pith. sign in

arxiv: 2603.02811 · v2 · submitted 2026-03-03 · 🌌 astro-ph.GA

Overmassive and Undermassive Massive Black Holes: The Role of Environment and Gravitational-Wave Recoils

David Izquierdo-Villalba This is my paper

Pith reviewed 2026-05-15 17:25 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords overmassive black holesundermassive black holesM_BH-M_* relationgravitational recoilsgalaxy mergerssemi-analytical modelsgalaxy evolution
0
0 comments X

The pith

Outliers in the black hole-stellar mass relation arise through multiple channels whose importance shifts with galaxy mass and redshift.

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

This paper traces the origins of galaxies whose central black holes sit above or below the expected M_BH-M_* scaling relation using a semi-analytical model run on large cosmological simulations. Overmassive black holes mainly trace galaxies that underwent frequent mergers and strong secular fueling, often with rapid early growth at high redshift. Some low-redshift cases instead occur when the surrounding environment strips away stellar mass, lifting the galaxy above the relation without extra black-hole growth. Undermassive black holes appear in massive galaxies after gravitational recoils eject the original nucleus during a merger, allowing a lighter replacement black hole to take over, and in low-mass galaxies that experienced quiet histories with little fueling. The central finding is that these outliers reflect an interplay of environmental, recoil, and fueling processes rather than any single driver.

Core claim

Outliers of the M_BH-M_* relation do not arise from a single mechanism, but from the interplay between environmental effects, gravitational recoils, and diverse MBH fueling histories, whose relative importance varies with galaxy mass and redshift.

What carries the argument

Distinct evolutionary pathways identified in the L-Galaxies-BH semi-analytical model: enhanced merger and secular activity for overmassive cases, gravitational recoil ejections plus replacement black holes for undermassive massive galaxies, and quiescent limited-growth histories for undermassive low-mass galaxies.

If this is right

  • Overmassive black holes at redshift greater than 4 commonly form via early rapid growth that includes super-Eddington accretion episodes.
  • At low redshift, roughly 20 percent of overmassive cases result from environmental reduction of the host galaxy's stellar mass.
  • In massive galaxies, gravitational recoil can temporarily leave the galaxy without its original nucleus, after which a lighter black hole from a prior merger becomes central but remains undermassive.
  • In galaxies below 10^9 solar masses, undermassive black holes arise mainly from limited mergers and weak secular activity that suppress efficient growth.

Where Pith is reading between the lines

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

  • The scatter around the scaling relation may encode recoverable information about a galaxy's merger rate and local density if black-hole masses can be measured across redshift bins.
  • In dense environments such as galaxy clusters, environmental stripping could produce a higher fraction of overmassive outliers than in the field.
  • Cosmological simulations that assume a single tight universal relation may under- or over-predict black-hole feedback in galaxy populations dominated by one of these outlier channels.

Load-bearing premise

The semi-analytical model and its calibration to the Millennium simulations accurately reproduce MBH accretion, mergers, recoils, and environmental interactions without systematic biases in the outlier populations.

What would settle it

A survey finding that undermassive black holes in massive galaxies are equally common in systems with no merger history or recoil signatures would undermine the recoil channel as a primary driver.

Figures

Figures reproduced from arXiv: 2603.02811 by David Izquierdo-Villalba.

Figure 1
Figure 1. Figure 1: MBH − M∗ plane at z = 0, 1, 3, 5. Different colors represent different populations. The results have been compared with the z ∼ 0 sample of Erwin & Gadotti (2012) (squares) Reines & Volonteri (2015) (diamonds) and Capuzzo-Dolcetta & Tosta e Melo (2017) (cir￾cles), Ferré-Mateu et al. (2021) (pentagons) and Ramsden et al. (2026) (crosses). The z = 1 and z = 3 results presents the observational sam￾ple of Suh… view at source ↗
Figure 2
Figure 2. Figure 2: Redshift evolution of the median MBH/M∗ ratio for the 5 different samples: +3σ (red), +2σ (coral), 1σ (orange), −2σ (blue) and −3σ (purple). Solid lines with circles represent the results for galaxies with M∗ > 108 M⊙ while dashed lines with squares represent the same but for galaxies with M∗ > 1010 M⊙. The shaded areas correspond to the 16th − 84th percentiles. one order of magnitude at lower redshifts. T… view at source ↗
Figure 3
Figure 3. Figure 3: Examples of evolutionary pathways for overmassive and undermassive MBHs. The upper panels show the galaxy merger trees, the middle panels illustrate the assembly of stellar mass and MBH mass, and the lower panels present the evolution of the ratio MBH/M∗. The first column corresponds to an overmassive MBH whose growth is driven by the gradual stripping of the host galaxy. The second column shows an underma… view at source ↗
Figure 4
Figure 4. Figure 4: Upper panel: Redshift evolution of the fraction of galaxies that are undergoing a gradual stripping (fSatellite). Lower panel: Redshift evolution of the median fraction of stellar mass lost by galaxies due to gradual stripping (fMass Stripped). In all panels, there are 5 different sam￾ples: +3σ (red), +2σ (coral), 1σ (orange), −2σ (blue) and −3σ (pur￾ple). The left column corresponds to galaxies with 108 <… view at source ↗
Figure 5
Figure 5. Figure 5: First panel: Redshift evolution of the fraction of galaxies that underwent an ejection of their central MBH due to GW recoils (fejection). Second panel: Median time spent in the dynamical-friction phase (tDF) by MBHs that re-filled an empty galactic nucleus due to a GW ejection. Third panel: Redshift evolution of the median redshift at which the MBH was ejected from the center of the galaxy (zejection). Th… view at source ↗
Figure 6
Figure 6. Figure 6: Redshift evolution of the median MBH/M∗ ratio for a model in which no GW kicks and ejections are included. The upper (lower) panel corresponds to galaxies with M∗ > 108 M⊙ (M∗ > 1010 M⊙) and solid lines correspond to the model without (with) ejections after gravi￾tational recoils. The color coding and mass dependence are the same as in the upper panel of [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Upper panel: Redshift evolution of the median number of minor mergers that triggered the growth of MBHs hosted in different galaxies (Nminor, merg). Lower panel: Redshift evolution of the median maximum baryonic mass ratio of minor mergers (mmax R,minor) that triggered the MBH growth in different galaxies. The color coding and mass dependence are the same as in [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: First panel: Redshift evolution of the fraction of galaxies whose central MBH underwent at least one (solid line) or five (pale lines) super-Eddington phases (fSupEdd). Second panel: Redshift evolution of the epoch at which MBHs within a given stellar mass bin expe￾rienced their most recent super-Eddington accretion phase (z Last SupEdd). Third panel: Redshift evolution of the epoch at which MBHs within a … view at source ↗
read the original abstract

Understanding the connection between galaxy properties and their central massive black holes (MBHs) is key to unveiling their co-evolution. We use the ${\tt L{-}Galaxies{-} \it BH}$ semi-analytical model and the ${\tt Millennium}$ suite of simulations to investigate the physical origin of galaxies hosting overmassive and undermassive MBHs with respect to the $M_{\rm BH}-M_*$ relation, across stellar mass and cosmic time. We find that distinct evolutionary pathways drive different offsets from the scaling relation. Overmassive MBHs are primarily associated with galaxies that experienced enhanced merger history and secular activity. At $z\,{>}\,4$, this activity often leads to early, rapid MBH growth, frequently involving super-Eddington accretion episodes. At low redshift, a minority of overmassive systems ($20\%$) instead arise from environmental effects that reduce the stellar mass of the host, shifting galaxies above the relation without requiring additional MBH growth. Undermassive MBHs originate from two main channels. In massive galaxies, gravitational recoil following MBH mergers can eject the central MBH, temporarily leaving the galaxy without a nucleus. During this phase, MBHs coming from previous galaxy mergers can become the new central MBHs, but their masses remain below the expected ones from the scaling relation, as they never co-evolved with their new host galaxy. In low-mass galaxies ($M_*<10^9 M_\odot$), undermassive MBHs are more commonly linked to a quiescent evolutionary history, with limited mergers and weak secular processes that suppress an efficient MBH growth. We therefore conclude that outliers of the $M_{\rm BH}-M_*$ do not arise from a single mechanism, but from the interplay between environmental effects, gravitational recoils, and diverse MBH fueling histories, whose relative importance varies with galaxy mass and redshift.

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

1 major / 2 minor

Summary. The manuscript uses the L-Galaxies-BH semi-analytical model on the Millennium simulations to trace the origins of overmassive and undermassive MBHs relative to the M_BH-M_* relation. Overmassive systems are linked to enhanced merger/secular activity (including super-Eddington episodes at z>4) or, in a minority (~20%) of low-z cases, to environmental reduction of stellar mass; undermassive systems arise either from post-recoil MBH replacement in massive galaxies or from quiescent histories with limited mergers in low-mass galaxies (M_*<10^9 M_⊙). The central claim is that outliers result from the interplay of environment, gravitational recoils, and fueling histories, with channel dominance varying by galaxy mass and redshift.

Significance. If the model's accretion, merger, and recoil prescriptions are reliable, the work provides a concrete multi-channel framework for interpreting M_BH-M_* outliers across cosmic time, with direct relevance to high-z JWST observations and future gravitational-wave constraints on recoil velocities.

major comments (1)
  1. [analysis of undermassive MBHs in low-mass galaxies] In the analysis of undermassive MBHs in low-mass galaxies (M_* < 10^9 M_⊙), the attribution to quiescent histories with limited mergers rests on accurate tracking of minor mergers and environmental interactions. The Millennium dark-matter particle mass (~8.6 × 10^8 M_⊙) implies that galaxies near this threshold are resolved by only a few particles, which can suppress detection of minor mergers and bias systems toward the quiescent channel. This resolution limitation is load-bearing for the mass-dependent channel claim and requires explicit validation or resolution tests.
minor comments (2)
  1. [Abstract] The abstract states that 20% of low-redshift overmassive systems arise from environmental effects; the precise redshift boundary used for 'low redshift' should be stated explicitly for reproducibility.
  2. [Figures] Notation for stellar mass (M_*) and black-hole mass (M_BH) is generally clear, but figure captions should explicitly note whether the plotted scaling relation is the model's own calibrated relation or an observational fit.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive and detailed review of our manuscript. We have carefully considered the major comment and provide a point-by-point response below. We agree that the resolution limitations warrant additional discussion and have revised the manuscript to address this.

read point-by-point responses

  1. Referee: In the analysis of undermassive MBHs in low-mass galaxies (M_* < 10^9 M_⊙), the attribution to quiescent histories with limited mergers rests on accurate tracking of minor mergers and environmental interactions. The Millennium dark-matter particle mass (~8.6 × 10^8 M_⊙) implies that galaxies near this threshold are resolved by only a few particles, which can suppress detection of minor mergers and bias systems toward the quiescent channel. This resolution limitation is load-bearing for the mass-dependent channel claim and requires explicit validation or resolution tests.

    Authors: We thank the referee for raising this important numerical caveat. The Millennium simulation's dark-matter particle mass of ~8.6×10^8 M_⊙ indeed means galaxies with M_* ≲ 10^9 M_⊙ are only marginally resolved, which can affect the detection of minor mergers and environmental interactions in the merger trees. Our classification of the quiescent channel in low-mass systems is derived directly from the model's merger and accretion histories, but we acknowledge that this resolution floor may preferentially suppress minor-merger events and thereby bias some systems toward appearing quiescent. In the revised manuscript we will add an explicit paragraph in Section 2 (Methods) and the discussion of low-mass undermassive systems (Section 4.2) that (i) states the resolution limit, (ii) quantifies the typical number of particles per galaxy at the M_* = 10^9 M_⊙ threshold, and (iii) notes that the reported mass-dependent channel distinction should be interpreted with this caveat. We will also mention that higher-resolution runs (e.g., Millennium-II) would be required for a full convergence test. We do not believe the overall conclusion—that distinct channels dominate at different masses—is invalidated, because the same qualitative trends appear across the full resolved mass range, but we will qualify the low-mass results accordingly. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper uses the L-Galaxies-BH semi-analytical model run on Millennium simulations to trace distinct evolutionary channels (merger histories, secular activity, recoils, environmental stripping) that produce offsets from the M_BH-M_* relation. The relation itself is an observed benchmark against which simulated galaxies are compared; the classification of overmassive/undermassive systems is a post-processing label, not an input that is refitted or redefined inside the derivation. No equation or claim reduces by construction to a fitted parameter or to a self-citation whose content is the target result. The central conclusion—that multiple channels operate with mass- and redshift-dependent weights—follows from the simulation’s merger trees and accretion tracking rather than from any definitional loop or renamed empirical pattern.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claim depends on the L-Galaxies-BH model containing accurate prescriptions for super-Eddington accretion, merger-driven growth, and gravitational-wave recoil velocities, all of which are calibrated rather than derived from first principles.

free parameters (3)
  • accretion efficiency and Eddington ratio caps
    Control the rate of MBH growth during merger and secular phases and are tuned to reproduce observed black hole masses.
  • merger timescale and dynamical friction parameters
    Determine how quickly galaxies and black holes coalesce and are adjusted to match simulation merger rates.
  • recoil velocity distribution parameters
    Set the kick speeds after black hole mergers and are chosen to produce realistic ejection fractions.
axioms (2)
  • domain assumption The observed M_BH-M_* relation represents the equilibrium state around which galaxies evolve.
    Used as the reference to classify systems as overmassive or undermassive.
  • standard math Gravitational-wave recoils can remove the central black hole from its host galaxy for a cosmologically relevant time.
    Invoked to explain undermassive cases in massive galaxies.

pith-pipeline@v0.9.0 · 5658 in / 1518 out tokens · 62784 ms · 2026-05-15T17:25:14.323701+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.

Forward citations

Cited by 1 Pith paper

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

  1. 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

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

Reference graph

Works this paper leans on

95 extracted references · 95 canonical work pages · cited by 1 Pith paper

  1. [1]

    M., et al

    Agazie, G., Anumarlapudi, A., Archibald, A. M., et al. 2023, ApJ, 951, L8

    work page 2023

  2. [2]

    L., Georgakakis, A., et al

    Aird, J., Coil, A. L., Georgakakis, A., et al. 2015, MNRAS, 451, 1892 Anglés-Alcázar, D., Özel, F., & Davé, R. 2013, ApJ, 770, 5

    work page 2015

  3. [3]

    Angulo, R. E. & White, S. D. M. 2010, MNRAS, 405, 143

    work page 2010

  4. [4]

    2012, MNRAS, 423, 2533

    Barausse, E. 2012, MNRAS, 423, 2533

    work page 2012

  5. [5]

    & Rezzolla, L

    Barausse, E. & Rezzolla, L. 2009, ApJ, 704, L40

    work page 2009

  6. [6]

    S., Comerford, J

    Barrows, R. S., Comerford, J. M., Negus, J., & Muller-Sanchez, F. 2025, ApJ, 992, 38

    work page 2025

  7. [7]

    & Tremaine, S

    Binney, J. & Tremaine, S. 2008, Galactic Dynamics: Second Edition

    work page 2008

  8. [8]

    2022, MNRAS, 512, 3703

    Bird, S., Ni, Y ., Di Matteo, T., et al. 2022, MNRAS, 512, 3703

    work page 2022

  9. [9]

    J., Loeb, A., & Hernquist, L

    Blecha, L., Cox, T. J., Loeb, A., & Hernquist, L. 2011, MNRAS, 412, 2154

    work page 2011

  10. [10]

    2018, MNRAS, 477, 3910

    Bonetti, M., Haardt, F., Sesana, A., & Barausse, E. 2018, MNRAS, 477, 3910

    work page 2018

  11. [11]

    2025, arXiv e-prints, arXiv:2509.12325

    Bonoli, S., Izquierdo-Villalba, D., Spinoso, D., et al. 2025, arXiv e-prints, arXiv:2509.12325

    work page arXiv 2025

  12. [12]

    Boylan-Kolchin, M., Springel, V ., White, S. D. M., Jenkins, A., & Lemson, G. 2009, MNRAS, 398, 1150

    work page 2009

  13. [13]

    & Tosta e Melo, I

    Capuzzo-Dolcetta, R. & Tosta e Melo, I. 2017, Monthly Notices of the Royal Astronomical Society, 472, 4013

    work page 2017

  14. [14]

    2020, A&A, 642, A65

    Carraro, R., Rodighiero, G., Cassata, P., et al. 2020, A&A, 642, A65

    work page 2020

  15. [15]

    2013, ARA&A, 51, 393

    Conroy, C. 2013, ARA&A, 51, 393

    work page 2013

  16. [16]

    Croton, D. J. 2006, MNRAS, 369, 1808

    work page 2006

  17. [17]

    J., Springel, V ., White, S

    Croton, D. J., Springel, V ., White, S. D. M., et al. 2006, MNRAS, 365, 11 Davé, R., Anglés-Alcázar, D., Narayanan, D., et al. 2019, MNRAS, 486, 2827

    work page 2006

  18. [18]

    2017, MNRAS, 466, 1462

    DeGraf, C., Dekel, A., Gabor, J., & Bournaud, F. 2017, MNRAS, 466, 1462

    work page 2017

  19. [19]

    2015, MNRAS, 454, 913 Di Matteo, T., Springel, V ., & Hernquist, L

    DeGraf, C., Di Matteo, T., Treu, T., et al. 2015, MNRAS, 454, 913 Di Matteo, T., Springel, V ., & Hernquist, L. 2005, Nature, 433, 604

    work page 2015

  20. [20]

    D., et al

    Ding, X., Onoue, M., Silverman, J. D., et al. 2023, Nature, 621, 51 Dong-Páez, C. A., V olonteri, M., Dubois, Y ., Beckmann, R. S., & Trebitsch, M. 2025, A&A, 695, A231 D’Orazio, D. J. & Duffell, P. C. 2021, ApJ, 914, L21 D’Orazio, D. J., Haiman, Z., & MacFadyen, A. 2013, MNRAS, 436, 2997

    work page 2023

  21. [21]

    2015, MNRAS, 448, 3603

    Dotti, M., Merloni, A., & Montuori, C. 2015, MNRAS, 448, 3603

    work page 2015

  22. [22]

    2010, MNRAS, 402, 682

    Dotti, M., V olonteri, M., Perego, A., et al. 2010, MNRAS, 402, 682

    work page 2010

  23. [23]

    & Richstone, D

    Dressler, A. & Richstone, D. O. 1988, ApJ, 324, 701 EPTA Collaboration, InPTA Collaboration, Antoniadis, J., et al. 2023, A&A, 678, A50

    work page 1988

  24. [24]

    & Gadotti, D

    Erwin, P. & Gadotti, D. A. 2012, Advances in Astronomy, 2012, 946368

    work page 2012

  25. [25]

    D., Duffell, P., MacFadyen, A

    Farris, B. D., Duffell, P., MacFadyen, A. I., & Haiman, Z. 2014, ApJ, 783, 134

    work page 2014

  26. [26]

    & Merritt, D

    Ferrarese, L. & Merritt, D. 2000, ApJ, 539, L9 Ferré-Mateu, A., Mezcua, M., & Barrows, R. S. 2021, MNRAS, 506, 4702

    work page 2000

  27. [27]

    Freeman, K. C. 1970, ApJ, 160, 811

    work page 1970

  28. [28]

    2000, ApJ, 539, L13

    Gebhardt, K., Bender, R., Bower, G., et al. 2000, ApJ, 539, L13

    work page 2000

  29. [29]

    Genzel, R., Hollenbach, D., & Townes, C. H. 1994, Reports on Progress in Physics, 57, 417

    work page 1994

  30. [30]

    & Townes, C

    Genzel, R. & Townes, C. H. 1987, ARA&A, 25, 377

    work page 1987

  31. [31]

    & Sesana, A

    Gerosa, D. & Sesana, A. 2015, MNRAS, 446, 38

    work page 2015

  32. [32]

    W., Erwin, P., Caon, N., & Trujillo, I

    Graham, A. W., Erwin, P., Caon, N., & Trujillo, I. 2001, ApJ, 563, L11

    work page 2001

  33. [33]

    Graham, A. W. & Li, I.-h. 2009, ApJ, 698, 812

    work page 2009

  34. [34]

    S., et al

    Habouzit, M., Genel, S., Somerville, R. S., et al. 2019, MNRAS, 484, 4413

    work page 2019

  35. [35]

    S., et al

    Habouzit, M., Li, Y ., Somerville, R. S., et al. 2021, MNRAS, 503, 1940

    work page 2021

  36. [36]

    2023, ApJ, 959, 39 Häring, N

    Harikane, Y ., Zhang, Y ., Nakajima, K., et al. 2023, ApJ, 959, 39 Häring, N. & Rix, H.-W. 2004, ApJ, 604, L89

    work page 2023

  37. [37]

    Henriques, B. M. B., White, S. D. M., Thomas, P. A., et al. 2015, MNRAS, 451, 2663

    work page 2015

  38. [38]

    Henriques, B. M. B., Yates, R. M., Fu, J., et al. 2020, MNRAS, 491, 5795

    work page 2020

  39. [39]

    1990, ApJ, 356, 359 Herrero-Carrión, D., Spinoso, D., Izquierdo-Villalba, D., et al

    Hernquist, L. 1990, ApJ, 356, 359 Herrero-Carrión, D., Spinoso, D., Izquierdo-Villalba, D., et al. 2026, MN- RAS[arXiv:2511.10725]

    work page arXiv 1990

  40. [40]

    Hopkins, P. F. & Hernquist, L. 2009, ApJ, 698, 1550

    work page 2009

  41. [41]

    F., Richards, G

    Hopkins, P. F., Richards, G. T., & Hernquist, L. 2007, ApJ, 654, 731

    work page 2007

  42. [42]

    K., Feng, Y ., & Ma, C.-P

    Huang, K.-W., Di Matteo, T., Bhowmick, A. K., Feng, Y ., & Ma, C.-P. 2018, MNRAS, 478, 5063

    work page 2018

  43. [43]

    2025, ApJ, 988, L22

    Inayoshi, K. 2025, ApJ, 988, L22

    work page 2025

  44. [44]

    & Fabian, A

    Ishibashi, W. & Fabian, A. C. 2012, MNRAS, 427, 2998

    work page 2012

  45. [45]

    2026, arXiv e-prints, arXiv:2601.18986

    Islam, T., Venumadhav, T., & Wadekar, D. 2026, arXiv e-prints, arXiv:2601.18986

    work page arXiv 2026

  46. [46]

    2020, MNRAS, 495, 4681

    Izquierdo-Villalba, D., Bonoli, S., Dotti, M., et al. 2020, MNRAS, 495, 4681

    work page 2020

  47. [47]

    2019, MNRAS, 488, 609

    Izquierdo-Villalba, D., Bonoli, S., Spinoso, D., et al. 2019, MNRAS, 488, 609

    work page 2019

  48. [48]

    2022, MNRAS, 509, 3488

    Izquierdo-Villalba, D., Sesana, A., Bonoli, S., & Colpi, M. 2022, MNRAS, 509, 3488

    work page 2022

  49. [49]

    2023b, MNRAS, 519, 2083

    Izquierdo-Villalba, D., Sesana, A., & Colpi, M. 2023b, MNRAS, 519, 2083

    work page 2083

  50. [50]

    2024, A&A, 686, A183

    Izquierdo-Villalba, D., Sesana, A., Colpi, M., et al. 2024, A&A, 686, A183

    work page 2024

  51. [51]

    L., Kocevski, D

    Jones, B. L., Kocevski, D. D., Pacucci, F., et al. 2025, arXiv e-prints, arXiv:2510.07376

    work page arXiv 2025

  52. [52]

    D., Onoue, M., Inayoshi, K., et al

    Kocevski, D. D., Onoue, M., Inayoshi, K., et al. 2023, ApJ, 954, L4

    work page 2023

  53. [53]

    1988, ApJ, 325, 128

    Kormendy, J. 1988, ApJ, 325, 128

    work page 1988

  54. [54]

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

    work page 2013

  55. [55]

    & Richstone, D

    Kormendy, J. & Richstone, D. 1992, ApJ, 393, 559

    work page 1992

  56. [56]

    & Richstone, D

    Kormendy, J. & Richstone, D. 1995, ARA&A, 33, 581

    work page 1995

  57. [57]

    O., Zlochower, Y ., Dotti, M., & V olonteri, M

    Lousto, C. O., Zlochower, Y ., Dotti, M., & V olonteri, M. 2012, Phys. Rev. D, 85, 084015

    work page 2012

  58. [58]

    2025, arXiv e-prints, arXiv:2512.04803

    Lu, Y ., SiTu, H., Li, J., et al. 2025, arXiv e-prints, arXiv:2512.04803

    work page arXiv 2025

  59. [59]

    Lupi, A., Quadri, G., V olonteri, M., Colpi, M., & Regan, J. A. 2024, A&A, 686, A256

    work page 2024

  60. [60]

    2014, ApJ, 784, L38

    Madau, P., Haardt, F., & Dotti, M. 2014, ApJ, 784, L38

    work page 2014

  61. [61]

    1998, AJ, 115, 2285

    Magorrian, J., Tremaine, S., Richstone, D., et al. 1998, AJ, 115, 2285

    work page 1998

  62. [62]

    2024, A&A, 691, A145

    Maiolino, R., Scholtz, J., Curtis-Lake, E., et al. 2024, A&A, 691, A145

    work page 2024

  63. [63]

    & Hunt, L

    Marconi, A. & Hunt, L. K. 2003, ApJ, 589, L21

    work page 2003

  64. [64]

    A., Mutch, S

    Marshall, M. A., Mutch, S. J., Qin, Y ., Poole, G. B., & Wyithe, J. S. B. 2020, MNRAS, 494, 2747 Martín-Navarro, I., Brodie, J. P., Romanowsky, A. J., Ruiz-Lara, T., & van de

    work page 2020

  65. [65]

    2018, Nature, 553, 307

    Ven, G. 2018, Nature, 553, 307

    work page 2018

  66. [66]

    P., Brammer, G., et al

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

    work page 2024

  67. [67]

    M., Koerding, E., Knigge, C., Uttley, P., & Fender, R

    McHardy, I. M., Koerding, E., Knigge, C., Uttley, P., & Fender, R. P. 2006, Nature, 444, 730

    work page 2006

  68. [68]

    & Heinz, S

    Merloni, A. & Heinz, S. 2008, MNRAS, 388, 1011

    work page 2008

  69. [69]

    2024, ApJ, 966, L30

    Mezcua, M., Pacucci, F., Suh, H., Siudek, M., & Natarajan, P. 2024, ApJ, 966, L30

    work page 2024

  70. [70]

    2023, ApJ, 943, L5

    Mezcua, M., Siudek, M., Suh, H., et al. 2023, ApJ, 943, L5

    work page 2023

  71. [71]

    F., Frenk, C

    Navarro, J. F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563

    work page 1996

  72. [72]

    2023, ApJ, 957, L3

    Pacucci, F., Nguyen, B., Carniani, S., Maiolino, R., & Fan, X. 2023, ApJ, 957, L3

    work page 2023

  73. [73]

    Peters, P. C. & Mathews, J. 1963, Phys. Rev., 131, 435

    work page 1963

  74. [74]

    M., Ferrarese, L., Gilbert, K

    Peterson, B. M., Ferrarese, L., Gilbert, K. M., et al. 2004, ApJ, 613, 682

    work page 2004

  75. [75]

    2019, MNRAS, 490, 3196 Planck Collaboration, Ade, P

    Pillepich, A., Nelson, D., Springel, V ., et al. 2019, MNRAS, 490, 3196 Planck Collaboration, Ade, P. A. R., Aghanim, N., et al. 2014, A&A, 571, A16

    work page 2019

  76. [76]

    Quinlan, G. D. & Hernquist, L. 1997, New A, 2, 533

    work page 1997

  77. [77]

    L., & Nicholl, M

    Ramsden, P., McGee, S. L., & Nicholl, M. 2026, ApJ, 998, L25

    work page 2026

  78. [78]

    J., Zic, A., Shannon, R

    Reardon, D. J., Zic, A., Shannon, R. M., et al. 2023, ApJ, 951, L6

    work page 2023

  79. [79]

    Reines, A. E. & V olonteri, M. 2015, ApJ, 813, 82 Sánchez Almeida, J. 2023, A&A, 678, A118

    work page 2015

  80. [80]

    Savorgnan, G. A. D., Graham, A. W., Marconi, A. r., & Sani, E. 2016, ApJ, 817, 21

    work page 2016

Showing first 80 references.