Genus statistics using the Delaunay tessellation field estimation method: (I) tests with the Millennium Simulation and the SDSS DR7

Abstract

We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogues generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We introduce a new method for constructing galaxy density fields and for measuring the genus statistics of its isodensity surfaces. It is based on a Delaunay tessellation field estimation (DTFE) technique that allows the definition of a piece-wise continuous density field and the exact computation of the topology of its polygonal isodensity contours, without introducing any free numerical parameter. Besides this new approach, we also employ the traditional approaches of smoothing the galaxy distribution with a Gaussian of fixed width, or by adaptively smoothing with a kernel that encloses a constant number of neighboring galaxies. Our results show that the Delaunay-based method extracts the largest amount of topological information. Unlike the traditional approach for genus statistics, it is able to discriminate between the different theoretical galaxy catalogues analyzed here, both in real space and in redshift space, even though they are based on the same underlying simulation model. In particular, the DTFE approach detects with high confidence a discrepancy of one of the semi-analytic models studied here compared with the SDSS data, while the other models are found to be consistent.

14 pages, 9 figures, accepted by ApJ

References in corpus (34)

• The Sloan Digital Sky Survey: Technical Summary
• The cosmological simulation code GADGET-2
• The Seventh Data Release of the Sloan Digital Sky Survey
• Simulating the joint evolution of quasars, galaxies and their large-scale distribution
• The many lives of active galactic nuclei: cooling flows, black holes and the luminosities and colours of galaxies
• Populating a cluster of galaxies - I. Results at z=0
• The broken hierarchy of galaxy formation
• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• The 2dF Galaxy Redshift Survey: Spectra and redshifts
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Likelihoods and Parameters from the WMAP data
• The hierarchical formation of the brightest cluster galaxies
• NYU-VAGC: a galaxy catalog based on new public surveys
• The Galaxy Luminosity Function and Luminosity Density at Redshift z=0.1
• The large-scale structure of the Universe
• Constraining Galaxy Formation and Cosmology with the Conditional Luminosity Function of Galaxies
• Galaxy Groups in the SDSS DR4: III. the luminosity and stellar mass functions
• Internal and Collective Properties of Galaxies in the Sloan Digital Sky Survey
• Galaxy Clustering & Galaxy-Galaxy Lensing: A Promising Union to Constrain Cosmological Parameters
• Morphology Segregation of Galaxies in the Color-Color Gradient Space
• Evolution of One-Point Distributions from Gaussian Initial Fluctuations
• Populating Dark Matter Haloes with Galaxies: Comparing the 2dFGRS with Mock Galaxy Redshift Surveys
• Minkowski Functionals of SDSS galaxies I : Analysis of Excursion Sets
• Luminosity dependence of the spatial and velocity distributions of galaxies: Semi-analytic models versus the Sloan Digital Sky Survey
• The Topology of the IRAS Point Source Catalogue Redshift Survey
• Topology of structure in the Sloan Digital Sky Survey: model testing
• Three-Dimensional Genus Statistics of Galaxies in the SDSS Early Data Release
• Effects of Gravitational Evolution, Biasing, and Redshift Space Distortion on Topology
• The Stellar Mass Components of Galaxies: Comparing Semi-Analytical Models with Observation
• 3D Genus Topology of Luminous Red Galaxies
• Density Estimators in Particle Hydrodynamics: DTFE versus regular SPH
• Genus Statistics of the Virgo N-body simulations and the 1.2-Jy Redshift Survey
• Filament and Shape Statistics: A Quantitative Comparison of Cold + Hot and Cold Dark Matter Cosmologies vs. CfA1 Data
• The Topology of Large Scale Structure in the 1.2 Jy IRAS Redshift Survey
• Topology of non-linear structure in the 2dF Galaxy Redshift Survey

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• MEDUSA: Minkowski functionals estimated from Delaunay tessellations of the three-dimensional large-scale structure
• Cosmological Parameter Estimation from the Two-Dimensional Genus Topology -- Measuring the Expansion History using the Genus Amplitude as a Standard Ruler
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