There are many physical and numerical challenges modeling stars as they approach their Eddington limit. One important challenge is the treatment of convective regions which are locally super-Eddington due to their high luminosity and opacity peaks from atomic transitions in H, He, and Fe. In the limit where the optical depth is low enough that radiative diffusion can carry significant flux while remaining convectively unstable, τ ≲ τcrit, this can lead to numerically challenging and physically suspect phenomena such as density inversions.
In all stellar evolutionary calculations which attempt to model massive stars as they approach the Eddington limit, there are some “stellar engineering” techniques designed to get around these numerical and physical challenges. For example, one can artificially enhance the pressure at the model’s outer boundary, or using the density scale height in place of a pressure scale height in the formulation of Mixing Length Theory (MLT). Another common choice is the "MLT++" formalism, a stellar-engineering approach developed for MESA in order to reduce super-adiabaticity, introduced in the MESA III instrument paper. This treatment works via enhanced convective energy transport: simply enforce that convection is capable of carrying the flux!
It is important to remember that MLT++ is an ad hoc ‘engineering’ choice; though it has some support by results from 3D simulations (e.g. Jiang et al. 2015; Schultz et al 2020, 2023), the method is not calibrated to detailed simulations or observations. Another limitation of MLT++ is that it is a non-local explicit method, so large step-to-step variations in the superadiabatic reduction may produce unphysical results and cause numerical challenges for the solver.
This motivated the introduction of the "superadiabatic reduction" technique in the MESA VI Instrument Paper: an alternative, fully implicit local method for reducing the superadiabaticity (think: flattening the entropy profile and enhancing the efficiency of convective transport). This minilab is primarily focused on exploring the impact of that engineering choice on the resulting stellar structure.
First, make sure you have downloaded the lab materials and unzipped the starting directory provided for MINILAB1, called MINILAB1_superad. Reminder that we will call your parent working directory by the variable name $TUESDAY_MASSIVE_STARS
Navigate to the starting directory MINILAB1_superad:
cd $TUESDAY_MASSIVE_STARS/MINILAB1_superad
Once you are ready, proceed to the first task (in the Main Tasks tab of Minilab1)!