AST-9802918 Freeman About two-thirds of spiral galaxies are observed to be barred spirals. One type of ring, the inner resonance ring, appears in 76% of SBabSBc type galaxies. Thus rings are important in at least half of all spiral galaxies. Analytic studies and computer simulations of these rings will be carried out to see what they can also tell us about the pattern speeds of the bars and the disk/halo properties of galaxies. The latter are relevant to the dark matter problem. An analytic formulation permits determination of properties of resonance ring galaxies using basic observations of the rotation curve and an image of the galaxy. The disk gas clouds and stars' motion is reduced to a damped harmonic oscillation about a circular orbit. Rings occur near resonances of this oscillation with turning bars. Matching the analytic model to the morphology of the rings in a galaxy gives the galaxy's inclination, line of nodes, bar strength and pattern speed. Velocity data can also be used for more inclined galaxies. A variety of resonance ring galaxies will be modeled for which the data is available. Besides pattern speed and bar strength, we propose to use the matches to study whether four-fold resonances are important for outer as well as inner rings. Resonance rings appear to be a very good star formation laboratory. Star formation is promoted in rings when gas clouds are crowded near the end of the bar. As these stars orbit away from the bar, they age and their colors change. In contrast to difficulties in observing this effect across spiral arms, the change in color with increasing angle away from the bar is clear in the galaxy NGC 3081. Methods will be developed by using analytic theory and simulations to determine bar pattern speeds relative to the rotation curve. The change in color index with angle can thus be calibrated in years. This relation should be an alternative to and a test of theoretical color models versus ages in years of star formation complexes. These age determinations are important for star formation studies in other galaxies. ***
