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A modified time-frequency pattern-recognition method can search for gravitational waves from sub-solar-mass compact binaries in an unexplored chirp-mass window.

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2026-08-03 17:05 UTC pith:T4QXX7WB

load-bearing objection Solid technical improvement to the GFH pipeline, but the 'previously unexplored gap' claim conflicts with the paper's own review of tCW reach and needs a literature check. the 4 major comments →

arxiv 2512.10539 v3 pith:T4QXX7WB submitted 2025-12-11 gr-qc astro-ph.IM

BinaryGFH-v2: Improved method to search for gravitational waves from sub-solar-mass, ultra-compact binaries using the Generalized Frequency-Hough Transform

Andrew L. Miller , Lorenzo Pierini This is my paper
classification gr-qc astro-ph.IM
keywords gravitational wavesprimordial black holessub-solar-mass binariesGeneralized Frequency-Hough transformtime-frequency analysischirp massdark mattertransient continuous waves
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.

This paper claims that a pattern-recognition search, the Generalized Frequency-Hough transform, can be adapted to detect gravitational-wave inspirals from ultra-compact binaries with chirp masses between 10^-2 and 10^-1 solar masses — a range previously considered too long for matched filtering and too short for time-frequency methods. Two modifications make this possible: a non-uniform grid in the transformed frequency coordinate that prevents signal power from spreading across many bins, and a data-driven per-pixel noise normalization that makes the detection statistic a standard normal in Gaussian noise. The authors validate the method with injections in Gaussian noise, show it agrees with theoretical sensitivity predictions, and project that such a search could constrain the primordial-black-hole fraction of dark matter with current and future detectors. The central claim is that this mass window, unexplored by gravitational-wave searches, is now accessible.

Core claim

The discovery is that the Generalized Frequency-Hough transform, originally built for slowly evolving transient continuous waves, can handle rapidly chirping signals with frequency derivatives up to a few Hz/s if the Hough grid is evaluated at each frequency rather than over-resolved uniformly, and if the critical ratio is computed using per-pixel expected mean and variance instead of a global statistic. In Gaussian noise the resulting critical ratio has mean zero and standard deviation one, so candidates can be assigned a statistical meaning; with injections, the empirical efficiency matches the theoretical distance reach. The authors state this opens the chirp-mass range [10^-2,10^-1] M_su

What carries the argument

The machinery is the Generalized Frequency-Hough transform acting on a time-frequency peakmap. A track is defined by the power-law chirp f_dot = k f^{11/3}, and the frequency coordinate is transformed as x = f^{1-n} so that each track becomes a straight line x = x0 - (8/3)k(t-t0). The Hough map accumulates peaks along lines, and the critical ratio is computed per pixel. Two improvements carry the argument: (1) the x0 spacing is evaluated at each instantaneous frequency, making the grid non-uniform and matched to the peakmap's frequency resolution; (2) the expected mean and variance of Hough counts are estimated empirically from the data via the peak survival probability p0, giving a per-pixe

Load-bearing premise

The signal's time-frequency track is assumed to follow the leading-order Newtonian chirp with zero eccentricity and negligible post-Newtonian corrections over the entire search band; any deviation spreads signal power across many Hough tracks and reduces the detection efficiency that the injection study assumes.

What would settle it

Inject a simulated signal with chirp mass 5e-2 solar masses and initial eccentricity 0.1 at 10 Hz into Gaussian noise at the amplitude corresponding to the claimed 95% detection distance; if the recovery efficiency falls well below 95%, the leading-order circular track assumption is load-bearing.

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

If this is right

  • The method can recover injected signals with chirp masses from 1.0e-2 to 1.0e-1 solar masses using five time-coherence configurations, with efficiency matching theoretical predictions.
  • The critical ratio is interpretable as a standard normal in Gaussian noise, enabling confidence-level statements about candidates.
  • A search over the optimal frequency band in current-generation detector data would project upper limits on primordial-black-hole formation rate density and dark-matter fraction; next-generation detectors could reach f_PBH < 1 even with strong suppression.
  • The improvements generalize to other GFH searches, e.g., spinning-down neutron stars with different power-law indices, since they address the same over-resolution and non-Gaussian count issues.
  • The method handles signals with frequency derivatives up to about 4 Hz/s, whereas the previous version could only handle about 1 Hz/s.

Where Pith is reading between the lines

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

  • Inference: If real detector noise contains non-Gaussian artifacts, the empirical per-pixel normalization may absorb some signal power or create correlated background; the method's performance in real observing data remains untested.
  • Inference: The leading-order circular-orbit assumption may be the main vulnerability: binaries formed in the early universe may have non-negligible eccentricity, which would curve the track and spread power; a test with eccentric injections would clarify the reach.
  • Inference: The approach could be combined with a post-Newtonian extension of the track model to extend control over the chirp band without a large template bank.
  • Inference: If applied to real data, the empirically estimated peak survival probability from the data itself couples the noise normalization to any signal present; a strong signal could bias the background estimate, though the authors note the signal contributes at most one peak per FFT.

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

4 major / 5 minor

Summary. The paper presents BinaryGFH-v2, a modified Generalized Frequency-Hough (GFH) pipeline intended to search for gravitational-wave inspirals from sub-solar-mass ultra-compact binaries with chirp masses in [1e-2, 1e-1] M_sun. The two main algorithmic modifications are (i) a non-uniform grid in the transformed frequency variable x0, designed to avoid over-resolving the Hough map for rapidly chirping signals, and (ii) a per-pixel noise normalization that computes the expected mean and variance of the Hough number counts, thereby producing a critical ratio with approximately zero mean and unit variance in Gaussian noise. The authors validate the method with 50 injections per amplitude over 35 amplitudes in stationary Gaussian noise for five search configurations (T_FFT from 4 s to 0.5 s), compare the empirical sensitivity with theoretical distance-reach formulas from previous work, and use the resulting efficiency curves to project rate-density and PBH dark-matter-fraction constraints for O4a and Cosmic Explorer. The central claim is that BinaryGFH-v2 can search a chirp-mass window that has not yet been constrained by gravitational-wave searches.

Significance. If the method performs on real data as it does on the Gaussian-noise injections, it would address a genuine gap in detection pipelines: matched filtering becomes computationally prohibitive below M ~ 0.1 M_sun, while continuous-wave/tCW methods were thought to be insensitive to signals that chirp too quickly. The paper's strengths are the explicit injection campaign with a large number of injections, the quantitative comparison between empirical efficiency and published theoretical sensitivity formulas, and the concrete proposal for a five-configuration O4a search. The per-pixel normalization is a useful statistical improvement over the original GFH and makes the output detection statistic interpretable in terms of a standard normal distribution. However, the scientific claim that the mass range is 'previously unexplored' and 'unconstrained' is not supported by the paper's own references, and several technical details of the normalization and of the noise-validity scope require clarification. The projected PBH constraints are illustrative but depend on extrapolating white-noise-tested sensitivity to realistic detector noise.

major comments (4)
  1. [Abstract; Sec. I; Sec. II; refs [51-54]] The paper's headline claim is that chirp masses [1e-2, 1e-1] M_sun constitute a 'previously unexplored gap' and remain 'unconstrained with gravitational waves.' Section II, however, states that tCW methods (including GFH and refs [39,53,54,67,68]) 'can probe [10^-5, 10^-1] M_sun', and the Introduction cites [51-54] as efforts to search for inspiraling compact objects in this regime. The injection campaign in Sec. V tests the pipeline but says nothing about whether refs [53,54] already placed upper limits in [1e-2, 1e-1]. Please provide an explicit comparison of the mass range, frequency band, and upper limits of [51-54] (and any other relevant searches), or revise the novelty claim. As written, the paper is internally inconsistent on the central scientific motivation.
  2. [Sec. III.D.1, Eqs. (11)-(13)] The empirical probability p0 is defined as 'the ratio of the number of selected peaks to the total number of available frequency bins N_bin.' Since the peakmap contains about 2 T_PM/T_FFT time steps, this definition is not a per-pixel probability: it yields a number proportional to the total number of peaks in the map, not the probability that a given (t,f) bin contains a peak. If p0 is used in Eq. (11) in this form, mu(x0,k) will be overestimated by roughly the number of time steps, and the resulting CR in Eq. (13) will not have mean 0 and variance 1. Please clarify whether p0 is averaged per time step (i.e., divided by the number of time columns), or correct the text. This point is central to the claimed statistical improvement.
  3. [Sec. V.A; Sec. VI] The efficiency measurements are performed in stationary Gaussian noise with a constant PSD S_n = 7.94e-24 Hz^{-1/2}. The projected O4a and Cosmic Explorer constraints in Sec. VI instead use realistic PSDs, with Eq. (17) extrapolated from the white-noise-tested theory. While agreement with theory in white noise is encouraging, it does not validate the efficiency in a nonstationary PSD with spectral lines and glitches. Because the abstract asserts the mass range is 'unconstrained' and the paper proposes a search on O4a data, the authors should either demonstrate the method on at least one configuration with an O4a-like noise realization or clearly state that the O4a projections assume the white-noise efficiency remains valid.
  4. [Sec. III.D.1; Sec. V.A; Table I] The per-pixel normalization relies on the central limit theorem. Fig. 5 demonstrates normality for T_FFT = 4 s and T_PM = 9266 s, but the shortest configurations (T_FFT = 1 s and 0.5 s; T_PM = 577 s and 314 s) have many fewer contributing FFTs, and the paper itself notes that the CR histogram becomes less normally distributed. The Gaussian assumption enters the efficiency model Eq. (22) and the threshold CR_thr = 7 used in Sec. VI. Please quantify the false-alarm rate or the distribution of CR for the short configurations, or restrict the Gaussian CR claim to the configurations where it holds.
minor comments (5)
  1. [Throughout] Typos: 'sensitivty' in Sec. V; 'ino' for 'into' near the end of Sec. I.
  2. [References] Reference [52] and [65] appear to be the same work (Andres-Carcasona et al., PoS EPS-HEP2023). Please merge to avoid duplication.
  3. [Fig. 5 caption] The reported mean and standard deviation are written as '=-0.017, =0.997' without the symbols mu and sigma. Please correct.
  4. [Eq. (15)] Equation (15) cites [54] for T_opt_FFT, but the reference uses fmax = 126.8 Hz while the search band here is [71,169] Hz. Please verify the numerical constant and clarify how the cited formula is adapted to this frequency band.
  5. [Availability] No data or code availability statement is included. The injection study is described in adequate detail, but reproduction would be easier if the code were made available.

Circularity Check

0 steps flagged

No significant circularity: the method's sensitivity is independently validated by injections, and the theoretical formulas are not fitted to the detection statistic.

full rationale

The derivation chain is self-contained for the paper's actual methodological claims. The signal model (Eq. 1) is the standard quasi-Newtonian chirp, and the GFH track transformation (Eqs. 6-7) is a coordinate change of Eq. (2); no fitted parameter is renamed as a prediction. The per-pixel normalization in Sec. III.D.1 uses an empirical p0 taken from the peakmap, but this is explicitly a data-driven noise calibration ('This empirical value replaces the analytic estimate for p0'), not the quantity being predicted; the theoretical sensitivity in Sec. V (Eqs. 16-20) uses the analytic p0,p1 from theta_thr and is then compared with injections, providing an independent check. The agreement between empirical BinaryGFH-v2 and theoretical curves in Fig. 9 is therefore not forced by construction. The Laplace rate-density estimate (Eq. 23) is an asymptotic evaluation of Eq. (22), not an input. The frequent self-citations to the authors' earlier GFH papers describe the underlying algorithm and prior validations, but the new claims are validated by the injection campaign in this paper, so those citations are not load-bearing. The only flagged issue is a correctness/novelty inconsistency, not circularity: Sec. I calls [1e-2,1e-1] M_sun 'unexplored by both current tCW and matched-filtering searches,' while Sec. II states that tCW methods 'can probe [10^-5,10^-1] M_sun' and cites [51-54] as prior efforts in this regime. If refs [53,54] already searched or constrained this band, the abstract's 'previously unexplored gap' and 'remains to-date unconstrained' statements need reconciliation; this is a literature-check/support issue outside the derivation chain and does not raise the circularity score.

Axiom & Free-Parameter Ledger

1 free parameters · 6 axioms · 0 invented entities

The central claim rests on standard GW modeling (Newtonian chirp), a Gaussian-noise assumption, and published PBH rate formulas. No new particles or entities are introduced. The only hand-chosen parameter is the peak-selection threshold. The leading-order chirp and zero-eccentricity assumptions are the most fragile inputs.

free parameters (1)
  • peak selection threshold θ_thr = 2.5
    Chosen by hand (standard value from earlier GFH/CW literature). It controls p0 and p1 in Eqs. (18)–(19), which enter the theoretical sensitivity and the Hough-map normalization.
axioms (6)
  • domain assumption Newtonian quadrupole approximation for the GW frequency evolution (Eq. 1)
    The entire track search assumes f_dot = (96/5)π^{8/3}(GM/c^3)^{5/3} f^{11/3}, used at Section II Eq. (1) and Section III.B.
  • domain assumption Zero eccentricity and negligible higher-order post-Newtonian corrections over the search band
    Implicit in the f^{-11/3} power law. Any eccentricity or merger-phase deviation would break the assumed track.
  • domain assumption Noise is stationary and Gaussian with known PSD for sensitivity projections
    All injections and the theoretical sensitivity (Eqs. 16–17) assume Gaussian noise; real detector noise is non-stationary and non-Gaussian. The paper acknowledges this only implicitly.
  • domain assumption Peak selection probabilities follow the analytic forms in Eqs. (18)–(19)
    Derived from a thresholded Rayleigh/exponential model for noise peaks, used in the theoretical sensitivity and p1 estimate.
  • domain assumption PBH merger rate density formula from Raidal et al. (Eq. 25)
    Projected f_PBH constraints rely on this early-universe binary formation rate and the suppression factor model; substantial astrophysical uncertainty.
  • standard math Laplace approximation for the space-time volume (Eq. 23)
    Used to approximate the integral of the efficiency function; the paper explicitly compares it to the 'Full' integration and finds it conservative in Gaussian noise.

pith-pipeline@v1.3.0-alltime-deepseek · 16070 in / 13890 out tokens · 135446 ms · 2026-08-03T17:05:16.066273+00:00 · methodology

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read the original abstract

Observing gravitational waves from sub-solar-mass, inspiraling compact binaries would provide almost smoking-gun evidence for primordial black holes. Here, we develop a method to search for ultra-compact binaries with chirp masses ranging from $[10^{-2},10^{-1}]M_\odot$. This mass range represents a previously unexplored gap in gravitational-wave searches for compact binaries: it was thought that the signals would too long for matched-filtering analyses but too short for time-frequency pattern-recognition techniques. Despite this, we show that a pattern-recognition technique, the Generalized frequency-Hough (GFH), can be employed with particular modifications that allow us to handle rapidly spinning-up binaries and to increase the statistical robustness of our method, and call this improved method BinaryGFH-v2. We then design a hypothetical search for binaries in this mass regime, compare the empirical and theoretical sensitivities of this method, and project constraints on formation rate densities and the fraction of dark matter that primordial black holes could compose in both current- and future-generation gravitational-wave detectors. Our results show that our method can be used to search for sub-solar-mass, ultra-compact objects in a mass regime that remains to-date unconstrained with gravitational waves.

Figures

Figures reproduced from arXiv: 2512.10539 by Andrew L. Miller, Lorenzo Pierini.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
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Figure 10. Figure 10: FIG. 10 [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
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Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_12.png] view at source ↗

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Forward citations

Cited by 2 Pith papers

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

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  2. Subsolar mass black holes from stellar collapse induced by primordial black holes

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Reference graph

Works this paper leans on

75 extracted references · 56 linked inside Pith · cited by 2 Pith papers

  1. [1]

    Expected mean and variance of Hough-map number counts in Gaussian noise To model the statistical properties of the Hough number-count map in Gaussian noise, we compute the expected mean and variance of each pixel in the time– frequency plane. In eachHough map, we evaluate the noise-only expectation valueµ(x 0, k) and standard devi- ationσ(x 0, k) for a se...

  2. [2]

    Preskill, M

    J. Preskill, M. B. Wise, and F. Wilczek, Phys. Lett. B 120, 127 (1983)

    1983

  3. [3]

    Full”) and (2) approximating the integral using Laplace’s method (“Laplace

    Computational cost TheBinaryGFH-v2 leverages the same MATLAB func- tions that are used in theGFH-v2, permitting an order- of-magnitude speed-up with respect to theGFH-v1. However, the non-uniform grid inx 0 requires the addi- tional MATLAB functiondiscretize, which checks, for each point computed through Eq. (8), which bin it falls in. While very efficien...

    2000

  4. [4]

    Abbott and P

    L. Abbott and P. Sikivie, Phys. Lett. B120, 133 (1983)

    1983

  5. [5]

    Hawking, Mon

    S. Hawking, Mon. Not. Roy. Astron. Soc.152, 75 (1971)

    1971

  6. [6]

    Jungman, M

    G. Jungman, M. Kamionkowski, and K. Griest, Phys. Rept.267, 195 (1996), arXiv:hep-ph/9506380

    Pith/arXiv arXiv 1996

  7. [7]

    Boyarsky, M

    A. Boyarsky, M. Drewes, T. Lasserre, S. Mertens, and O. Ruchayskiy, Prog. Part. Nucl. Phys.104, 1 (2019), arXiv:1807.07938 [hep-ph]

    Pith/arXiv arXiv 2019

  8. [8]

    B. Carr, S. Clesse, J. Garc ´ ıa-Bellido, and F. K¨ uhnel, Phys. Dark Univ.31, 100755 (2021), arXiv:1906.08217 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  9. [9]

    M. Y. Khlopov, Res. Astron. Astrophys.10, 495 (2010), arXiv:0801.0116 [astro-ph]

    Pith/arXiv arXiv 2010

  10. [10]

    B. Carr, F. Kuhnel, and M. Sandstad, Phys. Rev. D94, 083504 (2016), arXiv:1607.06077 [astro-ph.CO]

    Pith/arXiv arXiv 2016

  11. [11]

    Clesse and J

    S. Clesse and J. Garc ´ ıa-Bellido, Phys. Dark Univ.22, 137 (2018), arXiv:1711.10458 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  12. [12]

    Escriv` a, F

    A. Escriv` a, F. Kuhnel, and Y. Tada, (2022), arXiv:2211.05767 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  13. [13]

    A. G. Abacet al.(LIGO Scientific, VIRGO, KAGRA), (2025), arXiv:2508.18082 [gr-qc]

    Pith/arXiv arXiv 2025

  14. [14]

    A. M. Green and B. J. Kavanagh, J. Phys. G48, 043001 (2021), arXiv:2007.10722 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  15. [15]

    Clesse and J

    S. Clesse and J. Garcia-Bellido, Phys. Dark Univ.38, 101111 (2022), arXiv:2007.06481 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  16. [16]

    Bertoneet al., SciPost Phys

    G. Bertoneet al., SciPost Phys. Core3, 007 (2020), arXiv:1907.10610 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  17. [17]

    A. L. Miller, (2025), arXiv:2503.02607 [astro-ph.HE]

    arXiv 2025

  18. [18]

    Bertone, Nucl

    G. Bertone, Nucl. Phys. B1003, 116487 (2024), arXiv:2404.11513 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  19. [19]

    Gravitational waves from sub-solar mass primordial black holes,

    A. L. Miller, “Gravitational waves from sub-solar mass primordial black holes,” inPrimordial Black Holes, edited by C. Byrnes, G. Franciolini, T. Harada, P. Pani, and M. Sasaki (Springer Nature Singapore, Singapore,

  20. [20]

    Singh, M

    D. Singh, M. Ryan, R. Magee, T. Akhter, S. Shandera, D. Jeong, and C. Hanna, Phys. Rev. D104, 044015 (2021), arXiv:2009.05209 [astro-ph.CO]

    Pith/arXiv arXiv 2021

  21. [21]

    B. P. Abbottet al.(LIGO Scientific Collabora- tion, Virgo), Phys. Rev. Lett.121, 231103 (2018), arXiv:1808.04771 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  22. [22]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. Lett.123, 161102 (2019), arXiv:1904.08976 [astro- ph.CO]

    Pith/arXiv arXiv 2019

  23. [23]

    K. S. Phukon, G. Baltus, S. Caudill, S. Clesse, A. De- passe, M. Fays, H. Fong, S. J. Kapadia, R. Magee, and A. J. Tanasijczuk, (2021), arXiv:2105.11449 [astro- ph.CO]

    Pith/arXiv arXiv 2021

  24. [24]

    A. H. Nitz and Y.-F. Wang, Phys. Rev. Lett.126, 021103 (2021), arXiv:2007.03583 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  25. [25]

    Abbottet al.(LIGO Scientific Collaboration, Virgo, KAGRA), Phys

    R. Abbottet al.(LIGO Scientific Collaboration, Virgo, KAGRA), Phys. Rev. Lett.129, 061104 (2022), arXiv:2109.12197 [astro-ph.CO]

    Pith/arXiv arXiv 2022

  26. [27]

    A. H. Nitz and Y.-F. Wang, The Astrophysical Journal 915, 54 (2021), arXiv:2102.00868

    Pith/arXiv arXiv 2021

  27. [28]

    A. H. Nitz and Y.-F. Wang, Phys. Rev. Lett.127, 151101 (2021), arXiv:2106.08979 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  28. [29]

    Yuan and Q.-G

    C. Yuan and Q.-G. Huang, JCAP09, 051 (2024), arXiv:2404.03328 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  29. [30]

    Abbottet al.(LIGO Scientific, VIRGO, KAGRA), Mon

    R. Abbottet al.(LIGO Scientific, VIRGO, KAGRA), Mon. Not. Roy. Astron. Soc.524, 5984 (2023), [Er- ratum: Mon.Not.Roy.Astron.Soc. 526, 6234 (2023)], arXiv:2212.01477 [astro-ph.HE]

    Pith/arXiv arXiv 2023

  30. [31]

    A. H. Nitz and Y.-F. Wang, Phys. Rev. D106, 023024 (2022), arXiv:2202.11024 [astro-ph.HE]

    Pith/arXiv arXiv 2022

  31. [32]

    Baguiet al.(LISA Cosmology Working Group), Living Rev

    E. Baguiet al.(LISA Cosmology Working Group), Living Rev. Rel.28, 1 (2025), arXiv:2310.19857 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  32. [33]

    A. L. Miller, N. Aggarwal, S. Clesse, F. De Lillo, S. Sachdev, P. Astone, C. Palomba, O. J. Piccinni, and L. Pierini, Phys. Rev. Lett.133, 111401 (2024), arXiv:2402.19468 [gr-qc]

    Pith/arXiv arXiv 2024

  33. [34]

    A. G. Abacet al.(LIGO Scientific Collaboration, VIRGO, KAGRA), (2025), arXiv:2511.19911 [gr-qc]

    arXiv 2025

  34. [35]

    Acernese, M

    F. Acernese, M. Agathos, K. Agatsuma, D. Aisa, N. Alle- mandou, A. Allocca, J. Amarni, P. Astone, G. Balestri, G. Ballardin, and et al., CQGra32, 024001 (2015), arXiv:1408.3978 [gr-qc]

    Pith/arXiv arXiv 2015

  35. [36]

    T. S. Yamamoto, R. Inui, Y. Tada, and S. Yokoyama, Phys. Rev. D109, 103514 (2024), arXiv:2401.00044 [gr- qc]

    Pith/arXiv arXiv 2024

  36. [37]

    too short

    that sub-solar-mass binaries in the mass rangeM= [10−5,10 −2]M⊙ would emit GWs during their inspiral for O(hours−days), and can thus be probed with pattern- recognition techniques that attempt to find tracks in time–frequency representations of the data, where each track corresponds to a unique chirp mass. The method in [37] derives from so-called transie...

  37. [38]

    J. Aasi, B. P. Abbott, R. Abbott, T. Abbott, M. R. Aber- nathy, K. Ackley, C. Adams, T. Adams, P. Addesso, and et al., CQGra32, 074001 (2015), arXiv:1411.4547 [gr-qc]

    Pith/arXiv arXiv 2015

  38. [39]

    Akutsuet al.(KAGRA), PTEP2021, 05A101 (2021), arXiv:2005.05574 [physics.ins-det]

    T. Akutsuet al.(KAGRA), PTEP2021, 05A101 (2021), arXiv:2005.05574 [physics.ins-det]

    arXiv 2021

  39. [40]

    A. L. Miller, S. Clesse, F. De Lillo, G. Bruno, A. Depasse, and A. Tanasijczuk, Phys. Dark Univ.32, 100836 (2021), arXiv:2012.12983 [astro-ph.HE]

    Pith/arXiv arXiv 2021

  40. [41]

    R. Prix, S. Giampanis, and C. Messenger, Physical Re- view D84, 023007 (2011), arXiv:1104.1704 [gr-qc]

    Pith/arXiv arXiv 2011

  41. [42]

    Oliver, D

    M. Oliver, D. Keitel, and A. M. Sintes, Physical Review D99, 104067 (2019)

    2019

  42. [43]

    Sun and A

    L. Sun and A. Melatos, Phys. Rev. D99, 123003 (2019), arXiv:1810.03577 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  43. [44]

    Banagiri, L

    S. Banagiri, L. Sun, M. W. Coughlin, and A. Melatos, Phys. Rev. D100, 024034 (2019), arXiv:1903.02638 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  44. [45]

    Keitel, G

    D. Keitel, G. Woan, M. Pitkin, C. Schumacher, B. Pearl- stone, K. Riles, A. G. Lyne, J. Palfreyman, B. Stappers, and P. Weltevrede, arXiv preprint arXiv:1907.04717 (2019)

    Pith/arXiv arXiv 1907

  45. [46]

    B. P. Abbottet al., The Astrophysical Journal875, 160 (2019)

    2019

  46. [47]

    Jaranowski, A

    P. Jaranowski, A. Kr´ olak, and B. F. Schutz, Physical Review D58, 063001 (1998), arXiv:gr-qc/9804014 [gr- qc]

    Pith/arXiv arXiv 1998

  47. [48]

    Krishnan, A

    B. Krishnan, A. M. Sintes, M. A. Papa, B. F. Schutz, S. Frasca, and C. Palomba, Physical Review D70, 082001 (2004), arXiv:gr-qc/0407001 [gr-qc]

    Pith/arXiv arXiv 2004

  48. [49]

    A. M. Sintes and B. Krishnan,Gravitational waves. Proceedings, 6th Edoardo Amaldi Conference, Amaldi6, Bankoku Shinryoukan, June 20-24, 2005, J. Phys. Conf. Ser.32, 206 (2006), arXiv:gr-qc/0601081 [gr-qc]

    Pith/arXiv arXiv 2005

  49. [50]

    Astone, A

    P. Astone, A. Colla, S. D’Antonio, S. Frasca, and C. Palomba, Phys. Rev. D90, 042002 (2014), arXiv:1407.8333 [astro-ph.IM]

    Pith/arXiv arXiv 2014

  50. [51]

    Keitel, Physical Review D93, 084024 (2016), arXiv:1509.02398 [gr-qc]

    D. Keitel, Physical Review D93, 084024 (2016), arXiv:1509.02398 [gr-qc]. 14

    Pith/arXiv arXiv 2016

  51. [52]

    Suvorova, L

    S. Suvorova, L. Sun, A. Melatos, W. Moran, and R. J. Evans, Physical Review DD93, 123009 (2016), arXiv:1606.02412 [astro-ph.IM]

    Pith/arXiv arXiv 2016

  52. [53]

    B. P. Abbottet al.(LIGO Scientific, Virgo), Phys. Rev. D100, 024004 (2019), arXiv:1903.01901 [astro-ph.HE]

    Pith/arXiv arXiv 2019

  53. [54]

    Study of data analysis methods for the search of gravitational waves from primordial black hole binaries,

    E. Velcani, “Study of data analysis methods for the search of gravitational waves from primordial black hole binaries,”https://tds.virgo-gw.eu/ql/?c=20230 (2022), master Thesis, Sapienza University of Rome

    2022

  54. [55]

    Andr´ es-Carcasona, O

    M. Andr´ es-Carcasona, O. J. Piccinni, M. Mart ´ ınez, and L.-M. Mir, PoSEPS-HEP2023, 067 (2024)

    2024

  55. [56]

    Andr´ es-Carcasona, O

    M. Andr´ es-Carcasona, O. J. Piccinni, M. Mart ´ ınez, and L. M. Mir, Phys. Rev. D111, 043019 (2025), arXiv:2411.04498 [gr-qc]

    Pith/arXiv arXiv 2025

  56. [57]

    Alestas, G

    G. Alestas, G. Morras, T. S. Yamamoto, J. Garcia- Bellido, S. Kuroyanagi, and S. Nesseris, Phys. Rev. D 109, 123516 (2024), arXiv:2401.02314 [astro-ph.CO]

    Pith/arXiv arXiv 2024

  57. [58]

    A. L. Miller, N. Aggarwal, S. Clesse, and F. De Lillo, Phys. Rev. D105, 062008 (2022), arXiv:2110.06188 [gr- qc]

    Pith/arXiv arXiv 2022

  58. [59]

    Abbottet al.(LIGO Scientific Collaboration, Virgo, KAGRA), Phys

    R. Abbottet al.(LIGO Scientific Collaboration, Virgo, KAGRA), Phys. Rev. D106, 102008 (2022), arXiv:2201.00697 [gr-qc]

    Pith/arXiv arXiv 2022

  59. [60]

    A. L. Miller, N. Aggarwal, S. Clesse, F. De Lillo, S. Sachdev, P. Astone, C. Palomba, O. J. Piccinni, and L. Pierini, Phys. Rev. D110, 082004 (2024), arXiv:2407.17052 [astro-ph.IM]

    Pith/arXiv arXiv 2024

  60. [61]

    Tisserandet al.(EROS-2), Astron

    P. Tisserandet al.(EROS-2), Astron. Astrophys.469, 387 (2007), arXiv:astro-ph/0607207

    Pith/arXiv arXiv 2007

  61. [62]

    Niikura, M

    H. Niikura, M. Takada, S. Yokoyama, T. Sumi, and S. Masaki, Phys. Rev.D99, 083503 (2019), arXiv:1901.07120 [astro-ph.CO]

    Pith/arXiv arXiv 2019

  62. [63]

    Croon, D

    D. Croon, D. McKeen, N. Raj, and Z. Wang, Phys. Rev. D102, 083021 (2020), arXiv:2007.12697 [astro-ph.CO]

    Pith/arXiv arXiv 2020

  63. [64]

    Clesse and J

    S. Clesse and J. Garc ´ ıa-Bellido, Phys. Dark Universe15, 142 (2017)

    2017

  64. [65]

    Garc ´ ıa-Bellido and S

    J. Garc ´ ıa-Bellido and S. Clesse, Phys. Dark Univ.19, 144 (2018), arXiv:1710.04694 [astro-ph.CO]

    Pith/arXiv arXiv 2018

  65. [66]

    Reitzeet al., Bull

    D. Reitzeet al., Bull. Am. Astron. Soc.51, 035 (2019), arXiv:1907.04833 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  66. [67]

    Maggiore,Gravitational Waves: Volume 1: Theory and Experiments, Vol

    M. Maggiore,Gravitational Waves: Volume 1: Theory and Experiments, Vol. 1 (Oxford University Press, 2008)

    2008

  67. [68]

    Andr´ es-Carcasona, O

    M. Andr´ es-Carcasona, O. J. Piccinni, M. Mart ´ ınez, and L.-M. Mir, PoSEPS-HEP2023, 067 (2023)

    2023

  68. [69]

    Milleret al., Phys

    A. Milleret al., Phys. Rev. D98, 102004 (2018), arXiv:1810.09784 [astro-ph.IM]

    Pith/arXiv arXiv 2018

  69. [70]

    Sun and A

    L. Sun and A. Melatos, Physical Review D99, 123003 (2019)

    2019

  70. [71]

    A. L. Milleret al., Phys. Rev. D100, 062005 (2019), arXiv:1909.02262 [astro-ph.IM]

    Pith/arXiv arXiv 2019

  71. [72]

    Astone, S

    P. Astone, S. Frasca, and C. Palomba, Class. Quant. Grav.22, S1197 (2005)

    2005

  72. [73]

    S. S. Menonet al., (2025), arXiv:2512.09878 [astro- ph.IM]

    Pith/arXiv arXiv 2025

  73. [74]

    Forma- tion of Primordial Black Hole Binaries and Their Merger Rates,

    M. Raidal, V. Vaskonen, and H. Veerm¨ ae, “Forma- tion of Primordial Black Hole Binaries and Their Merger Rates,” inPrimordial Black Holes, edited by C. Byrnes, G. Franciolini, T. Harada, P. Pani, and M. Sasaki (2025) arXiv:2404.08416 [astro-ph.CO]

    Pith/arXiv arXiv 2025

  74. [75]

    Weber and W

    M. Weber and W. de Boer, Astron. Astrophys.509, A25 (2010), arXiv:0910.4272 [astro-ph.CO]

    Pith/arXiv arXiv 2010

  75. [76]

    H¨ utsi, M

    G. H¨ utsi, M. Raidal, V. Vaskonen, and H. Veerm¨ ae, JCAP03, 068 (2021), arXiv:2012.02786 [astro-ph.CO]

    Pith/arXiv arXiv 2021