  In this paper, I investigate the processes that regulate the rate of star
formation in regions of galaxies where the neutral interstellar medium is
predominantly composed of non-star-forming HI. In such regions, found today
predominantly in low-metallicity dwarf galaxies and in the outer parts of large
spirals, the star formation rate per unit area and per unit mass is much
smaller than in more molecule-rich regions. While in molecule-rich regions the
ultraviolet radiation field produced by efficient star formation forces the
density of the cold neutral medium to a value set by two-phase equilibrium, I
show that the low rates of star formation found in molecule-poor regions
preclude this condition. Instead, the density of the cold neutral gas is set by
the requirements of hydrostatic balance. Using this result, I extend the
Krumholz, McKee, & Tumlinson model for star formation and the atomic to
molecular transition to the molecule-poor regime. This "KMT+" model matches a
wide range of observations of the star formation rate and the balance between
the atomic and molecular phases in dwarfs and in the outer parts of spirals,
and is well-suited to implementation as a subgrid recipe for star formation in
cosmological simulations and semi-analytic models. I discuss the implications
of this model for star formation over cosmological times.
