= Metallicity distribution in the half-rate infall model
{title2=$dN/dZ=\kappa M_0/y$}
For $\nu=1/2$ and initially pristine gas, $M=M_0(1-Z/(2y))$ and the formed stellar mass is $S=2(M_0-M)=M_0Z/y$. If a fixed <initial mass function> supplies $\kappa$ surviving tracers per unit formed mass, then $N(<Z)=\kappa M_0Z/y$ and $dN/dZ=\kappa M_0/y$ until the current gas abundance. Complete exhaustion gives a uniform normalized <metallicity distribution function> on $0<Z<2y$. This is uniform in linear metallicity, not in its logarithm.
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