Gravity or turbulence? – VI. The physics behind the Kennicutt–Schmidt relation

ABSTRACT We explain the large variety of star formation laws in terms of one single, simple law that can be inferred from the definition of the star formation rate and basic algebra. The resulting equation, ${\rm SFR}= {\epsilon _\mathrm{ff}}\ M_\mathrm{collapse}/{\tau _{\rm ff}}$, although it has been presented elsewhere, is interpreted in terms of clouds undergoing collapse rather than being turbulence supported, an idea that different groups have pursued this century. Under such assumption, one can explain the constancy of ${\epsilon _\mathrm{ff}}$, the different intra-cloud correlations observed in Milky Way’s molecular clouds, as well as the resolved and unresolved extragalactic relationships between SFR and a measurement of the mass in CO, HCN, and CO + HI. We also explain why the slope of the correlation changes when the orbital time ${\tau _{\rm orb}}$ is considered instead of the free-fall time, and why estimations of the free-fall time from extragalactic observations skew the correlation, providing a false sublinear correlation. We furthermore show that the apparent nearly linear correlation between the star formation rate and the dynamical equilibrium pressure in the mid-plane of the galaxies, $P_{\rm DE}$, is just a consequence of $P_{\rm DE}$ values being dominated by the variation of the column density of molecular gas. All in all, we argue that the star formation law is driven by the collapse of cold, dense gas, which happens to be primarily molecular in the present Universe, and that the role of stellar feedback is just to shut down the star formation process, not to shape the star formation law.