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arxiv: 2505.18702 · v2 · submitted 2025-05-24 · 🌌 astro-ph.HE · astro-ph.SR

Eccentric millisecond pulsar + subdwarf B star from rotationally delayed accretion-induced-collapse scenario

Xiangcun Meng This is my paper

Pith reviewed 2026-05-19 12:56 UTC · model grok-4.3

classification 🌌 astro-ph.HE astro-ph.SR
keywords eccentric millisecond pulsarssubdwarf B starsaccretion-induced collapsebinary population synthesisGalactic birth rateorbital parametersmillisecond pulsar binariesneutron star formation
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The pith

Binary population synthesis within the rotationally delayed accretion-induced collapse scenario predicts eccentric millisecond pulsar plus subdwarf B star systems form at a Galactic rate of 0.67 to 1.5 times 10 to the minus 4 per year.

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

This paper investigates whether the rotationally delayed accretion-induced collapse process that may explain eccentric millisecond pulsar plus helium white dwarf binaries can also produce systems with subdwarf B star companions. The author applies binary population synthesis models to forecast the masses of the pulsar and companion, orbital periods, eccentricities, and the overall formation rate in the Galaxy. A reader would care because the resulting numbers supply specific targets that observers can use to search for these undetected systems and to test ideas about how millisecond pulsars gain their rapid spin and orbital eccentricity. The calculations indicate the systems are young, with ages of a few hundred million years, and that most pulsars in them have masses below 1.5 solar masses. The work extends an existing formation channel to a new companion type without introducing major new physical assumptions.

Core claim

Within the RD-AIC framework, binary population synthesis calculations predict orbital parameters for eccentric MSP + sdB systems and estimate their Galactic birth rate to be (0.67-1.5)×10^{-4} yr^{-1}, with a very conservative upper limit of 15000 systems in the Galaxy. These systems are relatively young with ages on the order of a few hundred Myr and should therefore be found in relatively young environments. Furthermore, most MSPs in such eccentric binaries have masses below 1.5 solar masses, and the most optimistic fraction of eccentric MSP + sdB systems among all MSP + sdB populations could reach up to 55 percent.

What carries the argument

Binary population synthesis calculations that apply the rotationally delayed accretion-induced collapse scenario to binaries containing a neutron star and a subdwarf B companion, tracking the evolution to produce eccentric orbits.

If this is right

  • These systems should appear in relatively young environments because their ages are only a few hundred million years.
  • Most millisecond pulsars in the predicted eccentric binaries have masses below 1.5 solar masses.
  • In the most optimistic case the eccentric systems could make up as much as 55 percent of all MSP plus subdwarf B populations.
  • The systems offer potential applications for testing ideas about binary evolution and millisecond pulsar formation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Targeted searches in regions of recent star formation could improve the chance of detecting these systems.
  • Confirmed detections would provide new tests of the assumptions used in modeling subdwarf B star formation.
  • The upper limit of 15000 systems implies they are rare enough that existing surveys could easily have missed them.
  • The same formation channel might apply to other types of companions not examined in this work.

Load-bearing premise

The rotationally delayed accretion-induced collapse scenario is a viable formation channel for eccentric millisecond pulsar plus helium white dwarf systems and can be extended to subdwarf B companions without major changes to the binary evolution physics.

What would settle it

A large survey of young stellar populations that finds no eccentric MSP + sdB systems or that measures pulsar masses consistently above 1.5 solar masses in any such binaries would contradict the model predictions.

Figures

Figures reproduced from arXiv: 2505.18702 by Xiangcun Meng.

Figure 1
Figure 1. Figure 1: The masses of two components of the eccentric MSP + sdB systems for different initial WD masses. magnetic field is, and then how long its lifetime. I will discuss this further in Section 4. Following Meng & Li (2019), the initial binary systems are ONeMg WD + MS systems, and mass transfer begins when the companions are on the MS or in the Hertzsprung gap (HG) (see also details in Meng & Podsiadlowski 2017)… view at source ↗
Figure 2
Figure 2. Figure 2: Panel (a): Eccentricities vs orbital periods of the systems from the RD-AIC scenario for different initial WD masses, where a sym￾metric collapse is assumed. Panel (b): Distributions of the eccentricities and orbital periods of the post-AIC systems from the pre-AIC systems of [MWD/M⊙, M2/M⊙ log(P/day)]=(1.5063, 0.4958, 0.4128), (1.6829, 0.53‘5, 0.9115), (1.9070, 0.4046, 1.3820) and (2.3358, 0.4101, 1.8727)… view at source ↗
Figure 3
Figure 3. Figure 3: The parameter spaces in (Mi 2 − log P i ) plane for different initial WD masses, in which a ONeMg WD + MS system may lead to an eccentric NS + sdB system via RD-AIC scenario (red lines). The black lines are those for SNe Ia from Meng & Podsiadlowski (2017, 2018) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: The distribution of the initial WD mass (top panel) and the WD mass before AIC (bottom panel) for two values of αCE [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: The evolution of the birth rates, ν, of the eccentric MSP + sdB systems from the RD-AIC scenario for two values of αCE and a constant star formation rate of SFR = 5 M⊙ yr−1 (top panel), or a single starburst of 1011 M⊙ (bottom panel) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: The distributions of WD and sdB masses at the moment of AIC in the MWD-M2 plane, where αCE = 1.0. The basic properties for the case of αCE = 3.0 is similar. 3.3. Distribution of WDs The main different assumptions between this paper and Freire & Tauris (2014) is that the WDs before AIC may be differential rotat￾ing, rather than just rigid rotating, and then the WD before AIC may be more massive than 1.48 M⊙… view at source ↗
Figure 7
Figure 7. Figure 7: Pre-AIC WD mass vs. post-AIC NS mass with an assumption of differ￾ential rotation, symmetric collapse and ejection of baryonic material of 0.02 M⊙ (solid line), or 0.01 M⊙ and 0.03 M⊙ (dotted line), respectively. The stars present observed results, where the symmetric collapse is assumed. Red stars show the systems with precise measurement of NS mass and eccentricity, while the green one shows the results … view at source ↗
read the original abstract

Eccentric millisecond pulsar + helium white dwarf (MSP + He WD) systems have attracted increasing attention, with the rotationally delayed accretion-induced collapse (RD-AIC) scenario proposed as a possible formation channel. Given the similarity between the formation channels of He WDs and subdwarf B (sdB) stars, eccentric MSP + sdB binaries could also exist in the Galaxy, though none have been detected so far. Theoretical predictions of their properties would greatly aid in their discovery. Here, within the RD-AIC framework, I present predictions for their orbital parameters, including MSP mass, secondary mass, eccentricity and orbital period. Based on two detailed binary population synthesis calculations, I estimate their Galactic birth rate to be $(0.67-1.5)\times10^{\rm -4}~{\rm yr^{\rm -1}}$. Then, a very conservative upper limit for their total number in the Galaxy is 15000, implying that the most optimistic fraction of eccentric MSP + sdB systems among all MSP + sdB populations could reach up to 55\%. These systems are relatively young, with ages on the order of a few hundred Myr, and should therefore be found in relatively young environments. Furthermore, most MSPs in such eccentric binaries have masses below 1.5 $M_{\odot}$. I also briefly discuss their potential future applications in various astrophysical context.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes that eccentric MSP + sdB binaries can form via the rotationally delayed accretion-induced collapse (RD-AIC) channel, by direct analogy to the MSP + He WD case. Using two binary population synthesis runs, it predicts distributions for MSP mass, companion mass, eccentricity and orbital period, and derives a Galactic birth rate of (0.67–1.5)×10^{-4} yr^{-1} together with a conservative upper limit of 15 000 systems (corresponding to an optimistic 55 % fraction among all MSP + sdB systems). The systems are stated to be young (∼few × 100 Myr) and to host MSPs predominantly below 1.5 M_⊙.

Significance. If the RD-AIC framework can be extended to sdB companions without substantial revision of the binary-evolution physics, the work supplies concrete orbital-parameter predictions and a birth-rate estimate that can directly inform targeted radio and optical searches. The emphasis on young ages and sub-1.5 M_⊙ MSPs offers falsifiable guidance for population studies and potential applications in gravitational-wave or timing-array contexts.

major comments (2)
  1. [Binary population synthesis calculations (results section)] The central birth-rate interval (0.67–1.5)×10^{-4} yr^{-1} and the 15 000-system upper limit rest on the assumption that the RD-AIC delay, common-envelope phase, and post-AIC orbital evolution remain unchanged when the companion is an sdB star rather than a He WD. The manuscript invokes similarity of formation channels but does not present explicit sensitivity tests or additional runs that vary the envelope-stripping efficiency or the timing of the AIC relative to sdB core-helium ignition. This assumption is load-bearing for the quantitative results.
  2. [Binary population synthesis calculations] The two population-synthesis calculations adopt standard values for common-envelope efficiency and supernova-kick dispersion, yet no table or figure quantifies how the predicted birth rate changes when these parameters are varied within the ranges used for the parent He-WD study. Because the output numbers inherit those choices, the quoted range cannot be regarded as robust without such a variation study.
minor comments (2)
  1. [Results] The abstract states that 'most MSPs in such eccentric binaries have masses below 1.5 M_⊙' but the corresponding histogram or cumulative distribution is not referenced by figure number in the text.
  2. [Throughout] Notation for the sdB mass and the post-AIC orbital period should be defined once at first use and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Binary population synthesis calculations (results section)] The central birth-rate interval (0.67–1.5)×10^{-4} yr^{-1} and the 15 000-system upper limit rest on the assumption that the RD-AIC delay, common-envelope phase, and post-AIC orbital evolution remain unchanged when the companion is an sdB star rather than a He WD. The manuscript invokes similarity of formation channels but does not present explicit sensitivity tests or additional runs that vary the envelope-stripping efficiency or the timing of the AIC relative to sdB core-helium ignition. This assumption is load-bearing for the quantitative results.

    Authors: We agree that the quantitative predictions rely on the assumption of similarity between the sdB and He WD channels. The manuscript explicitly frames the sdB case as a direct extension of the RD-AIC scenario already validated for He WDs, based on the shared binary-evolution physics of envelope stripping and AIC. No dedicated sensitivity runs varying envelope-stripping efficiency or AIC timing relative to core-helium ignition were performed for the sdB case in the present work. In revision we will add a new subsection that discusses the expected impact of these parameters, drawing on the ranges already explored in the parent He-WD study, together with a qualitative assessment of how they would affect the quoted birth-rate interval. revision: yes

  2. Referee: [Binary population synthesis calculations] The two population-synthesis calculations adopt standard values for common-envelope efficiency and supernova-kick dispersion, yet no table or figure quantifies how the predicted birth rate changes when these parameters are varied within the ranges used for the parent He-WD study. Because the output numbers inherit those choices, the quoted range cannot be regarded as robust without such a variation study.

    Authors: We acknowledge that the manuscript does not include an explicit variation study for common-envelope efficiency and supernova-kick dispersion. The two calculations employ the same standard parameter set used in the parent He-WD study precisely to enable a direct comparison of the sdB extension. To address the referee’s concern, the revised manuscript will contain an additional table (or figure) that reports the birth-rate range obtained when these parameters are varied across the intervals adopted in the He-WD reference work. This will make the dependence on those choices transparent and will allow readers to assess the robustness of the (0.67–1.5)×10^{-4} yr^{-1} interval. revision: yes

Circularity Check

0 steps flagged

No significant circularity in orbital predictions or birth-rate estimates

full rationale

The paper computes orbital parameters and a Galactic birth rate of (0.67-1.5)×10^{-4} yr^{-1} via two binary population synthesis runs inside the RD-AIC framework, treating the extension from He WD to sdB companions as a modeling assumption based on channel similarity. These outputs are simulation results driven by standard binary-evolution inputs rather than any redefinition, renaming, or statistical forcing of the target quantities back into the inputs. No quoted step equates a claimed prediction to a fitted parameter or reduces the central result to a self-citation chain whose validity is presupposed by the present work. The derivation therefore remains externally falsifiable by future detections and does not exhibit any of the enumerated circular patterns.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on the assumption that the RD-AIC channel operates for sdB companions in the same way as for He WDs, plus standard binary evolution physics whose parameters are taken from prior literature. No new particles or forces are introduced.

free parameters (2)
  • Common-envelope efficiency
    Standard parameter in binary population synthesis that controls orbital shrinkage during envelope ejection; its value is chosen to match observed populations and directly affects the predicted birth rate.
  • Supernova kick velocity distribution
    Parameter controlling the eccentricity imparted at neutron-star formation; tuned to reproduce observed MSP binaries and therefore influences the eccentric fraction.
axioms (2)
  • domain assumption The rotationally delayed accretion-induced collapse scenario is a physically viable formation channel for eccentric MSP systems.
    Invoked as the framework for all calculations; the paper does not re-derive or observationally validate the scenario itself.
  • domain assumption Binary population synthesis codes accurately capture the relevant mass-transfer and common-envelope phases for sdB formation.
    Underlying assumption of the two detailed calculations used to derive birth rates and orbital distributions.

pith-pipeline@v0.9.0 · 5778 in / 1678 out tokens · 35894 ms · 2026-05-19T12:56:28.822492+00:00 · methodology

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