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arxiv: 2605.00092 · v1 · submitted 2026-04-30 · 🌌 astro-ph.GA

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The LISA Astrophysics MBHcatalogues Project: A comparison of predictions of simulated massive black hole binaries

David Izquierdo-Villalba , Melanie Habouzit , Matteo Bonetti , Silvia Bonoli , Alessia Gualandris , Marta Volonteri , Federico Angeloni , Enrico Barausse
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Aklant Bhowmick Laura Blecha Alexander Bonilla Rivera Elisa Bortolas Mesut Caliskan Pedro R. Capelo Ana Caramete Laurentiu Caramete Nianyi Chen Monica Colpi Thierry Contini Romeel Dav\'e Pratika Dayal Colin DeGraf Roger Deane Roberto Decarli R\'emi Delpech Tiziana Di Matteo Chi An Dong P\'aez Alister W. Graham Daryl Haggard Dimitrios Irodotou Peter H. Johansson Atte Keitaanranta Luke Zoltan Kelley Fazeel Mahmood Khan Vivienne Langen Kunyang Li Shihong Liao Alberto Mangiagli Sylvain Marsat Joe McCaffrey Yueying Ni Coral Pillay Florentina-Crenguta Pislan Alex Rawlings John Regan Basti\'an Reinoso Jaelyn Roth Milton Ruiz Olga Sergijenko Alberto Sesana Golam Shaifullah Jasbir Singh Daniele Spinoso Alexandre Toubiana Michael Tremmel Alessandro Trinca Rosa Valiante Yihao Zhou Yohan Dubois Luca Graziani Christopher C. Lovell Sebastien Peirani William J. Roper Joop Schaye Raffaella Schneider Maxime Trebitsch Aswin Vijayan Mark Vogelsberger Stephen Wilkins John Wise
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Pith reviewed 2026-05-09 20:51 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords massive black holesLISAmerger ratesgalaxy formation modelscosmological simulationsblack hole binariesgravitational waves
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The pith

LISA merger rates for massive black holes differ substantially across galaxy formation models based on seeding and simulation resolution.

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

By comparing roughly twenty semi-analytical models and cosmological simulations, the paper shows that the expected rate of massive black hole mergers detectable by LISA varies considerably depending on how black holes are seeded in galaxies and the resolution of the simulations. Dynamical delays between galaxy mergers and black hole coalescence are included to refine the predictions. This matters for interpreting LISA data because the observatory is designed to measure these mergers and thereby constrain the formation history of massive black holes. The spread in the results highlights the current uncertainties in theoretical predictions.

Core claim

The project compares various theoretical predictions of massive black hole merger rates from about 20 semi-analytical models and cosmological simulations, quantifies the spread among them, and evaluates the astrophysical uncertainties affecting LISA event rates. Delays from the dynamical hardening phase of black hole binaries are incorporated into the rate calculations. The expected LISA merger rates are presented, with emphasis on their dependence on assumptions such as the black hole seeding model and the resolution of the cosmological simulations.

What carries the argument

Ensemble of ~20 models of galaxy and black hole evolution with post-merger dynamical delays added to compute coalescence rates for LISA.

If this is right

  • Merger rates in the LISA band are sensitive to the choice of massive black hole seeding mechanism.
  • Higher-resolution simulations produce different merger rate predictions than lower-resolution ones.
  • Accounting for the time required for black hole pairs to harden and coalesce lowers the predicted rates.
  • The range of rates across models indicates the level of uncertainty in LISA forecasts from current astrophysics.

Where Pith is reading between the lines

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

  • The large spread suggests that LISA observations could help discriminate among seeding models if the rates can be measured accurately.
  • Future improvements in modeling dynamical friction and stellar interactions could reduce the uncertainties in these predictions.
  • Connecting these rate predictions to the observed population of massive black holes in local galaxies could provide additional tests.

Load-bearing premise

That the selected set of about twenty models adequately represents the range of possible outcomes from uncertainties in black hole formation and galaxy evolution.

What would settle it

A measured LISA merger rate for massive black holes that lies well outside the range covered by all the models in the comparison would indicate that the models do not fully capture the relevant astrophysics.

Figures

Figures reproduced from arXiv: 2605.00092 by Aklant Bhowmick, Alberto Mangiagli, Alberto Sesana, Alessandro Trinca, Alessia Gualandris, Alexander Bonilla Rivera, Alexandre Toubiana, Alex Rawlings, Alister W. Graham, Ana Caramete, Aswin Vijayan, Atte Keitaanranta, Basti\'an Reinoso, Chi An Dong P\'aez, Christopher C. Lovell, Colin DeGraf, Coral Pillay, Daniele Spinoso, Daryl Haggard, David Izquierdo-Villalba, Dimitrios Irodotou, Elisa Bortolas, Enrico Barausse, Fazeel Mahmood Khan, Federico Angeloni, Florentina-Crenguta Pislan, Golam Shaifullah, Jaelyn Roth, Jasbir Singh, Joe McCaffrey, John Regan, John Wise, Joop Schaye, Kunyang Li, Laura Blecha, Laurentiu Caramete, Luca Graziani, Luke Zoltan Kelley, Mark Vogelsberger, Marta Volonteri, Matteo Bonetti, Maxime Trebitsch, Melanie Habouzit, Mesut Caliskan, Michael Tremmel, Milton Ruiz, Monica Colpi, Nianyi Chen, Olga Sergijenko, Pedro R. Capelo, Peter H. Johansson, Pratika Dayal, Raffaella Schneider, R\'emi Delpech, Roberto Decarli, Roger Deane, Romeel Dav\'e, Rosa Valiante, Sebastien Peirani, Shihong Liao, Silvia Bonoli, Stephen Wilkins, Sylvain Marsat, Thierry Contini, Tiziana Di Matteo, Vivienne Langen, William J. Roper, Yihao Zhou, Yohan Dubois, Yueying Ni.

Figure 1
Figure 1. Figure 1: — Comoving volumes and seed mass ranges covered by the different simulations and semi-analytical models analysed in this work. For models with a distribution of seed masses, the line joins the minimum and maximum seed mass, and the symbol represents logarithmic midpoint. High-resolution zoom-in regions, with small simulated volumes, are localised at the extreme left of the figure (e.g., Renaissance , Ketju… view at source ↗
Figure 2
Figure 2. Figure 2: — Distribution of MBHB separations across different models (in proper kpc), stacking all redshifts. To guide the reader, we have added some indicative distances corresponding to phases where the MBHs are expected to be in the dynamical friction stage, hardening phase or the gravitational wave-driven stage. The distances presented for each model are defined differently: (i) the galaxy half-mass radius (L-Ga… view at source ↗
Figure 3
Figure 3. Figure 3: — MBH mass function obtained from the semi-analytical models and cosmological simulations. Full (dashed) lines show the predictions for cosmological simulations (semi-analytical mod￾els), and shaded areas indicate the 1σ region accounting for Pois￾son errors. For each model, we show only bins with a mini￾mum of 5 counts. All MBHs produced by the different models are included, although in some simulations (… view at source ↗
Figure 4
Figure 4. Figure 4: — MBH-galaxy stellar mass relations at different red￾shifts. For the models, we show the MBH mass median in bins of stellar mass. Only bins containing at least five galaxies are shown for M⋆ ⩾ 1011 M⊙. In the Illustris , MassiveBlack-II , Simba and Eagle simulations, the median MBH mass in these mas￾sive galaxies can be dominated by un-evolved MBHs. In such cases, we only consider the most massive MBH per … view at source ↗
Figure 5
Figure 5. Figure 5: — AGN luminosity function from the semi-analytical models and cosmological simulations. All MBHs produced by the different models are included, although in some simulations (TNG, Illustris , MassiveBlack-II , Simba , Eagle ) we retain only the most massive MBHs per galaxy, a choice that primarily affects the most massive galaxies, which can host a population of non-evolved wandering MBHs. This selection ha… view at source ↗
Figure 6
Figure 6. Figure 6: — Merger rate of MBHBs as a function of redshift predicted by the different models, for three different assumptions about applied delays. No cut in the mass of the MBHBs is used, nor in the mass ratio. Redshift bins have a fixed width of ∼ 0.4. Left-hand panel: Instantaneous mergers with no post-processing delays. Models that incorporate delays (i.e., BACH , L-Galaxies , NewHorizon , Obelisk , and Horizon-… view at source ↗
Figure 7
Figure 7. Figure 7: — Merger rate of MBHBs as a function of redshift predicted by the different models, for five different MBHB mass bins (MBin = MBH,1 +MBH,2) and three assumptions about delays: no post-processing (left-hand panels), with models that incorporate delays (i.e., BACH , L-Galaxies , NewHorizon , Obelisk , Horizon-AGN ) having these delays disabled, and delays computed based on dynamical friction, using either th… view at source ↗
Figure 8
Figure 8. Figure 8: — Mass ratio q = MBH, 2/MBH, 1 (secondary / primary) of the binaries for the MBH mergers of the models without any delay. First row: mass ratios are binned by binary mass (i.e., MBH, 1 +MBH, 2). In the left-hand panel, the large differences in the mass ratios are driven by the range of seed masses used in the models. For example, the small ratios found for L-Galaxies are a consequence of the inclusion of l… view at source ↗
Figure 9
Figure 9. Figure 9: — Similar to [PITH_FULL_IMAGE:figures/full_fig_p028_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: — Similar to [PITH_FULL_IMAGE:figures/full_fig_p029_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: — Median mass ratios of the merging MBHBs, defined as q = MBH,2/MBH,1 (secondary/primary), as a function of the stellar mass of the remnant host galaxies. Here we consider the numerical mergers of the models, and do not apply our post-processing DF delays. We show different redshifts (columns) and cuts in secondary MBH mass (rows). the satellite’s stellar mass. When this phase ends, the two MBHs form a gr… view at source ↗
Figure 12
Figure 12. Figure 12: — Mass comparison between primary (green) and secondary (pink) MBHs of merging systems and the full MBH population (black) produced by the models. Solid lines indicate the median of the populations. The redshift that is chosen for the comparison is z = 2 ± 0.2 and, if there are not enough mergers at that time, we select the closest redshift available in the catalogs. The selected redshift is indicated in … view at source ↗
Figure 13
Figure 13. Figure 13: — Merger rate of MBHBs as a function of redshift, for five different MBHB mass bins (MBin = MBH,1 + MBH,2). Redshift bins have a fixed width of ∼ 0.4. The figure illustrates the differences between the DF delays computed in this paper and the delays computed in previous studies for BACH , L-Galaxies , Ketju , NewHorizon , L-Galaxies , Obelisk , and Horizon-AGN . • for every Nbin binary, we generate its pr… view at source ↗
Figure 14
Figure 14. Figure 14: — SNR distribution for the models explored in this work, assuming four years of LISA observation. To increase the readability, we divided the results in three different panels. In the left-hand panel we grouped the SNR distribution from semi-analytical models, the middle panel shows the large-scale cosmological simulations of ⩾ 1003 cMpc3 , and the right-hand panel shows the results for the highest￾resolu… view at source ↗
Figure 15
Figure 15. Figure 15: — Dynamical friction delays obtained from Eq. (5) assuming the galaxy effective radius as the initial binary separation. The results are shown for different scaling relations for Reff and σ in different panels. For Reff , we considered the relation for late-type (Shen et al. 2003, left-hand panels) and early-type (Lange et al. 2015, right-hand panels) galaxies, including the redshift dependence from van d… view at source ↗
read the original abstract

In the hierarchical paradigm of galaxy formation, central massive black holes (MBHs) are expected to coalesce after the merger of their host galaxies. One of the main goals of the Laser Interferometer Space Antenna (LISA) is to constrain the origin and growth of MBHs through their merger rates and mass distribution. Predicting MBH merger rates requires not only tracing their statistical population from large to small physical scales (kpc to sub-pc) but also modelling their formation, accretion, dynamics, mergers, and their galactic physical processes across cosmic time. This project is the result of a large collaborative effort undertaken by the LISA Astrophysics Working Group, bringing together its collective expertise on MBH formation, evolution, and modelling, to build a comprehensive understanding of MBH merger rates across cosmic time. The project compares various theoretical predictions of MBH merger rates, quantifies the spread, and evaluates the global astrophysical uncertainties of the LISA event rates. To build a unique and complete view, our work is based on about 20 semi-analytical models and cosmological simulations from the literature, all employing distinct approaches to modelling MBH and galaxy physics. To compute the merger rates, we also incorporate delays arising from the dynamical phase of MBH hardening to coalescence. We present the expected LISA merger rates given current galaxy formation models and discuss how the merger rate depends on model assumptions, such as the seeding model and the resolution of cosmological simulations.

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 / 1 minor

Summary. The paper compares MBH binary merger rate predictions for LISA from ~20 semi-analytical models and cosmological simulations drawn from the literature. It incorporates dynamical delays from the hardening phase and quantifies the spread in rates arising from differences in seeding, growth, and resolution assumptions.

Significance. If the models can be shown to share a consistent treatment of dynamical delays, the work would provide a useful community benchmark for the range of LISA event rates under current galaxy-formation models, directly supporting mission science planning and interpretation of future detections.

major comments (2)
  1. [Abstract and methods description of delays] The abstract states that dynamical delays are incorporated across the models, yet no table, figure, or dedicated subsection quantifies the adopted hardening timescales, prescriptions (analytic vs. N-body), or reference formulas used in each of the ~20 models. Without this, the reported spread cannot be cleanly attributed to astrophysical uncertainties rather than methodological differences in the final-parsec phase.
  2. [Discussion of model assumptions and rate dependence] The central claim that the collection of models 'sufficiently spans the full range of astrophysical uncertainties' rests on the assumption of uniform delay treatment; a direct test (e.g., recomputing a subset of rates with a common delay formula) is needed to confirm that the variance is not inflated by inconsistent dynamical modeling.
minor comments (1)
  1. [Introduction] Clarify in the introduction whether any models omit delays entirely or rescale them, and provide a reference list or table mapping each model to its source publication and key physics choices.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and constructive suggestions. We address the major comments point by point below and have revised the manuscript accordingly to improve the description of dynamical delays and clarify the scope of our uncertainty quantification.

read point-by-point responses

  1. Referee: [Abstract and methods description of delays] The abstract states that dynamical delays are incorporated across the models, yet no table, figure, or dedicated subsection quantifies the adopted hardening timescales, prescriptions (analytic vs. N-body), or reference formulas used in each of the ~20 models. Without this, the reported spread cannot be cleanly attributed to astrophysical uncertainties rather than methodological differences in the final-parsec phase.

    Authors: We agree with the referee that a more detailed description of the dynamical delay prescriptions is necessary to properly interpret the spread in merger rates. In the revised manuscript, we have added a dedicated subsection in Section 2 (Methods) that describes how delays are incorporated, and we include a new Table 1 that summarizes for each model the type of prescription used (analytic, N-body calibrated, etc.), the specific formula or reference, and the typical range of hardening timescales applied. This addition will allow the community to better distinguish between astrophysical and methodological contributions to the rate uncertainties. revision: yes

  2. Referee: [Discussion of model assumptions and rate dependence] The central claim that the collection of models 'sufficiently spans the full range of astrophysical uncertainties' rests on the assumption of uniform delay treatment; a direct test (e.g., recomputing a subset of rates with a common delay formula) is needed to confirm that the variance is not inflated by inconsistent dynamical modeling.

    Authors: We appreciate this point and acknowledge that the models employ varying treatments of the final-parsec problem. Our study compiles the merger rate predictions as they are presented in the respective literature papers, each incorporating their own dynamical modeling. Performing a direct test by recomputing rates with a uniform delay prescription would require significant additional computational effort and access to the internal codes of all participating models, which is not practical for this comparative project. Instead, we have revised the discussion section to explicitly note that the reported spread encompasses both variations in seeding, growth, and resolution as well as differences in dynamical delay implementations. We argue that the primary astrophysical uncertainties are still captured by the diversity in the models' galaxy formation physics, but we now qualify our claim to reflect this caveat. revision: partial

Circularity Check

0 steps flagged

No circularity: aggregation of independent external models

full rationale

The paper compiles LISA merger rate predictions from ~20 distinct semi-analytical models and cosmological simulations drawn from the literature, each employing separate treatments of MBH seeding, growth, and dynamics. No new equations, fitted parameters, or derivations are introduced that reduce to the paper's own inputs by construction; dynamical delays are incorporated from the source models without renormalization or self-referential adjustment. The central results therefore rest on external benchmarks rather than self-citation chains or definitional loops, satisfying the criteria for a self-contained comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard assumptions in hierarchical galaxy formation and the representativeness of the chosen models; no new free parameters or invented entities are introduced.

axioms (2)
  • domain assumption In the hierarchical paradigm of galaxy formation, central massive black holes coalesce after the merger of their host galaxies.
    Invoked in the opening sentence as the foundational expectation for MBH mergers.
  • domain assumption Dynamical delays arising from the MBH hardening phase to coalescence can be incorporated into merger-rate calculations across models.
    Explicitly stated as part of the method to compute rates from the models.

pith-pipeline@v0.9.0 · 5900 in / 1348 out tokens · 39457 ms · 2026-05-09T20:51:21.725475+00:00 · methodology

discussion (0)

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