= Power-law opacity radiative envelope
{title2=$\nabla_{\rm rad}=P^{n+1}/(CT^{n+s+4})$}
A thin <radiative envelope> with constant enclosed mass, luminosity and <mean molecular weight>, <ideal gas> pressure and opacity $\kappa=\kappa_0\rho^nT^{-s}$ has $a=n+1$, $b=n+s+4$, and $C=16\pi a_{\rm rad}cGM/[3\kappa_0(\mu m_u/k_B)^nL]$. Combining <radiative diffusion in a star> with <hydrostatic equilibrium> gives $\nabla_{\rm rad}=P^a/(CT^b)$, so $P^a-P_0^a=(aC/b)(T^b-T_0^b)$ for nonzero exponents. Zero exponents give logarithmic limits. The model must be stopped or modified if the <Schwarzschild criterion> predicts <convection>.
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