Pith. sign in

REVIEW 2 major objections 5 minor 4 cited by

Hierarchical Black Hole Mergers in Nuclear Star Clusters: A Combined Dynamical-Secular Channel for GW231123-like Events

T0 review · 2 major / 5 minor · reviewed 2026-08-03 · deepseek-v4-flash

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

Pith's one-line read The paper claims that GW231123-like black-hole mergers originate in Milky Way-like nuclear star clusters through a two-step binary-single interaction sequence, with the central supermassive black hole's von Zeipel-Lidov-Kozai effect driving

desk verdict Plausible new mechanism for 2G/2G mergers in NSCs, but the GW231123 rate consistency rides on an assumed 2G abundance rather than a derived one. read the letter →

arxiv 2511.13820 v2 pith:3NDRARPY submitted 2025-11-17 astro-ph.HE gr-qc

Bin Liu , Dieran Wang , Dong Lai This is my paper
classification astro-ph.HEgr-qc
keywords blackholemergerssecond-generationholesnuclearstarclustersvonZeipel-Lidov-Kozaieffectbinary-singleinteractionsgravitationalwavesGW231123hierarchical
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

The paper aims to explain the origin of GW231123, a gravitational-wave event in which both black holes are so massive and so rapidly spinning that they cannot be first-generation remnants of single stars. The authors propose that in the nuclear star cluster of a Milky Way-like galaxy, a second-generation black hole (the product of an earlier black-hole merger) first binds to a star through a three-body encounter, then swaps that star for another second-generation black hole, leaving a wide 2G/2G binary. Such wide binaries would ordinarily be ionized by subsequent encounters before merging; the key step is that the tidal field of the central supermassive black hole, through the von Zeipel-Lidov-Kozai effect, periodically drives the binary's eccentricity to extreme values, causing gravitational-wave emission to outpace evaporation. In their steady-state kinetic model, this binary-single channel dominates over gravitational-wave-capture and tidal-capture channels and reproduces the inferred GW231123 rate when roughly one star in every two thousand in the cluster is a 2G black hole. The model also predicts a large population of 2G-black-hole/star binaries, potentially visible as micro tidal disruption events or as low-frequency gravitational-wave sources.

What carries the argument

The key mechanism is the combination of binary-single interactions and the von Zeipel-Lidov-Kozai (ZLK) effect from the central supermassive black hole. Binary-single encounters first produce a wide 2G/star binary, then a second 2G BH exchanges the star and leaves a wide 2G/2G binary. The ZLK effect, which in a hierarchical triple causes the binary's eccentricity to oscillate to high values, shortens the gravitational-wave merger time below the evaporation time. The analysis uses the analytic relation T_ZLK ≈ T_m,0 (1 - e_max^2)^3 to compute the fraction of binaries that merge within the evaporation time, and a four-population kinetic model (single 2G BHs, 2G/S binaries, 2G/2G binaries, 3G r

What would settle it

A direct census of ~100 M☉ black holes in the Milky Way's nuclear star cluster (e.g., via microlensing) that yields a fraction f_2G < 0.01% — five times below the fiducial 0.05% — would push the predicted GW231123-like merger rate below the observed lower bound and falsify the central rate claim.

Watch

Extended reading notes

Core claim

The paper argues that 2G black holes (remnants of earlier BH mergers) can merge in NSCs via a two-step dynamical path: first a 2G BH and a stellar binary form a wide 2G/star binary through a binary-single interaction; then a second 2G BH exchanges out the star, making a wide 2G/2G binary. The SMBH's ZLK effect drives this wide binary to high eccentricity, so it merges by GW emission before evaporation. The authors' steady-state rate model finds the binary-single channel dominates over GW capture and tidal capture, and matches the GW231123 rate if f_2G ≳ 0.05%. They also show that the merger kick usually ejects the 3G remnant, limiting repeated hierarchical growth.

Load-bearing premise

The predicted rate assumes a steady, pre-existing population of second-generation black holes at a fractional abundance of order 0.05% of stars; the paper treats this abundance as an input rather than deriving it, so if the true retained fraction is an order of magnitude smaller the predicted rate falls below the observed GW231123 rate.

Editorial extensions

If this is right

  • For a Milky Way-like nuclear star cluster with a 2G fraction f_2G ≳ 0.05% and exchange probability f_1 ≈ 10%, the predicted 2G/2G merger rate agrees with the inferred GW231123 rate.
  • The binary-single channel is the dominant 2G/2G production route; gravitational-wave capture is 10^2–10^3 times less efficient, and tidal capture fails because the intermediate 2G/star binary merges before exchanging into a 2G/2G binary.
  • A substantial population of 2G-black-hole/star binaries is produced; their mergers could appear as micro tidal disruption events, and their long inspiral as low-frequency gravitational-wave sources for future space-based detectors.
  • The channel operates most efficiently in galaxies with SMBH masses ≲5×10^7 M☉; in more massive galaxies the high velocity dispersion suppresses the ZLK window, leaving only the inefficient GW-capture channel.
  • Most 3G remnants from 2G/2G mergers receive recoil kicks above the local escape speed and are ejected, so repeated hierarchical growth in NSCs is largely suppressed.

Reading between the lines

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

  • If this channel is representative, the rate of GW231123-like events should be roughly flat with host SMBH mass below ~5×10^7 M☉ and then drop sharply; a future catalog of high-mass-gap mergers with host-galaxy masses could test this cutoff.
  • The predicted 2G/star binaries are, in effect, a probe of the 2G population that the model currently treats as an input; a search for micro tidal disruption events in quiescent galactic nuclei could measure f_2G directly and thereby turn the paper's rate prediction into a constraint on the birth efficiency of 2G BHs.
  • The same sequential binary-single plus ZLK logic may also operate for intermediate-mass black hole seeds in denser clusters, but the paper's kick results suggest a natural ceiling on hierarchical growth via this route; detecting several 2G/2G events with moderate effective spins would test whether the 3G escape prediction holds.
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

2 major / 5 minor

Summary. The paper proposes that the high-mass, high-spin merger GW231123 can be explained by 2G/2G black-hole mergers forming in Milky Way-like nuclear star clusters through a two-step dynamical-secular channel: a 2G BH first forms a wide 2G/star binary via binary-single interaction with a stellar binary, then exchanges the star for another 2G BH, and the resulting wide 2G/2G binary is driven to merger by the SMBH-induced ZLK effect. Using semi-analytic timescales and a multi-stage ODE model, the authors compare three channels (GW capture, tidal capture, binary-single), conclude that binary-single plus ZLK dominates, and report a rate consistent with the inferred GW231123 rate for a 2G abundance f_2G ≳ 0.05% and exchange probability f_1 = 10%. They also estimate 2G/1G and 1G/1G merger rates and argue that large merger kicks suppress most 3G growth.

Significance. If correct, the proposed channel provides a specific, physically grounded dynamical route to high-mass-gap, high-spin hierarchical mergers and makes falsifiable predictions: an abundant population of 2G/star binaries (potentially micro tidal disruption events) and a low-frequency population of 2G/1G inspirals. The central mechanism comparison is transparent and the timescale arguments in Fig. 2 are based on standard dynamical physics, with the tidal-capture failure and ZLK necessity clearly quantified. However, the headline rate claim is conditional on the assumed steady-state 2G abundance f_2G, which is not derived from the model; as written, the rate consistency with GW231123 is a consistency with an input parameter rather than an unconditional prediction.

major comments (2)
  1. [Merger rate; Eq. (16); Appendix A] The claimed rate consistency with GW231123 is not an independent prediction because f_2G is an input. In Eq. (16), Γ = (dN2G0/dlnR)(f1 f2/TA)[1 + ...], and since N2G0 = f_2G N_s, the rate is proportional to f_2G. The fiducial f_2G = 0.05% is set at the threshold where the rate matches the observed GW231123 rate (Fig. 5). The source term in Eq. (12) is set to zero by the steady-state ansatz, and the 1G/1G merger channel computed in Fig. 3 (bottom) is never used to derive f_2G. At minimum, the authors should either compute f_2G self-consistently from their own 1G/1G supply or explicitly reframe the rate as conditional on f_2G and soften the abstract's claim that the model 'produces a merger rate consistent' with GW231123.
  2. [Appendix A; Eq. (12)] The steady-state assumption is not harmless: it demands a 2G replenishment rate. For R ~ 0.1–1 pc and T_A ~ 5×10^8 yr, the required source is ∫(dN2G0/dlnR)/T_A dlnR ~ 10^-6 yr^-1 per galaxy, corresponding to thousands of retained 2G BHs over a Hubble time. The paper never checks whether the 1G/1G merger channel it models can supply this, and since Γ ∝ f_2G, an order-of-magnitude lower true steady-state abundance would put the predicted rate below the observed rate. A consistency check between the source and sink terms in the ODE system is needed before the rate claim can be taken quantitatively.
minor comments (5)
  1. [Appendix A] The definition 'f_2G = n_s/n_2G' is inverted; it should read n_2G/n_s, consistent with the main text.
  2. [Introduction] Typo: 'straightward' should be 'straightforward'.
  3. [Eq. (16)] The exponential term is typeset ambiguously. It should be written with parentheses as 1 + (T_m e^{-T_H/T_m} − T_B e^{-T_H/T_B})/(T_B − T_m).
  4. [Fig. 2 and §Dynamical process] The quantity T_m^{2G/S} is used in the figure comparison but never formally defined in the text; please define it as the GW merger time of the 2G/S binary.
  5. [Footnote 91] The assumed outer-orbit eccentricity ~0.5 for the ZLK calculation is a significant input; the authors should state whether the reported f_2 values are sensitive to this choice.

Circularity Check

1 steps flagged · score 4.0 of 10

Rate consistency with GW231123 is normalized by the assumed 2G abundance f_2G; the dynamical channel mechanism itself is not circular.

  1. fitted input called prediction [Appendix A, Eq. (16) and Fig. 5; input assumption set in 'Dynamical process' (Eq. 1) and ODE system Eq. (12)]
    "We find that such channel is able to predict a merger rate in agreement with the detection rate of GW231123 when the 2G BH fraction f_2G ≳0.05%."

    The binary-single merger rate in Eq. (16) is Γ = (dN_2G0/dlnR) f1 f2 [1 + ...]/T_A, and dN_2G0/dlnR is proportional to the assumed input n_2G = f_2G n_s. The paper never derives f_2G from the 1G/1G merger supply; the steady-state source term in dN_2G/dt = -N_2G/T_A + (dN_2G/dt)_source ≃ 0 is left unevaluated. The quoted 'prediction' states that for f_2G ≳ 0.05% the input-normalized curve reaches the observed GW231123 rate. Thus the agreement is an inversion of the assumed abundance rather than an independent, first-principles prediction.

full rationale

The comparison of Channels 1-3 and the necessity of SMBH-induced ZLK are based on standard encounter-rate and secular-dynamics formulas, with the relevant timescales stated in the text; those parts are self-contained and not circular. The circular element is confined to the quantitative rate claim: Γ ∝ f_2G, where f_2G is an assumed steady-state input (fiducial 0.05%), and no source calculation closes the ODE. The paper is transparent about this dependence and frames it as a condition ('when f_2G ≳ 0.05%'), so this is a partial normalization-by-input rather than a fully circular derivation. No uniqueness theorem or hidden ansatz is imported from self-citations; references [13], [69], [91] provide numerical/analytic tools, but the central channel comparison stands on the equations given in the paper.

Assumptions & free parameters 7 free parameters · 7 assumptions · 0 invented entities

The central quantitative claim (rate ≈ 0.08 Gpc^-3 yr^-1) rests on one fitted abundance (f_2G), two adopted probabilities (f_1, f_2), several fiducial fractions (f_b, f_1G), and an assumed outer eccentricity (~0.5). The qualitative mechanism — binary-single channel dominates, tidal capture fails, ZLK accelerates mergers — is robust to these choices, as the paper shows by varying γ and f_2G. The steady 2G population is assumed, not derived. No new physical entities are introduced.

free parameters (7)
  • f_2G (2G BH abundance) = 0.05% fiducial; rate consistency requires ≳ 0.05%
    Unconstrained steady-state fraction of stars that are ~100 Msun 2G BHs. The headline rate Γ ∝ f_2G is matched to GW231123 by choosing this abundance (Fig. 5, Appendix A).
  • f_1 (2G/S → 2G/2G exchange probability) = 10%
    Adopted by hand; Appendix A states it “should ideally be determined via N-body simulations”; the rate scales linearly with it.
  • f_2 (ZLK-window merger fraction) = ≲ 15%
    Taken from the self-cited method of [13] with an assumed outer-orbit eccentricity ~0.5 (footnote 91); not reproduced or validated in this paper.
  • f_b, f_1G (stellar binary and 1G BH fractions) = 10%, 1%
    Fiducial population fractions; rates of competing channels scale with them; no constraint cited.
  • γ (stellar density slope) = 1.75 fiducial; 1.5–2.25 varied
    Observationally motivated by Galactic-center constraints [78], but rates depend sensitively on it (Fig. 3).
  • Outer-orbit eccentricity for ZLK calculation = ~0.5
    Footnote 91: “we model the 2G/2G binary as moving on a moderately eccentric orbit (eccentricity ~0.5) around the central SMBH”; this sets the ZLK timescale and hence f_2.
  • 2G/S hardening factor = a' = a/2
    Assumed factor-2 semimajor-axis reduction by field-star scattering before the exchange encounter (Channels 2 and 3).
assumptions (7)
  • domain assumption NSC density profile n_s = 1.35e6 Msun/pc^3 (R/0.25 pc)^(-γ) matches the Galactic center [78]
    Eq. (1); anchors all encounter rates. If real NSCs deviate from this profile, rates shift.
  • domain assumption All populations share velocity dispersion σ_s = sqrt(GM•/[R(1+γ)]) after mass segregation
    Invoked in the Dynamical-process section; the paper notes it neglects population-dependent density profiles [81–83].
  • domain assumption Steady-state 2G supply with dN_2G/dt = source ≃ 0
    Eq. (12) and Appendix A; without continuous production/retention of 2G BHs at f_2G ≳ 0.05%, the headline rate claim fails.
  • standard math Tidal dissipation model ΔE_tide with A = 0.24, β = 3.1 (polytrope index 4/3)
    Taken from Portegies Zwart & Meinen 1993 [85] and Lai 1997 [86]; used for Channel 2 timescales.
  • standard math Hardness criterion E_b ≲ -m_s v_s^2/2 for survival against stellar encounters
    Sets all characteristic semi-major axes (Eqs. 2, 5, 7, 11); standard binary-evaporation physics [87].
  • standard math ZLK secular dynamics with isotropic orbital orientations
    f_2 is computed “assuming isotropic orbital orientations [13]”; standard von Zeipel-Lidov-Kozai framework [59–75].
  • standard math Peters (1964) GW merger timescales and GW-capture energy loss
    Used for Channel 1 and all merger-time estimates [84].

how reviews work

0 comments
Cite this review

Pith. "Pith review of Hierarchical Black Hole Mergers in Nuclear Star Clusters: A Combined Dynamical-Secular Channel for GW231123-like Events." pith.science (2026). https://pith.science/paper/3NDRARPY

@misc{pith2026251113820,
  author       = {Pith},
  title        = {Pith review of: Hierarchical Black Hole Mergers in Nuclear Star Clusters: A Combined Dynamical-Secular Channel for GW231123-like Events},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3NDRARPY}},
  note         = {Machine review of arXiv:2511.13820}
}
read the original abstract

The recent binary black hole (BH) merger GW231123, with both components likely in the high-mass gap and with high spins, challenges standard BH binary formation models. It is usually thought that the BHs are of second (or higher) generation (2G), resulting from the mergers of smaller BHs. But the physical processes that produce the merging 2G BH binaries are unclear and highly unconstrained. We show that such 2G mergers can be naturally produced in the nuclear star cluster of Milky Way-like galaxy. The dominant channel combines a sequence of binary-single interactions with secular evolution driven by the central supermassive BH. Our model produces a merger rate consistent with GW231123 and further predicts an abundant population of 2G BH-star (or low-mass BH) binaries; these binaries may observationally manifest as micro tidal disruption events or low-frequency gravitational-wave (GW) sources. Detecting these binaries would provide crucial insights into the dynamical pathways of hierarchical BH assembly.

Figures

Figures reproduced from arXiv: 2511.13820 by the authors.

Figure 1
Figure 1. FIG. 1. Dynamical pathways for 2G/2G mergers in NSCs. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Key timescales for forming 2G/2G mergers via differ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Top panel: 2G/2G BHB merger rates versus the [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Distribution of merger kick velocity versus final [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Merger rate of 2G/2G binaries versus galactocentric [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

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

  1. Highly eccentric non-spinning binary black hole mergers: quadrupolar post-merger waveforms

    gr-qc 2026-04 unverdicted novelty 7.0 of 10

    Polynomial models for the (2,2) post-merger waveform amplitudes of eccentric non-spinning binary black holes are constructed from numerical-relativity data as functions of symmetric mass ratio and two merger-time dyna...

  2. Uncovering Hierarchical Sub-Population of Binary Black Holes

    astro-ph.HE 2026-07 conditional novelty 6.0 of 10

    A flexible six-component fit to 259 LIGO/Virgo/KAGRA black-hole mergers finds a roughly geometric sequence of mass peaks but no aligned-spin signal except in the lowest-mass component.

  3. Black Hole Binary Detection Landscape for the Laser Interferometer Lunar Antenna (LILA): Signal-to-Noise Calculations & Science Cases

    astro-ph.HE 2026-05 unverdicted novelty 5.0 of 10

    LILA can detect IMBH binaries at redshifts 20-30, IMRIs, and provide months-to-years early warnings with high-SNR events for gravity tests.

  4. Remnant recoil and host environments of GWTC-4.0 binary black-hole mergers

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

    Five O4 gravitational-wave events prefer dynamical cluster formation; typical recoil kicks eject remnants from globular clusters but allow possible retention in nuclear star clusters, disfavoring efficient hierarchica...

Reference graph

Works this paper leans on

99 extracted references · 8 linked inside Pith · cited by 4 Pith papers

  1. [1]

    The LIGO Scientific Collaboration, the Virgo Collab- oration, and the KAGRA Collaboration (LIGO Scien- tific, VIRGO, KAGRA), arXiv:2508.18083 (2025)

    arXiv 2025

  2. [2]

    LIGO Scientific Collaboration and Virgo Collaboration, Phys. Rev. Lett.125, 101102 (2020)

    2020

  3. [3]

    The LIGO Scientific Collaboration, the Virgo Collab- oration, and the KAGRA Collaboration (LIGO Scien- tific, VIRGO, KAGRA), arXiv:2507.08219 (2025)

    arXiv 2025

  4. [4]

    V. M. Lipunov, K. A. Postnov, and M. E. Prokhorov, Astron. Lett.23, 492 (1997)

    1997

  5. [5]

    V. M. Lipunov, V. Kornilov, E. Gorbovskoy, D. A. H. Buckley, N. Tiurina, P. Balanutsa, A. Kuznetsov, J. Greiner, V. Vladimirov, D. Vlasenko et al., Mon. Not. R. Astron. Soc.465, 3656 (2017)

    2017

  6. [6]

    Podsiadlowski, S

    P. Podsiadlowski, S. Rappaport, and Z. Han, Mon. Not. R. Astron. Soc.341, 385 (2003)

    2003

  7. [7]

    Belczynski, M

    K. Belczynski, M. Dominik, T. Bulik, R. O’Shaughnessy, C. Fryer, and D. E. Holz, Astro- phys. J. Lett.715, L138 (2010)

    2010

  8. [8]

    Belczynski, D

    K. Belczynski, D. E. Holz, T. Bulik, and R. O’Shaughnessy, Nature (London)534, 512 (2016)

    2016

Show all 99 references
  1. [9]

    Dominik, K

    M. Dominik, K. Belczynski, C. Fryer, D. E. Holz, E. Berti, T. Bulik, I. Mandel, and R. O’Shaughnessy, As- trophys. J.759, 52 (2012)

    2012

  2. [10]

    Dominik, K

    M. Dominik, K. Belczynski, C. Fryer, D. E. Holz, E. Berti, T. Bulik, I. Mandel, and R. O’Shaughnessy, As- trophys. J.779, 72 (2013)

    2013

  3. [11]

    Dominik, E

    M. Dominik, E. Berti, R. O’Shaughnessy, I. Mandel, K. Belczynski, C. Fryer, D. E. Holz, T. Bulik, and F. Pannarale, Astrophys. J.806, 263 (2015)

    2015

  4. [12]

    Stevenson, A

    S. Stevenson, A. Vigna-G´ omez, I. Mandel, J. W. Bar- rett, C. J. Neijssel, D. Perkins, and S. E. de Mink, Na- ture Commun.8, 14906 (2017)

    2017

  5. [13]

    Liu and D

    B. Liu and D. Lai, Mon. Not. R. Astron. Soc.502, 2049 (2021)

  6. [14]

    Samsing and K

    J. Samsing and K. Hotokezaka, Astrophys. J.923, 126 (2021)

    2021

  7. [15]

    Gerosa and M

    D. Gerosa and M. Fishbach, Nature Astron.5, 749 (2021)

    2021

  8. [16]

    E., Astrophys

    Stegmann J., Olejak A., de Mink S. E., Astrophys. J. Lett.992, L26 (2025)

    2025

  9. [17]

    A., arXiv:2509.05415 (2025)

    Kıro˘ glu F., Kremer K., Rasio F. A., arXiv:2509.05415 (2025)

    2025

  10. [18]

    Paiella L., Ugolini C., Spera M., Branchesi M., Arca Sedda M., arXiv:2509.10609 (2025)

    2025 arXiv

  11. [19]

    E., Nathaniel K., McKernan B., Ford K

    Delfavero V., Ray S., Cook H. E., Nathaniel K., McKernan B., Ford K. E. S., Postiglione J., et al., arXiv:2508.13412 (2025)

    2025 arXiv

  12. [20]

    Bartos I., Haiman Z., arXiv:2508.08558 (2025)

    2025

  13. [21]

    D., Borchers A., Fishbach M., Ye C

    Passenger L., Banagiri S., Thrane E., Lasky P. D., Borchers A., Fishbach M., Ye C. S., arXiv:2510.14363 (2025)

    2025

  14. [22]

    D., Issa D., Li S

    Gottlieb O., Metzger B. D., Issa D., Li S. E., Renzo M., Isi M., arXiv:2508.15887 (2025)

    2025

  15. [23]

    Baruteau, J

    C. Baruteau, J. Cuadra, and D. N. C. Lin, Astrophys. 6 J.726, 28 (2011)

    2011

  16. [24]

    McKernan, K

    B. McKernan, K. E. S. Ford, W. Lyra, and H. B. Perets, Mon. Not. Roy. Astron. Soc.425, 460 (2012)

    2012

  17. [25]

    McKernan, K

    B. McKernan, K. E. S. Ford, J. Bellovary, N. W. C. Leigh, Z. Haiman, B. Kocsis, W. Lyra, M. M. MacLow, B. Metzger, M. O’Dowd, S. Endlich, and D. J. Rosen, Astrophys. J.866, 66 (2018)

    2018

  18. [26]

    Bartos, B

    I. Bartos, B. Kocsis, Z. Haiman, and S. M´ arka, Astro- phys. J.835, 165 (2017)

    2017

  19. [27]

    N. C. Stone, B. D. Metzger, and Z. Haiman, Mon. Not. Roy. Astron. Soc.464, 946 (2017)

    2017

  20. [28]

    N. W. C. Leigh, A. M. Geller, B. McKernan, K. E. S. Ford, M. M. Mac Low, J. Bellovary, Z. Haiman, W. Lyra, J. Samsing, M. O’Dowd, B. Kocsis, and S. Endlich, Mon. Not. Roy. Astron. Soc.474, 5672 (2018)

    2018

  21. [29]

    B. Liu, D. Lai, and Y.-H. Wang, Astrophys. J. Lett. 883, L7 (2019)

    2019

  22. [30]

    Secunda, J

    A. Secunda, J. Bellovary, M.-M. Mac Low, K. E. S. Ford, B. McKernan, N. W. C. Leigh, W. Lyra, and Z. S´ andor, Astrophys. J.878, 85 (2019)

    2019

  23. [31]

    Y. Yang, I. Bartos, V. Gayathri, K. E. S. Ford, Z. Haiman, S. Klimenko, B. Kocsis, S. M´ arka, Z. M´ arka, B. McKernan, and R. O’Shaughnessy, Phys. Rev. Lett. 123, 181101 (2019)

    2019

  24. [32]

    Liu, and D

    B. Liu, and D. Lai, Phys. Rev. D102, 023020 (2020)

    2020

  25. [33]

    Gr¨ obner, W

    M. Gr¨ obner, W. Ishibashi, S. Tiwari, M. Haney, and P. Jetzer, Astron. Astrophys.638, A119 (2020)

    2020

  26. [34]

    Ishibashi and M

    W. Ishibashi and M. Gr¨ obner, Astron. Astrophys.639, A108 (2020)

    2020

  27. [35]

    Tagawa, Z

    H. Tagawa, Z. Haiman, and B. Kocsis, Astrophys. J. 898, 25 (2020)

    2020

  28. [36]

    Tagawa, B

    H. Tagawa, B. Kocsis, Z. Haiman, I. Bartos, K. Omukai, J. Samsing, Astrophys. J.908, 194 (2021)

    2021

  29. [37]

    Tagawa, B

    H. Tagawa, B. Kocsis, Z. Haiman, I. Bartos, K. Omukai, J. Samsing, Astrophys. J. Lett.907, L20 (2021)

    2021

  30. [38]

    Tagawa, Z

    H. Tagawa, Z. Haiman, I. Bartos, B. Kocsis, K. Omukai, Mon. Not. Roy. Astron. Soc.507, 3362 (2021)

    2021

  31. [39]

    Y. P. Li, A. M. Dempsey, S. Li, H. Li, and J. Li, Astro- phys. J.911, 124 (2021)

    2021

  32. [40]

    K. E. S. Ford and B. McKernan, arXiv:2109.03212 [astro-ph.HE] (2021)

    2021 arXiv

  33. [41]

    Samsing, I

    J. Samsing, I. Bartos, D. J. D’Orazio, Z. Haiman, B. Kocsis, N. W. C. Leigh, B. Liu, M. E. Pessah, and H. Tagawa, Nature,603, 237 (2022)

    2022

  34. [42]

    Li and D

    R. Li and D. Lai, arXiv:2202.07633 [astro-ph.HE] (2022)

    2022 arXiv

  35. [43]

    Li and D

    J. Li and D. Lai, arXiv:2203.05584 [astro-ph.HE] (2022)

    2022 arXiv

  36. [44]

    Chattopadhyay, J

    D. Chattopadhyay, J. Stegmann, F. Antonini, J. Barber, I. M. Romero-Shaw, Mon. Not. Roy. Astron. Soc.526, 4908 (2023)

    2023

  37. [45]

    Y. Su, C. Rowan, M. Rozner, Mon. Not. R. Astron. Soc. 543, 1864 (2025)

    2025

  38. [46]

    Rozner, E

    M. Rozner, E. Ramirez-Ruiz, Astrophys. J. Lett.988, L21 (2025)

    2025

  39. [47]

    S. F. P. Zwart and S. L. W. McMillan, Astrophys. J. Lett.528, L17 (2000)

    2000

  40. [48]

    R. M. O’Leary, F. A. Rasio, J. M. Fregeau, N. Ivanova, and R. OShaughnessy, Astrophys. J.637, 937 (2006)

    2006

  41. [49]

    M. C. Miller and V. Lauburg, Astrophys. J.692, 917 (2009)

    2009

  42. [50]

    Banerjee, H

    S. Banerjee, H. Baumgardt, and P. Kroupa, Mon. Not. R. Astron. Soc.402, 371 (2010)

    2010

  43. [51]

    J. M. B. Downing, M. J. Benacquista, M. Giersz, and R. Spurzem, Mon. Not. R. Astron. Soc.407, 1946 (2010)

    1946

  44. [52]

    B. M. Ziosi, M. Mapelli, M. Branchesi, and G. Tormen, Mon. Not. R. Astron. Soc.441, 3703 (2014)

    2014

  45. [53]

    C. L. Rodriguez, M. Morscher, B. Pattabiraman, S. Chatterjee, C.-J. Haster, and F. A. Rasio, Phys. Rev. Lett.115, 051101 (2015)

    2015

  46. [54]

    Samsing and E

    J. Samsing and E. Ramirez-Ruiz, Astrophys. J. Lett. 840, L14 (2017)

    2017

  47. [55]

    Samsing and D

    J. Samsing and D. J. D’Orazio, Mon. Not. R. Astron. Soc.481, 5445 (2018)

    2018

  48. [56]

    C. L. Rodriguez, P. Amaro-Seoane, S. Chatterjee, and F. A. Rasio, Phys. Rev. Lett.120, 151101 (2018)

    2018

  49. [57]

    Gond´ an, B

    L. Gond´ an, B. Kocsis, P. Raffai, and Z. Frei, Astrophys. J.860, 5 (2018)

    2018

  50. [58]

    Rozner, H

    M. Rozner, H. B. Perets, Astrophys. J.931, 149 (2022)

    2022

  51. [59]

    von Zeipel, Astronomische Nachrichten183, 345 (1910)

    H. von Zeipel, Astronomische Nachrichten183, 345 (1910)

    1910

  52. [60]

    M. L. Lidov, Planetary and Space Science9, 719 (1962)

    1962

  53. [61]

    Kozai, Astron

    Y. Kozai, Astron. J.67, 591 (1962)

    1962

  54. [62]

    Naoz, Annu

    S. Naoz, Annu. Rev. Astron. Astrophys.54, 441 (2016)

    2016

  55. [63]

    M. C. Miller and D. P. Hamilton, Astrophys. J.576, 894 (2002)

    2002

  56. [64]

    Wen, Astrophys

    L. Wen, Astrophys. J.598, 419 (2003)

    2003

  57. [65]

    Antonini and H

    F. Antonini and H. B. Perets, Astrophys. J.757, 27 (2012)

    2012

  58. [66]

    Antonini, S

    F. Antonini, S. Toonen, and A. S. Hamers, Astrophys. J.841, 77 (2017)

    2017

  59. [67]

    Silsbee and S

    K. Silsbee and S. Tremaine, Astrophys. J.836, 39 (2017)

    2017

  60. [68]

    Petrovich and F

    C. Petrovich and F. Antonini, Astrophys. J.846, 146 (2017)

    2017

  61. [69]

    Liu and D

    B. Liu and D. Lai, Astrophys. J.863, 68 (2018)

    2018

  62. [70]

    Randall and Z.-Z

    L. Randall and Z.-Z. Xianyu, Astrophys. J.853, 93 (2018)

    2018

  63. [71]

    Hoang, S

    B.-M. Hoang, S. Naoz, B. Kocsis, F. A. Rasio, and F. Dosopoulou, Astrophys. J.856, 140 (2018)

    2018

  64. [72]

    Liu and D

    B. Liu and D. Lai, Mon. Not. R. Astron. Soc.483, 4060 (2019)

    2019

  65. [73]

    Fragione and B

    G. Fragione and B. Kocsis, Mon. Not. R. Astron. Soc. 486, 4781 (2019)

    2019

  66. [74]

    Fragione, E

    G. Fragione, E. Grishin, N. W. C. Leigh, H. B. Perets, and R. Perna, Mon. Not. R. Astron. Soc.488, 47 (2019)

    2019

  67. [75]

    Zevin, J

    M. Zevin, J. Samsing, C. Rodriguez, C.-J. Haster, and E. Ramirez-Ruiz, Astrophys. J.871, 91 (2019)

    2019

  68. [76]

    Alexander, ARA&A55, 17 (2017)

    T. Alexander, ARA&A55, 17 (2017)

    2017

  69. [77]

    J. N. Bahcall and R. A. Wolf, Astrophys. J.209, 214 (1976)

    1976

  70. [78]

    Genzel, F

    R. Genzel, F. Eisenhauer, and S. Gillessen, Rev. Mod. Phys.82, 3121 (2010)

    2010

  71. [79]

    Alexander, Astrophys

    T. Alexander, Astrophys. J.527, 835 (1999)

    1999

  72. [80]

    Alexander and O

    T. Alexander and O. Pfuhl, Astrophys. J.780, 148 (2014)

    2014

  73. [81]

    Linial, R

    I. Linial, R. Sari, Astrophys. J.940, 101 (2022)

    2022

  74. [82]

    B. Rom, I. Linial, R. Sari, Astrophys. J.951, 14 (2023)

    2023

  75. [83]

    Rom and R

    B. Rom and R. Sari, Astrophys. J.991, 146 (2025)

    2025

  76. [84]

    P. C. Peters, Phys. Rev.136, B1224 (1964)

    1964

  77. [85]

    S. F. Portegies Zwart and A. T. Meinen, Astron. Astro- phys.280, 174 (1993)

    1993

  78. [86]

    Lai, Astrophys

    D. Lai, Astrophys. J.490, 847 (1997)

    1997

  79. [87]

    Binney and S

    J. Binney and S. Tremaine, Galactic dynamics (1987). [88]T evap adopted in our model refers toT evap ≃ (m2G/ms)2T2G/2G−S, in whichT 2G/2G−S denotes the timescale for a 2G/2G binary to interact with a field star, i.e.,T 2G/2G−S = nsπ(4Gm2Ga2G/2G/vs + 7 a2 2G/2Gvs) −1 . If the s...

    1987

  80. [89]

    F. Yu, D. Lai, Astrophys. J.977, 268 (2024)

    2024

  81. [90]

    B. Liu, D. J. Mu˜ noz, and D. Lai, Mon. Not. Roy. Astron. Soc.447, 747 (2015)

    2015

  82. [91]

    To account for the ZLK effect, we model the 2G/2G binary as moving on a moderately eccentric orbit (ec- centricity∼0.5) around the central SMBH

  83. [92]

    M. R. Blanton et al. (SDSS), Astrophys. J.592, 819 (2003)

    2003

  84. [93]

    Joop Schaye et al., Mon. Not. R. Astron. Soc.446, 521 (2014)

    2014

  85. [94]

    Tremaine, K

    S. Tremaine, K. Gebhardt, R. Bender, G. Bower, A. Dressler, S. M. Faber, A. V. Filippenko, R. Green, C. Grillmair, L. C. Ho, J. Kormendy, T. R. Lauer, J. Magorrian, J. Pinkney, and D. Richstone, Astrophys. J.574, 740 (2002)

    2002

  86. [95]

    Fuller and L

    J. Fuller and L. Ma, Astrophys. J. Lett.881, L1 (2019)

    2019

  87. [96]

    C. O. Lousto, M. Campanelli, Y. Zlochower, and H. Nakano, Class. Quant. Grav.27, 114006 (2010)

    2010

  88. [97]

    Amaro-Seoane, H

    P. Amaro-Seoane, H. Audley, S. Babak, J. Baker, E. Barausse, P. Bender, E. Berti, P. Binetruy et al., arXiv:1702.00786 [astro-ph.IM] (2017)

    2017 arXiv

  89. [98]

    Luo, L.-S

    J. Luo, L.-S. Chen, H.-Z. Duan, Y.-G. Gong, S. Hu, J. Ji, Q. Liu, J. Mei, V. Milyukov, M. Sazhin, C.-G. Shao, V. T. Toth, H.-B. Tu, Y. Wang, Y. Wang, H.-C. Yeh, M.-S. Zhan, Y. Zhang, V. Zharov, and Z.-B. Zhou, Classical and Quantum Gravity33, 035010 (2016)

    2016

  90. [99]

    Hu and Y.-L

    W.-R. Hu and Y.-L. Wu, National Science Review4, 685 (2017)

    2017

  91. [100]

    intermediate populations

    The LIGO Scientific Collaboration, the Virgo Collab- oration, and the KAGRA Collaboration (LIGO Scien- tific, VIRGO, KAGRA), Astrophys. J. Lett.993, L21 (2025). A: Merger rate This section presents the merger rate calculations used in the main text for a typical galaxy. For th...

    2025

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.