Pith. sign in

REVIEW 6 minor 1 cited by

Gravitational waves from primordial black holes passing by neutron stars: observational prospects for the Galactic center

T0 review · 0 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A 10-year search with current gravitational-wave detectors would have less than a one-in-a-hundred-million chance of catching a primordial black hole grazing a neutron star in the Galactic center, and even repeated periastron bursts from bo

desk verdict A solid, honest null result: PBH-NS GW bursts from the Galactic center are effectively undetectable at current sensitivity, and the bound-channel subdominance is robust. read the letter →

arxiv 2602.23429 v2 pith:DU23EEIF submitted 2026-02-26 astro-ph.HE

Nicolas Esser , Juan García-Bellido , Peter Tinyakov This is my paper
classification astro-ph.HE
keywords primordialblackholesneutronstarsgravitationalwavesGalacticcenterdarkmattereccentricorbitsburstsignalsdetectionprobability
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 tries to establish that gravitational-wave bursts from planetary-mass primordial black holes passing near neutron stars in the Galactic center are effectively undetectable with current detectors over a decade. It computes the probability of detecting at least one such burst from both unbound encounters and bound eccentric pairs, finding P ≲ 10⁻⁸ in both cases, with bound pairs subdominant despite many repeated periastron passages. A sympathetic reader would care because it quantifies whether this dark-matter probe is viable, concluding it is not with present sensitivity, though unbound grazing encounters remain the most promising channel.

What carries the argument

The key object is the highly eccentric orbit characterized by periastron distance r_p, where each periastron passage generates a GW burst with strain set by the parabolic-limit power spectrum. Detection requires SNR > 10 in current detector sensitivity; the rate calculation uses the direct-capture injection rate of bound orbits, the energy loss per passage (GW emission for r_p > R, dynamical friction for r_p < R), the resulting inspiral time via a Hurwitz zeta function, and a Poisson probability that at least one burst falls in the observation window.

What would settle it

A single unambiguous gravitational-wave burst from the Galactic center with a waveform consistent with a ~10⁻⁴ solar-mass primordial black hole grazing a neutron star, or a series of repeating bursts from one sky location with a decaying orbital period, would falsify the claim that the detection probability is below 10⁻⁸.

Watch

Extended reading notes

Core claim

The central claim is that GW emission from PBH–NS systems in the Galactic center yields a detection probability below 10⁻⁸ over 10 years with current sensitivity, and that the repeated-burst nature of bound eccentric PBH–NS pairs does not make them the dominant signal; unbound grazing encounters dominate. This follows from combining a SNR > 10 threshold with the injection rate of bound orbits, energy loss via gravitational radiation and dynamical friction, inspiral times, and a steady-state population calculation.

Load-bearing premise

The load-bearing premise is that a detection requires a single periastron burst with SNR greater than 10; if multiple bursts from the same bound pair can be combined to pass threshold, the bound-channel detection probability could be much higher.

Editorial extensions

If this is right

  • Current gravitational-wave detectors will not see PBH–NS bursts from the Galactic center within a decade; searches should not expect them.
  • The repeated-burst channel does not improve detection odds; bound PBH–NS pairs are subdominant to unbound encounters.
  • The most promising scenario remains unbound encounters with periastron distances of about 1000 km, and even those have a per-decade probability near 10⁻⁸.
  • Future detectors with roughly an order-of-magnitude sensitivity improvement still leave the detection probability below O(1) for the inner parsec, so PBH–NS bursts are not a promising near-term probe.
  • Indirect population effects, such as pulsar destruction or r-process enhancement, may be better routes to probing planetary-mass PBHs than direct GW detection.

Reading between the lines

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

  • If repeated bursts from a bound pair were coherently or incoherently stacked, the effective SNR for late-inspiral systems could exceed the single-burst threshold, potentially raising the bound-channel detection probability and reversing the subdominance conclusion.
  • The calculation assumes a uniform dark-matter density and a fixed neutron-star population; if PBHs are clustered around neutron stars or a dark-matter spike is steeper than assumed, the rate could be boosted by orders of magnitude, though the paper estimates even that is insufficient.
  • The same rate machinery could be applied to other compact-object targets, such as white dwarfs or the Galactic bulge rather than the center, possibly shifting the optimal PBH mass window.
  • A search strategy that explicitly targets correlated series of subthreshold bursts with matched filtering could test the bound-channel prediction even if single bursts are below the nominal detection threshold.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

0 major / 6 minor

Summary. The paper computes the rate and 10-year detection probability of gravitational-wave bursts from planetary-mass primordial black holes interacting with neutron stars in the Galactic center, under LVK O4 sensitivity. Three channels are considered: unbound hyperbolic encounters (Eq. 2), bound systems losing energy through dynamical friction during NS crossings (Eqs. 9, 15, 16), and bound systems evolving by GW emission with repeated periastron bursts (Eqs. 8, 17, 18). Bound-system formation is modeled by two-body capture (Eq. 7) with a Gould-corrected Press-Spergel injection rate, and the maximum bound apastron is limited to r_c ~ 350 AU by stellar perturbations (§IV D). The central result is that the probability of detecting at least one signal in 10 years is P ≲ 10^-8, and that unbound encounters dominate over the repeated-burst bound channel. The authors conclude that this channel is unlikely to be observable with current instruments and remains below O(1) even under optimistic DM-spike and Einstein Telescope assumptions.

Significance. If correct, the paper provides a quantitative negative result for a previously under-explored PBH detection channel and identifies the unbound-encounter channel as the most promising among the three. The calculation is a forward model with no fitted parameters: the injection rate, energy-loss formulas, and inspiral times are taken from external references, and the paper gives transparent scaling relations (e.g., SNR ∝ m/d, N_DF ∝ 1/m). The authors deliberately use optimistic assumptions — f_PBH = 1, all Milky Way NSs placed at the Galactic center, and a square-well PSD — so that errors in the optimistic direction only strengthen the conclusion that the detection probability is small. The explicit comparison of bound versus unbound channels and the treatment of correlated repeated bursts are useful contributions. The main qualitative claim appears robust.

minor comments (6)
  1. [§V.B, Eq. (17) and following text] In the n_c → 0 limit, Eq. (17) gives P_S = 1 because the ζ term equals t_ins, whereas the text states that P_S → t_obs/t_ins and that Eq. (18) recovers Eq. (15). These statements are mutually inconsistent. The affected short-lifetime region is plausibly negligible for the final numbers, but the equation/prose should be corrected and the numerical impact of the mismatch stated explicitly.
  2. [§V.A, Eq. (16)] Eq. (16) is written without the SNR>10 detection criterion. The paper assumes SNR is constant at its r_p=R value for r_p<R, so Eq. (16) should be restricted (e.g., by a step function θ(SNR(R)-10)) or the text should clarify that Fig. 3 applies this threshold. Otherwise the DF curve in Fig. 3 is not directly obtained from Eq. (16).
  3. [§V, after Eq. (18)] The statement that PBHs starting with r_p > 1000 km and later entering the detectable band contribute negligibly is not supported by any displayed estimate. Since this approximation justifies restricting the GW-channel integration to initial r_p ≤ 1000 km, please provide the estimate or a concise bounding argument, either in the text or in a short appendix.
  4. [§II, caption of Fig. 1 and text] ‘Power Spectral Distribution’ should be ‘Power Spectral Density’ (PSD). Also, the repeated spacing in ‘L VK’ appears to be a typographical artifact; use ‘LVK’.
  5. [§VI, first paragraph] The abstract and §VI use slightly different phrasings for the same result: ‘P ≲ 10^-8’ versus ‘P ∼ 10^-8’. Please make these consistent, since the latter could be read as a larger central value.
  6. [§II, Eq. (5) and Fig. 2] The square-well PSD approximation and the parabolic-limit power spectrum (Eq. 4) are coarse approximations; the paper should state explicitly how much error these introduce in the SNR threshold, e.g., by comparing with a full PSD integral for one representative case.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: detection probabilities follow from a forward calculation with independently cited inputs; self-citations are supporting but not load-bearing.

full rationale

The paper's central claims—the extremely small detection probability P≲10^-8 and the subdominance of bound PBH-NS signals—are obtained by a forward calculation from the injection rate (Eq. 7, based on Press & Spergel with Gould's correction), the GW power spectrum (Eq. 4, from Berry & Gair), the inspiral-time formula (Eq. 11, a standard Hurwitz-zeta expression), and the SNR>10 detection criterion. No parameter is fitted to the target detection probability, and no predicted quantity is defined in terms of the result it is supposed to predict. Several cited inputs are from the authors' own prior work (e.g., the stellar-perturbation limit r_c≈350 AU from [34] and the static-perturber cross-check from [28]), but these serve as supporting estimates for an integration cutoff whose precise value is not decisive for the overall conclusion; the alternative value from [28] is only a factor of ~3 larger and the rates are dominated by the lower integration bound. The n_c→0 limiting statement in Sec. V B has an internal wording inconsistency (Eq. 17 actually gives P_S→1 while the text says P_S→t_obs/t_ins), but this is a consistency issue in a negligible parameter region, not a circular definition or a fit disguised as a prediction. The derivation is therefore self-contained in the sense relevant for circularity analysis.

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

The paper introduces no new physical entities. It relies on established gravitational-wave and dynamical-friction formulas, plus several simplified astrophysical models for the NS interior, stellar perturbations, and Galactic-center environment. The most consequential free parameter is the implicit f_PBH=1, which converts the quoted P into an upper bound.

free parameters (6)
  • f_PBH = 1 (implicit)
    The PBH dark-matter fraction enters n_PBH linearly (Eq. 2) and is never explicitly set in the abstract or figure captions; the reported P≲1e-8 corresponds to f_PBH=1. Existing constraints exclude this for m~1e-4 Msun, so the quoted probability is an upper bound.
  • rho_DM = 10 GeV/cm^3
    Fiducial DM density in the Galactic center used for all rates (Sec. VI); the true density is uncertain and could be higher in the inner parsec, which would raise P proportionally.
  • vbar = sqrt(2)*200 km/s
    Velocity dispersion of PBHs/NSs; enters the capture rate as 1/vbar^3 (Eq. 7) and the unbound rate as 1/vbar (Eq. 2).
  • N_NS = 1e9
    Total number of neutron stars in the Milky Way, all placed at the Galactic center; this is an optimistic upper bound.
  • r_c = 350 AU
    Maximum apastron for bound orbits set by stellar perturbations (Sec. IV D); chosen independent of r_p though it varies between 300 and 440 AU.
  • ln Lambda = 10
    Coulomb logarithm in dynamical friction, Eq. (9); chosen as ln(M/m) for the typical mass ratio.
assumptions (6)
  • domain assumption Press-Spergel phase-space capture rate (Eq. 6) with the Gould factor-2 correction is the correct injection rate for PBHs onto bound orbits.
    Used in Sec. III to derive Eq. (7). External result from Press & Spergel (1985), corrected by Gould (1987); it assumes a Maxwellian velocity distribution and two-body capture.
  • domain assumption The GW power spectrum for parabolic orbits (Berry & Gair Eq. 23) approximates the emission of highly eccentric bound orbits.
    Used in Sec. II to compute SNR (Eq. 4). The paper states this is an estimate because most contributing orbits are very eccentric.
  • ad hoc to paper Dynamical friction on a uniform-density NS with the PBH crossing length ~2R at escape velocity gives the energy loss of Eq. (9).
    Simplified model in Sec. IV B; ignores density gradients, magnetic fields, and velocity dependence along the trajectory.
  • domain assumption Stellar perturbations in the inner kpc (density 10 pc^-3, dispersion 200 km/s) limit bound apastrons to r_c ~350 AU via the impulse approximation.
    Sec. IV D; uses Eq. (17) of Esser (2025). The opposite static-perturber limit gives r_c~1100 AU, a factor 3 uncertainty.
  • domain assumption The bound PBH population is in steady state, with creation rate (Eq. 7) balanced by inspiral/merger over the Milky Way age.
    Sec. V; requires the inspiral time t_ins to be shorter than the Galaxy age for the relevant parameters, which the paper states is the case.
  • ad hoc to paper The single-burst SNR threshold SNR>10 is the detection criterion; repeated bursts are not stacked.
    Sec. II and V; the correlated series is used only for the timing statistics, not for combined signal detection.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Gravitational waves from primordial black holes passing by neutron stars: observational prospects for the Galactic center." pith.science (2026). https://pith.science/paper/DU23EEIF

@misc{pith2026260223429,
  author       = {Pith},
  title        = {Pith review of: Gravitational waves from primordial black holes passing by neutron stars: observational prospects for the Galactic center},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DU23EEIF}},
  note         = {Machine review of arXiv:2602.23429}
}
abstract

We investigate the gravitational wave (GW) signals emitted by planetary-mass primordial black holes (PBHs) passing nearby or traversing neutron stars (NSs). While previous studies mainly focused on the detailed waveforms of the signals, we estimate the rate of PBH-NS gravitational-wave events originating from the Galactic center and compute the probability of detecting a signal over 10 years of LIGO-Virgo-KAGRA observations. We examine in detail the case of PBHs bound to NSs, focusing on eccentric orbits that give rise to repeated GW bursts emitted in correlated series, each burst corresponding to a periastron passage. Despite the enhancement from the large number of bursts produced by a single PBH-NS pair, the total number of signals produced in this way remains subdominant to those due to random unbound encounters of PBHs with NSs. We also find that both types of signals have a very small probability $P\lesssim 10^{-8}$ to be detected in a 10 year period.

Figures

Figures reproduced from arXiv: 2602.23429 by the authors.

Figure 2
Figure 2. FIG. 2. Periastron distances of PBHs orbiting neutron stars [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Probability of detecting GW signals from PBH-NS [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Primordial Black Holes Formation Beyond the Standard Cosmic QCD Transition

    astro-ph.CO 2026-04 unverdicted novelty 4.0 of 10

    The paper reviews primordial black hole formation during the cosmic QCD phase transition in a microscopical model and explores how beyond-Standard-Model physics affects the equation of state and PBH probability distri...

Reference graph

Works this paper leans on

43 extracted references · 1 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Y. B. Zel’dovich and I. D. Novikov, Soviet Astronomy 10, 602 (1967)

    1967

  2. [2]

    Hawking, Monthly Notices of the Royal Astronomical Society152, 75 (1971)

    S. Hawking, Monthly Notices of the Royal Astronomical Society152, 75 (1971)

    1971

  3. [3]

    B. Carr, S. Clesse, J. Garcia-Bellido, M. Hawkins, and F. Kuhnel, Physics Reports1054, 1 (2024)

    2024

  4. [4]

    Clesse and J

    S. Clesse and J. Garc ´ ıa-Bellido, Physical Review D92, 023524 (2015)

    2015

  5. [5]

    Garc ´ ıa-Bellido, Philosophical Transactions A377, 20190091 (2019)

    J. Garc ´ ıa-Bellido, Philosophical Transactions A377, 20190091 (2019)

    2019

  6. [6]

    B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Re- ports on Progress in Physics84, 116902 (2021)

    2021

  7. [7]

    A. M. Green and B. J. Kavanagh, Journal of Physics G 48, 043001 (2021)

    2021

  8. [8]

    Raidal, V

    M. Raidal, V. Vaskonen, and H. Veerm¨ ae, inPrimor- dial Black Holes, edited by C. Byrnes, G. Franciolini, T. Harada, P. Pani, and M. Sasaki (2024)

    2024

Show all 43 references
  1. [9]

    Garc ´ ıa-Bellido, Journal of Physics: Conference Series 840, 012032 (2017)

    J. Garc ´ ıa-Bellido, Journal of Physics: Conference Series 840, 012032 (2017)

    2017

  2. [10]

    IFT Centro de Excelencia Severo Ochoa CEX2020-001007-S

    It is clear from comparing Eq. (8) and (9) that dy- namical friction is the dominant energy loss mechanism when a PBH crosses a neutron star, except in rare cases when it only grazes the surface. C. PBH inspiral time As explained in the previous subsection, in the high- eccent...

  3. [11]

    Clesse and J

    S. Clesse and J. Garc ´ ıa-Bellido, Physics of the Dark Uni- verse15, 142 (2017)

    2017

  4. [12]

    G´ enolini, P

    Y. G´ enolini, P. D. Serpico, and P. Tinyakov, Physical Review D102, 083004 (2020)

    2020

  5. [13]

    Holst, Y

    I. Holst, Y. G´ enolini, and P. D. Serpico, Journal of Cos- mology and Astroparticle Physics09, 050

  6. [14]

    Q. Gao, N. Dai, Y. Gong, C. Zhang, C. Zhang, and Y. Zhao, The Astrophysical Journal978, 8 (2025)

    2025

  7. [15]

    T. W. Baumgarte and S. L. Shapiro, Physical Review D 110, L021303 (2024)

    2024

  8. [16]

    Capela, M

    F. Capela, M. Pshirkov, and P. Tinyakov, Physical Re- view D87, 023507 (2013)

    2013

  9. [17]

    Tinyakov, inPrimordial Black Holes, edited by C

    P. Tinyakov, inPrimordial Black Holes, edited by C. Byrnes, G. Franciolini, T. Harada, P. Pani, and M. Sasaki (2025)

    2025

  10. [18]

    Binney and S

    J. Binney and S. Tremaine,Galactic Dynamics: Second Edition(2008)

    2008

  11. [19]

    Garc ´ ıa-Bellido and S

    J. Garc ´ ıa-Bellido and S. Nesseris, Physics of the Dark Universe21, 6169 (2018)

    2018

  12. [20]

    C. P. L. Berry and J. R. Gair, Physical Review D82 (2010)

    2010

  13. [21]

    C. J. Moore, R. H. Cole, and C. P. L. Berry, Classical and Quantum Gravity32, 015014 (2014)

    2014

  14. [22]

    Maggiore,Gravitational Waves: Volume 1: Theory and Experiments(Oxford University Press, 2007)

    M. Maggiore,Gravitational Waves: Volume 1: Theory and Experiments(Oxford University Press, 2007)

    2007

  15. [23]

    A. G. Abacet al.(LIGO Scientific, KAGRA, VIRGO), Astrophysical Journal Letters995, L18 (2025)

    2025

  16. [24]

    T. W. Baumgarte and S. L. Shapiro, Physical Review D 110, 023021 (2024)

    2024

  17. [25]

    Bartoloet al., Journal of Cosmology and Astroparticle Physics12, 026

    N. Bartoloet al., Journal of Cosmology and Astroparticle Physics12, 026

  18. [26]

    Zou and Y.-F

    Z.-C. . Zou and Y.-F. . Huang , The Astrophysical Jour- nal Letters928, L13 (2022)

    2022

  19. [27]

    Capela, M

    F. Capela, M. Pshirkov, and P. Tinyakov, Physical Re- view D90, 083507 (2014)

    2014

  20. [28]

    Oncins, J

    M. Oncins, J. Miralda-Escud´ e, J. L. Guti´ errez, and P. Gil-Pons, Monthly Notices of the Royal Astronomi- cal Society517, 2837 (2022)

    2022

  21. [29]

    Esser and P

    N. Esser and P. Tinyakov, Physical Review D107, 103052 (2023)

    2023

  22. [30]

    Capela, M

    F. Capela, M. Pshirkov, and P. Tinyakov, Physical Re- view D87, 123524 (2013)

    2013

  23. [31]

    W. H. Press and D. N. Spergel, The Astrophysical Jour- nal296, 679 (1985)

    1985

  24. [32]

    Gould, The Astrophysical Journal321, 571 (1987)

    A. Gould, The Astrophysical Journal321, 571 (1987)

    1987

  25. [33]

    P. C. Peters, Physical Review136, B1224 (1964)

    1964

  26. [34]

    Chandrasekhar, The Astrophysical Journal97, 255 (1943)

    S. Chandrasekhar, The Astrophysical Journal97, 255 (1943)

    1943

  27. [35]

    Esser, Physical Review D112, 043021 (2025)

    N. Esser, Physical Review D112, 043021 (2025)

    2025

  28. [36]

    P. J. McMillan, Monthly Notices of the Royal Astronom- ical Society465, 76 (2016)

    2016

  29. [37]

    Raghavan, H

    D. Raghavan, H. A. McAlister, T. J. Henry, D. W. Latham, G. W. Marcy, B. D. Mason, D. R. Gies, R. J. White, and T. A. ten Brummelaar, The Astrophysical Journal Supplement Series190, 142 (2010)

    2010

  30. [38]

    Caiozzo, G

    R. Caiozzo, G. Bertone, and F. K¨ uhnel, Journal of Cos- mology and Astroparticle Physics07, 091

  31. [39]

    Gondolo and J

    P. Gondolo and J. Silk, Physical Review Letters83, 1719 (1999)

    1999

  32. [40]

    Schodelet al., Astronomy and Astrophysics469, 125 (2007)

    R. Schodelet al., Astronomy and Astrophysics469, 125 (2007)

    2007

  33. [41]

    Maggioreet al.(ET), Journal of Cosmology and As- troparticle Physics03, 050

    M. Maggioreet al.(ET), Journal of Cosmology and As- troparticle Physics03, 050

  34. [42]

    Abacet al.(ET), arXiv preprint , arXiv:2503.12263 (2025)

    A. Abacet al.(ET), arXiv preprint , arXiv:2503.12263 (2025)

    2025 arXiv

  35. [43]

    G. M. Fuller, A. Kusenko, and V. Takhistov, Physical Review Letters119(2017)

    2017

Pith tools

Reviewed August 2, 2026 · model on record in the stance chip above.