  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.
