MULTISCALE GEOMETRIC ANALYSIS OF THE 2DF DATA

Abstract

The distribution of galaxies seen in the available galaxy redshift catalogues shows complex structures such as voids, filaments, walls, or clusters. In order to compare the data with the simulations resulting from the cosmological models, we need to extract statistical or morphological information from the data. The two-point correlation (2CF), extensively used by Peebles , is certainly the most popular indicator to describe the spatial clustering of the galaxy distribution. Many different 2CF estimators have been proposed in the past . A detailed description of these estimators may be found in refs. 5,6 and they are compared in refs. . The two-point correlation function can been generalized to the N-point correlation function . Other statistical measures to characterize the spatial distribution of points have also been developed, such as the void probability function , the multifractal approach , the Minkowski functionals , the J function , the minimal spanning tree , or the wavelet . The Sloan Digital Sky Survey (Early Data Release) has recently been analyzed using a 3D Genus Statistics 25 and results were consistent with that predicted by simulations of a Λ-dominated spatially-flat cold dark matter model. The Genus is calculated by (i) convolving the data by a kernel, generally a Gaussian, (ii) setting to zero all values under a threshold ν in the obtained distribution, and (iii) taking the difference D between the number of holes and the number of isolated regions. The Genus curve G(ν) is obtained by varying the threshold level ν. The first step of the algorithm, the convolution by a Gaussian, may be dramatic for the description of filaments, which are spread out along all directions . Is has been shown that replacing the Gaussian smoothing by a wavelet denoising leads to much more reliable results . The wavelet-Genus method has been applied to both the 2DF data and a set of 22 Λ CDM simulations and the 2DF genus curve is clearly not compatible with the simulations . Figure 1 shows the wavelet genus function of the 2DF data. The solid line is the genus for the 2DF data and the crosses are the mean genus for 22 realizations of the λ-CDM simulations with the 3σ error bars. Question: How to explain the discrepancy ? In , the discrepancy was attributed to the presence of a super cluster in the data, which was not in the simulation. Therefore, even if there is a discrepancy, the λ-CDM model is still considered as a good model for representing the 2DF data. In order to better investigate this difference between the 2DF and the λ-CDM simulations, we have achieved a Multiscale Geometric Analysis (MGA) 27 of the 2DF data. Section 2 presents the MGA approach and the data (simulations and 2DF data) are described in section 3. Results are given in section 4.