The meaning and consequences of star formation criteria in galaxy models with resolved stellar feedback

We consider the effects of different criteria for determining where stars will form in gas on galactic scales, in simulations with high (1 pc) resolution, with explicitly resolved physics of Giant Molecular Cloud (GMC) formation and destruction, and stellar feedback from supernovae, radiation pressure, stellar winds and photoheating. We compare: (1) a self-gravity criterion (based on the local virial parameter and the assumption that self-gravitating gas collapses to high density in a single free-fall time), (2) a fixed density threshold, (3) a molecular-gas law, (4) a temperature threshold, (5) a requirement that the gas be Jeans unstable, (6) a criteria that cooling times be shorter than dynamical times and (7) a convergent-flow criterion. We consider all of these in both a Milky Way (MW)-like and high-density (starburst or high-redshift) galaxy. With feedback present, all models produce identical integrated star formation rates (SFRs), in good agreement with the Kennicutt relation; without feedback all produce orders-of-magnitude excessive SFRs. This is totally dependent on feedback and independent of the star formation (SF) law, even if the 'local' collapse efficiency is 100 per cent. However, the predicted spatial and density distribution depend strongly on the SF criteria. Because cooling rates are generally fast within galaxy discs, and gas is turbulent, criteria (4)-(7) are very 'weak' and spread the SF uniformly over most of the disc (down to densities n similar to 0.01-0.1 cm(-3)). A molecular criterion (3) localizes to slightly higher densities, but still a wide range; for metallicity near solar, it is almost identical to a fixed density threshold at n similar to 1 cm(-3) (well below the mean density in the central MW or starburst systems). A fixed density threshold (2) can always select the highest resolved densities, but must be adjusted both for simulation resolution and individual galaxy properties - the same threshold that works well in a MW-like simulation will select nearly all gas in a starburst. Binding criteria (1) tend to adaptively select the largest local overdensities, independent of galaxy model or resolution, and automatically predict clustered SF. We argue that this SF model (possible with other secondary criteria) is most physically motivated and presents significant numerical advantages in simulations with a large dynamic range.