{"id":"14895738-6baa-4107-96d6-6557c9c708e2","arxiv_id":"2504.17009","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Fast-rotating low-metallicity massive stars strip themselves by chemical mixing, capping pre-pair-instability black hole masses at the critical CO core mass of about 35 to 36 solar masses.","lead":"This paper models rapidly rotating, low-metallicity massive stars and finds that fast rotators become chemically homogeneous, so their final black hole mass is capped near 35 to 36 solar masses before pair-instability supernovae set in. The result may explain the pile-up of black holes around 35 solar masses seen in LIGO/Virgo data.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Rotational CHE at Omega/Omega_crit ~0.6 is the load-bearing assumption; it is uncalibrated and self-declared debated, so the 35-36 M_sun cap needs a mixing-reduction test.","rationale":"The reader's weakest_assumption precisely identifies the same load-bearing concern: the realization of rotationally-induced chemical homogeneity at Omega/Omega_crit ~0.6 with the adopted diffusive mixing coefficients. The paper explicitly concedes that the physics of CHE is under debate and that there is no empirical evidence for faster rotation in low-Z WR stars, yet the entire mass-cap conclusion depends on CHE occurring in the models. This is not an internal inconsistency but a correctness risk rooted in uncalibrated input physics. The proposed test—reducing the rotational mixing efficiency and checking for CHE—would directly settle whether the cap is robust or an artifact of the chosen mixing coefficients. Because the concern is already the basis of the reader's CONDITIONAL verdict, my assessment does not change the verdict; it reinforces the conditionality. The M_crit experiment and the core mass criterion itself are independently grounded in previous work and are not the weakest link.","tokens_in":25476,"tokens_out":5225,"duration_ms":46579,"concrete_test":"Re-run Model B2 (100 M_sun, Z=1/100 Z_sun, Omega/Omega_crit=0.6, Table 3) with (i) all rotational diffusion coefficients multiplied by 0.1 and (ii) D_ES=0, and check whether the surface hydrogen abundance drops below 0.01 before core H exhaustion. If CHE is not achieved in either variant, the Omega/Omega_crit ~0.6 CHE threshold and the resulting 35-36 M_sun BH mass cap are artifacts of the uncalibrated mixing prescription.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that rapid rotation caps BH masses at the CO critical core mass via chemically homogeneous evolution—rests entirely on the occurrence of CHE at Omega/Omega_crit ~0.6 in the adopted MESA models. The paper itself flags the fragility of this in Section 2.2: 'The physics of rotationally-induced chemically homogenous evolution is still under debate, and requires very efficient rotational mixing. However there is no empirical evidence that low metallicity WR stars rotate any more rapidly than higher metallicity counterparts.' The CHE threshold is not a physical invariant; it is a consequence of the diffusive mixing coefficients (Heger et al. 2000) for Eddington-Sweet circulation, secular shear, and GSF instabilities, none of which are calibrated in this paper. Their own test with D_ES=0 (Figure 13) changes the HRD track and reduces mass loss, but they do not report whether that model still becomes chemically homogeneous. If CHE does not occur, stars retain an H envelope, M_final > M_CO, and the maximum BH mass is set by the H-rich boundary (up to ~93 M_sun in Winch et al. 2024), not by the 35-36 M_sun cap. The LIGO/Virgo bump alignment, the population pile-up, and the headline conclusion all disappear without CHE. Thus the load-bearing assumption is the realization of CHE at the adopted mixing efficiency, not the M_CO,crit criterion itself, which is independently supported by the M_crit experiment.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper extends the pair-instability boundary study of Winch et al. (2024) to rapidly rotating, low-metallicity massive stars. The authors implement a mechanical mass-loss prescription in MESA for models that approach the OmegaGamma limit, run an M_crit experiment up to Omega/Omega_crit = 0.8, and find that the critical CO core mass for the BH/PPI boundary remains approximately constant (M_CO,crit,high = 35.0 +/- 2.3 Msun, within error of the earlier 36.3 Msun). They then run a grid of models, derive empirical fits for final and core masses, and use these in a simple population synthesis. The central claim is that fast rotators become chemically homogeneous, so that the final BH mass is capped by the CO critical core mass, producing a pile-up around 27-36 Msun that they associate with the LIGO/Virgo bump at about 35 Msun.","tokens_in":25906,"tokens_out":4904,"duration_ms":46115,"significance":"If the central claim holds, the paper provides a concrete mechanism - rotation-induced chemical homogeneity - that links stellar evolution to the observed bump in the black hole mass distribution near 35 Msun, a topic of current interest. The M_crit experiment at high rotation is a useful independent check of the critical core mass criterion, and the mechanical mass-loss implementation in MESA is a practical contribution that will be of value to the massive-star modeling community. The paper is clearly organized and the synthetic population is a straightforward illustration of the model consequences. However, the headline conclusion rests heavily on the realization of chemically homogeneous evolution at Omega/Omega_crit ~ 0.6, an assumption the authors themselves note is debated, and the population feature is in part imposed by applying the derived critical core mass cutoff to the fits. These points need to be addressed before the central claim can be considered robust.","major_comments":[{"comment":"The paper's main conclusion - that rapid rotation caps BH masses near 35-36 Msun - depends on models becoming chemically homogeneous at Omega/Omega_crit ~ 0.6. The authors explicitly acknowledge in Sec. 2.2 that the physics of rotationally induced CHE is still under debate and that there is no empirical evidence that low-metallicity WR stars rotate faster than their high-metallicity counterparts. The D_ES = 0 test in Sec. 4.1 (Fig. 13) changes the HRD track and final mass, but the authors do not report whether that model still becomes chemically homogeneous or retains an H envelope. This is load-bearing: if CHE does not occur at the adopted mixing efficiency, the maximum BH mass reverts to the H-rich boundary (~93 Msun) and the LIGO/Virgo bump interpretation disappears. Please run a set of models with reduced rotational mixing efficiencies (e.g., D_ES = 0, reduced secular shear, or a factor of a few lower diffusion coefficients) and report the resulting M_final, M_CO, and whether the star is still fully mixed at core He exhaustion. This directly tests the robustness of the 36 Msun cap.","section":"Sec. 2.2 and Sec. 3.2 (cf. Sec. 4.1, Fig. 13)"},{"comment":"The population synthesis in Sec. 3.4 applies the critical CO core mass criterion from Sec. 3.2 as a hard cutoff to the fitted final masses, and the resulting pile-up below ~36 Msun is therefore largely a construction of that imposed criterion rather than an independent prediction. The large error on the CO core mass fit (M_CO,fit = +/- 9.09 Msun) is not propagated into the population histogram, so the sharp drop at 36.3 Msun and the claimed alignment with the LIGO/Virgo bump at ~35 Msun are not robust. Please propagate the fit uncertainties into the synthetic population (e.g., via Monte Carlo over the fit coefficients) and show the resulting distribution with error bands. In addition, show the histogram produced from the final-mass fit alone, without the M_CO,crit cutoff, so the reader can see what fraction of the pile-up is physical rather than imposed. If the bump disappears or shifts substantially, the wording should be softened from an alignment claim to a consequence of the adopted criterion.","section":"Sec. 3.3 and Sec. 3.4 (Eqs. 14-15, Fig. 12)"},{"comment":"The high-rotation M_crit experiment is performed at a single fiducial metallicity (Z = 1/10 Z_sun, as stated in the Fig. 7 caption), while the population synthesis spans Z/Z_sun from 1/5 to 1/1000. The occurrence of CHE and the effectiveness of mechanical mass loss are metallicity-dependent, so the applicability of the 35-36 Msun cap across the full metallicity range is not directly demonstrated. Please clarify whether the constancy of M_CO,crit at high rotation has been checked at other metallicities, or state explicitly that the metallicity dependence is assumed to be negligible and justify that assumption with references or a small number of test models.","section":"Sec. 3.2 (Fig. 7) and Sec. 3.4"}],"minor_comments":[{"comment":"The typeset equations for the fits are garbled: the branch conditions and coefficients run together, making it difficult to reproduce the fits. Please reformat these equations with explicit piecewise definitions and list all coefficients, ideally also in a machine-readable table.","section":"Sec. 3.3 (Eqs. 14-16)"},{"comment":"Table 2 lists the grid parameters but the layout is confusing; it is not obvious which combinations of M_ZAMS, Z/Z_sun, and Omega/Omega_crit are actually run. A full factorial grid or an explicit statement of which combinations were omitted would help.","section":"Table 2"},{"comment":"The quantity called M_BH in Table 4 is actually the final stellar mass before collapse, not a directly predicted BH mass, since no core-collapse simulation is performed. The caption should make this explicit, even though the text notes it.","section":"Sec. 3.4 and Table 4"},{"comment":"The comparison with Sibony et al. (2024) shows a ~20% final-mass difference for similar initial conditions. The authors attribute this to rotational mixing and mass-loss implementation, but the discussion is brief; a sentence summarizing the main reason for the difference (e.g., GENEC vs. MESA mixing treatment) would strengthen the comparison.","section":"Sec. 4.1 (Fig. 13)"}],"recommendation":"major_revision","confidential_remarks":"The paper is within the scope of MNRAS and the M_crit result is a solid piece of work. My main concern is that the central astrophysical claim (rotation caps BH masses at ~36 Msun and explains the LIGO/Virgo bump) is contingent on chemically homogeneous evolution, which is contested; the authors acknowledge this but do not provide a robustness test. In addition, the population-synthesis pile-up is partly an artifact of imposing the critical core mass cutoff, and the large fit errors are not propagated. These issues are addressable with additional model runs and a revised analysis, so I recommend major revision rather than rejection. I would also suggest the authors consider citing recent work on rotational mixing calibration and on the observed rotation rates of WR stars at low metallicity, to better justify their adopted mixing efficiency."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is the Vink group's follow-up to Winch et al. 2024, pushing the Mcrit experiment to Omega/Omega_crit = 0.8 and adding mechanical mass loss to MESA. The new physics is the rotation-boost implementation with the Maeder & Meynet small-angle approximation relaxed, and the mechanical mass-loss prescription. The main result—that fast rotators become chemically homogeneous and cap pre-PI BH masses near 35-36 M_sun—is a clean extension of their constant critical core mass idea. The Mcrit experiment at high rotation gives 35.0 +/- 2.3 M_sun, within error of 36.3, which is a genuine check rather than a re-fit.\n\nThe paper is honest. It flags in Section 2.2 that rotationally induced CHE is debated and depends on very efficient mixing, and the comparison to Geneva and Bonn tracks is useful. The ST dynamo test is a nice negative result. But the honesty in the text is not matched by the abstract and conclusions, which state the mass cap as a definitive result. The stress-test is right: the cap lives or dies with CHE at Omega/Omega_crit ~0.6. The D_ES=0 model in Figure 13 is only compared on the HRD; the paper never reports whether that model still becomes chemically homogeneous. That is the obvious missing test.\n\nOther soft spots: the fit to M_CO has +/- 9.09 M_sun error, which is not propagated into the population histograms; the mechanical mass-loss implementation is described in prose but no inlists or code are available yet, only a promise to release via the MESA marketplace; and the LIGO/Virgo bump alignment is suggestive but the steep drop after 36.3 M_sun is largely produced by imposing the Mcrit cutoff in the population synthesis. The agreement with the observed bump is therefore not an independent validation of the boundary, though the paper mostly presents it as \"could be a contributor.\"\n\nWho should read this: anyone working on PI boundaries, massive star rotation, or GW progenitor populations. The paper deserves a serious referee. The core result—constant CO critical core mass under fast rotation—is supported by the Mcrit experiment. The CHE robustness needs a dedicated test, the error bars need to be carried through the population synthesis, and the mechanical mass loss needs a release with the paper. If those are addressed, this will be a useful citable paper. My recommendation: engage with it, send it to review.","headline":"A solid follow-up that extends the Mcrit boundary to fast rotation, but the 35-36 M_sun cap sits on the uncalibrated CHE assumption and the LIGO bump alignment is partly built from the input cutoff.","tokens_in":26414,"tokens_out":2939,"would_cite":true,"duration_ms":28029,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Rotation at about 60% of critical speed can fully mix a massive star, capping black hole masses before pair instability near the critical CO core mass of roughly 35–36 solar masses.","keywords":["black hole mass gap","pair-instability supernova","stellar rotation","chemically homogeneous evolution","mechanical mass loss","gravitational wave sources","massive star evolution","low metallicity stars"],"falsifier":"A survey of rotating low-metallicity massive stars that finds no chemically homogeneous objects at the rotation rates assumed, or a single-star black hole above about 36 solar masses whose progenitor was fully mixed, would break the cap.","tokens_in":25302,"feed_emoji":"🕳️","tokens_out":9961,"duration_ms":83693,"temperature":0.7,"pith_summary":"This paper tries to establish that fast stellar rotation, at roughly 60% of critical speed, can make a massive star's entire interior chemically homogeneous, so that the star evolves like an already stripped star. In that state, the final black hole mass before a pair-instability supernova is set by the critical carbon-oxygen core mass, which the authors compute as 36.3 solar masses, with their high-rotation experiment giving 35.0 ± 2.3 solar masses. If true, the heaviest black holes formed from single rapidly rotating low-metallicity stars should pile up around that cap, naturally producing the bump seen near 35 solar masses in gravitational-wave black hole merger data. The paper also adds a mechanical mass-loss treatment for stars at critical rotation and derives fits for core and final masses across rotation rate and metallicity.","feed_headline":"Rapid rotation caps black hole masses near 36 solar masses","feed_subtitle":"Gravitational-wave detections show a bump near 35 solar masses; new models tie it to rotationally stripped stars.","key_machinery":"The load-bearing object is the critical carbon-oxygen core mass, defined through a global stability integral of the first adiabatic index; the star becomes pair-unstable when this integrated index drops below the stability threshold. The new mechanism is the chemically homogeneous (stripped-star) limit reached at high rotation: once rotational mixing homogenizes the whole star, the core mass saturates at the final mass, and the pair-instability boundary becomes a hard cap on the final black hole mass. The implementation also uses a rotation-boosted radiative wind formalism combined with a mechanical mass-loss term that switches on when the surface speed crosses 98% of the critical value, preventing models from spinning up to supercritical rotation.","core_discovery":"The central claim is that rotation at Ω/Ω_crit ≈ 0.6 triggers chemically homogeneous evolution, turning a massive low-metallicity star into a stripped star whose core mass equals its final mass. For these fully mixed stars, the helium core mass loses its independent meaning, and the pair-instability boundary is set by a fixed critical carbon-oxygen core mass, M_CO,crit = 36.3 M_sun (with the high-rotation extension giving 35.0 ± 2.3 M_sun). Consequently, the maximum black hole mass from this channel is capped by the critical core mass rather than by the initial stellar mass. Population synthesis using the new fits produces a strong pile-up of black hole progenitors near 27–36 M_sun with a steep drop just above 36 M_sun, matching the bump in the gravitational-wave black hole mass distribution.","pith_inferences":["Editorial inference: If the cap is real, the 35 M_sun pile-up in gravitational-wave data should be strongest for mergers whose progenitors formed at low metallicity, and it should weaken near solar metallicity where winds remove angular momentum before homogenization.","Editorial inference: The same mechanism would sharpen the upper edge of the second mass gap at about 36 M_sun rather than the wider 50–120 M_sun range, implying that any future single-star black hole above roughly 40 M_sun would require an alternative formation channel such as dynamical mergers or later accretion.","Editorial inference: The paper's fits predict that the black hole mass cap is nearly independent of initial mass for fast rotators above about 80 M_sun; a cluster of remnants all lying within 35 ± 3 M_sun would support the mechanism, while a wide scatter above the cap would weaken it."],"forward_implications":["The maximum black hole mass from single, rapidly rotating, low-metallicity stars is set by the critical CO core mass of about 35–36 M_sun; heavier black holes in the pair-instability gap would require a different formation path.","Population synthesis with the new fits produces a black hole progenitor pile-up around 27–36 M_sun and a steep drop just above 36 M_sun, matching the observed bump in gravitational-wave remnant masses.","Below about 1/100th solar metallicity, mechanical mass loss dominates over radiative winds, often contributing 35–70% of the total mass lost, which further lowers the final black hole masses.","Stars rotating faster than roughly 0.4–0.5 of critical speed become chemically homogeneous and stripped, so final mass equals core mass and the helium core mass ceases to be a useful predictor for these objects.","The presence or absence of the internal magnetic-field dynamo changes final masses significantly only at higher metallicity, not at low metallicity, contrary to a previously proposed explanation for differences between stellar evolution codes."],"supporting_citations":[{"why":"Derives the critical CO core mass M_CO,crit = 36.3 M_sun and provides the low-rotation parameter space that this paper extends to fast rotators.","marker":"Winch et al. 2024"},{"why":"Shows that 90–100 M_sun low-metallicity stars can produce cores small enough to avoid pair instability while retaining their H envelope, motivating the critical core-mass criterion.","marker":"Vink et al. 2021"},{"why":"Supplies the global adiabatic-index stability integral used to define the pair-instability boundary in the critical core mass experiment.","marker":"Stothers 1999"},{"why":"Provides the rotation-enhanced mass-loss formalism and the ΩΓ limit that the paper implements for near-critical rotators.","marker":"Maeder & Meynet 2000"},{"why":"Gives the rapid-rotation criterion for pair instability that the paper checks against its own models.","marker":"Marchant & Moriya 2020"},{"why":"Lists the diffusive rotational mixing instabilities whose efficient action produces chemically homogeneous evolution.","marker":"Heger et al. 2000"},{"why":"Provides the low-metallicity massive-star mass-loss framework extended here with the full rotation boost and mechanical mass loss.","marker":"Sabhahit et al. 2023"}],"fun_headline_variants":["Rotation strips stars, capping black holes at ~36 solar masses","Rotation caps black hole masses: critical core mass 36.3 M_sun","High rotation bends pair-instability boundary, cap at 36 M_sun","Fast rotators set black hole mass ceiling near 36 M_sun"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that rotation near 60% of critical speed really does mix the entire star chemically, an assumption the paper acknowledges is still under debate and lacks direct empirical support.","fun_headline_variants_meta":{"raw":{"variants":["Rotation strips stars, capping black holes at ~36 solar masses","Rotation caps black hole masses: critical core mass 36.3 M_sun","High rotation bends pair-instability boundary, cap at 36 M_sun","Fast rotators set black hole mass ceiling near 36 M_sun"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000212,"raw_usage":{"total_tokens":1449,"prompt_tokens":1006,"completion_tokens":443,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":622,"completion_tokens_details":{"reasoning_tokens":362}},"tokens_in":622,"tokens_out":443,"duration_ms":4617,"temperature":1.0,"reasoning_tokens":362,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:51:58.458661+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A survey of rotating low-metallicity massive stars that finds no chemically homogeneous objects at the rotation rates assumed, or a single-star black hole above about 36 solar masses whose progenitor was fully mixed, would break the cap.","supporting_citations":[],"review_version":1}