Eddington-model convective-core mass fraction ($M_c/M=1/(4{\nabla }_{\mathrm{ad}})={\Gamma }_2/[4({\Gamma }_2-1)]$)

The global Eddington closure $L=(1-\beta )4\pi cGM/\kappa$, combined with a representative stellar gas-pressure fraction, makes the exterior stellar radiative temperature gradient approximately $M/(4m)$ when the luminosity is constant outside the core. Matching it to the adiabatic temperature gradient estimates the displayed boundary mass. This is a closure estimate: imposing exactly uniform $\beta$ throughout a finite-mass radiative envelope also conflicts with constant luminosity, as described by the constant-beta radiative-envelope obstruction.