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Dynamical traction and black hole orbital migration

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A black hole moving through a rotating stellar disc can be pulled outward by 'dynamical traction' — a systematic transfer of angular momentum from streaming stars — and in a cold, fragmenting disc this can eject it from the galactic centre.

desk verdict Warm-disc dynamical traction is real and worth taking seriously; the cold-disc two-stage instability is not supported by the authors' own self-gravitating run and should be demoted from the abstract. read the letter →

arxiv 2507.09674 v1 pith:7W7VBUJ6 submitted 2025-07-13 astro-ph.GA

C.M. Boily , T.L. François , J. Freundlich , F. Combes , A.-L. Melchior , Y. Hénin This is my paper · ORCID
classification astro-ph.GA
keywords dynamicaltractionfrictionblackholemigrationangularmomentumtransferFokker-PlanckdiffusionN-bodysimulationgalacticnucleiJeansinstability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a black hole drifting in a rotating, anisotropic stellar disc does not simply sink to the galactic centre under dynamical friction. Instead, the streaming motion of the stars exerts a systematic torque — 'dynamical traction' — that transfers angular momentum to the black hole, so a radially infalling black hole can be deflected onto an outward-migrating orbit. In a dynamically cold, fragmenting disc, the paper identifies a two-stage instability: a clump of stars pulls the black hole out of the centre, and dynamical traction then boosts its angular momentum so it keeps migrating outward. The authors propose a stability criterion based on the ratio of velocity dispersion to streaming motion, and they show that warm, nearly isotropic stellar environments keep the black hole near the centre, consistent with the Milky Way's nuclear cluster. The paper matters because it suggests that young galaxies with cold rotating discs may naturally host off-centred black holes, matching recent observations of offset AGN.

What carries the argument

The central mechanism is the sign-changing torque derived from the Fokker-Planck diffusion coefficient in Eq. (10): $\langle \Delta v_\phi\rangle \propto v_\phi\, f_\perp(0)\, [\mp 2\pi + x e^{x^2}\mathrm{erfc}(x)]\, dK/dv$, where $K^2=(R\Omega - v_\phi)^2 + v_\perp^2$. The first-order term $v_\phi \langle \Delta v_\phi\rangle$ carries the sign of $R\Omega - v_\phi$, so when the black hole lags the rotating stellar flow it gains angular momentum; this is the 'dynamical traction' that opposes dynamical friction. The transition to sustained angular-momentum growth occurs when this term dominates the quadratic velocity-diffusion terms, and the paper charts that transition as a stability line in the $M_\bullet$–$v_\phi$ plane for different velocity dispersions $\sigma_\star$ (Fig. 4). The N-body models realize the mechanism with a live Miyamoto–Nagai disc embedded in a frozen isochrone (Hénon) spherical halo, the frozen component being what keeps the Jeans-unstable clumps artificially bound.

What would settle it

Re-run the cold-disc radial-infall simulation with the halo fully live at the same resolution as the disc (the paper's fully self-gravitating run used 8.4 million particles with softening 32 pc) and check whether the Jeans-unstable clumps survive long enough to dislodge the black hole and whether the black hole migrates outward by ~1 kpc within ~1 Gyr; the paper's own self-gravitating run suggests clumps dissolve and the black hole remains at the centre, which would falsify the two-stage instability as stated.

Watch

Extended reading notes

Core claim

The paper's central claim is that gravitational focusing in a rotating stellar background produces a transverse acceleration, not just the parallel drag of Chandrasekhar dynamical friction. For a distribution function of the form $f(E, L_z)$, the Fokker-Planck diffusion coefficient $\langle \Delta v_\phi\rangle$ is proportional to a term that changes sign with $R\Omega - v_\phi$: a black hole lagging the stellar flow is pulled forward, and one leading the flow is dragged back. When the streaming-motion term $v_\phi \langle \Delta v_\phi\rangle$ overtakes the quadratic diffusion (heating) terms, the black hole systematically gains angular momentum and its orbit transitions from a low-$L_z$ box orbit to a high-$L_z$ loop orbit — the dynamical traction transition. In a warm disc this delays in-spiral by several hundred Myr and then drives outward migration; in a cold, Jeans-unstable disc the black hole's own perturbation triggers fragmentation, and a two-stage instability can remove it from the centre entirely. The paper states this strongest form as: 'In a dynamically cold environment, a BH is removed from the central region through a two-stage orbital migration instability.'

Load-bearing premise

The load-bearing modelling choice is to freeze the hot, spherical isochrone halo while evolving the cold disc; the paper itself states that this artificially enhances the binding energy of the stellar clumps and that relaxing the frozen constraint would change the outcome significantly (its one fully self-gravitating run dissolves the clumps and keeps the black hole at the centre).

Editorial extensions

If this is right

  • In a warm, non-fragmenting disc, a low-angular-momentum black hole first sinks for ~500 Myr, then gains angular momentum and migrates outward; the migration to the centre is delayed by several hundred million years.
  • In a cold disc, the outcome hinges on clump binding energy: strongly bound clumps can scatter the black hole and trigger outward migration, while weakly bound clumps dissolve in its tidal field and the black hole stays at the centre.
  • The proposed stability criterion is a threshold in isotropic velocity dispersion relative to streaming (angular momentum) motion: above it the black hole settles, below it the two-stage instability can remove it.
  • The Milky Way's nuclear star cluster is close to isotropic ($v_\phi/\sigma_\star \simeq 0.8$), below the critical line for its parameters, so its central black hole is expected to stay at the barycentre.
  • An outward-migrating $1.25\times10^7\,M_\odot$ black hole can move by ~1 kpc over roughly 750 Myr to 1 Gyr, in the range of the recently detected off-centre AGN at $z\simeq7.3$.

Reading between the lines

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

  • Because the fully self-gravitating run is the only one without the frozen halo, the two-stage instability may be an artifact of artificially enhancing clump binding energy; the paper's own analysis in §7.1 leaves that as the leading interpretation.
  • If dynamical traction is generic, the same torque should act on any massive perturber in a rotating disc — satellite galaxies, globular clusters, or gas clumps — so the mechanism may govern angular-momentum exchange in a wider class of systems than black holes.
  • The $v_\phi/\sigma_\star$ threshold could be translated into observable quantities (rotation curve, velocity dispersion, surface brightness) and used to predict which high-redshift discs should host off-centred active nuclei, something the paper does not do.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 5 minor

Summary. The paper studies the orbital evolution of a massive black hole in a rotating, anisotropic stellar background. Using a Fokker-Planck diffusion calculation with a Dirac-delta azimuthal distribution function, the authors derive a first-order angular-momentum diffusion term (Eq. 10) that changes sign with RΩ−vφ, and they name this systematic transfer of angular momentum to the BH 'dynamical traction'. Restricted N-body simulations of a Miyamoto-Nagai disc in a frozen isochrone halo show that a BH on a radial orbit in a warm disc acquires angular momentum and migrates outward after an initial friction phase (§5.1), while in a cold disc the response is dominated by Jeans-unstable clumps. The paper claims a 'two-stage orbital migration instability' in which bound clumps dislodge the BH and traction then drives outward migration, and it proposes a stability criterion based on the ratio of velocity dispersion to streaming motion. The paper also confronts the mechanism with the Milky Way nuclear cluster and with JWST observations of an off-centred AGN at z≈7.3.

Significance. If the warm-disc traction result is correct, it adds a genuine and potentially important effect: in rotating stellar backgrounds, dynamical friction on a massive perturber is not always inward, and angular-momentum exchange with streaming stars can stall or reverse migration. The paper's numerical demonstration in §5.1 is supported by angular-momentum conservation checks (Appendix C) and by a rough quantitative comparison with the Fokker-Planck rates in §6. The authors are also transparent about the main limitation: §7.1 reports a fully self-gravitating run in which clumps dissolve and 'the BH remains at the heart of the system'. However, the abstract and §8 present the two-stage instability as an established result, which is not supported by the evidence in the manuscript. The paper therefore contains a solid core (dynamical traction in warm discs) and an overreaching claim (cold-disc instability) that needs substantial revision.

major comments (3)
  1. [§7.1, Fig. 15, Abstract, §8] The headline 'two-stage orbital migration instability' is not supported by the paper's own fully self-gravitating calculation. In the Bonsai run with a live disc and live isochrone component (8.4×10^6 particles, l=32 pc), only ~62% of the clump mass is bound, the clump dissolves in the BH's tidal field, and 'the BH remains at the heart of the system' over 1.5 Gyr. The authors state that freezing the isochrone halo means 'the binding energy of the clumps is enhanced artificially, and we expect that relaxing the constraint of a frozen component will change the outcome of the numerical integration significantly.' The abstract and §8 nevertheless present the instability as a main result without this caveat. The claim should be reframed as contingent on a frozen, hot halo, and a fully self-gravitating run at the reference resolution should be provided before the instability can be considered established.
  2. [§3.2, Eq. (7); §3.3, Eq. (10); Fig. 4] The analytic derivation of dynamical traction uses a Dirac-delta distribution function in azimuthal velocity, D(vφ−RΩ), which removes the azimuthal velocity dispersion entirely. The sign-changing first-order term in Eq. (10) and the quantitative stability boundary in Fig. 4 are therefore computed for a DF with zero spread in vφ, not for the warm discs whose dispersion is the point of comparison. Because the warm-disc N-body runs independently support the existence of traction, this is not fatal to the mechanism, but the proposed criterion (a threshold in isotropic velocity dispersion versus streaming motion) is not demonstrated for finite azimuthal dispersion. Please recompute the diffusion coefficients with a finite σφ (e.g., a Gaussian or Schwarzschild DF) and show how the critical curves of Fig. 4 shift.
  3. [§5.2.1, clump S452] Even within the frozen-halo reference set-up, the cold-disc radial-orbit run does not show a scattering event off a bound stellar clump: clump S452 has positive total mechanical energy (E_k/|W| between about 1.77 and 1.88), and the paper concludes that 'self-gravity plays only a minor role in the interaction of the clump with the BH.' The two-stage scenario instead requires clumps 'with much binding energy' (§7), which occur only when the halo is frozen or partially live. The causal chain from Jeans-unstable clump to BH ejection is therefore not demonstrated in any simulation with a live halo, and the paper should either supply such a simulation or explicitly label the chain as a working hypothesis rather than an outcome.
minor comments (5)
  1. [§7, first paragraph] The sentence 'we have illustrated the transition from one regime to the other for an BH on a radial orbit in a hot disc (Fig. 6)' should cite Fig. 5; Fig. 6 is the circular-orbit warm-disc case.
  2. [§3.3 and elsewhere] Typos 'the on-set', 'offof', and '1:1 resonant trapping at co-rotation' should be corrected to 'onset', 'off of', and 'corotation'.
  3. [§3.5 and Abstract] The 300 Myr estimate is obtained by integrating the diffusion coefficients while holding R and z fixed; the authors acknowledge this caveat, but the abstract's '300 Myr or less' should carry this caveat explicitly.
  4. [§4.2 and §6] The text gives M•/m⋆=781 for the reference model and then rounds it to 10^3 in the comparison with Fig. 2; the two values should be reconciled in the text rather than in a parenthetical remark.
  5. [Eq. (2)] The placement of lnΛ in the denominator is visually ambiguous; please add parentheses or a derivation note.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the traction derivation is self-contained, the warm-disc N-body runs independently validate it, and the cold-disc caveat is an admitted robustness limitation rather than a circular step.

full rationale

The central analytical result, Eq. (10), follows from standard Chandrasekhar diffusion coefficients (Eq. 1) applied to an explicit distribution function f(E,L_z) specified in Eqs. (7)-(8). The sign-changing term in the angular-momentum transfer rate is a mathematical consequence of the Rosenbluth-potential derivatives and the definition dK/dv = -(RΩ v_phi/v - v)/K, not an input assumption that already contains the conclusion. The warm-disc N-body runs provide an independent check: §5.1.1 shows the radial-orbit BH gaining L_z while friction shrinks the orbit, and §6 compares measured Δv_phi with the analytical rates using parameters fixed by the numerical setup (N_s=1e5, m⋆=1.6e4 M⊙), finding approximate agreement. No parameter is fitted to the target result and then renamed a prediction. The Fig. 3 timescale and Fig. 4 stability line are model-generated criteria, but the paper does not use those same curves as the validation; the N-body simulations are the external benchmark. The cold-disc two-stage instability is genuinely fragile: the reference runs freeze the hot isochrone component ('We freeze the other (dynamically hot) stellar orbits completely', §4.1), and the authors explicitly concede that 'the binding energy of the clumps is enhanced artificially, and we expect that relaxing the constraint of a frozen component will change the outcome of the numerical integration significantly' (§7.1). Their one fully self-gravitating Bonsai run (8.4e6 particles) shows only ~62% of clump stars bound, the clump dissolving in the BH tidal field, and 'the BH remains at the heart of the system' (§7.1). That is an admitted validity limitation, not a circular derivation: the instability claim is contingent on a model assumption, but the outcome is not equivalent to the assumption by construction. The self-citation to Boily et al. (2008) for co-planar orbit coupling is used to motivate freezing the hot component, but §7.1 directly tests the consequence of that choice, so the citation is not load-bearing in a circular way. No uniqueness theorem is imported from the authors' prior work, and no known result is merely renamed and presented as an independent derivation. Overall, the paper's main derivation chain is self-contained and externally benchmarked, and the admitted cold-disc caveat is better classified as a robustness risk than as circularity.

Assumptions & free parameters 3 free parameters · 5 assumptions · 2 invented entities

The central claim rests on the frozen-halo modeling choice (which enhances fragment binding), the local Fokker-Planck approximation with a Dirac-delta streaming DF, and the co-planar coupling assumption. The traction mechanism itself is grounded in standard Chandrasekhar theory, but the instability scenario is sensitive to the halo treatment.

free parameters (3)
  • initial BH velocity (v∥=v⊥≈3 km/s) = 3 km/s
    Chosen to avoid singularity in diffusion coefficients; sets the start of the time integration in Fig 3, influencing the derived 300 Myr traction timescale (§3.4).
  • mass ratio rounding M•/m⋆ = 731 rounded to 10^3
    In §6 the authors round the BH-to-star mass ratio from 731 to 10^3 'to simplify the algebra', changing the analytic rates by tens of percent before comparing with N-body outputs.
  • disc-to-halo mass ratio MD/MIs = 1/6
    Chosen to boost the disc orbit fraction; the disc/halo mass split is a modeling choice that affects whether fragments survive (§4.1).
assumptions (5)
  • standard math Chandrasekhar dynamical friction and the Rosenbluth potential diffusion coefficients apply to a massive perturber in a locally homogeneous stellar background
    Used throughout Appendix A to derive Eq. (10), the central analytic result.
  • domain assumption The stellar DF has the separable form f(E,Lz) with a Dirac-delta streaming term: f = f⊥(v⊥)D(vϕ−RΩ)
    Eq. (7); restricts the study to perfectly circular streaming and removes velocity dispersion in the azimuthal direction, which amplifies the traction effect.
  • ad hoc to paper The spherical isochrone (Hénon) halo can be frozen while the disc evolves
    §4.1; the authors freeze hot orbits to save cost, and §7.1 states this artificially enhances fragment binding energy and changes the outcome. The central two-stage instability claim depends on this assumption.
  • domain assumption Co-planar loop orbits couple most strongly to the BH (Boily et al. 2008 Fig. 14b)
    Used in §4.1 to justify focusing on disc orbits within ±18° of the BH plane.
  • standard math Toomre and Jeans local stability analysis applies to the disc with a frozen halo
    Appendix D computes Q≈0.87 and the Jeans length to argue the disc is marginally unstable to fragmentation.
invented entities (2)
  • dynamical traction (named mechanism) independent evidence
    purpose: Net angular momentum transfer from a rotating stellar background to a black hole, producing outward migration and opposing dynamical friction.
    Demonstrated in warm-disc N-body runs (§5.1) where BH Lz grows steadily; conceptual counterpart to Chandrasekhar friction. It is a labeling of a gravitational torque, not a new physical constituent, so it does not carry the graviton problem.
  • two-stage orbital migration instability
    purpose: Describes the scenario where a BH first sinks via dynamical friction then is dislodged by massive clumps and migrates outward via traction.
    Proposed in abstract and §5.4; only occurs in runs with a frozen halo. In the fully self-gravitating run (§7.1) clumps dissolve and the BH remains at the center, so independent observational or modal evidence is lacking.

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Cite this review

Pith. "Pith review of Dynamical traction and black hole orbital migration." pith.science (2026). https://pith.science/paper/7W7VBUJ6

@misc{pith2026250709674,
  author       = {Pith},
  title        = {Pith review of: Dynamical traction and black hole orbital migration},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7W7VBUJ6}},
  note         = {Machine review of arXiv:2507.09674}
}
read the original abstract

We investigate the circumstances which allow a black hole to remain put at the galactic centre when the stellar core is anisotropic. We use N-body calculations to study the response of stellar orbit families embedded in a larger, isotropic isochrone (H\'enon) background potential. When the BH orbits in an odd f[E,Lz] velocity distribution function, they transfer angular momentum to it. We call this dynamical traction: it takes place whenever the kinetic energy drawn from f[E,Lz] has an excess of streaming motion over its (isotropic) v-dispersion. For a dynamically cold disc, the outcome depends on both the orbit of the BH and that of a Jeans-unstable stellar sub-structures. When the stellar clumps have much binding energy, a BH may scatter off of them after they formed. In the process the BH may be dislodged from the centre and migrate outward due to dynamical traction. When the stellar clumps are less bound, they may still migrate to the centre where they either dissolve or merge with the BH. The final configuration is similar to a nuclear star cluster which may yet be moving at ~10 km/s wrt the barycentre. The angular momentum transferred to a BH by dynamical traction delays the migration to the galactic centre by several hundred million years. The efficiency of angular momentum transfer is a strong function of the fragmented (cold) state of the stellar space density. In a dynamically cold environment, a BH is removed from the central region through a two-stage orbital migration instability. A criterion against this instability is proposed in the form of a threshold in isotropic velocity dispersion compared to streaming motion. For a BH to settle at the heart of a galaxy on time-scales of ~ 300 Myr or less requires that a large fraction of Lz be dissipated, or, alternatively, that the BH grows in situ in an isotropic environment devoid of sub-structures.

Figures

Figures reproduced from arXiv: 2507.09674 by the authors.

Figure 1
Figure 1. Sketch of gravitational accelerations for two di [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Rates of specific kinetic energy diffusion, ⟨∆E⟩ as a function of the azimuthal velocity vϕ. The rates are evaluated from Eqs. (A.7) and (A.3) for two values of the stellar velocity dispersion, σ⋆ : 20 km s−1 (in black or grey); and 10 km s−1 (in blue or skyblue). A) Setting M• = 1 × 107 M⊙, with M•/m⋆ ≃ 103 , the figure graphs each quadratic component and the first-order parallel one ( v∥ ⟨∆v∥⟩, dark solid lines; n… view at source ↗
Figure 3
Figure 3. Amplitude of the BH velocity components as a func [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (11 more)
Figure 5
Figure 5. Figure 5: The case when an BH is let go from R = 1.5 kpc in a (dynamically) warm stellar disc ( [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]
Figure 6
Figure 6. Figure 6: As for Fig. 5, but now for the BH started at [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Top left to bottom right: evolution of the system when the BH is released from rest at at radius [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Transition to a fragmented morphology for a galactic disc perturbed by a massive black hole. Left-hand panels: density map [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: The case of an BH falling from rest on a radial orbit. a) The solid black curve graphs the angular momentum accrued over [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: As for Fig. 9, but now the BH is launched from the origin at [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: Top left to bottom right: evolution of the BH set on a circular orbit initially of radius [PITH_FULL_IMAGE:figures/full_fig_p015_11.png]
Figure 12
Figure 12. Figure 12: Runs of angular momentum, radius and velocity components as function of time for an BH started on a circular orbit. a) [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: Runs of angular momentum and radius for three BH orbits: circular; an elliptical orbit with small eccentricity [PITH_FULL_IMAGE:figures/full_fig_p016_13.png]
Figure 14
Figure 14. Figure 14: A) The figure graphs the specific angular momentum [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]
Figure 15
Figure 15. Figure 15: Two examples of the interaction between the central BH and stellar sub-structures. In (A, top row), when the background [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

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Reference graph

Works this paper leans on

80 extracted references · 68 canonical work pages · cited by 1 Pith paper

  1. [1]

    2015, , 800, 127

    Angl \'e s-Alc \'a zar , D., \"O zel , F., Dav \'e , R., et al. 2015, , 800, 127

    work page 2015

  2. [2]

    Arg \"u elles , C. R. & Collazo , S. 2023, Universe, 9, 372

    work page 2023

  3. [3]

    Bahcall , J. N. & Wolf , R. A. 1976, , 209, 214

    1976

  4. [4]

    2021, Proc

    Balasubramanian , V. 2021, Proc. Natl. Acad. Sci., USA National Library of Medicine, 32, 118

    work page 2021

  5. [5]

    & van den Bosch , F

    Banik , U. & van den Bosch , F. C. 2021, , 912, 43

    work page 2021

  6. [6]

    & van den Bosch , F

    Banik , U. & van den Bosch , F. C. 2022, , 926, 215

    work page 2022

  7. [7]

    & Hut , P

    Barnes , J. & Hut , P. 1986, , 324, 446

    work page 1986

  8. [8]

    G., Kocevski , D

    Barro , G., P \'e rez-Gonz \'a lez , P. G., Kocevski , D. D., et al. 2024, , 963, 128

    work page 2024

Show all 80 references
  1. [9]

    M., Cleary , C

    Bellovary , J. M., Cleary , C. E., Munshi , F., et al. 2019, , 482, 2913

    2019

  2. [10]

    & Tremaine , S

    Binney , J. & Tremaine , S. 2008, Galactic Dynamics , 2^ nd edn. (Princeton: The University Press)

    2008

  3. [11]

    & Gerhard , O

    Bland-Hawthorn , J. & Gerhard , O. 2016, , 54, 529

    2016

  4. [12]

    D., Natarajan , P., et al

    Bogd \'a n , \'A ., Goulding , A. D., Natarajan , P., et al. 2024, Nature Astronomy, 8, 126

    2024

  5. [13]

    M., Padmanabhan , T., & Paiement , A

    Boily , C. M., Padmanabhan , T., & Paiement , A. 2008, , 383, 1619

    2008

  6. [14]

    2023, Nature Astronomy, 7, 731

    Boylan-Kolchin , M. 2023, Nature Astronomy, 7, 731

    2023

  7. [15]

    1943, , 97, 255

    Chandrasekhar , S. 1943, , 97, 255

    1943

  8. [16]

    2013, , 429, 3114

    Chapon , D., Mayer , L., & Teyssier , R. 2013, , 429, 3114

    2013

  9. [17]

    K., Gerhard , O., et al

    Chatzopoulos , S., Fritz , T. K., Gerhard , O., et al. 2015, , 447, 948

    2015

  10. [18]

    M., et al

    Chen , Z., Do , T., Ghez , A. M., et al. 2023, , 944, 79

    2023

  11. [19]

    & Kataria , S

    Chiba , R. & Kataria , S. K. 2024, , 528, 4115

    2024

  12. [20]

    2023, , 522, 948

    Chu , A., Boldrini , P., & Silk , J. 2023, , 522, 948

    2023

  13. [21]

    R., Dehnen , W., Read , J

    Cole , D. R., Dehnen , W., Read , J. I., & Wilkinson , M. I. 2012, , 426, 601

    2012

  14. [22]

    2018, , 475, 1574

    de Vita , R., Trenti , M., & MacLeod , M. 2018, , 475, 1574

    2018

  15. [23]

    M., Elmegreen , B

    Elmegreen , D. M., Elmegreen , B. G., Ravindranath , S., & Coe , D. A. 2007, , 658, 763

    2007

  16. [24]

    L., Bagley , M

    Finkelstein , S. L., Bagley , M. B., Ferguson , H. C., et al. 2023, , 946, L13

    2023

  17. [25]

    2015, , 806, 117

    Fouvry , J.-B., Binney , J., & Pichon , C. 2015, , 806, 117

    2015

  18. [26]

    K., Chatzopoulos , S., Gerhard , O., et al

    Fritz , T. K., Chatzopoulos , S., Gerhard , O., et al. 2016, ApJ, 821, 44

    2016

  19. [27]

    2007, , 59, 1095

    Fujii , M., Iwasawa , M., Funato , Y., & Makino , J. 2007, , 59, 1095

    2007

  20. [28]

    & Heggie , D

    Fukushige , T. & Heggie , D. C. 2000, , 318, 753

    2000

  21. [29]

    2023, , 674, A37

    Gaia Collaboration , Drimmel , R., Romero-G \'o mez , M., et al. 2023, , 674, A37

    2023

  22. [30]

    & Hut , P

    Heggie , D. & Hut , P. 2003, The Gravitational Million-Body Problem: A Multidisciplinary Approach to Star Cluster Dynamics (IOP Publishing Ltd)

    2003

  23. [31]

    Hopkins , P. F. & Quataert , E. 2011, , 415, 1027

    2011

  24. [32]

    Julian , W. H. & Toomre , A. 1966, , 146, 810

    1966

  25. [33]

    Kalnajs , A. J. 1972, in Astrophysics and Space Science Library, Vol. 31, IAU Colloq. 10: Gravitational N-Body Problem, ed. M. Lecar , 13

    1972

  26. [34]

    & Sridhar , S

    Kaur , K. & Sridhar , S. 2018, , 868, 134

    2018

  27. [35]

    & Stone , N

    Kaur , K. & Stone , N. C. 2022, , 515, 407

    2022

  28. [36]

    & Nelson , R

    Kley , W. & Nelson , R. P. 2012, , 50, 211

    2012

  29. [37]

    & Tremaine , S

    Kocsis , B. & Tremaine , S. 2015, , 448, 3265

    2015

  30. [38]

    & Ho , L

    Kormendy , J. & Ho , L. C. 2013, , 51, 511

    2013

  31. [39]

    2023, , 616, 266

    Labb \'e , I., van Dokkum , P., Nelson , E., et al. 2023, , 616, 266

    2023

  32. [40]

    2021, , 505, 172

    Lapiner , S., Dekel , A., & Dubois , Y. 2021, , 505, 172

    2021

  33. [41]

    Lau , J. Y. & Binney , J. 2021, , 507, 2241

    2021

  34. [42]

    Launhardt , R., Zylka , R., & Mezger , P. G. 2002, , 384, 112

    2002

  35. [43]

    S., & Volonteri , M

    Lescaudron , S., Dubois , Y., Beckmann , R. S., & Volonteri , M. 2023, , 674, A217

    2023

  36. [44]

    & Kalnajs , A

    Lynden-Bell , D. & Kalnajs , A. J. 1972, , 157, 1

    1972

  37. [45]

    P., Brammer , G., et al

    Matthee , J., Naidu , R. P., Brammer , G., et al. 2024, , 963, 129

    2024

  38. [46]

    2004, , 92, 201304

    Merritt , D. 2004, , 92, 201304

    2004

  39. [47]

    2013, Dynamics and Evolution of Galactic Nuclei , 1^ st edn

    Merritt , D. 2013, Dynamics and Evolution of Galactic Nuclei , 1^ st edn. (Princeton Univ. Press, Princeton, NJ)

    2013

  40. [48]

    2007, , 133, 553

    Merritt , D., Berczik , P., & Laun , F. 2007, , 133, 553

    2007

  41. [49]

    C., & White , S

    Mo , H., van den Bosch , F. C., & White , S. 2010, Galaxy Formation and Evolution , 1^ st edn. (Princeton Univ. Press, Princeton, NJ)

    2010

  42. [50]

    P., Oesch , P

    Naidu , R. P., Oesch , P. A., van Dokkum , P., et al. 2022, , 940, L14

    2022

  43. [51]

    2020, , 28, 4

    Neumayer , N., Seth , A., & B \"o ker , T. 2020, , 28, 4

    2020

  44. [52]

    2024, , 685, A93

    Nieuwmunster , N., Schultheis , M., Sormani , M., et al. 2024, , 685, A93

    2024

  45. [53]

    T., et al

    Nogueras-Lara , F., Sch \"o del , R., Gallego-Calvente , A. T., et al. 2020, Nature Astronomy, 4, 377

    2020

  46. [54]

    Ostriker , E. C. 1999, , 513, 252

    1999

  47. [55]

    & Kocsis , B

    Panamarev , T. & Kocsis , B. 2022, , 517, 6205

    2022

  48. [56]

    Papaloizou , J. C. B. 2021, Celestial Mechanics and Dynamical Astronomy, 133, 30

    2021

  49. [57]

    I., van Elteren , A., de Vries , N., et al

    Pelupessy , F. I., van Elteren , A., de Vries , N., et al. 2013, , 557, A84

    2013

  50. [58]

    A., Gualandris , A., & Read , J

    Petts , J. A., Gualandris , A., & Read , J. I. 2015, , 454, 3778

    2015

  51. [59]

    L., Volonteri , M., et al

    Pfister , H., Dai , J. L., Volonteri , M., et al. 2021, , 500, 3944

    2021

  52. [60]

    2019, , 486, 101

    Pfister , H., Volonteri , M., Dubois , Y., Dotti , M., & Colpi , M. 2019, , 486, 101

    2019

  53. [61]

    & McMillan , S

    Portegies Zwart , S. & McMillan , S. 2018, Astrophysical Recipes; The art of AMUSE , IOP Astronomy / AAS (IOP Publishing, Bristol, UK)

    2018

  54. [62]

    Portegies Zwart , S., McMillan , S. L. W., van Elteren , E., Pelupessy , I., & de Vries , N. 2013, Computer Physics Communications, 184, 456

    2013

  55. [63]

    Rauch , K. P. & Tremaine , S. 1996, , 1, 149

    1996

  56. [64]

    I., Goerdt , T., Moore , B., et al

    Read , J. I., Goerdt , T., Moore , B., et al. 2006, , 373, 1451

    2006

  57. [65]

    Reid , M. J. & Brunthaler , A. 2004, , 616, 872

    2004

  58. [66]

    Renaud , F., Gieles , M., & Boily , C. M. 2011, , 418, 759

    2011

  59. [67]

    B., & Agertz , O

    Renaud , F., Romeo , A. B., & Agertz , O. 2021, , 508, 352

    2021

  60. [68]

    Schawinski , K., Koss , M., Berney , S., & Sartori , L. F. 2015, , 451, 2517

    2015

  61. [69]

    1987, Dynamical evolution of globular clusters (Princeton University Press)

    Spitzer , L. 1987, Dynamical evolution of globular clusters (Princeton University Press)

    1987

  62. [70]

    1964, , 139, 1217

    Toomre , A. 1964, , 139, 1217

    1964

  63. [71]

    O., Byun , Y.-I., et al

    Tremaine , S., Richstone , D. O., Byun , Y.-I., et al. 1994, , 107, 634

    1994

  64. [72]

    & Weinberg , M

    Tremaine , S. & Weinberg , M. D. 1984, , 209, 729

    1984

  65. [73]

    G., et al

    \"U bler , H., Maiolino , R., P \'e rez-Gonz \'a lez , P. G., et al. 2024, , 531, 355

    2024

  66. [74]

    2019, , 482, 1525

    Vasiliev , E. 2019, , 482, 1525

    2019

  67. [75]

    2012, Science, 337, 544

    Volonteri , M. 2012, Science, 337, 544

    2012

  68. [76]

    D., Gillessen , S., Stadler , J., et al

    von Fellenberg , S. D., Gillessen , S., Stadler , J., et al. 2022, , 932, L6

    2022

  69. [77]

    & Haas , J

    S ubr , L. & Haas , J. 2014, , 786, 121

    2014

  70. [78]

    Weinberg , M. D. 1989, , 239, 549

    1989

  71. [79]

    Weinberg , M. D. 1998, , 299, 499

    1998

  72. [80]

    2024, , 684, A214

    Zoccali , M., Rojas-Arriagada , A., Valenti , E., et al. 2024, , 684, A214

    2024

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