Accurate Incorporation of Self-Gravitating N-Body Components in Galactic Models: Global and Intermediate Scale Spiral Structures.
The research presented in this dissertation involves two major areas of study. The first area pertains to the calculation of the gravitational force (or potential) due to a distribution of point masses in a two-dimensional galactic disk, i.e. the calculation of the self-gravity. The widely used Fast Fourier Transform (FFT) methods introduce an unphysical softening parameter into the calculation of the potential in order to avoid large unphysical forces and increase the relaxation time of the system. In the past this parameter has been chosen in an ad hoc fashion and without formal justification. The development of a quantitative method for testing the accuracy and flexibility of any self-gravity method has led to the conclusion that if the addition of the softening parameter is interpreted as a way to give a two-dimensional disk an effective thickness, then a correct value for the softening parameter exists for FFT methods in the limit as the grid size goes to zero. The dependence of the correct softening length on the disk's vertical and radial density profiles has been found and it has been determined that a correct softening value cannot always be found when the FFT grid is finite. Also, an algorithm for computing the self-gravity via solution of the Poisson equation is described and the computational feasibility of this method is discussed along with the modeling advantages it has over traditional FFT methods. The second area of research pertains to the development of an analytical/computational model for studying the evolution of spiral galaxies. Recently a number of modifications have been made to increase the flexibility of the existing model. The changes include, but are not limited to, the addition of an exponential disk and spherical bulge and halo components, as well as a new method for accurately computing the dispersion in cases that exhibit a substantial level of noncircular systematic motion. Methods have also been developed to study the underlying dynamics related to the evolution of intermediate scale features that can form when a self-similar spiral mode is included in the evolutionary model. These features have been analyzed to determine the dominant mechanisms responsible for their evolution. This study has revealed that, due to competition between self-gravity and shear forces, these intermediate scale features can behave like nonlinear wave packets that propagate inward along the spiral arms.
- Pub Date:
- January 1995
- Mathematics, Physics: Astronomy and Astrophysics