Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Physics and Astronomy

First Advisor

Joel E. Tohline


In an effort to better understand the formation and evolution of barred galaxies, the properties of orbits in the effective potential of one specific model of a rapidly rotating, steady-state gas-dynamical bar that has been constructed via a self-consistent hydrodynamical simulation have been examined. This bar is used to test the following idea. If primordial galaxies evolve to a rapidly rotating, bar-like configuration before a significant amount of star formation has taken place, and then stars form from the gas that makes up the bar, the initial stellar distribution function should be much different than those used in previous bar formation studies. As a first step towards understanding such a distribution function, orbits in the two-dimensional, equatorial slice of the above mentioned bar are studied. Orbits that result from a systematic search of initial conditions are compared to orbits that have initial conditions determined by the Restriction Hypothesis. The Restriction Hypothesis is the implementation of the idea that stars are forming from the gas that makes up the bar. Specifically, the initial velocities of Restriction Hypothesis orbits are set equal to the known gas velocities at the points of formation. It is found that Restriction Hypothesis orbits are a subset of all possible orbits and that the most important regular orbit family has a "bow tie" shape. These orbits are vastly different than the main family of orbits previously thought to sustain bar shaped distributions. Extending the Restriction Hypothesis to the fully three-dimensional bar potential, a method of characterizing the resulting orbits based on the number of conserved quantities respected by the orbits has been utilized. These conserved quantities are known as integrals of motion and are related to the number of dimensions that a phase space orbit exists in. This technique is found to be robust and provides a straightforward way of categorizing orbits. Using this technique, it has been determined that a large percentage of examined three-dimensional Restriction Hypothesis orbits respect at least two integrals of motion.