Feedback-regulated star formation in molecular clouds and galactic discs

We present a two-zone theory for feedback-regulated star formation in galactic discs, consistently connecting the galaxy-averaged star formation law with star formation proceeding in giant molecular clouds (GMCs). Our focus is on galaxies with gas surface density Sigma(g) greater than or similar to 100 M-circle dot pc(-2), where the interstellar medium (ISM) can be assumed to be fully molecular. This regime includes most star formation in the Universe and our basic framework can be extended to other galaxies. In our theory, the galactic disc consists of Toomre-mass GMCs embedded in a volume-filling ISM. Radiation pressure on dust disperses GMCs and most supernovae explode in the volume-filling medium. A galaxy-averaged star formation law is derived by balancing the momentum input from supernova feedback with the vertical gravitational weight of the disc gas. This star formation law is in good agreement with observations for a CO conversion factor depending continuously on Sigma(g). We argue that the galaxy-averaged star formation efficiency per free-fall time, epsilon(gal)(ff), is only a weak function of the efficiency with which GMCs convert their gas into stars, epsilon(GMC)(int). This is possible because the rate limiting step for star formation is the rate at which GMCs form: for large efficiency of star formation in GMCs, the Toomre Q parameter obtains a value slightly above unity so that the GMC formation rate is consistent with the galaxy-averaged star formation law. We contrast our results with other theories of turbulence-regulated star formation and discuss predictions of our model. Using a compilation of data from the literature, we show that the galaxy-averaged star formation efficiency per free-fall time is non-universal and increases with increasing gas fraction, as predicted by our model. We also predict that the fraction of the disc gas mass in bound GMCs decreases for increasing values of the GMC star formation efficiency. This is qualitatively consistent with the smooth molecular gas distribution inferred in local ultraluminous infrared galaxies and the small mass fraction in giant clumps in high-redshift galaxies.