2012ApJ...745...69K

Star formation laws are rules that relate the rate of star formation in a particular region, either an entire galaxy or some portion of it, to the properties of the gas, or other galactic properties, in that region. While observations of Local Group galaxies show a very simple, local star formation law in which the star formation rate per unit area in each patch of a galaxy scales linearly with the molecular gas surface density in that patch, recent observations of both Milky Way molecular clouds and high-redshift galaxies apparently show a more complicated relationship in which regions of equal molecular gas surface density can form stars at quite different rates. These data have been interpreted as implying either that different star formation laws may apply in different circumstances, that the star formation law is sensitive to large-scale galaxy properties rather than local properties, or that there are high-density thresholds for star formation. Here we collate observations of the relationship between gas and star formation rate from resolved observations of Milky Way molecular clouds, from kpc-scale observations of Local Group galaxies, and from unresolved observations of both disk and starburst galaxies in the local universe and at high redshift. We show that all of these data are in fact consistent with a simple, local, volumetric star formation law. The apparent variations stem from the fact that the observed objects have a wide variety of three-dimensional size scales and degrees of internal clumping, so even at fixed gas column density the regions being observed can have wildly varying volume densities. We provide a simple theoretical framework to remove this projection effect, and we use it to show that all the data, from small solar neighborhood clouds with masses ∼10³ M_☉ to submillimeter galaxies with masses ∼10¹¹ M_☉, fall on a single star formation law in which the star formation rate is simply ∼1% of the molecular gas mass per local free-fall time. In contrast, proposed star formation laws in which the star formation timescale is set by the galactic rotation period are inconsistent with the data from the Milky Way and the Local Group, while those in which the star formation rate is linearly proportional to the gas mass above some density threshold fail both in the Local Group and for starburst galaxies.