Kennicutt–Schmidt law

In astronomy, the Kennicutt–Schmidt Law (or simply Schmidt Law) is an empirical relation between the gas density and star formation rate (SFR) in a given region. The relation was first examined by Maarten Schmidt in a 1959 paper in which he proposed that the SFR surface density scales as some positive power $n$ of the local gas surface density.^[1] 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.

More recently, Robert Kennicutt examined the connection between gas density and SFR for nearly 100 nearby galaxies to estimate a value of $n = 1.4 \pm 0.15$.^[2]

References

1. Schmidt, Maarten (1959). "The Rate of Star Formation". The Astrophysical Journal. 129: 243. Bibcode:1959ApJ...129..243S. doi:10.1086/146614.
2. Kennicutt, Robert C., Jr. (1998). "The Global Schmidt Law in Star-forming Galaxies". The Astrophysical Journal. 498: 541. arXiv:astro-ph/9712213. Bibcode:1998ApJ...498..541K. doi:10.1086/305588.