A Universal, Turbulence-regulated Star Formation Law: From Milky Way Clouds to High-redshift Disk and Starburst Galaxies

While the star formation rate (SFR) of molecular clouds and galaxies is key in understanding galaxy evolution, the physical processes that determine the SFR remain unclear. This uncertainty about the underlying physics has resulted in various different star formation (SF) laws, all having substantial intrinsic scatter. Extending upon previous works that define the column density of star formation () by the gas column density (), we develop a new universal SF law based on the multi-freefall prescription of gas. This new SF law relies predominantly on the probability density function and on the sonic Mach number of the turbulence in the star-forming clouds. By doing so we derive a relation where the SFR correlates with the molecular gas mass per multi-freefall time, whereas previous models had used the average, single-freefall time. We define a new quantity called maximum (multi-freefall) gas consumption rate (MGCR) and show that the actual SFR is only about 0.4% of this maximum possible SFR, confirming the observed low efficiency of SF. We show that placing observations in this new framework ( versus MGCR) yields a significantly improved correlation with 3?4 times reduced scatter compared to previous SF laws and a goodness-of-fit parameter . By inverting our new relationship, we provide sonic Mach number predictions for kiloparsec-scale observations of Local Group galaxies as well as unresolved observations of local and high-redshift disk and starburst galaxies that do not have independent, reliable estimates for the turbulent cloud Mach number.