  We propose a simple analytic model to understand when star formation is
time-steady versus bursty in galaxies. Recent models explain the observed
Kennicutt-Schmidt relation between star formation rate and gas surface
densities in galaxies as resulting from a balance between stellar feedback and
gravity. We argue that bursty star formation occurs when such an equilibrium
cannot be stably sustained, and identify two regimes in which galaxy-scale star
formation should be bursty: i) at high redshift (z>~1) for galaxies of all
masses, and ii) at low masses (depending on gas fraction) for galaxies at any
redshift. At high redshift, characteristic galactic dynamical timescales become
too short for supernova feedback to effectively respond to gravitational
collapse in galactic discs (an effect recently identified for galactic nuclei),
whereas in dwarf galaxies star formation occurs in too few bright star-forming
regions to effectively average out. Burstiness is also enhanced at high
redshift owing to elevated gas fractions in the early Universe. Our model can
thus explain the bursty star formation rates predicted in these regimes by
recent high-resolution galaxy formation simulations, as well as the bursty star
formation histories observationally-inferred in both local dwarf and
high-redshift galaxies. In our model, bursty star formation is associated with
particularly strong spatio-temporal clustering of supernovae. Such clustering
can promote the formation of galactic winds and our model may thus also explain
the much higher wind mass loading factors inferred in high-redshift massive
galaxies relative to their z~0 counterparts.
