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Numerical restricted-three-body and analytic calculations are used to study the formation and propagation of cylindrically symmetric stellar ring waves in galaxy disks. These calculations assume a number of different gravitational potentials or potential components in the target galaxies, including softened point-mass, Hubble-like, and Plummer potentials, exponential disks, and a nearly isothermal halo. A variety of ring morphologies are found depending on the coUisional disturbance amplitude, and the form of the potentials. Alternately, the models suggest that morphological features, including: the number of separate nonoverlapping stellar rings, ring widths, and ring-to-ring separations, can provide useful information about the gravitational potential in ring galaxies. The application of singularity theory techniques to the kinematic radial oscillation model for rings of Lynds and Toomre (1976) and Toomre (1978) allows the analytic derivation of ring formation time; ring width as a function of time, position, ring number, and coUisional perturbation amplitude; and the relative overdensities of rings versus inter-ring regions. Good agreement is found between the analytic and numerical results which indicates that the approximations made in the simple kinematic model are valid, at least to the degree that the restricted three-body method represents real galaxies. Comparison of the models to real ring galaxies may provide certain knowledge of the properties of these galaxies, as well as impose constraints on the collision parameters responsible for their formation.

Simulational studies of the formation and properties of ring galaxies and leading one-arm spirals due to galaxy encounters