlation functions. The characteristic thickness (T), breadth (B) and length (L) of the superclusters are measured using the available 10 realizations of $\tau$CDM. While T$\le$B and T, B$\in$[1,17] h$^{-1}$Mpc, we find the top 10 superclusters to be as long as 90 h$^{-1}$Mpc, with the longest superclusters identified at percolation to be rare objects with their length as large as 150 h$^{-1}$Mpc. The $\tau$CDM superclusters are found to be significantly longer than those in $\L$CDM. Thickness (T), breadth (B), planarity (P) and mass/volume$-$weighted planarity and filamentarity of the superclusters are found to be useful to compare the two models (abridged).