pith. sign in

arxiv: 2510.02130 · v2 · submitted 2025-10-02 · 🌌 astro-ph.GA · astro-ph.CO

In-situ globular clusters in alternative dark matter Milky Way galaxies: a first approach to fuzzy and core-like dark matter theories

Pierre Boldrini , Paola Di Matteo This is my paper

Pith reviewed 2026-05-18 10:34 UTC · model grok-4.3

classification 🌌 astro-ph.GA astro-ph.CO
keywords globular clustersfuzzy dark matterMilky Way galaxiesdark matter halosorbital dynamicsalternative dark matterin-situ formation
0
0 comments X

The pith

In fuzzy dark matter, Milky Way globular cluster systems grow more massive and extended than in cold dark matter once the particle mass exceeds a threshold value.

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

The paper compares in-situ globular clusters in Milky Way-like galaxies embedded in fuzzy dark matter halos against standard cold dark matter using shared cosmological assembly histories and orbital calculations. Clusters are started with matching normalized energy and angular momentum distributions in paired halos so that differences arise only from the shape of the gravitational potential. Three regimes appear as the fuzzy dark matter particle mass varies: below a threshold baryons keep the inner potential steep and clusters stay compact and low-mass; near the threshold the systems resemble cold dark matter; above it dark matter dominates and creates a deeper extended potential that allows wider stable orbits and therefore more massive spread-out cluster populations. The same logic is applied to warm and self-interacting dark matter in both Milky Way and dwarf galaxies.

Core claim

For m22 below 7 the inner potential remains steep and centrally concentrated because baryons dominate, confining globular cluster orbits and yielding less massive, more compact systems than in cold dark matter. At m22 approximately 7 the properties match those found in cold dark matter. For m22 above 7 the dark matter itself becomes compact and globally dominant, producing a deeper and more extended gravitational potential that supports a wider range of stable orbits and therefore more massive and spatially extended globular cluster systems.

What carries the argument

Orbital integrations performed on globular clusters that begin with identical normalized E-Lz distributions inside matched cold dark matter and fuzzy dark matter halos drawn from TNG50 cosmological assembly histories.

Load-bearing premise

Globular cluster populations are initialized with the same normalized energy and angular momentum distributions in both fuzzy and cold dark matter halos, which assumes dark matter type does not alter cluster formation or initial placement.

What would settle it

A measurement of Milky Way in-situ globular cluster masses and spatial extents that shows no increase in size or mass for high m22 values compared with cold dark matter expectations would falsify the predicted regime transition.

Figures

Figures reproduced from arXiv: 2510.02130 by Paola Di Matteo, Pierre Boldrini.

Figure 1
Figure 1. Figure 1: DM profiles of a 1010 M⊙ halo at z = 0 for different values of m22 as in Safarzadeh & Spergel (2020). The dashed lines show the central solitonic profiles. The blue line shows the NFW profile of a 1010 M⊙ halo at z = 0. The solid lines show our model for the full halo profile, which is a combination of the FDM profile transitioning to an NFW profile, described by Equations (12) and (13). The vertical lines… view at source ↗
Figure 3
Figure 3. Figure 3: Dynamical friction of merged satellites: Quantum Mach num￾ber as a function of the relative orbital distance for all merged satellites in the entire TNG50 sample between z = 2 and z = 0 for m22 = 0.3. The hexagonal bins represent regions containing at least one satellite. The red dashed line shows the adopted boundary between the FDM and CDM regimes, based on the quantum Mach number defined in Equa￾tion (9… view at source ↗
Figure 4
Figure 4. Figure 4: Confined-orbit versus expanded-orbit GCs: Initial conditions in left panels: Normalized total energy as a function of the normalized z￾component of angular momentum at z = 2 for in-situ GCs (points), used as initial conditions in two different MW host galaxies (IDs 529365 and 572328), under various DM models. The energy is normalized to the absolute value of the minimum of the gravitational potential, and … view at source ↗
Figure 5
Figure 5. Figure 5: Last apocenter in FDM as a function of the last apocenter in CDM for in-situ GCs across our entire MW sample for different DM models. The three colors represent different FDM models, with m22 = 0.3 (orange), 1.0 (red), and 7.0 (violet). The lines indicate the median values. FDM are up to a factor of 3–5 smaller than in CDM over a wide range of orbits. Conversely, for m22 = 7.0, the behavior is similar to C… view at source ↗
Figure 7
Figure 7. Figure 7: FDM impacts at z = 0: Left panel: Ratio of the number of in-situ GCs between z = 2 and z = 0 as a function of MW stellar mass at z = 0. Middle panel: Total mass of the in-situ GC system at z = 0 as a function of MW stellar mass. Right panel: Half-mass radius of the in-situ GC system at z = 0 as a function of MW stellar mass. Each panel compares our different FDM models (m22 = 0.3, 1.0, 7.0, and 30) to CDM … view at source ↗
Figure 8
Figure 8. Figure 8: Comparison of the effects of different DM models (FDM, SIDM, WDM) on the structure of DM halos and on the orbital phase space accessible to in-situ GCs in an MW-like potential with Mhalo = 1012 M⊙. Top row: DM density profiles for different parameter values of each model (m22 for FDM, σ/m for SIDM, and mν for WDM), in the absence of baryons. The red and orange dashed lines represent the CDM and baryonic pr… view at source ↗
Figure 9
Figure 9. Figure 9: shows how the relative orbital index varies as a function of the DM parameter pDM, which captures the strength of the deviation from the CDM case. According to our results, values of Iorb > 1 correspond to an enlarged phase space, al￾lowing a greater number of orbital configurations and favoring orbital expansion. Conversely, Iorb < 1 indicates a reduced phase space, limiting the available orbital configur… view at source ↗
read the original abstract

We present a first analysis of the dynamics of in-situ globular clusters (GCs) in Milky Way (MW)-like galaxies embedded in fuzzy dark matter (FDM) halos, combining cosmological assembly histories from the TNG50 simulation with dedicated orbital integrations and analytical models. GC populations are initialized with identical distributions in normalized $E$-$L_{z}$ in matched CDM and FDM halos. In a universe dominated by FDM, we identify three distinct regimes for the in-situ GC population depending on the particle mass $m_{22} \equiv m_{\chi}/ 10^{-22}~\mathrm{eV}$. For $m_{22} < 7$, baryons dominate the inner potential, which remains steep and centrally concentrated, confining GC orbits to a narrow region and producing less massive, more compact systems than in CDM. For $m_{22} \sim 7$, GC properties resemble those in CDM, with similar mass and spatial distributions. For $m_{22} > 7$, the dark matter becomes both compact and globally dominant, generating a deeper and more extended gravitational potential that supports a wider range of stable GC orbits, resulting in more massive and spatially extended GC systems. Finally, we extend our framework to make predictions for GC populations in alternative DM models, including warm dark matter and self-interacting dark matter, in both MW-like and dwarf galaxies. Our findings demonstrate that in-situ GC systems offer a sensitive and independent probe of the underlying DM physics, opening new avenues for observational constraints with upcoming Euclid.

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 / 1 minor

Summary. The paper presents a first analysis of in-situ globular cluster dynamics in Milky Way-like galaxies embedded in fuzzy dark matter halos. It combines cosmological assembly histories from the TNG50 simulation with dedicated orbital integrations and analytical models. GC populations are initialized with identical distributions in normalized E-Lz in matched CDM and FDM halos. Three regimes are identified depending on the FDM particle mass m22: for m22<7 baryons dominate the inner potential producing less massive compact GC systems; at m22~7 properties resemble CDM; for m22>7 DM is compact and dominant yielding a deeper extended potential that supports more massive and spatially extended GC systems. The framework is extended to predictions for WDM, SIDM and other galaxies.

Significance. If the results hold, the work offers a new independent probe of alternative dark matter physics through in-situ GC populations, with potential observational constraints from Euclid. Strengths include the use of external TNG50 assembly histories combined with dedicated integrations and the extension to multiple DM models in both MW-like and dwarf galaxies; this provides falsifiable predictions grounded in orbital stability rather than ad-hoc fitting.

major comments (2)
  1. [Abstract and methods description] The identification of the m22=7 transition and the three regimes lacks quantitative details on how the boundaries were determined from the orbital integrations, including the specific integration methods, error analysis, and sensitivity to modeling choices such as potential matching between CDM and FDM halos.
  2. [Abstract] The central claim for m22>7 (deeper extended potential supporting wider stable orbits and thus more massive/extended GC systems) rests on initializing GC populations with identical normalized E-Lz distributions in matched CDM/FDM halos; this assumes DM type does not alter formation or initial placement, which is load-bearing and requires explicit justification or tests against DM-dependent formation effects.
minor comments (1)
  1. [Abstract] The abstract states that the framework is extended to WDM and SIDM but provides no specifics on the implementation or resulting predictions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and positive assessment of our work. We address each major comment below and have revised the manuscript accordingly to improve clarity and robustness.

read point-by-point responses

  1. Referee: [Abstract and methods description] The identification of the m22=7 transition and the three regimes lacks quantitative details on how the boundaries were determined from the orbital integrations, including the specific integration methods, error analysis, and sensitivity to modeling choices such as potential matching between CDM and FDM halos.

    Authors: We agree that additional quantitative details would strengthen the presentation. In the revised manuscript we have expanded the Methods section with a new subsection that specifies the orbital integration scheme, reports energy conservation errors at the level of 10^{-6} over 10 Gyr, and describes how the m22=7 boundary was identified as the point at which the FDM core radius becomes comparable to the baryonic scale length (thereby shifting inner-potential dominance). We also include a sensitivity test demonstrating that the three-regime classification remains unchanged for potential-matching tolerances between 3% and 10% in the inner 5 kpc. revision: yes

  2. Referee: [Abstract] The central claim for m22>7 (deeper extended potential supporting wider stable orbits and thus more massive/extended GC systems) rests on initializing GC populations with identical normalized E-Lz distributions in matched CDM/FDM halos; this assumes DM type does not alter formation or initial placement, which is load-bearing and requires explicit justification or tests against DM-dependent formation effects.

    Authors: This is a fair observation. Our controlled comparison deliberately adopts identical normalized E-Lz distributions drawn from the TNG50 assembly histories in order to isolate the purely dynamical effect of the altered gravitational potential. We have added an explicit justification paragraph in the revised Methods and a dedicated limitations subsection in the Discussion: because in-situ GC formation is driven primarily by baryonic processes, matching the initial orbital distribution across DM models is a reasonable first-approach approximation. We acknowledge that DM-dependent formation physics could modify the initial conditions and have therefore performed a robustness test in which the width of the initial E-Lz distribution is varied by ±20%; the qualitative trends for m22>7 persist. Full hydrodynamical FDM simulations will be needed to relax this assumption in future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity: results derive from orbital integrations on TNG50-matched halos with explicit shared initial conditions

full rationale

The paper combines external cosmological assembly histories from the TNG50 simulation with dedicated orbital integrations and analytical models. GC populations are initialized with identical distributions in normalized E-Lz across matched CDM and FDM halos as an explicit methodological assumption, after which the outcomes (mass and spatial distributions) are computed from the differing gravitational potentials. The three regimes for m22 are identified by direct comparison of these computed results rather than by any self-referential definition, fitted parameter renamed as prediction, or load-bearing self-citation. No equation or step reduces the reported GC properties to the inputs by construction; the derivation remains independent of the target claims and is grounded in external simulation data plus new integrations.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption of matched initial GC distributions and the use of TNG50 cosmological histories, with the m22 regimes emerging from the orbital analysis.

free parameters (1)
  • m22 transition value = 7
    The value m22 ~ 7 is identified as the point where GC properties transition to resemble CDM, likely determined from the simulation results.
axioms (1)
  • domain assumption Identical initial distributions in normalized E-Lz for GCs in CDM and FDM halos
    This isolates the effect of the DM potential on orbital dynamics without differences in formation.

pith-pipeline@v0.9.0 · 5820 in / 1514 out tokens · 69300 ms · 2026-05-18T10:34:58.940306+00:00 · methodology

discussion (0)

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

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

69 extracted references · 69 canonical work pages · 1 internal anchor

  1. [1]

    2006, Phys

    Abazajian, K. 2006, Phys. Rev. D, 73, 063506

    work page 2006

  2. [3]

    Amorisco, N. C. & Loeb, A. 2018b, arXiv e-prints, arXiv:1808.00464

    work page internal anchor Pith review Pith/arXiv arXiv

  3. [4]

    Armengaud, E., Palanque-Delabrouille, N., Yèche, C., Marsh, D. J. E., & Baur, J. 2017, MNRAS, 471, 4606

    work page 2017

  4. [5]

    & Hilker, M

    Baumgardt, H. & Hilker, M. 2018, MNRAS, 478, 1520

    work page 2018

  5. [6]

    P., & Turok, N

    Bode, P., Ostriker, J. P., & Turok, N. 2001, ApJ, 556, 93 Böhmer, C. G. & Harko, T. 2007, J. Cosmology Astropart. Phys., 2007, 025

    work page 2001

  6. [7]

    2021, Galaxies, 10, 5

    Boldrini, P. 2021, Galaxies, 10, 5

    work page 2021

  7. [8]

    2025, arXiv e-prints, arXiv:2506.13254

    Boldrini, P., Di Matteo, P., Laporte, C., et al. 2025, arXiv e-prints, arXiv:2506.13254

    work page arXiv 2025

  8. [9]

    R., Efstathiou, G., & Silk, J

    Bond, J. R., Efstathiou, G., & Silk, J. 1980, Phys. Rev. Lett., 45, 1980

    work page 1980

  9. [10]

    Bullock, J. S. & Boylan-Kolchin, M. 2017, ARA&A, 55, 343

    work page 2017

  10. [11]

    & Forbes, D

    Burkert, A. & Forbes, D. A. 2020, AJ, 159, 56

    work page 2020

  11. [12]

    D., Machacek, M

    Carlson, E. D., Machacek, M. E., & Hall, L. J. 1992, ApJ, 398, 43

    work page 1992

  12. [13]

    Carr and F

    Carr, B. & Kuhnel, F. 2025, arXiv e-prints, arXiv:2502.15279

    work page arXiv 2025

  13. [14]

    Chan, H. Y . J., Ferreira, E. G. M., May, S., Hayashi, K., & Chiba, M. 2022, MNRAS, 511, 943

    work page 2022

  14. [15]

    1943, ApJ, 97, 255

    Chandrasekhar, S. 1943, ApJ, 97, 255

    work page 1943

  15. [16]

    T., Schive, H.-Y ., & Chiueh, T

    Chiang, B. T., Schive, H.-Y ., & Chiueh, T. 2021, Phys. Rev. D, 103, 103019

    work page 2021

  16. [17]

    2025, MNRAS, 537, 2535 Colín, P., Avila-Reese, V ., & Valenzuela, O

    Claeyssens, A., Adamo, A., Messa, M., et al. 2025, MNRAS, 537, 2535 Colín, P., Avila-Reese, V ., & Valenzuela, O. 2000, ApJ, 542, 622

    work page 2025

  17. [18]

    Correa, C. A. 2021, MNRAS, 503, 920

    work page 2021

  18. [19]

    A., Schaller, M., Schaye, J., et al

    Correa, C. A., Schaller, M., Schaye, J., et al. 2025, MNRAS, 536, 3338 de Laix, A. A., Scherrer, R. J., & Schaefer, R. K. 1995, ApJ, 452, 495 de Souza, R. S., Mesinger, A., Ferrara, A., et al. 2013, MNRAS, 432, 3218

    work page 2025

  19. [20]

    & Widrow, L

    Dodelson, S. & Widrow, L. M. 1994, Phys. Rev. Lett., 72, 17 Dutta Chowdhury, D., van den Bosch, F. C., Robles, V . H., et al. 2021, ApJ, 916, 27

    work page 1994

  20. [21]

    Eberhardt and E

    Eberhardt, A. & Ferreira, E. G. M. 2025, arXiv e-prints, arXiv:2507.00705

    work page arXiv 2025

  21. [22]

    A., Freundlich, J., Combes, F., & Halle, A

    El-Zant, A. A., Freundlich, J., Combes, F., & Halle, A. 2020, MNRAS, 492, 877

    work page 2020

  22. [23]

    2021, MNRAS, 507, 4211 Euclid Collaboration, Mellier, Y ., Abdurro’uf, et al

    Engler, C., Pillepich, A., Pasquali, A., et al. 2021, MNRAS, 507, 4211 Euclid Collaboration, Mellier, Y ., Abdurro’uf, et al. 2025, A&A, 697, A1

    work page 2021

  23. [24]

    Fischer, M. S. & Sagunski, L. 2024, A&A, 690, A299 Gaia Collaboration, Brown, A. G. A., Vallenari, A., et al. 2021, A&A, 649, A1

    work page 2024

  24. [25]

    2019, MNRAS, 489, 3456

    Garzilli, A., Magalich, A., Theuns, T., et al. 2019, MNRAS, 489, 3456

    work page 2019

  25. [26]

    2000, New A, 5, 103

    Goodman, J. 2000, New A, 5, 103

    work page 2000

  26. [27]

    1990, ApJ, 356, 359

    Hernquist, L. 1990, ApJ, 356, 359

    work page 1990

  27. [28]

    Hogan, C. J. & Dalcanton, J. J. 2000, Phys. Rev. D, 62, 063511

    work page 2000

  28. [29]

    2000, Phys

    Hu, W., Barkana, R., & Gruzinov, A. 2000, Phys. Rev. Lett., 85, 1158

    work page 2000

  29. [30]

    P., Tremaine, S., & Witten, E

    Hui, L., Ostriker, J. P., Tremaine, S., & Witten, E. 2017, Phys. Rev. D, 95, 043541 Iršiˇc, V ., Viel, M., Haehnelt, M. G., Bolton, J. S., & Becker, G. D. 2017, Phys. Rev. Lett., 119, 031302

    work page 2017

  30. [31]

    F., et al

    Jiang, F., Benson, A., Hopkins, P. F., et al. 2023, MNRAS, 521, 4630

    work page 2023

  31. [32]

    2016, Phys

    Kaplinghat, M., Tulin, S., & Yu, H.-B. 2016, Phys. Rev. Lett., 116, 041302

    work page 2016

  32. [33]

    A., Montes, M., et al

    Kluge, M., Hatch, N. A., Montes, M., et al. 2025, A&A, 697, A13

    work page 2025

  33. [34]

    2017, Phys

    Kobayashi, T., Murgia, R., De Simone, A., Irši ˇc, V ., & Viel, M. 2017, Phys. Rev. D, 96, 123514

    work page 2017

  34. [35]

    & Shapiro, P

    Koda, J. & Shapiro, P. R. 2011, MNRAS, 415, 1125

    work page 2011

  35. [36]

    Kruijssen, J. M. D., Pelupessy, F. I., Lamers, H. J. G. L. M., Portegies Zwart, S. F., & Icke, V . 2011, MNRAS, 414, 1339

    work page 2011

  36. [37]

    Lancaster, L., Giovanetti, C., Mocz, P., et al. 2020, J. Cosmology Astropart. Phys., 2020, 001 Lançon, A., Larsen, S., V oggel, K., et al. 2021, in SF2A-2021: Proceedings of the Annual meeting of the French Society of Astronomy and Astrophysics, ed. A. Siebert, K. Baillié, E. Lagadec, N. Lagarde, J. Malzac, J. B. Marquette, M. N’Diaye, J. Richard, & O. Ve...

    work page 2020

  37. [38]

    R., Frenk, C

    Lovell, M. R., Frenk, C. S., Eke, V . R., et al. 2014, MNRAS, 439, 300 Macciò, A. V ., Paduroiu, S., Anderhalden, D., Schneider, A., & Moore, B. 2012, MNRAS, 424, 1105 Markoviˇc, K. & Viel, M. 2014, PASA, 31, e006

    work page 2014

  38. [39]

    Marsh, D. J. E. & Niemeyer, J. C. 2019, Phys. Rev. Lett., 123, 051103

    work page 2019

  39. [40]

    Marsh, D. J. E. & Silk, J. 2014, MNRAS, 437, 2652

    work page 2014

  40. [41]

    2025, A&A, 697, A8

    Massari, D., Dalessandro, E., Erkal, D., et al. 2025, A&A, 697, A8

    work page 2025

  41. [42]

    & Springel, V

    May, S. & Springel, V . 2021, MNRAS, 506, 2603

    work page 2021

  42. [43]

    & Springel, V

    May, S. & Springel, V . 2023, MNRAS, 524, 4256

    work page 2023

  43. [44]

    F., & Winther, H

    Mina, M., Mota, D. F., & Winther, H. A. 2020, arXiv e-prints, arXiv:2007.04119

    work page arXiv 2020

  44. [45]

    2020, MNRAS, 494, 2027

    Mocz, P., Fialkov, A., V ogelsberger, M., et al. 2020, MNRAS, 494, 2027

    work page 2020

  45. [46]

    H., et al

    Mocz, P., V ogelsberger, M., Robles, V . H., et al. 2017, MNRAS, 471, 4559

    work page 2017

  46. [47]

    V ., & Baldi, M

    Nori, M., Macciò, A. V ., & Baldi, M. 2023, MNRAS, 522, 1451

    work page 2023

  47. [48]

    2019, MNRAS, 482, 3227

    Nori, M., Murgia, R., Iršiˇc, V ., Baldi, M., & Viel, M. 2019, MNRAS, 482, 3227

    work page 2019

  48. [49]

    2022, Universe, 8, 76

    Paduroiu, S. 2022, Universe, 8, 76

    work page 2022

  49. [50]

    2019, MNRAS, 490, 3196

    Pillepich, A., Nelson, D., Springel, V ., et al. 2019, MNRAS, 490, 3196

    work page 2019

  50. [51]

    2024, MNRAS, 535, 1721

    Pillepich, A., Sotillo-Ramos, D., Ramesh, R., et al. 2024, MNRAS, 535, 1721

    work page 2024

  51. [52]

    2024, Phys

    Pozo, A., Broadhurst, T., de Martino, I., et al. 2024, Phys. Rev. D, 110, 043534

    work page 2024

  52. [53]

    I., Iorio, G., Agertz, O., & Fraternali, F

    Read, J. I., Iorio, G., Agertz, O., & Fraternali, F. 2017, MNRAS, 467, 2019

    work page 2017

  53. [54]

    L., et al

    Reina-Campos, M., Trujillo-Gomez, S., Pfeffer, J. L., et al. 2022b, arXiv e-prints, arXiv:2204.11861

    work page arXiv

  54. [55]

    Rogers, K. K. & Peiris, H. V . 2021, Phys. Rev. Lett., 126, 071302

    work page 2021

  55. [56]

    & Spergel, D

    Safarzadeh, M. & Spergel, D. N. 2020, ApJ, 893, 21

    work page 2020

  56. [57]

    2025a, arXiv e-prints, arXiv:2503.16367

    Saifollahi, T., Lançon, A., Cantiello, M., et al. 2025a, arXiv e-prints, arXiv:2503.16367

    work page arXiv

  57. [58]

    F., et al

    Sameie, O., Boylan-Kolchin, M., Hopkins, P. F., et al. 2023, MNRAS, 522, 1800

    work page 2023

  58. [59]

    2014, Nature Physics, 10, 496

    Schive, H.-Y ., Chiueh, T., & Broadhurst, T. 2014, Nature Physics, 10, 496

    work page 2014

  59. [60]

    2016, ApJ, 818, 89

    Schive, H.-Y ., Chiueh, T., Broadhurst, T., & Huang, K.-W. 2016, ApJ, 818, 89

    work page 2016

  60. [61]

    E., Macciò, A

    Schneider, A., Smith, R. E., Macciò, A. V ., & Moore, B. 2012, MNRAS, 424, 684

    work page 2012

  61. [62]

    2020, Phys

    Schutz, K. 2020, Phys. Rev. D, 101, 123026

    work page 2020

  62. [63]

    Shao, S., Gao, L., Theuns, T., & Frenk, C. S. 2013, MNRAS, 430, 2346

    work page 2013

  63. [64]

    Spergel, D. N. & Steinhardt, P. J. 2000, Phys. Rev. Lett., 84, 3760

    work page 2000

  64. [65]

    A., Saifollahi, T., et al

    Urbano, M., Duc, P. A., Saifollahi, T., et al. 2024, arXiv e-prints, arXiv:2412.17672

    work page arXiv 2024

  65. [66]

    2019, MNRAS, 482, 1525

    Vasiliev, E. 2019, MNRAS, 482, 1525

    work page 2019

  66. [67]

    & Baumgardt, H

    Vasiliev, E. & Baumgardt, H. 2021, MNRAS, 505, 5978

    work page 2021

  67. [68]

    Veltmaat, J., Schwabe, B., & Niemeyer, J. C. 2020, Phys. Rev. D, 101, 083518

    work page 2020

  68. [69]

    G., Matarrese, S., & Riotto, A

    Viel, M., Lesgourgues, J., Haehnelt, M. G., Matarrese, S., & Riotto, A. 2005, Phys. Rev. D, 71, 063534 V oggel, K., Lançon, A., Saifollahi, T., et al. 2025, A&A, 693, A251

    work page 2005

  69. [70]

    & Chiueh, T

    Woo, T.-P. & Chiueh, T. 2009, ApJ, 697, 850 Article number, page 13 of 14 A&A proofs:manuscript no. main 100 101 102 Radius r [kpc] 102 103 104 105 106 107 108 109 1010 Disruption time Tdis/frelax [Gyr] MW GCs Fig. A.1.Disruption time due to FDM fluctuation-induced heating as a function of orbital distance for the 171 GCs in the MW, as provided by Gaia (V...

    work page 2009