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Spin evolution and mass distribution of the Galactic Binary Neutron Stars

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

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Pith's one-line read This paper argues that the radio-silent majority of heavy binary neutron stars explains why the Milky Way's radio-selected systems cluster near 2.6–2.7 $M_\odot$ while GW190425 weighs about 3.4 $M_\odot$.

desk verdict Careful spin-evolution population synthesis with a genuinely new selection-effect claim, but the mass-dependent radio-lifetime result hangs on unvaried magnetar-field assumptions that a referee should push hard on. read the letter →

arxiv 2412.15464 v2 pith:HLNILC5V submitted 2024-12-19 astro-ph.HE astro-ph.GAastro-ph.SR

Qingbo Chu , Youjun Lu , Shenghua Yu This is my paper · ORCID
classification astro-ph.HEastro-ph.GAastro-ph.SR
keywords binaryneutronstarsstarspinevolutionpulsarrecyclingradioselectioneffectsgravitational-wavesourcespopulationsynthesismagneticfieldsmagnetars
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 argues that the mass difference between radio-detected binary neutron stars in the Milky Way (total masses clustered near 2.6–2.7 $M_\odot$) and the gravitational-wave event GW190425 (about 3.4 $M_\odot$) is a selection effect rather than evidence for different formation channels. Using an upgraded binary population synthesis code that tracks neutron star spin through every accretion phase, the authors show that low-mass systems recycle the first-born neutron star into a long-lived millisecond pulsar, so they remain radio-bright for up to a Hubble time. Most high-mass systems, by contrast, keep strong magnetic fields and fade from the radio band within roughly a million years, making them nearly invisible to radio surveys. The model reproduces the observed $P{-}\dot{P}$, $P_{\rm orb}{-}e$, and total-mass distributions of Galactic binary neutron stars, and predicts that 19–22 percent of merging binaries at redshift zero weigh more than 3 $M_\odot$, consistent with the gravitational-wave detections.

What carries the argument

The load-bearing object is the neutron star spin evolution model grafted onto the binary star evolution code, which advances the first-born neutron star through an ejector phase, rapid rotator, propeller, super- and sub-Keplerian magnetic inhibition, subsonic settling accretion, Bondi-Hoyle-Littleton accretion, and finally Roche-lobe overflow spin-up. Each phase has an analytic torque or spin-down rate, with a death line separating radio-loud from radio-quiet pulsars, and an exponential magnetic field decay with a shorter timescale during accretion ($10^6$ yr) than otherwise ($10^9$ yr). The crucial input is the initial field: neutron stars from progenitors below 20 $M_\odot$ draw log-normal fields around $10^{13}$ G, while those from more massive stars are assigned uniform fields of $10^{14}$–$10^{15}$ G, producing the short radio lifetimes of heavy binaries.

What would settle it

Find one Galactic binary neutron star with a recycled, radio-emitting pulsar and a total mass at or above 3 $M_\odot$, well outside the observed 2.6–2.7 $M_\odot$ peak. Under the model's magnetic-field assumptions such a system should be extremely rare; a single secure detection, or a radio survey that finds a population of them, would falsify the selection-effect explanation. A complementary test is to measure the initial spin-down-inferred fields of young pulsars whose progenitors' masses are constrained to exceed 20 $M_\odot$; if those fields fall below $10^{14}$ G, the predicted radio silence of heavy binaries disappears.

Watch

Extended reading notes

Core claim

The paper's central claim is that the paucity of massive binary neutron stars in the radio-selected Galactic sample is a consequence of neutron star spin and magnetic field evolution during the high-mass X-ray binary phase. First-born neutron stars in low total-mass binaries experience prolonged Roche-lobe overflow, which recycles them into millisecond pulsars whose radio lifetime can exceed the Hubble time; the observed narrow mass peak near 2.6–2.7 $M_\odot$ therefore reflects what survives as radio-bright. In massive binaries the donor star is heavier than about 20 $M_\odot$, so the newborn neutron star is assumed to be a magnetar with an initial field of $10^{14}$–$10^{15}$ G, which shortens the radio lifetime to about $10^5$ yr and leaves most heavy systems radio-quiet. With the Milky Way's star formation and metallicity history folded in, the model matches the observed $P{-}\dot{P}$ and $P_{\rm orb}{-}e$ diagrams and the total-mass histogram, and yields a merger population at $z\sim0$ with 19–22 percent of systems above 3 $M_\odot$, which the authors take to be compatible with GW170817 and GW190425.

Load-bearing premise

The explanation relies on neutron stars born from stars heavier than 20 solar masses being born with magnetic fields near magnetar strength ($10^{14}$–$10^{15}$ G) that do not decay away before the binary becomes radio-quiet; if those fields are weaker or decay faster, heavy binaries would remain radio-bright and the mass discrepancy would need another explanation.

Editorial extensions

If this is right

  • Radio surveys of the Milky Way should keep seeing recycled-pulsar binaries only below about 3 $M_\odot$; heavy systems like GW190425 should stay radio-silent even if they are intrinsically common.
  • The intrinsic merger population is heavier than the radio-selected Galactic sample suggests: 19–22 percent of binary neutron star mergers at $z\sim0$ exceed 3 $M_\odot$.
  • A sample of roughly 60–100 additional Galactic binary neutron stars should sharpen the bimodal mass distribution and directly test whether the selection effect explains the missing heavy systems.
  • Radio-detectable Galactic binary neutron stars should be dominated by single recycled pulsars paired with radio-quiet neutron stars, with pulsar-pulsar binaries making up only about 3.7 percent of the detectable population.

Reading between the lines

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

  • If the model is right, third-generation gravitational-wave detectors should see a high-mass tail in the merger mass distribution that radio-selected Galactic samples will never fully reproduce, making the two observables complementary probes of the same population.
  • The same mass-dependent recycling logic may apply to other compact binaries, so any radio-versus-gravitational-wave mass discrepancy in future data could be a sign of selection rather than of new formation physics.
  • A targeted test is to measure magnetic fields of young pulsars whose natal progenitors can be shown, through kinematics or association, to have been more massive than 20 $M_\odot$; a field distribution that does not extend to $10^{14}$–$10^{15}$ G would weaken the heavy-binary radio invisibility.
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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 presents a binary population synthesis model, based on a modified BSE code, that follows the spin evolution of the first-born neutron star through the high-mass X-ray binary phase and uses the resulting radio lifetimes to construct the present-day population of Galactic binary neutron stars with pulsar components. The authors argue that low-total-mass BNSs (Mtot around 2.6–2.7 \(M_\odot\)) are typically recycled into long-lived millisecond pulsars, whereas high-mass BNSs (Mtot above about 3 \(M_\odot\), such as GW190425) retain strong magnetic fields and have short radio lifetimes, so they are largely absent from radio surveys. The model is compared with the observed P–Pdot, Porb–e, and total-mass distributions of the roughly 19 measured Galactic BNSs and is claimed to match them well, and it predicts that 19–22% of BNSs merging at redshift zero have Mtot > 3 \(M_\odot\). The paper also discusses sensitivity to the wind velocity law, the subsonic accretion model, and the neutron star equation of state.

Significance. The paper addresses a genuine and timely puzzle: the mass discrepancy between radio-detected Galactic BNSs and the gravitational-wave events GW170817 and GW190425. Its strengths include a detailed treatment of multiple accretion and spin-down phases, the use of observationally motivated star formation and metallicity enrichment histories for the Milky Way, and explicit sensitivity tests for the wind prescription, the subsonic accretion mechanism, and the EOS. The prediction that about 19–22% of z=0 BNS mergers have Mtot > 3 \(M_\odot\) is falsifiable with future gravitational-wave observations, and the proposed mechanism (progenitor-mass-dependent initial fields plus accretion-induced field decay) is physically plausible. However, the central selection-effect conclusion currently rests on a small number of unvaried assumptions, and the claimed agreement with observation is not quantified statistically, so the result should be viewed as promising rather than firmly established.

major comments (3)
  1. [Section 2.2.3, Eq. (30), and Section 4] The central claim that high-Mtot BNSs are radio-quiet depends on two assumptions that are not varied in the robustness tests of Section 4: (i) neutron stars from ZAMS stars with M >= 20 \(M_\odot\) are assigned a uniform initial magnetic field of 1e14–1e15 G rather than the log-normal distribution (mean 1e13 G) used for lower-mass progenitors, and (ii) the magnetic-field decay timescale during accretion is td = 1e6 yr. A concrete test shows the issue: if the same log-normal initial field is used for all neutron stars, Eq. (30) gives B ~ 2e11 G after 4 Myr of accretion, Eq. (29) gives an equilibrium spin period near 0.1 s, and the death-line crossing time from Eq. (11) is on the order of 100 Myr, so heavy BNSs would be radio-visible for a substantial fraction of a Hubble time and the observed absence of Mtot > 3 \(M_\odot\) radio BNSs would not be reproduced. Since the radio/GW mass split is the paper's main result, the authors should repeat the population synthesis with these alternatives, or provide a quantitative justification for why the bimodal initial-field and fast-decay assumptions are necessary.
  2. [Section 3.2, Figs. 6 and 7] The manuscript repeatedly states that the model 'can well match' the observed P–Pdot, Porb–e, and total-mass distributions, but this is based on visual inspection with only ~19 observed systems and no statistical test (e.g., a two-sample Kolmogorov–Smirnov or Anderson–Darling test) is reported. Because the model produces thousands of synthetic pulsar-bearing BNSs, such tests on the relevant marginals are feasible and would give a quantitative measure of agreement. Without them, the 'well match' language is stronger than the evidence supports, especially given the small observed sample and the acknowledged neglect of radio selection effects.
  3. [Section 3.2 and Section 4] The paper explicitly sets aside beaming, radio luminosity, and survey selection, treating every neutron star with P < P_death (Eq. (11)) as equally observable. For the central argument that the radio-selected sample is biased against high-Mtot BNSs, the relevant quantity is not radio lifetime alone but lifetime multiplied by beaming fraction and by the luminosity/selection probability. If beaming or luminosity correlate with spin period or magnetic field—as is observed for recycled versus young pulsars—the relative detectability of low- and high-mass systems could change, potentially altering the conclusion. The authors should include a simple beaming/luminosity prescription as a sensitivity test, or demonstrate explicitly that the lifetime effect dominates over plausible variations of these factors.
minor comments (6)
  1. [Section 5] The first paragraph of the conclusions refers to the 'P – e diagram,' but this should be the 'P_orb – e diagram.'
  2. [Section 4] The phrase 'in the the cases C and D' contains a duplicated article and should read 'in the cases C and D.'
  3. [Section 2.2.3] The author name in 'Os lowski et al. (2011)' has an erroneous space and should be 'Osłowski et al. (2011).'
  4. [Section 3.1] The abbreviation 'HXMB' appears in several places (e.g., 'the HXMB stage') and should be 'HMXB.'
  5. [Section 2.2] The definitions of R_mag,1 and R_mag,2 are written with ambiguous parentheses; for example, 'R_mag,1 = (µ^2/2 ẌM √2GMNS)^(2/7)' should be typeset as [µ^2 / (2 ẌM √(2 G M_NS))]^(2/7).
  6. [Section 4] In the sentence citing the star formation and metallicity enrichment history, the citation to Licquia & Newman (2015) is misplaced because that work provides the total stellar mass of the Milky Way, not the SFH; please adjust the citation or the attributions.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the mass-dependent radio-lifetime result is an explicit model consequence of an externally anchored initial-field assumption, not a fitted or self-citational prediction.

full rationale

The paper's derivation chain is a forward population-synthesis calculation. The initial magnetic field for low-mass progenitors is taken from isolated-pulsar constraints (Faucher-Giguère & Kaspi 2006; Igoshev & Popov 2013), and for massive progenitors from the magnetar catalog (Olausen & Kaspi 2014; Esposito et al. 2021). These are external benchmarks, not quantities fitted to the Galactic BNS mass distribution that the paper seeks to explain. The conclusion that high-mass BNSs are radio-quiet follows from the §2.2.3 assumption that NSs from M ≳ 20 M☉ progenitors are born with B_ini ~ 10^14–10^15 G together with the short HMXB phase; this is an explicit assumption-dependent model result, which is a robustness concern rather than circularity. The P–Pdot, Porb–e, and total-mass comparisons in Figures 6–7 are forward outputs compared with observed samples, not fits to those samples. The choice α_CE = 3 is calibrated to the Galactic BNS merger rate, but the paper does not present that rate as a prediction, and the mass-fraction results are not reducible to this calibration. The code is based on the authors' earlier BSE paper (Chu et al. 2022), but the spin-evolution implementation is described and tested here; this is routine self-citation and is not load-bearing for the central claim. Section 4 itself notes that telescope selection effects and small-number statistics are not fully modeled, but these caveats weaken the comparison without making it circular. No equation or parameter in the claimed derivation chain is equivalent to the predicted output by construction.

Assumptions & free parameters 8 free parameters · 9 assumptions · 0 invented entities

The central claim rests on a web of adopted recipes rather than a fundamental derivation. The key free inputs are the initial magnetic field distribution, especially magnetar-strength fields for massive progenitors, the field decay timescale, and the calibrated common-envelope efficiency. The P-Pdot comparison is an output of these choices, but the specific high-mass radio-quiet conclusion is not fitted to the observed binary neutron stars.

free parameters (8)
  • Common envelope efficiency alpha_CE = 3
    Chosen because the population synthesis model 'can best reproduce the BNS merger rate in our Galaxy' (Section 2.1). Shapes orbital periods and merger delay times.
  • Stellar wind velocity exponent beta = 1
    Sets wind acceleration and hence Bondi radius and accretion rate; the paper explores beta=4 and 7 in Section 4.
  • Initial magnetic field of NSs from M<20 Msun progenitors = log-normal mean 13, scatter 0.55 dex
    Adopted from isolated pulsar constraints; controls recycling efficiency of low-mass binary neutron stars.
  • Initial magnetic field of NSs from M>20 Msun progenitors = uniform 10^14 to 10^15 G
    Assumed magnetar fields; directly drives the short radio lifetimes of high-mass binary neutron stars, which is the central selection effect.
  • Magnetic field decay timescales = 10^6 yr when accreting, 10^9 yr otherwise
    Accretion-induced field burial is a key assumption for producing recycled millisecond pulsars; if wrong, the P-Pdot distribution changes.
  • Initial spin period P0 = 0.01 s
    Imposed for all newly born neutron stars; the authors state that varying it has little effect on final results.
  • Subsonic settling accretion torque factor K = 40
    Non-dimensional factor in Eq. 23, adopted from Popov and Turolla (2012); affects the equilibrium spin in the subsonic accretion phase.
  • Natal kick dispersions = 30 km/s for ECSN and USSN, 265 km/s for CCSN
    Adopted from Vigna-Gomez et al. (2018) and Hobbs et al. (2005); determines survival of binary neutron stars and their orbital eccentricities.
assumptions (9)
  • domain assumption The BSE code (Hurley et al. 2000, 2002) with modifications correctly tracks stellar and binary evolution, including mass loss, mass transfer, and common envelope phases.
    All population synthesis results inherit the accuracy of this code; referenced in Section 2.1.
  • domain assumption Initial binary population follows the adopted IMF, uniform mass ratio, separation distribution, and circular orbits.
    Section 2.1; these are standard but unverified choices that affect which systems become binary neutron stars.
  • domain assumption The spin-evolution phase recipes from the HMXB literature apply to neutron stars during binary neutron star formation.
    Section 2.2; every phase transition and torque formula is taken from prior HMXB studies and assumed transferable.
  • domain assumption Radio quietness is set by the death line P_death = sqrt(B / (1.7e11 G)) s.
    Eq. 11; the paper notes that some pulsars violate this criterion, so it is a simplified threshold.
  • domain assumption Magnetic fields decay exponentially with timescales 10^6 yr when accreting and 10^9 yr otherwise.
    Section 2.2.3; central for whether low-mass binary neutron stars can become millisecond pulsars.
  • domain assumption Case BB mass transfer is always stable and removes the whole helium envelope.
    Section 2.1, following Vigna-Gomez et al. (2018) and Riley et al. (2022); drives formation of short-period recycled systems.
  • domain assumption Milky Way star formation and metallicity histories are those of Ferreras et al. (2003) for the bulge and Snaith et al. (2014) for the disc, with the stated total stellar masses.
    Sections 2.1 and 3.2; the inferred surviving binary neutron star population scales with these histories.
  • standard math Peters (1964) equations govern gravitational wave driven orbital decay and merger times after binary neutron star formation.
    Section 2.3; standard result.
  • domain assumption Neutron star moment of inertia is I = 0.4 M R^2 and the radius-mass relation is from the chosen EOS with spin ignored.
    Section 2.1; simplification stated by the authors.

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Pith. "Pith review of Spin evolution and mass distribution of the Galactic Binary Neutron Stars." pith.science (2026). https://pith.science/paper/HLNILC5V

@misc{pith2026241215464,
  author       = {Pith},
  title        = {Pith review of: Spin evolution and mass distribution of the Galactic Binary Neutron Stars},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HLNILC5V}},
  note         = {Machine review of arXiv:2412.15464}
}
abstract

Binary neutron stars (BNSs) detected in the Milky Way have the total masses distributing narrowly around $\sim2.6-2.7M_\odot$, while the BNS merger GW190425 detected via gravitational wave has a significantly larger mass ($\sim3.4M_\odot$). This difference is not well understood, yet. In this paper, we investigate the BNS spin evolution via an improved binary star evolution model and its effects on the BNS observability, with implementation of various relevant astrophysical processes. We find that the first-born neutron star component in low-mass BNSs can be spun up to millisecond pulsars by the accretion of Roche-lobe overflow from its companion and its radio lifetime can be comparable to the Hubble time. However, most high-mass BNSs have substantially shorter radio lifetime than the low-mass BNSs, and thus smaller probability being detected via radio emission. Adopting the star formation and metal enrichment history of the Milky Way given by observations, we obtain the survived Galactic BNSs with pulsar components from our population synthesis model and find that their distributions on the diagrams of spin period versus spin-period-time-derivative ($P-\dot{P}$) and orbital period versus eccentricity ($P_{\rm orb}-e$) can well match those of the observed Galactic BNSs. The total mass distribution of the observed Galactic BNSs can also be matched by the model. A significant fraction ($\sim19\%-22\%$) of merging BNSs at redshift $z\sim0$ have masses $\gtrsim3M_\odot$, which seems compatible with the GW observations. Future radio observations may detect many more Galactic BNSs, which will put strong constraint on the spin evolution of BNSs during their formation processes.

Figures

Figures reproduced from arXiv: 2412.15464 by the authors.

Figure 1
Figure 1. A flow chart for the spin evolution of BNSs. are relatively large in value, resulting in large spin pe￾riod of the neutron star. If there is a significant differ￾ence in mass between the input binary components (i.e., a smaller mass ratio) and the total mass is relatively low, the HMXB exists for a longer time duration and at the end of the HMXB state, the magnetic field declines sig￾nificantly. In this way, the fir… view at source ↗
Figure 2
Figure 2. Spin evolution of the two neutron star components of a binary system, in which the first-born neutron star experienced wind-fed accretion during the HMXB stage. The finally formed BNS has a total mass of Mtot ∼ 2.6 M⊙, similar to those Galactic BNSs. The total evolution period of the HMXB (from first SN to second SN) is ∼ 11 Myr, and the initial and the final orbital periods of the HMXB are Porb,i ∼ 53.3 day and Por… view at source ↗
Figure 3
Figure 3. Legend is similar to [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Legend is the same as that for [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Legend is the same as that for [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: The P −P˙ diagram (left panel) and the orbital period-eccentricity (Porb−e) diagram (right panel) for survived BNSs with pulsar components in the Milky Way at the present time obtained from our population synthesis model. The red and green stars represent the pulsar-pu…
Figure 7
Figure 7. Figure 7: The probability density functions (PDFs) of the BNS total mass for the survived BNSs with pulsar compo￾nents at z = 0 in the Milky Way obtained from the pop￾ulation synthesis model, and those from observations. The red histogram shows the results of the survived BNSs w…
Figure 8
Figure 8. Figure 8: The spin evolution tracks of the first-born neutron star in the HMXB stage for four example BNSs with different wind velocity prescriptions. The black, blue, and red lines represent the results obtained by choosing the wind velocity prescription described by Eq. (2) wi…
Figure 9
Figure 9. Figure 9: The spin evolution tracks of the first-born neutron star in the HMXB stage for four example BNSs obtained by choosing two different accretion mechanisms at M <˙ M˙ c2. The black and red lines represent the results obtained by adopting the subsonic settling accretion me…
Figure 10
Figure 10. Figure 10: The spin evolution tracks of the first-born neutron star in the HMXB stage for four example BNSs by using different EOSs. The black and red lines represent the results obtained by adopting the DD2 EOS and the SLy4 EOS, respectively. Panels from left to right show the …
Figure 11
Figure 11. Figure 11: The probability density functions of the BNS total mass of different formation channels. The black line shows the result of all BNSs formed in the population syn￾thesis model. The red, cyan, green, and blue lines show the results obtained from the CCSN + CCSN, CCSN + …

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Pith tools

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