Double bars have been proposed as a means of transporting molecular gas past inner Lindblad resonances into the nuclear regions, where it can fuel active or starburst nuclei. Thus far, the existence of double bars has been determined predominantly through analysis of near-infrared images, which can tell us little about the dynamics and inflow rates of these systems. We have observed two double-bar galaxy candidates (NGC 2273 and NGC 5728) in 12CO J = 1-0 with the Owens Valley Radio Observatory Millimeter Array. Despite the similarity in the near-infrared images of these galaxies, we see rather different nuclear morphologies in the CO maps. NGC 2273 shows evidence of a nuclear gas bar, aligned with the nuclear stellar bar seen in the near-infrared images. Both the nuclear gaseous and the stellar bars are misaligned from the large-scale bar by ~90°, which also allows the possibility that both are the result of stars and gas populating the x2 orbits of the primary bar. Estimates using dynamical friction arguments and star formation rates suggest significant gas inflow rates along the nuclear bar of NGC 2273. Conversely, NGC 5728 does not show any evidence for a nuclear molecular bar but shows an arc of CO clumps that peaks just to the southwest of the dynamical center and curves to the southeast, where it follows the dust lane to the south. Models of double-barred galaxies suggest that these galaxies should contain large amounts of molecular gas in their nuclei. Our calculations suggest that both galaxies contain sufficient amounts of gas in their nuclei, but only NGC 2273 shows evidence for a nuclear gas bar. This may be the result of past episodes of star formation exhausting and dispersing the nuclear gas of NGC 5728, but it is more likely evidence that NGC 5728 has undergone a minor merger event.
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