Effect of quark-hadron phase transitions on the neutron star mass distribution

Chunhua Zhu; Guoliang L\"u; Helei Liu; Renyu Luo; Shuai Zha; Sufen Guo; XuRun Huang; Zhijun Wang

REVIEW

Effect of quark-hadron phase transitions on the neutron star mass distribution

Renyu Luo, XuRun Huang, Shuai Zha, Guoliang Lü, Chunhua Zhu, Sufen Guo, Helei Liu, Zhijun Wang

High Energy Astrophysical Phenomena · Submitted 30 Oct 2026 · Published version · 114 references

Pith's verdict: A solid, honest 1D parameter study whose new 1.7 Msun peak claim rests on counting prematurely terminated runs as successful explosions.

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arXiv ID2610.41242 (version 1)

Pith IDDADR3JIQ, Pith's permanent record of this paper and its review

CitationChunhua Zhu, Guoliang L\"u, Helei Liu, Renyu Luo, Shuai Zha, Sufen Guo, XuRun Huang, Zhijun Wang. "Effect of quark-hadron phase transitions on the neutron star mass distribution." arXiv:2610.41242 (2026). https://pith.science/paper/DADR3JIQ

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Editor's note

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New here is a systematic look: two hybrid EOSs with a first-order quark-hadron phase transition, 13–120 Msun progenitors, 1D GR1D, and an IMF-weighted birth mass distribution. That grid is genuinely new in this subfield, and the benchmark against Khosravi Largani et al. on the s40 progenitor, within 0.02 Msun for four EOSs, gives me real confidence in the numerical setup. The paper also identifies a channel that had not been emphasized: low-compactness progenitors whose first shock stalls keep accreting, hit the PT boundary late, and then explode via the second shock, ending up as relatively massive NSs. That mechanism is physically coherent, and the clustering explanation—a fixed PT boundary in thermodynamic space gives a narrow range of PNS masses at second collapse—makes sense.

The authors are honest. They state up front that they omit turbulence/STIR, fallback, and neutrino flavor conversion, and they flag the early-termination issue. That last one is the load-bearing soft spot, and it is bigger than they let on. Every PT-channel success is a run that terminated at 500–2000 km once Ye left the EOS table; the criterion for counting it as a NS is that the second shock was launched. The paper says this may miss delayed black hole formation and argues it affects only relative numbers, not the peak position. But the peak's prominence in an IMF-weighted histogram is precisely a relative-number statement. If a meaningful fraction of those terminated runs later fail, the 1.7 Msun feature weakens or disappears. The authors' robustness claim in the conclusion does not address that.

Fallback omission is acknowledged and affects masses as well as the success/failure inventory: remnants are frozen before the shock crosses the envelope. 1D without calibrated turbulence is also acknowledged, but it matters because it shifts the explosion boundary that determines which compactness regime the PT has to save. There is no data release, so it is hard to reweight or reclassify runs independently.

The abstract says the study provides "important astrophysical constraints" on dense matter and massive-NS formation. That overstates what the paper delivers: this is a plausible mechanism and a parameter study, not a constraint. No parameter was fitted to the observed NS mass distribution, so there is no circularity, and the citation pattern looks fine.

Who gets value: PT supernova people and anyone building NS birth-mass models. I would send it to referees, with one referee asked to stress-test the success criterion and see whether plausible late-failure or fallback assumptions kill the peak. As it stands, the 1.7 Msun peak should be treated as a prediction only if that criterion survives the test.

Referee report

Significance

If correct, the paper offers a single-star, EOS-driven mechanism for a high-mass component in the neutron-star birth mass function, complementing scenarios based on the explosion of high-compactness progenitors, and it yields a falsifiable prediction: if a first-order quark-hadron transition occurs at the assumed onset densities, newborn neutron stars should cluster near the EOS-dependent onset mass (about 1.55-1.73 Msun here) rather than spread smoothly in mass. Concrete strengths of the work include the transparent, reproducible setup (GR1D, public EOS families, full grid listed in Table I); the benchmark validation against an independent radiation-hydrodynamics code at the 0.02 Msun level (Appendix A, Fig. 6); the internally consistent physical narrative for the threefold role of the PT onset density; and the fact that no parameter is fitted to the observed neutron-star mass distribution, so the peak prediction is not circular in the technical sense.

Major objections (3)

[Section II.B and Figures 3-4] The success/failure inventory of the terminated runs is the load-bearing assumption for the central population-level claim, and the authors' own defense of it does not meet the actual risk. The paper counts as successful PT explosions every model in which the second shock was launched before the code terminated because Y_e left the EOS table at shock radii of roughly 500-2000 km (sentence b73), and explicitly concedes that delayed black-hole formation or late-time failure could occur. The rebuttal in b74, that this affects only the relative number of PT-channel NSs and not the peak position, is insufficient: in the IMF-weighted, normalized histogram of Fig. 4, the relative number of PT-channel NSs sets the height (and even the visibility) of the 1.70 Msun feature relative to the ~1.4 Msun component. The Appendix A benchmark validates the mass extraction and fates for the s40 runs, but those four runs (two clear black holes, two explosions) are not representative of the borderline low-compactness cases that dominate the IMF weighting. The revision should (i) state how many of the Table I success entries are of the terminated-launched-shock type and report their termination shock radii and post-launch evolution time; (ii) provide a robustness test in which the least-advanced of these runs (e.g., smallest shock radius at termination) are reclassified as black holes and show that a pronounced ~1.7 Msun peak survives; and (iii) justify the launch-implies-explosion criterion with a physical diagnostic, such as positive shock velocity at termination or a few representative runs continued beyond the EOS-table boundary by extending the Y_e range. The authors acknowledge this: “We note, however, that this early termination may cause our simulations to miss some cases of delayed black hole for- mation or late time failures that would occur at later stages if the EOS permitted further evolution.”
[Sections III.B-III.C and IV (b68-b69, b142, b186)] The height of the claimed high-mass peak is controlled by which progenitors enter the PT channel, and that assignment is dynamical rather than EOS-determined. Because the IMF favors low masses, the peak in Fig. 4 is dominated by the 13-17 Msun successes (Table I, Fig. 5), which in this 1D setup are precisely the models whose first shock fails and which then accrete for about 1-2 s until the PT triggers (the 'novel channel' of Section III.C). Whether such stars actually reach the PT onset in nature depends on whether the neutrino-driven mechanism, with the turbulent convection the authors acknowledge as decisive (b69), would have exploded them earlier at about 1.4 Msun. With the STIR model not activated (b68), Fig. 4 effectively assumes that none of these stars explodes by the standard channel before the PT triggers. The concluding robustness claim (b186) that the new channel and the clustering are determined by the equation of state rather than by fluid-dynamical instabilities is therefore stronger than what is demonstrated: the EOS fixes the mass at which PT explosions cluster, but it does not fix the number of progenitors that reach the PT. I request a sensitivity test for Fig. 4 in which a stated fraction (e.g., all or half) of the low-compactness PT successes is reassigned to the standard ~1.4 Msun channel, together with a demonstration that a pronounced ~1.7 Msun peak survives; if it does not, the population-level claim should be weakened accordingly.
[Sections II.B and IV (b85-b88, b143)] The masses themselves are read off before the explosion has run its course, so the two-decimal precision of Table I and the interpretive step toward the observed ~1.8 Msun peak are both affected by the acknowledged neglect of post-explosion fallback accretion. The paper states (b85-b88) that capturing fallback is not feasible at the reached evolutionary stage and that the mass criterion is validated against continued simulations in Ref. [90]; however, no estimate of the expected fallback magnitude for the IMF-relevant 13-20 Msun range is provided, and the Ref. [90] validation concerns the higher-mass s40 runs. Late accretion would shift and broaden the claimed peak (the authors' own suggestion in b143 that accretion moves the peak toward 1.8 Msun implies the shift is non-negligible), and for remnants born near the maximum supported mass it could even alter the fate classification. I recommend adding a quantitative estimate of fallback for the relevant mass range (for example, using the scaling of Ref. [107]) and stating the corresponding expected shift and broadening of the peak, rather than presenting the termination-stage masses as final birth masses. The authors acknowledge this: “It is important to note that the NS masses derived in this study do not include the effects of post-explosion fallback accretion.”

Minor objections (6)

[Section II.B] The sentence 'the electron fractiY e tends to exceed the upper limit' contains a typo and should read 'electron fraction Y_e'; similar typos appear elsewhere, such as 'coldM garv' in Section III.A and 'pro-supernova' in Sections III.B and IV.
[Section IV] The conclusion states that the simulations cover '9 to 120 Msun', but the simulations performed in this work start at 13 Msun, with the 9-13 Msun range taken from Sukhbold et al.; the wording (and the stray word 'spinning' in the same sentence) should be corrected to reflect what was actually computed.
[Table I] The row for 55.0 Msun with RDF1.1 lists t_bounce = 2.096 s, which is an order of magnitude larger than every other bounce time in the table (about 0.22-0.39 s); please check and correct this entry.
[Figure 4] The histogram construction should be specified explicitly: the bin width in gravitational mass, how each 0.2-Msun grid point is weighted under the IMF, how the irregularly spaced 31-120 Msun grid is binned, and how the normalization over the mixed sample (PT-channel successes, standard-channel masses for M<13 Msun, and excluded black-hole progenitors) is performed.
[Section III.B and Figure 3] The paper states that the failure band for RDF1.1 is xi_1.75 approximately 0.59-0.69 and for RDF1.2 approximately 1.04-1.07; since Table I shows a ragged alternation of successes and failures (for example, RDF1.1 successes at 13.0-13.8, failures at 14.0-14.8, then successes again at 15.0-17.8), a sentence explaining that this alternation traces the shell-structure-induced oscillation of compactness would help the reader reconcile the band statements with the data.
[Introduction and Section III.B] The observational second peak is quoted as lying at 1.75-1.8 Msun (Refs. [18-21]) while the simulated birth-mass peak is at about 1.70 Msun (RDF1.1); the paper should state this mismatch explicitly and identify the binary-accretion argument in Section III.B as the necessary bridge, rather than presenting the simulated peak as directly matching the observed one.

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The paper

The paper claims

This paper argues that a first-order quark-hadron phase transition inside a collapsing massive star can by itself create the high-mass peak seen in the neutron-star mass distribution.

The reading

The paper argues that a first-order quark-hadron phase transition inside a collapsing massive star can do what standard supernova models have struggled to do: produce a second, high-mass peak in the neutron-star birth mass distribution. Using one-dimensional general-relativistic collapse simulations with two hybrid equations of state that include such a transition, the authors find that successful explosions leave neutron stars clustered around $1.70\,M_\odot$ for RDF1.1 and within $1.55$--$1.70\,M_\odot$ for RDF1.2, instead of the canonical $\sim 1.4\,M_\odot$. The mechanism is a phase-transition-induced second shock: when the proto-neutron-star core crosses the transition boundary, it collapses again and bounces, and the outward shock truncates accretion at a mass set by the boundary itself. Because that boundary is a fixed feature of the equation of state, the resulting masses cluster rather than spreading smoothly, and low-compactness progenitors whose first shock fails can still explode through this second shock. If this is right, a single-star channel, without binary accretion, can account for the high-mass end of the observed mass distribution.

What carries the argument

The load-bearing object is the phase-transition boundary built into the hybrid equations of state RDF1.1 and RDF1.2. Each combines a hadronic phase, based on the DD2 relativistic mean-field description with an additional excluded-volume correction in RDF1.2, with a quark phase described by a relativistic density functional using a string-flip mechanism for confinement and vector repulsions, joined by a Gibbs construction so the transition is first order. The boundary fixes the thermodynamic state at which the proto-neutron-star core begins its second collapse; when the pure quark phase stiffens the equation of state, the infalling matter bounces and launches a second shock. That second shock does the causal work in the paper: it truncates accretion, and because the boundary is fixed, it does so at a characteristic mass, which is why the remnant masses cluster. The numerical code with its neutrino-transport scheme supplies the hydrodynamics, but the phase-transition boundary carries the explanatory weight.

Extended reading notes

Core claim

The paper's central claim is that the quark-hadron phase transition is not a marginal correction to core-collapse supernova theory but a primary agent in setting which stars explode and how massive their neutron stars are. In the simulations, the phase-transition onset density produces a threefold outcome: low-compactness progenitors explode with accretion truncated early and lower remnant masses; critical-compactness progenitors either explode or become black holes depending on whether the transition arrives before the proto-neutron-star mass exceeds the quark-core support limit; and high-compactness progenitors collapse to black holes sooner when the onset density is lower. The paper also reports a formation channel that standard neutrino-driven models lack: low-compactness progenitors whose first shock fails continue to accrete until the second collapse, and the phase-transition-driven second shock revives the explosion and leaves a relatively massive neutron star. Because the phase-transition boundary is a fixed geometric structure of the equation of state rather than a stochastic outcome, the final masses concentrate in a narrow high-mass band, producing a peak near $1.70\,M_\odot$ for RDF1.1 and $1.55$--$1.70\,M_\odot$ for RDF1.2 after weighting by the stellar initial mass function.

Load-bearing premise

The load-bearing premise is that a launched phase-transition second shock guarantees explosion and neutron-star formation, even though the simulations stop at shock radii of roughly 500 to 2000 km, before late-time fallback or delayed black-hole collapse can be followed.

Editorial extensions

If this is right

The observed high-mass peak in the neutron-star mass distribution could be produced by single-star evolution, without requiring binary accretion or multidimensional turbulence.
The peak position becomes a measurable probe of the phase-transition onset density: RDF1.1 clusters remnants near $1.70\,M_\odot$, while RDF1.2 spreads them across $1.55$--$1.70\,M_\odot$.
The neutron-star-to-black-hole ratio shifts with the equation of state, because the lower onset density of RDF1.2 moves the explosion-failure boundary to higher compactness.
Abundant low-compactness progenitors, which are favored by the stellar initial mass function, would no longer be mainly a source of canonical $1.4\,M_\odot$ neutron stars but could form the upper end of the mass distribution through the second-shock channel.
If binary accretion or fallback adds mass after birth, the predicted peak would move upward and could coincide with the observed high-mass peak near $\sim 1.8\,M_\odot$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A sharp prediction implicit in the paper is that any first-order phase-transition equation of state should imprint its own characteristic mass peak, so comparing the observed distribution against several hybrid equations of state could be used to select among quark-matter models.
The authors argue that the clustering mechanism depends on the equation-of-state boundary rather than on fluid instabilities, so the peak's location may survive in multidimensional simulations even if the success-failure boundary shifts; the peak's height is the part that still depends on the explosion-counting criterion.
Because the paper draws on earlier work describing a phase-transition neutrino signal, a testable extension would be to search for an electron-antineutrino burst from a nearby supernova and check whether the remnant left behind is a massive neutron star.
At the population level, many observed neutron stars have been recycled by accretion, so a direct test of the birth-mass peak would require separating minimally accreted systems from the rest of the sample.

Original abstract

The neutron star (NS) mass distribution serves as a crucial probe of the dense matter equation of state (EOS) and core-collapse supernova explosion mechanisms. Although observations reveal a bimodal NS mass distribution, existing theoretical simulations often struggle to naturally reproduce the high-mass peak, and the impact of the quark-hadron phase transition (PT) in high-density nuclear matter remains largely unexplored. Employing the 1D general-relativistic hydrodynamics code GR1D with hybrid EOSs incorporating a first-order PT (RDF1.1 and RDF1.2), we systematically simulate core-collapse supernovae for progenitors with zero-age main-sequence masses ranging from 13 to 120 $M_\odot$. Our results reveal a threefold impact of the PT onset density on the final supernova fate: in low-compactness progenitors, an early PT truncates accretion and produces less massive NSs; in the critical-compactness regime, it facilitates successful explosions; and in high-compactness progenitors, it accelerates black hole formation. Compared with the $\sim 1.4\,M_\odot$ peak typical of the conventional core-collapse scenario, the inclusion of the PT produces NSs with masses centered around $1.70\,M_\odot$ for RDF1.1 and within $1.55$--$1.70\,M_\odot$ for RDF1.2. Furthermore, we identify a novel formation channel whereby low-compactness progenitors with failed initial shocks can form more massive NSs via a PT-induced second shock. Due to the fixed nature of the PT boundary, the final NS masses exhibit a pronounced clustering effect. This study elucidates the critical role of the quark-hadron PT in shaping the NS mass distribution, providing important astrophysical constraints on the properties of high-density nuclear matter and the formation mechanism of massive NSs.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-11-02: 1 request, 6,756 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.70 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.90 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

The neutron star (NS) mass distribution serves as a crucial probe of the dense matter equation of state (EOS) and core-collapse supernova explosion mechanisms. Although observations reveal a bimodal NS mass distribution, existing theoretical simulations often struggle to naturally reproduce the high-mass peak, and the impact of the quark-hadron phase transition (PT) in high-density nuclear matter remains largely unexplored. Employing the 1D general-relativistic hydrodynamics code GR1D with hybrid EOSs incorporating a first-order PT (RDF1.1 and RDF1.2), we systematically simulate core-collapse supernovae for progenitors with zero-age main-sequence masses ranging from 13 to 120 $M_\odot$. Our results reveal a threefold impact of the PT onset density on the final supernova fate: in low-compactness progenitors, an early PT truncates accretion and produces less massive NSs; in the critical-compactness regime, it facilitates successful explosions; and in high-compactness progenitors, it accelerates black hole formation. Compared with the $\sim 1.4\,M_\odot$ peak typical of the conventional core-collapse scenario, the inclusion of the PT produces NSs with masses centered around $1.70\,M_\odot$ for RDF1.1 and within $1.55$--$1.70\,M_\odot$ for RDF1.2. Furthermore, we identify a novel formation channel whereby low-compactness progenitors with failed initial shocks can form more massive NSs via a PT-induced second shock. Due to the fixed nature of the PT boundary, the final NS masses exhibit a pronounced clustering effect. This study elucidates the critical role of the quark-hadron PT in shaping the NS mass distribution, providing important astrophysical constraints on the properties of high-density nuclear matter and the formation mechanism of massive NSs.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The neutron star (NS) mass distribution serves as a crucial probe of the dense matter equation of state (EOS) and core-collapse supernova explosion mechanisms.	background 1.00	0.04	0.03	asserted 1.00
s1	Although observations reveal a bimodal NS mass distribution, existing theoretical simulations often struggle to naturally reproduce the high-mass peak, and the impact of the quark-hadron phase transition (PT) in high-density nuclear matter remains largely unexplored.	gap 0.97	0.06	0.03	asserted 0.98
s2	Employing the 1D general-relativistic hydrodynamics code GR1D with hybrid EOSs incorporating a first-order PT (RDF1.1 and RDF1.2), we systematically simulate core-collapse supernovae for progenitors with zero-age main-sequence masses ranging from 13 to 120 $M_\odot$.	method 0.99	0.96	0.03	asserted 0.93
s3	Our results reveal a threefold impact of the PT onset density on the final supernova fate: in low-compactness progenitors, an early PT truncates accretion and produces less massive NSs; in the critical-compactness regime, it facilitates successful explosions; and in high-compactness progenitors, it accelerates black hole formation.	result 1.00	0.96	0.36	asserted 1.00
s4	Compared with the $\sim 1.4\,M_\odot$ peak typical of the conventional core-collapse scenario, the inclusion of the PT produces NSs with masses centered around $1.70\,M_\odot$ for RDF1.1 and within $1.55$--$1.70\,M_\odot$ for RDF1.2.	result 1.00	0.95	0.23	asserted 1.00
s5	Furthermore, we identify a novel formation channel whereby low-compactness progenitors with failed initial shocks can form more massive NSs via a PT-induced second shock.	result 1.00	0.95	0.10	asserted 1.00
s6	Due to the fixed nature of the PT boundary, the final NS masses exhibit a pronounced clustering effect.	result 0.86	0.86	0.10	asserted 1.00
s7	This study elucidates the critical role of the quark-hadron PT in shaping the NS mass distribution, providing important astrophysical constraints on the properties of high-density nuclear matter and the formation mechanism of massive NSs.	interpretation 0.99	0.84	0.89	asserted 1.00

What kind of paper the classifier reports this is: simulation study 1.00 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** FIG. 1: Properties of compact stars described by the RDF1.1 (blue) and RDF1.2 (red) EOSs. (a) Cold mass-radius

**Figure 2.** FIG. 2: Time evolution of shock radius (panels a, d, g), central density (panels b, e, h), and PNS mass (defined as

**Figure 3.** shows the explosion simulation results of presupernova models with MZAMS ranging from 13 to 40 M⊙ (the complete data for 13–120 M⊙ are listed in Appendix B). The horizontal axis represents the initial mass MZAMS, and the vertical axis denotes the compactness parameter ξ1.75. In

**Figure 4.** FIG. 4: Probability density function (PDF) of the neutron star gravitational mass distribution for the RDF1.1 (left

**Figure 5.** FIG. 5: The left panel shows the gravitational mass

**Figure 6.** FIG. 6: Time evolution of shock radius (panels a), central density (panels b), and PNS mass (defined as the

Figures reproduced from arXiv:2610.41242 by the authors.

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Discussion

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