Stellar yield ($y_z$)

The stellar yield is the newly synthesized metal mass returned to gas per unit mass locked into long-lived stars, under a specified recycling convention and initial mass function.

Let a fraction $R$ of gross stellar birth mass return immediately, and let the new metal source be $bR\Psi$. The yield per permanently locked mass is then $y=bR/(1-R)$. Metal conservation in an initially pristine closed box gives $Z=y\ln (M_0/M_g)$. A coefficient defined by the metal source must not be confused with a yield normalized per locked stellar mass; the source convention must be stated, especially when taking $R\to 0$ or $R\to 1$ limits.