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arxiv: 2606.12851 · v1 · pith:UFXSR75Mnew · submitted 2026-06-11 · 🌌 astro-ph.GA

Supermassive Black Hole Assembly from Heavy Seeds with Dynamical Friction in the BRAHMA Simulations: Implications for JWST, LISA, and the Local Universe

Aklant K. Bhowmick , Laura Blecha , Paul Torrey , Luke Zoltan Kelley , Rachel S. Somerville , Rainer Weinberger , Priyamvada Natarajan , Tiziana Di Matteo
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Lars Hernquist Mark Vogelsberger Alex M. Garcia
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Pith reviewed 2026-06-27 06:53 UTC · model grok-4.3

classification 🌌 astro-ph.GA
keywords supermassive black holesheavy seedsdynamical frictioncosmological simulationsblack hole mergersoccupation fractionJWSTLISA
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The pith

Lenient heavy black hole seed models in BRAHMA simulations produce merger rates above 100 per year and near-unity occupation fractions in galaxies down to 10 million solar masses, while strict models yield rates around 1 per year and fracti

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

The paper compares two lenient heavy-seed prescriptions, in which black hole seeds of 10,000 or 100,000 solar masses form in every halo containing sufficient dense and metal-poor gas, against a strict prescription that adds further direct-collapse constraints. These prescriptions are implemented inside the BRAHMA cosmological simulations together with a subgrid dynamical friction model that governs how seeds sink and merge. By redshift 5 the lenient cases produce overmassive black holes whose luminosities overlap with those inferred for JWST sources, while by the present day they also generate high merger rates and high occupation fractions even in low-mass galaxies. The differences imply that measurements of merger rates and local occupation fractions can distinguish the dominant seeding pathways.

Core claim

In the BRAHMA simulations, lenient seed models in which all halos with sufficient dense and metal-poor gas form 10,000 and 100,000 solar-mass seeds generate by z approximately 5 multiple systems with black-hole-to-stellar-mass ratios at or above 0.01 that reach luminosities of 10^43 to 10^45 erg per second, while at z equals 0 they produce merger rates of at least 100 per year and occupation fractions near unity even for galaxies with stellar masses below 10 million solar masses; the strict seed model, which forms 100,000 solar-mass seeds only under additional direct-collapse conditions, instead produces merger rates of only about 1 per year and occupation fractions below 10 percent for gala

What carries the argument

The subgrid dynamical friction model combined with lenient versus strict criteria for forming 10,000 and 100,000 solar-mass seeds inside halos that contain sufficient dense and metal-poor gas, run inside the BRAHMA cosmological simulations.

If this is right

  • Lenient production of 100,000 solar-mass seeds produces multiple overmassive systems with black-hole-to-stellar-mass ratios at or above 0.01 inside galaxies that host 100 million to 1 billion solar-mass black holes.
  • All three seed models produce black-hole-to-stellar-mass relations broadly consistent with the local universe for galaxies above 1 billion solar masses by redshift 5.
  • The lenient scenarios also generate systems near the upper envelope of the observed local scatter in the black-hole-to-stellar-mass relation.
  • Future gravitational-wave event rates and measurements of local black hole occupation fractions will constrain the dominant pathways for high-redshift black hole assembly.

Where Pith is reading between the lines

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

  • If observations favor the lenient models, then mergers contribute a larger fraction of black hole growth at high redshift than they do under strict seeding.
  • The overmassive black holes produced at redshift 5 in lenient models suggest that seeding alone, without requiring sustained super-Eddington accretion, can account for some JWST detections.
  • High occupation fractions in present-day dwarf galaxies would favor lenient seeding even if the strict model matches other observables.
  • The efficiency of the dynamical friction model in driving seed mergers sets the scale of the predicted rate differences between the two classes of models.

Load-bearing premise

The subgrid dynamical friction model and the specific criteria defining sufficient dense and metal-poor gas for lenient seeding versus additional direct-collapse constraints for strict seeding accurately represent unresolved high-redshift astrophysical processes.

What would settle it

A measurement of the present-day black hole occupation fraction in galaxies with stellar mass near 10 million solar masses that is either near 100 percent or below 10 percent would distinguish the lenient from the strict seed models.

Figures

Figures reproduced from arXiv: 2606.12851 by Aklant K. Bhowmick, Alex M. Garcia, Lars Hernquist, Laura Blecha, Luke Zoltan Kelley, Mark Vogelsberger, Paul Torrey, Priyamvada Natarajan, Rachel S. Somerville, Rainer Weinberger, Tiziana Di Matteo.

Figure 1
Figure 1. Figure 1: Visualizations of the boxes at the final snapshots, illustrating the implementation of the Lenient-Heavy and Strict-Heavy seed models. The larger panels correspond to SUITE-z5 at z = 5, and the inset panels correspond to SUITE-z0 at z = 0. The left halves of the 2D maps show the gas density field, which smoothly transitions to the gas metallicity field on the right halves. Since all simulations with the sa… view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the BH number density for our three different seed models. The leftmost panel shows the overall number density, whereas middle and right panels show the number density of ≳ 105 M⊙ and ≳ 106 M⊙ BHs respectively. In the rightmost panel, the black marker shows the range of observational constraints obtained by integrating the range of z = 0 BHMF measurements compiled by Porras-Valverde et al. (20… view at source ↗
Figure 3
Figure 3. Figure 3: Similar to the previous figure, but here we com￾pare the number density evolution produced by our subgrid￾DF based BRAHMA-18-D5 boxes vs. prior results using reposi￾tioning (Bhowmick et al. 2025a) for our Lenient-Heavy and Strict-Heavy seed models. Under subgrid-DF, there is a substantial delay in the assembly of ≳ 106 M⊙ BHs com￾pared to respositioning. possible in the BRAHMA simulations. However, these h… view at source ↗
Figure 4
Figure 4. Figure 4: For the DGB simulations, we show the fractional contribution to BH growth from seeding and mergers as opposed to gas accretion. For the different seed models, this is shown as a function of BH mass for populations at z = 0 (left) and z = 5 (right). In the early phase of BH growth, the majority (≳ 50%) of the BH mass is contributed by seeding and mergers, while gas accretion becomes dominant in the later ph… view at source ↗
Figure 5
Figure 5. Figure 5: BHMFs predicted by different seeding models at z = 5 (top row) and z = 0 (bottom row). Thick lines show the DGB predictions, while thin lines show the calibrated ESD predictions. The dashed lines indicate the repositioning-based predictions for the Lenient-Heavy seed model. The left column shows the full BH population, while the right column includes only active BHs with Lbol ≳ 1043 erg s−1 . Black data po… view at source ↗
Figure 7
Figure 7. Figure 7: Predictions for the M∗–MBH relation for different seeding models. We focus exclusively on central BHs, plotting the mass of the most massive BH in each halo against the total stellar mass. Each panel corresponds to a given seeding model; smaller circles show DGB boxes and larger circles show calibrated ESD boxes. The top and bottom rows show results at z = 5 and z = 0, respectively. On the top row, black p… view at source ↗
Figure 8
Figure 8. Figure 8: Bolometric luminosity versus BH mass for the overmassive z = 5 BHs in the Lenient-Heavy boxes. Blue and orange symbols correspond to BHs in the ESD and DGB boxes, respectively. The error bars indicate luminos￾ity variability, estimated as the median values of the max￾imum and minimum luminosities in 50 Myr time bins over z = 4.8–5.2. The dashed line marks the Eddington limit. Although mass assembly in thes… view at source ↗
Figure 9
Figure 9. Figure 9: Similar to the [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Delay times between BH mergers and their corresponding host galaxy mergers in the Lenient-Heavy, Strict-Heavy, and Lenient-LowMass seed models within the DGB boxes. From left to right, the panels show the delay time as a function of halo merger redshift, total BH mass, BH mass ratio, and merged host halo mass. Merger delays increase toward lower redshifts and in more massive halos. As a result, the lenien… view at source ↗
Figure 11
Figure 11. Figure 11: BH–BH merger rates predicted by our simulations for the three different seed models. The left panel shows the total merger rates, the middle panel includes only mergers between BHs with masses ≳ 105 M⊙, and the right panel shows mergers between BHs with masses ≳ 106 M⊙. Colors indicate the different seed models. For each model, thick lines correspond to the SUITE-z5 boxes, while thin lines correspond to t… view at source ↗
Figure 12
Figure 12. Figure 12: BH occupation fractions at z = 5 (top) and z = 0 (bottom) predicted by our DGB simulations. Solid lines show the predictions for the different seed models. Dotted lines show predictions from previous BRAHMA boxes that used BH repositioning (Bhowmick et al. 2024b, 2025a). Grey and pink regions show lower limits on the local occupation fractions inferred from observations by Miller et al. (2015) and Burke e… view at source ↗
Figure 13
Figure 13. Figure 13: Left Panel: For the DGB simulations, we plot the galaxy masses and redshifts at which descendant BHs with Mbh = MESD = 8 Mseed assemble. Each data point (filled circle) corresponds to an assembly event traced along galaxy merger trees. In the Lenient-LowMass seed model, this represents the assembly of ∼ 105 M⊙ descendants from ∼ 104 M⊙ seeds (note that this simulation is evolved only to z = 5). In the Len… view at source ↗
Figure 14
Figure 14. Figure 14: Comparison of the two-point correlation function predicted by the DGB (solid) and ESD (dashed) simulations for BHs with Mbh > MESD at z = 0 (left) and z = 5 (right). Because the clustering signal can depend on simulation volume—since larger volumes sample more diverse environments across all spatial scales—we performed additional ESD simulations in the same (18 Mpc) volume as the DGB runs, albeit at eight… view at source ↗
Figure 15
Figure 15. Figure 15: Calibration of the contribution from unresolved minor mergers in the stochastic seed model: The y-axis shows the mass growth due to unresolved minor mergers (∆Munresolved minor ) per resolved merger, in units of the ESD mass (MESD). This quantity is added to the remnant BH mass for every resolved merger occurring in the ESD simulations. The solid lines show the predicted contribution derived from the DGB … view at source ↗
Figure 16
Figure 16. Figure 16: Validation of the stochastic seed model: Comparison of the BH number density evolution (leftmost panel) and the BHMFs at z = 5 & 0 (remaining three panels) between the DGB (solid) and ESD (dashed) simulations. Importantly, both DGB and ESD simulations have the same volume and initial condition (IC) realization, although the ESD simulations have 8× lower mass resolution. The three seed models are shown wit… view at source ↗
read the original abstract

The JWST discoveries of supermassive black holes (BHs) at $z \gtrsim 5$ may provide key insights into their seeding origins. Using new $[18{-}72~\rm Mpc]^3$ BRAHMA cosmological simulations, we investigate how variations in heavy-seed prescriptions, coupled with a subgrid dynamical friction model, shape BH populations at $z \sim 5$ and $z \sim 0$. We consider two "lenient'' seed models, in which all halos containing sufficient dense & metal-poor gas form $\sim10^4$ and $\sim10^5~M_{\odot}$ seeds, and a "strict'' seed model, in which $\sim10^5 M_{\odot}$ seeds form only under additional constraints motivated by direct collapse black hole formation. By $z \sim 5$, all models produce $M_*-M_{\rm BH}$ relations broadly consistent with the observed local Universe for $M_*\gtrsim10^9~M_{\odot}$ galaxies, but only the lenient scenarios generate systems near the upper envelope of the observed local scatter. In galaxies hosting $M_{\rm BH} \sim 10^8$-$10^9~M_{\odot}$ BHs, lenient production of $\sim10^5~M_{\odot}$ seeds also produces multiple overmassive systems with $M_{\rm BH}/M_* \gtrsim 0.01$. Although their growth is dominated by seeding and mergers, these systems reach luminosities of $\sim10^{43}$-$10^{45}\mathrm{erg s^{-1}}$, comparable to those inferred for JWST-detected BHs. As a key observational signature, the lenient seed models yield merger rates of $\gtrsim100\mathrm{yr^{-1}}$ and near-unity local BH occupation fractions even in galaxies with $M_* \lesssim 10^7~M_{\odot}$. In contrast, the strict seed model produces merger rates of only $\sim1\mathrm{yr^{-1}}$ and local occupation fractions of $\lesssim10\%$ for galaxies with $M_* \lesssim 10^8~M_{\odot}$. Future gravitational-wave event rates and measurements of local BH occupation fractions will therefore provide strong constraints on the dominant pathways responsible for high-redshift BH assembly.

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

1 major / 0 minor

Summary. The manuscript presents results from the BRAHMA cosmological simulations investigating the assembly of supermassive black holes from heavy seeds under different seed formation prescriptions coupled with a subgrid dynamical friction model. It reports that lenient seed models, allowing seed formation in halos with sufficient dense and metal-poor gas for ~10^4 and ~10^5 M_sun seeds, lead to high BH merger rates of ≳100 yr^{-1} and near-unity local occupation fractions even in low-mass galaxies (M_* ≲ 10^7 M_⊙). In contrast, a strict seed model with additional direct-collapse constraints yields merger rates of ~1 yr^{-1} and occupation fractions ≲10% for M_* ≲ 10^8 M_⊙. The models produce M_*-M_BH relations consistent with local observations for massive galaxies, with lenient models also producing overmassive BHs.

Significance. If the results hold, they demonstrate that variations in seed prescriptions can lead to dramatically different predictions for observable quantities like merger rates and BH occupation fractions, providing potential constraints from JWST, LISA, and local universe observations. The work highlights the sensitivity of high-redshift BH assembly to seeding criteria.

major comments (1)
  1. [Abstract (subgrid dynamical friction model and seed criteria)] The central claims regarding the distinction in merger rates (≳100 vs ~1 yr^{-1}) and occupation fractions (near-unity vs ≲10%) between lenient and strict models rely on the subgrid dynamical friction implementation and the specific seed formation criteria. The provided text reports simulation outputs but provides no details on validation, convergence tests, or error quantification for the subgrid DF model or the 'dense & metal-poor gas' thresholds, making the quantitative predictions model-dependent without independent checks against resolved high-z calculations.

Simulated Author's Rebuttal

1 responses · 1 unresolved

We thank the referee for their constructive comments on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract (subgrid dynamical friction model and seed criteria)] The central claims regarding the distinction in merger rates (≳100 vs ~1 yr^{-1}) and occupation fractions (near-unity vs ≲10%) between lenient and strict models rely on the subgrid dynamical friction implementation and the specific seed formation criteria. The provided text reports simulation outputs but provides no details on validation, convergence tests, or error quantification for the subgrid DF model or the 'dense & metal-poor gas' thresholds, making the quantitative predictions model-dependent without independent checks against resolved high-z calculations.

    Authors: We agree that the manuscript would benefit from expanded details on the subgrid DF model and seed criteria. Section 2 describes the DF implementation (following the formulation validated in our prior BRAHMA papers) and the seed thresholds (motivated by dense, metal-poor gas conditions for direct-collapse scenarios). In the revision we will add an explicit paragraph summarizing the referenced validation and convergence tests from those works, plus a short discussion of threshold sensitivity. We will also note the model dependence of the quantitative rates more prominently. Direct new comparisons to fully resolved high-z calculations remain outside the scope of this large-volume study. revision: partial

standing simulated objections not resolved
  • Independent checks against resolved high-z calculations for the subgrid DF model and seed thresholds

Circularity Check

0 steps flagged

No significant circularity; simulation outputs are direct consequences of input prescriptions

full rationale

The paper reports merger rates and occupation fractions as direct outputs from BRAHMA cosmological simulations run with two classes of heavy-seed prescriptions (lenient vs strict) plus a subgrid dynamical friction model. These quantities are generated by evolving the specified initial conditions and subgrid rules; they do not reduce via the paper's equations to quantities fitted to JWST, LISA, or local-universe data, nor do they rely on self-definitional loops, load-bearing self-citations, or ansatzes smuggled from prior author work. The central claims remain independent simulation predictions under the stated model variations.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claims rest on parameterized subgrid prescriptions for seed formation and dynamical friction whose specific thresholds and implementations are chosen to represent different physical scenarios rather than derived from first principles.

free parameters (2)
  • Seed mass
    The paper varies discrete seed masses of approximately 10^4 and 10^5 solar masses as part of the heavy-seed model prescriptions.
  • Formation criteria thresholds
    Lenient versus strict conditions on gas density, metallicity, and additional direct-collapse constraints are chosen model parameters.
axioms (2)
  • standard math Standard Lambda-CDM cosmological framework
    The BRAHMA simulations are cosmological and assume the standard background cosmology.
  • domain assumption Subgrid models for unresolved gas physics, star formation, and black hole dynamics
    The simulations rely on parameterized prescriptions for physics below the resolution scale, including the dynamical friction implementation.

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