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In astronomy, the Schmidt law is an empirical relationship between the surface density of gas in a galaxy and the rate at which stars form from that gas. ^{[1] [2]} It was first proposed in 1959 by Maarten Schmidt, in the context of star formation within our own Milky Way galaxy, but subsequent work has shown that it is valid within many different types of galaxies, ranging from the smallest star-forming dwarf galaxies to the largest starburst galaxies.

Formulation

If we write the star formation rate surface density (i.e. the rate at which star form per unit area of the Galactic disk) as ${\displaystyle \Sigma _{SFR}}$, and the gas surface density as ${\displaystyle \Sigma _{gas}}$, then the Schmidt law states that

${\displaystyle \Sigma _{SFR}\propto \Sigma _{gas}^{N}}$

The value of the exponent ${\displaystyle N}$ remains somewhat uncertain. Schmidt's original study found that ${\displaystyle N=2}$, but later observational studies found a value closer to ${\displaystyle N=1.5}$.

Within the past few years, however, it has become apparent that the value of ${\displaystyle N}$ depends upon the observational tracer used to determine ${\displaystyle \Sigma _{gas}}$. If the Schmidt law is written as a relationship between the star formation rate and the surface density of molecular gas, as traced by emission from carbon monoxide, then the standard value of ${\displaystyle N=1.5}$ is recovered. On the other hand, if the Schmidt law is written as a relationship between the star formation rate and an observational tracer of dense molecular gas, such as hydrogen cyanide, then a value of ${\displaystyle N=1}$ is recovered. ^[3]

Physical basis

References