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