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 (Σ SFR ) by the gas column density (Σ 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 (Σ 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.

Stars form in cold molecular clouds. However, molecular gas is difficult to observe because the most abundant molecule (H 2 ) lacks a permanent dipole moment. Rotational transitions of CO are often used as a tracer of H 2 , but CO is much less abundant and the conversion from CO intensity to H 2 mass is often highly uncertain. Here we present a new method for estimating the column density of cold molecular gas (Σ gas ) using optical spectroscopy. We utilise the spatially resolved Hα maps of flux and velocity dispersion from the Sydney-AAO Multi-object Integral-field spectrograph (SAMI) Galaxy Survey. We derive maps of Σ gas by inverting the multi-freefall star formation relation, which connects the star formation rate surface density (Σ SFR ) with Σ gas and the turbulent Mach number (M). Based on the measured range of Σ SFR = 0.005-1.5 M yr −1 kpc −2 and M = 18-130, we predict Σ gas = 7-200 M pc −2 in the star-forming regions of our sample of 260 SAMI galaxies. These values are close to previously measured Σ gas obtained directly with unresolved CO observations of similar galaxies at low redshift. We classify each galaxy in our sample as 'Star-forming' (219) or 'Composite/AGN/Shock' (41), and find that in 'Composite/AGN/Shock' galaxies the average Σ SFR , M, and Σ gas are enhanced by factors of 2.0, 1.6, and 1.3, respectively, compared to Star-forming galaxies. We compare our predictions of Σ gas with those obtained by inverting the Kennicutt-Schmidt relation and find that our new method is a factor of two more accurate in predicting Σ gas , with an average deviation of 32% from the actual Σ gas .

We determine the physical properties and turbulence driving mode of molecular clouds formed in numerical simulations of a Milky Way-type disc galaxy with parsec-scale resolution. The clouds form through gravitational fragmentation of the gas, leading to average values for mass, radii and velocity dispersion in good agreement with observations of Milky Way clouds. The driving parameter (b) for the turbulence within each cloud is characterised by the ratio of the density contrast (σ ρ/ρ0 ) to the average Mach number (M) within the cloud, b = σ ρ/ρ0 /M. As shown in previous works, b ∼ 1/3 indicates solenoidal (divergence-free) driving and b ∼ 1 indicates compressive (curl-free) driving. We find that the average b value of all the clouds formed in the simulations has a lower limit of b > 0.2. Importantly, we find that b has a broad distribution, covering values from purely solenoidal to purely compressive driving. Tracking the evolution of individual clouds reveals that the b value for each cloud does not vary significantly over their lifetime. Finally, we perform a resolution study with minimum cell sizes of 8, 4, 2 and 1 pc and find that the average b value increases with increasing resolution. Therefore, we conclude that our measured b values are strictly lower limits and that a resolution better than 1 pc is required for convergence. However, regardless of the resolution, we find that b varies by factors of a few in all cases, which means that the effective driving mode alters significantly from cloud to cloud.