The star formation law in molecule-poor galaxies

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 H i. 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 et al. 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.