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Scientific paper
Jan 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993phdt.........8q&link_type=abstract
Thesis (PH.D.)--THE FLORIDA STATE UNIVERSITY, 1993.Source: Dissertation Abstracts International, Volume: 54-09, Section: B, page
Other
3
Scientific paper
Two problems of galactic dynamics are studied. The first is the self-consistent problem of building equilibrium models for galaxies with an axis of symmetry. We consider models in which the distribution function f of stars in phase space depends on the two classical integrals, the total energy E, and the angular momentum about the symmetry axis J in axisymmetric systems or the magnitude of the angular momentum vector L in spherical systems. We have found a new analytic method which can be used to solve these equations generally. It gives f as a complex contour integral, which is an analogue of Eddington's (1916) solution for isotropic spherical galaxies, and is directly derived from the density. We have shown rigorously that our solution satisfies the integral solution, and have used it to obtain new distribution functions of three different systems. Among the axisymmetric systems that we have considered are the "flattened" isochrone (Evans et al 1990), Satoh's n= infty model (1980), generalized Hernquist models, and a family of models for which the density as a function of the potential and axial radial distance is only known implicitly. For spherical systems we have devised a method of constructing models with prescribed anisotropy parameter defined by Binney (1980). The distribution functions of these models can be found by the contour integral method which also provides some new simplified solutions. The second part of the dissertation concerns the potential-density relation on a flat disk. We have greatly simplified Lynden-Bell's results (1989) and found some large families of potential-density pairs using our simplification. In particular, we have found a complete set for the whole family of Kalnajs-Mestel disks (Evans & de Zeeuw 1992), of which the isochrone disk is a special case. We have also adapted our simplified method to find two new biorthogonal potential-density sets. One is related to Gaussian disks (Toomre 1963) and the other to general Toomre (1963) disk models, and both should be useful for the analyses of these disks. The latter includes Clutton-Brock's (1972) set as a special case. (Abstract shortened by UMI.).
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