Báo cáo hóa học: Analysis of the Spatial Distribution of Galaxies by Multiscale Methods

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Analysis of the Spatial Distribution of Galaxies by Multiscale Methods
Nội dung trích xuất từ tài liệu:
Báo cáo hóa học: " Analysis of the Spatial Distribution of Galaxies by Multiscale Methods"EURASIP Journal on Applied Signal Processing 2005:15, 2455–2469 c 2005 Hindawi Publishing CorporationAnalysis of the Spatial Distribution of Galaxiesby Multiscale Methods J-L. Starck DAPNIA/SEDI-SAP, Service d’Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France Email: jstarck@cea.fr V. J. Mart´nez ı Observatori Astronomic de la Universitat de Val`ncia, Edifici d’Instituts de Paterna, e ` Apartat de Correus 22085, 46071 Val`ncia, Spain e Email: vicent.martinez@uv.es D. L. Donoho Department of Statistics, Stanford University, Sequoia Hall, Stanford, CA 94305, USA Email: donoho@stanford.edu O. Levi Department of Statistics, Stanford University, Sequoia Hall, Stanford, CA 94305, USA Email: levio@bgumail.bgu.ac.il P. Querre DAPNIA/SEDI-SAP, Service d’Astrophysique, CEA-Saclay, 91191 Gif-sur-Yvette, France Email: philippe.querre@irsn.fr E. Saar Department of Cosmology, Tartu Observatory, Toravere 61602, Estonia Email: saar@aai.ee Received 17 June 2004; Revised 17 February 2005 Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy distribution and discriminate the different cosmological models. We present in this paper multiscale geometric transforms sensitive to clusters, sheets, and walls: the 3D isotropic undecimated wavelet transform, the 3D ridgelet transform, and the 3D beamlet transform. We show that statistical properties of transform coefficients measure in a coherent and statistically reliable way, the degree of clustering, filamentarity, sheetedness, and voidedness of a data set. Keywords and phrases: galaxy distribution, large-scale structures, wavelet, ridgelet, beamlet, multiscale methods.1. INTRODUCTION descriptors. This could be the distribution of galaxies of a specific type in deep redshift surveys of galaxies (or of clus-Galaxies are not uniformly distributed throughout the uni- ters of galaxies).1 In order to compare models of structure formation, the different distribution of dark matter particlesverse. Voids, filaments, clusters, and walls of galaxies can beobserved, and their distribution constrains our cosmologi-cal theories. Therefore we need reliable statistical methods 1 Making 3D maps of galaxies requires knowing how far away each galaxyto compare the observed galaxy distribution with theoretical is from Earth. One way to get this distance is to use Hubble’s law for themodels and cosmological simulations. expansion of the universe and to measure the shift, called redshift, to redder The standard approach for testing models is to define colors of spectral features in the galaxy spectrum. The greater the redshift,a point process which can be characterized by statistical the larger the velocity, and, by Hubble’s law, the larger the distance.2456 EURASIP Journal on Applied Signal Processingin N-body simulations could be analyzed as well, with the 2. THE 3D WAVELET TRANSFORMsame statistics. 2.1. The undecimated isotropic wavelet transform The two-point correlation function ξ (r ) has been the pri- For each a > 0, b1 , b2 , b3 ∈ R3 , the wavelet is defined bymary tool for quantifying large-scale cosmic structure [1].Assuming that the galaxy distribution in the Universe is arealization of a stationary and isotropic random process, ψa,b1 ,b2 ,b3 : R3 −→ R,the two-point correlation function can be defined from the x1 − b1 x2 − b2 x3 − b3probability δP of finding an object within a volume ele- ...