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At solar metallicity, a single fork decides how massive a black hole a dying star leaves behind: collapse as a cool supergiant and keep a heavy remnant, or be stripped into a Wolf-Rayet star and lose most of its mass to thick winds.

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2026-08-01 00:38 UTC pith:4CIWZ7GR

load-bearing objection A systematic and useful wind-era map of BH mass predictions at Z_sun; the supergiant-branch peak is an upper limit, and the framing should stop selling it as the prediction. the 3 major comments →

arxiv 2607.26147 v1 pith:4CIWZ7GR submitted 2026-07-28 astro-ph.SR astro-ph.GA

The Stellar Winds Atlas II: Black Hole Formation at Solar Metallicity

Amedeo Romagnolo , Floor S. Broekgaarden , Alex C. Gormaz-Matamala , Lucas M. de S\'a , Daniel Pauli , Avishai Gilkis , Lumen Boco , Michela Mapelli
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Konstantinos Antoniadis Laya Binu
This is my paper
classification astro-ph.SR astro-ph.GA
keywords black hole formationstellar windsWolf-Rayet starscool supergiant mass losssolar metallicitymassive star evolutionmass-loss prescriptionsHumphreys-Davidson limit
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

At solar metallicity, the mass of the black hole a massive star leaves behind is set less by how strong its winds are in detail than by which of two evolutionary paths it takes. The paper argues the decisive fork is whether the star loses its hydrogen envelope and becomes a Wolf-Rayet star before core collapse. Stars that enter the Wolf-Rayet stage have their final mass dictated by thick, optically thick winds, which erase nearly all memory of earlier mass loss. Stars that instead collapse while still cool supergiants retain their envelopes and form substantially heavier black holes, producing a peak around 30 solar masses near an initial mass of 40 solar masses. The result maps the wide spread in existing theoretical predictions onto two controllable bottlenecks — envelope stripping efficiency and Wolf-Rayet mass-loss rates — and this is what makes the problem tractable.

Core claim

The paper's central discovery is a bifurcation in black-hole remnant mass at solar metallicity. Across 14 wind prescriptions in a common 1D stellar evolution setup, final remnant mass converges to two branches: the Wolf-Rayet branch, where optically thick winds dominate and remove most of the mass, and the cool-supergiant branch, where the envelope is retained and the remnant is much heavier. The paper shows this bifurcation is universal: it appears in every model, and the choice of cool-supergiant mass loss — specifically the effective temperature at which those winds switch on — controls which branch a star takes. A 40-solar-mass star collapses into a 28.6-solar-mass black hole if cool sup

What carries the argument

The load-bearing object is the evolutionary bifurcation defined by the paper: whether a star collapses as a cool supergiant or first becomes a Wolf-Rayet star. The immediate switch controlling it is the effective-temperature threshold at which cool supergiant winds are initiated; moving this threshold by 0.5 kK can change a 40-solar-mass star's remnant mass by about 5 solar masses. For stars that pass the switch and enter the Wolf-Rayet stage, the optically thick wind prescription (especially for hydrogen-free Wolf-Rayet stars) takes over and dictates the final mass. The paper also uses the timing of the transition to optically thick winds as a diagnostic, linking it to the Humphreys-Davidso

Load-bearing premise

The paper assumes every star collapses directly to a black hole, conserving all its pre-collapse mass except 1% lost to neutrinos; the authors themselves note this likely overestimates remnant masses for stars that retain a loosely bound hydrogen envelope, and partial envelope ejection during core collapse could shrink the heavy supergiant branch.

What would settle it

A census of solar-metallicity black holes: if no isolated black holes appear in the roughly 20–30 solar mass range, the supergiant branch is suppressed. Separately, the Wolf-Rayet/OB ratio at luminosities around log(L/Lsun) ~ 6.3–6.5 can falsify timing predictions; for example, models that predict no OB stars above about 45–65 solar masses are in tension with the observed 110-solar-mass OB star Cyg OB2 #12.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the bifurcation is correct, the final black hole mass at solar metallicity reduces to two bottlenecks: envelope stripping efficiency (whether the star becomes a Wolf-Rayet star) and Wolf-Rayet mass-loss rates.
  • Stars collapsing as cool supergiants produce a black hole mass peak near 30 solar masses around an initial mass of 40 solar masses, so an observational census of isolated solar-metallicity black holes in the 20–30 solar mass range can test this branch.
  • Stars that enter the Wolf-Rayet phase yield similar final black hole masses regardless of their prior mass-loss history, meaning model disagreements trace to thick-wind prescriptions rather than main-sequence winds.
  • The timing of the transition to optically thick winds determines whether stars respect the Humphreys-Davidson limit, and the observed Wolf-Rayet/OB star ratio in the Milky Way is a direct model-independent probe of that timing.
  • If hydrogen-free Wolf-Rayet winds are weak, very massive solar-metallicity stars can enter the pair-instability pulsation regime; the absence of isolated black holes above roughly 30 solar masses would be evidence that such massive remnants require binary or dynamical formation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the bifurcation is universal, the same two bottlenecks may organize black hole mass predictions at lower metallicity, meaning calibrating envelope stripping and Wolf-Rayet winds at solar metallicity would sharpen predictions for high-redshift gravitational-wave merger rates.
  • The extreme sensitivity to a 0.5 kK shift in the cool-supergiant wind threshold suggests that direct empirical constraints on yellow supergiant winds, not just red supergiants, would be unusually high-leverage for black hole mass predictions.
  • The supergiant branch implies a distinctive dichotomy in remnant masses — heavy supergiant-collapse remnants versus lighter Wolf-Rayet remnants — that could be searched for in astrometric and X-ray binary black hole populations.
  • The paper deliberately leaves luminous blue variable eruptions unmodeled; if those eruptions are what enforce the Humphreys-Davidson limit by stripping envelopes, the supergiant branch would be suppressed, so the bifurcation may partly be an artifact of missing eruptive mass loss.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. This paper constructs a 'Wind Atlas' for solar-metallicity massive stars by running 14 wind prescriptions in a common 1D MESA framework over M_ZAMS = 20–300 Msun, then uses the StarEstate population-synthesis code to compare synthetic VMS populations with Galactic OB/WR samples. The central claim is that the final BH mass is set by a bifurcation: stars that lose enough envelope to become Wolf-Rayet stars end up with masses set by their thick winds, whereas stars that collapse as cool supergiants retain much of their envelope and form more massive BHs, producing a peak near M_ZAMS ~ 40 Msun in models with weak YSG winds. The paper argues that the cool-supergiant wind threshold (T_eff,trans) controls this bifurcation and identifies envelope stripping and WR mass-loss rates as the two key bottlenecks. It tests this framework against Cygnus X-1, the HD limit, and the Galactic WR/OB ratio.

Significance. If the central bifurcation claim holds, the paper provides a valuable organizing principle for a notoriously divergent literature: rather than focusing on the overall strength of winds, modelers should focus on envelope stripping efficiency and WR mass-loss rates. The study is unusually systematic, with 14 models in a common code, a controlled sensitivity test in Fig. 2, and open MESA inlists and population-synthesis code. The comparisons to Cygnus X-1, the HD limit, and observed OB/WR populations are genuine external checks, not fits to the target result. The main weakness is the direct-collapse assumption for supergiant remnants, which the paper itself flags as an upper limit; because the ~40 Msun peak is the flagship prediction, this assumption needs quantitative treatment before the bifurcation claim can be considered robust.

major comments (3)
  1. [Sec. 2.1; Fig. 1; Sec. 3.1.2] The direct-collapse assumption is load-bearing for the supergiant pathway. The text sets M_BH = M_pre-collapse - 1% neutrino mass for all progenitors, and note 4 concedes that neutrino mass loss can shock-eject loosely bound RSG envelopes (Nadezhin 1980; Lovegrove & Woosley 2013; Fernández et al. 2018). The 28.6 Msun BH at M_ZAMS = 40 Msun in FEScRSG/MScRSG is essentially the whole pre-collapse mass. If even a modest fraction of the H-rich envelope is ejected during collapse, the supergiant-branch remnants drop toward the CO-core mass, the prominent peak in Fig. 1 is strongly suppressed or shifted, and the contrast with the WR branch shrinks. Please add a quantitative sensitivity study (e.g., using a simple neutrino-mass-loss envelope-ejection prescription or reporting the CO-core mass as a lower bound for each track) and revise the abstract/conclusions so that the supergiant peak is pre
  2. [Sec. 3.1.3; Fig. 2] The claim that the cool-supergiant wind threshold 'universally controls' the BH mass bifurcation is based on a single 40 Msun FESc track. The sharp drop from 28.6 to 15.7 Msun between T_eff,trans = 4.0 and 5.0 kK is convincing for that case, but the text in Sec. 3.1.2 says the transition condition to optically thick winds is 'nearly irrelevant' in the 20–50 Msun range, while Fig. 1 shows nontrivial model-to-model scatter there. To support 'universally', please show at least a small grid in (M_ZAMS, T_eff,trans) or explicitly restrict the claim to stars near the bifurcation boundary.
  3. [Sec. 3.3; Fig. 4] The WR/OB population comparison is presented as a decisive test, but it depends on post-processed RLOF checks, the assumed binary fraction and period distribution, and the effective-single fraction (27–53% across models). This is a useful plausibility argument, but it is not a quantitative model-selection statistic. Please either add error bars or explicitly state that the comparison is qualitative; this would also make the text in Sec. 3.3 less vulnerable to over-interpretation.
minor comments (5)
  1. [Sec. 3.2.1] The text says the Z=0.019 version of MScV01 predicts a near-ZAMS transition at M_ZAMS >= 65 Msun 'due to weaker mass loss'. Higher Z should increase V01 rates; please clarify whether this is a scaling artifact or a typo.
  2. [Sec. 2.2; Fig. 4] The effective-single fractions and binary interaction criteria are model-dependent; please state the uncertainties in the synthetic population more explicitly in the text, not only in the figure caption.
  3. [Appendix C] When applying the direct-collapse minus 1% formula to literature final masses, the comparison is not apples-to-apples because those studies include different explosion prescriptions. Please note this explicitly in the caption or text.
  4. [Sec. 4.2] The statement that the bifurcation is dominated by winds 'rather than mass transfer events in binaries' (citing Shenar et al. 2020) is stronger than the cited work may support; a softer phrasing would be safer.
  5. [General] The paper relies heavily on the companion 'Atlas I' for the KABS model and calibration details. Since this manuscript may be read independently, please include a short self-contained description of the KABS transition and wind-switch rules in the text or a table footnote.

Circularity Check

0 steps flagged

No real circularity: the BH-mass bifurcation is computed from externally defined wind grids; the only self-citation is to Atlas I/StarEstate and is not load-bearing.

full rationale

Walking the derivation chain, I find no step where a predicted quantity is equivalent to an input by construction. The 14 wind schemes are externally defined (V01, dJ88, NL00, B20, SV20, GM23, K24, P25, A24, etc.), and the grid is evolved in MESA; the WR/supergiant bifurcation and the ~40 Msun peak are read off the resulting M_BH(M_ZAMS) curves, not imposed as a target. The only non-external inputs from the authors' own prior work are the KABS model (Atlas I; 'originally developed in Atlas I') and the StarEstate population-synthesis code; these are transparently cited and do not smuggle in the conclusion, because the same qualitative supergiant branch is produced by FEScRSG and MScRSG, which are constructed from literature recipes. The direct-collapse prescription (Sec. 2.1: 'we use an upper limit to the BH mass and assume that all stars face direct BH collapse, conserving the totality of their pre-core collapse mass minus 1% being ejected as neutrinos') is an explicitly acknowledged upper limit that inflates the supergiant-branch peak; this is a substantive physical caveat and the paper flags the RSG-envelope-ejection risk in the same section and in footnote 4, but an assumption labeled as an assumption is not circular. No fitted parameter is renamed as a prediction, no author-uniqueness theorem is invoked, and the WR/OB and Cygnus X-1 comparisons are independent tests. Minor self-citation (Atlas I, StarEstate, Romagnolo et al. 2024) is present but not load-bearing, hence score 2 rather than 0.

Axiom & Free-Parameter Ledger

3 free parameters · 8 axioms · 0 invented entities

No numbers are fitted to the target result; the paper is a comparison grid. The listed parameters and axioms are the model choices whose variation would most affect the bifurcation claim.

free parameters (3)
  • Cool supergiant wind onset temperature (T_eff, trans) = 4-10 kK (depends on model; see Fig 2)
    Chosen per model: FESc uses 10 kK, RSG-only variants use 4 kK. The sensitivity run in Sec 3.1.3 shows a 0.5 kK change around 4.5-5 kK shifts the 40 Msun BH mass from ~24 to ~16 Msun, so the location of this threshold controls whether the supergiant branch exists.
  • Neutrino mass-loss fraction at collapse = 1%
    Normalizes all reported BH masses under the direct-collapse upper limit (Sec 2.1).
  • Initial rotation Omega_init/Omega_crit = 0.4 (0.6 in FESchighrot)
    Set to a round value from the literature; the 0.6 variant shows negligible effect on final BH mass, so this parameter is not central.
axioms (8)
  • domain assumption All stars collapse directly to a BH, conserving pre-collapse mass minus 1% (Sec 2.1).
    Load-bearing for the supergiant branch masses; the paper flags it as an upper limit.
  • ad hoc to paper WR stars form as soon as the star develops optically thick winds (Sec 2.1).
    Defines the WR onset for all 14 models; different criteria (Gamma_e, eta, Xsurf) are compared, but the assumption that thick winds = WR is a simplification.
  • ad hoc to paper Cool supergiant winds are turned on at T_eff <= 10 kK (FESc) or <= 4 kK (RSG-only models).
    The central bifurcation is controlled by this threshold; the paper varies it only in one sensitivity test (Fig 2).
  • domain assumption Fixed mixing prescription: Ledoux + exponential overshoot f_ov=0.05, no semiconvection (Sec 2.1).
    Envelope stripping and WR formation depend on mixing; not varied across the grid.
  • domain assumption Initial rotation at 0.4 of critical velocity (Sec 2.1).
    Rotation drives surface enrichment and mass loss; only one variant tested.
  • domain assumption Pair-instability supernovae (PPSN/PSN) are ignored (Sec 2.1).
    Affects the upper-mass regime; the paper notes only the artificially-underestimated H-free WR wind model enters PPSN.
  • domain assumption Wind prescriptions from the literature (V01, dJ88, NL00, B20, SV20, GM23, A24, K24, P25, V17) are reliable within their claimed ranges.
    The grid's outcome is a direct consequence of these external rates; no re-calibration is attempted.
  • domain assumption Population synthesis parameters (binary fraction 75%, Sana+12 period/eccentricity distributions, Frankel+18 metallicity relation) describe the Milky Way VMS population (Sec 2.2).
    Underlies the WR/OB ratio comparison in Fig 4.

pith-pipeline@v1.3.0-alltime-deepseek · 35430 in / 17004 out tokens · 152761 ms · 2026-08-01T00:38:22.491673+00:00 · methodology

0 comments
read the original abstract

Stellar winds are a primary source of uncertainty in predicting the masses of black holes (BHs) from massive stars. At solar metallicity, theoretical models lead to widely divergent results due to differing wind prescriptions. A key obstacle remains the lack of systematic investigations across a common parameter space. To address this, we construct a ``Wind Atlas'' using detailed 1D MESA stellar evolution models and population synthesis techniques to estimate the Galactic population of solar metallicity BH progenitors. We systematically investigate 14 distinct wind models, ranging from the most traditional and widespread prescriptions to the most recent. By evaluating stellar evolution across this extensive grid, we show that the final BH mass is dictated by a fundamental bifurcation: whether a star collapses as a cool supergiant or is first stripped of its envelope to become a Wolf-Rayet (WR) star. If a star enters the WR stage, its strong thick winds dominate, making the final mass sensitive to the WR wind prescription while largely erasing the memory of its prior mass-loss history. Conversely, stars that face core collapse as supergiants form significantly more massive BHs, producing a mass peak around an initial mass of 40 $M_\odot$. Rather than simply reproducing these divergent outcomes, our comprehensive evaluation demonstrates that this bifurcation is universally controlled by the highly uncertain mass loss during the cool supergiant phase. This framework strongly constrains the problem of BH mass prediction by identifying two key bottlenecks for future studies: envelope stripping efficiency and WR mass-loss rates. Our atlas provides a clear baseline for interpreting current theoretical discrepancies and testing wind models against observational constraints, such as the Galactic WR/OB population ratio.

Figures

Figures reproduced from arXiv: 2607.26147 by Alex C. Gormaz-Matamala, Amedeo Romagnolo, Avishai Gilkis, Daniel Pauli, Floor S. Broekgaarden, Konstantinos Antoniadis, Laya Binu, Lucas M. de S\'a, Lumen Boco, Michela Mapelli.

Figure 1
Figure 1. Figure 1: — 𝑀BH as a function of 𝑀ZAMS for our models. The mass range of Cygnus X-1 BH (Ramachandran et al. 2025) in grey. The left figure represents a zoomed-in plot within 𝑀ZAMS = 55 𝑀⊙. The production of massive BHs at 𝑀ZAMS ≲ 50 𝑀⊙ is only achievable with weak mass loss during the cool supergiant regime (FEScRSG, MScRSG, KABS models). Only models that considerably underestimate H-free WR mass-loss rates (FEScnoH… view at source ↗
Figure 2
Figure 2. Figure 2: shows the evolution of a FESc 40 𝑀⊙ star under different𝑇eff,trans values. If cool supergiant winds are restricted to RSGs (𝑇eff,trans ∼ 4 kK), the time spent in this phase (Δ𝑡cool) is negligible, and the star collapses into a massive BH of 28.6 𝑀⊙. Increasing the threshold by just 0.5 kK to 4.5 kK initiates a brief cool supergiant phase (0.026 Myr) that is sufficient to lower 𝑀BH by nearly 5 𝑀⊙. Once 𝑇eff… view at source ↗
Figure 3
Figure 3. Figure 3: shows these transition ages, normalized by the stellar lifetime, as a function of 𝑀ZAMS, as well as the 𝑀ZAMS range at which selected models present a transition beyond the HD limit (log 𝐿 ≥ 5.5 and 10−5 × 𝑅 × √ 𝐿 ≥ 1), where we distinguish on whether the stars remain for an amount of time in their LBV phase (𝑡LBV), which we stress remains unmodeled in our analysis, that is more or less than 5% of their to… view at source ↗
Figure 4
Figure 4. Figure 4: — Comparison between empirical Galactic observations and our synthetic populations of 𝑀ZAMS ≥ 50 M⊙ VMSs scaled to 10% of the Galactic thin disk mass. The synthetic datasets account for both single stars and binary components that successfully avoid mass transfer throughout their evolutionary history. The cyan-shaded region represents the LBV regime, while the purple dotted vertical line indicates the log … view at source ↗
Figure 5
Figure 5. Figure 5: shows the HR evolution of each track, while Fig￾ure 6 displays the contribution of each mass loss scheme for a specific model, both in terms of the cumulative time a star spends in each wind phase, and in terms of the cumulative mass that was lost due to specific mass-loss rates. Different mass-loss rates impact differently the core size of the star, leading to different nuclear timescales ( [PITH_FULL_IM… view at source ↗
Figure 6
Figure 6. Figure 6: — Cumulative time and mass loss from each wind scheme for a 𝑀ZAMS = 20 𝑀⊙ star at 𝑍⊙, according to each proposed evolutionary model. On the top plot, we cut the cumulative time plot to enhance the visualization of the whole evolution. Despite the relatively short time such a star spends with cool supergiant winds, they are the major contributors to mass loss. The value of any bar with width below 0.02 Myr … view at source ↗
Figure 7
Figure 7. Figure 7: shows the HR evolution of a 40 𝑀⊙ star follow￾ing our evolutionary models [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: — Cumulative time and mass loss from each wind scheme for a 𝑀ZAMS = 40 𝑀⊙ star at 𝑍⊙, according to each proposed evolutionary model [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: — Cumulative time and mass loss from each wind scheme for a 𝑀ZAMS = 75 𝑀⊙ star at 𝑍⊙, according to each proposed evolutionary model. The major contributors are the optically thin and thick winds. 1 R 1 0 R 1 0 0 R 1 0 0 0 R 5.50 5.25 5.00 4.75 4.50 4.25 4.00 3.75 log(Teff/K) 5.6 5.8 6.0 6.2 6.4 lo g ( L / L ) Xsurf = 0.24 Xsurf = 0.47 Xsurf = 0.02 FEScRSG FESchighrot FEScnoHpoor MSc MScRSG Dutch-ish Dutch … view at source ↗
Figure 10
Figure 10. Figure 10: — HR diagram for 𝑀ZAMS = 75 𝑀⊙ stars at 𝑍⊙. Black dots rep￾resent TAMS positions, with the respective surface-H abundances. There is considerable evolutionary variability as a function of different mass-loss rates for optically thin and H-free WR winds. with roughly 1-2.5 times more mass loss. As for the lower￾mass cases, the high initial rotation from the FESchighrot model keeps the star compact, with hi… view at source ↗
Figure 11
Figure 11. Figure 11: — [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: — HR diagram for 𝑀ZAMS = 300 𝑀⊙ stars at 𝑍⊙. The colors representing each model remain the same as in [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 14
Figure 14. Figure 14: — The main evolutionary channels for BH progenitors. 𝑀BH is determined by a key bifurcation: stars that collapse as cool supergiants form higher-mass BHs, while those that evolve as WR stars lose more mass and form lower-mass remnants. The full single black line represents a generic behavior, while all the other lines represent the respective models in [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: — HR evolution of a 75 𝑀⊙ star at 𝑍⊙ following the FESc model and the FEScV01. The colorbar represents the evolution of Γe. Black lines are plotted under the stellar tracks’ scatter points to increase contrast. The red ravioli represent where Γe increases past the 0.5 threshold, the red crosses where Γe decreases under 0.5, and the blue dots when H-free winds are initiated. The Γe value goes briefly below… view at source ↗
Figure 16
Figure 16. Figure 16: — Fraction of 𝑀ZAMS lost with a specific wind scheme as a function of 𝑀ZAMS. The gray color is the remnant mass fraction, with the dashed white and dash-dotted aqua lines respectively the final core and envelope mass fractions. Top left: FESc model. Top center: MSc. Top right: 𝑋surf. Middle left: FEScRSG. Center: MScRSG. Middle right: Dutch. Bottom left: FESchighrot model. Bottom center: KABS. Bottom righ… view at source ↗
Figure 17
Figure 17. Figure 17: — Same as [PITH_FULL_IMAGE:figures/full_fig_p020_17.png] view at source ↗

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