Convective stability of a constant-opacity irradiated atmosphere
= Convective stability of a constant-opacity irradiated atmosphere
A constant radiative-diffusion coefficient and constant gravity give $T^4=T_0^4+4AP/g$. Thus $\nabla_{\rm rad}=AP/(gT^4)<1/4$ for $T_0>0$. A diatomic <ideal gas> has <adiabatic temperature gradient> $2/7$, so this idealized profile never becomes convective. A physical <radiative-convective boundary> requires additional <opacity>, flux, or thermodynamic variation.