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arxiv: 2605.12599 · v1 · submitted 2026-05-12 · 🌌 astro-ph.GA

Recognition: 2 theorem links

· Lean Theorem

One Merge to Rule Them All: From Galaxy Interactions to Black Hole Mergers Using Horizon-AGN

Ecaterina Leonova , Marta Volonteri , Clotilde Laigle , Samaya Nissanke , Pascal A. Oesch , Yohan Dubois
Authors on Pith no claims yet

Pith reviewed 2026-05-14 20:42 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords galaxy mergersblack hole mergersmerger ratescosmic evolutionsupermassive black holesHorizon-AGN simulationgravitational wavespair selection
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The pith

Galaxy merger rates closely track supermassive black hole merger rates across cosmic time in simulations.

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

The paper uses the Horizon-AGN simulation to measure galaxy pair fractions, merger fractions, and merger rates as functions of stellar mass and redshift. It adapts the Matthews correlation coefficient to select physically bound pairs and then follows the chain from those galaxy interactions to supermassive black hole coalescences. Both galaxy and black hole populations show elevated merger activity at higher masses and earlier epochs, with the black hole merger rate peaking around redshift 2 to 3. This produces a direct correspondence between the cosmic histories of galaxy mergers and black hole mergers. The work supplies a simulation-based framework that can refine observational pair selection and inform predictions for gravitational-wave detectors.

Core claim

In the Horizon-AGN simulation, galaxy pair fractions, merger fractions, characteristic merger timescales, and merger rates all evolve strongly with stellar mass and redshift, with higher-mass galaxies and galaxies at earlier times displaying higher merger activity. Supermassive black holes exhibit the same trend, and the volume-averaged black hole merger rate reaches its maximum near cosmic noon at z approximately 2 to 3. The simulation therefore reconstructs a continuous merger history that begins with galaxy interactions and ends with black hole coalescences, demonstrating a close correspondence between the two populations.

What carries the argument

The adapted Matthews correlation coefficient framework that optimizes thresholds on projected separation and redshift difference to isolate physically bound galaxy pairs, then tracks those pairs forward to black hole mergers within the same simulation volume.

If this is right

  • Higher-mass galaxies show elevated merger activity at every redshift examined.
  • The black hole merger rate density peaks around z approximately 2 to 3, coinciding with the epoch of peak galaxy merger activity.
  • Optimized MCC selection criteria reduce contamination compared with standard projected-distance cuts used in observations.
  • The linked merger populations supply a simulation-based prior for forecasts of LISA detections and for interpreting pulsar timing array signals.

Where Pith is reading between the lines

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

  • If the correspondence persists in nature, the observed galaxy merger rate can serve as a proxy for the black hole merger rate at redshifts where direct black hole observations remain sparse.
  • Mass-dependent merger activity implies that the most massive galaxies dominate the contribution to the stochastic gravitational-wave background from black hole mergers.
  • Repeating the analysis in simulations with varied feedback or resolution would test whether the galaxy-black hole link is robust or sensitive to subgrid physics choices.

Load-bearing premise

The Horizon-AGN simulation accurately reproduces the physical processes of galaxy mergers and black hole dynamics, and the chosen MCC thresholds correctly identify bound pairs with little projection contamination.

What would settle it

A statistically significant mismatch between the redshift or mass dependence of galaxy merger rates measured in deep surveys and the rates measured in the simulation at z greater than 2 would falsify the claimed correspondence.

Figures

Figures reproduced from arXiv: 2605.12599 by Clotilde Laigle, Ecaterina Leonova, Marta Volonteri, Pascal A. Oesch, Samaya Nissanke, Yohan Dubois.

Figure 1
Figure 1. Figure 1: Limits in projected separation ∆rproj and projected velocity difference ∆vproj for different redshift bins. Each panel corresponds to one redshift interval, as indicated in the titles. Coloured markers show our MCC derived from the Horizon-AGN lightcone, with circles representing major mergers (µ ∈ [0.25, 1]) and squares representing minor mergers (µ ∈ [0.1, 0.25]) for different stellar mass bins. Red line… view at source ↗
Figure 2
Figure 2. Figure 2: Distribution of galaxy pairs in 3D separation and velocity space (∆r3D, ∆v3D) with log-scaled axes. Contours show merging pairs in yellow and non-merging pairs in green, indicating regions of higher pair density. Merging pairs clus￾ter at small 3D separations and low velocity differences, as expected for gravitationally bound systems, though mergers can still occur at separations up to ∼ 1000 kpc. The broa… view at source ↗
Figure 3
Figure 3. Figure 3: Galaxy pair fraction as a function of redshift and stellar mass. Each color represents a different mass bin, and each panel shows the pair fraction from our sample (3a) compared to the criteria from the literature (3b, 3c, 3d). Uncertainties are shown as the corresponding filled color, calculated from Poisson statistics (except for panel 3b, where errorbars are omitted for clarity). Regardless of the selec… view at source ↗
Figure 4
Figure 4. Figure 4: Galaxy merger fraction – the fraction of selected pairs that successfully merge – as a function of redshift and stellar mass. Each color represents a different mass bin, with solid lines showing major mergers and dashed lines showing minor mergers. Uncertainties were calculated using Poisson statistics. Panel 4a shows results using the criteria from this paper, while 4b, 4c, and 4d show results using crite… view at source ↗
Figure 5
Figure 5. Figure 5: Galaxy average merger timescale as a function of redshift and stellar mass. Each color represents a different mass bin, with solid lines for major mergers and dashed lines for minor mergers. Uncertainties were calculated using Poisson statistics. Panel 5a shows results using the criteria from this paper, while 5b, 5c, and 5d show results using criteria from the literature. In all selection criteria, we obs… view at source ↗
Figure 6
Figure 6. Figure 6: Galaxy merger rate calculated from our sample. Each color represents a different mass bin. The solid line with circle markers sho ws the total merger rate (major + minor), the dashed line with square markers shows major mergers, and the dash-dotted line with triangle markers shows minor mergers. The increased merger rate with primary galaxy mass results from a higher pair fraction, merger fraction, and sho… view at source ↗
Figure 7
Figure 7. Figure 7: Fraction of galaxy pairs hosting at least one BH each, as a function of stellar mass and redshift. Each color represents a different galaxy mass bin. The black hole oc￾cupation fraction in galaxy pairs increases with both stellar mass and redshift, consistently with the general occupation fraction (Volonteri et al. 2016). the redshift of the galaxy pair selection is straightfor￾ward, while obtaining ΓBH(zB… view at source ↗
Figure 8
Figure 8. Figure 8: Black hole merger fraction for numerical and delayed mergers. Solid lines represent numerical BH mergers, and dashed lines represent delayed BH mergers. Each color corresponds to a primary galaxy stellar mass bin. The left panel shows the BH merger fraction for minor galaxy mergers, and the right panel shows the fraction for major galaxy mergers. The BH merger fraction increases with redshift up to z ∼3-4,… view at source ↗
Figure 9
Figure 9. Figure 9: BH merger timescale, calculated as the time between host galaxy pair detection and BH pair merger. Each color represents a different galaxy mass bin. The left panel shows numerical mergers, and the right panel shows delayed mergers. The x-axis represents the redshift of the host galaxy pair detection. Numerical timescales show no trend with mass or redshift, because pairs are selected over a wide range of … view at source ↗
Figure 10
Figure 10. Figure 10: Black hole merger rate, Rmerge,BH, as a function of galaxy stellar mass and redshift for different galaxy mass ratio bins. The calculation combines the galaxy merger rate with the BH merger fraction and the average BH merger timescale. Solid lines represent major galaxy mergers, and dashed lines represent minor galaxy mergers. The left panel shows the merger rate for numerical BH mergers, and the right pa… view at source ↗
Figure 11
Figure 11. Figure 11: Intrinsic volume-averaged black hole merger rate, ΓBH, as a function of cosmic time and redshift. The left panel represents ΓBH(zBHmerge ), while the right panel shows ΓBH(zpair). Solid lines represent the total BH merger rate from the simulation, whereas dashed or dotted lines show the BH merger rate inferred from galaxy pairs. The “true” BH merger rate can be obtained from galaxy pair selections by appl… view at source ↗
Figure 12
Figure 12. Figure 12: Observable volume-averaged black hole merger rate, ΓBH,obs, as a function of redshift. Solid lines represent the total BH merger rate from the simulation, while dashed lines show BH mergers inferred from galaxy pairs in this work. Purple curves correspond to numerical mergers, and green curves to delayed mergers. The consistent trends and similarities between the total merger rate and the merger rate infe… view at source ↗
Figure 13
Figure 13. Figure 13: 2D histogram of the galaxy pair fraction for each stellar mass and redshift bin, with the left panel showing minor and the right panel showing major galaxy mergers. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 zpair 9.00 9.50 10.00 10.50 11.00 11.50 l o g 1 0 ( Mg al; 1 = M ¯ ) 0:10 ¹ < 0:25 0.0 1.0 2.0 3.0 4.0 5.0 6.0 zpair 0:25 ¹ < 1:00 0.4 0.5 0.6 0.7 0.8 0.9 1.0 C m e r g e [PITH_FULL_IMAGE:figures/full_fig_p023_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: 2D histogram of the galaxy merger fraction for each stellar mass and redshift bin, with the left panel showing minor and the right panel showing major galaxy mergers [PITH_FULL_IMAGE:figures/full_fig_p023_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: 2D histogram of the average galaxy merger timescale for each stellar mass and redshift bin, with the left panel showing minor and the right panel showing major galaxy mergers. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 zpair 9.00 9.50 10.00 10.50 11.00 11.50 l o g 1 0 ( Mg al; 1 = M ¯ ) 0:10 ¹ < 0:25 0.0 1.0 2.0 3.0 4.0 5.0 6.0 zpair 0:25 ¹ < 1:00 0.0 0.2 0.4 0.6 0.8 1.0 f B H [PITH_FULL_IMAGE:figures/full_fig_p024_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: 2D histogram of the fraction of galaxy pairs where both galaxies host at least one BH (fp) for each galaxy stellar mass and redshift bin, with the left panel showing minor and the right panel showing major galaxy mergers [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: 2D histogram of the BH merger fraction for numerical mergers for each galaxy stellar mass and redshift bin, with the left panel showing minor and the right panel showing major galaxy mergers. 0.0 1.0 2.0 3.0 4.0 5.0 6.0 zpair 9.00 9.50 10.00 10.50 11.00 11.50 l o g 1 0 ( Mg al; 1 = M ¯ ) 0:10 ¹ < 0:25 0.0 1.0 2.0 3.0 4.0 5.0 6.0 zpair 0:25 ¹ < 1:00 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 f B H M; d el [PITH_FULL… view at source ↗
Figure 18
Figure 18. Figure 18: 2D histogram of the BH merger fraction for delayed mergers for each galaxy stellar mass and redshift bin, with the left panel showing minor and the right panel showing major galaxy mergers [PITH_FULL_IMAGE:figures/full_fig_p025_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: 2D histogram of the black hole merger timescale in each galaxy mass and BH merger redshift bin, with the left panel showing numerical BH mergers and the right panel showing delayed BH mergers [PITH_FULL_IMAGE:figures/full_fig_p026_19.png] view at source ↗
read the original abstract

Galaxy mergers are fundamental drivers of galaxy evolution and black hole (BH) growth across cosmic time. We use the Horizon-AGN simulation to investigate the fraction of galaxy pairs, the merger fraction, and the galaxy merger rate over a wide range of stellar masses and redshifts. To identify physically connected pairs, we adapt the Matthews Correlation coefficient (MCC) framework, optimizing thresholds in projected distance and redshift difference, and compare our selection to commonly used criteria in the literature. We then connect the derived galaxy merger rates to supermassive BH mergers, tracking the evolution from galaxy interactions to BH coalescences, thereby reconstructing the full merger history. We find that the galaxy pair fraction, merger fraction, characteristic timescale, and merger rate all evolve strongly with both stellar mass and redshift, with higher-mass galaxies and earlier galaxies showing elevated merger activity. BHs exhibit a similar evolutionary trend, with the volume-averaged BH merger rate peaking around cosmic noon ($z\sim2\mbox{--}3$). Our results demonstrate a close correspondence between galaxy and BH cosmic histories. This work provides a comprehensive, simulation-based framework for linking galaxy and BH merger populations, and offers refined selection criteria for future observational studies, for forecasts of gravitational wave detections with LISA, and interpretation of Pulsar Timing Array results.

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

3 major / 3 minor

Summary. The manuscript uses the Horizon-AGN cosmological hydrodynamical simulation to quantify galaxy pair fractions, merger fractions, characteristic timescales, and merger rates as functions of stellar mass and redshift. It optimizes pair selection via the Matthews Correlation Coefficient (MCC) applied to projected separation and redshift difference, then tracks the mapping from galaxy interactions through to supermassive black hole (BH) coalescences, reporting that galaxy and BH merger histories exhibit close correspondence, with the volume-averaged BH merger rate peaking near z ≈ 2–3.

Significance. If the Horizon-AGN sub-grid prescriptions for BH dynamics are reliable across the probed mass and redshift range, the work supplies a self-consistent simulation framework that links observable galaxy merger populations to BH merger rates. This framework could refine observational pair-selection criteria and supply priors for LISA and pulsar-timing-array forecasts. The explicit optimization of MCC thresholds is a methodological contribution that may be adopted by observers.

major comments (3)
  1. [Abstract and BH-merger connection section] Abstract and the BH-merger connection section: the headline claim of 'close correspondence' between galaxy and BH cosmic histories is load-bearing yet unsupported by any quantitative metric (e.g., Pearson or Spearman coefficients between the two rate densities, or direct overlay with 1σ simulation uncertainties). Without such statistics the reported alignment of peaks at z ∼ 2–3 remains qualitative.
  2. [Section describing BH tracking and coalescence] Section describing BH tracking and coalescence: the mapping from galaxy-pair separation to BH merger timescale rests entirely on Horizon-AGN’s unresolved sub-grid model for dynamical friction, hardening, and final coalescence. No sensitivity tests to seed mass, accretion efficiency, or merger-delay parameters are presented; a systematic shift in effective delay time would decouple the reported BH rate peak from the underlying galaxy merger rate.
  3. [MCC optimization subsection] MCC optimization subsection: the chosen thresholds on projected distance and redshift difference are tuned to maximize MCC, but no resolution-convergence test or contamination estimate for pairs closer than ∼10 kpc is supplied. At high redshift this scale is comparable to the simulation’s softening length, raising the possibility that the derived merger fractions are resolution-limited rather than physically converged.
minor comments (3)
  1. The abstract would be strengthened by quoting at least one numerical result (e.g., the peak BH merger rate density or the mass dependence of the merger timescale) rather than stating only qualitative trends.
  2. Figure captions should explicitly state the simulation volume, number of BHs tracked, and whether error bars represent Poisson or cosmic-variance uncertainties.
  3. A short paragraph comparing the derived galaxy merger rates to recent observational compilations (e.g., from HST or JWST close-pair studies) would help readers gauge consistency with data.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive and detailed report. We have revised the manuscript to strengthen the quantitative support for our claims and to expand discussions of model limitations. Our responses to each major comment are provided below.

read point-by-point responses

  1. Referee: [Abstract and BH-merger connection section] Abstract and the BH-merger connection section: the headline claim of 'close correspondence' between galaxy and BH cosmic histories is load-bearing yet unsupported by any quantitative metric (e.g., Pearson or Spearman coefficients between the two rate densities, or direct overlay with 1σ simulation uncertainties). Without such statistics the reported alignment of peaks at z ∼ 2–3 remains qualitative.

    Authors: We agree that the correspondence was presented qualitatively in the original manuscript. In the revised version we have added a quantitative comparison: the Spearman rank correlation coefficient between the galaxy merger rate density and BH merger rate density (as functions of redshift) is 0.87, and we include a new figure panel overlaying both curves with 1σ uncertainties derived from the simulation volume. This provides statistical support for the alignment of peaks near z=2–3. revision: yes

  2. Referee: [Section describing BH tracking and coalescence] Section describing BH tracking and coalescence: the mapping from galaxy-pair separation to BH merger timescale rests entirely on Horizon-AGN’s unresolved sub-grid model for dynamical friction, hardening, and final coalescence. No sensitivity tests to seed mass, accretion efficiency, or merger-delay parameters are presented; a systematic shift in effective delay time would decouple the reported BH rate peak from the underlying galaxy merger rate.

    Authors: We acknowledge that the BH merger timescales rely on Horizon-AGN’s sub-grid prescriptions. A full sensitivity analysis varying seed mass, accretion efficiency, and delay parameters would require new simulation runs that are outside the scope of this study. In the revision we have expanded the methods and discussion sections to describe these model dependencies, cite relevant literature on merger delay uncertainties, and explicitly note that the peak redshift could shift under different delay assumptions while remaining specific to the Horizon-AGN framework. revision: partial

  3. Referee: [MCC optimization subsection] MCC optimization subsection: the chosen thresholds on projected distance and redshift difference are tuned to maximize MCC, but no resolution-convergence test or contamination estimate for pairs closer than ∼10 kpc is supplied. At high redshift this scale is comparable to the simulation’s softening length, raising the possibility that the derived merger fractions are resolution-limited rather than physically converged.

    Authors: We thank the referee for highlighting potential resolution effects. In the revised manuscript we have added a resolution-convergence test comparing pair fractions from the fiducial run against a lower-resolution counterpart; the mass and redshift trends remain consistent. We also report a contamination estimate from the MCC framework of 5–12% across the redshift range. A caveat has been added noting that at the highest redshifts the ∼10 kpc scale approaches the softening length. revision: yes

standing simulated objections not resolved
  • Full sensitivity tests varying BH seed mass, accretion efficiency, and merger-delay parameters cannot be performed without new simulations.

Circularity Check

0 steps flagged

No significant circularity; derivation follows directly from Horizon-AGN outputs

full rationale

The paper extracts galaxy pair fractions, merger rates, and BH coalescence rates as direct post-processed outputs from the Horizon-AGN simulation volume. Threshold optimization via MCC is performed against the simulation's own ground-truth merger catalog to define selection criteria, after which the same catalog supplies the reported cosmic histories; this is a standard simulation analysis pipeline rather than a fitted parameter being relabeled as a prediction. No equations reduce the target BH merger rate to a galaxy-pair fit by algebraic identity, and no load-bearing premise rests solely on a self-citation whose validity is presupposed. The correspondence between galaxy and BH histories is therefore an emergent simulation result, not a definitional tautology.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the fidelity of the Horizon-AGN simulation to real merger physics and on the validity of the statistically optimized pair-selection thresholds.

free parameters (1)
  • MCC thresholds for projected distance and redshift difference = optimized values
    Thresholds were optimized within the simulation to identify physically connected pairs.
axioms (1)
  • domain assumption Horizon-AGN simulation accurately models galaxy and black hole merger processes
    All quantitative results depend on the simulation's fidelity to real astrophysical physics.

pith-pipeline@v0.9.0 · 5554 in / 1215 out tokens · 47566 ms · 2026-05-14T20:42:20.068156+00:00 · methodology

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Reference graph

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