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 $n=1.4\pm 0.15$.