 Degenerate-core shell-burning mass-luminosity relation

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 $ϵ\propto \rho T^{10}$, 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 $L\propto C^2{M}_c^{16}{R}_c^{-13}$, 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.