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For fixed composition, electron-scattering opacity is effectively independent of mass density and temperature, so $\lambda =\nu =0$. With the specified CNO cycle exponent $\eta =16$, the homology relations for radiative stars giveThe radiative homology with CNO burning and electron scattering is thereforeThe Stefan–Boltzmann law now givesEquivalently $T_{\mathrm{eff}}\propto L^{9/76}$. These slopes are illustrated with arbitrary separate reference-model normalizations:

The proton–proton/Kramers model applies to the lower-mass regime; the CNO/electron-scattering model applies to the higher-mass regime. Higher-mass cores are hotter, making the more temperature-sensitive CNO cycle efficient, and highly ionized material favors electron-scattering opacity. These are the stated idealized radiative, gas-pressure-supported sequences: a fully convective low-mass star or a radiation-pressure-dominated massive star needs a different structural model. The intersection of independently normalized lines in the figure does not specify a physical crossover mass.

Retain the same stellar homology and gas-pressure assumptions, but use the specified CNO cycle law $ϵ\propto \rho T^{16}$ and constant electron-scattering opacity. The nuclear luminosity now scales asThe radiative diffusion in a star scaling becomesEquating the two yields $R^{19}\propto M^{15}$. Therefore radiative homology with CNO burning and electron scattering givesSince $R\propto L^{5/19}$, the Stefan–Boltzmann law givesThis is a model comparison using the exponent 16 prescribed here. Actual massive stars may have appreciable radiation pressure and convective cores, which violate the assumptions of this purely radiative gas-pressure family.