Constant flux in a plane-parallel radiative-equilibrium atmosphere
= Constant flux in a plane-parallel radiative-equilibrium atmosphere
Taking the first angular moment of the radiative-transfer equation gives $dF_\nu/dz=4\pi\alpha_\nu(S_\nu-J_\nu)$. Radiative equilibrium sets the frequency integral of the right-hand side to zero, so the bolometric flux is constant with depth.