{"id":"a125e01b-3b03-46c0-8522-3415a09814ec","arxiv_id":"2508.21233","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Rotating massive stars form black holes at lower initial masses than non-rotating stars, and a pair-instability mass gap is predicted between about 90 and 150 solar masses.","lead":"This paper uses a large grid of stellar evolution models to map how massive stars die across initial mass, metallicity, and rotation. It predicts the types of supernovae and compact remnants, and the resulting black hole mass gap, which upcoming surveys can test.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"CO core mass-to-remnant mapping (Table 1) is the load-bearing assumption; the paper acknowledges its uncertainty but never quantifies its effect on any result.","rationale":"The reader's weakest_assumption identifies the same load-bearing point I find: the paper's fate predictions are not derived from direct explosion simulations but from an adopted relationship between M_CO and remnant/SN type (Table 1). I agree that this is the right place to attach the main correctness risk. The paper is honest about the uncertainty, citing later studies that find different explodability islands, but it does not quantify how its conclusions would change under those alternatives. This is not an internal inconsistency—the logic is clear—but it is a serious, unquantified mapping uncertainty. Several borderline models in Table A2 make the sensitivity concrete: a small threshold shift flips NS vs BH classifications for models that influence the claimed rotation effect. A threshold-sensitivity or alternative-mapping test is feasible and would directly determine whether the qualitative claims are robust or mapping-dependent. Since the reader's verdict is already CONDITIONAL and this concern is exactly what that conditionality rests on, I do not see a reason to change the verdict. The paper deserves credit for its transparent caveats, the broad GENEC grid, and tabulated model data, but the quantitative predictions should remain conditional until the mapping uncertainty is tested.","tokens_in":32640,"tokens_out":8629,"duration_ms":92916,"concrete_test":"Reclassify the models in Table A2 using bracketing shifts of the 6/8/12/40/60/130 Msun boundaries by ±1 Msun and ±3 Msun, and also using the explodability-band locations implied by the post-2020 studies cited in §2.3 (Wang et al. 2022; Maltsev et al. 2025). Recompute the aggregate fractions in Tables A3-A4 and the maximum BH masses in Table 4 / Fig. 5 under each mapping. The concern is settled if the qualitative conclusions—rotation shifts the NS/BH boundary to lower M_ini for Z>0.002, max BH below the gap <50 Msun at SMC, gap ~90-150 Msun—survive all reclassifications; if boundaries move by more than ~10-20% in M_ini or the max BH crosses 50 Msun, the headline predictions are conditional on Table 1 and need mapping-dependent error bars.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claims are produced by applying the fixed M_CO thresholds of Table 1 to GENEC models stopped at the end of core-He burning. Table 1 is imported, not derived; Section 2.3 concedes that newer explodability studies (Wang et al. 2022; Boccioli et al. 2023; Maltsev et al. 2025) find explodability islands at 'very different masses' with metallicity dependence. This matters because many of the models driving the abstract's qualitative statements sit within ~1 Msun of a Table 1 boundary. Examples from Table A2: at Z=0.002, the rotating 25 Msun model has M_CO=6.25, just above the 6 Msun NS/BH cut, while the non-rotating 25 Msun model has M_CO=5.66, just below it; at Z=1e-5, the non-rotating 30 Msun model has M_CO=7.57 (BH(NS) band) and the rotating 30 Msun model has M_CO=4.81 (NS). A shift of the 6/8/12 Msun cuts by even 1 Msun therefore changes which side of the NS/BH boundary a non-negligible set of models falls on. Since every remnant fraction, SN fraction, maximum BH mass, and mass-gap boundary in Figs. 3-10 and Tables A3-A4 is a consequence of these cuts, the quantitative predictions inherit the full mapping uncertainty. The paper reports no error bars and no test of alternative explodability mappings, so it cannot distinguish a robust rotation/metallicity trend from an artifact of one particular set of thresholds. This is a correctness risk, not an internal inconsistency: the caveat is stated, but it is stated and then used as a deterministic table.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses the GENEC grid of rotating and non-rotating stellar models (initial masses 9–500 Msun, metallicities Z=1e-5 to 0.02) to predict the final fates of massive stars. The fate is diagnosed from the CO core mass at the end of core helium burning, using fixed thresholds (Table 1) to assign neutron star, black hole, PPISN, or PISN outcomes, and from envelope H/He masses to assign spectroscopic supernova types (Table 2). The authors produce remnant-type and supernova-type maps as a function of initial mass and metallicity, compute black hole mass distributions (including a PPISN fit from Eq. 3), and then weight the outcomes by Salpeter and top-heavy IMFs to derive population fractions. The main claims are that rotation significantly alters remnant types and supernova engines, that metallicity strongly controls the fates with maximum black hole masses below 50 Msun at SMC and higher metallicities, and that a pair-instability mass gap is predicted between about 90 and 150 Msun.","tokens_in":33173,"tokens_out":8431,"duration_ms":77106,"significance":"If the mapping from CO core mass to remnant type is reliable, the paper provides a broad and homogeneous census of single-star fates across cosmic times, connecting stellar evolution grids to gravitational-wave and supernova observations. The release of the model grid and Table A2 is a valuable resource. The qualitative trends — e.g., that rotation can promote or inhibit black hole formation depending on metallicity, and that higher metallicity suppresses the most massive remnants — are physically plausible and worth publishing. However, the quantitative results (fractions, maximum BH masses, mass-gap edges) are all derived from a small number of imported explodability thresholds and from linear interpolation over a sparse grid, and the paper provides no uncertainty quantification on these steps. The abstract additionally overstates the rotation effect at low metallicity. The strengths are the parameter-space coverage and the falsifiability of the predictions, but the numerical precision implied by the paper exceeds what the underlying assumptions can support.","major_comments":[{"comment":"The remnant-type classification uses fixed M_CO thresholds (6, 8, 12, 40, 60, 130 Msun) taken from a subset of the explodability literature. The paper itself concedes that later studies (Wang et al. 2022; Boccioli et al. 2023; Maltsev et al. 2025) find islands of explodability at very different masses with metallicity dependence. Many models in Table A2 lie within ~1 Msun of a boundary: at Z=0.002 the non-rotating 25 Msun model has M_CO=5.66 (NS) while the rotating model has M_CO=6.25 (BH(NS)); at Z=1e-5 the non-rotating 30 Msun model has M_CO=7.57 (BH(NS)) and the rotating one 4.81 (NS). A ±1 Msun shift of the 6/8/12 Msun cuts changes which side of the NS/BH boundary these models fall on. Since all remnant fractions, BH mass distributions, and mass-gap edges in Figs. 3–10 and Tables A3–A4 are derived from these cuts, the quantitative predictions inherit the full mapping uncertainty. The","section":"Section 2.3 / Table 1"},{"comment":"The abstract states that 'rotating stars favouring black hole formation at lower initial masses than their non-rotating counterparts.' This is not supported by the paper's own models at low metallicity. For Z=1e-5 and M_ini < 60 Msun, rotation reduces the CO core mass (hydrogen-burning-shell effect, Section 3.2, first case) and produces more NS, not BH; e.g., the rotating 30 Msun model has M_CO=4.81 (NS) versus 7.57 (BH(NS)) for the non-rotating model. The effect of rotation is described in Section 3.2 as mass- and metallicity-dependent, with four regimes where mixing or mass loss dominates. The abstract should be revised to state that rotation can either promote or inhibit BH formation depending on metallicity and mass, or to restrict the claim to subsolar but not extremely metal-poor metallicities.","section":"Abstract; Section 3.2"},{"comment":"The contour maps use linear interpolation over a sparse and unevenly spaced grid (e.g., initial masses 9,12,15,20,25,32,40,60,85,120,150,200,300,500 Msun per metallicity, Table A1). The paper correctly notes that interpolation 'may also result in missing features,' but the interpolated boundaries are used to derive all population fractions and the BH mass distribution. For instance, the NS/BH boundary between 25 and 32 Msun at Z=0.002 is estimated from endpoints with M_CO=5.66 and 8.59; the crossing mass could shift by several Msun if the true M_CO(M_ini) relation is non-linear. This is a known limitation, but it is propagated into the quantitative claims without an uncertainty estimate. Please either report the discrete model values on the contour plots, use the model grid directly for the population synthesis, or provide an interpolation-error estimate.","section":"Section 3 (interpolation); Fig. 3"},{"comment":"The black-hole remnant masses for PPISN are computed with Eq. (3), a fit taken from Farmer et al. (2019) with fixed coefficients. The uncertainty in this fit and in the assumed M_CO ranges (40–60, 60–130 Msun) is not propagated into the predicted mass gap of ~90–150 Msun or the maximum BH masses in Table 4. Since these numbers are directly compared to GW190521 and GW231123, the gap boundaries should be presented as ranges reflecting the fit and threshold uncertainties, not as sharp values.","section":"Section 3.3 / Eq. (3)"}],"minor_comments":[{"comment":"'Eluded to' should be 'alluded to'.","section":"Section 2.3"},{"comment":"The superscript origin codes are difficult to parse in the typeset version; please display them in a clearer format so each initial mass is unambiguously associated with its source grid.","section":"Table A1"},{"comment":"The four rotation regimes described in Section 3.2 are not indicated on the figure; adding region labels or shading would help the reader connect the text to the plots.","section":"Figures 3 and 4"},{"comment":"'Increase in failed supernova leading to BH' should be 'increase in failed supernovae leading to BHs'.","section":"Section 5.1.2"},{"comment":"The assumption that the rotating 500 Msun Z=0.02 model has the same properties as the rotating 300 Msun model is stated in the text but not flagged in the figure caption or Table A2; this should be clearly marked wherever the interpolated 500 Msun values appear.","section":"Section 3 / Fig. 4 caption"}],"recommendation":"major_revision","confidential_remarks":"The paper is in scope and the underlying GENEC grid is valuable. The main weakness is not internal inconsistency but the unquantified dependence of the paper's headline numbers on the adopted explodability mapping and on sparse-grid interpolation. The authors already acknowledge these caveats in words, but they do not translate them into error bars or alternative-mapping tests. I would encourage the editor to request a sensitivity analysis, even if simple, and to ensure the abstract is corrected to reflect the complex, metallicity-dependent role of rotation. The paper should be publishable after such a revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nYou should know this paper is a genuinely useful synthesis. It takes the GENEC grids (9–500 M_sun, Z=1e-5 to 0.02, rotating and non-rotating) and maps each model to a remnant type and supernova type using the CO core mass and envelope composition, then folds the results through two IMFs to give population fractions. That is a practical reference for anyone comparing massive-star fates with observed SN rates or GW black hole masses.\n\nThe qualitative results are credible and, as far as they go, not new in direction but now drawn on a wider grid: rotation tends to shift the boundary for black hole formation to lower initial masses (via mixing) at most metallicities, while at very low Z the hydrogen-burning-shell interaction in some rotating models lowers CO core masses. The predicted PI mass gap of ~90–150 M_sun and the cap on BH mass below the gap at SMC and above are clear, testable claims. The authors are upfront about many caveats, which I appreciate.\n\nThe soft spot is exactly the one the stress-test note identifies, and it is not manufactured. Table 1, the mapping from M_CO to remnant type, is imported from the literature, not derived here. The paper even says that newer explodability studies (Wang et al., Boccioli et al., Maltsev et al.) find islands at very different masses and with metallicity dependence. Then it proceeds to treat the table as deterministic, with no error bars, no sensitivity test. The examples in the note are on point: at Z=0.002, rotating 25 M_sun has M_CO=6.25, just above the 6 M_sun NS/BH cut, while the non-rotating one has 5.66, just below. A 1 M_sun shift in the threshold flips those classifications. Since all the quantitative rates, maximum BH masses, and mass-gap edges come from these cuts, the numbers should be read with caution.\n\nThat said, the broad trends—rotation and metallicity change the fates—are probably robust, because they follow from the overall behavior of the CO core mass, not from one knife-edge cut. The paper would be much stronger if it showed results for a second plausible explodability mapping or quantified the threshold uncertainty.\n\nOther, minor issues: the rotating 500 M_sun Z=0.02 model is replaced by the 300 M_sun one (reasonable but ad hoc), and the linear interpolation over sparse grid points is acknowledged. The observational comparison for SN types is rough, as they admit.\n\nI would cite this as a reference map and bring it to a reading group for a discussion about how to present uncertain explodability mappings. It deserves peer review, and the referee should push for a sensitivity analysis. Overall, an honest, useful paper that slightly overstates the precision of its quantitative predictions.","headline":"Useful, honest fate map for massive stars, but the quantitative predictions lean on an unsettled explodability mapping that the paper itself flags and then uses deterministically.","tokens_in":33648,"tokens_out":4195,"would_cite":true,"duration_ms":41729,"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":"A massive star's fate is set at the end of helium burning by its carbon–oxygen core mass and envelope composition; rotation shifts the remnant boundaries enough to change black-hole masses and supernova-type rates.","keywords":["massive stars","stellar rotation","black hole formation","pair-instability supernovae","neutron stars","stellar evolution","carbon–oxygen core mass","initial mass function"],"falsifier":"If gravitational-wave detections confirm merging black holes with component masses inside the predicted 90–150 solar-mass gap from isolated stellar evolution, the central mapping fails; alternatively, a null result in near-infrared searches for high-redshift pair-instability supernovae would put the framework under pressure.","tokens_in":32606,"feed_emoji":"🌌","tokens_out":10365,"duration_ms":95612,"temperature":0.7,"pith_summary":"This paper maps what happens to massive single stars when they die, using a homogeneous grid of one-dimensional stellar evolution models spanning initial masses from 9 to 500 times the Sun's mass and metallicities from nearly zero to supersolar, each with and without rotation. The guiding claim is that a star's fate is already fixed at the end of core helium burning: the mass of its carbon–oxygen core determines whether it leaves a neutron star, a black hole, or no remnant, while the remaining hydrogen and helium envelope determines the supernova's spectroscopic type. The central new result is that rotation is not a minor correction — through extra mixing it makes black hole formation occur at lower initial masses across most of the parameter space, while at extremely low metallicity a hydrogen-shell interaction does the opposite and raises the neutron-star fraction. The paper also predicts a pair-instability mass gap between about 90 and 150 solar masses, with no black holes above roughly 50 solar masses at Small Magellanic Cloud or higher metallicity. These predictions matter because they can be checked against gravitational-wave detections, supernova surveys, and chemical-enrichment models.","feed_headline":"Rotation shifts the black-hole threshold","feed_subtitle":"Rotation shifts the black-hole threshold; the pair-instability gap lands at 90–150 solar masses.","key_machinery":"The carbon–oxygen (CO) core mass at the end of core helium burning, defined as the mass coordinate where the helium mass fraction first drops below 1%, is the load-bearing quantity. It is used because it sets the pre-collapse compactness of the core, which governs whether the supernova shock revives or the star collapses directly into a black hole. Table 1 encodes the fate map: M_CO < 6 M_sun -> neutron star; 6–8 -> black hole with possible neutron star; 8–12 -> neutron star with possible black hole; 12–40 -> direct black hole; 40–60 -> pulsational pair-instability supernova leaving a black hole; 60–130 -> pair-instability supernova leaving no remnant; >130 -> direct black hole. The companio","core_discovery":"The paper's central claim is that two quantities read off at the end of core helium burning — the carbon–oxygen core mass and the hydrogen/helium envelope mass — are sufficient to classify the fate of a massive star. The CO core mass sets the remnant through the compactness-based Table 1 mapping: below 6 solar masses a neutron star; 6–8 a black hole with possible neutron star; 8–12 a neutron star with possible black hole; 12–40 a direct black hole; 40–60 a pulsational pair-instability supernova leaving a black hole; 60–130 a pair-instability supernova leaving nothing; above 130 a direct black hole again. On top of this, envelope thresholds assign spectroscopic types (IIP, IIL, IIb, Ib, Ic).","pith_inferences":["If the CO-core-mass mapping were replaced by the newer explodability islands the paper cites, the absolute remnant boundaries would move, but the qualitative rotation trend — shifting boundaries relative to non-rotating stars — might survive; recomputing the contour maps with those islands would test this.","The predicted 90–150 solar-mass gap gives a clean interpretation test for events like GW190521: a single-star remnant inside the gap would violate the gap, so a confirmed event there would favour hierarchical mergers in dense clusters.","The extremely metal-poor hydrogen-shell effect predicts an elevated neutron-star fraction at very low metallicity relative to SMC metallicity; targeted searches for compact-object populations in very low-metallicity regions could discriminate this.","The factor-level deficit of Type Ic supernovae from single stars provides a quantitative upper bound on the fraction of Type Ic progenitors requiring binary mass transfer, which could be refined with binary population synthesis."],"forward_implications":["At Small Magellanic Cloud or higher metallicity, no black hole below the pair-instability gap is predicted above about 50 solar masses, so gravitational-wave events with heavy black holes must come from metal-poor environments.","The pair-instability gap is predicted to lie near 90–150 solar masses, and pair-instability supernovae appear only below solar metallicity for initial masses above about 100 solar masses; this sharpens the expected black-hole mass distribution and helps explain the lack of confirmed pair-instability supernovae in optical surveys.","Rotation lowers the initial mass at which black holes form in most environments, nearly doubling the predicted black-hole fraction at solar metallicity and changing the mix of supernova types in initial-mass-function-weighted populations.","Type Ic supernovae from single stars are rare in these models; the observed fraction is larger than predicted, implying that envelope stripping in binaries or other mechanisms must supply the missing progenitors.","A top-heavy initial mass function reproduces the observed core-collapse supernova type fractions much better than the Salpeter initial mass function, providing a population-level constraint on the massive-star mass distribution."],"supporting_citations":[{"why":"Supplies the compactness parameter and the explodability limit that grounds the neutron-star/black-hole boundary.","marker":"O'Connor & Ott 2011"},{"why":"Provides the low-CO-core-mass neutron-star condition and the direct-collapse range used in Table 1.","marker":"Patton & Sukhbold 2020"},{"why":"Supplies the 'island of explodability' for intermediate CO core masses and the non-monotonic compactness picture.","marker":"Sukhbold et al. 2016"},{"why":"Supplies the pulsational pair-instability and pair-instability mass ranges and the fitting relation for black-hole mass used in Eq. 3.","marker":"Farmer et al. 2019"},{"why":"Supplies the photodisintegration direct-collapse threshold above 130 solar masses and the hydrogen-envelope threshold for supernova types.","marker":"Heger et al. 2003"},{"why":"Supplies the solar-metallicity grid and the shared physical ingredients (abundances, reaction rates, opacities) used across the models.","marker":"Ekström et al. 2012"},{"why":"Supplies the extremely metal-poor grid and documents the hydrogen-burning-shell expansion that shapes the low-metallicity rotation results.","marker":"Sibony et al. 2024"},{"why":"Provides the standard initial mass function exponent used for population-weighted remnant and supernova fractions.","marker":"Salpeter 1955"},{"why":"Provides the top-heavy initial mass function exponent used as the alternative population weighting.","marker":"Schneider et al. 2018"}],"fun_headline_variants":["Rotation shifts black-hole threshold","Rotating stars favor black holes at lower mass","Pair-instability gap set at 90–150 solar masses","Metal-poor giants birth the heaviest black holes","Fate of massive stars: rotation is key"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The load-bearing premise is that a star's doom is already decided when helium burning ends: the carbon–oxygen core mass at that moment reliably dictates whether the star becomes a neutron star, a black hole, or a pair-instability supernova, even though the paper notes that newer studies place successful explosions at different core masses and convection remains a major uncertainty.","fun_headline_variants_meta":{"raw":{"variants":["Rotation shifts black-hole threshold","Rotating stars favor black holes at lower mass","Pair-instability gap set at 90–150 solar masses","Metal-poor giants birth the heaviest black holes","Fate of massive stars: rotation is key"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000229,"raw_usage":{"total_tokens":1365,"prompt_tokens":844,"completion_tokens":521,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":588,"completion_tokens_details":{"reasoning_tokens":450}},"tokens_in":588,"tokens_out":521,"duration_ms":5193,"temperature":1.0,"reasoning_tokens":450,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T14:26:51.947905+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"If gravitational-wave detections confirm merging black holes with component masses inside the predicted 90–150 solar-mass gap from isolated stellar evolution, the central mapping fails; alternatively, a null result in near-infrared searches for high-redshift pair-instability supernovae would put the framework under pressure.","supporting_citations":[{"cited_title":"D., 2011, The Astrophysical Journal, 730, 70","cited_arxiv_id":null,"evidence_quote":"Supplies the compactness parameter and the explodability limit that grounds the neutron-star/black-hole boundary."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the low-CO-core-mass neutron-star condition and the direct-collapse range used in Table 1."},{"cited_title":"M., Janka H.-T., 2016, The Astrophysical Journal, 821, 38","cited_arxiv_id":null,"evidence_quote":"Supplies the 'island of explodability' for intermediate CO core masses and the non-monotonic compactness picture."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the pulsational pair-instability and pair-instability mass ranges and the fitting relation for black-hole mass used in Eq. 3."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the photodisintegration direct-collapse threshold above 130 solar masses and the hydrogen-envelope threshold for supernova types."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the extremely metal-poor grid and documents the hydrogen-burning-shell expansion that shapes the low-metallicity rotation results."},{"cited_title":"E., 1955, Astrophysical Journal, vol","cited_arxiv_id":null,"evidence_quote":"Provides the standard initial mass function exponent used for population-weighted remnant and supernova fractions."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the top-heavy initial mass function exponent used as the alternative population weighting."}],"review_version":1}