Statistical properties of the spatial distribution of galaxies

Abstract

The methods of determining the fractal dimension and irregularity scale in simulated galaxy catalogs and the application of these methods to the data of the 2dF and 6dF catalogs are analyzed. Correlation methods are shown to be correctly applicable to fractal structures only at the scale lengths from several average distances between the galaxies, and up to (10-20)% of the radius of the largest sphere that fits completely inside the sample domain. Earlier the correlation methods were believed to be applicable up to the entire radius of the sphere and the researchers did not take the above restriction into account while finding the scale length corresponding to the transition to a uniform distribution. When an empirical formula is applied for approximating the radial distributions in the samples confined by the limiting apparent magnitude, the deviation of the true radial distribution from the approximating formula (but not the parameters of the best approximation) correlate with fractal dimension. An analysis of the 2dF catalog yields a fractal dimension of 2.20 ± 0.25 on scale lengths from 2 to 20 Mpc, whereas no conclusive estimates can be derived by applying the conditional density method for larger scales due to the inherent biases of the method. An analysis of the radial distributions of galaxies in the 2dF and 6dF catalogs revealed significant irregularities on scale lengths of up to 70 Mpc. The magnitudes and sizes of these irregularities are consistent with the fractal dimension estimate of D = 2.1-2.4

The Line-of-Sight Analysis of Spatial Distribution of Galaxies in the COSMOS2015 Catalogue

“…The works by Nabokov and Baryshev [8], Lovyagin [23], Shirokov et al [30], Park et al [31] emphasize the importance of the analysis of the LSSU for the development of modern cosmology, which has become an increasingly important task in the 21st century. The spatial distribution of galaxies reflects both the initial conditions in the early Universe and the evolution of primordial density perturbations.…”

“…We have developed Python software for the line-of-sight analysis based on works by Nabokov and Baryshev [7,8], Shirokov et al [9], Lovyagin [23]. Our method takes into account the integral values within each bin for all quantities that increase the mathematical rigor and certainty of the results.…”

“…where N model (z, ∆z) is the number of galaxies in the redshift bin (z, z + ∆z). The formula has three free parameters for the LSM: a, b, and C. We also used the empirical approximation function suggested in the works by Shirokov et al [9], Massey et al [15], Lovyagin [23]…”

“…However, factor A cannot be calculated directly from the formula (5) due to the high noise level. Therefore, accordingly to Lovyagin [23], it is necessary to search for it in the range from A − √ A to A + √ A. In addition, we considered a particular case of the function (4) for α = 1 and new labels for the parameters, ∆N emp2 (z, ∆z) = Az a e −bz ∆z , (…”