Irradiated Atmosphere

When the atm_option control has the value 'irradiated_grey', MESA defines the temperature structure of the atmosphere using the \(T(\tau)\) relation for the irradiated grey-atmosphere model of Guillot & Havel (2011, A&A 527, A20). A number of controls influence the evaluation of this model, as follows:

Controls for irradiated grey-atmosphere
Control	Meaning
`atm_irradiated_T_eq`	Equilibrium irradiation temperature \(T_{\rm eq}\)
`atm_irradiated_kap_v`	Mean visible opacity \(\kappa_{\rm v}\)
`atm_irradiated_kap_v_div_kap_th`	Ratio of mean visible opacity \(\kappa_{\rm v}\) to thermal opacity \(\kappa_{\rm th}\)

The pressure structure of the atmosphere is obtained by integrating the equation of hydrostatic equilibrium

\[\frac{{\rm d}P}{{\rm d}\tau} = \frac{g}{\kappa_{\rm th}}\]

under the assumption that the gravity \(g\) is spatially constant. The mean visible opacity, appearing in the \(T(\tau)\) relation, is evaluated via

\[\begin{split}\kappa_{\rm v} = \begin{cases} \kappa_{\rm th} \times {\tt atm\_irradiated\_kap\_v\_div\_v\_th} & {\tt atm\_irradiated\_kap\_v\_div\_v\_th} > 0 \\ {\tt atm\_irradiated\_kap\_v} & \text{otherwise} \end{cases}\end{split}\]

The atm_irradiated_opacity control determines how the thermal opacity \(\kappa_{\rm th}\) is evaluated, as follows:

The `atm_irradiated_opacity` control
Value	Meaning
`'fixed'`	Assume the same opacity at each optical depth (i.e. uniform opacity), equal to the the opacity in the outermost cell of the interior model. The equation of hydrostatic equilibrium is integrated analytically.
`'iterated'`	Assume the same opacity at each optical depth (again, uniform opacity), but use iteration to find an opacity consistent with the thermodynamic state at the base of the atmosphere. The equation of hydrostatic equilibrium is integrated analytically. Controls that affect the opacity iteration include `atm_irradiated_errtol` (sets the error tolerance) and `atm_irradiated_max_iters` (sets the maximum number of iterations).

Warning

MESA can sometimes run into convergence problems when the 'iterated' option is used.

Once the temperature and pressure structure of the atmosphere is known, MESA evaluates \(T(\tau)\) and \(P(\tau)\) at \(\tau=\tau_{\rm surf}\), providing the necessary \(T_{\rm surf}\) and \(P_{\rm surf}\) values for the boundary conditions. The nominal surface optical depth \(\tau_{\rm surf}\) is determined so that

\[P(\tau_{\rm surf}) = {\tt atm\_irradiated\_P\_surf}\]