Using observations from the GASS and COLD GASS surveys and complementary data from SDSS and GALEX, we investigate the nature of variations in gas depletion time observed across the local massive galaxy population. The large and unbiased COLD GASS sample allows us to assess the relative importance of galaxy interactions, bar instabilities, morphologies and the presence of AGN in regulating star formation efficiency. Both the H2 mass fraction and depletion time vary as a function of the distance of a galaxy from the main sequence in the SFR-M* plane. The longest gas depletion times are found in below-main sequence bulge-dominated galaxies that are either gas-poor, or else on average less efficient than disk-dominated galaxy at converting into stars any cold gas they may have. We find no link between AGN and these long depletion times. The galaxies undergoing mergers or showing signs of morphological disruptions have the shortest molecular gas depletion times, while those hosting strong stellar bars have only marginally higher global star formation efficiencies as compared to matched control samples. Our interpretation is that depletion time variations are caused by changes in the ratio between the gas mass traced by the CO(1-0) observations, and the gas mass in high density star-forming cores, with interactions, mergers and bar instabilities able to locally increase pressure and raise the ratio of efficiently star-forming gas to CO-detected gas. Building a sample representative of the local massive galaxy population, we derive a global Kennicutt-Schmidt relation of slope 1.18+/-0.24, and observe structure within the scatter around this relation, with galaxies having low (high) stellar mass surface densities lying systematically above (below) the mean relation, suggesting that gas surface density is not the only parameter driving the global star formation ability of a galaxy.
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