= Composition-dependent CNO homology
{title2=$L\propto\mu^4M^3/\kappa,\quad R\propto(X\kappa\mu^9)^{1/16}M^{3/4}$}
For homologous, chemically uniform, gas-pressure-supported radiative stars with specific energy generation $\epsilon\propto X\rho T^{13}$ and composition-dependent constant <opacity>, <stellar homology> gives $L_{\mathrm{nuc}}\propto X\mu^{13}M^{15}R^{-16}$ and $L_{\mathrm{rad}}\propto\mu^4M^3/\kappa$. Equating them gives the displayed scalings. <Hydrogen> depletion changes both <mean molecular weight> and <electron-scattering opacity>; holding composition fixed gives $R\propto M^{3/4}$ and $L\propto M^3$. The power-law burning approximation applies only while <hydrogen> fuel remains.
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