Weak Hopf algebra

In astronomy, the Kennicutt–Schmidt (or simply the Schmidt \lLaw) 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. i.e.

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

In general the SFR surface density $({\mathrm{\Sigma }}_{SFR})$ is in units of solar masses per year per square parsec $(M_{\odot }{\text{<mrow data-mjx-texclass="ORD">yr</mrow>}}^{-1}{\text{<mrow data-mjx-texclass="ORD">pc</mrow>}}^{-2})$ and the gas surface density in grams per square parsec $(\text{g}{\text{<mrow data-mjx-texclass="ORD">pc</mrow>}}^{-2})$. 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 $n=1.4\pm 0.15$.

References

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