Statistical Study Of Large-scale Structure Of The Universe

This thesis mainly focuses on the statistical study of the large-scale structure in the universe, which is done during my PhD research. The thesis contents include four chapters.First, we introduce the background of the large scale structure forma-tion in Chapter 1. There are four closely related subjects in the research of large-scale structure: the structure formation theories, the observations, the numerical simulations and the statistical analyses. The four sections in this chapter are obviously associated with these topics. I hope they will give you some clues of the research background and uptodate status.In Chapter 2, we present the simulations associated with the LAMOST project. The model parameters of simulations and the simulation procedures are discussed briefly. Bias model is employed in constructing the mock catalogues for different types of galaxies. To mimic the LAMOST redshift survey samples, several observational effects are imposed to the catalogues which are tested for their clustering properties.We study the large-scale structure based on the multiresolution anal-ysis of the discrete wavelet transformation (DWT) in Chapter 3. Besides the technical advantages of the computational feasibility for data sets with large volume and complex geometry, the DWT scale-by-scale decomposition provides a physical insight into the covariance matrix of the cosmic mass field. The method of measuring galaxy DWT power spectrum is presented in Section 3.2. This DWT estimator is optimized in the sense that the spa-tial resolution is adaptive automatically to the perturbation wavelength to be studied. The DWT power spectrum estimator for 3-dimensional samples has been studied in Section 3.3, in which we analyzed the Las Campanas redshift survey (LCRS) samples. The DWT estimator for higher than 1-dimensional samples provides two types of spectra with respect to diagonal and off-diagonal modes, respectively. The two types of modes have differ-ent spatial invariance, and therefore, the diagonal and off-diagonal DWT power spectra are very flexible to deal with configuration-related problems in the power spectrum detection. We established the algorithm to detect the redshift distortions using diagonal and off-diagonal DWT power spectra in Section 3.5. Theβfactor can be estimated without the assumption of cosmic models. After this, the DWT pairwise velocity dispersion can be measured and the real space DWT power spectrum can be recovered. While in Section 3.4, we analyzed the velocity field using DWT decomposition. The Probability Distribution of the DWT pairwise velocity shows a pure lognormal form which is supported by some nonlinear evolution models.The main contents of Chapter 4 can be divided into two parts. First we try to understand the weak galaxy-galaxy lensing shear measurements, from which to infer the mass and profile of the halos. Based on the recent galaxy-galaxy lensing measurements of Sloan Digital Sky Survey (McKay et al., 2002) and using the high resolution GIF simulations, we discussed the relation between the galaxies and their host halos in detail, and esti-mated the halo virial mass and the mass-to-light ratios. In the second part, we present a conditional luminosity function,Φ(L|M)dL, which gives the number of galaxies with luminosities in the range L±dL/2 that reside in a halo of mass M, to link the distribution of galaxies to that of dark matter haloes. Starting from the number density of dark matter haloes predicted by current models of structure formation, we seek the form ofΦ(L|M) that reproduces the galaxy luminosity function and the luminosity dependence of the galaxy clustering strength. We test the models ofΦ(L|M) by compar-ing the resulting mass-to-light ratios with constraints from the Tully-Fisher (TF) relation and from galaxy clusters. A comparison between model pre-dictions and current observations yields a number of stringent constraints on both galaxy formation and cosmology. In particular, this method can break the degeneracy betweenΩ₀ and the power-spectrum normalizationσ₈, inherent in current weak-lensing and cluster-abundance studies. For fiatΛCDM cosmogonies withσ₈ normalized by recent weak gravitational lens-ing observations, the best results are obtained forΩ₀～0.3;Ω₀≤0.2 leads to too large galaxy correlation lengths, whileΩ₀≥0.4 gives too high mass-to-light ratios to match the observed TF relation. The best-fit model for theΛCDM concordance cosmology withΩ₀=0.3 andΩ_Λ=0.7 predicts mass-to-light ratios that are slightly too high to match the TF relation. We discuss a number of possible effects that might remedy this problem, such as small modifications ofσ₈ and the Hubble parameter with respect to the concordance values, the assumption that the universe is dominated by warm dark matter, systematic errors in current observational data, and the exis-tence of dark galaxies. We use the conditional luminosity function derived from the present data to predict several statistics about the distribution of galaxy light in the local Universe. We show that roughly 50 percent of all light is produced in haloes less massive than 2×10¹²h^-1M_⊙. We also de-rive the probability distribution P(M|L)dM that a galaxy of luminosity L resides in a halo with virial masses in the range M±dM/2.Some numerical staffs concerning the DWT and the two dimensional projection of NFW profile are presented in the Appendix.