= Saturating closed-box enrichment law
{title2=$Z_g=1-\mu^Y$}
A finite-metal-fraction variant of the <closed-box model of galactic chemical evolution> uses effective <stellar yield> $Y(1-Z_g)$, rather than constant yield. With pristine initial gas and $Y>0$, metal accounting gives $dZ_g/d\log(1/\mu)=Y(1-Z_g)$ and hence $Z_g=1-\mu^Y$. The mass-weighted mean <stellar metallicity> is $[Y-(Y+1)\mu+\mu^{Y+1}]/[(Y+1)(1-\mu)]$. At final gas fraction $\mu_f$, the <metallicity distribution function> is $(1-z)^{1/Y-1}/[Y(1-\mu_f)]$ on $0<z<1-\mu_f^Y$. For trace abundances, $Z_g\simeq-Y\log\mu$ and the usual <closed-box metallicity distribution> is recovered to leading order.
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