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. Kennicutt-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 ($\sim$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 timescale and
strength; (4) even in a model where $\tilde Q_{\rm gas}$ deterministically
dictates star formation locally, time evolution, variation in local conditions
(e.g., gas fractions and dynamical times), and variations between galaxies can
destroy much of the observable correlation between SFR and $\tilde Q_{\rm gas}$
in resolved galaxy surveys. Additionally, this model exhibits large scatter in
SFRs at low gas surface densities, in agreement with observations of flat outer
HI disk velocity dispersion profiles.
