We present an analysis of the molecular gas distributions in the 29 barred and 15 unbarred spirals in BIMA SONG. For CO-bright galaxies, we confirm the conclusion by Sakamoto et al. (1999b) that barred spirals have higher molecular gas concentrations in the central kiloparsec. The SONG sample also includes 27 galaxies below the CO brightness limit used by Sakamoto et al. Even in these CO-faint galaxies we show that high central gas concentrations are more common in barred galaxies, consistent with radial inflow driven by the bar. However, there is a significant population of early-type (Sa--Sbc) barred spirals (6 of 19) that have little or no molecular gas detected in the nuclear region and out to the bar co-rotation radius. In these galaxies, the bar has already driven most of the gas within the bar to the nuclear region, where it has been consumed by star formation. The median nuclear gas mass is over four times higher in early type bars; since the gas consumption rate is an order of magnitude higher in early type bars, early types must have significantly higher bar-driven inflows. The lower inflow rates in late type bars can be attributed to differences in bar structure between early and late types. Despite bar-driven inflows, the data indicate that it is highly unlikely for a late type galaxy to evolve into an early type via bar-induced gas inflow. Nonetheless, secular evolutionary processes are undoubtedly present, and pseudo-bulges are inevitable; evidence for pseudo-bulges is likely to be clearest in early-type galaxies because of their high gas inflow rates and higher star formation activity (abridged).
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