We use the high spatial and spectral resolution of the PAWS CO(1-0) survey of the inner 9 kpc of the iconic spiral galaxy M51 to examine the effect of gas streaming motions on the star-forming properties of individual GMCs. We compare our view of gas flows in M51 -- which arise due to departures from axi-symmetry in the gravitational potential (i.e. the nuclear bar and spiral arms) -- with the global pattern of star formation as traced by Halpha and 24mu m emission. We find that the dynamical environment of GMCs strongly affects their ability to form stars, in the sense that GMCs situated in regions with large streaming motions can be stabilized, while similarly massive GMCs in regions without streaming go on to efficiently form stars. We argue that this is the result of reduced surface pressure felt by clouds embedded in an ambient medium undergoing large streaming motions, which prevents collapse. Indeed, the variation in gas depletion time expected based on the observed streaming motions throughout the disk of M51 quantitatively agrees with the variation in observed gas depletion time scale. The example of M51 shows that streaming motions, triggered by gravitational instabilities in the form of bars and spiral arms, can alter the star formation law; this can explain the variation in gas depletion time among galaxies with different masses and morphologies. In particular, we can explain the long gas depletion times in spiral galaxies compared to dwarf galaxies and starbursts. We suggest that adding a dynamical pressure term to the canonical free-fall time produces a single star formation law that can be applied to all star-forming regions and galaxies, across cosmic time.
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