= Retained-ejecta chemical evolution
{title2=$d(gZ)/ds=-(1-\beta f)Z/(1-\beta)+yf$}
Under the <instantaneous recycling approximation>, forming mass $dM$ locks $ds=(1-\beta)dM$ into <stars>. If a fraction $f$ of returned material remains in the <interstellar medium>, the retained original metal mass is $\beta fZ\,dM$, and retained newly made metal mass is $fy\,ds$, where $y$ is the <stellar yield> per locked mass. Subtracting the metal mass $Z\,dM$ initially consumed gives the displayed equation. Pristine <galactic gas inflow> adds gas but no metals; enriched inflow adds its metal mass separately. The retained fraction applies to both old and newly made metals in this idealization.
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