Mathematics – Logic
Scientific paper
Apr 1997
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997phdt.........1f&link_type=abstract
Thesis (PHD). UNIVERSITY OF VIRGINIA , Source DAI-B 57/10, p. 6305, Apr 1997, 214 pages.
Mathematics
Logic
Scientific paper
This thesis examines several problems concerning gravitational galaxy clustering in the nonlinear regime. First it shows that galaxy merging can affect the spatial distribution function significantly. The evolving galaxy luminosity function also constrains merging. These two constraints show that fainter galaxies must become relatively less luminous as a result of merging. Merging must retain the dynamically relaxed state of clustering. Second, the thesis analyzes the spatial distribution of possible intergalactic dark matter by studying galaxies' peculiar motions for several general classes of models. Comparisons of these models with observations show that the peculiar velocities of galaxies are not simply induced by dominant gravity from the dark matter either in cluster cores or throughout clusters, or by massive attractors outside the clusters. A velocity distribution function considering only the mutual gravitational interactions of the galaxies gives a better explanation for the observations. Observational uncertainties would not affect this conclusion significantly. Third, the thesis investigates fundamental aspects of the thermodynamic description of the cosmological many-body problem. It shows explicitly how the thermodynamic description involves only the local fluctuating part of the gravitational field. Then it shows that there is an increasing length scale within which the overall clustering of galaxies is relaxed and its averaged macroscopic properties evolve slower than the expansion of the universe. This ensures a quasi-equilibrium evolution of the clustering. Finally, it shows how physical boundary conditions constrain the functional form of the ratio of gravitational correlation energy to the kinetic energy of peculiar velocities. This completes the equations of state, specifying the thermodynamic behavior. Fourth, the thesis extends the Jeans gravitational instability into the nonlinear regime to show how nonlinear coupling of the perturbations at different wavelengths strongly affects their growth. The many-body dynamical equation in the expanding universe is examined. As an illustration, a forced double-well oscillator is shown to have chaotic motion if it has constant damping, but not if it is dampen by the expanding universe. The galaxy spatial distribution is found to relax into a form described well by the quasi-equilibrium thermodynamic theory.
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