{"id":"12ddfcf3-46fb-45dc-8a9d-7a00020a34d7","arxiv_id":"2501.12917","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A new PARSEC v2.0 grid of more than 1,100 stellar tracks predicts a pair-instability black hole mass gap of roughly 100 to 130 solar masses and publishes the tracks, ejecta, and ionizing photon tables.","lead":"This paper releases a new, consistent set of stellar evolution models for stars ranging from 2 to 2000 times the Sun's mass, across metallicities from the first stars to super-solar. The full library, including final fates, chemical ejecta, and ionizing photon rates, is public and ready to use in studies of black hole mergers and galaxy formation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Both edges of the claimed 100–130 M⊙ gap are set by sharp external MHe thresholds (≈34 and ≈130 M⊙) applied to pre-SN helium cores that are themselves extremely mixing-sensitive; without a robustness study the exact gap is not established.","rationale":"The paper is a valuable, largely reproducible data-release from an established group, and the reader's CONDITIONAL verdict is appropriate. The central claim, however, is a sharp quantitative statement: the combined pair-instability mass gap spans just 100–130 M⊙. That statement depends on at least three layers: (i) the PARSEC pre-SN helium-core masses, (ii) the external fate mapping from MHe to final remnant (Woosley 2017), and (iii) the discrete sampling in mass and metallicity. The reader's weakest assumption identifies layer (i), specifically the convective overshooting and dredge-up treatment. I partially agree, but the fate-mapping thresholds and the sparse metallicity/mass grid are at least as load-bearing: the lower edge is a 100 M⊙ Z=10^-11 track sitting just below the ≈34 M⊙ PPISN threshold, and the upper edge is an interpolated ≈130 M⊙ MHe threshold at a single metallicity. The paper itself acknowledges the sensitivity and the chaotic nature of the dredge-up transitions (Appendix C), yet provides no propagated uncertainty and no variation of the key parameters. This is not an internal inconsistency; it is a robustness gap. The paper's comparisons with other codes and with the Tarantula Nebula data provide genuine supporting evidence for the tracks as a whole, but they do not calibrate the exact gap edges. A focused rerun around the two edges with varied mixing parameters and a small fate-mapping threshold shift would settle whether the 100–130 M⊙ interval is a robust prediction or a coincidental product of the adopted prescriptions. Until then, the headline result should be presented as conditional on the mixing and fate-mapping choices, exactly as the reader's verdict states.","tokens_in":43549,"tokens_out":8544,"duration_ms":89887,"concrete_test":"Run a focused robustness suite around the two edges: compute MZAMS=90, 95, 100, 105, 110, 115 at Z=10^-11 (spanning the lower edge) and MZAMS=120, 125, 130, 135, 140 at Z=0.004, 0.006, and 0.008 (spanning the upper edge), using the same PARSEC v2.0 physics but varying envelope overshooting Λ_env to 0.3 and 1.0 H_P and core overshooting λ_ov to 0.35 and 0.65 H_P. If the maximum sub-gap BH mass or minimum super-gap BH mass moves into 100–130 M⊙ in any variant, the claimed combined gap is not robust to the adopted mixing prescription; also re-map the final fates with the Woosley (2017) MHe thresholds shifted by ±5 M⊙ to quantify the fate-mapping contribution.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim reduces to two boundary cases: the lower edge (99.5 M⊙) is the Z=10^-11, MZAMS=100 M⊙ track whose final MHe≈33 M⊙ just falls below the adopted PPISN threshold, and the upper edge (≈129.4 M⊙) is an interpolated DBH threshold at Z=0.006 where MHe crosses 130 M⊙. Both thresholds come from the Woosley (2017) fate mapping via Goswami et al. (2021), not from PARSEC itself (§3.3). The pre-SN MHe values entering this mapping are highly sensitive to the convective mixing treatment: core overshooting λ_ov=0.5 and especially envelope overshooting Λ_env=0.7 H_P with the Schwarzschild criterion control the deep dredge-up that lowers MHe below the threshold (§2.1, Appendix C). The paper itself notes the evolution is 'chaotic' and that tiny variations can change the final fate (Appendix C). Yet Table 4 quotes gap edges with no uncertainties, and no variation of mixing parameters or fate thresholds is explored. The grid also has a 10 M⊙ step in the 100–300 M⊙ mass range and only 13 metallicities; since MHe(MZAMS) is non-monotonic because of dredge-up, the interpolated upper edge is not robust. Thus the 'just between 100 and 130 M⊙' claim is a point prediction resting on unquantified sensitivities.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper releases a new homogeneous grid of non-rotating PARSEC v2.0 stellar evolution tracks covering 2 to 2000 solar masses at thirteen metallicities from Z=10^-11 to Z=0.03. The models are evolved to advanced burning stages or to the onset of the pair instability, and the authors use an external mapping from pre-SN helium and carbon-oxygen core masses to assign final fates and remnant masses. They provide wind and explosive ejecta tables and tabulated ionizing photon rates, and they compare the tracks with other stellar evolution codes and with massive stars in 30 Doradus. The headline physical result is that the combined black-hole pair-instability mass gap across all metallicities is 'just between 100 and 130 M_sun', narrower than previous estimates, which they attribute to deep dredge-up episodes that reduce the helium core mass.","tokens_in":43859,"tokens_out":7841,"duration_ms":76221,"significance":"The grid is a valuable public resource: it is homogeneous, publicly available, and already used in population-synthesis applications, and the accompanying ejecta, ionizing-photon, and pure-He track products extend the PARSEC library in useful ways. The comparisons with MIST, GENEC, FRANEC, and with the Tarantula Nebula data provide a useful benchmark. The external fate mapping is not circular, since it uses independently published grids, but the load-bearing point is that the pre-SN core masses entering that mapping are highly sensitive to the adopted convective mixing treatment. The manuscript does not currently quantify that sensitivity, so the central claim is not yet established at the precision claimed in the abstract; the requested robustness analysis can, however, be accommodated within the scope of a revision.","major_comments":[{"comment":"The headline claim that the combined BH pair-instability gap 'spans just between 100 and 130 M_sun' is presented without any uncertainty or robustness analysis, even though both edges are threshold-sensitive. The lower edge (99.5 M_sun) is set by the Z=10^-11, M_ZAMS=100 M_sun model, whose pre-SN M_He=32.96 M_sun sits only a few tenths of a solar mass below the approximately 34 M_sun PPISN threshold; the upper edge (129.4 M_sun at Z=0.006) comes from interpolating the M_He=130 M_sun crossing. Appendix C itself states that small variations can lead to 'big evolutionary differences' and describes the evolution as chaotic. Please add a sensitivity study (for example, varying lambda_ov and Lambda_env, or using alternative fate mappings and threshold choices) or rephrase the abstract and conclusions to present the 100-130 M_sun interval as a model-dependent estimate rather than a precise prediction.","section":"Sec. 3.3, Table 4, App. C"},{"comment":"The upper edge of the gap is obtained by interpolating M_He(M_ZAMS) across a mass range where Table 2 has a 10 M_sun step. Since Fig. 5 and Appendix C show that M_He and M_CO are non-monotonic functions of M_ZAMS because of dredge-up, linear interpolation between grid points cannot reliably locate the M_He=130 M_sun crossing; the difference between columns 3 and 4 of Table 4 (up to about 11 M_sun) shows that the interpolation is not a minor correction. Please compute additional tracks around the transition or provide an explicit interpolation uncertainty.","section":"Sec. 3.3, Table 2"},{"comment":"The deep dredge-up that lowers M_He and closes the gap is controlled by the Schwarzschild criterion, lambda_ov=0.5, and especially Lambda_env=0.7 H_P envelope overshooting. Table 5 shows that other codes adopt substantially different convection parameters, and Section 4.1 compares HR tracks only; it does not validate the final fates or the gap edges. The absence of any test of the mixing parameters leaves the central mass-gap result contingent on an unvalidated prescription. Please either run test models with different overshooting values or explicitly state that the gap edges are conditional on the adopted mixing scheme.","section":"Sec. 2.1, Sec. 4.1"}],"minor_comments":[{"comment":"In the Z=10^-11 block, the M_ZAMS=1000 M_sun row lists M_remnant=9993.1 M_sun, which is likely a typo for 999.31 M_sun; in the Z=10^-6 block, the M_ZAMS=2000 M_sun row lists M_remnant=1981.27 M_sun, which exceeds the listed pre-SN mass of 1950.40 M_sun. Please correct these values in the table and in the public database.","section":"Table F.1"},{"comment":"The caption identifies the center panel as Z=0.001, while the panel label and the text of Sec. 3.1.2 identify it as Z=0.0001; please harmonize the caption with the panel.","section":"Fig. 1 caption"},{"comment":"The text uses both 'Schwarzchild' and 'Schwarzschild' for the convective stability criterion; please make the spelling consistent.","section":"Sec. 2.1"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know. First, this is a major data-release paper: a new homogeneous PARSEC v2.0 grid from 2 to 2000 M_sun across 13 metallicities, plus pure-He tracks, ejecta tables, and ionizing-photon rates, all public. That alone makes it worth having. Second, the central physics claim, a pair-instability mass gap 'just between 100 and 130 M_sun', is a real consequence of the models but is considerably less robust than the abstract's tone suggests; both edges sit on sharp external thresholds applied to mixing-sensitive helium cores.\n\nThe genuinely new material is the grid itself and the derived tabulations. The paper does a careful job of documenting the updated input physics, and the comparisons against GENEC, MIST, FRANEC, and the Tarantula/R136 data are honest about where discrepancies arise. The consistency checks with observed BHs (Cyg X-1, Gaia BH3) are a nice sanity check. The public availability of tracks and derived products is a service to the community. Credit is due for the range and homogeneity of the models.\n\nThe soft spots are real but not fatal. The abstract and conclusions quote the 100-130 M_sun gap as if it were a settled edge, while the paper itself notes that the pre-SN structure is sensitive to overshooting, mixing, and the choice of external fate mapping (Woosley 2017 via Goswami et al. 2021). The stress-test description is accurate: the lower edge is essentially one track (Z=10^-11, 100 M_sun) that ends with M_He ~33 M_sun, barely below the adopted PPISN threshold, and the upper edge is an interpolation at Z=0.006 where M_He crosses 130 M_sun. With a 10 M_sun step in the 100-300 M_sun range and no variation of mixing parameters or fate thresholds, the precise edges are not established. The paper acknowledges these dependencies in Sec. 3.3 but does not attach uncertainties to the quoted numbers. There is also a clear typo in Table F.1 (a 1000 M_sun star with remnant mass 9993.1 M_sun) and the code itself is not released, only the tracks. These are fixable.\n\nWho should read it: anyone doing population synthesis, gravitational-wave progenitor studies, or galaxy-formation modeling will want these tracks. It deserves a serious referee and a revise-and-resubmit: the data release should go through, but the mass-gap edges need a robustness discussion or an uncertainty estimate, and the table typo should be corrected. I would not hold the central mass-gap claim as a decisive measurement of the gap; it's a model-dependent prediction that should be used with that caveat in mind.","headline":"A valuable PARSEC v2.0 data release whose headline mass-gap edges are more fragile than the abstract admits; the grid itself deserves refereed publication.","tokens_in":44515,"tokens_out":4303,"would_cite":true,"duration_ms":41072,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["85A15"],"pacs":["97.10.Cv","97.60.Bw","97.60.Lf"],"model":"deepseek-v4-flash","headline":"A new set of stellar evolution models predicts that single stars leave no black holes between about 100 and 130 solar masses, a far narrower pair-instability gap than standard estimates.","keywords":["stellar evolution","pair-instability supernovae","black hole mass gap","convective dredge-up","very massive stars","ionizing photons","chemical yields","PARSEC models"],"falsifier":"Detect a single-star-born black hole with a mass between 100 and 130 $M_\\odot$, for example from a gravitational-wave event whose progenitor is shown to be a single star rather than a merger or accretion product, and the gap is not that narrow. Alternatively, rerun the same grid with an independently calibrated convective mixing scheme and check whether any 80 to 140 $M_\\odot$ model still produces a helium core below the pair-instability threshold; if none does, the gap widens.","tokens_in":43315,"feed_emoji":"🕳️","tokens_out":8148,"duration_ms":76444,"temperature":0.7,"pith_summary":"This paper presents a new, homogeneous grid of stellar evolution models computed with the PARSEC v2.0 code, covering initial masses from 2 to 2000 solar masses across thirteen metallicities from primordial to super-solar. Its central claim is that, for single stars, the pair-instability black-hole mass gap, the range of black-hole masses that no single-star collapse should produce, is much narrower than previously thought, about 100 to 130 solar masses rather than roughly 50 to 140 solar masses. The narrowing is driven by deep convective dredge-up episodes that shave down helium core masses and keep some stars from entering the pair-instability regime. The same models reproduce the masses of observed black holes such as the GW190521 primary, Cygnus X-1, and Gaia BH3, and provide new tables of chemical ejecta and ionizing-photon rates. If correct, the result reshapes predictions for gravitational-wave sources and for the most massive remnants single stars can leave behind.","feed_headline":"Black-hole mass gap narrows to 100-130 solar masses","feed_subtitle":"Deep convective mixing shaves helium cores in new stellar tracks, letting single stars bridge most of the old gap.","key_machinery":"The helium-core mass $M_{\\mathrm{He}}$ at the pre-supernova stage is the organizing quantity: PARSEC v2.0 evolves each star with an implicit diffusive mixing scheme that couples nuclear burning and element transport, using the Schwarzschild convection criterion with core overshooting $\\lambda_{\\rm ov}=0.5$ (about 0.25 pressure scale heights) and envelope overshooting $\\Lambda_{\\rm env}=0.7\\,H_P$. Deep convective dredge-up during core helium burning can push the base of the convective envelope into the helium core, reducing $M_{\\mathrm{He}}$ and $M_{\\mathrm{CO}}$; the paper identifies these episodes, not just winds, as the reason the pair-instability gap narrows. Final fates, namely core-collapse supernova, failed supernova, pulsational pair-instability supernova, pair-instability supernova, or direct collapse, are assigned by mapping the computed $M_{\\mathrm{He}}$ and $M_{\\mathrm{CO}}$ onto remnant and ejecta tables, with the Stothers criterion $\\langle\\Gamma_1\\rangle < 4/3$ marking entry into the pair-instability regime.","core_discovery":"The paper claims that, when all metallicities are combined, no single star leaves a black hole with mass between roughly 100 and 130 $M_\\odot$; this combined pair-instability mass gap is far narrower than the $\\sim 50$ to $\\sim 140$ $M_\\odot$ range predicted in previous studies. The narrowing is traced to convective dredge-up episodes: during central helium burning the base of the convective envelope can penetrate the helium core, lowering $M_{\\mathrm{He}}$ and $M_{\\mathrm{CO}}$ by enough to keep stars that would otherwise explode as pair-instability supernovae stable, so they end as failed supernovae or direct-collapse black holes. The same models place the most massive single-star black hole below the gap at about 99.5 $M_\\odot$ at $Z=10^{-11}$ and reproduce the masses inferred for GW190521, Cygnus X-1, and Gaia BH3. The models also predict pulsational pair-instability and pair-instability supernovae at near-solar metallicity, contrasting with the usual assumption that such events require very low metallicity.","pith_inferences":["Beyond the paper, the width of the 100 to 130 $M_\\odot$ gap is a prediction of one mixing prescription rather than a theorem, so the gap width should be treated as a test of convective mixing physics, not as a fixed number.","Beyond the paper, because the models are non-rotating, rotation-induced mixing and mass-loss enhancement could shift the effective dredge-up efficiency and move the gap edges by tens of solar masses.","Beyond the paper, binary-stripped stars, which the accompanying pure-helium tracks are designed to serve, could retain enough mass to land inside the 100 to 130 $M_\\odot$ range, so the gap is a property of single-star evolution rather than of all black-hole formation channels.","Beyond the paper, asteroseismic or eclipsing-binary measurements of core sizes in red supergiants would provide a direct check of the deep dredge-up geometry assumed here, and a mismatch would be the fastest route to revising the gap."],"forward_implications":["There should be no single-star black holes with masses between about 100 and 130 $M_\\odot$ in the local universe, so gravitational-wave events with a primary in that range require exotic formation channels.","GW190521's roughly 85 $M_\\odot$ primary can be produced by a low-metallicity single star, with the lower edge of the gap reaching about 76.5 $M_\\odot$ at $Z=0.001$.","Pulsational pair-instability and full pair-instability supernovae can occur at near-solar metallicity, so future surveys such as LSST may find these events in metal-rich environments.","The models place the maximum black-hole mass at solar and galactic metallicity around $40\\pm6$ $M_\\odot$, consistent with Cygnus X-1 and with several other evolutionary codes.","The public grids of stellar tracks, ejecta, and ionizing photons give population-synthesis and galaxy-formation models a homogeneous input from 2 to 2000 $M_\\odot$ across thirteen metallicities."],"supporting_citations":[{"why":"Provides the pulsational pair-instability and pair-instability remnant-mass and ejecta interpolation tables that set the helium-core mass boundaries used for final fates.","marker":"Woosley (2017)"},{"why":"Supplies the pair-instability full-destruction and direct-collapse prescriptions used to classify fates and remnant masses.","marker":"Heger & Woosley (2002)"},{"why":"Introduced the implicit diffusive mixing treatment and documented how dredge-up affects pair-instability stability in earlier PARSEC versions.","marker":"Costa et al. (2021)"},{"why":"Supplies the method that maps pre-supernova helium-core and carbon-oxygen core masses to final fates and chemical ejecta.","marker":"Goswami et al. (2021)"},{"why":"Defines the previous PARSEC massive-star release that this new grid extends and supersedes, including its wind and convection baseline.","marker":"Chen et al. (2015)"},{"why":"Describes the PARSEC v2.0 code updates in mixing and equation of state on which the new tracks are built.","marker":"Nguyen et al. (2022)"},{"why":"Represents the standard wider pair-instability mass-gap prediction that this paper's narrower combined gap is compared against.","marker":"Farmer et al. (2020)"},{"why":"First noticed the non-monotonic trends of helium-core and carbon-oxygen core masses with initial mass using a subset of these tracks.","marker":"Iorio et al. (2023)"}],"fun_headline_variants":["Convective dredge-up narrows black-hole mass gap to 100-130 Msun","Single stars can now bridge most of the black-hole mass gap","New PARSEC models tighten pair-instability gap to 100-130 Msun","Black-hole gap slims to 30 solar masses wide in new tracks","Massive star models shrink black-hole mass gap to 100-130 Msun"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The central result depends on the assumed convective mixing recipe, core overshooting of about a quarter of a pressure scale height plus envelope overshooting of 0.7 pressure scale heights, because deeper mixing than real would shrink helium cores too much, pulling the gap edges together, while weaker mixing would probably widen the gap.","fun_headline_variants_meta":{"raw":{"variants":["Convective dredge-up narrows black-hole mass gap to 100-130 Msun","Single stars can now bridge most of the black-hole mass gap","New PARSEC models tighten pair-instability gap to 100-130 Msun","Black-hole gap slims to 30 solar masses wide in new tracks","Massive star models shrink black-hole mass gap to 100-130 Msun"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000696,"raw_usage":{"total_tokens":3249,"prompt_tokens":1152,"completion_tokens":2097,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":768,"completion_tokens_details":{"reasoning_tokens":1993}},"tokens_in":768,"tokens_out":2097,"duration_ms":15421,"temperature":1.0,"reasoning_tokens":1993,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T16:37:37.134910+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Detect a single-star-born black hole with a mass between 100 and 130 $M_\\odot$, for example from a gravitational-wave event whose progenitor is shown to be a single star rather than a merger or accretion product, and the gap is not that narrow. Alternatively, rerun the same grid with an independently calibrated convective mixing scheme and check whether any 80 to 140 $M_\\odot$ model still produces a helium core below the pair-instability threshold; if none does, the gap widens.","supporting_citations":[],"review_version":1}