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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 ${\displaystyle n}$ of the local gas surface density. i.e.

${\displaystyle \Sigma _{SFR}\propto (\Sigma _{gas})^{n}}$.

In general, the SFR surface density ${\displaystyle (\Sigma _{SFR})}$ is in units of solar masses per year per square parsec ${\displaystyle (M_{\odot }~{\textrm {yr}}^{-1}{\textrm {pc}}^{-2})}$ and the gas surface density in grams per square parsec ${\displaystyle ({\textrm {g}}~{\textrm {pc}}^{-2})}$. 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 ${\displaystyle n\approx 2}$ (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${\displaystyle \alpha }$ intensities in a sample of 15 galaxies could be fit with the earlier Schmidt relations with a power law index of ${\displaystyle n=1.3\pm 0.3}$. More recently, he examined the connection between surface gas density and SFR for a larger set of galaxies to estimate a value of ${\displaystyle n=1.4\pm 0.15}$.

References

1. The name "Schmidt law" is now commonly used for a general relation between volume gas density and star formation rate, and the Kennicutt-Schmidt law for the surface gas density and star formation rate.
2. Schmidt, Maarten (1959). "The Rate of Star Formation". The Astrophysical Journal. 129: 243. Bibcode:1959ApJ...129..243S. doi:10.1086/146614.
3. Kennicutt, Robert C. Jr. (1989). "Star Formation Law in Galactic Disks". The Astrophysical Journal. 344 (2): 685. Bibcode:1989ApJ...344..685K. doi:10.1086/167834.
4. Kennicutt, Robert C. Jr. (1998). "The Global Schmidt Law in Star-forming Galaxies". The Astrophysical Journal. 498 (2): 541–552. arXiv:astro-ph/9712213. Bibcode:1998ApJ...498..541K. doi:10.1086/305588. S2CID 250812069.
5. Kennicutt, Robert C. Jr.; Evans, Neal II (2012). "Star Formation in the Milky Way and Nearby Gaalxies". Annual Review of Astronomy & Astrophysics. 50: 531–585. arXiv:1204.3552v2. Bibcode:2012ARA&A..50..531K. doi:10.1146/annurev-astro-081811-125610. S2CID 118667387.

• Stellar astronomy
• Galaxies
• Star formation