Eddington Grey Atmosphere

What you are seeing: the textbook temperature profile of a grey stellar atmosphere in radiative equilibrium $T(\tau) = T_\text{eff} [3/4 (\tau + 2/3)]^{1/4}$. Three special points are marked: the photosphere at $\tau = 2/3$ where $T = T_\text{eff}$, the boundary $\tau = 0$ where $T = T_\text{eff}/\sqrt[4]{2}$, and the deep-interior asymptote $T \to T_\text{eff} (3\tau/4)^{1/4}$.

The right panel shows the linear Eddington limb-darkening law $I(\mu)/I(1) = 0.4 + 0.6\mu$ (with $\mu = \cos\theta$). The center of the solar disk is bright; the limb is dimmer by 60 percent. This is what gives the Sun its visible darkening toward the edge.