Quantitative Descriptions of Nonlinear Gravitational Galaxy Clustering
Abstract
In order to investigate nonlinear gravitational galaxy clustering, three different quantitative analyses were carried out: twopoint correlation functions, xi (r); fractal dimensions, D_q; and f(N) statistics. The relation between the exponent gamma of the correlation function [xi (r)~ r(gamma ) ] and the fractal dimensions, D_q, was derived with the help of the probability distribution function, f(N), for finding N galaxies within a volume V. The methods were applied to analyze the results of Nbody simulations with power law initial density fluctuations (delta_ {mbox {boldmath k}}(2~) k(n) , n=1, 0, 1 and 2). These analyses show that the exponent, gamma , of the power law xi (r) is approximately 2 in the nonlinear regime for models with n=1 and 0. For models with n=1 and 2, the correlation functions comprise two parts of the intermediate and small scales in the nonlinear regime. The exponent of xi (r) is about 2 in the intermediate scale and is approximately 1 in the small scale. The fractal dimensions D_0, and D_2, describe this type double structure clearly: that is, the Hausdorff dimension, D_0, represents the intermediate structures and correlation dimension, D_2, gives the average value of the powerlaw exponents of the intermediate and small scales. The results of the analyses are qualitatively consistent with the scaling solution of the BBGKY hierarchy in the nonlinear regime. Moreover, the correlation functions generally contain the form of xi (r)~ r(2) in part. The relation with Saslaw's theory which predicts that the exponent gamma converges to 2, regardless of initial conditions is discussed.
 Publication:

Publications of the Astronomical Society of Japan
 Pub Date:
 August 1990
 Bibcode:
 1990PASJ...42..481I
 Keywords:

 Computational Astrophysics;
 Galactic Clusters;
 Gravitational Effects;
 Astronomical Models;
 Many Body Problem;
 Nonlinear Equations;
 Probability Distribution Functions;
 Spatial Distribution;
 Astrophysics;
 CLUSTERING OF GALAXIES;
 COSMOLOGY;
 STATISTICS