Leaky-box model of galactic chemical evolution

The leaky-box model adds a galactic outflow to the closed box. If the outflow has the ambient gas metallicity and constant mass-loading factor $\lambda$, its effective yield is reduced to $y/(1+\lambda )$ when returned fractions are absorbed into the definitions.

For initially pristine gas, zero bulk mass return, a constant stellar yield $y$ and a well-mixed galactic outflow of mass-loading factor $\nu$, gas conservation gives $d{M}_g=-(1+\nu )d{M}_s$ and metal accounting gives $M_{g}dZ=yd{M}_s$. Consequently $M_g=M_{g,0}{e}^{-Z/y_e}$ with $y_e=y/(1+\nu )$. Since $d{M}_s/dZ=M_g/y$, complete depletion gives a normalized mass-weighted metallicity distribution function $p(Z)=e^{-Z/y_e}/y_e$ and mean stellar metallicity $y_e$. A time-independent initial mass function makes the distribution of surviving tracers proportional to this distribution; a sample selected by light need not have the same weights.

The effective yield is the yield that a simple closed-box relation would need to reproduce an observed gas fraction and metallicity. Outflow and pristine inflow generally lower it below the nucleosynthetic yield.