Kennicutt–Schmidt law

In astronomy, the Kennicutt–Schmidt law is an empirical relation between the surface gas density and star formation rate (SFR) in a given region. The relation was first examined by Maarten Schmidt in a 1959 paper  where he proposed that the SFR surface density scales as some positive power $$n$$ of the local gas surface density. i.e.
 * $$\Sigma_{SFR} \propto (\Sigma_{gas})^n$$.

In general, the SFR surface density $$(\Sigma_{SFR})$$ is in units of solar masses per year per square parsec $$(M_\odot ~\textrm{ yr}^{-1} \textrm{ pc}^{-2})$$ and the gas surface density in grams per square parsec $$(\textrm{g}~\textrm{pc}^{-2})$$. Using an analysis of gaseous helium and young stars in the solar neighborhood, the local density of white dwarfs and their luminosity function, and the local helium density, Schmidt suggested a value of $$n \approx 2$$ (and very likely between 1 and 3). All of the data used were gathered from the Milky Way, and specifically the solar neighborhood.

In 1989, Robert Kennicutt found that the H$$\alpha $$ intensities in a sample of 15 galaxies could be fit with the earlier Schmidt relations with a power law index of $$n = 1.3 \pm 0.3$$. More recently, he examined the connection between surface gas density and SFR for a larger set of galaxies to estimate a value of $$n = 1.4 \pm 0.15$$.