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We explore a class of simple non-equilibrium star formation models within theframework of a feedback-regulated model of the ISM, applicable tokiloparsec-scale resolved star formation relations (e.g. Kennicutt-Schmidt).Combining a Toomre-Q-dependent local star formation efficiency per free-falltime with a model for delayed feedback, we are able to match the normalizationand scatter of resolved star formation scaling relations. In particular, thissimple model suggests that large ($\sim$dex) variations in star formation rates(SFRs) on kiloparsec scales may be due to the fact that supernova feedback isnot instantaneous following star formation. The scatter in SFRs at constant gassurface density in a galaxy then depends on the properties of feedback and whenwe observe its star-forming regions at various points throughout theircollapse/star formation "cycles". This has the following importantobservational consequences: (1) the scatter and normalization of theKennicutt-Schmidt relation are relatively insensitive to the local(small-scale) star formation efficiency, (2) but gas depletion times andvelocity dispersions are; (3) the scatter in and normalization of theKennicutt-Schmidt relation is a sensitive probe of the feedback timescale andstrength; (4) even in a model where $\tilde Q_{\rm gas}$ deterministicallydictates star formation locally, time evolution, variation in local conditions(e.g., gas fractions and dynamical times), and variations between galaxies candestroy much of the observable correlation between SFR and $\tilde Q_{\rm gas}$in resolved galaxy surveys. Additionally, this model exhibits large scatter inSFRs at low gas surface densities, in agreement with observations of flat outerHI disk velocity dispersion profiles.

A Simple Non-equilibrium Feedback Model for Galaxy-Scale Star Formation: Delayed Feedback and SFR Scatter