A Study of Hierarchical Clustering of Galaxies in an Expanding Universe
Abstract
The nonlinear hierarchical clustering of galaxies in an Einsteinde Sitter ((OMEGA) = 1), initially white noise mass fluctuations (n = 0) model universe is investigated, and shown to be in contradiction with previous results. The model is done in terms of an 11,000body numerical simulation. The independent statistics of 0.72 million particles are used to simulate the boundary conditions. It is found that by an expansion of a = 16 over the initial conditions, on length scales around a correlation length ((xi) (DBLTURN) 1), the spatial autocorrelation function has the power law form: (xi) (PROPORTIONAL) r('1.5) in contradiction to (xi) (PROPORTIONAL) r('3) derived from previous numerical work. The pairwise velocity dispersion <(nu)(,12)('2)>(' 1/2) increases with particle separation on length scales around a correlation length. Both of these measures are consistent with observed galaxy clustering. However, there is disagreement in the amplitude of the pairwise velocity dispersion which is unresolved at this time. A new method for integrating the Newtonian Nbody gravity equations, which has controllable accuracy, incorporates a recursive center of mass reduction, and regularizes two body encounters is used to do the simulation. The coordinate system used here is well suited for the investigation of galaxy clustering, incorporating the independent positions and velocities of an arbitrary number of particles into a logarithmic hierarchy of center of mass nodes. The boundary for the simulation is created by using this hierarchy to map the independent statistics of 0.72 million particles into just 4,000 particles. This method for simulating the boundary conditions also has controllable accuracy. The results of galaxy clustering presented here are counter to previous results revealed by Fourier codes (including PPPM) at large expansion factors such as a (GREATERTHEQ) 14. Fourier codes produce the correlation function (xi) (PROPORTIONAL) r('3) at all expansion factors a (GREATERTHEQ) 2 from an (OMEGA) = 1, n = 0 initial condition, whereas the new results from this thesis demonstrate that the same initial condition produces the correlation function (xi) (PROPORTIONAL) r('1.5) near a correlation length in agreement with observations of galaxy clustering today. Both types of simulations produce, (xi) (PROPORTIONAL) r('3) near a correlation length at early times, which may be due to the cold initial state and discreteness effects.
 Publication:

Ph.D. Thesis
 Pub Date:
 1985
 Bibcode:
 1985PhDT.........7P
 Keywords:

 NBODY;
 NUMERICAL;
 SIMULATION;
 Physics: Astronomy and Astrophysics;
 Astronomical Models;
 Boundary Value Problems;
 Galactic Clusters;
 Hierarchies;
 Nonlinearity;
 Boundary Conditions;
 Center Of Mass;
 Fourier Series;
 Mathematical Models;
 Position (Location);
 Astrophysics