{"id":"d3edab1a-39ee-4cef-9b84-5e9a4ca49ffc","arxiv_id":"2501.06784","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":13,"one_line_summary":"Across about 1,500 core-collapse simulations, neutrino heating rises steeply with progenitor compactness, so high-compactness stars revive their stalled shock and explode, contrary to many 1D explodability recipes.","lead":"This paper analyzes about 1,500 computer simulations of collapsing massive stars and finds that the most compact cores produce the strongest neutrino heating, reviving the explosion shock. The result challenges a widely used assumption in astronomy that high-compactness stars fail to explode and form black holes directly.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim equates shock revival with explosion; this is unsupported for high-compactness progenitors that may form a black hole before shock breakout.","rationale":"The paper has real strengths: a large multi-code sample including 3D simulations, a clear physical mechanism connecting compactness to neutrino heating, and an explicit acknowledgment of EOS and code dependencies. The reader's conditional verdict already identifies shock revival versus explosion as the weakest assumption, and my reading agrees. The most load-bearing step is temporal extrapolation: a shock that reaches thousands of km within a few seconds is called an explosion, but for high-compactness progenitors the central object may collapse to a black hole before the shock breaks out. The paper's own caveats in Section 6 — citing groups that see no shock revival or revival followed by early BH formation — show that the field has not converged on late-time outcomes. The Sykes & Müller criterion is a plausible resolution, but it is not checked for the specific simulations used to make the headline claim. Therefore the central assertion remains conditional rather than established. The conditional verdict stands, and the proposed sonic-point test would either retire or confirm the concern.","tokens_in":39514,"tokens_out":6641,"duration_ms":71607,"concrete_test":"Post-process the final snapshots of all xi_2.0 > 0.5 models in Fig. 3 using the Sykes & Müller (2025) criterion: for each model, compute the sonic-point radius R_sonic in the unshocked progenitor envelope ahead of the shock at the final output time. If R_shock > R_sonic, breakout is expected even if a BH forms; if R_shock < R_sonic in any model, that model is not a proven explosion. Optionally, continue three representative models (xi_2.0 ≈ 0.6, 0.7, 0.8) to BH formation or >10 s post-bounce to confirm the criterion. If a non-negligible fraction (say >10%) of the sample has R_shock < R_sonic, the paper's explosion claim fails; if all pass, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim — \"all of the 2D and 3D simulations with compactness xi_2.0 larger than about 0.5 explode\" (Section 3.1) — rests on equating shock revival with explosion. The simulations are run only to 1–5 s post-bounce, so \"explosion\" is defined by shock expansion to thousands of km, not by breakout or envelope ejection. High-compactness progenitors are precisely those where the central PNS can collapse to a black hole on a short timescale; if BH formation precedes the shock passing the sonic point in the envelope, the breakout is quenched. The paper cites Sykes & Müller (2025) for the sonic-point criterion but does not apply it to the 150+ simulations analyzed here. The paper itself concedes (Section 6) that other groups find either no shock revival or revival followed by early BH formation (Kuroda et al. 2018; Summa et al. 2018; Walk et al. 2020). Hence the inference from shock revival to successful supernova is an extrapolation beyond the simulated time, and the central claim is not established for the full high-compactness population.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper uses a large set of one-dimensional, 1D+, 2D, and 3D core-collapse supernova simulations (~1500 runs, of which 173 are multi-D) to argue that the maximum neutrino heating in the gain region, Qdot_nu^max, rises steeply with pre-SN compactness xi_2.0, and that this rise is sufficient to revive the stalled shock for high-compactness progenitors (xi_2.0 ≳ 0.5). The authors further show that 1D+ models with the STIR mixing-length treatment reproduce the multi-D heating and explodability trend, derive piecewise semi-analytic fits for Qdot_nu^max(xi_2.0) based on the Janka (2012) heating formula, and compare their 1D+ results against other 1D explosion models (O'Connor & Ott 2011, PUSH, Ertl et al. 2016, Mueller et al. 2016, Pejcha & Thompson 2015). The central observational claim is that common assumptions that high-compactness stars fail are incorrect: instead, these stars undergo successful shock revival and, the authors argue, produce successful explosions.","tokens_in":39859,"tokens_out":6449,"duration_ms":67744,"significance":"If the central claim holds, this is an important result for CCSN theory and for population synthesis: it reverses a widely used rule that high-compactness progenitors form black holes without explosions, and it quantifies how neutrino heating grows with compactness. The strengths of the paper are its unusually large multi-dimensional sample (98 2D Fornax, 55 2D FLASH, 20 3D Fornax), the direct comparison of 1D+/multi-D heating rates, and the explicit, reproducible fit formulas in Eqs. (12)-(14) and Appendix B. The identification of t_max ≈ t_Si/O for xi_2.0 < 0.5 and the regime change at xi_2.0 ≈ 0.72 are useful diagnostics for the explosion mechanism. However, the inference from shock revival to successful explosion is not established by the simulations presented, and the semi-analytic curves carry less independent weight than the text suggests, because their coefficients are fitted to the same simulations. A careful revision that separates empirical trends from interpretive claims would make the paper much more solid.","major_comments":[{"comment":"The central inference equates shock revival with explosion. The text states 'we can assume that simulations, where the shock has been successfully revived, yield an explosion' and 'all of the 2D and 3D simulations with compactness xi_2.0 ≳ 0.5 explode.' The simulations are run only to 1-5 s post-bounce, which is not enough to guarantee shock breakout for high-compactness stars; the paper itself cites Kuroda et al. (2018), Summa et al. (2018), and Walk et al. (2020) for cases with no revival or with revival followed by early black-hole formation. The sonic-point criterion of Sykes & Müller (2025) is invoked but never evaluated on the shock trajectories analyzed here. I therefore do not think the abstract's language 'successful shock revival' can be equated with 'successful explosion' for the full high-compactness population without an additional breakout analysis.","section":"Section 3.1"},{"comment":"The derivation of the Qdot_nu^max versus xi_2.0 curves is not an independent prediction. The slope and intercept of the neutrino-energy evolution in Eqs. (B2)-(B3), the luminosity-mass-radius combinations in Eqs. (B4) and (B5), and the t_Si/O relation in Eq. (B7) are all fits to the same 1D/1D+ simulations used for Figure 3, and an additional factor 0.8 is applied by hand in Section B2. Eq. (16) introduces the tuned radius Rbar_g, and Appendix A fixes a 0.6 net-to-total heating fraction. Consequently Eqs. (12)-(14) should be described as empirical fits with a physics-motivated functional form, not as a derivation that independently explains the observed trend. The current wording in Sections 3.1 and 4 ('we can show', 'the only difference is') overstates the explanatory power.","section":"Appendix B"},{"comment":"The piecewise fit is discontinuous at the nominal transition xi_2.0 = 0.72. Evaluating the brackets at xi_2.0 = 0.72 gives approximately 1.9 for Eq. (13) and approximately 4.1 for Eq. (14), i.e. a factor ~2.2 jump in Qdot_nu^max. Since the observed Qdot_nu^max values in Figure 3 are a continuous function of compactness, the two expressions cannot both represent the data near the boundary. The fit discontinuity needs to be addressed numerically, or the piecewise representation should be explicitly qualified as a non-continuous approximation.","section":"Equations (13)-(14)"},{"comment":"The multi-D sample is heterogeneous in neutrino transport (co-moving-frame M1 in Fornax vs lab-frame M1 in FLASH), opacities (Kompaneets vs elastic neutrino-nucleon scattering), equations of state (SFHo and several Schneider et al. 2019 models), and grid geometry. The paper acknowledges that these differences 'prevent a detailed and thorough comparison,' yet the central claim treats all 2D and 3D simulations above xi_2.0 ~ 0.5 as one homogeneous population. The offset between 2D Fornax and 2D FLASH at low compactness and the shift of the heating curve with stiffer EOS show that these systematic differences are not negligible. A quantitative estimate of the resulting uncertainty in the threshold xi_2.0 ~ 0.5 is needed before this can be presented as a universal explodability condition.","section":"Section 3, first two paragraphs"}],"minor_comments":[{"comment":"The Acknowledgements contain the typo 'anonymus referee'; it should be 'anonymous referee'.","section":"Acknowledgements"},{"comment":"The last paragraph of Section 6 states explosion energies of '0.01-3.5 10^51 erg/s'; explosion energies are measured in erg, not erg/s, and the typesetting '3.51051' is missing the multiplication sign.","section":"Section 6"},{"comment":"The acronym STIR is used throughout but never expanded; a brief expansion at first use (e.g., 'the subgrid turbulence model of Couch et al. 2020, known as STIR') would help readers unfamiliar with the literature.","section":"Section 2.1"},{"comment":"The bottom panel plots failed explosions on top of successful ones, and the caption notes that overlapping points make the number of failures look larger than it is; a partially transparent marker or a separate panel would make the raw counts of successes/failures above xi_2.0 = 0.5 visible.","section":"Figure 3"},{"comment":"The net-to-total heating fraction of 0.6 is introduced in Appendix A with only a one-sentence justification; this value should be stated at Eq. (15) where it is first used, since it is a free parameter of the semi-analytic formula.","section":"Appendix A"}],"recommendation":"major_revision","confidential_remarks":"The manuscript contains a genuinely useful empirical survey, but the abstract and Section 3.1 overstate the conclusion from shock revival to successful explosion. The authors' own Section 6 acknowledges that some groups see no revival or revival followed by early black-hole formation. I would encourage the editor to require either a breakout-oriented analysis of the existing shock trajectories or a consistent rephrasing of the claims in terms of 'shock revival' rather than 'explosion'. The Appendix B fits would also benefit from being reframed as fits, because their current presentation invites the circularity criticism. The paper is within reasonable scope for MNRAS, and none of the issues I raise appear to be unfixable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Worth your time. The paper's core observation is that neutrino heating rises steeply with compactness, with a break around xi_2.0 ~0.72, and that 1D+ models reproduce multi-D heating. That is new and useful. The compilation of roughly 1500 simulations from FLASH, Fornax, and GR1D is a real asset, and the careful definition of the gain region (density and entropy cuts) is a step up from many earlier studies. The Appendix B derivation is also transparent about its assumptions, even if those assumptions are tuned to the data.\n\nThe soft spot is the central claim as stated. The paper says \"all of the 2D and 3D simulations with compactness xi_2.0 larger than about 0.5 explode.\" But the simulations run only 1-5 seconds post-bounce, and \"explosion\" means shock revival to thousands of km, not breakout. The paper itself concedes that other groups see no revival or early black-hole quenching (Kuroda, Summa, Walk), and it cites Sykes & Müller for the sonic-point criterion without applying it to these simulations. So the abstract overreaches: the evidence supports strong shock revival, not necessarily successful envelope ejection for every high-compactness progenitor. The scaling laws in Eqs. (12)-(14) are also fits to the same simulations, with several hand-tuned coefficients and no error bars, so they are descriptive rather than predictive. And \"data available upon request\" is weak for a paper built on such a large simulation suite.\n\nNone of that kills the paper. The trend across codes is consistent, the 1D+ validation is genuinely useful, and the implications for population synthesis are worth taking seriously. A serious referee should send this back for revision, not reject it. The authors need to temper the explosion language, apply the sonic-point criterion or otherwise argue for breakout, and release the data and analysis artifacts. If they do, this becomes a solid contribution.","headline":"High-compactness stars probably do revive their shocks, but the paper's jump from revival to successful explosion is a real overreach.","tokens_in":40379,"tokens_out":1234,"would_cite":true,"duration_ms":14704,"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":"High-compactness supernova progenitors explode, not fail","keywords":["core-collapse supernovae","neutrino heating","compactness","shock revival","neutrino-driven convection","mixing-length theory","explodability","black hole formation"],"falsifier":"A decisive check would be a long-term 3D simulation of a progenitor with $\\xi_{2.0}\\gtrsim0.5$ (for example the 25 $M_\\odot$ model used here) that follows the shock for several seconds after bounce: if the shock is revived but then falls back and the proto-neutron star collapses to a black hole before the shock passes the envelope's sonic point, the paper's identification of revival with explosion would fail for that case. A simpler empirical falsifier is the black-hole mass distribution: a population of 20--30 $M_\\odot$ remnants with no accompanying supernova ejecta would contradict the claim that these explosions typically accompany black-hole formation.","tokens_in":39315,"feed_emoji":"💥","tokens_out":11066,"duration_ms":91350,"temperature":0.7,"pith_summary":"This paper argues that the conventional cut between exploding and failed core-collapse supernovae is wrong at the high-density end: progenitors with high compactness $\\xi_{2.0} \\gtrsim 0.5$ do not quietly fail but revive their stalled shock through very strong neutrino heating. Compactness here is the ratio of $2\\,M_\\odot$ of enclosed baryonic mass to the radius enclosing it, a proxy for how dense the pre-collapse core is. The authors reach this conclusion by comparing about 150 two-dimensional and 20 three-dimensional simulations with spherically symmetric '1D+' models that approximate neutrino-driven convection by mixing-length theory. They find a common curve of maximum neutrino heating versus compactness that rises steeply for $\\xi_{2.0} \\gtrsim 0.5$, and identify the mechanism: convection keeps the shock stalled at large radius, so the gain region stays massive long enough for rising neutrino energies from the accreting proto-neutron star to power the explosion. If correct, this flips a standard assumption used in population synthesis and galactic chemical evolution, where high-compactness stars are assigned to black-hole formation without explosion, and it makes cheap large-scale explodability surveys of high-compactness stars feasible.","feed_headline":"High-compactness stars explode after all, simulations show","feed_subtitle":"At compactness above about 0.5, neutrino heating rises fast enough to revive the stalled shock in 2D and 3D models.","key_machinery":"The load-bearing object is the gain region--the volume behind the stalled shock where net neutrino heating is positive (defined here with density below $3\\times10^{10}\\,\\mathrm{g\\,cm^{-3}}$ and entropy per baryon above $6$)--together with the STIR closure, a mixing-length model that adds turbulent kinetic-energy generation, dissipation, and energy flux to spherically symmetric hydrodynamics. Convection does two things: it keeps the shock stalled at roughly constant radius for hundreds of milliseconds, so the gain-region mass $M_g$ does not collapse as it does in pure 1D, and it transports hot bubbles plus dissipates turbulence into heat near the shock. Because the proto-neutron star keeps accreting during that time, neutrino root-mean-square energies $\\langle\\epsilon_\\nu^2\\rangle$ rise, and since $\\dot{Q}_\\nu \\propto M_g\\langle\\epsilon_\\nu^2\\rangle L_\\nu/\\bar{R}_g^2$, the net heating grows with time rather than peaking and decaying at about 100 ms. The paper packages this into three fitted curves for $\\dot{Q}_\\nu^{\\max}(\\xi_{2.0})$--one for 1D, one for multi-D and 1D+ below $\\xi_{2.0}=0.72$, one above--that the simulation suites all follow.","core_discovery":"On its own terms, the paper establishes a compactness--heating--outcome relation. Across about 150 2D and 20 3D simulations, every high-compactness progenitor with $\\xi_{2.0} \\gtrsim 0.5$ (except four 1D+ cases and one 2D case tied to very stiff equations of state) undergoes successful shock revival, and the maximum net neutrino heating $\\dot{Q}_\\nu^{\\max}$ grows steeply with $\\xi_{2.0}$, with a break near $\\xi_{2.0} \\simeq 0.72$ that the paper traces to neutrino luminosities rising during the accretion phase. The same trend is reproduced by the 1D+ models (GR1D+ and 1D+ FLASH) that include neutrino-driven convection through the STIR closure. The quantitative core is a semi-analytic heating identity, $\\dot{Q}_\\nu = 5.18\\times10^{51}\\,\\mathrm{erg\\,s^{-1}} (M_g/0.01\\,M_\\odot)(\\bar{R}_g/100\\,\\mathrm{km})^{-2}\\sum_{\\nu_e,\\bar\\nu_e}\\langle\\epsilon_\\nu^2\\rangle/(18\\,\\mathrm{MeV})^2\\, L_\\nu(\\bar{R}_g)/(3\\times10^{52}\\,\\mathrm{erg\\,s^{-1}})$, which reproduces the simulations and shows that the gain-region mass $M_g$, sustained by convection, is what lets heating climb during the stalled-shock phase. The paper concludes that high-compactness progenitors explode even though they also form black holes quickly, and that 1D+ models are adequate for future large explodability surveys.","pith_inferences":["A testable extension of the paper's fits would convert the $\\dot{Q}_\\nu^{\\max}(\\xi_{2.0})$ curve into a probabilistic explodability prescription by measuring the scatter of multi-D outcomes around the curve, including the equation-of-state dependence.","If high-compactness stars explode while forming black holes quickly, the gravitational-wave black-hole mass function could carry a fingerprint: a population of 20--30 $M_\\odot$ remnants with associated supernova ejecta, which future detectors could separate from silent collapse.","The paper stops at shock revival; an observational inference is that the optical transients of such explosions should be fast and dim (with possibly strong fallback), which wide-field surveys targeting low-metallicity host galaxies could catch.","Because the paper notes that 1D+ models underestimate early neutrino heating at low compactness, a prompt-convection correction to the STIR closure might be needed before the method is trusted outside the high-compactness regime."],"forward_implications":["If the central claim holds, explodability studies should stop treating $\\xi_{2.0}\\gtrsim0.5$ as a failed-explosion zone: those stars can yield successful shock revival and, per the cited long-term simulations, eventual shock breakout.","Population synthesis and galactic chemical evolution calculations that currently assign high-compactness stars to direct black-hole formation should be re-run with a compactness-dependent explodability prescription, because a 20--30 $M_\\odot$ black hole can be accompanied by a supernova.","The 1D+ STIR approach can serve as a cheap survey tool for the high-compactness regime, since it reproduces the multi-dimensional $\\dot{Q}_\\nu^{\\max}$ trend and explosion outcomes to within the scatter among codes.","The accretion of the Si/O interface sets the explosion clock for $\\xi_{2.0}\\lesssim0.5$ but not for $\\xi_{2.0}\\gtrsim0.5$, and explosion time is not a reliable proxy for heating strength because high-compactness shocks move faster once revived.","Stiffer equations of state shift the whole heating-versus-compactness curve downward, so the precise critical compactness for revival depends on the nuclear equation of state."],"supporting_citations":[{"why":"introduced the compactness-based criterion that classified high-compactness progenitors as failed explosions, the baseline claim this paper overturns.","marker":"O'Connor & Ott (2011)"},{"why":"supplied the semi-analytic neutrino-heating expression that Eq. (15) adapts and evaluates in the gain region.","marker":"Janka (2012)"},{"why":"developed the STIR mixing-length 1D+ model used for the FLASH 1D+ simulations and comparison.","marker":"Couch et al. (2020)"},{"why":"generalized STIR to general-relativistic hydrodynamics in GR1D+, providing the main 1D+ simulations analyzed.","marker":"Boccioli et al. (2021)"},{"why":"provided the 341 GR1D 1D+/1D simulations that anchor the timescale and heating fits.","marker":"Boccioli & Fragione (2024)"},{"why":"contributed the 100 2D Fornax simulations whose explosion outcomes and heating are compared against 1D+ models.","marker":"Vartanyan & Burrows (2023)"},{"why":"supplied the 3D Fornax simulations used to confirm the high-compactness heating trend in full three dimensions.","marker":"Burrows et al. (2020)"},{"why":"provided the KEPLER progenitor grid that most 2D, 3D, and 1D+ simulations in this paper are evolved from.","marker":"Sukhbold et al. (2016)"},{"why":"showed that shock breakout can follow early black-hole formation, supporting the paper's assumption that revival yields an explosion.","marker":"Sykes & Müller (2025)"},{"why":"exemplifies a widely used 1D model (PUSH) whose calibration forces high-compactness stars to fail, the contrast this paper diagnoses.","marker":"Ebinger et al. (2019)"}],"fun_headline_variants":["Neutrino heating climbs with compactness, reviving shocks","1D+ models reproduce multi-D neutrino-driven explosions","Compactness drives neutrino heating, overturning failed-explosion lore","High-compactness progenitors explode via neutrino heating","Dense cores revive stalled shocks as neutrino heating soars"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that a successfully revived shock--one that expands to thousands of kilometres within the simulated few seconds--will go on to become a real supernova; if late-time black-hole formation cuts off the neutrino heating and the shock before breakout, the high-compactness 'explosions' would leave no visible supernova despite early revival.","fun_headline_variants_meta":{"raw":{"variants":["Neutrino heating climbs with compactness, reviving shocks","1D+ models reproduce multi-D neutrino-driven explosions","Compactness drives neutrino heating, overturning failed-explosion lore","High-compactness progenitors explode via neutrino heating","Dense cores revive stalled shocks as neutrino heating soars"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000714,"raw_usage":{"total_tokens":3347,"prompt_tokens":1221,"completion_tokens":2126,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":837,"completion_tokens_details":{"reasoning_tokens":2045}},"tokens_in":837,"tokens_out":2126,"duration_ms":15818,"temperature":1.0,"reasoning_tokens":2045,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:50:14.749383+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A decisive check would be a long-term 3D simulation of a progenitor with $\\xi_{2.0}\\gtrsim0.5$ (for example the 25 $M_\\odot$ model used here) that follows the shock for several seconds after bounce: if the shock is revived but then falls back and the proto-neutron star collapses to a black hole before the shock passes the envelope's sonic point, the paper's identification of revival with explosion would fail for that case. A simpler empirical falsifier is the black-hole mass distribution: a population of 20--30 $M_\\odot$ remnants with no accompanying supernova ejecta would contradict the claim that these explosions typically accompany black-hole formation.","supporting_citations":[],"review_version":1}