{"id":"2b5f792d-4d05-47bc-a33e-dc3f06f37869","arxiv_id":"2608.05582","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In relativistic mean field theory, a larger effective nucleon mass softens the supernova equation of state, yielding more compact proto-neutron stars, earlier black hole collapse, and higher-energy neutrino emission.","lead":"Two nuclear equations of state designed with different effective nucleon masses are fed into supernova simulations. The softer relativistic EOS makes proto-neutron stars more compact, triggers earlier black hole formation, and changes neutrino emission signals.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The study does not isolate the effective mass from correlated RMF vector-repulsion changes; the earlier black-hole collapse and high neutrino energies may be driven by the high-density vector potential, not by M* itself.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the TM1m/TM1e comparison changes not only M* but also the vector repulsion, so the dynamical differences cannot be unambiguously attributed to the effective mass. This concern is real and central because the paper's headline claim is explicitly causal ('leads to compact proto-neutron stars and early collapse ... due to the softness'). The evidence for the correlation is solid: the simulations are internally consistent, the qualitative trends match earlier non-relativistic studies, and the paper is honest in Section IV about the coupled nature of the RMF parameters. However, the causal isolation is not established, and a pressure-component decomposition is needed to determine whether the earlier collapse is driven by the effective mass or by the associated vector-field changes. Since the reader already assigned a CONDITIONAL verdict on this basis, my read does not change the verdict; it reinforces the need for the proposed decomposition. Other weaknesses, such as the hybrid low-density EOS and incomplete treatment of effective-mass dependence in reaction rates, are secondary and explicitly acknowledged in the paper. No internal inconsistency or numerical red flag was found in the presented results.","tokens_in":16295,"tokens_out":2535,"duration_ms":24025,"concrete_test":"Decompose the TM1m and TM1e pressures, at the densities and temperatures sampled by the 40 Msun S16 run between 0.30 and 0.64 s after bounce, into the kinetic term (which depends on M*), the scalar-field contribution, and the isoscalar-vector-field contribution, using the same RMF Lagrangian that generated the tables. If the vector-potential contribution, or its density derivative, dominates the TM1m-TM1e pressure difference in the region where the PNS contracts, then the observed earlier collapse cannot be attributed to the effective mass alone. A complementary check would be to rerun the S16 model with a hybrid EOS that keeps TM1m's effective mass but substitutes the TM1e isoscalar-vector mean field; if the black-hole formation time shifts significantly toward the TM1e value of 1.03 s, the confound is confirmed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim attributes the earlier collapse and more energetic neutrino emission to the large effective mass and the resulting softness of the TM1m EOS. However, the comparison between TM1m and TM1e does not vary M* alone: in the RMF Lagrangian, a larger M* is obtained by weakening the scalar coupling, and the vector mean field changes in tandem. Figure 2 shows that the TM1m isoscalar-vector potential grows linearly and exceeds the TM1e vector potential for nucleon densities above roughly 1.3 fm^-3. Section II A explicitly notes that the vector potential for TM1m 'overcomes the case of TM1e at high densities >= 1.3 fm^-3'. The black-hole-forming trajectories in the 40 Msun S16 run reach central densities around 1.0x10^15 g cm^-3 at 0.60 s, corresponding to baryon densities of order 0.5-0.7 fm^-3, below the crossing, but the matter at larger radii and later times probes densities where the vector repulsion difference is substantial. The abstract's causal phrase 'due to the softness' is therefore ambiguous: the softness itself originates from a particular correlated choice of scalar and vector couplings, and the high-density stiffening of TM1m is caused by the growing vector potential. Section IV concedes that 'the effective mass is not a simple parameter but a determining factor of the attraction,' which undercuts a clean one-to-one attribution to M*. Without a decomposition of the pressure into kinetic, scalar, and vector contributions along the actual simulation trajectories, the headline claim remains equivocal.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper investigates the influence of the nucleon effective mass in relativistic mean field (RMF) theory on core-collapse supernova dynamics and proto-neutron star (PNS) cooling. The authors use two published equation-of-state (EOS) tables, TM1e and TM1m, which share the same saturation properties but differ in effective mass (M*/M = 0.634 and 0.793, respectively). They perform one-dimensional general relativistic neutrino-radiation hydrodynamics simulations of gravitational collapse and bounce for 11.2, 15, and 40 solar-mass progenitors, and quasi-hydrostatic PNS cooling simulations. The main findings are that the larger effective mass (TM1m) yields a softer EOS below about 10^15 g/cm^3, leading to more compact PNSs, earlier black hole formation (0.64 s vs. 1.03 s after bounce for the 40 solar-mass S16 progenitor), and higher neutrino luminosities and average energies during PNS cooling. The differences are attributed to the effective mass through its effect on the scalar and vector mean-field potentials.","tokens_in":16622,"tokens_out":12590,"duration_ms":100562,"significance":"This is the first systematic RMF-based comparison of effective mass effects in supernova simulations, complementing earlier studies that used non-relativistic Skyrme-type EOS. The numerical setup follows established and validated algorithms, and the EOS tables are publicly available, which makes the results reproducible. The predicted differences in black hole formation times and neutrino signals are falsifiable with future observations, and the paper explicitly discusses the distinct role of the effective mass in relativistic frameworks. The main caveat, which the authors partially acknowledge, is the intrinsic correlation between the effective mass and the vector potential in RMF parameterizations; this is a point that needs clarification but does not overturn the central trend.","major_comments":[{"comment":"The causal attribution of the early black-hole collapse and energetic neutrino emission to the 'softness' caused by the large effective mass is not fully isolated, because the TM1m and TM1e parameterizations also differ in the isoscalar-vector potential (Fig. 2). The authors should explicitly state that the crossing of the vector potentials at about 1.3 fm^-3 occurs above the central densities reached in the simulations (approximately 0.6 fm^-3 at 0.60 s for the 40 solar-mass S16 case, Fig. 8), so that the softening in the probed density range is indeed connected to the effective mass. A short decomposition of the pressure into kinetic, scalar, and vector contributions along the simulation trajectories would remove this ambiguity.","section":"Section IV, Fig. 2"},{"comment":"The maximum proto-neutron star mass sequence in Fig. 6 is computed under beta equilibrium without neutrinos, whereas the dynamical simulations that lead to black hole formation include trapped neutrinos and lepton fractions well above the beta-equilibrium value. The authors should clarify whether the approximately 0.2 solar mass difference between TM1m and TM1e persists under the lepton-rich conditions of the simulations, for example by evaluating the maximum mass along the actual simulation trajectories. This would make the interpretation of the collapse times more robust.","section":"Section II B, Fig. 6"}],"minor_comments":[{"comment":"The phrase 'high energy neutrinos in short burst from the black hole formation' in the abstract could be misread as a distinct burst with higher energies for the large-effective-mass model; the simulations actually show a truncation of the neutrino signal at earlier times. Consider rephrasing to 'earlier termination of the neutrino signal'.","section":"Abstract"},{"comment":"The initial models for the proto-neutron star cooling simulations are based on the entropy and electron fraction profiles from a simulation using the original TM1 EOS (Ref. [61]), not TM1e or TM1m. While the comparison between the two EOS is still meaningful because both use the same initial profiles, the authors should explicitly note this inconsistency and its possible effect on the early cooling evolution.","section":"Section III B"},{"comment":"In Fig. 8, the right panels show the effective mass profiles; adding a vertical line or label for the central density or the neutrinosphere radius would help the reader connect the density and temperature panels.","section":"Fig. 8"},{"comment":"The statement that 'the effective mass is not a simple parameter but a determining factor of the attraction' is somewhat vague; elaborating on the relation between M*, the scalar coupling, and the vector potential would make the summary more precise.","section":"Section IV"}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a valuable addition to the supernova EOS literature. The simulations are well executed and the results are credible. The main concern about the isolation of the effective mass effect is not fatal because the vector-potential crossing occurs at densities above those reached in the collapse simulations, but the authors should make this point explicitly. I recommend minor revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a worthwhile, sober sensitivity study from the Shen EOS program, and the qualitative result holds. In RMF, choosing a larger effective mass at fixed saturation properties softens the high-density EOS, makes proto-neutron stars more compact, triggers black-hole formation earlier in failed 40-solar-mass collapses, and raises neutrino energies and luminosities during PNS cooling. The new content is the application of the TM1m table to full collapse, black-hole formation, and PNS-cooling simulations; prior effective-mass studies mostly lived in nonrelativistic or analytic thermal frameworks. The paper also does several right things: it uses fixed, externally published EOS tables, runs more than one progenitor, shows that the maximum-PNS-mass sequence is consistent with the black-hole formation times, and openly lists its limitations in Section IV (hybrid TM1e low-density EOS, incomplete effective-mass dependence in reaction rates, spherical symmetry). The citation pattern is normal for this group, and the self-citations point to the actual table construction and prior code validation.\n\nSoft spots, in proportion. The main one is causal attribution. TM1m and TM1e are tuned to the same saturation properties, but M* is not an isolated dial in RMF; the scalar and vector mean fields move together. Their own Section II notes that the TM1m vector potential overtakes TM1e above roughly 1.3 fm^-3. So the abstract's phrase “due to the softness” is a little too clean. The stress-test concern is real, but I would not call it disqualifying: the comparison is still a controlled EOS-table comparison, and the sequence in Fig. 6 plus the two 40-solar-mass runs makes the general softening/compactness story credible. For full isolation you would want a decomposition of pressure into kinetic, scalar, and vector contributions along the actual simulation trajectories. That would make the paper stronger and seems doable from their tables. The absence of released code or data and the lack of convergence tests are also gaps, though minor for a phenomenological simulation paper of this kind.\n\nWho benefits: people modeling neutrino signals from black-hole formation and PNS cooling, and anyone tracking EOS sensitivities across relativistic versus nonrelativistic frameworks. The paper deserves serious refereeing. I would send it out and ask for a tightened abstract that says “correlated with the larger effective mass” or “in this RMF parameter family” rather than “due to the softness,” plus a quantitative or at least more explicit acknowledgment of the vector-repulsion covariance. After that, it is publishable.","headline":"A solid, honest EOS sensitivity study from the Shen program; the larger-effective-mass table gives more compact PNSs and earlier black-hole collapse, though M* is not fully isolated from correlated vector-repulsion changes.","tokens_in":17171,"tokens_out":3050,"would_cite":true,"duration_ms":28493,"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":"In a relativistic framework, a larger nucleon effective mass softens the supernova equation of state, making proto-neutron stars denser and quicker to collapse into black holes.","keywords":["effective mass","relativistic mean field theory","supernova equation of state","core-collapse supernovae","proto-neutron star cooling","black hole formation","neutrino emission","TM1m EOS"],"falsifier":"Rerun the 40 solar mass black-hole-formation simulation with two RMF EOS tables that keep the vector mean-field potential identical at all densities while varying only the scalar coupling and hence $M^*$; if the black hole formation time does not move when $M^*$ changes under fixed vector repulsion, the claim that the effective mass drives the earlier collapse would be contradicted.","tokens_in":16105,"feed_emoji":"💥","tokens_out":9655,"duration_ms":70327,"temperature":0.7,"pith_summary":"This paper asks whether the nucleon effective mass changes the evolution of supernova cores and the neutrinos they emit, once the effective mass is computed self-consistently in the relativistic mean field theory rather than inserted only into a kinetic term. It compares two EOS tables, TM1e and TM1m, that share the same saturation density, incompressibility, symmetry energy, and symmetry-energy slope, but differ in the effective mass ratio ($M^*/M = 0.634$ vs $0.793$). The central finding is that the larger effective mass softens the high-density EOS, making proto-neutron stars more compact and, once compression dominates, hotter, so they reach the maximum supported mass and collapse to a black hole earlier. In the 40 solar mass S16 model the black hole forms at 0.64 s after bounce with TM1m, versus 1.03 s with TM1e, and the neutrino burst is shorter but more energetic. The paper also shows that the same physics lengthens proto-neutron star cooling and raises the luminosity and average energy of the emitted neutrinos, giving a distinct imprint in the supernova neutrino signal.","feed_headline":"Larger effective mass hastens stellar black hole collapse","feed_subtitle":"Simulations show a high effective mass yields hotter neutrinos and collapses the core about 0.4 seconds earlier.","key_machinery":"The central object is the nucleon effective mass $M^*$ in the RMF theory, defined through the Dirac mass term generated by the scalar meson mean field. The comparison pair, TM1e and TM1m, is built so that $M^*$ differs while saturation properties match; the machinery is the self-consistent balance between scalar attraction and vector meson repulsion, which makes a larger $M^*$ simultaneously reduce pressure at intermediate densities and increase entropy per baryon at fixed temperature. This coupled change in stiffness and thermodynamics, rather than the kinetic term alone as in non-relativistic Skyrme-type models, drives the compact proto-neutron stars, earlier black hole collapse, and the altered neutrino signal.","core_discovery":"In a relativistic mean field description, a larger nucleon effective mass is not an independent stiffness parameter: it arises from a weaker scalar attraction, which also weakens the vector repulsion that supplies saturation, and together those changes soften the equation of state at densities around and above nuclear saturation. The paper demonstrates this by taking two RMF parametrizations with identical saturation properties except the effective mass and running general relativistic neutrino-radiation hydrodynamics for collapse, bounce, black hole formation, and proto-neutron star cooling. The result is that the TM1m EOS with $M^*/M=0.793$ supports a maximum proto-neutron star mass about 0.2 solar masses smaller than TM1e's, produces more compact proto-neutron stars with higher central density and, after compression dominates, higher temperature, and collapses the 40 solar mass S16 core to a black hole at 0.64 s after bounce instead of 1.03 s; the WW95 40 solar mass case gives 0.82 s versus 1.13 s. During cooling, the compact TM1m star traps neutrinos longer, so the antineutrino luminosity and average energy stay higher over tens of seconds.","pith_inferences":["The causal role of $M^*$ is not fully isolated, because within RMF the effective mass and the vector repulsion change together, and the TM1m vector potential crosses and exceeds TM1e's above about 1.3 fm${}^{-3}$; part of the earlier black hole collapse could come from high-density vector repulsion rather than from $M^*$ itself.","If the neutrino imprint is as clear as these simulations suggest, a measured black-hole formation time from a future galactic failed-supernova neutrino burst could discriminate between effective masses, provided the progenitor and accretion history are known independently.","The same EOS pair in multi-dimensional simulations with convection and the standing accretion shock instability could change the explosion outcome, and the effective mass may also alter neutrino opacities beyond what is implemented in this study."],"forward_implications":["A larger effective mass lowers the maximum mass a hot proto-neutron star can support by about 0.2 solar masses relative to TM1e, so a given massive progenitor collapses to a black hole earlier.","Failed supernovae from 40 solar mass progenitors emit a shorter neutrino burst before black hole formation with a larger effective mass: 0.64 s versus 1.03 s after bounce in the S16 model, and 0.82 s versus 1.13 s in the WW95 model.","The same EOS softness makes the proto-neutron star more compact during cooling, keeping neutrino luminosity and average energy higher over tens of seconds, so the effective mass leaves an imprint on the late-time neutrino signal.","At early post-bounce times for 11.2 and 15 solar mass progenitors the differences are modest: the larger effective mass gives slightly higher central density and lower central temperature, while the bounce conditions and shock position stay close."],"supporting_citations":[{"why":"Supplies the TM1m EOS table with the larger effective mass and the same saturation properties as TM1e; this is the model whose dynamics are compared.","marker":"[58]"},{"why":"Supplies the TM1e EOS table used as the baseline and for sub-saturation matter in both models.","marker":"[59]"},{"why":"Establishes the earlier non-relativistic result that large effective mass compacts proto-neutron stars; the paper compares its RMF result with this.","marker":"[36]"},{"why":"Provides the prior equation-of-state and progenitor dependence of black hole formation timing that the short neutrino burst results are compared against.","marker":"[46]"},{"why":"Shows in an analytic non-relativistic treatment that large effective mass prolongs proto-neutron star cooling; the paper reproduces that tendency with self-consistent RMF thermodynamics.","marker":"[57]"},{"why":"Supplies the general relativistic Boltzmann neutrino-radiation hydrodynamics code used for collapse, bounce, and black hole formation runs.","marker":"[25]"},{"why":"Provides the quasi-hydrostatic proto-neutron star cooling code and neutrino transport method used for the long-term cooling runs.","marker":"[53]"},{"why":"Sets the comparison procedure and prior use of the Shen EOS variations that the new simulations follow.","marker":"[63]"}],"fun_headline_variants":["Heavy nucleons soften EOS, hasten black hole birth","Effective mass skews supernova fate: faster collapse","Softer EOS from nucleon mass speeds up black hole formation","High effective mass yields hotter neutrinos, earlier black hole"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The two EOS tables are assumed to differ only in nucleon effective mass, so the dynamical differences are attributed to that mass; in the RMF theory, however, changing the effective mass also changes the scalar and vector mean-field potentials, so the role of the mass alone is not fully isolated.","fun_headline_variants_meta":{"raw":{"variants":["Heavy nucleons soften EOS, hasten black hole birth","Effective mass skews supernova fate: faster collapse","Softer EOS from nucleon mass speeds up black hole formation","High effective mass yields hotter neutrinos, earlier black hole"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000212,"raw_usage":{"total_tokens":1457,"prompt_tokens":1024,"completion_tokens":433,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":640,"completion_tokens_details":{"reasoning_tokens":363}},"tokens_in":640,"tokens_out":433,"duration_ms":4638,"temperature":1.0,"reasoning_tokens":363,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T10:06:34.213619+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Rerun the 40 solar mass black-hole-formation simulation with two RMF EOS tables that keep the vector mean-field potential identical at all densities while varying only the scalar coupling and hence $M^*$; if the black hole formation time does not move when $M^*$ changes under fixed vector repulsion, the claim that the effective mass drives the earlier collapse would be contradicted.","supporting_citations":[{"cited_title":"Influence of the symmetry energy on the birth of neutron stars and supernova neutrinos","cited_arxiv_id":"astro-ph/9506024","evidence_quote":"Supplies the TM1m EOS table with the larger effective mass and the same saturation properties as TM1e; this is the model whose dynamics are compared."},{"cited_title":"Neutrino signals from the formation of black hole: a probe of equation of state of dense matter","cited_arxiv_id":"astro-ph/0608509","evidence_quote":"Provides the prior equation-of-state and progenitor dependence of black hole formation timing that the short neutrino burst results are compared against."},{"cited_title":"Sotani, Understanding supernova gravitational waves with protoneutron star asteroseis- mology, Classical and Quantum Gravity43, 093001 (2026)","cited_arxiv_id":null,"evidence_quote":"Supplies the general relativistic Boltzmann neutrino-radiation hydrodynamics code used for collapse, bounce, and black hole formation runs."},{"cited_title":"Yasin, S","cited_arxiv_id":null,"evidence_quote":"Provides the quasi-hydrostatic proto-neutron star cooling code and neutrino transport method used for the long-term cooling runs."}],"review_version":1}