 Homogeneous fuel-depletion luminosity feedback

For a fixed-mass fully mixed hydrogen burning star with $\mu =4/(3+5X)$ whose radiative stellar homology gives $L\propto {\mu }^7$, put $s=3+5X$. The luminosity is $L=L_0(s_0/s{)}^7$ and fuel conservation gives $M{E}_H\dot{X}=-L$. Hence $d(s^8)/dt=-40L_0{s}_0^7/(M{E}_H)$, producing the displayed feedback law. This applies both to CNO homology with density-dependent inverse-cubic opacity and to radiative homology with fifth-power hydrogen burning and inverse-cubic opacity, at fixed metal mass fraction in the latter. Its physical domain ends at $X=0$, before the formal denominator vanishes. The idealization holds the coefficient normalizations fixed while stellar composition changes through the mean molecular weight and fuel abundance.