Probability Distribution Functions and Moments in Cosmological N-Body Simulations and Comparison with Thermodynamic Theory
Previous analyses have revealed that thermodynamic distribution function can represent the galaxy distributions in various observational and numerical data very well. In their analyses, the value of b in the thermodynamic function was used as a fitting parameter. The thermodynamic function is determined by b and the mean number density /line n. Therefore, the statistical properties which are derived from the distribution function, for example the k-th order moments, can be represented by b and /line n. We compared the second-order moment, skewness and kurtosis of numerical data of power-law models with those that are predicted by fitted values of b. We found that the fitted values of b cannot give the second-order moment, skewness and kurtosis correctly, though agreements between the thermodynamic and experimental distribution functions are fairly good. Small deviations between them cause large deviations in the moments. However, these deviations can give clues concering the initial density fluctuations, because they strongly depend on the initial power-law indices. We also confirm that the galaxy distributions in our data are homogeneous and isotropic, even in evolved stages, by using White's relation. It is necessary to confirm it, because the thermodynamic function and the general properties of the distribution function are derived under the condition that the distributions are homogeneous and isotropic.
Publications of the Astronomical Society of Japan
- Pub Date:
- October 1995
- GALAXIES: CLUSTERING;
- METHODS: NUMERICAL;