= Homogeneous fuel-depletion luminosity feedback
{title2=$L(t)=L_0\left(1-\frac{40L_0t}{ME_H(3+5X_0)}\right)^{-7/8}$}
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 $d(s^8)/dt=-40L_0s_0^7/(ME_H)$, 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.
Back to article page
