Pith. sign in

REVIEW 4 major objections 5 minor 80 references

Recoiling supermassive black holes in analytical and numerical galaxy potential

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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

Pith's one-line read This paper establishes that evolving numerical merger remnant potentials give supermassive black hole escape velocities up to about 25 percent lower than static analytical potentials, making spatially offset active galactic nuclei more…

desk verdict A solid numerical check that static potentials overestimate recoil escape velocities in major mergers, but the headline 25 per cent rests on one extreme orbit and needs robustness testing before being used quantitatively. read the letter →

arxiv 1908.02563 v1 pith:IJVPIJD2 submitted 2019-08-07 astro-ph.GA

Majda Smole , Miroslav Micic , Ana Mitrašinović This is my paper · ORCID
classification astro-ph.GA
keywords supermassiveblackholerecoilgravitational-wavekickgalaxymergerremnantsviolentrelaxationescapevelocityoffsetactivegalacticnucleiN-bodysimulations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the common shortcut of modelling a post-merger galaxy as a fixed, analytic potential makes recoiling supermassive black holes look harder to eject than they really are. In N-body simulations of major mergers, violent relaxation removes mass from the outer galaxy, so the escape velocity faced by a kicked black hole drops by up to about 25 percent relative to the analytic model. Since the same mass redistribution does not occur in minor mergers or in the static models, the difference is largest exactly for the major mergers that produce the biggest kicks. If the claim holds, offset active galactic nuclei—galaxies whose black hole is displaced from the centre—should be more numerous and more widely separated than static-potential estimates say.

What carries the argument

The engine of the comparison is the N-body merger simulation evolving the galactic potential while the recoiling black hole travels through it, set against a static analytical potential built from an NFW dark halo, a power-law bulge, and an exponential disc treated as spherical. Violent relaxation—the rapid, collisionless rearrangement of particle energies during a merger that pushes weakly bound stars beyond the virial radius—is the physical mechanism that reduces the outer mass profile and hence the escape velocity. The paper measures escape velocity as the kick speed needed for the black hole to return to the host halo after about 10 Gyr, and integrates the trajectory with Chandrasekhar dynamical friction included.

What would settle it

Run a suite of equal-mass merger simulations of $10^{12}$ solar-mass progenitors with orbital eccentricities from 0.3 to 1.0 and pericentres from 0.5 to 10 percent of the virial radius at fixed resolution; if the mean numerical escape velocity stays within a few percent of the static analytical value for the non-parabolic orbits, the claim that numerical potentials reduce escape velocities by up to 25 percent would not generalise.

Watch

Extended reading notes

Core claim

The central claim is that escape velocities of recoiling supermassive black holes in numerical major merger remnant galaxies are up to about 25 percent lower than in analytical models, because violent relaxation during the merger lowers the galaxy's mass profile at large radii. The paper shows that the numerical and analytical models agree for isolated progenitor galaxies, isolating the merger itself as the source of the difference. In major merger remnants, the numerical potential has lower enclosed mass at large radii and a higher central density, and the outer mass loss wins: a black hole needs a smaller kick to leave and, for a given kick, reaches several to ten times larger maximum galactocentric distance over a Hubble time. The paper concludes that static analytical models overestimate escape velocities and underestimate the number of spatially offset active galactic nuclei.

Load-bearing premise

The 25 percent gap rests on one simulated merger geometry—a parabolic encounter with pericentre 0.5 percent of the primary virial radius and $10^6$ particles—being representative of the violent-relaxation mass loss in real major mergers; with less radial orbits or different resolution, the gap could shrink.

Editorial extensions

If this is right

  • Offset active galactic nuclei should be more common than static-potential estimates predict, because lower kick speeds can still displace the black hole and a displaced black hole spends more time on bound orbits outside the nucleus.
  • For a given kick-to-escape ratio, numerical major merger remnants put recoiling black holes up to about ten times farther from the centre than analytical models do, making them easier to detect.
  • Black hole retention is lower after major than after minor mergers, so merger-driven black hole growth should be somewhat suppressed in major-merger remnants.
  • Escape velocities of roughly $10^{11}$ and $10^{12}$ solar-mass remnants fall in ranges of about 170–350 and 500–700 km/s depending on black hole mass and merger type, so typical kicks below a few hundred km/s matter most for the smaller host.

Reading between the lines

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

  • I infer that the 25 percent headline is tied to the one orbital family tested (parabolic, pericentre 0.5 percent of the primary virial radius); real mergers with smaller eccentricity or larger pericentre would likely lose less mass, so the analytical–numerical gap should shrink.
  • A testable extension would be to rerun the same comparison varying orbital parameters and numerical resolution; if the gap persists across a realistic orbit distribution, observational campaigns for offset active galactic nuclei should weight the numerical predictions more heavily.
  • I infer that the enhanced separations at $v_{\rm kick}/v_{\rm esc} \sim 0.2$ translate directly into discovery-rate predictions: the same spin-alignment assumptions that keep black holes in the central kiloparsec in analytic models place them several kiloparsecs out in numerical remnants.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper compares the trajectories of recoiling supermassive black holes (SMBHs) in static analytical galaxy potentials and in GADGET-2 N-body merger simulations, for remnant masses 10^11 and 10^12 Msun, major (1:1) and minor (1:10) mergers, and two SMBH mass scalings (Mgal/10^5 and Mgal/10^3). The numerical setup is first validated against analytical models for isolated progenitors by comparing escape velocities and maximal SMBH separations (Figs 2 and 3). The authors then simulate mergers with a single orbital configuration (e=1, pericentric distance 0.5% of the primary virial radius), construct analytical remnants from conserved progenitor masses, and compare escape velocities, mass profiles, and SMBH orbits. The central claim is that static analytical models overestimate SMBH escape velocities, with numerical major-merger remnants having escape velocities up to ~25 per cent lower, because violent relaxation during major mergers reduces the mass at large radii. The paper concludes that numerical models predict more spatially offset AGNs.

Significance. If the quantitative claim is robust, this is a useful and potentially important result: it identifies a systematic bias in static-potential models of post-merger galaxies and suggests that recoiling SMBHs are retained less often and found at larger offsets than those models predict. The paper has real strengths: the numerical method is validated against analytical models for progenitor galaxies (Figs 2 and 3), the stability of the initial galaxy models is checked, a softening-length test is reported, and the comparison with Illustris-based results of Blecha et al. (2016) grounds the work in the existing literature. The qualitative direction of the effect, driven by mass loss in major mergers, is plausible and physically well motivated. However, the headline magnitude of the effect rests on a narrow numerical setup: one orbital configuration, one realization per case, and an analytical remnant construction that needs to be stated more precisely. These limitations matter because the 25 per cent figure is the paper's main quantitative deliverable and is repeated in the abstract and conclusions.

major comments (4)
  1. [Section 2.3.1; Fig. 4; conclusion item (i)] The central quantitative claim that numerical major-merger escape velocities are up to ~25 per cent lower than analytical ones is established for only one orbital configuration: e=1 with Rperi=0.5% Rvir,1, which the manuscript itself describes as an almost head-on collision chosen to save computational time. The mass loss that drives the reduced escape velocity is expected to depend strongly on orbital angular momentum, so a near-radial encounter is likely to maximize the effect. I request either an additional merger simulation (or an energy-based estimate) with a more typical pericentric distance to show that the effect is not an artifact of this extreme orbit, or a revision of the abstract and conclusions to present the 25 per cent figure as an upper bound for near-radial mergers rather than as the typical difference.
  2. [Section 2.3.1; Figs 4 and 8] All merger outcomes are based on single realizations with no scatter estimates or multiple random seeds. The ratios rmax,n/rmax,a in Fig. 8 reach factors of ~10 for kicks near the escape velocity, and the claim that numerical models predict a greater number of spatially offset AGNs depends on these large ratios. Without a measure of realization-to-realization variance, the reader cannot assess whether the differences are statistically significant or partly due to the particular initial particle draw. At minimum, the authors should report the variance across realizations or soften the quantitative claims accordingly.
  3. [Section 2.3.2; Section 3.3] The construction of the analytical merger remnants needs to be stated precisely because it is load-bearing for the main comparison. The sentence 'We make numerical models of isolated galaxies and then fit their mass profiles in order to produce analytical galaxies with the same properties' is ambiguous: if the analytical remnant parameters in Table 2 are fits to the numerical post-merger mass profiles, then the escape-velocity comparison would be partly circular. If instead the analytical remnants are constructed from conserved progenitor masses and the same density-profile shapes as the progenitors, with no fitting to the post-merger profiles shown in Fig. 5, that should be stated explicitly. The current wording does not rule out the circular reading.
  4. [Section 2.2.1; Fig. 6] The escape velocity is operationally defined as the kick velocity needed for the SMBH to return to the host halo after ~10 Gyr, rather than the classical escape speed of the instantaneous potential. This is a legitimate choice, but the comparison in Figs 4 and 5 is made at the time of SMBH merger/ejection, when the numerical remnant is still evolving (Fig. 6 shows continued central-profile evolution after ejection). The authors should justify that their conclusions are not sensitive to the chosen ejection time, for example by evaluating whether the early relaxation of the central regions is fully captured before the SMBH is kicked.
minor comments (5)
  1. [Introduction, Section 1] The phrase 'so-cold final parsec problem' should read 'so-called final parsec problem'.
  2. [Section 2.3.1 and Section 3.5] There are typographical repetitions: 'adopt the the similar approach' in Section 2.3.1 and 'the the galactic nucleus' in Section 3.5; these should be corrected.
  3. [Figure 5 caption] The caption says 'Panels show major and minor merger remnants' but the individual panels are not labeled in the caption text; identifying which panel corresponds to which case (for example, left versus right, upper versus lower) would improve readability.
  4. [Section 3.2] The text states that 'Escape velocities in weakened potential of major merger remnant are ≲ 25 per cent lower compared to minor merger remnants' before introducing the analytical-versus-numerical comparison in Section 3.3; the reader should be told explicitly that this is a statement about numerical models only, to avoid confusion with the 25 per cent figure presented later.
  5. [General] The reference list contains a few formatting inconsistencies (for example 'Gonz´ alez' and the incomplete journal name in the 2007 reference), and the phrase 'decreasement' should be replaced by 'decrease' throughout the text.

Circularity Check

1 steps flagged · score 2.0 of 10

Central numerical-vs-analytical escape-velocity comparison is self-contained; only a minor progenitor-fitting consistency check reduces by construction.

  1. other [Section 2.1.2 and Section 2.2.2 (progenitor galaxy validation, Figs 2 and 3)]
    "Those parameters represent a fit to the mass profiles of galaxy components resulting from numerical models. ... In order to validate the accuracy of numerical method, we compare escape velocities from analytical and numerical models of progenitor galaxies."

    The analytical progenitor models are calibrated by fitting their density-profile parameters to the numerical mass profiles. Since escape velocity is a global integral of the mass distribution, matching the mass profiles makes the escape-velocity agreement in Figs 2-3 partly a consistency check by construction rather than an independent test of the numerical method. This is a minor, non-central self-consistency: the paper's headline result is the post-merger gap, which is produced by mass loss during the N-body merger and is not fitted into the analytical remnant models.

full rationale

The central claim—that numerical major-merger remnants have escape velocities up to ~25 per cent lower than static analytical remnants—is not circular. The analytical merger-remnant models are constructed from the summed progenitor masses and fitted to isolated galaxy models, while the numerical remnants lose mass through violent relaxation during the merger itself; the reduction in escape velocity therefore emerges from the N-body dynamics, not from a fitted parameter. The only step that reduces by construction is the progenitor-level validation: analytical profile parameters are fitted to numerical mass profiles, and escape velocities derived from those profiles agree largely by definition. The paper discloses this fitting explicitly, and it is a consistency check rather than the main result. Self-citations (Smole 2015; Micic et al. 2011) are used as background and as inputs for kick-velocity ranges; they are not invoked as uniqueness theorems or as the sole support for the central derivation. The adopted spherical-disc potential is an external approximation from Geehan et al. (2006), not an ansatz smuggled in via self-citation. The orbital-choice robustness concern (e = 1, Rperi = 0.5% Rvir) is a physical limitation and a correctness risk, not a circularity. Overall, the derivation is self-contained apart from a minor fitted-input consistency check, so the circularity score is low.

Assumptions & free parameters 5 free parameters · 6 assumptions · 0 invented entities

The central comparison depends on empirical scaling relations (M_BH-M_halo, M_bulge-M_BH, M_DM-M_gal,b) to set component masses, the Chandrasekhar formula with an adopted Coulomb logarithm, and a single chosen merger orbit. No new physical entities are introduced.

free parameters (5)
  • Coulomb logarithm ln(Lambda) = 3.1 (adopted from Blecha & Loeb 2008)
    Sets the strength of Chandrasekhar dynamical friction in the analytical model (Equation 8); escape velocities depend on it. It is not measured or fitted in this paper, but chosen from prior literature.
  • SMBH merger time delay = 0.1 Gyr/q; q=1 for major, q=0.1 for minor
    Added because the final SMBH merger occurs below resolution (Section 2.3.1); determines when the kick is applied relative to remnant relaxation and thus affects where in the mass-loss phase the SMBH is ejected.
  • Gravitational softening length = 0.1 kpc for all particle types
    Numerical resolution parameter; test with 0.5 kpc for DM showed less than 1% change in escape velocity, so sensitivity is low, but it is a chosen parameter.
  • SMBH mass scaling = Mgal/10^5 and Mgal/10^3
    Two hand-chosen central SMBH mass models used to bracket the expected range from scaling relations (Section 2); escape velocities depend strongly on this choice.
  • Kick velocity sampling points = 0.2, 0.4, 0.6, 0.8, 1.0 times vesc
    Discrete choices used to bracket the escape velocity; the resolution of vesc is limited to the 0.2 step, and interpolation between points is not modeled.
assumptions (6)
  • standard math Chandrasekhar dynamical friction formula with Maxwellian velocity distribution (Equation 8)
    Used in the analytical trajectory integration; standard but an approximation for anisotropic, non-spherical remnants.
  • domain assumption Galaxy escape velocity is the kick velocity that returns the SMBH to the halo after about 10 Gyr (Section 2.2.1)
    Operational definition; a longer time or stricter return criterion would shift vesc.
  • domain assumption All mergers use parabolic orbits e=1 with pericenter 0.5% of the primary virial radius (Section 2.3.1)
    Single orbital configuration; violent relaxation and mass loss depend on orbital parameters, so the 25% figure may not generalize.
  • domain assumption SMBH mass ratio equals galaxy mass ratio, q=1 for major and q=0.1 for minor (Section 2.3.1)
    Used to set merger time delay and kick-velocity intervals; not directly measured.
  • domain assumption Analytical disc is treated as a spherical mass distribution (Geehan et al. 2006 toy model, Equation 7)
    Approximation adopted because a true exponential disc potential has no closed form.
  • domain assumption Violent relaxation (Lynden-Bell 1967) is the mechanism producing mass loss in the numerical remnants (Section 3.2)
    Interpretive assumption used to explain the mass-profile differences; not directly derived from the simulations.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Recoiling supermassive black holes in analytical and numerical galaxy potential." pith.science (2026). https://pith.science/paper/IJVPIJD2

@misc{pith2026190802563,
  author       = {Pith},
  title        = {Pith review of: Recoiling supermassive black holes in analytical and numerical galaxy potential},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IJVPIJD2}},
  note         = {Machine review of arXiv:1908.02563}
}
abstract

We follow trajectories of recoiling supermassive black holes (SMBHs) in analytical and numerical models of galaxy merger remnants with masses of $10^{11} \rm{M_{sun}}$ and $10^{12} \rm{M_{sun}}$. We construct various merger remnant galaxies in order to investigate how the central SMBH mass and the mass ratio of progenitor galaxies influence escape velocities of recoiling SMBHs. Our results show that static analytical models of major merger remnant galaxies overestimate the SMBHs escape velocities. During major mergers violent relaxation leads to the decrease of galaxy mass and lower potential at large remnant radii. This process is not depicted in static analytical potential but clearly seen in our numerical models. Thus, the evolving numerical model is a more realistic description of dynamical processes in galaxies with merging SMBHs. We find that SMBH escape velocities in numerical major merger remnant galaxies can be up to 25 per cent lower compared to those in analytical models. Consequently, SMBHs in numerical models generally reach greater galactocentric distances and spend more time on bound orbits outside of the galactic nuclei. Thus, numerical models predict a greater number of spatially-offset active galactic nuclei (AGNs).

Figures

Figures reproduced from arXiv: 1908.02563 by the authors.

Figure 1
Figure 1. Mass profiles in analytical (dashed lines) and numerical (solid lines) galaxy models. For numerical models mass profiles of individual galaxy components are shown at the beginning of the simulation and 3 Gyr later [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Escape velocities from progenitor galaxies in analyt￾ical models as a function of their escape velocities in numerical models, for galaxies with different central SMBH masses (open and filled symbols). Major merger remnants are represented with triangles and minor merger remnants with squares. 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 rmax,n [kpc] 100 200 300 400 500 rmax,a [kpc] 1:1 − triangle 1:1… view at source ↗
Figure 3
Figure 3. Maximal separation of a recoiling SMBH from the galaxy centre over a Hubble time in analytical models, as a func￾tion of rmax in numerical models. SMBH kick velocity is equal to the escape velocity for each galaxy model. Notations are the same as in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: shows galaxy escape velocity in analytical models as a function of escape velocity in numerical models for galaxies with mass of Mgal = 1012 M (upper panel) and Mgal = 1011 M (lower panel). Triangles and squares represent ma￾jor and minor merger remnants, respectively.…
Figure 5
Figure 5. Figure 5: Total mass profile of numerical and analytical models of merger remnant galaxies. Red lines correspond to the analytical models and black lines to numerical models at the first pericentric passage (dashed lines) and SMBH merger (solid lines). Panels show major and mino…
Figure 6
Figure 6. Figure 6: Evolution of total mass profiles of numerical merger remnant galaxies. Black lines represent mass profile at the time of SMBH merger, while blue, green and orange lines show evolution of the total mass profiles during the simulation. Red lines represent total mass prof…
Figure 7
Figure 7. Figure 7: Maximal separation of a recoiling SMBH from the galaxy centre over a Hubble time, as a function of kick velocity. Kick velocities are chosen to represent vkick = 0.2, 0.4, 0.6, 0.8, 1.0 × vesc for each galaxy model. For example, SMBH in numerical major merger remnant o…
Figure 9
Figure 9. Figure 9: Maximal separation of a recoiling SMBH from the galaxy centre over a Hubble time as a function of vkick/vesc,n, for galaxies with mass Mgal = 1012 M (diamond symbols) i Mgal = 1011 M (asterisk symbols). Shaded region represents results obtained by Blecha et al. (2016).…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

80 extracted references · 71 canonical work pages

  1. [1]

    C., Blandford R

    Begelman M. C., Blandford R. D., Rees M. J., 1980, Nature, 287, 307

    1980

  2. [2]

    J., 2005, MNRAS, 358, 551

    Benson A. J., 2005, MNRAS, 358, 551

    work page 2005

  3. [3]

    Berczik P., Merritt D., Spurzem R., Bischof H.P., 2006, ApJ, 642, L21

    work page 2006

  4. [4]

    Berentzen I., Preto M., Berczik P., Merritt D., Spurzem R., 2009, ApJ, 695, 455

    work page 2009

  5. [5]

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

    2008

  6. [6]

    Blecha L., Loeb A., 2008, MNRAS, 390, 1311

    work page 2008

  7. [7]

    J., Loeb A., Hernquist L., 2011, MNRAS, 412, 2154

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

    work page 2011

  8. [8]

    Z., Torrey P., Vogelsberger M., Nelson D., Springel V., Snyder G., Hernquist L., 2016, MNRAS, 456, 961

    Blecha L., Sijacki D., Kelley L. Z., Torrey P., Vogelsberger M., Nelson D., Springel V., Snyder G., Hernquist L., 2016, MNRAS, 456, 961

    work page 2016

Show all 80 references
  1. [9]

    Blecha L., Brisken W., Burke-Spolaor S., Civano F., Comerford J., Darling J., Lazio T. J. W., Maccarone T. J., 2019, Science White Paper submitted to the Astro2020 Decadal Survey, arXiv:1903.09301

    2019 arXiv

  2. [10]

    Bovy J., Rix H.-W., 2013, ApJ, 779, 115

    2013

  3. [11]

    Bovy J., 2015, ApJS, 216, 29

    2015

  4. [12]

    C., Jiang F., Hearin A., Campbell D., Watson D., Padmanabhan N., 2014, MNRAS, 445, 1713

    van den Bosch F. C., Jiang F., Hearin A., Campbell D., Watson D., Padmanabhan N., 2014, MNRAS, 445, 1713

    2014

  5. [13]

    Callegari S., Mayer L., Kazantzidis S., Colpi M., Governato F., Quinn T., Wadsley J., 2009, ApJ, 696, L89

    2009

  6. [14]

    M., Quinn T., Wadsley J., 2011, ApJ, 729, 85

    Callegari S., Kazantzidis S., Mayer L., Colpi M., Bellovary J. M., Quinn T., Wadsley J., 2011, ApJ, 729, 85

    2011

  7. [15]

    O., Zlochower Y., Merritt D., 2007, Phys

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

    2007

  8. [16]

    Chandrasekhar S., 1943, ApJ, 97, 255

    1943

  9. [17]

    P., Silk J., Moster B., 2017, MNRAS, 472, 1526

    Choksi N., Behroozi P., Volonteri M., Schneider R., Ma C. P., Silk J., Moster B., 2017, MNRAS, 472, 1526

    2017

  10. [18]

    J., Jonsson P., Somerville R

    Cox T. J., Jonsson P., Somerville R. S. Primack J. R., Dekel A.,2008, MNRAS, 384, 386

    2008

  11. [19]

    Dehnen W., 2001, MNRAS, 324, 273

    2001

  12. [20]

    Devecchi B., Rasia E., Dotti M., Volonteri M., Colpi M., 2009, MNRAS, 394, 633

    2009

  13. [21]

    K., 1991, Nature, 354, 212

    Ebisuzaki T., Makino J., Okumura S. K., 1991, Nature, 354, 212

    1991

  14. [22]

    B., Coppi P

    Escala A., Larson R. B., Coppi P. S., Mardones D., 2004, ApJ, 607, 765

    2004

  15. [23]

    B., Coppi P

    Escala A., Larson R. B., Coppi P. S., Mardones D., 2005, ApJ, 630, 152

    2005

  16. [24]

    Ferrarese L., 2002, ApJ, 578, 90

    2002

  17. [25]

    Fiacconi D., Mayer L., Ro s kar R., Colpi M., 2013, ApJ, 777, L14

    2013

  18. [26]

    L., Athanassoula E

    Gajda G., Łokas E. L., Athanassoula E.. 2018, ApJ, 868, 10

    2018

  19. [27]

    J., Fardal M

    Geehan J. J., Fardal M. A., Babul A., Guhathakurt P., 2006, MNRAS, 366, 996

    2006

  20. [28]

    G., Sesana A., Cuadra J., Stasyszyn F., 2017, MNRAS, 472, 514

    Goicovic F. G., Sesana A., Cuadra J., Stasyszyn F., 2017, MNRAS, 472, 514

    2017

  21. [29]

    A., Hannam M., Sperhake U., Brugmann B., Husa S., 2007, Phys

    Gonz\' a lez J. A., Hannam M., Sperhake U., Brugmann B., Husa S., 2007, Phys. Rev. Lett., 98w1101G

    2007

  22. [30]

    Gualandris A., Merritt D., 2008, ApJ, 678, 780

    2008

  23. [31]

    Gualandris A., Read J., Dehnen W., Bortolas E., 2017, MNRAS, 464, 11

    2017

  24. [32]

    Guedes J., Madau P., Mayer L., Callegari S., 2011, ApJ, 729, 125

    2011

  25. [33]

    Haiman Z., 2004, ApJ, 613, 36

    2004

  26. [34]

    P., Thomas J., Burkert A., Jesseit R., 2012, MNRAS, 3136, 311

    Hilz M., Naab T., Ostriker J. P., Thomas J., Burkert A., Jesseit R., 2012, MNRAS, 3136, 311

    2012

  27. [35]

    M., Just A., Merritt D., 2011, ApJ, 732, 89

    Khan F. M., Just A., Merritt D., 2011, ApJ, 732, 89

    2011

  28. [36]

    M., Holley-Bockelmann K., Berczik P., Just A., 2013, ApJ, 773, 100

    Khan F. M., Holley-Bockelmann K., Berczik P., Just A., 2013, ApJ, 773, 100

    2013

  29. [37]

    M., Fiacconi D., Mayer L., Berczik P., Just A., 2016, ApJ, 828, 73

    Khan F. M., Fiacconi D., Mayer L., Berczik P., Just A., 2016, ApJ, 828, 73

    2016

  30. [38]

    Khochfar S., Burkert A., 2006, A&A, 445, 403

    2006

  31. [39]

    Komossa S., Merritt D., 2008, ApJ, 689, L89

    2008

  32. [40]

    C., 2013, ARA&A, 51, 511

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

    2013

  33. [41]

    Kuijken K., Dubinski J., 1995, MNRAS, 277, 1341

    1995

  34. [42]

    Loeb A., 2007, Phys. Rev. Lett., 99, 041103

    2007

  35. [43]

    O., Zlochower Y., 2011, Phys

    Lousto C. O., Zlochower Y., 2011, Phys. Rev. Lett., 107, 1102

    2011

  36. [44]

    Lynden-Bell D., 1967, MNRAS, 136, 101

    1967

  37. [45]

    Madau P., Quataert E., 2004, ApJ, 606, L17

    2004

  38. [46]

    K., 2003, ApJ, 589, L21

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

    2003

  39. [47]

    Quantum Gravity, 30, 244008

    Mayer L., 2013, Class. Quantum Gravity, 30, 244008

    2013

  40. [48]

    Mayer L., Kazantzidis S., Madau P., Colpi M., Quinn T., Wadsley J., 2007, Science, 316, 187

    2007

  41. [49]

    J., Ma C.-P., 2013, ApJ, 764, 184

    McConnell N. J., Ma C.-P., 2013, ApJ, 764, 184

    2013

  42. [50]

    McMillan P., 2011, MNRAS, 414, 2446

    2011

  43. [51]

    Merritt D., 1996, AJ, 111, 2462

    1996

  44. [52]

    Merritt D., Milosavljevi \'c M., Favata M., Hughes S.A., Holz D.E., 2004, ApJ, 607, L9

    2004

  45. [53]

    Micic M., Abel T., Sigurdsson S., 2006, MNRAS, 372, 154

    2006

  46. [54]

    Micic M., Holley Bockelmann K., Sigurdsson S., 2011, MNRAS, 414, 1127

    2011

  47. [55]

    Milosavljevi \'c M., Merritt D., 2001, ApJ, 563, 34

    2001

  48. [56]

    P., Naab T., White S

    Moster B. P., Naab T., White S. D. M., 2013, MNRAS, 428, 3121

    2013

  49. [57]

    F., Frenk C

    Navarro J. F., Frenk C. S., White S. D. M., 1997, ApJ, 490, 493

    1997

  50. [58]

    F., Jenkins A., Frenk C

    Power C., Navarro J. F., Jenkins A., Frenk C. S., White S. D. M., Springel V., Stadel J., Quinn T., 2003, MNRAS, 338, 14

    2003

  51. [59]

    Preto M., Berentzen I., Berczik P., Spurzem R., 2011, ApJ, 732, L26

    2011

  52. [60]

    Rantala A., Pihajoki P., Johansson P., Naab T., Lah\' e n N., Sawala T., 2017, ApJ, 840, 53

    2017

  53. [61]

    H., Rees M

    Redmount I. H., Rees M. J., 1989, Comments on Astrophysics, 14, 165

    1989

  54. [62]

    R., Wadsley J., 2015, MNRAS, 449, 494

    Ro s kar R., Mayer L., Fiacconi D., Kazantzidis S., Quinn T. R., Wadsley J., 2015, MNRAS, 449, 494

    2015

  55. [63]

    L., 2016, in IAU Symposium, Vol

    Schechter P. L., 2016, in IAU Symposium, Vol. 317, The General Assembly of Galaxy Halos: Structure, Origin and Evolution, ed. A. Bragaglia, M. Arnaboldi, M. Rejkuba, D. Romano, 35\-38

    2016

  56. [64]

    D., 2007, ApJ, 667, L133

    Schnittman J. D., 2007, ApJ, 667, L133

    2007

  57. [65]

    Sesana A., 2007, MNRAS, 382, L6

    2007

  58. [66]

    G., 2011, MNRAS, 414, 3656

    Sijacki D., Springel V., Haehnelt M. G., 2011, MNRAS, 414, 3656

    2011

  59. [67]

    Smole M., 2015, Serb. Astron. J, 191, 17

    2015

  60. [68]

    Springel V., 2005, MNRAS, 364, 1105

    2005

  61. [69]

    Tanaka T., Haiman Z., 2009, ApJ, 696, 1798

    2009

  62. [70]

    R., Pontzen A., 2018, MNRAS, 475, 4967

    Tremmel M., Governato F., Volonteri M., Quinn T. R., Pontzen A., 2018, MNRAS, 475, 4967

    2018

  63. [71]

    Vogelsberger M., Genel S., Springel V., Torrey P., Sijacki D., Xu D., Snyder G., Bird S., Nelson D., Hernquist L., 2014a, Nature, 509, 177

  64. [72]

    Vogelsberger M., Genel S., Springel V., Torrey P., Sijacki D., Xu D., Snyder G., Nelson D., Hernquist L., 2014b, MNRAS, 444, 1518

  65. [73]

    Volonteri M., 2007, ApJ, 663, L5

    2007

  66. [74]

    Volonteri M., Gultekin K., Dotti M., 2010, MNRAS, 404, 2143

    2010

  67. [75]

    M., Dubinski J., 2005, ApJ, 631, 838

    Widrow L. M., Dubinski J., 2005, ApJ, 631, 838

    2005

  68. [76]

    M., Pym B., Dubinski J., 2008, ApJ, 679, 1239

    Widrow L. M., Pym B., Dubinski J., 2008, ApJ, 679, 1239

    2008

  69. [77]

    del Valle L., Escala A., Maureira-Fredes C., Molina J., Cuadra J., Amaro-Seoane P., 2015, ApJ, 811, 5

    2015

  70. [78]

    J., Geller M

    Zahid H. J., Geller M. J., Fabricant D. G., Hwang H. S., 2016, ApJ, 832, 20

    2016

  71. [79]

    J., Sohn J., Geller M

    Zahid H. J., Sohn J., Geller M. J., 2018, ApJ, 859, 96

    2018

  72. [80]

    Zhang T., Liao S., Li M., Gao L., 2019, MNRAS, 487, 1227

    2019

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.