On the Functional form of the Universal Star-Fomation 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 S μ 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: Sgas, S t , S t 3 2 gas orb gas ff and Sgas v 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.