= Radiative homology with proton-proton burning and Kramers opacity
With <proton–proton chain> energy generation $\epsilon\propto\rho T^4$ and <Kramers opacity law> $\kappa\propto\rho T^{-7/2}$, <homology relations for radiative stars> give
$$
R\propto M^{1/13},\qquad L\propto M^{71/13},\qquad
T_{\rm eff}\propto L^{69/284}.
$$
The <Hertzsprung-Russell diagram> relation has $d\log L/d\log T_{\rm eff}=284/69$, with <effective temperature> increasing toward the left in the usual plotting convention.
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