Morphology of Mock SDSS Catalogues

Abstract

ABSTRACT We measure the geometry, topology and morphology of the superclusters in mock 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 measured using APM catalogue on scales between 1 to 10 h−1Mpc. We compute the Minkowski Functionals (hereafter, MFs) for the cosmic density fields using SURFGEN (Sheth et al.2003) and use the available 10 realizations of τCDM to study the effect of cosmic variance in estimation ofMFs 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 galaxy- distribution. We show that though all the mock catalogues of galaxies have the same two-point correlation function and similar clustering amplitude, the global MFs due to τCDM show systematically lower amplitude compared to those due to ΛCDM, an indirect, but detectable effect due to nonzero, higher order correlation functions. This enables us to successfully distinguish the two models of structure formation. We further measure the characteristic thickness (T), breadth (B) and length (L) of the superclusters using the available 10 realizations of τCDM. While T6B and T, B∈[1,17] h−1Mpc, we find the top 10 superclusters to be as long as 90 h−1Mpc, with the longest superclusters identified at percolation to be rare objects with their length as large as 150 h−1Mpc. The dominant morphology of the large superclusters is found to be filamentary. The thickness, breadth and planarity of the superclusters follow well- defined distributions which are different for the two models. Thus, these are found to be sensitive to the cosmological parameter-set and are noted to be candidate statis- tics which can compare the rival models of structure formation. Further, the longest structures of τCDM are found to be significantly longer than those in ΛCDM. Finally, mass and volume-weighted dimensionless Shapefinders – Planarity and Filamentarity – are found to be well-constrained statistics useful to discriminate the two models. We note some interesting effects of bias and stress the importance of incorporating realistic treatment of bias in preparing and analysing the mock catalogues.