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 Sµ S  ˙ G L 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 S ˙ scaling that are widely studied in the literature: SS S , , t t gas 3 2 gas orb gas ff and S v gas 2 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.