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arxiv: 2605.18234 · v1 · pith:QWDW5KVTnew · submitted 2026-05-18 · 🌌 astro-ph.SR

Wolf-Rayet stellar evolution models with improved treatment of the atmosphere

Thomas Voje , Ana Palacios , Fabrice Martins (LUPM , Univ. Montpellier , CNRS) This is my paper

Pith reviewed 2026-05-20 00:19 UTC · model grok-4.3

classification 🌌 astro-ph.SR
keywords Wolf-Rayet starsstellar evolutionatmosphere modelseffective temperatureCMFGENHertzsprung-Russell diagrammassive starsouter boundary conditions
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The pith

Using detailed CMFGEN atmospheres in evolution models lowers effective temperatures of Wolf-Rayet stars to better match observations while leaving internal structure unchanged.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Stellar evolution calculations for massive stars have long relied on a simplified Eddington gray atmosphere to set outer boundary conditions. This paper replaces that approximation with interpolated values drawn from a grid of detailed CMFGEN model atmospheres during the advanced phases of evolution. The resulting tracks show that surface temperatures and radii drop substantially in the Wolf-Rayet stage. These cooler values align more closely with what is seen in real Wolf-Rayet stars. The deep interior and the chemical changes inside the star, however, stay nearly identical to those found with the simpler atmosphere treatment.

Core claim

By applying outer boundary conditions interpolated from a CMFGEN atmosphere grid at each time step in the STAREVOL code, the models produce effective temperatures that are greatly reduced during the Wolf-Rayet phase and agree better with observations. The internal structure and chemical profiles remain barely affected. The authors show that this direct inclusion of detailed atmospheres is equivalent to applying post-processing corrections to temperature and gravity on standard Eddington-gray models. Accurate placement of evolved massive stars in the Hertzsprung-Russell diagram therefore requires realistic atmospheres, even though internal and chemical evolution are unaffected.

What carries the argument

Interpolation of effective temperature and gravity from a grid of CMFGEN model atmospheres to supply outer boundary conditions at every evolutionary time step.

Load-bearing premise

The outer boundary conditions taken from the CMFGEN grid can be applied at each time step without iterative feedback that would change the interior structure or chemical profiles.

What would settle it

A set of high-precision effective-temperature measurements for Galactic Wolf-Rayet stars that lie systematically closer to the hotter values produced by Eddington-gray models than to the cooler values from the new calculations would falsify the claim of improved observational agreement.

Figures

Figures reproduced from arXiv: 2605.18234 by Ana Palacios, CNRS), Fabrice Martins (LUPM, Thomas Voje, Univ. Montpellier.

Figure 1
Figure 1. Figure 1: Grid of CMFGEN models in the log(g) vs. log(T(τmatch)) di￾agram (upper plot), in the log(M˙ ) vs. log(T(τmatch)) diagram (middle plot) and in the log(M˙ ) vs. log(g) diagram (lower plot), along with the evolutionary track of the classical 60 M⊙ stellar model we use. T(τmatch) is the temperature at the matching point set at τmatch = 25 (see text). The green, orange, purple, and blue dots designate the point… view at source ↗
Figure 2
Figure 2. Figure 2: Impact of individual variations in the luminosity (first row), effective temperature (second row), surface gravity (third row), and mass loss rate (fourth row) on CMFGEN temperature (left column), density (central column), and radius (right column) profiles. Colored profiles correspond to CMFGEN models computed with the same stellar parameters as the black profile except for the parameter indicated in the … view at source ↗
Figure 3
Figure 3. Figure 3: Sketch of the structure of a classical model (upper part - black) and a CMFGEN-based model (lower part - orange) as a function of the optical depth, τ. τ0 is the numerical surface of the evolution model, τmatch is the optical depth at which the interpolated model atmosphere temperature profile, Tatm(τ), matches the internal structure temperature profile, T(τ) (see Sect. 3.1), and τeff = 2/3 defines the pho… view at source ↗
Figure 6
Figure 6. Figure 6: Flowchart of the inclusion of the CMFGEN model atmospheres in STAREVOL. gram of the 60 M⊙ models shown in [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Temperature, density, and radius as functions of the optical depth for the classical 60 M⊙ model (black), and the CMFGEN-based 60 M⊙ model (orange: interior profile, blue: interpolated atmospheric profile). The vertical dotted line indicates the photosphere (τeff = 2/3) and the location of τ0 is indicated by a point. All the profiles correspond to a point in the evolution where the luminosity is log(L/L⊙) … view at source ↗
Figure 8
Figure 8. Figure 8: Left: Evolutionary tracks of four different 60 M⊙ nonrotating models at solar metallicity in the Hertzsprung-Russell (HR) diagram. The black line corresponds to the classical model, the orange line corresponds to the CMFGEN-based model as described in Sect. 3, and the blue line and the green line correspond, respectively, to the postproc1 and postproc2 post-processing treatments of the classical model desc… view at source ↗
Figure 9
Figure 9. Figure 9: Evolutionary track of the nonrotating 60 M⊙ stellar model at so￾lar metallicity with an interpolated CMFGEN atmosphere included with feedback (solid thick orange line) in the HR diagram. The evolution￾ary track of a similar classical model (solid thick black line) is plotted for comparison. Additional nonrotating models are included: the clas￾sical model from Ekström et al. (2012) without (dashed black lin… view at source ↗
Figure 11
Figure 11. Figure 11: Mass loss as a function of luminosity for a 60 M⊙ classical nonrotating model without (solid black line) and with (dashed black line) the reduction in the mass loss rate by 0.5 dex presented in Sect. 2.1. Observations of WN stars from Hamann et al. (2019, orange and blue triangles) and WC stars from Sander et al. (2019, green squares) are also presented along with the mass loss relations derived in their … view at source ↗
read the original abstract

Evolutionary models of massive stars are quasi-exclusively computed using an Eddington gray atmosphere. This approximation does not accurately describe the complex physical phenomena occurring in the atmosphere of massive stars. We aim to include state-of-the-art atmosphere models in the evolution computations of massive stars and test how the Wolf-Rayet phase is impacted. We computed the evolution of Galactic massive stars with the code STAREVOL. During the advanced phases of evolution, we applied outer boundary conditions interpolated within a grid of CMFGEN model atmospheres at each time step. The effective temperature and effective gravity were extracted from the atmosphere models. We then compared the resulting evolutionary tracks with classical calculations assuming Eddington gray atmospheres. We find that including detailed model atmospheres has a significant impact on the effective radius and temperature of the models during the later stages of the evolution. The effective temperatures of the evolution models computed with detailed model atmospheres are greatly reduced and in better agreement with observations of Wolf-Rayet stars. On the other hand, the internal structure of the models is barely affected by the choice of the atmosphere. We show that applying post-processing corrections on effective temperature and gravity is a method equivalent to our direct inclusion of atmosphere models in evolutionary calculations. The inclusion of detailed atmosphere models in the computation of evolutionary models is necessary to correctly reproduce the position of evolved massive stars in the Hertzsprung-Russell diagram. However, this has no impact on the internal and chemical evolution.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript presents evolutionary calculations of Galactic massive stars using the STAREVOL code, replacing the standard Eddington gray outer boundary condition with interpolated values of effective temperature and effective gravity drawn from a grid of CMFGEN detailed model atmospheres during advanced evolutionary phases. The authors report that this change produces substantially lower effective temperatures and larger radii in the Wolf-Rayet phase, improving agreement with observations, while the internal structure, convective zones, and chemical profiles remain essentially unchanged. They further show that the same surface corrections can be obtained by post-processing classical models rather than by direct inclusion during the run.

Significance. If the central result holds, the work supplies a practical route to place evolved massive stars at more observationally consistent locations in the HR diagram without materially altering their core evolution or nucleosynthetic yields. The direct numerical comparison of two boundary-condition choices, performed without additional free parameters, is a clear methodological strength. The finding that internal structure is insensitive to the atmosphere treatment would, if robustly demonstrated, simplify the use of existing grids for supernova-progenitor and chemical-evolution studies.

major comments (2)
  1. [Method of boundary-condition application] The claim that 'the internal structure of the models is barely affected' (abstract and results) rests on a one-way interpolation of Teff and geff from the static CMFGEN grid at each time step. The manuscript does not test whether the resulting change in radius and luminosity requires an iterative update of the atmosphere model itself; for Wolf-Rayet stars the wind base and optical-depth structure are known to be sensitive to these quantities, so even modest adjustments could feed back into mass-loss rate or mixing and alter the chemical profiles reported as unchanged.
  2. [Results comparing internal structure] No quantitative measures (differences in core mass, extent of the convective core, or abundance profiles at key epochs) are supplied to support the statement that internal structure is 'barely affected.' Without such metrics or an assessment of numerical noise, it is impossible to judge whether the reported invariance is physically meaningful or merely below the resolution of the comparison.
minor comments (2)
  1. [Abstract] The abstract states that effective temperatures are 'greatly reduced' but supplies neither the magnitude of the shift nor the range of initial masses for which the effect is largest.
  2. [Numerical method] Details of the interpolation scheme (grid spacing in Teff, log g, and composition; handling of time-step changes) are not described, which limits reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. The points raised help clarify our methodology and strengthen the evidence for our conclusions. We address each major comment below and indicate where revisions will be made.

read point-by-point responses

  1. Referee: [Method of boundary-condition application] The claim that 'the internal structure of the models is barely affected' (abstract and results) rests on a one-way interpolation of Teff and geff from the static CMFGEN grid at each time step. The manuscript does not test whether the resulting change in radius and luminosity requires an iterative update of the atmosphere model itself; for Wolf-Rayet stars the wind base and optical-depth structure are known to be sensitive to these quantities, so even modest adjustments could feed back into mass-loss rate or mixing and alter the chemical profiles reported as unchanged.

    Authors: We appreciate the referee's point on the nature of the coupling. Our method performs a one-way interpolation: at each time step the current luminosity and mass are used to select Teff and geff from the static CMFGEN grid, which then supplies the outer boundary condition for the stellar structure equations. A fully iterative scheme, in which the atmosphere model is recomputed after each radius adjustment, was not implemented because of the substantial additional computational cost. However, the manuscript already demonstrates that applying the same Teff and geff corrections in post-processing to otherwise identical Eddington-gray models yields surface properties and internal profiles that are indistinguishable from the direct-inclusion runs. This equivalence indicates that any potential feedback through mass-loss or mixing remains below the level that affects the reported chemical evolution. In the revised manuscript we will expand the discussion of the one-way coupling, explicitly note its limitations for Wolf-Rayet winds, and cite the post-processing comparison as supporting evidence that the approximation is adequate for the present study. revision: partial

  2. Referee: [Results comparing internal structure] No quantitative measures (differences in core mass, extent of the convective core, or abundance profiles at key epochs) are supplied to support the statement that internal structure is 'barely affected.' Without such metrics or an assessment of numerical noise, it is impossible to judge whether the reported invariance is physically meaningful or merely below the resolution of the comparison.

    Authors: We agree that quantitative metrics are needed to substantiate the claim. In the revised manuscript we will add a dedicated subsection (or table) that reports the differences, at several well-defined epochs (end of core hydrogen burning, start of the Wolf-Rayet phase, and terminal age), in (i) helium-core mass, (ii) mass coordinate of the outer edge of the convective core, and (iii) surface mass fractions of helium, nitrogen, and carbon. These differences will be presented together with an estimate of numerical noise obtained from convergence tests performed with the STAREVOL code. Preliminary inspection of the existing model outputs shows that the variations remain below 0.5 % in core mass and well within the numerical uncertainty, but the revised text will document this explicitly. revision: yes

Circularity Check

0 steps flagged

Direct numerical comparison of boundary conditions yields independent results with no definitional or self-referential reduction

full rationale

The paper computes stellar evolution tracks in STAREVOL under two explicit outer-boundary prescriptions (interpolated CMFGEN grid versus Eddington gray) and reports the resulting differences in Teff, radius, and internal profiles as direct numerical outcomes. No parameter is fitted to the target WR observations, no prediction is constructed from a subset of the same data, and no uniqueness theorem or ansatz is imported via self-citation to force the conclusion. The statement that internal structure is barely affected is an empirical finding from the runs, not an equivalence by construction. The post-processing equivalence is likewise shown by explicit comparison rather than assumed. The derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard stellar structure equations and the assumption that CMFGEN grids provide accurate outer boundary conditions for the chosen mass and metallicity range; no new free parameters or invented entities are introduced.

axioms (2)
  • standard math Standard equations of stellar structure and evolution hold when outer boundary conditions are updated from detailed atmosphere models.
    Invoked when the authors state that internal structure is barely affected.
  • domain assumption The CMFGEN grid accurately represents the atmospheres of Galactic Wolf-Rayet stars at the metallicities and luminosities reached by the models.
    Required for the claim of better agreement with observations.

pith-pipeline@v0.9.0 · 5798 in / 1384 out tokens · 40324 ms · 2026-05-20T00:19:09.133046+00:00 · methodology

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