# 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:

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

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

The `atm_irradiated_opacity`

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

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