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Whilst the star formation rate (SFR) of molecular clouds and galaxies is keyin understanding galaxy evolution, the physical processes which determine theSFR remain unclear. This uncertainty about the underlying physics has resultedin various different star formation laws, all having substantial intrinsicscatter. Extending upon previous works that define the column density of starformation (Sigma_SFR) by the gas column density (Sigma_gas), we develop a newuniversal star formation (SF) law based on the multi-freefall prescription ofgas. This new SF law relies predominantly on the probability density function(PDF) and on the sonic Mach number of the turbulence in the star-formingclouds. By doing so we derive a relation where the star formation rate (SFR)correlates with the molecular gas mass per multi-freefall time, whereasprevious models had used the average, single-freefall time. We define a newquantity called maximum (multi-freefall) gas consumption rate (MGCR) and showthat the actual SFR is only about 0.4% of this maximum possible SFR, confirmingthe observed low efficiency of star formation. We show that placingobservations in this new framework (Sigma_SFR vs. MGCR) yields a significantlyimproved correlation with 3-4 times reduced scatter compared to previous SFlaws and a goodness-of-fit parameter R^2=0.97. By inverting our newrelationship, we provide sonic Mach number predictions for kpc-scaleobservations of Local Group galaxies as well as unresolved observations oflocal and high-redshift disk and starburst galaxies that do not haveindependent, reliable estimates for the turbulent cloud Mach number.

A universal, turbulence-regulated star formation law: from Milky Way clouds to high-redshift disk and starburst galaxies