The Star Formation Law in Atomic and Molecular Gas

We propose a simple theoretical model for star formation in which the local star formation rate (SFR) in a galaxy is determined by three factors. First, the interplay between the interstellar radiation field and molecular self-shielding determines what fraction of the gas is in molecular form and thus eligible to form stars. Second, internal feedback determines the properties of the molecular clouds that form, which are nearly independent of galaxy properties until the galactic interstellar medium (ISM) pressure becomes comparable to the internal giant molecular cloud (GMC) pressure. Above this limit, galactic ISM pressure determines molecular gas properties. Third, the turbulence driven by feedback processes in GMCs makes star formation slow, allowing a small fraction of the gas to be converted to stars per free-fall time within the molecular clouds. We combine analytic estimates for each of these steps to formulate a single star formation law, and show that the predicted correlation between SFR, metallicity, and surface densities of atomic, molecular, and total gas agree well with observations.