This test checks the implementation of the control use_T_tau_gradr_factor, which modifies the radiative gradient so that regions of low optical depth have a temperature that follows the $$T(\tau)$$ relation specified by atm_T_tau_relation. This is useful if you’d like to include regions of small optical depth as if they’re part of the interior model.

The test changes atm_T_tau_relation every 10 steps to cycle through all the available options. At each step, it computes the sum of squared differences (stored as chi2) between the stellar model’s temperature profile and the target $$T(\tau)$$ relation in layers with $$\tau$$ < 0.1. If new atm_T_tau_relation options are added to MESA, they must be added to this test case by hand. That is, the implementation does not automatically track all the available options.

The target $$T(\tau)$$ relation is stored in the extra profile column T_check, which can be compared to T_face and not T, because the optical depth tau is evaluated at the cell faces.

If the test fails because chi2 is slightly larger than the tolerance, there are two possibly benign explanations.

1. The interpolation error in T_face contributes too much to chi2. The tolerance can be increased or the mesh resolution increased.
2. There are layers included in the sum that are becoming convective, in which case the temperature gradient won’t follow the (radiative) $$T(\tau)$$ relation. The sum can be restricted to smaller optical depths.

If the test fails because chi2 is much larger (orders of magnitude larger) than the tolerance, then there might be a bug in the implementation of the T_tau_gradr_factor.

Most options are deliberately left at their default values because they shouldn’t influence the test’s result.

Last-Updated: 2020-10-27 (mesa r14711) by Warrick Ball