 Independent-volume supernova quenching

Before local expulsion, a linear star-formation law $\psi =\nu {\rho }_g$ without return gives ${\rho }_g={\rho }_0{e}^{-\nu t}$. If $q=\gamma E_{\mathrm{SN}}$ is the energy supplied per unit stellar mass, accumulated energy is $q{\rho }_0(1-e^{-\nu t})$. A fixed binding energy per unit remaining gas mass $B(r)$ gives the threshold $q(e^{\nu t}-1)=B(r)$. This assumes a specified retained gravitational profile and neglects exchange between volumes.