2015ApJ...804...54E

We study the functional form of the star-formation law using the Vaschy-Buckingham Pi theorem. We find that it should have the form {dot}Σ_* ∝ sqrt(G/L)Σ_gas^3/2, where L is a characteristic length that is related to an integration scale. With a reasonable estimate for L, we find that galaxies of different types and redshifts, including low-surface-brightness galaxies and individual star-forming regions in our Galaxy, obey this single star-formation law. We also find that, depending on the assumption for L, this star-formation law adopts different formulations of {dot}Σ_* scaling that are widely studied in the literature: Σ_gas^3/2, Σ_gas/t_orb, Σ_gas/t_ff and Σ_gas²/ν_turb. We also study secondary controlling parameters of the star-formation law based on the current evidence from numerical simulations, and we find that for galaxies the star-formation efficiency should be controlled, at least, by the turbulent Toomre parameter and the sonic and Alfvénic Mach numbers.