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REVIEW 3 major objections 6 minor 89 references

Challenges in Forming Millisecond Pulsar-Black Holes from Isolated Binaries

T0 review · 3 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper argues that isolated binary evolution at solar metallicity cannot form millisecond pulsar–black hole binaries, because no mass transfer onto the neutron star occurs after the first supernova.

desk verdict Solid, transparent population synthesis study whose main null result is only as strong as POSYDON's rotation-limited accretion prescription. read the letter →

arxiv 2412.15521 v1 pith:QIWAP6JK submitted 2024-12-20 astro-ph.HE

Camille Liotine , Vicky Kalogera , Jeff J. Andrews , Simone S. Bavera , Max Briel , Tassos Fragos , Seth Gossage , Konstantinos Kovlakas
show 7 more authors
Matthias U. Kruckow Kyle A. Rocha Philipp M. Srivastava Meng Sun Elizabeth Teng Zepei Xing Emmanouil Zapartas
This is my paper · ORCID
classification astro-ph.HE
keywords millisecondpulsarsneutronstar-blackholebinariesbinarypopulationsynthesismasstransfercommonenvelopeevolutionpulsarrecyclingsupernovakicksglobularclusters
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper models the formation of neutron star–black hole binaries in the Galactic field at solar metallicity, concentrating on systems where the neutron star forms first and could in principle be spun up to millisecond periods. It finds such systems are rare, with birth rates below one per Myr in a Milky Way-like galaxy, and 2–3 orders of magnitude rarer than binaries where the black hole forms first. The paper reports that none of its simulated neutron-star-first binaries experience any mass transfer, stable or unstable, after the first supernova, which removes the only known mechanism for spinning the neutron star up to millisecond rotation. The conclusion, if correct, is that millisecond pulsar–black hole binaries cannot form from isolated binaries, and pulsar surveys should target dynamically active environments instead.

What carries the argument

The load-bearing mechanism is the code's treatment of rotationally-limited accretion onto non-degenerate companions: a star can only accept mass until it reaches critical rotation, after which boosted winds eject further transferred material. This makes mass ratio reversal possible only for binaries with zero-age main-sequence mass ratios near unity, and it prevents the companion from later filling its Roche lobe and transferring mass onto the neutron star after the first supernova. The other central element is the double common envelope treatment, which lets near-equal-mass binaries tighten their orbits before the first supernova but still leaves them detached afterward.

What would settle it

A confirmed detection of a millisecond pulsar in a binary with a black hole in the Galactic field, with no evidence of a dynamical exchange history, would falsify the claim that isolated evolution cannot form such systems. A more direct computational test would be to rerun the same populations with an accretion treatment that is not capped by the accretor's critical rotation and check whether any post-first-supernova mass transfer onto the neutron star appears.

Watch

Extended reading notes

Core claim

The paper claims that, within the physics implemented in its population synthesis code, every neutron-star-first black hole binary progenitor undergoes a mass ratio reversal before the first supernova, through mass transfer during hydrogen main-sequence evolution. These progenitors then either evolve fully detached (Channel I) or pass through a double common envelope phase before the first supernova (Channel II), but in both channels no mass transfer occurs after the first supernova. Because accretion is required to recycle a neutron star to millisecond periods, the authors conclude that millisecond pulsar–black hole binaries have no isolated formation channel in these models, leaving dynamical formation as the only remaining route.

Load-bearing premise

The null result rests on the code's assumption that a non-degenerate star can only accrete until it reaches critical rotation, so only near-equal-mass binaries reverse their mass ratios and no companion can later dump mass onto the neutron star.

Editorial extensions

If this is right

  • If correct, current and upcoming pulsar surveys should expect no Galactic-field millisecond pulsar–black hole detections from isolated binary evolution.
  • Dynamically active environments, such as globular clusters and nuclear clusters, become the only plausible birth sites for these systems.
  • The neutron-star-first black hole birth rate below 1 Myr$^{-1}$ means these systems contribute negligibly to gravitational-wave merger rates compared with black-hole-first systems.
  • The properties of these binaries, including which formation channel dominates, depend strongly on the supernova remnant prescription, natal kick assumptions, and common-envelope efficiency.
  • The one detected millisecond pulsar with a compact companion in NGC 1851 is consistent with a dynamical origin, matching the paper's conclusions.

Reading between the lines

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

  • A testable extension left implicit by the paper: if isolated millisecond pulsar–black hole binaries do form, they would most likely appear as wide, detached, unrecycled pulsar–black hole systems, so a field discovery of a recycled pulsar with a black hole companion would directly contradict this channel.
  • The gap between this result and an earlier population synthesis study that found recycled neutron stars appears to be driven mainly by the rotation cap on accretion; a systematic comparison of accretion physics, rather than supernova physics, would decide which population's neutron-star-first binaries are closer to reality.
  • Future supernova remnant prescriptions that produce different remnant masses, or a revised physical treatment of double common envelope onset, could reopen a narrow isolated formation channel even within this code.
  • The rotation-limited accretion assumption could be tested observationally by comparing simulated mass ratios of double neutron star and X-ray binary populations against measured systems, since those constrain how much mass non-degenerate accretors actually retain.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper uses the POSYDON v2 population-synthesis code to evolve 10^7 solar-metallicity binaries and isolate the subpopulation of NS\,–\,BH binaries in which the neutron star forms first (NSBH). It reports Galactic NSBH birth rates below about 1.6\,Myr$^{-1}$, two to three orders of magnitude below BH-first systems, and identifies two formation channels: fully detached evolution after the hydrogen main sequence (Channel I) and a double common-envelope phase before the first supernova (Channel II). The central result is that no NSBH binary in any of the tested populations undergoes mass transfer, stable or unstable, after the first supernova, so the neutron star cannot be recycled into a millisecond pulsar. The authors conclude that isolated binary evolution cannot form MSP\,–\,BH binaries and that dynamical environments may be the only remaining channel, placing this result in explicit contrast with the COMPAS-based conclusions of Chattopadhyay et al. (2021).

Significance. If the central null result holds, the paper would settle an important disputed question in binary population synthesis by closing the isolated formation channel for MSP\,–\,BH binaries at solar metallicity, with direct consequences for pulsar-survey targeting. The study's strengths are that the result emerges from detailed MESA-based binary grids rather than from fitted outcomes, and that the authors test multiple supernova remnant prescriptions, kick settings, common-envelope efficiencies, and an alternative interpolation scheme, while transparently listing many model limitations. The main caveat, identified in the paper itself in Section 4.1, is that the absence of post-supernova mass transfer is a direct consequence of POSYDON's rotation-limited accretion prescription for non-degenerate companions. Because that prescription is not independently calibrated or varied here, the categorical statement that MSP\,–\,BH binaries 'cannot form' is stronger than the modeling actually supports.

major comments (3)
  1. [§4.1, §2.2] The central null result is load-bearing on a single code-specific assumption: POSYDON's treatment of mass accretion onto non-degenerate stars, which is limited by the accretor's critical rotation rate and by rotationally enhanced winds. The paper itself states in §4.1 that COMPAS's more conservative accretion allows mass-ratio reversal for more unequal ZAMS binaries, leading to a common-envelope phase and accretion onto the neutron star after the first supernova, whereas POSYDON restricts mass-ratio reversal to near-unity mass ratios. Section 2.2 also notes that star\,–\,disk interactions could change the accretion and spin-up assumptions. No test, calibration, or quantitative comparison of this assumption is provided. Because the abstract's conclusion "MSP\,–\,BH binaries cannot form" rests on this prescription, the claim is not yet robust. I would ask the authors to add a model variation that relaxes the rotation-limited accretion assumption (for example, allowing a fixed fraction of the transferred mass to be accreted regardless of spin, or adopting a COMPAS-like conservative accretion limit) and to report whether any post-supernova mass-transfer channel appears; alternatively, the conclusion should be explicitly conditional on the accretion treatment rather than stated as a universal formation barrier.
  2. [§4.2] The model-uncertainties section does not include the rotation-limited accretion assumption among the factors that could change the main result. Section 4.2 discusses uncertainties in the core-collapse prescription, double-CE onset, stellar winds, interpolation, and grid resolution, but the discussion of the comparison with COMPAS in §4.1 makes clear that the absence of post-supernova mass transfer is controlled by the accretion physics. Since the abstract draws a categorical conclusion from this null result, the limitation section should explicitly state that the no-recycling result is conditional on POSYDON's treatment of non-degenerate accretion, and should discuss what would happen if that treatment were modified. This is not a cosmetic omission; it is the difference between a robust population-synthesis result and a code-dependent artifact.
  3. [Abstract and §5] The conclusion that "MSP\,–\,BH binaries cannot be formed" overstates the scope of the simulations. The models cover only solar metallicity, only isolated binaries, and only the specific set of physical prescriptions adopted in POSYDON. The abstract itself contains the qualifier "in isolation," but the final sentence, "Thus, dynamical environments and processes may provide the only formation channels," presents the result as an absolute barrier. A more accurate statement would be that no MSP\,–\,BH binaries form through the isolated-binary channels modeled here at solar metallicity, given the tested prescriptions. The distinction matters for the paper's survey-strategy implications, and the authors should either soften the claim or provide evidence that the tested parameter space is representative of the physical possibilities.
minor comments (6)
  1. [Figure 4 caption] In the caption, "potted" should be "plotted": "Binaries with initial mass ratios ≤ 0.95 are potted on the q = 0.9 grid slice."
  2. [Table 1 caption] The caption begins "T able 1." with a stray space; it should read "Table 1."
  3. [Introduction] The acronym "F AST" in the list of surveys should be "FAST".
  4. [Acknowledgments] The phrase "supported by the the Swiss National Science Foundation" contains a duplicated "the" and appears twice.
  5. [Section 2.2] The sentence describing the rotationally enhanced wind model says the wind keeps the stellar rotation rate "always below its critical threshold," but the same paragraph discusses critically rotating stars; consider writing "at or below" for consistency with the earlier description.
  6. [Figure 4] The legend labels "Stable reverse mass-transfer phase" and "Unstable reverse mass-transfer phase" are rendered in different colors in the figure, but the caption text does not define all color/symbol combinations unambiguously; a compact legend description in the caption would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the null result is an emergent population-synthesis outcome, not an input or a fitted target.

full rationale

The paper's derivation chain is self-contained and does not reduce to its own assumptions by construction. The central claim—that no NSBH binary in the modeled populations undergoes mass transfer after the first supernova, so MSP-BH binaries cannot form in isolation—is an emergent property of POSYDON's pre-computed MESA grids, not a fitted or definitional input. Initial conditions (Kroupa IMF, Sana period distribution, flat mass ratios) and physical prescriptions (Fryer+12 delayed, Sukhbold+16 N20, Hobbs+05 and Mandel & Mueller kicks, Podsiadlowski+04 ECSN, alpha-lambda CE) are taken from independent literature and are not tuned to produce the absence of post-supernova mass transfer. The paper explicitly diagnoses the difference from Chattopadhyay et al. (2021) as arising from POSYDON's rotation-limited accretion onto non-degenerate companions, and it flags star-disk interactions as a potential modification (Section 2.2); this is model dependence, which belongs to correctness risk rather than circularity. Self-citations to Fragos et al. (2023) and Andrews et al. (2024) function as code documentation, not as a load-bearing uniqueness theorem, and the relevant accretion physics is described concretely in the text rather than deferred entirely to those citations. No equation is shown to be equivalent to its inputs by construction, and no fitted parameter is renamed as a prediction. Score 0 reflects the absence of circular steps.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central null result is an emergent property of the simulation, so the ledger lists the hand-set parameters and modeling assumptions that shape it. The most important is the rotation-limited accretion prescription; if that assumption is relaxed, the COMPAS-style channel with post-SN mass transfer and pulsar recycling reopens (Section 4.1).

free parameters (4)
  • Common envelope efficiency alpha = 1 (default); 0.5 and 0.1 in variations
    Chosen by hand; controls whether binaries survive double CE in Channel II and changes the NSBH birth rate by up to 62%.
  • CCSN kick velocity dispersion = 265 km/s (default, Hobbs et al. 2005); 120 km/s NS and 60 km/s BH (low-kick variation, Mandel & Muller 2020)
    Sampled from a Maxwellian; determines whether binaries remain bound after the first SN and changes NSBH rates by factors of 2 to 10.
  • Maximum NS mass for F12d remnant model = 2.5 Msun
    Hand-set cutoff that determines NS vs BH classification in the Fryer et al. (2012) delayed prescription; directly shapes the NSBH parameter space.
  • Milky Way star formation rate for rate normalization = 1.65 Msun/yr
    Taken from Licquia & Newman (2015); used to rescale simulated binary counts to Galactic birth rates.
assumptions (6)
  • domain assumption Mass accretion onto non-degenerate stars is limited by the accretor's critical rotation rate, with excess mass lost through boosted winds.
    Invoked in Sections 2.2 and 4.1; this limits mass ratio reversal to near-unity ZAMS binaries and underlies the absence of post-first-SN MT. It is a modeling choice, not an observational constraint.
  • ad hoc to paper A binary enters a double common envelope when both stars fill their Roche lobes, at least one is post-MS, and unstable MT is initiated.
    Section 2.3; the authors note the physical onset conditions for double CE are uncertain and may overestimate the frequency of Channel II systems (Section 4.2).
  • domain assumption Hertzsprung-gap donor stars can survive a common envelope phase (the 'optimistic' CE scenario).
    Section 2.3; standard assumption in the literature (e.g., Vigna-Gomez et al. 2018) that increases binary survival.
  • domain assumption Remnant masses and remnant types follow either the Fryer et al. (2012) delayed or Sukhbold et al. (2016) N20 prescriptions.
    Section 2.4; these prescriptions determine NS vs BH formation and are the dominant source of rate uncertainty.
  • domain assumption Ultra-stripped supernovae are not modeled in POSYDON.
    Section 2.4; the authors argue this does not affect NSBH binaries where the NS forms first, relying on Chattopadhyay et al. (2021).
  • domain assumption The MESA stellar models and the Dutch wind scheme for high-mass stars approximate the binary physics correctly.
    Sections 2 and 4.2; the interpolation grids encode these physics, and the authors note that changes to winds could affect orbital separation and mass transfer.

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Cite this review

Pith. "Pith review of Challenges in Forming Millisecond Pulsar-Black Holes from Isolated Binaries." pith.science (2026). https://pith.science/paper/QIWAP6JK

@misc{pith2026241215521,
  author       = {Pith},
  title        = {Pith review of: Challenges in Forming Millisecond Pulsar-Black Holes from Isolated Binaries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QIWAP6JK}},
  note         = {Machine review of arXiv:2412.15521}
}
abstract

Binaries harboring a millisecond pulsar (MSP) and a black hole (BH) are a key observing target for current and upcoming pulsar surveys. We model the formation and evolution of such binaries in isolation at solar metallicity using the next-generation binary population synthesis code POSYDON. We examine neutron star (NS)-BH binaries where the NS forms first (labeled NSBH), as the NS must be able to spin-up to MSP rotation periods before the BH forms in these systems. We find that NSBHs are very rare and have a birth rate < 1 Myr$^{-1}$ for a Milky Way-like galaxy in our typical models. The NSBH birth rate is 2-3 orders of magnitude smaller than that for NS-BHs where the BH forms first (labeled BHNS). These rates are also sensitive to model assumptions about the supernova (SN) remnant masses, natal kicks, and common-envelope efficiency. We find that 100% of NSBHs undergo a mass ratio reversal before the first SN and up to 64% of NSBHs undergo a double common envelope phase after the mass ratio reversal occurs. Most importantly, no NSBH binaries in our populations undergo a mass transfer phase, either stable or unstable, after the first SN. This implies that there is no possibility of pulsar spin-up via accretion, and thus MSP-BH binaries cannot form. Thus, dynamical environments and processes may provide the only formation channels for such MSP-BH binaries.

Figures

Figures reproduced from arXiv: 2412.15521 by the authors.

Figure 1
Figure 1. The primary ZAMS masses of all NSBH progen￾itors in our S16 and F12d populations. The differing mass ranges between prescriptions is a result of how each computes remnant masses and assigns CO types (Section 3.1). 0.88 0.90 0.92 0.94 0.96 0.98 1.00 qZAMS 0 10 20 30 40 50 Count Sukhbold+16 Fryer+12-delayed [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. The mass ratio distributions at ZAMS (qZAMS) for all NSBH progenitors. In both the F12d and S16 popu￾lations, the ZAMS mass ratios are close to unity. culate birth rates by rescaling the number of binaries in a given subpopulation with the average star formation rate of the Milky Way, which we take to be SFRMW = 1.65 M⊙/yr (Licquia & Newman 2015). We normalize our simulations by: multiplying the number of systems [… view at source ↗
Figure 3
Figure 3. The number of NSBH binaries in the F12d and S16 populations that form through Channel I (pink) vs. Channel II (green) (Sections 3.2.2 & 3.2.3). We show the subset of binaries in each channel that merge in a Hubble time (solid) and those that do not merge, or remain detached (hatched). close to one (Section 3.2, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: The HMS–HMS grid slices from POSYDON’s library of binary star models for ZAMS mass ratios q = 0.9 and q = 1.0. The different grid symbols summarize the evolution of each of the pre-computed MESA models. The ZAMS binary orbital periods vs. primary masses for all NSBH pr…
Figure 5
Figure 5. Figure 5: BH vs. NS masses for all NSBH binaries at their formation in both the F12d (black) and S16 (green/pink) populations. Each population is separated into binaries that merge and do not merge in a Hubble time with the large and small markers, respectively. For the S16 popu…
Figure 6
Figure 6. Figure 6: Eccentricity vs. orbital period for all NSBH bi￾naries at their formation in both the F12d (black) and S16 (green/pink) populations. Each population is separated into binaries that merge and do not merge in a Hubble time with the large and small markers, respectively. …

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