REVIEW
The Mass Function of Neutron Stars from Core-Collapse Supernova Simulations
High Energy Astrophysical Phenomena · Submitted 18 Aug 2026 · 299 references
Pith's verdict: A transparent but partly circular attempt to derive the neutron star mass function from 3D supernova simulations; worth refereeing, but the 'prediction' is heavily fitted and the scatter-free mapping likely creates artificial sharp features.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
The paper claims that modern 3D core-collapse supernova theory can explain the observed neutron star mass function, from the ~1.35 $M_\odot$ peak to the high-mass tail, and yields a ~21% black hole birth fraction.
The reading
What carries the argument
The load-bearing object is the compactness parameter $\xi_M = (M/M_\odot)/(R(M)/1000\,{\rm km})$, evaluated at $M=1.75\,M_\odot$, which measures how tightly bound the pre-collapse core is. A polynomial fit to the 3D simulation suite converts $\xi_{1.75}$ into a gravitational birth mass $M_{\rm birth}$ for each progenitor, and this is combined with a separate $\xi_{1.75}$-versus-$M_{\rm ZAMS}$ relation from stellar evolution models and a Salpeter IMF $dN/dM \propto M^{-2.35}$ to assign weights to discrete birth-mass points. On the observational side, black-hole-forming progenitor islands defined in a companion 3D study are masked with fitted removal fractions, accretion corrections from spin-period relations shift observed masses downward, and a simple kick-depletion step removes a fraction of remnants above $1.5\,M_\odot$. The machinery turns progenitor structure into a testable mass function through two deterministic mappings plus two fitted selection effects.
Extended reading notes
Core claim
The central claim, stated on the paper's own terms, is that the neutron star mass function observed in binaries is a convolution of a broad spectrum of birth masses with three physical filters: black hole formation in islands of progenitor compactness, post-birth accretion from a companion, and mass-dependent natal kicks. The default theoretical birth function, built from the $\xi_{1.75}$-to-$M_{\rm birth}$ mapping, peaks at $1.2$\textendash$1.3\,M_\odot$ and has a secondary enhancement at $1.5$\textendash$1.7\,M_\odot$, overproducing the intermediate- and high-mass ranges relative to observation. Applying the best-fitting black-hole masks removes about $20.7\%$ of progenitors in the $9$\textendash$120\,M_\odot$ range (Salpeter-weighted), and a phenomenological removal of half the remnants between $1.5$ and $2.0\,M_\odot$ as a natal-kick selection yields a final distribution that broadly reproduces the accretion-corrected observed masses from the $1.35\,M_\odot$ peak to the tail. The paper also argues that the sharp low-mass cutoff near $1.2\,M_\odot$ is physical: observed claims of neutron stars below roughly $1.1\,M_\odot$ are attributed to measurement error, and the scarcity of objects below $1.2\,M_\odot$ motivates a reduced neutron-star formation efficiency in the $8$\textendash$9\,M_\odot$ progenitor range.
Load-bearing premise
The entire calculation rests on the assumption that a core's compactness $\xi_{1.75}$ uniquely determines the neutron star's gravitational birth mass through a deterministic fit with no scatter, along with the companion assumption that the stellar-evolution mapping from $M_{\rm ZAMS}$ to $\xi_{1.75}$ is representative.
Editorial extensions
If this is right
- The observed peak near $1.35\,M_\odot$ is, in this picture, partly a selection effect: lower-mass neutron stars receive weaker kicks and preferentially survive in binaries, while heavier remnants are more often unbound.
- Black hole formation is not monotonic in ZAMS mass; the islands of high compactness that collapse to black holes remove about $21\%$ of the $9$\textendash$120\,M_\odot$ progenitor population, so the neutron-star/black-hole dichotomy has a patchy, structure-dependent origin.
- The theoretical minimum neutron star birth mass is near $1.15$\textendash$1.2\,M_\odot$, which predicts that supposedly sub-$1.1\,M_\odot$ neutron stars are measurement artifacts and that neutron-star formation is suppressed in part of the $8$\textendash$9\,M_\odot$ range.
- Because the mapping is deterministic, the sharp features of the birth function (the dominant low-mass peak and the $2.0\,M_\odot$ cutoff) are directly testable predictions for future, less biased samples of neutron star masses.
Reading between the lines
- A testable extension is to replace the Salpeter ZAMS weighting with a distribution of carbon-oxygen core masses from binary population synthesis; the paper notes multiplicity is ubiquitous, and this substitution could shift the low-mass peak without changing the compactness-to-mass mapping.
- If future 3D suites reveal even modest scatter in birth mass at fixed $\xi_{1.75}$, the sharp cutoff and narrow peaks in the theoretical distribution would smear; calibrating the scatter is the quickest way to judge how much of the claimed shape is robust.
- The fitted black hole fraction of about $21\%$ has an implicit consequence the paper does not develop: it implies a local birth rate of stellar-mass black holes that could be compared with gravitational-wave merger-rate inferences, once delay times and selection are folded in.
- The kick-depletion step is intentionally phenomenological; a self-consistent population synthesis using simulation-calibrated kick distributions would test whether removing half of the remnants above $1.5\,M_\odot$ is realistic or an artifact of the simplified treatment.
Original abstract
Using the mapping between progenitor core structure and the gravitational mass of neutron stars derived from sophisticated 3D supernova simulations, we determine the theoretical mass distribution of neutron stars at birth and compare it with neutron star mass function measurements. In the process, we explore the effects of islands of black hole formation and subsequent mass accretion. We show that supernova theory can explain the observed neutron star mass function from its lower-mass peak near $\sim$1.35 $M_{\odot}$ to its higher-mass tail. Moreover, the lower predicted kick speeds expected during the birth of lower-mass neutron stars and the higher expected kick speeds expected on average for higher mass neutron stars both sculpt the observed mass function in desired directions. The upshot of all these influences is to imprint upon the measured neutron star mass function features that reflect the varied physics of both neutron star origins and the neutron-star/black-hole dichotomy. Very approximately, we derive a black hole birth fraction of $\sim$21\%. In summary, we suggest that supernova theory can now be used to explain, however provisionally, various measured attributes of the population of compact objects and that an era of productive engagement between supernova theory and observation is at hand.
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.
The abstract, sentence by sentence
Using the mapping between progenitor core structure and the gravitational mass of neutron stars derived from sophisticated 3D supernova simulations, we determine the theoretical mass distribution of neutron stars at birth and compare it with neutron star mass function measurements. In the process, we explore the effects of islands of black hole formation and subsequent mass accretion. We show that supernova theory can explain the observed neutron star mass function from its lower-mass peak near $\sim$1.35 $M_{\odot}$ to its higher-mass tail. Moreover, the lower predicted kick speeds expected during the birth of lower-mass neutron stars and the higher expected kick speeds expected on average for higher mass neutron stars both sculpt the observed mass function in desired directions. The upshot of all these influences is to imprint upon the measured neutron star mass function features that reflect the varied physics of both neutron star origins and the neutron-star/black-hole dichotomy. Very approximately, we derive a black hole birth fraction of $\sim$21\%. In summary, we suggest that supernova theory can now be used to explain, however provisionally, various measured attributes of the population of compact objects and that an era of productive engagement between supernova theory and observation is at hand.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Using the mapping between progenitor core structure and the gravitational mass of neutron stars derived from sophisticated 3D supernova simulations, we determine the theoretical mass distribution of neutron stars at birth and compare it with neutron star mass function measurements. | contribution 0.72 | 0.94 | 0.11 | asserted 0.98 |
| s1 | In the process, we explore the effects of islands of black hole formation and subsequent mass accretion. | method 0.54 | 0.82 | 0.02 | asserted 0.67 |
| s2 | We show that supernova theory can explain the observed neutron star mass function from its lower-mass peak near $\sim$1.35 $M_{\odot}$ to its higher-mass tail. | result 0.99 | 0.92 | 0.74 | asserted 1.00 |
| s3 | Moreover, the lower predicted kick speeds expected during the birth of lower-mass neutron stars and the higher expected kick speeds expected on average for higher mass neutron stars both sculpt the observed mass function in desired directions. | interpretation 0.64 | 0.78 | 0.09 | asserted 0.98 |
| s4 | The upshot of all these influences is to imprint upon the measured neutron star mass function features that reflect the varied physics of both neutron star origins and the neutron-star/black-hole dichotomy. | interpretation 0.97 | 0.75 | 0.17 | asserted 0.99 |
| s5 | Very approximately, we derive a black hole birth fraction of $\sim$21\%. | result 1.00 | 0.95 | 0.06 | asserted 0.59 |
| s6 | In summary, we suggest that supernova theory can now be used to explain, however provisionally, various measured attributes of the population of compact objects and that an era of productive engagement between supernova theory and observation is at hand. | future work 0.51 | 0.42 | 0.50 | hedged possibility 1.00 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:2608.18198 by the authors.
References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it · 1 sentence without a confident label
Cites it as background 1 paper
-
For recent reviews of the neutrino-driven mechanism (the delayed neutrino mechanism), see, e.g., [ref] , and for recent papers, see, e.g., [ref] .
Supernova 1987A was a "failed supernova" twenty thousand years before its jet-driven explosion · Introduction · 1.00
What it cites · 68 sentences without a confident label
Contests 1 paper
-
Moreover, the [ref] were unable to birth neutron stars with masses above 1.7 $M_⊙$.
Core-Collapse Supernovae from 9 to 120 Solar Masses Based on Neutrino-powered Explosions · Method · contest 0.84
Uses the method or tool of 1 paper
-
We apply the accretion-correction prescriptions of [ref] and [ref] .
Study of measured pulsar masses and their possible conclusions · Accretion Correction of Observed Neutron Star Mass · 1.00
Uses data or values from 3 papers
-
The lowest neutron star gravitational mass found theoretically is 1.188 $M_⊙$ [ref] , with another study pegging this at 1.192 $M_⊙$ [ref] .
Electron-Capture and Low-Mass Iron-Core-Collapse Supernovae: New Neutrino-Radiation-Hydrodynamics Simulations · Discussion of Outstanding Issues · 0.84
-
These progenitor intervals, also known as black hole forming channels, were taken from [ref] .
Channels of Stellar-mass Black Hole Formation · Removing Black-Hole-Forming Candidates · 0.81
-
[ref] suggested that the single-Gaussian model does not describe the millisecond pulsar (MSP) population adequately, whereas the preferred bimodal Gaussian mixture contains a low-mass component centered at \(1.393^+0.031_-0.029 M_⊙\) with width \(0.064^+0.064_-0.025 M_⊙\) and a high-mass component centered at \(1.807^+0.081_-0.132 M_⊙\) with width \(0.177^+0.115_-0.072 M_⊙\).
The millisecond pulsar mass distribution: Evidence for bimodality and constraints on the maximum neutron star mass · Post-Formation Accretion · 0.95
Compares with 2 papers
-
These results were consistent with those obtained by [ref] .
The millisecond pulsar mass distribution: Evidence for bimodality and constraints on the maximum neutron star mass · Inferred Mass Functions · 0.94
-
The magnitude of this shift is slightly smaller than the $0.122 M_⊙$ shift obtained with the [ref] prescription, consistent with the generally less pronounced bin-by-bin redistribution seen in Figure [ref].
Study of measured pulsar masses and their possible conclusions · Accretion Correction of Observed Neutron Star Mass · 0.91
Cites as support 3 papers
-
In particular, and what motivates this paper is the suggestion in [ref] that there could be a monotonic relationship between the gravitational mass ($M_G$) of a neutron star birthed in a core-collapse supernova explosion and the final core structure of the progenitor massive star, in particular its “compactness" [ref] (see [ref] and Table [ref]).
Black Hole Formation in Failing Core-Collapse Supernovae · Introduction · 1.00
-
In particular, and what motivates this paper is the suggestion in [ref] that there could be a monotonic relationship between the gravitational mass ($M_G$) of a neutron star birthed in a core-collapse supernova explosion and the final core structure of the progenitor massive star, in particular its “compactness" [ref] (see [ref] and Table [ref]).
Physical Correlations and Predictions Emerging from Modern Core-Collapse Supernova Theory · Introduction · 1.00
-
Importantly, black hole formation may not be monotonic with ZAMS mass $-$ there may be islands of black hole formation, some accompanied by supernova explosions [ref] .
Channels of Stellar-mass Black Hole Formation · Conclusions · 0.97
Cites as background 18 papers
-
Nevertheless, several studies have applied Bayesian statistical methods to neutron star mass observations and inferred distribution functions ( [ref] .
The millisecond pulsar mass distribution: Evidence for bimodality and constraints on the maximum neutron star mass · Measured Masses · 0.80
-
Nevertheless, several studies have applied Bayesian statistical methods to neutron star mass observations and inferred distribution functions ( [ref] .
2511.07393 · Measured Masses · 0.80
-
Nevertheless, several studies have applied Bayesian statistical methods to neutron star mass observations and inferred distribution functions ( [ref] .
Maximum gravitational mass $M_{\rm TOV}=2.25^{+0.08}_{-0.07}M_\odot$ inferred at about $3\%$ precision with multimessenger data of neutron stars · Measured Masses · 0.80
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.