Browsing by Author "Sheth, Jatush V."

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Exploring the Geometry, Topology and Morphology of Large Scale Structure using Minkowski Functionals
(2005-02-01) Sheth, Jatush V.; Sahni, Varun
Modern redshift surveys such as the 2 degree ﬁeld Galaxy Redshift Survey (2dFGRS) and the Sloan Digital Sky Survey (SDSS) reveal the fully 3 dimensional distribution of a million or so galaxies over a large cosmological volume. Visually galaxies appear to be distributed along sheet-like and/or ﬁlamentary superclusters. The CfA Great Wall, Southern Great Wall and the recently discovered SDSS Great Wall are very spectacular superclusters. Clearly theoretical predictions for galaxy clustering must be tested against these rich datasets. This can be achieved by means of the Minkowski Functionals (MFs). A MF-based approach provides an excellent description of superclusters and voids and allows one to quantify the properties of the cosmic web. In this review we give a summary of the progress made in this direction. After reviewing the status of observations and of numerical simulations, we comment upon the nature of bias which serves as a link between theoretical predictions and observations. We also summarise the methods developed for eﬃcient numerical estimation of MFs for cosmological datasets and list several important results obtained using these methods. Speciﬁcally, we stress the discriminatory power of MFs and of the derived morphological statistics, the Shapeﬁnders. Shapeﬁnders are an excellent tool with which to study the shapes and sizes of superclusters and voids. We also discuss some of the important eﬀects of scale-dependent bias which are brought out by a MF-based study of the mock catalogues of galaxies. Such eﬀects, we note, should be accounted for before comparing theoretical models with observations.
Measuring the geometry and topology of large scale structure using SURFGEN: Methodology and preliminary results
(2002-03-22) Sheth, Jatush V.; Sahni, Varun; Shandarin, S.F.; et al.
Observations of the universe reveal that matter within it clusters on a variety of scales. On scales between 10 - 100 Mpc, the universe is spanned by a percolating network of superclusters interspersed with large and almost empty regions – voids. This paper, the ﬁrst in a series, presents a new ansatz which can successfully be used to determine the morphological properties of the supercluster-void network. The ansatz is based on a surface modelling scheme (SURFGEN), developed explicitly for the purpose, which generates a triangulated surface from a discrete data set representing (say) the dis- tribution of galaxies in real (or redshift) space. The triangulated surface describes, at progressively lower density thresholds, clusters of galaxies, superclusters of galaxies and voids. Four Minkowski functionals (MFs) – surface area, volume, extrinsic curva- ture and genus – describe the geometry and topology of the supercluster-void network. On a discretised and closed triangulated surface the MFs are determined using SUR- FGEN. Ratio’s of the Minkowski functionals provide us with an excellent diagnostic of three dimensional shapes of clusters, superclusters and voids. Minkowski function- als can be studied at diﬀerent levels of the density contrast and therefore probe the morphology of large scale structure on a variety of length scales. Our method for determining the Minkowski functionals of a triangulated iso-density surface is tested against both simply and multiply connected eikonal surfaces such as triaxial ellipsoids and tori. The performance of our code is thereby evaluated using density distribu- tions which are pancake-like, ﬁlamentary, ribbon-like and spherical. Remarkably, the ﬁrst three Minkowski functionals are computed to better than 1% accuracy while the fourth (genus) is known exactly. SURFGEN also gives very accurate results when ap- plied to Gaussian random ﬁelds. We apply SURFGEN to study morphology in three cosmological models, ΛCDM, τCDM and SCDM, at the present epoch. Geometrical properties of the supercluster-void network are found to be sensitive to the underlying cosmological parameter set. For instance, the percolating supercluster in ΛCDM turns out to be more ﬁlamentary but topologically simpler than superclusters in τCDM and SCDM. It occupies just 0.6% of the total simulation-box volume yet contains about 4% of the total mass. Our results indicate that the surface modelling scheme to calculate Minkowski functionals is accurate and robust and can successfully be used to quantify the topology and morphology of the supercluster-void network in the universe.
Morphology of Mock SDSS Catalogues
(2011-07-05) Sheth, Jatush V.
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.
Morphology of the supercluster-void network in /\ CDM cosmology
(2011-07-05) Shandarin, S.F.; Sheth, Jatush V.; Sahni, Varun
We report here the ﬁrst systematic study of the supercluster-void network in the ΛCDM concordance cosmology in which voids and superclusters are treated on an equal footing. Superclusters are deﬁned as individual members of an over-dense excur- sion set and voids are deﬁned as individual members of a complementary under-dense excursion set at the same density threshold. We determine the geometric, topological and morphological properties of the cosmic web at a large set of density levels by computing Minkowski functionals for every supercluster and void using SURFGEN (Sheth et al. 2003). The properties of the largest (percolating) supercluster and the complementary void are found to be very diﬀerent from properties of individual su- perclusters and voids. Individual superclusters totally occupy no more than about 5% of the total volume and contain no more than 20% of mass if the largest supercluster is excluded. Likewise, individual voids totally occupy no more than 14% of volume and contain no more than 4% of mass if the largest void is excluded. Although super- clusters are more massive and voids are more voluminous the diﬀerence in maximum volumes is not greater than by an order of magnitude. The genus value of individual superclusters can be ∼ 5 while the genus of individual voids can reach ∼ 40, implying signiﬁcant amount of substructure in superclusters and especially in voids. One of our main results is that large voids, as deﬁned through the density ﬁeld (read dark matter distribution) can be distinctly non-spherical.
Size of the longest filaments in the Universe
(2011-07-05) Bharadwaj, Somnath; Bhavsar, Suketu P.; Sheth, Jatush V.
We analyze the ﬁlamentarity in the Las Campanas redshift survey (LCRS) and determine the length scale at which ﬁlaments are statistically signiﬁcant. The largest length-scale at which ﬁlaments are statistically signiﬁcant, real objects, is between 70 to 80 h−1 Mpc, for the LCRS −3o slice. Filamentary features longer than 80 h−1 Mpc, though identiﬁed, are not statistically signiﬁcant; they arise from chance alignments. For the ﬁve other LCRS slices, ﬁlaments of lengths 50 h−1 Mpc to 70 h−1 Mpc are statistically signiﬁcant, but not beyond. These results indicate that while individual ﬁlaments up to 80 h−1 Mpc are statistically signiﬁcant, the impression of structure on larger scales is a visual eﬀect. On scales larger than 80 h−1 Mpc the ﬁlaments interconnect by statistical chance to form the the ﬁlament-void network. The reality of the 80 h−1 Mpc features in the −3o slice make them the longest coherent features in the LCRS. While ﬁlaments are a natural outcome of gravitational instability, any numerical model attempting to describe the formation of large scale structure in the universe must produce coherent structures on scales that match these observations.