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The evolution of galaxies is driven by the intricate power play between magnetically driven turbulence and the mass and gravity of its comprising gas and dust, a system which governs the formation of stars in the dense cores of the interstellar medium’s giant molecular clouds. The rate at which such stars form is hence a pivotal quantity in tracing a galaxy’s fundamental properties and distribution of matter and activity. However, the parameterisation of the column density of star formation (Sigma_SFR) of a molecular cloud of gas in a galaxy has been a highly debatable topic for more than two decades, with historical parameterisations including the mean column density of available gas (Sigma_gas), as well as the ratio between Sigma_gas and the mean free-fall time (time it would take the molecular cloud to collapse under its own gravitational attraction) of the medium. Both these attempts at describing the Sigma_SFR have resulted in significant intrinsic scatter, and follow-up analysis of these models via computer simulations have determined that the observed scatter may be primarily attributed to the physical variations in the Mach number of the turbulence. This results in separate relations for the star formation rate depending on the Mach number of the medium, differing from each other by up to an order of magnitude. This discrepancy has shed light on the need for a more global description of the behaviour of the molecules in a gas cloud, illuminating the incompetency of a mere mean of the gas column density and free-fall time in accurately predicting the star-formation rate of a galactic medium. Instead, a cloud of gas would enclose molecules with a distribution of these two fundamental parameters, and the probability density function of volume densities and corresponding free-fall times as well as the Mach number of turbulence need be considered when endeavouring to construct a universal law for star formation rate. Addressing such concerns, we incorporate the distribution of probability densities to formulate a more universally encapsulating star formation rate law. We apply resolved observations from Milky Way molecular clouds to identify this relationship, and discern a correlation in which the star formation rate is equal to ~0.4% of molecular gas mass per multi-free-fall time. Employing our newly discovered relationship, we make 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 reliable estimates for such values. |
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