# Modules for Experiments in Stellar Astrophysics (MESA): Time-Dependent Convection, Energy Conservation, Automatic Differentiation, and Infrastructure

**Authors:** Adam S. Jermyn, Evan B. Bauer, Josiah Schwab, R. Farmer, Warrick H. Ball, Earl P. Bellinger, Aaron Dotter, Meridith Joyce, Pablo Marchant, Joey S. G. Mombarg, William M. Wolf, Tin Long Sunny Wong, Giulia C. Cinquegrana, Eoin Farrell, R. Smolec, Anne Thoul, Matteo Cantiello, Falk Herwig, Odette Toloza, Lars Bildsten  
**arXiv:** [2208.03651](https://arxiv.org/abs/2208.03651)  
**Date:** 2022-08-07  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2208.03651v1/

## Key points

- Introduction of a new module called auto_diff that implements automatic differentiation
- Elimination of the need for hard-coded analytic expressions or finite difference approximations
- Importance of accurately modeling the growth and decay of convection during late-stage nuclear burning in massive stars and electron degenerate ignition events
- Improvements in MESA's treatment of the equation of state, energy accounting, and solver accuracy
- Enhancements related to the energy equation, stellar atmospheres, molecular opacities, Compton opacities, conductive opacities, element diffusion coefficients, and nuclear reaction rates
- Treatments for starspots and modifications for superadiabatic convection in radiation-dominated regions
- New approaches to increase efficiency in calculating monochromatic opacities and radiative levitation
- Introduction of a new operator split nuclear burning mode for evolving late stages of massive stars more efficiently
- Significant updates to MESA's software infrastructure to enhance source code development and community engagement

## Summary

In this study, the authors present updates and enhancements to the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). They introduce a new module called auto_diff that implements automatic differentiation, eliminating the need for hard-coded analytic expressions or finite difference approximations. This capability is particularly important for accurately modeling the growth and decay of convection during late-stage nuclear burning in massive stars and electron degenerate ignition events. The researchers also improve MESA's treatment of the equation of state, energy accounting, and solver accuracy. They discuss various features and enhancements related to the energy equation to quantify these improvements. Additionally, they describe key updates to the treatment of stellar atmospheres, molecular opacities, Compton opacities, conductive opacities, element diffusion coefficients, and nuclear reaction rates to enhance star modeling in MESA. The study introduces treatments for starspots which are crucial considerations for low-mass stars. Furthermore, modifications are made for superadiabatic convection in radiation-dominated regions. The authors also propose new approaches to increase efficiency in calculating monochromatic opacities and radiative levitation. For evolving late stages of massive stars more efficiently they introduce a new operator split nuclear burning mode. Lastly, significant updates are made to MESA's software infrastructure to enhance source code development and community engagement; these improvements aim to facilitate collaboration among researchers using MESA and promote further advancements in stellar astrophysics simulations. Overall this study presents a comprehensive set of updates and refinements that significantly enhance the capabilities of MESA for studying stellar astrophysics phenomena. The improved modules and treatments enable more accurate simulations and provide researchers with valuable tools for investigating various aspects of stellar evolution.