We report high-resolution 12CO(J?= 2-1), 13CO(J?= 2-1), and 12CO(J?= 3-2) imaging of the Seyfert 1/starburst ring galaxy NGC?1097 with the Submillimeter Array for the purpose of studying the physical and kinematic properties of the 1?kpc circumnuclear starburst ring. Individual star clusters as detected in the Hubble Space Telescope map of Paα line emission have been used to determine the star formation rate (SFR), and are compared with the properties of the molecular gas. The molecular ring has been resolved into individual clumps at the giant molecular cloud association (GMA) scale of 200-300?pc in all three CO lines. The intersection between the dust lanes and the starburst ring, which is associated with the orbit-crowding region, is resolved into two physically/kinematically distinct features in the 15 × 10 (105 × 70?pc) 12CO(J?= 2-1) map. The clumps associated with the dust lanes have broader line widths, higher surface gas densities, and lower SFRs, while the narrow line clumps associated with the starburst ring have opposite characteristics. A Toomre-Q value lower than unity at the radius of the ring suggests that the molecular ring is gravitationally unstable to fragmentation at GMA scale. The line widths and surface density of the gas mass of the clumps show an azimuthal variation related to the large-scale dynamics. The SFR, on the other hand, is not significantly affected by the dynamics, but has a correlation with the intensity ratio of 12CO (J = 3-2) and 12CO(J?= 2-1), which traces the denser gas associated with star formation. Our resolved CO map, especially in the orbit-crowding region, observationally demonstrates for the first time that the physical/kinematic properties of GMAs are affected by the large-scale bar-potential dynamics in NGC?1097.
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