Emergence of the Kennicutt-Schmidt Relation from the Small-Scale   SFR-Density Relation
  We use simulations of isolated galaxies with a few parsec resolution to explore the connection between the small-scale star formation rate - gas density relation and the induced large-scale correlation between the star formation rate surface density and the surface density of the molecular gas (the Kennicutt-Schmidt relation). We find that, in the simulations, a power-law small-scale "star formation law" directly translates into an identical power-law Kennicutt-Schmidt relation. If this conclusion holds in the reality as well, it implies that the observed approximately linear Kennicutt-Schmidt relation must reflect the approximately linear small-scale "star formation law". 
Nickolay Y. Gnedin, Elizabeth J. Tasker, Yusuke Fujimoto
astro-ph.GA