 Solution

In the Sun's cool outer layers, partial ionization lowers the adiabatic temperature gradient, while large opacity makes radiative transport inefficient. The required radiative gradientcan exceed ${\nabla }_{\mathrm{ad}}$, so convection carries part of the outward luminosity. The Sun therefore has an outer convective envelope, above its primarily radiative interior. Here $a$ is the radiation constant, $\kappa$ opacity per unit mass and $m_r,L_r$ the enclosed mass and luminosity. Near the visible surface, radiative losses are again important and the flow need not be perfectly adiabatic.