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Evolutionary models for the Very Massive Stars in the R136 cluster of 30 Doradus in the Large Magellanic Cloud

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Single-star evolution can explain the three most massive stars known, with R136a2 and R136a3 born heavier than record-holder R136a1.

desk verdict A careful, reproducible grid of VMS models whose headline ≳500 M_sun initial masses for R136a2/a3 depend on a mass-loss switch that disagrees with those stars' observed wind rates by an order of magnitude. read the letter →

arxiv 2506.15230 v2 pith:YUPX4CZL submitted 2025-06-18 astro-ph.SR astro-ph.GAastro-ph.HEastro-ph.IM

Z. Keszthelyi , S.A. Brands , A. de Koter , N. Langer , J. Puls This is my paper · ORCID
classification astro-ph.SRastro-ph.GAastro-ph.HEastro-ph.IM
keywords verymassivestarsstellarevolutionmasslossWolf-RayetR13630Doradusheliumenrichmentsupernovaprogenitors
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that single-star evolution, with no binary merger, can explain the three most massive stars known: R136a1, R136a2, and R136a3 in the LMC's R136 cluster. Its key move is a mass-loss switch: once a very massive star's surface hydrogen drops below 40 percent, Wolf-Rayet-type winds strip it so fast that its luminosity and mass plummet, so the initially heaviest star can end up lighter than a star born lighter. This resolves the helium conundrum -- the currently brightest star is the least helium-rich -- by making R136a2 and R136a3 the initially most massive, now in the 'down-stream' phase. Fitting luminosity, effective temperature, and surface helium with a Markov-Chain Monte Carlo analysis over interpolated grids yields an initial mass around $346 \pm 41\,M_\odot$ for R136a1 and $\gtrsim 500\,M_\odot$ for the other two. If right, the record-breaking stars need not be exotic merger products, but their winds reshape their fate, precluding pair-instability supernovae and leading to Type Ib/c if they explode.

What carries the argument

The load-bearing mechanism is a two-regime mass-loss prescription. While surface hydrogen $X>0.4$, winds follow the empirically calibrated wind-momentum luminosity relation; below $X=0.4$, the models switch to Wolf-Rayet-type rates, which are so strong that the star's mass and luminosity plunge on a short timescale. This switch creates a 'down-stream' trajectory and the mass turnover that lets initial masses be reconstructed only with added constraints like surface helium. The comparison machinery is an interpolated grid of 20 million points with a Markov-Chain Monte Carlo fit to three observables: luminosity, effective temperature, and surface helium mass fraction.

What would settle it

Show that R136a2 or R136a3 has a surface helium mass fraction below about 0.50, or measure its luminosity holding steady over a decade rather than dropping by roughly 1 dex per Myr, and the down-stream, initially-heavier-than-R136a1 interpretation is ruled out.

Watch

Extended reading notes

Core claim

The central discovery is the mass turnover: at LMC metallicity, an initially 800 $M_\odot$ model loses mass so rapidly once Wolf-Rayet-type winds begin that it becomes less massive than an initially 100 $M_\odot$ model within the main sequence. Applied to R136, the turnover means the current luminosity ranking is not the birth ranking. The authors propose R136a2 and R136a3 are past the turnover, having shed hundreds of solar masses and revealing near-core helium, while R136a1 is younger and still evolving redward. From simultaneous fits to luminosity, effective temperature, and surface helium, they estimate $M_\mathrm{ini}=346\pm41\,M_\odot$ for R136a1 and $\gtrsim500\,M_\odot$ for R136a2 and R136a3, with ages 1.02, 1.45, and 1.48 Myr. The fiducial grid predicts no pair-instability and no gamma-ray-burst progenitors, and any supernova would be Type Ib/c.

Load-bearing premise

The inference that R136a2 and R136a3 began above 500 solar masses rests on switching to Wolf-Rayet mass-loss rates once surface hydrogen drops below 40 percent, rates that are order-of-magnitude uncertain and calibrated for hydrogen-free stars; if that switch happens later or weaker, the mass turnover and inferred birth masses change.

Editorial extensions

If this is right

  • At LMC metallicity, all stars born above about 250 $M_\odot$ should become helium-rich main-sequence stars, regardless of initial spin or internal coupling scheme.
  • The mass turnover means present-day masses in young clusters cannot be read back as initial masses; by the time the first supernova explodes, no model star exceeds roughly 130 $M_\odot$ in the fiducial grid.
  • R136a2 and R136a3 should currently be losing luminosity at about 1 dex per Myr while staying hot, a change of roughly 25 ppm per decade in visual magnitude.
  • The fiducial models predict no pair-instability supernovae and no long gamma-ray-burst progenitors at LMC metallicity; the most massive pre-supernova stars have carbon-oxygen cores below the pair-instability limit.
  • If these stars explode, the supernovae should be Type Ib/c, and the stars should not form exceptionally massive black holes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If R136a2 and R136a3 really started above 500 $M_\odot$, their formation in the local universe strains standard massive-star formation theories; testing that would require studying the molecular-cloud conditions that could concentrate hundreds of solar masses in one core.
  • The paper's own factor-of-two wind test shows the outcome is brittle: reducing all mass-loss rates by half roughly doubles pre-supernova masses and can restore pulsational pair-instability, so a future empirical calibration of Wolf-Rayet wind rates at low metallicity would be a sharper test than any new spectrum of R136 itself.
  • A cleaner observational discriminator is the helium abundance of R136a1, the most disputed measurement; if a re-analysis pushed it above about 0.6, R136a1 too could be in the down-stream phase, which would change the inferred age and initial mass.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. This paper presents rotating single-star MESA evolutionary models for very massive stars (100–800 Msun) at LMC metallicity, adopting an empirical wind-momentum–luminosity relation calibrated from R136 stars for the optically-thin regime and switching to Sander & Vink (2020) Wolf-Rayet-type rates when the surface hydrogen mass fraction drops below 0.4. The authors build interpolated grids and use an MCMC analysis to fit the luminosity, effective temperature, and surface helium abundance of the three WNh stars R136a1/a2/a3, inferring an initial mass of 346±41 Msun for R136a1 and ≳500 Msun for both R136a2 and R136a3, which they interpret as being in a 'down-stream' phase of rapid mass loss and decreasing luminosity after the mass-turnover.

Significance. If the central inference holds, the paper would establish that R136a2 and R136a3, currently less luminous than R136a1, were initially more massive and are now in a mass-loss-dominated evolutionary stage, with implications for the stellar upper-mass limit, the interpretation of WNh stars, and the formation of massive black holes and supernovae. The paper has notable strengths: the full model grid, inlists, and analysis scripts are openly available on Zenodo; the parameter space in mass, rotation, angular-momentum transport, and MLT++ is explored systematically; the mass-turnover phenomenon is clearly identified; and the sensitivity to alternative wind prescriptions is tested for at least one branch. The work also produces falsifiable predictions, such as Type Ib/c supernova progenitors, no pair-instability supernovae, no GRB progenitors, and a measurable luminosity decline that can be checked with future monitoring.

major comments (3)
  1. [§4.6.1 and Appendix C.2] The MCMC likelihood is constructed from log L, log Teff, and log Ysurf only; log Mdot and surface nitrogen are deliberately excluded because including them worsens the fit (Appendix C.2). As acknowledged in §4.6.1, the posterior mass-loss rates for R136a2 and R136a3 are about an order of magnitude higher than the values spectroscopically determined by Brands et al. (2022). This is not a peripheral tension: the down-stream phase into which the paper places R136a2/a3 is defined by the switch to Sander & Vink (2020) WR-type rates at X<0.4 (§2.6.2), and the same switch drives both the rapid mass drop (Figure 3) and the factor-of-ten overprediction. If the measured mass-loss rates are correct, these stars cannot presently be in the high-Mdot WR phase, and the surface helium enrichment must be produced by another mechanism, removing the need for Mini>500 Msun. I request that the authors either include log Mdot in the likelihood with realistic systematic uncertainties, or provide a dedicated sensitivity test showing how the inferred initial masses shift when the WR rates are reduced by the factor needed to match the observed rates.
  2. [§2.6.1 and §4.1] The fiducial optically-thin mass-loss rates are the empirical WLR calibration of Brands et al. (2022), and both the fitted observables (L, Teff, Ysurf) and the mass-loss rates used for comparison in Table 2 are also from Brands et al. (2022). This means the models are calibrated to the same system they are then used to fit, reducing the independence of the evolutionary inference. In particular, the WLR parameters x and log D0 were derived including R136a1-a3, so the early main-sequence mass loss is effectively tuned to reproduce these stars. The paper should quantify how the inferred initial masses and ages change when an alternative WLR (e.g., from a sample excluding the WNh stars, or from the theoretical Vink et al. 2001 rates) is adopted.
  3. [§2.6.4 and §3.2] The sensitivity tests with halved mass-loss rates and with Nugis & Lamers (2002) WR rates are run for a single branch (TS, 300 km/s, MLT++) and are not propagated through the MCMC. This matters because the inferred initial masses for R136a2/a3 are the central quantitative claim, and the WR-rate normalization is estimated to be uncertain by an order of magnitude (§2.6.2). Section 3.2 shows that halving the mass-loss rates roughly doubles the maximum pre-supernova mass (from 24 to 67 Msun), so the ≳500 Msun lower limits are unlikely to be robust to the WR-rate uncertainty. I ask that the reduced chi^2 projection onto initial mass (Appendix C.5) be recomputed for the alternative wind branches, or that an explicit argument be given why the MCMC grids need not include them.
minor comments (4)
  1. [§1] Radcliff136 should be written as 'Radcliffe 136'.
  2. [Figure 4 caption] Taylor-Spruit should be 'Tayler-Spruit' to match the notation used elsewhere in the paper.
  3. [§2.9] mesaSoftware Development Kit should be 'MESA Software Development Kit'.
  4. [Appendix C.2] The statement that the mass-loss and surface nitrogen constraints 'cancel out' is qualitative; please show the individual chi^2 distributions or a corner plot with these quantities included so the reader can assess the trade-off.

Circularity Check

1 steps flagged · score 4.0 of 10

The mass-loss 'recovery' for R136a1 is a fitted-input echo, but the central helium-based inference for R136a2 and R136a3 is not circular.

  1. fitted input called prediction [Section 2.6.1 and Section 4.6.1 (Eq. 3; posterior mass-loss discussion)]
    "We adopt x=2.00 (implying α′=0.5, slightly different than the value 2/3 discussed above) and D0 = 17.05 from Brands et al. (2022), which have been derived for both massive stars and VMSs in the R136 cluster ... Particularly for the most massive WNh stars (R136a1, R136a2, and R136a3), these parameters provide a reasonably good match to their observationally-inferred mass-loss rates ... For R136a1, the posterior probability distribution of the mass-loss rates (around log ˙M∼−4.2 M⊙yr−1) approximately recovers the empirically inferred values (Table 2)."

    The posterior mass-loss 'recovery' is by construction: the models' optically-thin mass-loss rates are evaluated from Eq. (3) with x=2.00 and logD0=17.05, coefficients fitted by Brands et al. (2022) to the observationally-inferred mass-loss rates of the very same R136 WNh stars. Any model that reproduces the observed luminosity of R136a1 will therefore produce a WLR-based mass-loss rate close to the observed value; the agreement is the input calibration echoed back, not an independent evolutionary prediction.

full rationale

Aside from the recovered mass-loss fit, the paper's main derivation chain is not circular. Initial masses are inferred by MCMC matching of models to observed logL, logTeff, and Ysurf over an interpolated grid; Ysurf is an external spectroscopic constraint measured by Crowther et al. (2010), Bestenlehner et al. (2020), and Brands et al. (2022), and the down-stream branch for R136a2 and R136a3 is triggered by applying Sander & Vink (2020) WR-type rates at X<0.4, a theoretical prescription not fitted to these stars. The mass-turnover degeneracy is broken by the helium abundance, which is an independent observable rather than a model output. The main weaknesses are acknowledged in the paper: posterior mass-loss rates for R136a2 and R136a3 are about an order of magnitude above the spectroscopic rates, and the MCMC deliberately omits log Mdot and surface nitrogen because they worsen the fit (Appendix C.2, Section 4.6.1). That is an incomplete confrontation and a correctness risk, but it is not a circular reduction of the central initial-mass claim. The self-citation to Brands et al. (2022) is load-bearing for input physics but is an empirical spectroscopic analysis with independent data, and the conclusions are cross-checked against other groups' measurements, so it does not by itself constitute circularity. Score 4 reflects one fitted-input-echoed-as-prediction while the central helium-based inference retains independent content.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central inference rests on the adopted mass-loss prescriptions (WLR calibration and the WR switch), the rotational mixing parameters, the overshoot and MLT++ choices, and the single-star assumption. No new physical entities are introduced. The key free parameters are the empirical WLR fit and the hydrogen-abundance switch for WR winds; both directly control the mass turnover and thus the inferred initial masses.

free parameters (6)
  • WLR slope x and offset logD0 = x=2.00, logD0=17.05
    Mass-loss relation calibrated to R136 stars including the targets (Brands et al. 2022), used in Eq. 3 to set the optically-thin wind mass-loss rate.
  • Surface hydrogen switch for WR winds, X<0.4 = X=0.4 (with interpolation between 0.44 and 0.36)
    Ad hoc threshold for switching to Sander & Vink (2020) rates; controls the onset of down-stream evolution.
  • Rotational mixing efficiency f_c = 0.05
    Uncalibrated for VMSs, adopted from Yoon et al. (2006) and Brott et al. (2011a); scales chemical transport relative to AM transport.
  • Composition-gradient shielding f_mu = 0.1
    Adopted from prior literature to reduce the stabilizing effect of mean molecular weight gradients.
  • Terminal velocity factor f_inf = 3.5
    Chosen to match WNh stars in R136; affects wind momentum through Eq. 5.
  • Core overshoot parameter = about 0.2 local pressure scale height
    Assumed to extend the convective core; standard but uncertain.
assumptions (6)
  • domain assumption MESA 1D diffusive treatment of rotation is a sufficient approximation for VMS evolution.
    The entire grid relies on the diffusive AM transport scheme (Eq. 1) with three coupling choices; no 2D or 3D validation is attempted.
  • domain assumption The Ledoux criterion is effectively reduced to Schwarzschild, and semiconvection and thermohaline mixing are ignored.
    Section 2.2; justified by recent 3D simulations, but remains a simplification.
  • domain assumption The three target stars are single stars and their surface helium is produced in their own cores, not gained through mergers or accretion.
    Section 5.2 argues against close companions and mergers; the MCMC inference uses this to relate Ysurf to core production.
  • domain assumption Episodic mass loss (LBV eruptions) does not significantly affect the main-sequence evolution.
    Section 2.6.2 states episodic mass loss is not accounted for; such events could alter the mass-loss history.
  • ad hoc to paper The Sander & Vink (2020) WR rates, derived for hydrogen-free atmospheres, can be applied to helium-enriched but not fully stripped surfaces once X<0.4.
    This is a key modeling choice for the down-stream evolution; the rates are order-of-magnitude uncertain and possibly inappropriate for partially hydrogen-rich surfaces.
  • ad hoc to paper MLT++ artificially increases convective luminosity to prevent envelope inflation, and models without MLT++ are reliable on the main sequence despite convergence failures afterward.
    The HRD comparison uses models without MLT++, but post-main-sequence predictions rely on models with MLT++; the paper argues TAMS properties are broadly consistent (Section 3.1.1).

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Pith. "Pith review of Evolutionary models for the Very Massive Stars in the R136 cluster of 30 Doradus in the Large Magellanic Cloud." pith.science (2026). https://pith.science/paper/YUPX4CZL

@misc{pith2026250615230,
  author       = {Pith},
  title        = {Pith review of: Evolutionary models for the Very Massive Stars in the R136 cluster of 30 Doradus in the Large Magellanic Cloud},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YUPX4CZL}},
  note         = {Machine review of arXiv:2506.15230}
}
abstract

The cluster R136 in the LMC contains a population of stars in excess of 100 M$_\odot$, including R136a1, the most massive star known. Very Massive Stars (VMSs) play an influential role in feedback processes and may potentially produce exotic supernova types and black holes of tens of solar masses. The evolutionary history and final fate of the three most luminous stars, R136a1, R136a2, and R136a3, has been a puzzling issue. We aim to resolve this by rotating single-star MESA models. We produce interpolated model grids and apply a Markov-Chain Monte Carlo analysis to compare our models with observations. The nature of supernova progenitors strongly depends on mass loss and the AM coupling schemes. We predict no pair-instability and no GRB progenitors from our fiducial model grid at LMC metallicity. The onset of Wolf-Rayet-type mass-loss rates on the main sequence leads to a rapid decrease in stellar mass and luminosity. The mass turnover implies that the evolutionary history can only be inferred if additional constraints are available. We utilise the surface helium abundance, which poses a conundrum: R136a1, the most luminous star, is less enriched in helium than R136a2 and R136a3. We propose that this can be explained if both R136a2 and R136a3 were initially more massive than R136a1. From a rigorous confrontation of our models to spectroscopically-derived observables, we estimate an initial mass of 346$\pm41$ M$_\odot$ for R136a1, and $\gtrsim$500 M$_\odot$ for R136a2 and R136a3. Even though VMSs are only present in the youngest clusters below 2 Myr of age, our study strengthens their role in local and galaxy evolution. At LMC metallicity, they will be observable as helium-enriched massive stars after their drastic mass loss, produced via single-star evolution. If the core collapse leads to a supernova, it will be of Type Ib/c. [abridged]

Figures

Figures reproduced from arXiv: 2506.15230 by the authors.

Figure 1
Figure 1. Comparison of evolutionary models with different internal angular momentum coupling schemes (HY: hydrodynamical, SB: solid body, TS: Tayler-Spruit) and with (w) or without (w/o) MLT++ in a typical VMS model with initial mass of 315 M⊙ and initial rotational velocity of 300 km s−1 during the main-sequence evolution from ZAMS to TAMS. Left: Hertzsprung-Russell diagram. For reference, the position of R136a1 according t… view at source ↗
Figure 2
Figure 2. HRD of the main-sequence evolution of the most massive models in our grid within the TS scheme without MLT++. The initial rotational velocity is 300 km s−1 . Initial masses in solar units are indicated next to the starting point of the models. The colour-coding shows the logarithmic mass-loss rate. Stars with Mini > 250 M⊙ follow a ‘down-stream’ of rapidly decreasing luminosity evolution and become helium-rich objec… view at source ↗
Figure 3
Figure 3. Evolution of stellar mass as a function of time. Models within the Tayler-Spruit coupling scheme with MLT++ are shown for an ini￾tial rotational velocity of 300 km s−1 . The grey vertical line indicates the time when the first supernova takes place. Mobs,max indicates the maxi￾mum stellar mass observable at that time. MpreCC,max is the highest pre￾core collapse mass by the end of the evolution of all models. Green s… view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Post-main sequence evolutionary tracks in the Taylor-Spruit scheme with vini = 300 km s−1 . Left panel: HRD from the Terminal Age Main Sequence (TAMS with squares), through the helium-TAMS (diamonds), until carbon-TAMS (blue stars). The colours denote different initial…
Figure 5
Figure 5. Figure 5: Maximum carbon-oxygen core mass as a function of initial stellar mass. The HY, TS, and SB coupling schemes are shown on the top left, top right, and lower left, respectively. These panels include all initial rotational velocities calculated in our grid (shown with diff…
Figure 6
Figure 6. Figure 6: Specific angular momentum in the central 5 solar masses of the stellar model at representative evolutionary stages. Shown are the ini￾tially 315 M⊙ models with an initial rotational velocity of 300 km s−1 , using the hydrodynamical (top panel), Tayler-Spruit (middle pa…
Figure 7
Figure 7. Figure 7: Average specific angular momentum within the central 5 solar masses of the core at the end of carbon core burning versus the initial mass. Left: hydrodynamical coupling scheme. Right: Our experiment with different mass-loss rates. The symbols denote different initial r…
Figure 8
Figure 8. Figure 8: HRD colour-coded with the surface helium mass fraction in our models (using the Taylor-Spruit scheme without MLT++ with an initial rotational velocity of 300 km s−1 ) and in observations of the WNh stars R136a1 (star), R136a2 (circle), and R136a3 (square). The initial …
Figure 9
Figure 9. Figure 9: Interpolated models on the HRD with colour-coding showing the surface helium mass fraction. The Brands et al. 2022 observations are adopted as in [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: Surface helium mass fraction as a function of time. The evolu￾tionary models are shown with black lines with decreasing initial mass from left to right. The model with Mini = 500 M⊙ is highlighted with thicker line. The colour-coding shows the interpolated models as a…

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Pith tools

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