Elusive Plunges and Heavy Intermediate-mass-ratio Inspirals from Single and Binary Supermassive Black Holes

Antti Rantala; Lazaros Souvaitzis; Thorsten Naab

arxiv: 2510.09743 · v2 · submitted 2025-10-10 · 🌌 astro-ph.GA · gr-qc

Elusive Plunges and Heavy Intermediate-mass-ratio Inspirals from Single and Binary Supermassive Black Holes

Lazaros Souvaitzis , Antti Rantala , Thorsten Naab This is my paper

Pith reviewed 2026-05-18 07:28 UTC · model grok-4.3

classification 🌌 astro-ph.GA gr-qc

keywords supermassive black holesintermediate-mass black holesdirect plungesintermediate-mass-ratio inspiralsgravitational wavesgalactic nucleiN-body simulations

0 comments

The pith

A companion supermassive black hole more than doubles the rate at which intermediate-mass black holes plunge directly into the central one.

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

The paper evolves groups of ten intermediate-mass black holes, each about 100,000 solar masses, orbiting a central supermassive black hole of a billion solar masses. It runs the systems both alone and with an added perturbing secondary supermassive black hole using regularized orbital integration that includes relativistic corrections. The central result is that the secondary black hole raises the count of direct plunges by more than a factor of two, turning plunges into the leading merger channel instead of gradual inspirals. These events add mass to the largest black holes but generate signals too short or too weak for pulsar timing arrays and most planned detectors to register. Only around lower-mass central black holes, below roughly 100 million solar masses, do the inspirals become bright enough for the LISA mission to detect and thereby test whether such intermediate-mass objects exist.

Core claim

Evolving compact subsystems of ten 10^5 solar mass IMBHs around a 10^9 solar mass SMBH using regularized integration with relativistic corrections shows that a perturbing secondary SMBH enhances IMBH direct plunges by more than a factor of two over the isolated case, establishing plunges as the dominant merger channel. These events contribute to central SMBH growth yet evade detection by PTAs and future interferometers, while heavy IMRIs around lower-mass SMBHs (M ≲ 10^8 solar masses) become observable with LISA.

What carries the argument

Regularized N-body integration including post-Newtonian terms up to 3.5PN, applied to IMBH subsystems in isolation versus under perturbation by a companion SMBH.

Load-bearing premise

Enough intermediate-mass black holes migrate inward to assemble into compact groups of ten objects at the chosen densities around the central supermassive black hole.

What would settle it

A simulation of the identical ten-IMBH subsystem without the secondary SMBH that yields fewer than half as many direct plunges as the perturbed run.

read the original abstract

The most massive galaxies in the Universe also host the largest supermassive black holes (SMBHs), with masses of $10^9 \: \mathrm{M_{\odot}}$ and above. During their hierarchical assembly, these galaxies have experienced only a few major mergers at low redshift, but have accreted many low-mass galaxies across cosmic time, possibly hosting intermediate mass black holes (IMBHs). If some of these IMBHs migrate to the galactic center, they may form compact subsystems around the central SMBH. We investigate the evolution of such subsystems, consisting of ten $10^5 \: \mathrm{M_{\odot}}$ IMBHs at three different concentrations around a $10^9 \: \mathrm{M_{\odot}}$ SMBH. We evolve these systems both in isolation and in the presence of a companion SMBH, using \texttt{MSTAR}, a regularized integration method including relativistic effects up to post-Newtonian order 3.5PN. Our analysis focuses on gravitational--wave--driven intermediate--mass--ratio inspirals (heavy IMRIs) and direct plunges. We show that perturbations from a secondary SMBH enhance the number of IMBH direct plunges by more than a factor of two, making them the dominant merger channel. These plunges and IMRIs with a central $10^9 \: \mathrm{M_{\odot}}$ SMBH will contribute to SMBH growth but will likely evade detection with future gravitational-wave interferometers and pulsar timing arrays (PTAs). However, for galaxies with lower--mass SMBHs ($M_\bullet \lesssim 10^8 \:\mathrm{M_{\odot}}$), heavy IMRIs will be detectable with the Laser Interferometer Space Antenna (LISA) and can provide direct observational constraints on the existence of IMBHs, while the more numerous plunges will still remain hidden.

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.

Desk Editor's Note private letter to a colleague

The simulations find that a companion SMBH more than doubles direct IMBH plunges and makes them dominant, but only for the specific ten-IMBH subsystems at the three chosen concentrations.

read the letter

The main result is that adding a secondary SMBH increases the number of direct plunges by the ten 10^5 solar mass IMBHs by more than a factor of two, flipping the dominant channel from inspirals to plunges. The paper runs regularized N-body integrations with 3.5PN terms using the MSTAR code on these subsystems around a 10^9 solar mass primary, both isolated and with the companion, at three different initial concentrations. The comparison isolates the perturbation effect on plunge versus inspiral outcomes and ties it to SMBH growth and future detector visibility. This setup is new in its direct treatment of the binary SMBH case with heavy IMRIs and plunges. The numerical method is appropriate for tracking close encounters and relativistic effects without heavy parameter fitting, which gives the channel dominance claim a concrete basis. The discussion of why these events mostly stay hidden from PTAs and LISA while lower-mass cases could be seen by LISA is a useful observational link. The soft spot is the initial conditions. The subsystems are stated as given for both the isolated and binary runs without showing how migration would produce those densities or testing changes in number or radial spread. If real clusters form differently, the factor-of-two boost and dominance do not necessarily carry over. The abstract also gives no error bars or details on plunge classification, though the full methods may address some of this. This is for readers working on SMBH assembly, IMBH dynamics, and LISA source populations. It shows clear engagement with the dynamical problem and relevant literature. I would bring it to a reading group to discuss the numerical results and the initial-condition question. It should go to peer review rather than desk reject so referees can check the robustness of the enhancement under varied setups.

Referee Report

2 major / 2 minor

Summary. The paper claims that subsystems of ten 10^5 M_⊙ IMBHs at three different initial concentrations around a 10^9 M_⊙ SMBH evolve differently when perturbed by a secondary SMBH. Using the MSTAR regularized integrator with post-Newtonian terms up to 3.5PN, the authors report that the secondary enhances the number of direct plunges by more than a factor of two relative to isolated runs, making plunges the dominant channel over heavy IMRIs. These events contribute to SMBH growth but are largely undetectable by future GW instruments, except for heavy IMRIs around lower-mass SMBHs (M_• ≲ 10^8 M_⊙) which may be visible to LISA.

Significance. If the reported factor-of-two enhancement is robust, the result would be significant for models of IMBH dynamics in galactic nuclei, showing that binary SMBH perturbations can shift merger channels toward direct plunges and thereby increase their contribution to central SMBH mass assembly. The work also provides concrete predictions for the (non-)detectability of these events with LISA and PTAs. The use of a regularized N-body code with high-order PN corrections is a methodological strength for accurately capturing close encounters and relativistic effects.

major comments (2)

[Abstract] Abstract and setup description: the headline claim that secondary-SMBH perturbations enhance IMBH direct plunges by more than a factor of two (making them dominant) is demonstrated exclusively for subsystems initialized with exactly ten 10^5 M_⊙ IMBHs at three specific concentrations. These concentrations are stated as given initial conditions without derivation from migration timescales, without a sensitivity study on IMBH number/mass/radial distribution, and without demonstration that such compact subsystems form at the required densities. This assumption is load-bearing for the channel-dominance conclusion.
[Methods] Methods and results sections: the distinction between direct plunges and gravitational-wave-driven inspirals is central to the quantitative enhancement factor, yet the abstract (and presumably the methods) provides no details on the classification criteria, any radial or energy thresholds employed, error bars on the event counts, or convergence tests with respect to integration accuracy or particle number.

minor comments (2)

[Abstract] The abstract refers to 'three different concentrations' but does not quote their numerical values; stating them explicitly would improve reproducibility and allow readers to assess the setup.
A compact table summarizing plunge and IMRI counts (with uncertainties if available) for each concentration in both isolated and binary configurations would greatly clarify the factor-of-two result.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address the major comments point by point below, indicating where revisions will be made to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract and setup description: the headline claim that secondary-SMBH perturbations enhance IMBH direct plunges by more than a factor of two (making them dominant) is demonstrated exclusively for subsystems initialized with exactly ten 10^5 M_⊙ IMBHs at three specific concentrations. These concentrations are stated as given initial conditions without derivation from migration timescales, without a sensitivity study on IMBH number/mass/radial distribution, and without demonstration that such compact subsystems form at the required densities. This assumption is load-bearing for the channel-dominance conclusion.

Authors: We agree that the reported enhancement and channel dominance are shown specifically for subsystems of ten 10^5 M_⊙ IMBHs at the three concentrations explored. These initial conditions were selected to represent compact configurations that could arise from IMBH migration in galactic nuclei, as motivated in the introduction with references to dynamical friction and migration studies. We did not derive the exact concentrations from migration timescales or conduct a broad sensitivity study on number, mass, or distribution within this work. In the revised manuscript we will expand the setup section to provide additional justification for the chosen parameters, add explicit discussion of the limited scope, and qualify the dominance conclusion as applying to the explored setups. A full sensitivity analysis lies beyond the present scope but will be noted as future work. revision: partial
Referee: [Methods] Methods and results sections: the distinction between direct plunges and gravitational-wave-driven inspirals is central to the quantitative enhancement factor, yet the abstract (and presumably the methods) provides no details on the classification criteria, any radial or energy thresholds employed, error bars on the event counts, or convergence tests with respect to integration accuracy or particle number.

Authors: We thank the referee for highlighting the need for greater detail on event classification. The methods section describes the MSTAR integrator with 3.5PN terms and our focus on IMRIs versus direct plunges, but we acknowledge that explicit criteria (e.g., radial or energy thresholds used to distinguish rapid plunges from gradual inspirals), statistical error bars, and convergence tests are not presented with sufficient clarity. We will revise the methods and results sections to include these specifics, such as the precise classification thresholds, the number of realizations contributing to the reported counts, and tests confirming robustness with respect to integration accuracy and particle number. revision: yes

Circularity Check

0 steps flagged

No circularity: results are direct outputs of numerical integration on explicitly stated initial conditions

full rationale

The paper reports outcomes from direct N-body integrations with the MSTAR code on subsystems initialized with exactly ten 10^5 M⊙ IMBHs at three chosen concentrations around a 10^9 M⊙ SMBH. The reported factor-of-two enhancement in direct plunges is a computed simulation result, not an analytic quantity obtained by fitting parameters to a data subset and then re-deriving a related observable, nor by self-definition, self-citation of a uniqueness theorem, or smuggling an ansatz. The initial configurations are presented as the study's setup rather than quantities derived inside the paper; therefore no load-bearing step reduces to its own inputs by construction. The work is self-contained as a numerical experiment.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The headline result rests on the chosen initial number, masses, and spatial concentrations of the ten IMBHs plus the assumption that the MSTAR integrator with 3.5PN terms accurately captures the plunge versus inspiral distinction over the simulated timescales.

free parameters (2)

IMBH number and mass
Fixed at ten objects of 10^5 solar masses each; these values are chosen rather than derived.
Three concentration parameters
Initial spatial distributions of the IMBHs around the central SMBH are set by hand for the three cases.

axioms (1)

domain assumption Post-Newtonian expansion up to 3.5PN is sufficient to model energy loss and plunge dynamics in this mass-ratio regime.
Invoked by the choice of MSTAR integrator including relativistic effects up to 3.5PN.

pith-pipeline@v0.9.0 · 5892 in / 1511 out tokens · 31272 ms · 2026-05-18T07:28:50.084615+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

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

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We evolve these systems both in isolation and in the presence of a companion SMBH, using MSTAR, a regularized integration method including relativistic effects up to post-Newtonian order 3.5PN. Our analysis focuses on gravitational-wave-driven intermediate-mass-ratio inspirals (heavy IMRIs) and direct plunges.
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the presence of a secondary SMBH enhances the number of IMBH direct plunges by more than a factor of two

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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.