= Constant gas-radiation ratio vertical disc structure
{title2=$T\propto1-z^2/H^2,\quad\rho\propto T^3,\quad p\propto T^4$}
For constant positive $\lambda=p_r/p_g$ and molecular gas constant $\mathcal R=k/(\mu_m m_p)$, the gas–radiation <equation of state> gives $\rho=4\sigma T^3/(3c\lambda\mathcal R)$. Vertical <hydrostatic equilibrium> in harmonic central gravity therefore gives $T=T_0(1-z^2/H^2)$ with $T_0=\Omega^2H^2/[8(1+\lambda)\mathcal R]$. The <mass density> and <pressure> powers are three and four. Integrating both faces yields $\Sigma=(32/35)\rho_0H$ and $\int p\,dz=\Sigma\Omega^2H^2/9$. With constant <opacity>, <radiative diffusion> produces a linear flux and height-independent <dynamic viscosity> $\mu=4c\lambda/[9\kappa(1+\lambda)]$. This is an interior formal profile; its low-density surface requires a photospheric treatment beyond diffusion.
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