= Degenerate-core shell-burning mass-luminosity relation
{title2=$L\propto M_c^{32/3}$}
In a thin-shell giant model with a nonrelativistic degenerate core, $R_c\propto M_c^{-1/3}$. For a gas-pressure radiative layer with $\kappa\propto\rho T^{-3}$ and specific energy generation $\epsilon\propto\rho T^{10}$, the deep profile has $P\propto T^4$, $\rho\propto T^3$ and $T\propto M_c/r$. Integrating the strongly concentrated shell power gives $L\propto C^2M_c^{16}R_c^{-13}$, while radiative transport gives $C^2\propto M_c/L$. Therefore $L^2\propto M_c^{17}R_c^{-13}$, yielding the displayed exponent. This is a model-specific scaling, not a universal core-mass law; it fails when envelope stripping removes the shell fuel or the confining structure.
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