A simple non-equilibrium feedback model for galaxy-scale star formation: delayed feedback and SFR scatter

We explore a class of simple non-equilibrium star formation models within the framework of a feedback-regulated model of the ISM, applicable to kiloparsec-scale resolved star formation relations (e.g, Kennicult-Schmidt), Combining a Toomre-Q-dependent local star formation efficiency per free-fall time with a model for delayed feedback, we are able to match the normalization and scatter of resolved star formation scaling relations. In particular, this simple model suggests that large (similar to dex) variations in star formation rates (SFRs) on kiloparsec scales may be due to the fact that supernova feedback is not instantaneous following star formation. The scatter in SFRs at constant gas surface density in a galaxy then depends on the properties of feedback and when we observe its star-forming regions at various points throughout their collapse/star formation 'cycles'. This has the following important observational consequences: (1) the scatter and normalization of the Kennicutt Schmidt relation are relatively insensitive to the local (small-scale) star formation efficiency; (2) but gas depletion times and velocity dispersions are, (3) the scatter in and normalization of the Kennicutt Schmidt relation is a sensitive probe of the feedback time-scale and strength; (4) even in a model where (Q) over tilde gas deterministically dictates star formation locally, lime evolution, variation in local conditions (e.g. gas fractions and dynamical limes), and variations between galaxies can destroy much of the observable correlation between SFR and (Q) over tilde gas in resolved galaxy surveys, Additionally, this model exhibits large scatter in SFRs at low gas surface densities, in agreement with observations of dal outer H I disc velocity dispersion proliles.