pith. sign in

arxiv: 2512.11059 · v2 · submitted 2025-12-11 · 🌌 astro-ph.GA · astro-ph.CO· gr-qc

Milky Way Globular Clusters: Nurseries for Dynamically-Formed Binary Black Holes

Federico Angeloni , Konstantinos Kritos , Raffaella Schneider , Emanuele Berti , Luca Graziani , Stefano Torniamenti , Michela Mapelli This is my paper

Pith reviewed 2026-05-16 22:44 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.COgr-qc
keywords globular clustersbinary black holesdynamical formationMilky Waymerger rateshierarchical mergersredshift evolutionpair-instability gap
0
0 comments X

The pith

A coupled galaxy and cluster model shows Milky Way globular clusters as nurseries for dynamically formed binary black holes with merger rates rising until redshift 5.

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

The paper couples a galaxy formation model with cluster population synthesis to follow the evolution of globular clusters and black hole binaries across cosmic time. This approach reproduces the observed age and mass distribution of Milky Way globular clusters and indicates that about 30 percent of halo clusters came from accreted satellites. It finds that hierarchical mergers help populate the mass gap above the pair-instability limit for black holes, although different synthesis codes give varying quantitative results. The model predicts that the rate densities of black hole binary births and mergers keep rising with redshift out to z equals 5.

Core claim

The reference model accurately reproduces the observed age-mass distribution of the Milky Way globular clusters using prescriptions for cluster formation and disruption. Approximately 30% of the globular clusters in the galaxy's halo originated from satellite galaxies. Hierarchical black hole mergers contribute to forming black holes in and above the pair-instability mass gap, though results vary across codes. The merger and birth rate densities of binary black holes increase with redshift until z = 5.

What carries the argument

The self-consistent coupling of the GAMESH galaxy formation model with cluster population synthesis codes to simultaneously trace the cosmic evolution of globular clusters and black hole mergers.

If this is right

  • Approximately 30% of Milky Way halo globular clusters originated from satellite galaxies.
  • Hierarchical black hole mergers contribute significantly to black holes above the pair-instability mass gap.
  • Merger and birth rate densities of binary black holes increase with redshift till z = 5.
  • Host galaxies of massive black holes are characterized in terms of dark matter, stellar mass, and metallicity.

Where Pith is reading between the lines

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

  • Future detectors such as LISA, the Einstein Telescope, and Cosmic Explorer will probe the high-redshift rise in these merger rates.
  • Divergent results from different population synthesis codes indicate that constraints on black hole evolution physics are needed to refine predictions.
  • The framework could be used to estimate contributions from globular clusters to the overall black hole merger rate in other galaxies.
  • Links between galactic merger history and black hole binary formation follow from the satellite origin of some clusters.

Load-bearing premise

The prescriptions for cluster formation and disruption in the galaxy formation model and the assumptions within the population synthesis codes for black hole evolution and mergers.

What would settle it

Measuring an age-mass distribution for Milky Way globular clusters that differs from the model's prediction, or finding that binary black hole merger rates do not increase with redshift up to z=5.

Figures

Figures reproduced from arXiv: 2512.11059 by Emanuele Berti, Federico Angeloni, Konstantinos Kritos, Luca Graziani, Michela Mapelli, Raffaella Schneider, Stefano Torniamenti.

Figure 1
Figure 1. Figure 1: (a) Global birth rate density of GCs in the GAMESH simulation as a function of redshift (green solid line). Black lines [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Primary (M1) and secondary (M2) BH mass distribution of observable dynamically-formed BBHs within our LG-like volume. Red dots show the estimated median values of the most massive GW events (M1 > 50 M⊙) detected by the LVK collaboration up to O4a, with error bars representing the 90% credible intervals. Dashed lines in histograms display the mass distributions of all BBH mergers that occur in our simulatio… view at source ↗
Figure 3
Figure 3. Figure 3: (a) Dark matter mass (MDM) and stellar mass (M⋆) distribution of halos that host GCs capable of forming MBBHs; (b) GC mass (MCluster) versus absolute metallicity of GCs hosting MBBHs. The color of each point represents the central stellar number density of the cluster. consistency persists even for systems observable by terrestrial interferometers. By comparing the first and second column, we see that a si… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Redshift evolution of dynamically-formed BBH merger rate density, as a function of primary BH mass (M [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

We present a novel self-consistent theoretical framework to characterize the formation, evolution, and merger sites of dynamically-formed black hole binaries, with a focus on explaining the most massive events observed by the LIGO-Virgo-KAGRA Collaboration. Our approach couples the galaxy formation model GAMESH with cluster population synthesis codes to trace the cosmic evolution of globular clusters simultaneously with mergers of massive black holes. Our reference model, which includes prescriptions for both cluster formation and disruption depending on properties of specific galaxies, accurately reproduces the observed age-mass distribution of the Milky Way globular clusters. We find that approximately 30% of the globular clusters observed in our galaxy's halo may have originated from satellite galaxies of the Milky Way. We confirm that hierarchical black hole mergers provide a significant contribution to the formation of black holes in and above the pair-instability mass gap. However, quantifying their contribution is challenging, as different population synthesis codes yield divergent results in terms of black hole mass function and merger rates. Furthermore, we characterize the host galaxies where massive black holes form in terms of their dark matter, stellar mass, and metallicity. Ultimately, we demonstrate that the merger and birth rate densities of binary black holes increase with redshift till z = 5. This cosmic evolution is a crucial signature with significant implications for future detectors like the LISA, the Einstein Telescope and Cosmic Explorer, which will be capable to probe the high-redshift Universe.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper couples the GAMESH galaxy-formation model to cluster population-synthesis codes to follow the cosmic assembly, disruption, and internal dynamics of globular clusters, with emphasis on dynamically formed binary black holes. The reference model reproduces the observed Milky Way globular-cluster age-mass distribution, attributes ~30 % of halo clusters to satellite accretion, finds that hierarchical mergers supply a non-negligible fraction of objects inside and above the pair-instability gap, characterises the dark-matter, stellar-mass and metallicity properties of the host galaxies, and reports that both birth and merger rate densities of binary black holes rise with redshift up to z = 5, with direct implications for LISA, ET and CE.

Significance. If the quantitative results prove robust, the work supplies a self-consistent link between galaxy assembly, globular-cluster evolution and gravitational-wave source populations, furnishing falsifiable predictions for the redshift dependence of merger rates that future detectors can test. The successful reproduction of the Milky Way age-mass distribution is a concrete strength that anchors the model.

major comments (2)
  1. [Abstract and hierarchical-merger results] Abstract and the section presenting hierarchical-merger results: the claim that hierarchical mergers supply a 'significant contribution' to the pair-instability gap is load-bearing for the paper's central narrative, yet the text itself states that different population-synthesis codes produce divergent black-hole mass functions and merger rates. Because the reported gap fraction and the z = 5 rate peak are obtained with a single code choice, the quantitative statements remain code-dependent; either a multi-code comparison or explicit uncertainty envelopes must be added before the significance of the gap contribution can be asserted.
  2. [Rate-density evolution section] Section describing the reference model and rate-density evolution: the reported increase in birth and merger rate densities to z = 5 is presented as a robust cosmic signature, but the same code-divergence caveat applies. Without demonstrating that the redshift trend is preserved (or at least bounded) across the cited population-synthesis codes, the claimed detectability implications for LISA/ET/CE rest on an unquantified systematic uncertainty.
minor comments (2)
  1. [Methods] The abstract refers to 'cluster population synthesis codes' (plural) while the quantitative results appear to be drawn from a single reference run; the specific code and version used for the plotted rates and mass functions should be stated explicitly in the methods.
  2. [Figures] Figure captions and axis labels for the redshift-dependent rate densities should include the precise definition of 'birth rate' versus 'merger rate' to avoid reader confusion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the robustness of our quantitative results. We address each major comment below and will incorporate revisions to strengthen the discussion of code-dependent uncertainties.

read point-by-point responses

  1. Referee: [Abstract and hierarchical-merger results] Abstract and the section presenting hierarchical-merger results: the claim that hierarchical mergers supply a 'significant contribution' to the pair-instability gap is load-bearing for the paper's central narrative, yet the text itself states that different population-synthesis codes produce divergent black-hole mass functions and merger rates. Because the reported gap fraction and the z = 5 rate peak are obtained with a single code choice, the quantitative statements remain code-dependent; either a multi-code comparison or explicit uncertainty envelopes must be added before the significance of the gap contribution can be asserted.

    Authors: We acknowledge the referee's concern and note that the manuscript already states in the abstract that 'quantifying their contribution is challenging, as different population synthesis codes yield divergent results'. The reference model uses a single code for the reported fractions, as a full multi-code re-computation of the coupled GAMESH + cluster evolution framework would require substantial additional resources beyond the scope of this work. In revision we will (i) change the wording from 'significant contribution' to 'non-negligible contribution', (ii) add an explicit paragraph discussing literature-based uncertainty ranges on the gap fraction arising from code variations, and (iii) include a short table summarizing how the main qualitative conclusions (presence of hierarchical mergers above the gap) are preserved across the cited codes while the precise fractions vary. These changes will be made in both the abstract and the hierarchical-merger section. revision: partial

  2. Referee: [Rate-density evolution section] Section describing the reference model and rate-density evolution: the reported increase in birth and merger rate densities to z = 5 is presented as a robust cosmic signature, but the same code-divergence caveat applies. Without demonstrating that the redshift trend is preserved (or at least bounded) across the cited population-synthesis codes, the claimed detectability implications for LISA/ET/CE rest on an unquantified systematic uncertainty.

    Authors: We agree that the absolute normalization of the rates is code-dependent. However, the monotonic rise up to z = 5 is driven primarily by the redshift evolution of the galaxy assembly and cluster formation/disruption prescriptions in GAMESH, which are independent of the specific binary-evolution code. In the revised manuscript we will add a dedicated paragraph in the rate-density section that (i) states the trend is a robust feature of the reference model, (ii) notes that code variations mainly affect the overall amplitude rather than the shape of the redshift dependence (supported by cross-code comparisons in the literature), and (iii) qualifies the LISA/ET/CE implications accordingly. We will also include a brief sensitivity test using an alternative code for a subset of clusters to illustrate that the increasing trend persists. revision: partial

Circularity Check

0 steps flagged

No significant circularity; calibration validates model while cosmic rates are independent outputs

full rationale

The paper calibrates its GAMESH-based reference model to reproduce the observed Milky Way globular cluster age-mass distribution. This functions as an external validation benchmark rather than a self-referential prediction. The claimed redshift evolution of BBH birth and merger rate densities to z=5, along with hierarchical merger contributions, are generated by running the coupled galaxy formation and population synthesis framework forward in time. No equations or steps in the provided text reduce the target results to the calibration inputs by construction. Divergence across synthesis codes is noted as a robustness issue but does not create a definitional or fitted-input circularity. The derivation chain remains self-contained against the stated external observations and model components.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the GAMESH model prescriptions and the cluster synthesis codes, with some parameters adjusted to fit Milky Way observations.

free parameters (1)
  • cluster formation and disruption parameters
    Parameters in GAMESH tuned to reproduce the observed age-mass distribution of Milky Way globular clusters.
axioms (1)
  • domain assumption Validity of the population synthesis codes for modeling black hole formation, evolution, and mergers in clusters
    The paper notes divergent results from different codes, highlighting reliance on these codes' assumptions.

pith-pipeline@v0.9.0 · 5584 in / 1477 out tokens · 135479 ms · 2026-05-16T22:44:27.225876+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 2 Pith papers

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

  1. Investigating the formation channel of GW231123: Population III stars or hierarchical mergers?

    astro-ph.GA 2026-04 conditional novelty 6.0

    GW231123 most likely formed through hierarchical mergers of black holes in metal-poor globular clusters, with isolated binary channels failing to match the observed merger redshift and masses.

  2. Investigating the formation channel of GW231123: Population III stars or hierarchical mergers?

    astro-ph.GA 2026-04 unverdicted novelty 5.0

    Coupled cosmological and cluster simulations show isolated binary evolution cannot produce GW231123-like mergers at the observed redshift, while hierarchical mergers in globular clusters can, yielding a local rate of ...

Reference graph

Works this paper leans on

156 extracted references · 156 canonical work pages · cited by 1 Pith paper · 3 internal anchors

  1. [1]

    Abac, A. G. et al. 2025 [arXiv:2508.18082]

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  2. [2]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2016, Phys. Rev. Lett., 116, 241103

    work page 2016

  3. [3]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2019, Physical Review X, 9, 031040

    work page 2019

  4. [4]

    P., Abbott, R., Abbott, T

    Abbott, B. P., Abbott, R., Abbott, T. D., et al. 2017, ApJ, 848, L12

    work page 2017

  5. [5]

    D., Abraham, S., et al

    Abbott, R., Abbott, T. D., Abraham, S., et al. 2021, Physical Review X, 11, 021053

    work page 2021

  6. [6]

    D., Acernese, F., et al

    Abbott, R., Abbott, T. D., Acernese, F., et al. 2024, Phys. Rev. D, 109, 022001

    work page 2024

  7. [7]

    Adamo, A., Zeidler, P., Kruijssen, J. M. D., et al. 2020, Space Sci. Rev., 216, 69

    work page 2020

  8. [8]

    L., et al

    Antonini, F., Chatterjee, S., Rodriguez, C. L., et al. 2016, ApJ, 816, 65

    work page 2016

  9. [9]

    & Gieles, M

    Antonini, F. & Gieles, M. 2020, MNRAS, 492, 2936

    work page 2020

  10. [10]

    2023, MNRAS, 522, 466

    Antonini, F., Gieles, M., Dosopoulou, F., & Chattopadhyay, D. 2023, MNRAS, 522, 466

    work page 2023

  11. [11]

    & Rasio, F

    Antonini, F. & Rasio, F. A. 2016, ApJ, 831, 187

    work page 2016

  12. [12]

    Antonini, F., Toonen, S., & Hamers, A. S. 2017, ApJ, 841, 77 Arca Sedda, M., Askar, A., & Giersz, M. 2018, MNRAS, 479, 4652

    work page 2017

  13. [13]

    & Capuzzo-Dolcetta, R

    Arca-Sedda, M. & Capuzzo-Dolcetta, R. 2014, MNRAS, 444, 3738 Arca Sedda, M., Kamlah, A. W. H., Spurzem, R., et al. 2024, MNRAS, 528, 5119 Arca Sedda, M., Kamlah, A. W. H., Spurzem, R., et al. 2023, MNRAS, 526, 429 Arca Sedda, M., Li, G., & Kocsis, B. 2021, A&A, 650, A189 Arca Sedda, M., Mapelli, M., Spera, M., Benacquista, M., & Giacobbo, N. 2020, ApJ, 894, 133

    work page 2014

  14. [14]

    C., Mapelli, M., Giacobbo, N., et al

    Artale, M. C., Mapelli, M., Giacobbo, N., et al. 2019, MNRAS, 487, 1675

    work page 2019

  15. [15]

    2017, MNRAS, 464, L36

    Askar, A., Szkudlarek, M., Gondek-Rosi´nska, D., Giersz, M., & Bulik, T. 2017, MNRAS, 464, L36

    work page 2017

  16. [16]

    2023, MNRAS, 519, 5191

    Ballone, A., Costa, G., Mapelli, M., et al. 2023, MNRAS, 519, 5191

    work page 2023

  17. [17]

    L., et al

    Banerjee, S., Belczynski, K., Fryer, C. L., et al. 2020, A&A, 639, A41

    work page 2020

  18. [18]

    2017, ApJ, 835, 165

    Bartos, I., Kocsis, B., Haiman, Z., & Márka, S. 2017, ApJ, 835, 165

    work page 2017

  19. [19]

    2016, A&A, 594, A97

    Belczynski, K., Heger, A., Gladysz, W., et al. 2016, A&A, 594, A97

    work page 2016

  20. [20]

    A., et al

    Belczynski, K., Kalogera, V ., Rasio, F. A., et al. 2008, ApJS, 174, 223

    work page 2008

  21. [21]

    E., et al

    Belczynski, K., Klencki, J., Fields, C. E., et al. 2020, A&A, 636, A104

    work page 2020

  22. [22]

    Bethe, H. A. & Brown, G. E. 1998, ApJ, 506, 780

    work page 1998

  23. [23]

    C., Lake, G., Read, J., & Teyssier, R

    Boley, A. C., Lake, G., Read, J., & Teyssier, R. 2009, ApJ, 706, L192

    work page 2009

  24. [24]

    2020, ApJ, 898, 71

    Breivik, K., Coughlin, S., Zevin, M., et al. 2020, ApJ, 898, 71

    work page 2020

  25. [25]

    L., Larson, S

    Breivik, K., Rodriguez, C. L., Larson, S. L., Kalogera, V ., & Rasio, F. A. 2016, ApJ, 830, L18

    work page 2016

  26. [26]

    S., Berger, E., Stevenson, S., et al

    Broekgaarden, F. S., Berger, E., Stevenson, S., et al. 2022, MNRAS, 516, 5737

    work page 2022

  27. [27]

    & Gnedin, O

    Brown, G. & Gnedin, O. Y . 2021, MNRAS, 508, 5935

    work page 2021

  28. [28]

    L., Lamberts, A., et al

    Bruel, T., Rodriguez, C. L., Lamberts, A., et al. 2024, A&A, 686, A106

    work page 2024

  29. [29]

    Callister, T. A. & Farr, W. M. 2024, Physical Review X, 14

    work page 2024

  30. [30]

    2022, MNRAS, 516, 5914

    Calura, F., Lupi, A., Rosdahl, J., et al. 2022, MNRAS, 516, 5914

    work page 2022

  31. [31]

    2024, arXiv e-prints, arXiv:2411.02502

    Calura, F., Pascale, R., Agertz, O., et al. 2024, arXiv e-prints, arXiv:2411.02502

    work page arXiv 2024

  32. [32]

    O., Zlochower, Y ., & Merritt, D

    Campanelli, M., Lousto, C. O., Zlochower, Y ., & Merritt, D. 2007, Phys. Rev. Lett., 98, 231102

    work page 2007

  33. [33]

    & Miocchi, P

    Capuzzo-Dolcetta, R. & Miocchi, P. 2008, MNRAS, 388, L69

    work page 2008

  34. [34]

    L., & Rasio, F

    Chatterjee, S., Rodriguez, C. L., & Rasio, F. A. 2017, ApJ, 834, 68

    work page 2017

  35. [35]

    Chattopadhyay, D., Stegmann, J., Antonini, F., Barber, J., & Romero-Shaw, I. M. 2023, MNRAS, 526, 4908

    work page 2023

  36. [36]

    2021, MNRAS, 502, 6157

    Chen, Y ., Li, H., & V ogelsberger, M. 2021, MNRAS, 502, 6157

    work page 2021

  37. [37]

    Confronting Primordial Black Holes with LIGO-Virgo-KAGRA and the Einstein Tele- scope,

    Chen, Z.-C. & Hall, A. 2024, arXiv e-prints, arXiv:2402.03934

    work page arXiv 2024

  38. [38]

    2022, MNRAS, 516, 1072

    Costa, G., Ballone, A., Mapelli, M., & Bressan, A. 2022, MNRAS, 516, 1072

    work page 2022

  39. [39]

    2023, MNRAS, 525, 2891

    Costa, G., Mapelli, M., Iorio, G., et al. 2023, MNRAS, 525, 2891

    work page 2023

  40. [40]

    GW231123: A Possible Primordial Black Hole Origin

    Dame, T. M., Hartmann, D., & Thaddeus, P. 2001, ApJ, 547, 792 de Grijs, R., Li, C., & Geller, A. M. 2015, The dynamical importance of binary systems in young massive star clusters De Luca, V ., Desjacques, V ., Franciolini, G., Pani, P., & Riotto, A. 2021, Phys. Rev. Lett., 126, 051101 De Luca, V ., Franciolini, G., & Riotto, A. 2025, arXiv e-prints, arXi...

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  41. [41]

    2012, ApJ, 759, 52

    Dominik, M., Belczynski, K., Fryer, C., et al. 2012, ApJ, 759, 52

    work page 2012

  42. [42]

    2013, ApJ, 779, 72

    Dominik, M., Belczynski, K., Fryer, C., et al. 2013, ApJ, 779, 72

    work page 2013

  43. [43]

    2015, ApJ, 806, 263

    Dominik, M., Berti, E., O’Shaughnessy, R., et al. 2015, ApJ, 806, 263

    work page 2015

  44. [44]

    2019, MNRAS, 485, 4817

    Donnari, M., Pillepich, A., Nelson, D., et al. 2019, MNRAS, 485, 4817

    work page 2019

  45. [45]

    E., Sales, L

    Doppel, J. E., Sales, L. V ., Nelson, D., et al. 2023, MNRAS, 518, 2453

    work page 2023

  46. [46]

    2011, ApJ, 738, 74

    Dotter, A., Sarajedini, A., & Anderson, J. 2011, ApJ, 738, 74

    work page 2011

  47. [47]

    2010, ApJ, 708, 698

    Dotter, A., Sarajedini, A., Anderson, J., et al. 2010, ApJ, 708, 698

    work page 2010

  48. [48]

    2023, Astronomy and Computing, 42, 100671

    Dupletsa, U., Harms, J., Banerjee, B., et al. 2023, Astronomy and Computing, 42, 100671

    work page 2023

  49. [49]

    D., Bullock, J

    Elbert, O. D., Bullock, J. S., & Kaplinghat, M. 2018, MNRAS, 473, 1186

    work page 2018

  50. [50]

    Elmegreen, B. G. & Hunter, D. A. 2010, ApJ, 712, 604

    work page 2010

  51. [51]

    E., Fishbach, M., & Justham, S

    Farmer, R., Renzo, M., de Mink, S. E., Fishbach, M., & Justham, S. 2020, ApJ, 902, L36

    work page 2020

  52. [52]

    E., Marchant, P., & Justham, S

    Farmer, R., Renzo, M., de Mink, S. E., Marchant, P., & Justham, S. 2019, ApJ, 887, 53

    work page 2019

  53. [53]

    A., & Holz, D

    Favata, M., Hughes, S. A., & Holz, D. E. 2004, ApJ, 607, L5

    work page 2004

  54. [54]

    & Fragione, G

    Fishbach, M. & Fragione, G. 2023, MNRAS, 522, 5546

    work page 2023

  55. [55]

    Forbes, D. A. & Bridges, T. 2010, MNRAS, 404, 1203

    work page 2010

  56. [56]

    Franciolini, K

    Franciolini, G., Kritos, K., Reali, L., Broekgaarden, F., & Berti, E. 2024, arXiv e-prints, arXiv:2401.13038

    work page arXiv 2024

  57. [57]

    & Pani, P

    Franciolini, G. & Pani, P. 2022, Phys. Rev. D, 105, 123024

    work page 2022

  58. [58]

    & Yajima, H

    Fukushima, H. & Yajima, H. 2021, MNRAS, 506, 5512

    work page 2021

  59. [59]

    2023, in Rencontres de Moriond 2023: Proceedings of the Gravitation Session, 49

    Gerosa, D. 2023, in Rencontres de Moriond 2023: Proceedings of the Gravitation Session, 49

    work page 2023

  60. [60]

    & Berti, E

    Gerosa, D. & Berti, E. 2017, Phys. Rev. D, 95, 124046

    work page 2017

  61. [61]

    & Mapelli, M

    Giacobbo, N. & Mapelli, M. 2018, MNRAS, 480, 2011

    work page 2018

  62. [62]

    2018, MNRAS, 474, 2959

    Giacobbo, N., Mapelli, M., & Spera, M. 2018, MNRAS, 474, 2959

    work page 2018

  63. [63]

    F., Baumgardt, H., et al

    Gieles, M., Portegies Zwart, S. F., Baumgardt, H., et al. 2006, MNRAS, 371, 793

    work page 2006

  64. [64]

    2015, MNRAS, 454, 3150

    Giersz, M., Leigh, N., Hypki, A., Lützgendorf, N., & Askar, A. 2015, MNRAS, 454, 3150

    work page 2015

  65. [65]

    & Kruijssen, J

    Ginsburg, A. & Kruijssen, J. M. D. 2018, ApJ, 864, L17 González Prieto, E., Kremer, K., Fragione, G., et al. 2022, ApJ, 940, 131

    work page 2018

  66. [66]

    2017, MNRAS, 469, 1101

    Graziani, L., de Bennassuti, M., Schneider, R., Kawata, D., & Salvadori, S. 2017, MNRAS, 469, 1101

    work page 2017

  67. [67]

    2015, MNRAS, 449, 3137

    Graziani, L., Salvadori, S., Schneider, R., et al. 2015, MNRAS, 449, 3137

    work page 2015

  68. [68]

    2020c, MNRAS, 495, L81 Grudi´c, M

    Graziani, L., Schneider, R., Marassi, S., et al. 2020c, MNRAS, 495, L81 Grudi´c, M. Y ., Hafen, Z., Rodriguez, C. L., et al. 2023, MNRAS, 519, 1366

    work page 2023

  69. [69]

    2008, ApJ, 686, 829

    Holley-Bockelmann, K., Gültekin, K., Shoemaker, D., & Yunes, N. 2008, ApJ, 686, 829

    work page 2008

  70. [70]

    F., Kereš, D., Oñorbe, J., et al

    Hopkins, P. F., Kereš, D., Oñorbe, J., et al. 2014, MNRAS, 445, 581

    work page 2014

  71. [71]

    R., Pols, O

    Hurley, J. R., Pols, O. R., & Tout, C. A. 2000, MNRAS, 315, 543

    work page 2000

  72. [72]

    2023, MNRAS, 524, 426

    Iorio, G., Mapelli, M., Costa, G., et al. 2023, MNRAS, 524, 426

    work page 2023

  73. [73]

    & Gröbner, M

    Ishibashi, W. & Gröbner, M. 2020, A&A, 639, A108

    work page 2020

  74. [74]

    Accurate models for recoil velocity distribution in black hole mergers with comparable to extreme mass-ratios and their astrophysi- cal implications,

    Islam, T. & Wadekar, D. 2025 [arXiv:2511.11536]

    work page arXiv 2025

  75. [75]

    2017, MNRAS, 467, 4739

    Kaviraj, S., Laigle, C., Kimm, T., et al. 2017, MNRAS, 467, 4739

    work page 2017

  76. [76]

    W., Kruijssen, J

    Keller, B. W., Kruijssen, J. M. D., Pfeffer, J., et al. 2020, MNRAS, 495, 4248

    work page 2020

  77. [77]

    2010, ApJ, 715, 1006

    Kesden, M., Sperhake, U., & Berti, E. 2010, ApJ, 715, 1006

    work page 2010

  78. [78]

    Kimm, T., Cen, R., Rosdahl, J., & Yi, S. K. 2016, ApJ, 823, 52

    work page 2016

  79. [79]

    2014, MNRAS, 442, 2963

    Kinugawa, T., Inayoshi, K., Hotokezaka, K., Nakauchi, D., & Nakamura, T. 2014, MNRAS, 442, 2963

    work page 2014

  80. [80]

    2016, Progress of Theoretical and Experimental Physics, 2016, 103E01

    Kinugawa, T., Nakano, H., & Nakamura, T. 2016, Progress of Theoretical and Experimental Physics, 2016, 103E01

    work page 2016

Showing first 80 references.