On the functional form of the universal star-formation law

Abstract

We study the functional form of the star-formation law-using the Vaschy-Buckingham Pi theorem. We find that it should have the-form σ∗ ∝ √ σG/L3/2gas, 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 σ∗scaling-that are widely studied in the literature: σ 3/2gas σgas/torb and σ 2gas/Vturb. 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.