Schmidt Law

Schmidt (1959) speculated that the star formation rate is proportional to a power of the surface density of the interstellar medium

$$\dot{\Sigma}_{\rm SF}\propto \Sigma_{\rm gas}^n,$$ (3.1)

where the power $n$ seems between 1 and 2 around the solar vicinity. If $n=2$, the star formation rate is thought to be determined by the collision rate of interstellar clouds. At that time Schmidt showed us $n\simeq 2$. On the other hand, if the gas passing through the galactic arms forms stars, the star formation rate seems proportional to the gas surface density and the arm-to-arm period. Thus this predicts $n=1$.