Fixed Surface Temperature

When the atm_option control has the value 'fixed_Tsurf', MESA sets \(T_{\rm surf}\) to the value specified by the atm_fixed_Tsurf control. The effective temperature is determined from the Eddington-grey \(T(\tau)\) relation

\[T_{\rm surf}^{4} = \frac{3}{4} T_{\rm eff}^{4} \left( \tau_{\rm surf} + 2/3 \right).\]

See here for a discussion of how the surface optical depth \(\tau_{\rm surf}\) is evaluated.

Then, MESA sets \(P_{\rm surf}\) to equal the radiation pressure associated with \(T_{\rm surf}\).