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

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, Richard H. D. Townsend, F. X. Timmes

arXiv:2208.03651v2astro-ph.SRastro-ph.EPastro-ph.HEastro-ph.IM

TL;DR

MESA VI addresses limitations in stellar-evolution modeling and software infrastructure by introducing automatic differentiation, time-dependent convection, and broad physics and infrastructure updates. The paper reports expanded and more robust capabilities for stellar models, while noting that scientific implications remain for future community work and that some new treatments have scope limitations.

  • Problem

    MESA’s hard-coded derivative calculations, steady-state convection assumptions, and broader modeling limitations constrain accurate and efficient stellar-evolution calculations.

  • Method

    The paper implements automatic differentiation, time-dependent convection, upgraded physics modules, new stellar treatments, efficiency improvements, and software-infrastructure updates throughout MESA.

  • Results

    MESA VI provides significant new capabilities and improvements in automatic differentiation, convection, energy treatment, stellar physics, nuclear calculations, and software infrastructure.

  • Takeaways & Limitations

    The updated capabilities open opportunities for future stellar-evolution investigations and increase the robustness of stellar-evolution models.

  • Takeaways & Limitations

    The paper does not fully explore the science implications of the new capabilities, and some treatments retain author-identified physical or computational scope limitations.

Abstract

from arXiv · show

We update the capabilities of the open-knowledge software instrument Modules for Experiments in Stellar Astrophysics (MESA). The new auto_diff module implements automatic differentiation in MESA, an enabling capability that alleviates the need for hard-coded analytic expressions or finite difference approximations. We significantly enhance the treatment of the growth and decay of convection in MESA with a new model for time-dependent convection, which is particularly important during late-stage nuclear burning in massive stars and electron degenerate ignition events. We strengthen MESA's implementation of the equation of state, and we quantify continued improvements to energy accounting and solver accuracy through a discussion of different energy equation features and enhancements. To improve the modeling of stars in MESA we describe key updates to the treatment of stellar atmospheres, molecular opacities, Compton opacities, conductive opacities, element diffusion coefficients, and nuclear reaction rates. We introduce treatments of starspots, an important consideration for low-mass stars, and modifications for superadiabatic convection in radiation-dominated regions. We describe new approaches for increasing the efficiency of calculating monochromatic opacities and radiative levitation, and for increasing the efficiency of evolving the late stages of massive stars with a new operator split nuclear burning mode. We close by discussing major updates to MESA's software infrastructure that enhance source code development and community engagement.

1. INTRODUCTION

MESA VI presents new capabilities and infrastructure improvements responding to expanding stellar observations and computational demands. The paper documents capabilities and limitations rather than fully exploring their scientific implications.

  • Motivation: Space- and ground-based instruments are producing an unprecedented volume of high-quality stellar measurements, strengthening the observational foundation of stellar astrophysics.Examples include microlensed distant stars, surveys, gravitational-wave detectors, neutrino networks, and missions measuring stellar properties.
  • Motivation: New and improved open-knowledge software instruments are reshaping how stellar theory, modeling, and simulations interact with experiments and observations.The paper places MESA among infrastructure developments including Astropy, Athena++, Castro, Dedalus, and other community tools.
  • Scope and limitations: The paper describes MESA capabilities and limitations while leaving the scientific potential of those capabilities to future work by the MESA research community.Its comparisons include other numerical or analytic results, but it does not fully explore the science implications.
  • Scope and organization: MESA VI updates automatic differentiation, time-dependent convection, the equation of state, energy treatment, atmospheres, opacities, diffusion, nuclear physics, and stellar-structure models.The paper also discusses starspots, superadiabatic convection, radiative levitation, operator-split burning, and software infrastructure.

2. AUTOMATIC DIFFERENTIATION

MESA introduces forward-mode operator-overloaded automatic differentiation to replace much hard-coded derivative code and reduce associated complexity and errors. Benchmarks show modest stellar-evolution overhead, with optimized routines sometimes outperforming explicit derivatives.

  • Motivation: MESA’s Newton-Raphson solver requires highly accurate partial derivatives, historically making hard-coded analytic expressions a major source of code complexity and error.Finite differences are often unsuitable because derivatives typically need accuracy of about one part in 10^6.
  • Implementation: Forward-mode operator-overloaded automatic differentiation now computes partial derivatives automatically with respect to input variables.MESA’s derived types store each value together with first or higher-order partial derivatives, whose number is specified at compile time.
  • Implementation: The auto_diff module uses generated, optimized chain-rule expressions translated into Fortran and supports MESA’s arithmetic, special, and trigonometric functions.Expressions are optimized by eliminating common subexpressions and reducing division operators; discontinuities receive defined derivative treatments.
  • Performance: For sufficiently complex operations, optimized automatic-differentiation functions outperform manually implemented explicit derivative routines.The comparison includes f = log(cosh(tanh(x))), while simple operations still incur overhead.
  • Performance: In stellar-evolution calculations, hand-coded expressions are modestly faster, but their overhead advantage is small relative to a full MESA timestep.Correct derivatives can reduce slow convergence and excessive small timesteps; some source code remains to be transitioned.
  • Applications: Automatic differentiation is applied to time-dependent convection, the equation of state, starspots, and superadiabatic convection, and is available for further MESA development.It can also be used in run_star_extras and in software outside MESA.

3. TIME-DEPENDENT LOCAL CONVECTION

MESA adds a time-dependent convection model for episodes in which stellar structure changes faster than convection reaches steady state. The implementation adapts the Kuhfuß formalism for stable use across short and long timescales.

  • Motivation: Steady-state mixing-length theory is appropriate when composition and structure evolve more slowly than convective timescales, but not during violent stellar episodes.The relevant cases include late-stage nuclear burning in massive stars and electron-degenerate ignition events.
  • Model: MESA implements the local-limit, one-equation Kuhfuß time-dependent convection formalism for general stellar-evolution calculations.The implementation builds on the RSP treatment previously used for radial stellar pulsations.
  • Model: Time-dependent convection introduces turbulent kinetic energy as an evolving variable that contributes to heat and momentum transport.The model includes turbulent pressure in the momentum equation and convective luminosity in the luminosity and total-energy equations.
  • Implementation choices: The default αr = 0 neglects radiative damping of convective motions, an approximation that changes the model’s physical completeness.Other defaults include α = 2, αD = 1, and αPt = 0.
  • Implementation choices: The implementation sets the turbulent-energy advection term Lt to zero in the local limit and omits viscous bulk-motion heating ϵq from the energy equation.With Ledoux stability, the model also uses the Ledoux gradient rather than the adiabatic gradient in its formulation.
  • Numerical behavior: The RSP formulation is effective on short convective or pulsational timescales but becomes numerically unstable on long evolutionary timescales.The instability arises because small errors in superadiabaticity can produce large luminosity errors that amplify through the entropy profile.

3.3. Flipped Equations

To stabilize time-dependent convection over long timescales, MESA reverses the usual TDC solve direction and treats luminosity as the solver variable. It then determines superadiabaticity from luminosity through numerical inversion.

  • Flipped equations: MESA implements TDC like MLT by using luminosity L as a solver variable for long-timescale numerical stability.The formulation flips the governing relation to solve for superadiabaticity Y rather than luminosity from Y.
  • Flipped equations: The inversion solves for Y given L while accounting for turbulent velocity’s dependence on Y.Setting Lt = 0 makes each cell’s superadiabaticity depend locally on its luminosity and other structure variables.

3.4. Numerical Method

The TDC numerical method computes convective velocity and luminosity from Y, then inverts the luminosity relation to obtain Y using robust root-finding and branch selection. It handles convection growth, decay, multiple roots, and derivative propagation for stellar-structure variables.

  • L given Y: The method solves for convective velocity at the end of each timestep, evaluates luminosity from Y, and then numerically inverts the luminosity relation to recover Y.The implementation fixes coefficients at end-of-step values, solves the velocity evolution implicitly, and uses the resulting luminosity relation for root finding.
  • L given Y: When the discriminant J2 > 0, convection is unstable and the long-timestep solution approaches a plateau independent of the initial convective velocity.The plateau is w → −(J + ξ1)/(2ξ2).
  • L given Y: When J2 < 0, convection can decay to w = 0 before the timestep ends, so the solver must detect the first zero and retain the radiative branch.The decay time satisfies δt* ∼ 1/J.
  • Numerical Inversion: For Y < 0 with initial w > 0, the luminosity equation can have up to three solutions because declining convection and increasing |Y| compete through the wY term.The method favors the smallest-|Y| solution, corresponding to the slowest-decaying convection.
  • Numerical Inversion: In a representative case, the three roots comprise two convective solutions and one purely radiative solution, with the slowest-decaying root having w ≈ 0.2 and Y ≈ −0.35.The plotted residual R(Y) and end-of-step w identify the roots and the special points separating solution branches.
  • Numerical Inversion: The solver identifies special points Y0 and Y1, partitions the search interval into monotonic subintervals, and applies bisection followed by Newton-Raphson refinement.The transformed variable Z = ln |Y| covers 10^-43 ≲ |Y| ≲ 10^43, while derivative propagation uses automatic differentiation for 33 stellar-structure variables.

3.5. Reduction to Cox MLT

The TDC formulation is modified so that its steady-state behavior matches Cox MLT, including a correction to the convective-efficiency term. With this correction, the two models solve the same luminosity equation and agree numerically to about seven decimal places in Y.

  • Reduction to Cox MLT: The correction is required even when αr > 0, while the derivation is presented using the αr = 0 approximation for clarity.The need for the correction is not removed by setting αr > 0.
  • Reduction to Cox MLT: The TDC luminosity equation is modified by including the factor Γ/(1 + Γ) so that its steady-state outputs match MLT.The correction addresses the Γ-dependent term controlling convective efficiency.
  • Reduction to Cox MLT: In Cox MLT, f1 = 1/8, and with the default TDC choice αD = 1, the corresponding luminosity factors are equal.The comparison evaluates Γ by calling MLT with the same inputs as TDC and holds it fixed during TDC iterations.
  • Reduction to Cox MLT: After the correction, TDC and Cox MLT solve the same luminosity equation with the same inputs and agree numerically to around seven decimal places in Y.The uncorrected formulation has qualitatively different inefficient-limit scaling, especially for convective velocity.

3.6. Accreting White Dwarfs

The accreting white-dwarf models show that time-dependent convection differs from Cox MLT when nuclear heating changes faster than convection can equilibrate. TDC adjusts more slowly, producing more superadiabatic convection and altered thermal, velocity, and composition profiles.

  • He shell flashes occur in white dwarfs accreting helium at rates ≲10^-6 M⊙yr^-1 and can lead to He novae or double-detonation type Ia supernovae.
  • Timescale regime: When the heating timescale becomes comparable to or shorter than the convective acceleration time, convection cannot reach steady state and TDC diverges from Cox MLT.For models 3 and 4, expansion begins when theat ≲ taccel; taccel can become up to 3 or 6 times smaller than teddy.
  • Model setup: The models accrete 99% ^4He and 1% ^14N onto a 1 M⊙ carbon-oxygen white dwarf, producing accumulated helium shells of 0.03–0.08 M⊙.Accretion rates span log(Ṁ/M⊙yr^-1) from −7.1 to −7.4.
  • Thermal structure: At fixed TBCZ, TDC has lower temperatures throughout the convection zone because heat builds up locally near the base and is transported outward less efficiently.The resulting stronger entropy gradient is accompanied by little evolution in T and s near the convection-zone top for 8.6 ≲ log(TBCZ/K) ≲ 8.8.
  • Velocity and composition: TDC and Cox MLT agree reasonably in convective velocity below log(TBCZ/K) ≲ 8.5, but TDC later yields lower or nearly frozen velocities as heating outruns convective adjustment.TDC reaches the same TBCZ earlier and has higher PBCZ, while Cox MLT generally produces higher ^12C abundance because it has more time and larger vc.
  • Conclusion: TDC is enabled by default in MESA, incorporating the growth and decay dynamics of convection during rapidly burning phases.The model produces slower, more superadiabatic convection than Cox MLT when heating changes rapidly.

4. EQUATION OF STATE

MESA improves its equation-of-state framework through expanded coverage, thermodynamically consistent Skye calculations, FreeEOS partial-ionization tables, and derivative-aware blending. These changes address crystallization, composition coverage, and solver accuracy while retaining explicit scope boundaries in blended regions.

  • Motivation: MESA EOS calls span roughly 10^4–10^10 evaluations, motivating accurate and efficient coverage across temperature, density, and composition regimes.
  • EOS coverage: Default EOS boundaries prioritize HELM at high temperature and low density, followed by Skye, FreeEOS, OPAL, SCVH, and finally an ideal-gas approximation where needed.Figure 7 shows these regions for solar-like and pure-metal compositions.
  • Skye: Skye includes positrons, relativity, electron degeneracy, Coulomb interactions, and nonlinear mixing effects for fully ionized matter.It is integrated into MESA with the same input physics and options as the standalone Skye instrument.
  • Crystallization: Skye smooths the crystallization phase parameter numerically and adds an energy-equation heat source to capture latent heat without smearing the phase-transition thermodynamics.This preserves numerical convergence and accurately captures crystallization latent heat.
  • Crystallization: The Skye treatment derives the phase diagram and latent-heat release self-consistently from first-principles Helmholtz free-energy thermodynamics.Its net latent-heat release is commensurate with the value from Salaris et al. (2000).
  • Partial ionization: FreeEOS version 2.2.1 expands partial-ionization composition coverage relative to OPAL and replaces MESA V’s eosPTEH tables.MESA provides tables spanning Z = 0 through 1.00, including carbon-oxygen options at high Z.
  • EOS blends: Derivative-aware EOS blending accounts for blending-coefficient derivatives, providing more accurate solver Jacobians and reducing Newton iterations.Fundamental quantities and derivative vectors are blended separately because they serve different physical and numerical purposes.
  • EOS consistency: Skye-active regions achieve thermodynamic consistency to near machine precision, with significant improvement for log(ρ/g cm^-3) ≳ 3.A band near log(T/K) ≈ 9–10 remains associated with the required Skye-to-HELM blend.

5. ENERGY EQUATIONS

MESA advances its energy-equation treatments by improving composition accounting, time-centering, solver diagnostics, and EOS handling. Tests show that centered eps grav performs best for degenerate evolution, while reported energy errors require formulation-specific interpretation.

  • 5.4. Results: 1M pre ms to 1TP: In 1 M⊙ tests, centered eps grav becomes dominated by EOS blend errors, so further resolution or energy-equation improvements cannot improve numerical energy conservation.For dedt, EOS errors are not reflected in rel run E err; therefore, this reported diagnostic must be interpreted according to the selected energy-equation form.
  • 5.1. Fundamentals and Implementations: MESA now includes composition changes and implicit trapezoidal time-centering by default in the eps grav energy equation.These changes add compensating source terms and replace end-of-step quantities with time-centered values, improving numerical energy conservation.
  • 5.2. Results: carbon kh: At fixed resolution, eps grav forms produce more accurate central-temperature evolution than dedt under degenerate conditions.All forms show first-order convergence, but the eps grav variants remain closer to the reference solution after the model reaches maximum temperature.
  • 5.2. Results: carbon kh: All energy-equation forms approximately show first-order convergence in total energy, but their cumulative energy-error behavior differs substantially with time resolution.The centered eps grav variant exhibits second-order convergence in numerical energy conservation, whereas dedt's error is largely resolution-independent.
  • 5.2. Results: carbon kh: The centered eps grav form provides the best balance between temperature accuracy and step-to-step energy conservation for degenerate carbon evolution.Its numerical energy-conservation error converges more rapidly than the end-of-step variant, while dedt can evolve total energy and temperature less accurately despite a smaller cumulative error.
  • 5.3. Quantifying EOS shortcomings: EOS derivatives, thermodynamic inconsistencies, and unavoidable EOS-blend inconsistencies remain key limits on energy conservation and solver performance.MESA mitigates these issues through improved derivative accounting, upgraded EOS components, reduced blending, and separate treatment of interpolants in equations and Jacobians.

6. ATMOSPHERE

MESA expands atmospheric boundary-condition options, fixes atmosphere–interior consistency and derivative errors, and adds helium-atmosphere white-dwarf tables that better reproduce reference calculations.

  • Atmosphere options: MESA supports T(τ), irradiated, and tabulated atmosphere options, with four selectable T(τ) relations and multiple opacity treatments.T(τ) surfaces can be located at optical depths far from the usual photospheric τ ≈ 2/3.
  • Numerical consistency: The atmosphere module now uses callback routines to keep EOS and opacity configurations consistent between the atmosphere and stellar interior.This addresses possible inconsistencies where the atmosphere and interior join.
  • Numerical consistency: Correct chain-rule derivatives for iterated T(τ) atmospheres prevent slow or failed convergence of the global Newton solver.The corrected derivatives apply to Ps and Ts with respect to L1, r1, ρ1, and T1.
  • White-dwarf atmospheres: New DB white-dwarf atmosphere tables cover 5,000 K < Teff < 40,000 K and 6.0 < log(g/cm s−2) < 9.4 for He-dominated surfaces.The tables assume nH = 10−5nHe and evaluate model atmospheres at τ = 25.
  • White-dwarf atmospheres: The tabulated atmospheres agree with Koester et al. (2020) to Teff ≈ 7,000 K, while Eddington T(τ) atmospheres diverge for Teff ≲ 15,000 K.At cooler temperatures, uncertainty in Mcvz is attributed to the EOS at the convection-zone base.
  • Atmosphere options: Among T(τ) opacity choices, 'varying' is more accurate than 'iterated', which is more accurate than 'fixed', with increasing computational cost.The ordering is based on opacity self-consistency.

7. CONVECTION IN THE OUTER LAYERS OF STARS

MESA adds starspot physics and a fully implicit local treatment for superadiabatic convection near the Eddington limit, improving smoothness and reproducing established starspot effects.

  • Starspots: MESA implements SPOTS-style starspots using coverage fraction fspot and temperature-contrast parameter xspot.The implementation modifies surface boundary conditions through magnetic pressure and perturbs the radiative gradient.
  • Starspots: For a 0.3 M⊙ M dwarf with fspot = 0.34 and xspot = 0.85, predicted radial inflation is approximately 3%–5%, consistent with SPOTS models.MESA tracks shift smoothly with increasing fspot, and lower xspot produces larger effects.
  • Superadiabatic convection: The new superadiabatic-convection method is fully implicit and local, unlike the non-local explicit MLT++ approach.It adjusts ∇rad near the Eddington limit and recomputes the convection model using the adjusted gradient.
  • Superadiabatic convection: In 30 M⊙ models, the new method produces smoother evolution while remaining closer to simulations without enhanced energy transport than MLT++.MLT++ shows undesirable numerical variations near TAMS and during red-to-blue evolution after envelope stripping.
  • Superadiabatic convection: Without enhanced energy transport, a massive-binary simulation stalls during its second mass-transfer phase, whereas the implicit method remains smooth.MLT++ evolves beyond detachment but produces large step-to-step changes in mass-transfer rates.

8. OPACITY

MESA broadens opacity physics across cool molecules, hot Compton scattering, conductive white-dwarf envelopes, and radiative levitation while improving evolutionary comparisons and computational efficiency.

  • Molecular opacities: MESA adds low-temperature molecular opacity tables from Lederer & Aringer and ÆSOPUS, including variable CNO abundances.These tables target cool stellar environments such as red giants, AGB stars, and R Coronae Borealis stars.
  • Molecular opacities: In 3 M⊙ TP-AGB models, MESA reaches higher peak L, smaller peak Teff, and larger peak R than Monash, while interpulse periods converge to ≃7.2×10^4 yr.The differences in L, Teff, and R decrease as evolution proceeds.
  • Compton and conductive opacities: At log(T/K) ≳ 8.7, MESA now uses the Poutanen (2017) Compton-scattering prescription instead of the previous Buchler & Yueh approach.These conditions occur in massive-star and neutron-star thermonuclear-burst simulations.
  • Compton and conductive opacities: MESA implements Blouin et al. (2020) analytical conductive-opacity fits for hydrogen and helium, relevant to DA and DB white-dwarf envelopes.Cooling calculations for a 0.9 M⊙ hydrogen-atmosphere white dwarf confirm the result of Blouin et al.
  • Radiative levitation: For main-sequence stars, the optimized radiative-levitation implementation is about 5 times faster while preserving κR and grad,i accuracy at ϵ = 10−4.It precomputes factors in two envelope regions and blends values near their boundary.

9. DIFFUSION COEFFICIENTS

MESA replaces strongly coupled liquid-regime diffusion coefficients with Caplan et al. molecular-dynamics-based fits, substantially improving agreement with reference calculations and generality across mixtures.

  • Motivation and method: Previous diffusion coefficients disagreed with more accurate molecular-dynamics methods by a factor of a few in strongly coupled plasmas.The updated approach targets the liquid regime needed for stellar models.
  • Motivation and method: Caplan et al. coefficients use an equivalent one-component-plasma molecular-dynamics fit scaled by mixture charge in the liquid regime 10 ≲ ΓMCP ≲ 200.The scaling separates global viscosity from charge-dependent effective ion sizes.
  • Implementation: MESA recasts the net diffusion coefficients into symmetric Burgers-equation resistance coefficients for use by its diffusion solver.The resistance coefficients reduce to the desired net coefficients under the required summation.
  • Validation: Residuals relative to Caplan et al. molecular-dynamics results are 10% or less, versus factors of two or more for Stanton & Murillo coefficients.The implementation is generalizable beyond C/O/Ne mixtures.
  • Implementation: MESA adopts the Caplan et al. coefficients by default for ΓMCP > 10, with a smooth transition from Stanton & Murillo coefficients over 3 < ΓMCP < 10.Liquid white-dwarf diffusion coefficients are accurate to approximately 10% for 10 ≲ ΓMCP ≲ 200.
  • Crystallization boundary: For crystallized material with ΓMCP ≳ 200, MESA smoothly turns diffusion off so velocities vanish for φ ≥ 0.5.The turnoff uses the smoothed phase parameter from Skye.

10. NUCLEAR PHYSICS

MESA updates its nuclear physics with revised reaction rates, operator-split burning, and expanded reaction-rate outputs. These changes improve treatment of low-temperature reactions, high-temperature burning, and solar-neutrino diagnostics.

  • Reaction rates updates: The new default 7Be electron-capture rate incorporates ionization contributions, extending its applicability below 10^7 K in stellar envelopes.The previous REACLIB rate assumed complete ionization and was defined only above 10^7 K.
  • Reaction rates updates: MESA now defines reverse reaction rates using nuclear masses from masslib 5.data for consistency with its adopted nuclear masses.This affects reactions whose nuclear masses are uncertain, including 55Cu (γ, p) 54Ni.
  • Operator-split nuclear burning: Operator-split burning evolves high-temperature composition with adaptive substeps at fixed T and ρ, improving numerical robustness while omitting temperature and density derivative terms.The omitted partial derivatives are set to zero in the matrix solver.
  • Operator-split nuclear burning: Nearly identical central T-ρ tracks persist until Tc ≈3 × 10^9 K, after which the fully coupled 30 M⊙ model reaches slightly larger ρ than the operator-split solution.The differences are comparable to variations from other physics choices, such as nuclear reaction-rate screening.
  • Operator-split nuclear burning: Operator splitting can significantly speed Si and Fe burning and may make some problems tractable, but is less efficient earlier and has uncertain relative accuracy.The authors suggest considering it for models beyond core C-depletion.
  • Reaction-rate outputs: MESA can now output individual reaction, neutrino-energy, nuclear-energy, and screened reaction rates to history or profile files.Users can request all raw rates or select a specific reaction.
  • Solar diagnostics: Solar-model electron-neutrino flux predictions show satisfactory agreement with observed fluxes after flavor-effect corrections.The comparison includes pp, pep, 7Be, and 8B neutrino fluxes.

11. CONSTANTS

MESA updates its constants module to use revised SI physical constants and IAU-recommended astronomical conventions. Some microphysics tables and expressions retain separate constants beyond these updates.

  • Scope of updates: Updated constants do not apply to some opacity, EOS, and reaction-rate tables or expressions that use independently constructed microphysics inputs.Such differences are described as usually beyond MESA’s control.
  • Physical constants: The constants module adopts exact revised-SI values for e, h, kB, and NA and uses CODATA 2018 for other physical constants such as G.Derived constants, including the Stefan-Boltzmann constant, are defined consistently from exact values.
  • Astronomical constants: MESA follows IAU 2015 recommendations for nominal solar and planetary quantities, deriving nominal masses from GM and the adopted G.Nominal planetary radii use equatorial radii by convention.

12. INFRASTRUCTURE

MESA’s infrastructure now supports GitHub-based collaboration, expanded continuous integration, community code sharing, and reproducible execution of older versions. TestHub provides rapid failure detection and detailed diagnostics across development branches.

  • Migration to GitHub: MESA’s 2020 migration from SVN to GitHub supports a new phase of collaborative development and broader interaction with the astrophysics community.The Git repository begins from SVN revision r15140, with the earlier history archived on Zenodo.
  • Migration to GitHub: Public releases now use date-based YY.MM.I identifiers rather than SVN commit-count revision numbers.Unreleased versions can be identified using the first seven characters of a Git commit hash when necessary.
  • MESA TestHub: TestHub dynamically tracks Git branches and commits through GitHub webhooks and APIs, while branch selectors organize commit-specific views.The system updates its internal commit tree when changes are pushed to GitHub.
  • MESA TestHub: Test submissions strongly correlate with commit activity, with deviations caused by testing-computer availability and commits that do not trigger automated tests.The SVN-to-Git transition appears smooth in the TestHub history.
  • Continuous integration: Most failures are detected within an hour and more than one-third within thirty minutes through distributed clusters checking for new commits every few minutes.Branches beyond the main branch can also be tested during feature development.
  • Continuous integration: TestHub records runtime, architecture, failure type, and compilation or test logs to support diagnosis of regressions.Failure pages link directly to available stdout and stderr logs.
  • Community contributions: The mesa-contrib repository and MESA hooks make user-contributed routines easier to share while reducing maintenance burdens.Current examples include atmospheric relations and angular-momentum transport routines.
  • NuDocker and provenance: NuDocker preserves reproducibility by running older MESA versions with age-appropriate environments and bit-for-bit consistency after version 7503.It reproduces a July 2014 MESA r6794 calculation on modern hardware.

13. SUMMARY

MESA VI documents substantial capabilities and improvements across stellar physics, numerical methods, nuclear modeling, and software infrastructure. The paper emphasizes future community use while noting that detailed scientific implications remain for subsequent work.

  • Scope: MESA VI explains new capabilities and improvements implemented since the MESA I–V software instrument papers.The paper covers automatic differentiation, time-dependent convection, energy treatment, stellar physics, microphysics, and infrastructure.
  • Scientific capabilities: The upgraded physics and numerical treatments are presented as supporting future investigations and more robust stellar-evolution modeling.The stated areas include automatic differentiation, time-dependent convection, EOS, opacities, diffusion, nuclear rates, and physical constants.
  • Software infrastructure: GitHub, TestHub, mesa-contrib, and NuDocker updates support more efficient and distributed source-code development.The infrastructure changes address collaboration, testing, code sharing, and execution of older MESA versions.
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