Whilst the star formation rate (SFR) of molecular clouds and galaxies is key in understanding galaxy evolution, the physical processes which determine the SFR remain unclear. This uncertainty about the underlying physics has resulted in various different star formation laws, all having substantial intrinsic scatter. Extending upon previous works that define the column density of star formation (Sigma_SFR) by the gas column density (Sigma_gas), we develop a new universal star formation (SF) law based on the multi-freefall prescription of gas. This new SF law relies predominantly on the probability density function (PDF) and on the sonic Mach number of the turbulence in the star-forming clouds. By doing so we derive a relation where the star formation rate (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 star formation. We show that placing observations in this new framework (Sigma_SFR vs. MGCR) yields a significantly improved correlation with 3-4 times reduced scatter compared to previous SF laws and a goodness-of-fit parameter R^2=0.97. By inverting our new relationship, we provide sonic Mach number predictions for kpc-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.
The following figure shows a comparison of previous star formation laws (the Kennicutt-Schmidt law in the left-hand panel and the Krumholz et al. 2012 law in the middle panel) with our new, universal, turbulence-regulated star formation law (right-hand panel). The scatter values shown each panel, the goodness-of-fit R^2 and the residuals demonstrate that the new universal law provides a significantly better correlation than any of the previous star formation laws.
This movie shows how the data points move from the single-freefall law by Krumholz et al. (2012) to our new multi-freefall star formation law. The correction factor from single- to multi-freefall clouds and galaxies is derived in the paper and depends on the turbulence (through its Mach number and driving) and the magnetic field strength. We note that the movie indicates that our new SF law overcorrects slightly, which is due to our assumption of zero magnetic field strength (which was the simplest assumption given the nonavailability of magnetic field measurements). This will be improved when detailed magnetic field measurements become available.
We thank Christopher McKee and the anonymous referee for useful comments, which improved this work. C.F. acknowledges funding provided by the Australian Research Council's (ARC) Discovery Projects (grants DP130102078 and DP150104329). L.J.K. gratefully acknowledges the support of an ARC Future Fellowship and ARC Discovery Project DP130103925.