 Radiative homology with proton-proton burning and Kramers opacity

With proton–proton chain energy generation $ϵ\propto \rho T^4$ and Kramers' opacity law $\kappa \propto \rho T^{-7/2}$, homology relations for radiative stars giveThe Hertzsprung-Russell diagram relation has $d\log L/d\log T_{\mathrm{eff}}=284/69$, with effective temperature increasing toward the left in the usual plotting convention.