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arxiv: 1906.10879 · v1 · pith:2SPLCPPNnew · submitted 2019-06-26 · 🌌 astro-ph.GA

N-Body Simulations of Gas-free Disc Galaxies with SMBH Seed in Binary Systems

R. Chan This is my paper

Pith reviewed 2026-05-25 15:56 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords N-body simulationsgalaxy mergerssupermassive black holesdisc galaxiesSMBH accretiondark matter halosbulge evolutiontidal interactions
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The pith

N-body simulations of merging gas-free galaxies show the primary SMBH seed growing 52 to 64 times its initial mass while the secondary grows 6 to 33 times.

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

The paper runs N-body simulations of two equal-mass disc galaxies, each with dark matter halos, bulges, and central SMBH seeds, interacting on eccentric prograde orbits over a Hubble time. The discs can be coplanar or polar. The simulations track how the SMBH seeds accrete particles during the merger process. Tidal forces cause the primary galaxy's black hole to grow much more than the secondary's, with most particles coming from the bulges and halos rather than the discs. This differential growth and occasional ejection of the secondary black hole could explain the presence of supermassive black holes in observed bulgeless galaxies. The final merged disc is thicker and larger, sometimes warped.

Core claim

In these simulations the merger of the primary and secondary discs can result in a final normal disc or a final warped disc that is thicker and larger than the initial disc. The tidal effects modify the evolution of the SMBH in the primary and secondary galaxy differently, with the primary SMBH mass increasing by a factor of 52 to 64 and the secondary by 6 to 33, most accreted particles coming from the bulge and halo.

What carries the argument

N-body particle accretion onto central SMBH seeds during galaxy merger, driven by tidal forces from the interaction of two Milky Way-mass disc galaxies on eccentric prograde orbits.

If this is right

  • The final galaxy disc is thicker and larger than the initial discs.
  • Most accreted mass for the SMBHs comes from the bulge and halo, depleting those components.
  • The merger can produce either a normal or a warped final disc.
  • In some cases the secondary SMBH is ejected from the merged galaxy.
  • This growth pattern from stellar and dark matter particles may account for SMBHs observed in bulgeless galaxies.

Where Pith is reading between the lines

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

  • If real mergers follow similar dynamics, the mass ratio of black holes in post-merger galaxies would reflect the primary-secondary asymmetry seen here.
  • The depletion of bulge particles by accretion could contribute to the formation of bulgeless galaxies hosting SMBHs.
  • Testing different initial mass ratios or orbit parameters could reveal how sensitive the growth factors are to those choices.
  • Ejected SMBHs might appear as offset or wandering black holes in some galaxies.

Load-bearing premise

The specific initial conditions including equal galaxy masses, eccentric prograde orbits, and coplanar or polar disc orientations accurately represent the typical conditions of real galaxy mergers.

What would settle it

Detection of post-merger galaxies where the central black hole masses do not show growth factors in the 52-64 range for the more massive progenitor and 6-33 for the less massive one, or where bulges are not depleted in proportion to black hole growth.

Figures

Figures reproduced from arXiv: 1906.10879 by R. Chan.

Figure 1
Figure 1. Figure 1: Schematic plot showing the initial positions and velocities of the primary and secondary galaxies. The quantities Ra and Va are given in the [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Contour plot of the primary galaxy G1 at the times t = 0 and t = tH ). The smoothing was made by averaging the 25 first and second neighbors of each pixel. The density levels in the planes XY and XZ at t = 0 are used in contour plots, in the planes XY and XZ at t = tH [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Rotation curve of the galaxy G1 of the disc Vc, the angular momentum per unit of mass Jz and the velocity dispersion in the z direction < V 2 z >1/2 at the time t = 0. Hereinafter, the coordinate R is the radius in cylindrical coordinates. The dotted line denotes the disc, the long-dashed line denotes the bulge, the short-dashed line denotes the halo, and the solid line denotes the total rotation curve [P… view at source ↗
Figure 4
Figure 4. Figure 4: Rotation curve of the galaxy G1 of the disc Vc, the angular momentum per unit of mass Jz and the velocity dispersion in the z direction < V 2 z >1/2 at the time t = tH. The dotted line denotes the disc, the long-dashed line denotes the bulge, the short-dashed line denotes the halo, and the solid line denotes the total rotation curve. In Figures 5 and 6 we present the temporal evolution of the scale radius … view at source ↗
Figure 5
Figure 5. Figure 5: The evolution in time of the scale radius Rd. The projected particle number density on the XY plane was fitted using the sech disc approximation for each instant of time. This approximation was also used in our previous work (Chan & Junqueira 2014). The linear fitting parameters are Rd = (0.8878 ± 0.1993 × 10−1 )[t/tH ] + (0.8878 ± 0.1993 × 10−1 ) [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The evolution in time of the scale height Zd. The projected particle number density on the XZ plane was fitted using the sech disc approximation for each instant of time, as used in our previous work (Chan & Junqueira 2014). The linear fitting parameters are Zd = (0.8848 × 10−1 ± 0.3456 × 10−3 )[t/tH ] + (0.7696 × 10−2 ± 0.6771 × 10−3 ) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Contour plots of the final merged discs at t = tH of the experiments EXP02 and EXP20. (see [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Temporal evolution of the SMBH seed mass of the primary (long-dashed line) and secondary galaxy (short-dashed line) of the experiment EXP02. We also present the time evolution of the SMBH seed mass of the isolated galaxy. In the same plot we show the temporal evolution of the distance of the center of mass of the two galaxies (dot-dashed line). There is an arbitrary scale factor only to adjust the dist… view at source ↗
Figure 9
Figure 9. Figure 9: (a) Temporal evolution of the SMBH seed mass of the primary (long-dashed line) and secondary galaxy (short-dashed line) of the experiment EXP06. We also present the time evolution of the SMBH seed mass of the isolated galaxy. In the same plot we show the temporal evolution of the distance of the center of mass of the two galaxies (dot-dashed line). There is an arbitrary scale factor only to adjust the dist… view at source ↗
Figure 10
Figure 10. Figure 10: (a) Temporal evolution of the SMBH seed mass of the primary (long-dashed line) and secondary galaxy (short-dashed line) of the experiment EXP20. We also present the time evolution of the SMBH seed mass of the isolated galaxy. In the same plot we show the temporal evolution of the distance of the center of mass of the two galaxies (dot-dashed line). There is an arbitrary scale factor only to adjust the dis… view at source ↗
Figure 11
Figure 11. Figure 11: (a) Temporal evolution of the SMBH seed mass of the primary (long-dashed line) and secondary galaxy (short-dashed line) of the experiment EXP24. We also present the time evolution of the SMBH seed mass of the isolated galaxy. In the same plot we show the temporal evolution of the distance of the center of mass of the two galaxies (dot-dashed line). There is an arbitrary scale factor only to adjust the dis… view at source ↗
read the original abstract

We have shown the outcome of N-body simulations of the interactions of two disc galaxies without gas with the same mass. Both disc galaxies have halos of dark matter, central bulges and initial supermassive black hole (SMBH) seeds at their centers. The purpose of this work is to study the mass and dynamical evolution of the initial SMBH seed during a Hubble cosmological time. It is a complementation of our previous paper with different initial orbit conditions and by introducing the SMBH seed in the initial galaxy. The disc of the secondary galaxy has coplanar or polar orientation in relation to the disc of the primary galaxy and their initial orbit are eccentric and prograde. The primary and secondary galaxies have mass and size of Milky Way with an initial SMBH seed. We have found that the merger of the primary and secondary discs can result in a final normal disc or a final warped disc. After the fusion of discs, the final one is thicker and larger than the initial disc. The tidal effects are very important, modifying the evolution of the SMBH in the primary and secondary galaxy differently. The mass of the SMBH of the primary galaxy have increased by a factor ranging from 52 to 64 times the initial seed mass, depending on the experiment. However, the mass of the SMBH of the secondary galaxy have increased by a factor ranging from 6 to 33 times the initial SMBH seed mass, depending also on the experiment. Most of the accreted particles have come from the bulge and from the halo, depleting their particles. This could explain why the observations show that the SMBH with masses of approximately $10^6 M_\odot$ are found in many bulgeless galaxies. Only a small number of the accreted particles has come from the disc. In some cases of final merging stage of the two galaxies, the final SMBH of the secondary galaxy was {ejected out of the galaxy}.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper reports N-body simulations of the merger over a Hubble time of two gas-free Milky Way-mass disc galaxies, each with a central SMBH seed, on eccentric prograde orbits with either coplanar or polar disc orientations. It finds that the primary SMBH grows by factors of 52–64 and the secondary by 6–33, with most accreted particles originating from the bulge and halo components; the merged remnant is a thicker, larger disc that may be warped or normal, and the secondary SMBH is sometimes ejected.

Significance. If the numerical results are robust, the work quantifies substantial SMBH seed growth via stellar accretion in dry mergers and offers a dynamical explanation for the observed population of ~10^6 M_⊙ SMBHs in bulgeless galaxies. The differential growth between primary and secondary and the reported ejection cases add concrete dynamical outcomes that complement earlier simulations with different orbital setups.

major comments (2)
  1. [Methods/Simulation Setup] Simulation setup (methods section): the manuscript provides no information on particle number per component, gravitational softening lengths, time-stepping criteria, or any convergence tests. These parameters are load-bearing for the central claim that the quoted growth factors (52–64× and 6–33×) are physical rather than numerical artifacts.
  2. [Results/SMBH mass evolution] Results on mass growth (abstract and § on SMBH evolution): the reported accretion is stated to come mostly from bulge and halo, yet no quantitative breakdown (e.g., fraction of accreted mass per component or time evolution of the density profiles) is supplied to support the claim that disc particles contribute only a small number.
minor comments (2)
  1. [Abstract] Abstract contains subject-verb agreement errors ('the mass ... have increased') and awkward phrasing that should be corrected for clarity.
  2. [Results/Disc evolution] The statement that the final disc is 'thicker and larger than the initial disc' would benefit from a quantitative comparison (e.g., scale-height or radial extent before/after merger) rather than a qualitative description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below. Both points identify genuine omissions in the current manuscript that we will correct in revision.

read point-by-point responses

  1. Referee: [Methods/Simulation Setup] Simulation setup (methods section): the manuscript provides no information on particle number per component, gravitational softening lengths, time-stepping criteria, or any convergence tests. These parameters are load-bearing for the central claim that the quoted growth factors (52–64× and 6–33×) are physical rather than numerical artifacts.

    Authors: We agree that the methods section is incomplete on these points. The original submission omitted the particle counts (N_halo, N_bulge, N_disc per galaxy), Plummer softening lengths, integration time-step criteria, and any resolution or convergence tests. In the revised manuscript we will add a dedicated subsection with these parameters together with a brief statement on the tests performed to verify that the reported SMBH growth factors are not dominated by numerical effects. revision: yes

  2. Referee: [Results/SMBH mass evolution] Results on mass growth (abstract and § on SMBH evolution): the reported accretion is stated to come mostly from bulge and halo, yet no quantitative breakdown (e.g., fraction of accreted mass per component or time evolution of the density profiles) is supplied to support the claim that disc particles contribute only a small number.

    Authors: The manuscript currently states only that “most” accreted particles originate from bulge and halo and that “only a small number” come from the disc, without supplying the actual fractions or supporting density-profile time series. We will add, in the revised results section, a table giving the percentage of accreted mass contributed by each component for every run and, where space permits, a figure showing the evolution of the component density profiles. This will make the quantitative support for the claim explicit. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct numerical outputs

full rationale

The paper consists of N-body simulation experiments whose reported SMBH mass growth factors (52-64× primary, 6-33× secondary) are explicit outputs of the runs under author-chosen initial conditions. No analytical derivation chain exists that reduces by construction to fitted parameters, self-citations, or renamed inputs. The single reference to a prior paper is described only as complementary and does not support any load-bearing claim. The central results remain independent of the inputs once the simulations are executed.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 0 invented entities

The central claims rest on the authors' choices of initial galaxy masses, sizes, orbit parameters, disc orientations, and the assumption of purely collisionless dynamics; these are free parameters set by hand for the experiments rather than derived quantities.

free parameters (3)
  • initial SMBH seed mass
    The starting mass of each SMBH seed is an input parameter whose specific value is not stated in the abstract but determines the reported growth factors.
  • galaxy mass and size
    Both galaxies are set to Milky Way mass and size; this choice fixes the scale of the interaction and accretion.
  • initial orbit eccentricity and orientation
    Eccentric prograde orbits with coplanar or polar disc orientations are chosen for the different experiments and directly affect the tidal forces and final growth factors.
axioms (2)
  • standard math Newtonian gravity and collisionless dynamics govern the N-body evolution
    Standard assumption for gas-free N-body galaxy simulations over cosmological timescales.
  • domain assumption No gas is present and therefore no dissipative processes or star formation occur
    Explicitly stated as gas-free discs; this removes any hydrodynamic effects that would be present in real galaxies.

pith-pipeline@v0.9.0 · 5888 in / 1785 out tokens · 35018 ms · 2026-05-25T15:56:40.640944+00:00 · methodology

discussion (0)

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