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Signatures of BH seeding on the $\mathrm{M_{\displaystyle \bullet}}-\sigma$ relation: Predictions from the BRAHMA simulations

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Black hole seeding reshapes the black-hole–sigma relation at high redshift, the paper claims.

desk verdict First cosmological hydro comparison of BH seeding on M-sigma, with a careful decomposition; the JWST 'match' is a consistency check of a JWST-tuned Jcrit, not an independent prediction. read the letter →

arxiv 2506.17476 v1 pith:FRQXRV5B submitted 2025-06-20 astro-ph.GA

Jonathan Kho , Aklant K. Bhowmick , Paul Torrey , Alex M. Garcia , Niusha Ahvazi , Laura Blecha , Mark Vogelsberger This is my paper · ORCID
classification astro-ph.GA
keywords supermassiveblackholeseedingM_bullet-sigmarelationBRAHMAsimulationsdirectcollapseholesJWSThigh-redshiftAGNhole-galaxycoevolutionmerger-drivengrowthvelocitydispersionscaling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper asks whether the way supermassive black hole seeds form leaves a measurable imprint on the tight relation between black hole mass and host galaxy stellar velocity dispersion, the M_bullet–$\sigma$ relation. Using four cosmological simulations that plant heavy ~$10^{5}$ solar-mass seeds under increasingly restrictive conditions, it finds that abundant-seed models produce high black hole masses at fixed $\sigma$ at z > 2, while restrictive models start low and catch up mostly at z < 2 in massive galaxies. The most lenient model keeps the M_bullet–$\sigma$ relation essentially unchanged from z = 5 to z = 0, which naturally explains JWST's early black holes that look overmassive on the M_bullet–M_star plane yet sit on the local M_bullet–$\sigma$ relation. If correct, the high-redshift M_bullet–$\sigma$ relation becomes a direct probe of black hole seeding physics.

What carries the argument

The load-bearing machinery is the BRAHMA simulation suite, which plants 1.5e5 M_sun seeds by cumulatively stacking four gas-based criteria: dense metal-poor gas, a Lyman-Werner flux above Jcrit = 10 J21, low gas spin below the Toomre instability threshold, and a rich merger environment. The paper's explanatory engine is a derivative identity that splits the time evolution of median black hole mass at fixed sigma into the slope of the M_bullet–M_star relation times the evolution of stellar mass at fixed sigma, plus the explicit time dependence of black hole mass at fixed M_star and sigma. This decomposition, together with the merger-versus-accretion growth regimes, converts seed abundance differences into concrete predictions for the normalization, slope, and scatter of the M_bullet–sigma relation across redshift.

What would settle it

A resolved radiation-hydrodynamic simulation of atomically cooled halos that finds Jcrit near 1000 J21 even when gas is dynamically heated during mergers would remove the foundation of the BI model, since BI's seed abundance rests on Jcrit = 10 J21; alternatively, direct stellar velocity dispersion measurements showing that z ~ 5 JWST AGN lie systematically above the local M_bullet–sigma relation would falsify the predicted non-evolution of the lenient model.

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Extended reading notes

Core claim

Across the four BRAHMA seed models, ranging from the most lenient (BI) to the most restrictive (BIV), the median M_bullet–$\sigma$ relation separates cleanly at z > 2 over the full velocity dispersion range probed, and at z = 0 it still separates for low dispersions of roughly 50–80 km/s. The most lenient model shows negligible redshift evolution of the relation, while the restrictive models show a bottom-up evolution: at fixed $\sigma$ near 100 km/s their black hole masses are well below the local relation at z > 2 and rise steeply between z = 2 and z = 0. The paper traces this behavior to the balance between merger-dominated black hole growth in low-mass galaxies below about $10^{9}$ M_sun and accretion-dominated growth in higher-mass galaxies, and it shows that the scatter at fixed $\sigma$ grows for restrictive models because many seeds never grow far beyond their initial mass.

Load-bearing premise

The load-bearing premise is that heavy ~$10^{5}$ M_sun seeds form abundantly when gas is dynamically heated during major mergers, so the critical Lyman-Werner flux is only 10 J21 rather than the canonical ~1000 J21; if the true threshold is much higher, the lenient seed model overproduces seeds and the claimed match to JWST collapses.

Editorial extensions

If this is right

  • At z > 2, the normalization of the M_bullet–sigma relation is a discriminant of black hole seed abundance across the full sigma range probed, so a single observed median relation can distinguish among seed models.
  • The most lenient seed model predicts negligible M_bullet–sigma evolution from z = 5 to z = 0, meaning high-redshift AGN should appear normal on this plane while still overmassive on the M_bullet–M_star plane.
  • Restrictive seed models predict that most of the rise in black hole mass at fixed sigma near 100 km/s occurs at z < 2 in galaxies above roughly 10^9 M_sun, implying rapid late-time accretion-driven assembly.
  • The scatter in M_bullet–sigma at fixed sigma near 100 km/s increases with seed restrictiveness, so precision scatter measurements at z = 0 can also constrain seeding.
  • Seed models have negligible effect on the M_star–sigma relation, so any seed-model variation in M_bullet–sigma must arise from the black hole side of the scaling relations rather than from galaxy structure changes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the true critical Lyman-Werner flux is near 1000 J21 rather than the adopted 10 J21, the BI model likely overproduces seeds, and its JWST agreement should be treated as an upper bound on black hole mass assembly rather than evidence for that specific seed channel.
  • Editorial inference: the paper's low-sigma regime at z = 0 (50–80 km/s) predicts a population of barely-grown seed remnants in low-dispersion galaxies; counting black holes in such dwarfs could directly measure the seed abundance ladder.
  • Editorial inference: the same derivative decomposition could be applied to other scaling relations, such as M_bullet versus halo mass or M_bullet versus galaxy size, to isolate seeding signatures from feedback effects.
  • Editorial inference: JWST sigma values are currently inferred from gas with a correction factor near 1.3; direct stellar velocity dispersion measurements at z ~ 5 would cleanly test the predicted non-evolution of the lenient model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper uses four cosmological hydrodynamical simulations from the BRAHMA suite (comoving [18 Mpc]^3 boxes, TNG-based galaxy formation, heavy ~1.5e5 Msun seeds) with progressively more restrictive seeding criteria (BI, BII, BIII, BIV) to study the M_bullet-sigma relation from z=5 to z=0. It reports that the normalization of M_bullet-sigma differs across seed models at z>2 for all probed sigma, and at z=0 for sigma ~50-80 km/s; the most lenient model (BI) shows negligible redshift evolution, while more restrictive models evolve upward from z~2 to 0, mostly at high sigma ~100 km/s. The paper attributes these trends to merger-dominated BH growth in low-mass galaxies versus accretion-dominated growth in high-mass galaxies, and uses a time-derivative decomposition (Eq. 2) validated against the data (Fig. 9). It also compares to JWST broad-line AGN and argues that the BI model naturally explains the JWST overmassive population on the M_bullet-M* plane while remaining consistent with the local M_bullet-sigma relation.

Significance. If the claims hold, this would be one of the first cosmological simulation-based predictions that the z>2 M_bullet-sigma relation discriminates between BH seed models, and it would bound heavy-seed merger timescales. The paper's strengths include public analysis code, an explicit numerical check of the decomposition against the simulation data (Fig. 9), and bootstrapped confidence intervals in Figures 5-7. However, the central JWST comparison is not an independent test: the lenient seeding model was tuned to match JWST BH masses via the adopted low critical LW flux (Section 2.2), so the 'natural explanation' wording overstates the evidential weight of the JWST comparison. The small box volume and optimistic merger treatment also limit the robustness of the quantitative predictions.

major comments (4)
  1. [2.2, 4.1] The paper adopts Jcrit=10 J21 (Section 2.2) explicitly 'to produce overmassive BHs consistent with JWST', citing Bhowmick et al. (2024c), and Section 4.1 then states that the BI model 'offers a natural explanation' for the same JWST population, with the Conclusions repeating that current observations 'appear to require the abundant formation of heavy seeds'. This is a circular validation: the JWST M_bullet-M* agreement was built into the seed abundance. The manuscript should either (a) present the JWST comparison as a consistency check with the calibration caveat stated prominently, or (b) run an additional simulation with Jcrit at a canonical value (~1000 J21, Shang et al. 2010; Sugimura et al. 2014) to show what M_bullet-sigma would look like if the seed density were two orders of magnitude lower, as the paper itself notes in Section 4.1. Without this, the headline claim that M_bullet-sigma discriminates between seed models is not a falsifiable prediction for the JWST-era comparison.
  2. [Appendix B] The slope-fit mass cut in Appendix B ('we perform a simple linear regression on the M_bullet-M* data at each redshift for systems with BH masses greater than 5 times the seed mass') is applied post hoc to remove the 'artificial flattening' that affects the restrictive models. This cut directly determines Component 2 of Eq. (2), and Figure 7b shows that the inversion of the slope ordering across seed models is the key driver of the M_bullet-sigma evolution. Because the cut removes the very population of ungrown seeds that the paper identifies as responsible for the increased scatter in restrictive models (Section 3.3), the decomposition may be systematically biased. Please show the sensitivity of Figures 7b and 9 to the 5x mass cut, either by repeating the analysis with a 3x or no cut, or by explicitly modeling the flattening instead of removing it.
  3. [2.1, 4.2] The merger treatment is explicitly optimistic: BHs are repositioned to the nearest potential minimum and 'every halo merger wherein both halos have been seeded will also result in a prompt BH merger' (Section 2.1). The paper's central mechanism—merger-dominated BH growth in low-mass galaxies—therefore rests on the assumption of zero merger delay. Section 4.2 mentions that Bhowmick et al. (2024c) found delays <750 Myr are needed to reproduce the JWST observations, but the paper does not show how the M_bullet-sigma predictions in Figures 3-5 respond to such delays. If realistic dynamical-friction delays are longer, the separation between BI and BIV could shrink or disappear at the low-sigma end, undermining the z=0 low-sigma discriminant. Please provide a quantitative sensitivity test or clearly state that all predictions are conditional on the prompt-merger assumption.
  4. [3.1, Figs. 6 and 9] The small [18 Mpc]^3 volume leaves few seeded subhalos at the high-sigma end for the restrictive models at z>2 and, for BIV at sigma=10^1.5 km/s, the top right panel of Fig. 9 has no data while the Fig. 6 error bars grow large. The abstract's claim of 'different normalizations at higher redshifts across all sigma' is therefore based on very sparse bins for BIII and BIV. Please state the number of subhalos per sigma bin and redshift for each model (for instance, in a small table or by annotating Figures 2/3), so the reader can assess how many objects support each median and whether the differences are statistically robust. This would also clarify whether the empty bins are a volume effect or a genuine prediction.
minor comments (5)
  1. [Section 1] The word 'nunmber' in the Introduction should be 'number'.
  2. [Figure 5 caption] The caption states 'very minimal redshift evolution for all seed models at sigma=10^1.5 km/s', but the panel behavior and the surrounding text indicate that the low-evolution bin is sigma=10^1.75 km/s; please correct the caption.
  3. [Equation (2)] The notation \bar{M}_\bullet is introduced in Eq. (2) without a definition; please state explicitly that it denotes the median logarithmic BH mass at fixed sigma.
  4. [Section 4.1] The phrase 'the extrapolated KH13 relation' is not defined; please specify how the extrapolation is performed and over what range of sigma it is intended to be valid.
  5. [Section 2.3] The kinematic-decomposition threshold of 1000 stars is applied only to TNG and not to BRAHMA; a short justification or a sensitivity test to this threshold would help the reader interpret the low-sigma end of the relations.

Circularity Check

1 steps flagged · score 4.0 of 10

The M•−σ predictions are genuine simulation outputs, but the JWST 'agreement' of the BI model partly re-imports the JWST-tuned Jcrit=10 calibration.

  1. fitted input called prediction [Section 2.2 (seeding prescriptions) and Section 4.1 (JWST comparison)]
    "But as shown in Bhowmick et al. (2024c), to produce overmassive BHs consistent with JWST, we need more abundant heavy seed formation. Therefore, we used a low value of J21 that has been shown to be feasible if gas is dynamically heated during major mergers (Regan et al. 2020b,a; Wise et al. 2019). ... This observation aligns strikingly well with our most lenient BI seed model, which produces similarly overmassive z∼5 BHs consistent with JWST data on the M•−M∗ relation, while simultaneously exhibiting negligible evolution in the M•−σ relation."

    The BI seeding model is not an independent input: its defining feature, the low critical Lyman-Werner flux Jcrit=10 J21, was explicitly adopted because prior work by the same group found that abundant heavy seed formation is needed to reproduce the JWST overmassive population on the M•−M∗ plane. The paper later presents the BI model's agreement with that same JWST population as a 'striking' alignment and a 'natural explanation.' The M•−M∗ agreement is therefore a restatement of the calibration target, not an independent prediction. The M•−σ consistency and the seed-model differences in M•−σ are separate emergent outputs because σ was not used to set Jcrit, so the circularity is partial rather than total.

full rationale

The core M•−σ analysis is self-contained: the four BRAHMA boxes are run with fixed seeding rules, and no M•−σ data enter the calibration. The claimed differences in normalization, redshift evolution, and scatter are emergent simulation outputs, and the component decomposition of Eq. 2 is an internal consistency check. The circular element is confined to the JWST-consistency narrative: Section 2.2 explicitly tunes Jcrit=10 'to produce overmassive BHs consistent with JWST,' and Section 4.1 then reads the BI model's agreement with that same JWST overmassive population as a validation. That portion of the argument is a calibrated input being presented as confirmation. The M•−σ consistency of BI with JWST is a genuinely independent emergent result because σ was not part of the calibration, and the seed-model differentiation of M•−σ is likewise not fitted. The self-citations to Bhowmick et al. (2024c, 2025) are used to interpret merger- versus accretion-driven growth regimes, but the paper re-derives the decomposition in Figs. 7 and 9, so those citations are not load-bearing in a circular sense. Overall score 4 reflects one fitted input called prediction in the JWST M•−M∗ portion, while the central M•−σ predictions retain independent content.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

All free parameters and axioms are inputs to the simulation, not derived from the M_bullet-sigma data. The paper's predictions are conditional on these inputs, the most fragile being the low-Jcrit seed formation channel and the optimistic BH merger prescription. No new physical entities are introduced.

free parameters (4)
  • Critical Lyman-Werner flux (Jcrit) = 10 J21
    Chosen to make heavy seeds abundant enough to reproduce JWST overmassive BHs; about 100 times below the canonical 1000 J21. Sets the seed abundance ladder and therefore the M_bullet-sigma normalization differences (Section 2.2).
  • Seed mass (Mseed) = 1.5e5 Msun
    Initial mass of every BH seed. Determines the low-mass floor of the M_bullet-sigma relation and the population of 'ungrown' seeds responsible for scatter in restrictive models (Section 2.2, Section 3.3).
  • Slope-fit mass cut = M_bullet > 5 x Mseed
    Applied when measuring the M_bullet-M* slope used as Component 2 in Eq. 2. Removes the artificial flattening from the fixed seed mass; shapes the inferred steepening for restrictive models (Appendix B).
  • Bulge decomposition threshold = kappa < 0.5
    Classifies stars as bulge or disk. Applied to all subhalos without a minimum star count, affecting the computed sigma in low-mass systems where seed-model differences persist (Section 2.3).
assumptions (5)
  • domain assumption The IllustrisTNG subgrid galaxy formation model, including Bondi-Hoyle Eddington-limited accretion and kinetic/thermal AGN feedback, is adopted without modification outside of BH seeding.
    Section 2.1 states BRAHMA inherits TNG physics. The BH growth channels (mergers vs accretion) that drive the M_bullet-sigma evolution depend on these choices.
  • domain assumption BHs merge promptly when their host halos merge, with no dynamical friction delay.
    Section 2.1: the repositioning scheme means every seeded halo merger yields a BH merger, 'a highly optimistic merger scenario'. The merger-dominated growth in low-mass galaxies, central to the seed-model differences, depends on this.
  • ad hoc to paper Direct-collapse seeds can form under Jcrit = 10 J21 when gas is dynamically heated during major mergers.
    Section 2.2 adopts this low threshold citing Regan et al. 2020a,b and Wise et al. 2019; it is not derived in the simulation and is two orders of magnitude below canonical small-scale chemistry values.
  • domain assumption The kinematic decomposition (kappa < 0.5) identifies the bulge and yields the relevant velocity dispersion even for subhalos with very few star particles.
    Section 2.3 applies it to all subhalos and acknowledges it is imperfect; the low-sigma bins (50-80 km/s) where seed models differ at z=0 rely on this.
  • domain assumption Observed high-z velocity dispersions inferred from gas with a 1.3 correction factor are comparable to the simulated stellar sigma.
    Section 4.1 uses this to place JWST AGN on the simulation M_bullet-sigma plane.

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Cite this review

Pith. "Pith review of Signatures of BH seeding on the $\mathrm{M_{\displaystyle \bullet}}-\sigma$ relation: Predictions from the BRAHMA simulations." pith.science (2026). https://pith.science/paper/FRQXRV5B

@misc{pith2026250617476,
  author       = {Pith},
  title        = {Pith review of: Signatures of BH seeding on the $\mathrmM_\displaystyle \bullet-\sigma$ relation: Predictions from the BRAHMA simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FRQXRV5B}},
  note         = {Machine review of arXiv:2506.17476}
}
abstract

The James Webb Space Telescope (JWST) has identified a large population of supermassive ($10^6$-$10^8~\mathrm{M}_\odot$) black holes (BHs) in the early universe ($z \sim 4$-$7$). Current measurements suggest that many of these BHs exhibit higher BH-to-stellar mass ratios than local populations, opening a new window into the earliest stages of BH-galaxy coevolution and offering the potential to place tight constraints on BH seeding and growth in the early universe. In this work, we use the BRAHMA simulations to investigate the impact of BH seeding on the $\mathrm{M_{\bullet}}-\sigma$ relation. These simulations adopt heavy $\sim10^5~\mathrm{M}_{\odot}$ seeds and systematically varied BH seeding models, resulting in distinct predictions for seed abundances. We find that different seed models lead to different normalizations of the $\mathrm{M_{\bullet}}-\sigma$ relation at higher redshifts ($z > 2$) across all $\sigma$, and at low redshift for systems with low $\sigma$ ($50~\mathrm{km\ s^{-1}} \lesssim \sigma \lesssim 80~\mathrm{km\ s^{-1}}$). The most lenient seed model also shows negligible evolution in the $\mathrm{M_{\bullet}}-\sigma$ relation across redshift, while more restrictive models have substantially lower normalization on the $\mathrm{M_{\bullet}}-\sigma$ relation for high $\sigma$ ($\sim 100~\mathrm{km\ s^{-1}}$) at high redshifts, and evolve upward toward the local relation. We demonstrate that the $\mathrm{M_{\bullet}}-\sigma$ evolution is a direct consequence of merger-dominated BH growth in low mass galaxies ($\lesssim 10^9~M_{\odot}$) and accretion dominated BH growth in high mass ($\gtrsim10^9~M_{\odot}$) galaxies. Furthermore, the scatter in the $\mathrm{M_{\bullet}}-\sigma$ relation is larger for the more restrictive models due to the inability of many BHs to grow significantly beyond their seed mass.

Figures

Figures reproduced from arXiv: 2506.17476 by the authors.

Figure 1
Figure 1. BH number density in comoving Mpc−3 for each of the four BRAHMA simulations as a function of redshift. With each incrementally more restrictive seed model, the number density of BHs decreases at all redshifts, and halos start to be seeded at later times. The onset of seeding and number density of BHs in TNG is greatly reduced due to its extremely restrictive halo mass requirement. Since the more restrictive seed mod… view at source ↗
Figure 2
Figure 2. Histograms of the full scatter of BHs for the most lenient and most restrictive seed models on the M• − σ relation. Plotted in blue and red is the median trend of the data, with error bars representing the interquartile range in BH mass. The dotted line shows the observed M• −σ by KH13. While the relation retains a tight correlation for the most lenient model across redshift, the scatter drastically increases with d… view at source ↗
Figure 3
Figure 3. Comparison of the BRAHMA and TNG simulations’ M• − σ relations at z = 5, 0. The local relation found by KH13 is plotted in both panels for reference, and high-z AGN candidates found by Maiolino et al. (2024b) and Juodˇzbalis et al. (2025) are shown in purple and blue in the z = 5 panel. With the exception of our most lenient seed model, the simulations all begin under-massive to the local relation at high-z and conv… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The M• − σ , M• − M∗ , and M∗ − σ relations for the four BRAHMA boxes and TNG. Each plot shows the relation for redshifts z = 5, 3, 1, 0 to provide a sense of their redshift evolution. The M• − σ and M• − M∗ columns show the local relations as reported by KH13, and the…
Figure 5
Figure 5. Figure 5: Redshift evolution of the median BH mass for the four BRAHMA simulations at fixed σ values. All lines have been normalized to the median BH mass at z = 5 to emphasize the different evolutions. Errorbars represent 95% confidence intervals about the median mass calculate…
Figure 6
Figure 6. Figure 6: Redshift evolution in the scatter (shown using the interquartile range (IQR)) of the M• − σ relation for subhalos of fixed σ. Errorbars again represent 95% confidence intervals calculated via boostrapping. With increasingly more restrictive seed models, the scatter and…
Figure 7
Figure 7. Figure 7: The evolution of the different components that determine the redshift evolution of the M• −σ relation, as identified in Equation 2. Errorbars in each panel represent 95% confidence intervals about the derivative being shown, obtained via bootstrapping of the data [PIT…
Figure 8
Figure 8. Figure 8: Redshift evolution of the half-mass radius of sub￾halos in the BI (most lenient model) for fixed stellar masses. The redshift evolution seen in the other three BRAHMA boxes is identical to that seen here, and so they are omitted to avoid redundancy. There is a strong i…
Figure 9
Figure 9. Figure 9: Approximated trends of the LHS (blue) and RHS (red) of Eqn. 2 as a function of redshift for σ = 101.5 , 101.75 , 102 km s−1 . Even with the various approximations we made, the trends clearly follow the same redshift evolution, and show that a combination of the slope o…

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