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REVIEW 2 major objections 5 minor 45 references

If the short radio period is the orbit and the long period is a spin-orbit beat, the two clocks must drift together at a measurable rate.

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2026-07-12 22:02 UTC pith:ANPHZMOF

load-bearing objection Clean, falsifiable timing relation for the WD–WD LPT channel; the only real soft spot is the a-priori period identification the authors already flag. the 2 major comments →

arxiv 2604.11317 v2 pith:ANPHZMOF submitted 2026-04-13 astro-ph.HE

A Falsifiable Timing Test for the Double-White-Dwarf Model of Long-Period Transients

Yejing Zhan , Di Wang , Fa-Yin Wang This is my paper
classification astro-ph.HE
keywords long-period transientsdouble white dwarfsspin-orbit beatorbital timingunipolar inductorgravitational wavesCHIME/ILT J1634+44
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Long-period radio transients show bursts that repeat on timescales of minutes to hours, and some of them look like they come from compact binary systems rather than isolated spinning stars. This paper focuses on sources like CHIME/ILT J1634+44, whose 841-second burst period, 4206-second modulation, and negative period derivative already favor an ultra-compact double white-dwarf binary. The central claim is that those two periods are not free parameters: if the short one is the orbital clock and the long one is the beat between the magnetic white dwarf's spin and the orbit, then gravitational-wave losses, magnetic torques, and tides force the beat period to evolve jointly with both clocks. For J1634-like parameters the predicted beat drift is about 10^{-10} seconds per second, large enough to produce an observed-minus-calculated timing residual of tens of seconds within a year. Measuring the two periods and both derivatives therefore supplies a clean, quantitative test that can confirm or rule out the ultra-compact binary picture without needing a full radio-emission model.

Core claim

In a double white-dwarf model for short-period long-period transients, identifying the burst period with the orbital period and the long modulation with the spin-orbit beat implies that the beat period is algebraically locked to the orbital and spin clocks. Their derivatives must therefore satisfy a linear relation set by gravitational-wave, tidal, and magnetic torques, yielding |Ṗ_b| ~ 10^{-10} s s^{-1} for J1634-like systems—an observed-minus-calculated drift of tens of seconds in one year that is hard to reproduce in isolated-star or less-compact binary scenarios.

What carries the argument

The beat-evolution identity: once Ω_b = |Ω_1 - Ω_0|, the period derivatives are linked by Ṗ_b = ±β^{2} Ṗ_0 ∓ (β ± 1)^{2} Ṗ_1 (Eq. 17), so the modulation is no longer an independent free timescale.

Load-bearing premise

The entire test rests on the identification that the observed 841-second period is exactly the orbital period and the 4206-second modulation is exactly the spin-orbit beat; if either assignment is wrong, the predicted joint drift disappears.

What would settle it

A multi-year timing campaign that measures both the 841 s burst period and the 4206 s modulation period together with their derivatives; if the observed Ṗ_b fails to match the linear relation required by the measured Ṗ_0 and the implied spin derivative, or if no O-C drift of tens of seconds appears after one year, the WD-WD beat model is ruled out for that source.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Near-term monitoring of J1634 and similar short-period LPTs can detect or exclude a beat drift of order 10^{-10} s s^{-1} within one to three years.
  • A confirmed joint drift would favor an ultra-compact WD-WD origin over isolated magnetars or less-compact WD-M-dwarf binaries for those sources.
  • The same systems become multi-messenger targets: their mHz gravitational-wave signals should be detectable by space-based detectors with high signal-to-noise at a few kpc.
  • The test is model-light: it does not require a detailed radio-emission microphysics calculation, only the clock identifications and the torque balance.

Where Pith is reading between the lines

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

  • If the beat drift is measured and matches the prediction, the same data set can be inverted to constrain the primary tidal quality factor and companion mass more tightly than energy-budget arguments alone.
  • Sources that show stable long-period modulation but zero secular Ṗ_b would be natural candidates for isolated or wider-binary channels, sharpening the taxonomic split among LPTs.
  • A non-detection of the expected GW counterpart at the predicted strain would force either a larger distance or a revision of the chirp-mass range, independent of the radio timing test.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. This Letter proposes a falsifiable timing diagnostic for the double-white-dwarf (WD–WD) interpretation of short-period long-period transients (LPTs), motivated by CHIME/ILT J1634+44. Under the identification that the 841 s burst period is the orbital clock P0 and the 4206 s modulation is the spin–orbit beat Pb = 2π/|Ω1 − Ω0|, the authors show that Pb is not independent: its derivative is algebraically coupled to ṖP0 and ṖP1 through gravitational-wave, unipolar-inductor, and tidal torques (Eqs. 12–17). For J1634-like parameters they obtain ṖP0 ∼ −7.7 × 10−12 s s−1 (consistent with the measured value) and |Pḃ| ∼ 10−10 s s−1, implying an O–C drift of tens of seconds in one year. Parameter scans over M2 and Q1 (Fig. 2) indicate that the |Pḃ| scale is robust except in a narrow cancellation window. The paper also sketches beat-modulated visibility geometry and notes a possible mHz GW counterpart.

Significance. If the period identification holds, the work supplies a clean, near-term observational test of an ultra-compact binary origin for J1634-like LPTs: joint measurement of P0, Pb and their derivatives must satisfy the linear relation (17). The prediction is quantitative, falsifiable on year-scale baselines, and rests on standard GW + tidal torque physics rather than a detailed emission model. That combination of minimal assumptions, algebraic coupling, and an explicit O–C forecast is a genuine contribution to the LPT literature and would, if confirmed, strongly favor the WD–WD channel over isolated-star or less-compact binary alternatives.

major comments (2)
  1. The central claim is conditional on the load-bearing identification that the observed 841 s period is exactly the orbital period and the 4206 s modulation is exactly the spin–orbit beat (Eq. 6, Sects. 3–5). The paper already frames the result as a test of that premise, but the manuscript should state more explicitly what would constitute a clean falsification (e.g., a measured Pḃ inconsistent with both branches of Eq. 17 at the predicted |Pḃ| ∼ 10−10 scale, or a stable Pb with no secular drift while ṖP0 remains nonzero). Without that, readers may treat the prediction as model-dependent rather than as a sharp null test.
  2. Sect. 5 and Fig. 2: the cancellation of Pḃ near Q1 ∼ 4 × 106 is acknowledged but not quantified as a prior. A short statement of how narrow that window is in log Q1 (and whether it is disfavored by independent WD tidal constraints) would strengthen the claim that |Pḃ| ∼ 10−10 is generic rather than contingent on avoiding a fine-tuned Q1.
minor comments (5)
  1. Eq. (1) and the definition of α: the geometric factor η and the relative weighting of orbital versus companion-spin contributions are left somewhat schematic; a one-sentence clarification of the fiducial α ∼ 0.2 choice would help.
  2. Fig. 1(b) and Appendix B: the single-to-double burst transition is illustrative; labeling the exact θ1/φ1 offsets used in the orange curves would make the figure reproducible.
  3. Notation: Ωb is used both for the beat frequency that controls visibility and (via ΔΩUI) for the relative motion that sets the EMF; a brief reminder that they are distinct (already noted in Sect. 3) would reduce possible confusion.
  4. Appendix D: the SNR estimate assumes a fixed distance of a few kpc; citing the actual distance constraint (or lack thereof) for J1634 would make the multimessenger claim more precise.
  5. Typographical: occasional spacing issues in units (e.g., “10 −10”) and the duplicated author-affiliation asterisks on the title page should be cleaned.

Circularity Check

0 steps flagged

No significant circularity: conditional algebraic coupling of clocks is derived from independent torque physics, not forced by construction or self-citation.

full rationale

The paper's central claim is explicitly conditional (abstract; Sect. 1; Sect. 4–5): if the observed 841 s burst period is identified with the orbital clock P0 and the 4206 s modulation with the spin-orbit beat Pb = 2π/|Ω1 − Ω0|, then the beat derivative is algebraically tied to the orbital and spin derivatives via Eq. (17), which is simply the differential of the beat definition (Eq. 6). The values of ˙P0 and ˙P1 themselves are obtained from standard, independent torques (GW emission Peters 1964, unipolar-inductor braking, and tidal torques Fuller & Lai 2012) written in Eqs. (12)–(15); these are not fitted to the target ˙Pb. The resulting |˙Pb| ∼ 10^{-10} s s^{-1} (and the associated O–C drift) is therefore a genuine forward prediction under the stated assumptions, robust across the scanned ranges of M2 and Q1 (Fig. 2). The match of the predicted ˙P0 to the measured value is presented only as a consistency check, not as a fit that forces ˙Pb. No equation reduces by construction to a fitted constant, no uniqueness theorem is imported from the authors' prior work, and no load-bearing premise rests on an unverified self-citation. The a-priori clock identification is an assumption of the model (explicitly framed as falsifiable), not a circular step inside the derivation. The paper is therefore self-contained against its external benchmarks.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 0 invented entities

The central claim rests on standard compact-binary torque physics plus a small set of domain assumptions that identify the two observed periods with the orbital and beat clocks and that adopt conventional white-dwarf structure and tidal quality factors. No new particles or forces are introduced; free parameters are scanned and shown not to erase the order-of-magnitude prediction.

free parameters (5)
  • secondary mass M_2 = 0.2 M_⊙ (fiducial)
    Fiducial value 0.2 M_⊙ chosen as a conservative low-mass WD; scanned 0.2-0.4 M_⊙. Affects GW torque and energy budget.
  • primary tidal quality factor Q_1 = 10^7 (fiducial)
    Fiducial 10^7; scanned 10^6-10^8. Controls spin evolution and therefore Ṗ_b.
  • magnetic dipole moment μ = 10^{34} G cm^3
    Set to 10^{34} G cm^3 to match radio luminosity via unipolar-inductor power.
  • effective asynchronism α = ~0.2
    Set ~0.2 from the observed beat offset |Ω_1-Ω_0|≈0.2 Ω_0; enters energy budget.
  • beam geometry angle χ = π/2
    Fiducial π/2 (ECMI-like); changes detailed visibility but not the existence of beat modulation.
axioms (5)
  • domain assumption Gravitational-wave orbital torque given by Peters (1964) formula (Eq. 12).
    Standard result for circular binaries; used without re-derivation in Sect. 4.
  • domain assumption Tidal torque on each WD follows Fuller & Lai (2012) with Love number k_2≃0.1 (Eq. 14).
    Adopted for white-dwarf tidal dissipation; controls Ṗ_1.
  • ad hoc to paper Beat frequency is exactly Ω_b = |Ω_1 - Ω_0| and the observed 4206 s period is that beat (Eq. 6).
    Core identification that turns the modulation into a coupled clock; introduced in Sect. 3.
  • domain assumption Unipolar-inductor EMF and power bounds set by flux-tube twist and vacuum impedance (Eqs. 3-5, App. A).
    Standard circuit model for magnetic WD binaries (Lai 2012; Piro 2012); used only for energy budget, not for the timing relation.
  • domain assumption Primary mass M_1 ≃ 0.8 M_⊙ from optical data; companion is an unmagnetized WD.
    Taken from Bloot et al. (2025); fixes chirp mass and moment of inertia.

pith-pipeline@v1.1.0-grok45 · 18306 in / 3147 out tokens · 29759 ms · 2026-07-12T22:02:33.467919+00:00 · methodology

0 comments
read the original abstract

Long-period transients (LPTs) are a newly identified class of radio sources with burst recurrence times from minutes to hours, and their diversity suggests multiple physical origins. CHIME/ILT J1634+44, with a short period of 841 s, a long-period modulation of 4206 s, and a significant negative period derivative, strongly suggests a binary origin. For such a short-period source, Roche-lobe constraints strongly favor an ultra-compact companion, motivating a double-white-dwarf (WD--WD) interpretation. In this Letter, we show that the WD--WD channel makes a sharp timing prediction: if the burst period is the orbital clock and the long-period modulation is a spin-orbit beat, then the modulation period is not a free timescale. Instead it must evolve jointly with the orbital clock and the spin clock through gravitational-wave losses, magnetic dissipation, and tidal interaction. For CHIME/ILT J1634+44-like parameters, we find that the beat clock drift $|\dot P_b|\sim 10^{-10} \text{ s s}^{-1}$, implying an observed-minus-calculated drift of tens of seconds in one year. Joint measurements of the burst period, modulation period, and their derivatives provide a minimal and falsifiable timing test of an ultra-compact binary origin.

Figures

Figures reproduced from arXiv: 2604.11317 by Di Wang, Fa-Yin Wang, Yejing Zhan.

Figure 1
Figure 1. Figure 1: (a) Schematic illustration of the emission geometry. The emission beam is centered on nˆ e, which is characterized by the specific angle χ. nˆ obs denotes the observer’s line of sight. (b) A fiducial example, motivated by J1634-like timing properties, showing the viewing angle arccos(nˆ e ·nˆ obs) as a function of beat phase. The green shaded region represents the visible condition, i.e., arccos(nˆ e · nˆ … view at source ↗
Figure 2
Figure 2. Figure 2: The dependence of the period evolution on the secondary mass M2 and the primary tidal factor Q1. To test the robustness of our results, we scan the sec￾ondary mass M2 and the primary tidal quality factor Q1, whose fiducial values are set to M2 = 0.2M⊙ and Q1 = 107 in the previous text. We focus on Q1 rather than the secondary asynchronism α or the secondary tidal quality factor Q2, since the latter paramet… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Same as [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

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Works this paper leans on

45 extracted references · 1 linked inside Pith

  1. [1]

    2017, Laser Interferometer Space Antenna, arXiv, doi: 10.48550/arXiv.1702.00786

    Amaro-Seoane, P., Audley, H., Babak, S., et al. 2017, Laser Interferometer Space Antenna, arXiv, doi: 10.48550/arXiv.1702.00786

    Pith/arXiv arXiv doi:10.48550/arxiv.1702.00786 2017

  2. [2]

    L., Rea, N., et al

    Anumarlapudi, A., Kaplan, D. L., Rea, N., et al. 2025, Monthly Notices of the Royal Astronomical Society, 542, 1208, doi: 10.1093/mnras/staf1227 9

    doi:10.1093/mnras/staf1227 2025

  3. [3]

    K., Bassa, C

    Bloot, S., Vedantham, H. K., Bassa, C. G., et al. 2025, Astronomy & Astrophysics, 699, A341, doi: 10.1051/0004-6361/202555131

    doi:10.1051/0004-6361/202555131 2025

  4. [4]

    R., Kilic, M., Prieto, C

    Brown, W. R., Kilic, M., Prieto, C. A., & Kenyon, S. J. 2010, The Astrophysical Journal, 723, 1072, doi: 10.1088/0004-637X/723/2/1072

    doi:10.1088/0004-637x/723/2/1072 2010

  5. [5]

    L., et al

    Caleb, M., Lenc, E., Kaplan, D. L., et al. 2024, Nature Astronomy, 8, 1159, doi: 10.1038/s41550-024-02277-w

    doi:10.1038/s41550-024-02277-w 2024

  6. [6]

    J., & Wadiasingh, Z

    Cooper, A. J., & Wadiasingh, Z. 2024, Monthly Notices of the Royal Astronomical Society, 533, 2133, doi: 10.1093/mnras/stae1813 de Ruiter, I., Rajwade, K. M., Bassa, C. G., et al. 2025, Nature Astronomy, 9, 672, doi: 10.1038/s41550-025-02491-0

    doi:10.1093/mnras/stae1813 2024

  7. [7]

    A., Shin, K., Law, C., et al

    Dong, F. A., Shin, K., Law, C., et al. 2025, The Astrophysical Journal Letters, 988, L29, doi: 10.3847/2041-8213/adeaab

    doi:10.3847/2041-8213/adeaab 2025

  8. [8]

    Walsworth, R. L. 2025, Physical Review D, 111, 044023, doi: 10.1103/PhysRevD.111.044023

    doi:10.1103/physrevd.111.044023 2025

  9. [9]

    2024, The Astrophysical Journal, 967, 24, doi: 10.3847/1538-4357/ad3aef

    Fan, Y.-N., Xu, K., & Chen, W.-C. 2024, The Astrophysical Journal, 967, 24, doi: 10.3847/1538-4357/ad3aef

    doi:10.3847/1538-4357/ad3aef 2024

  10. [10]

    2026, Monthly Notices of the Royal Astronomical Society, 546, doi: 10.1093/mnras/stag146

    Ferrario, L. 2026, Monthly Notices of the Royal Astronomical Society, 546, doi: 10.1093/mnras/stag146

    doi:10.1093/mnras/stag146 2026

  11. [11]

    2024, Physical Review D, 110, doi: 10.1103/PhysRevD.110.083009

    Fiacco, G. 2024, Physical Review D, 110, doi: 10.1103/PhysRevD.110.083009

    doi:10.1103/physrevd.110.083009 2024

  12. [12]

    2012, Monthly Notices of the Royal Astronomical Society, 421, 426, doi: 10.1111/j.1365-2966.2011.20320.x

    Fuller, J., & Lai, D. 2012, Monthly Notices of the Royal Astronomical Society, 421, 426, doi: 10.1111/j.1365-2966.2011.20320.x

    doi:10.1111/j.1365-2966.2011.20320.x 2012

  13. [13]

    B., Edwards, R

    Hobbs, G. B., Edwards, R. T., & Manchester, R. N. 2006, Monthly Notices of the Royal Astronomical Society, 369, 655, doi: 10.1111/j.1365-2966.2006.10302.x

    doi:10.1111/j.1365-2966.2006.10302.x 2006

  14. [14]

    2017, National Science Review, 4, 685, doi: 10.1093/nsr/nwx116

    Hu, W.-R., & Wu, Y.-L. 2017, National Science Review, 4, 685, doi: 10.1093/nsr/nwx116

    doi:10.1093/nsr/nwx116 2017

  15. [15]

    2022, Nature, 601, 526, doi: 10.1038/s41586-021-04272-x

    Hurley-Walker, N., Zhang, X., Bahramian, A., et al. 2022, Nature, 601, 526, doi: 10.1038/s41586-021-04272-x

    doi:10.1038/s41586-021-04272-x 2022

  16. [16]

    J., et al

    Hurley-Walker, N., Rea, N., McSweeney, S. J., et al. 2023, Nature, 619, 487, doi: 10.1038/s41586-023-06202-5

    doi:10.1038/s41586-023-06202-5 2023

  17. [17]

    J., Bahramian, A., et al

    Hurley-Walker, N., McSweeney, S. J., Bahramian, A., et al. 2024, The Astrophysical Journal Letters, 976, L21, doi: 10.3847/2041-8213/ad890e

    doi:10.3847/2041-8213/ad890e 2024

  18. [18]

    D., Lazio, T

    Hyman, S. D., Lazio, T. J. W., Kassim, N. E., et al. 2005, Nature, 434, 50, doi: 10.1038/nature03400

    doi:10.1038/nature03400 2005

  19. [19]

    2020, The Astronomy and Astrophysics Review, 29, 1, doi: 10.1007/s00159-020-00130-3

    Kochukhov, O. 2020, The Astronomy and Astrophysics Review, 29, 1, doi: 10.1007/s00159-020-00130-3

    doi:10.1007/s00159-020-00130-3 2020

  20. [20]

    2023, Journal of Astrophysics and Astronomy, 44, 1, doi: 10.1007/s12036-022-09899-4

    Konar, S. 2023, Journal of Astrophysics and Astronomy, 44, 1, doi: 10.1007/s12036-022-09899-4

    doi:10.1007/s12036-022-09899-4 2023

  21. [21]

    2012, The Astrophysical Journal, 757, L3, doi: 10.1088/2041-8205/757/1/L3

    Lai, D. 2012, The Astrophysical Journal, 757, L3, doi: 10.1088/2041-8205/757/1/L3

    doi:10.1088/2041-8205/757/1/l3 2012

  22. [22]

    Lee, Y. W. J., Caleb, M., Murphy, T., et al. 2025, Nature Astronomy, 9, 393, doi: 10.1038/s41550-024-02452-z

    doi:10.1038/s41550-024-02452-z 2025

  23. [23]

    2016, Classical and Quantum Gravity, 33, 035010, doi: 10.1088/0264-9381/33/3/035010

    Luo, J., Chen, L.-S., Duan, H.-Z., et al. 2016, Classical and Quantum Gravity, 33, 035010, doi: 10.1088/0264-9381/33/3/035010

    doi:10.1088/0264-9381/33/3/035010 2016

  24. [24]

    2021, The Astrophysical Journal, 911, 45, doi: 10.3847/1538-4357/abe62f

    Luo, J., Ransom, S., Demorest, P., et al. 2021, The Astrophysical Journal, 911, 45, doi: 10.3847/1538-4357/abe62f

    doi:10.3847/1538-4357/abe62f 2021

  25. [25]

    F., & Beloborodov, A

    Mahlmann, J. F., & Beloborodov, A. M. 2025, The Astrophysical Journal Letters, 981, L17, doi: 10.3847/2041-8213/adb5fd

    doi:10.3847/2041-8213/adb5fd 2025

  26. [26]

    R., Nelemans, G., & Steeghs, D

    Marsh, T. R., Nelemans, G., & Steeghs, D. 2004, Monthly Notices of the Royal Astronomical Society, 350, 113, doi: 10.1111/j.1365-2966.2004.07564.x

    doi:10.1111/j.1365-2966.2004.07564.x 2004

  27. [27]

    J., Hurley-Walker, N., Horváth, C., et al

    McSweeney, S. J., Hurley-Walker, N., Horváth, C., et al. 2025, Monthly Notices of the Royal Astronomical Society, 542, 203, doi: 10.1093/mnras/staf1203

    doi:10.1093/mnras/staf1203 2025

  28. [28]

    R., & Philippov, A

    Most, E. R., & Philippov, A. A. 2020, The Astrophysical Journal Letters, 893, L6, doi: 10.3847/2041-8213/ab8196

    doi:10.3847/2041-8213/ab8196 2020

  29. [29]

    2013, Nature, 501, 517, doi: 10.1038/nature12470

    Papitto, A., Ferrigno, C., Bozzo, E., et al. 2013, Nature, 501, 517, doi: 10.1038/nature12470

    doi:10.1038/nature12470 2013

  30. [30]

    Peters, P. C. 1964, Physical Review, 136, B1224, doi: 10.1103/PhysRev.136.B1224

    doi:10.1103/physrev.136.b1224 1964

  31. [31]

    Piro, A. L. 2012, The Astrophysical Journal, 755, 80, doi: 10.1088/0004-637X/755/1/80

    doi:10.1088/0004-637x/755/1/80 2012

  32. [32]

    2026, Discovery of a 36-Minute Long-Period Transient ASKAP J142431.2-612611, arXiv, doi: 10.48550/arXiv.2603.07857

    Pritchard, J., Murphy, T., Dobie, D., et al. 2026, Discovery of a 36-Minute Long-Period Transient ASKAP J142431.2-612611, arXiv, doi: 10.48550/arXiv.2603.07857

    doi:10.48550/arxiv.2603.07857 2026

  33. [33]

    2025, The Astrophysical Journal, 981, 34, doi: 10.3847/1538-4357/adb1b5

    Qu, Y., & Zhang, B. 2025, The Astrophysical Journal, 981, 34, doi: 10.3847/1538-4357/adb1b5

    doi:10.3847/1538-4357/adb1b5 2025

  34. [34]

    2026, Journal of High Energy Astrophysics, 52, 100566, doi: 10.1016/j.jheap.2026.100566

    Rea, N., Hurley-Walker, N., & Caleb, M. 2026, Journal of High Energy Astrophysics, 52, 100566, doi: 10.1016/j.jheap.2026.100566

    doi:10.1016/j.jheap.2026.100566 2026

  35. [35]

    2024, The Astrophysical Journal, 961, 214, doi: 10.3847/1538-4357/ad165d

    Rea, N., Hurley-Walker, N., Pardo-Araujo, C., et al. 2024, The Astrophysical Journal, 961, 214, doi: 10.3847/1538-4357/ad165d

    doi:10.3847/1538-4357/ad165d 2024

  36. [36]

    J., & Liu, C

    Robson, T., Cornish, N. J., & Liu, C. 2019, Classical and Quantum Gravity, 36, 105011, doi: 10.1088/1361-6382/ab1101

    doi:10.1088/1361-6382/ab1101 2019

  37. [37]

    2022, The Astrophysical Journal, 934, 184, doi: 10.3847/1538-4357/ac7cec

    Ronchi, M., Rea, N., Graber, V., & Hurley-Walker, N. 2022, The Astrophysical Journal, 934, 184, doi: 10.3847/1538-4357/ac7cec

    doi:10.3847/1538-4357/ac7cec 2022

  38. [38]

    G., Dehman, C., & Pons, J

    Suvorov, A. G., Dehman, C., & Pons, J. A. 2025, The Astrophysical Journal, 991, 134, doi: 10.3847/1538-4357/adfc55

    doi:10.3847/1538-4357/adfc55 2025

  39. [39]

    2025, Nature, 642, 583, doi: 10.1038/s41586-025-09077-w

    Wang, Z., Rea, N., Bao, T., et al. 2025, Nature, 642, 583, doi: 10.1038/s41586-025-09077-w

    doi:10.1038/s41586-025-09077-w 2025

  40. [40]

    J., & Wu, K

    Willes, A. J., & Wu, K. 2004, Monthly Notices of the Royal Astronomical Society, 348, 285, doi: 10.1111/j.1365-2966.2004.07363.x 10

    doi:10.1111/j.1365-2966.2004.07363.x 2004

  41. [41]

    2002, Monthly Notices of the Royal Astronomical Society, 331, 221, doi: 10.1046/j.1365-8711.2002.05190.x

    Wu, K., Cropper, M., Ramsay, G., & Sekiguchi, K. 2002, Monthly Notices of the Royal Astronomical Society, 331, 221, doi: 10.1046/j.1365-8711.2002.05190.x

    doi:10.1046/j.1365-8711.2002.05190.x 2002

  42. [42]

    2024, The Astrophysical Journal, 970, 2, doi: 10.3847/1538-4357/ad5319

    Xu, K., Yang, H.-R., Jiang, L., et al. 2024, The Astrophysical Journal, 970, 2, doi: 10.3847/1538-4357/ad5319

    doi:10.3847/1538-4357/ad5319 2024

  43. [43]

    2017, The Astrophysical Journal, 849, 36, doi: 10.3847/1538-4357/aa8ea2

    Yang, H., Liu, J., Gao, Q., et al. 2017, The Astrophysical Journal, 849, 36, doi: 10.3847/1538-4357/aa8ea2

    doi:10.3847/1538-4357/aa8ea2 2017

  44. [44]

    2026, The Astrophysical Journal, 997, 124, doi: 10.3847/1538-4357/ae2864

    Yang, Y.-P. 2026, The Astrophysical Journal, 997, 124, doi: 10.3847/1538-4357/ae2864

    doi:10.3847/1538-4357/ae2864 2026

  45. [45]

    Zalamea, I., Menou, K., & Beloborodov, A. M. 2010, Monthly Notices of the Royal Astronomical Society: Letters, 409, L25, doi: 10.1111/j.1745-3933.2010.00930.x

    doi:10.1111/j.1745-3933.2010.00930.x 2010