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Ring galaxies are formed when a companion galaxy passes through the disk of a gas rich spiral along its rotation axis. Models indicate that strong orbit crowding forces much of the spiral's ISM into a series of expanding rings, while significantly reducing the gas surface density over the remainder of the disk. The large differences in surface density between the rings and disk that arise make these systems valuable test cases for gas threshold models of Massive Star Formation (MSF) in galaxies. We have combined aperture synthesis HI maps with H$\alpha$ CCD images of two large southern ring galaxies, the Cartwheel and AM0644-741, in order to map the distributions of neutral atomic gas and MSF, and to determine the threshold surface density for star formation throughout each system. We find that the neutral atomic gas surface density equals or exceeds the critical value only in the outer rings, where MSF is restricted. The regions interior to the starburst rings are significantly below threshold and show no evidence of H$\alpha$ emission. These results support the idea of a gas surface density threshold for star formation on large scales, although the situation is more complicated in the rings themselves.
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