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The galaxy-AGN scaling relations over 13 billion years in SHARK v2.0 (I): SMBH masses

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Using SHARK v2.0, a semi-analytic model of galaxy formation, this paper predicts that supermassive black holes at z=9 were about ten times more massive than black holes in galaxies of the same stellar mass today, and that galaxy…

desk verdict A solid, open, well-comparisoned SAM prediction paper whose headline 1 dex evolution claim rests on manually re-tuned cold-gas accretion parameters with no sensitivity analysis. read the letter →

arxiv 2506.03354 v2 pith:XT62SADP submitted 2025-06-03 astro-ph.GA

Matías Bravo , Claudia del P. Lagos , Katy L. Proctor , Ángel Chandro-Gómez , Chris Power This is my paper
classification astro-ph.GA
keywords supermassiveblackholesgalaxyscalingrelationssemi-analyticformationmodelsholemassfunctionmorphologyAGNfeedbackcosmicevolutionenvironment
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

SHARK v2.0, a semi-analytic model of galaxy formation run on a large-volume dark-matter simulation, is used here to predict how supermassive black hole masses relate to host stellar mass and bulge mass from redshift 9 to the present. The authors find the model reproduces observed scaling relations across a wide redshift range while predicting that the relations evolve strongly: at fixed stellar mass, SMBH masses are roughly 1 dex (a factor of ten) lower at z=0 than at z=9, and the scatter around the relations grows by a factor of 2-5 toward low redshift. They also find that the bulge-to-total stellar mass ratio, a proxy for morphology, is the dominant predictor of the scatter around both relations, with environment and star formation playing weaker, mostly indirect roles. The paper presents these as large-volume predictions that upcoming AGN and redshift surveys can test. The z=0 normalization of the bulge-mass relation was used as a secondary calibration target, so the slope and the cosmic-time evolution are the genuine predictions.

What carries the argument

SHARK v2.0's SMBH growth module: seeded black holes grow by Bondi-like hot gas accretion (Equation 1), by episodic cold gas accretion during starbursts triggered by mergers or disc instabilities (Equations 2-3, with free parameters fSMBH=0.007 and eSB=2.0 manually re-tuned for the Planck-Millennium run), and by SMBH-SMBH mergers. These channels set the normalization, slope, and scatter of the scaling relations; the cold-gas channel dominates high-redshift growth and sets the local M_bulge-M_BH normalization, while the merger channel increasingly contributes at low redshift. The random forest regression applied to offsets from the fitted relations is the tool that attributes the scatter primarily to morphology.

What would settle it

Measure the M_star-M_BH and M_bulge-M_BH medians at z~4-6 with a large, selection-function-corrected sample (e.g., JWST and 4MOST); the paper's central claim would be contradicted if the median offset from local relations is much smaller than ~1 dex at fixed stellar mass once Lauer-type bias is corrected. A cheaper model-side falsifier is to rerun SHARK v2.0 with fSMBH varied over, say, 0.003-0.015 and eSB varied over 1-10; if the z=9-to-z=0 offset changes by more than ~0.5 dex, the evolution claim is an artifact of the manual calibration.

Watch

Extended reading notes

Core claim

The central discovery is a set of model predictions: the M_bulge-M_BH and M_star-M_BH relations in SHARK v2.0 are not universal but shift downward by about 1 dex in SMBH mass from z=9 to z=0 at fixed stellar mass, with the scatter increasing by a factor of roughly 2-5. The model produces a tight M_bulge-M_BH relation at all redshifts, with early- and late-type galaxies following distinct relations that separate by z~4; late-type galaxies have more massive SMBHs at fixed bulge mass but lower masses at fixed total stellar mass, and SMBHs are most massive in early-type galaxies. SMBH growth transitions from gas-accretion-dominated at high redshift to merger-dominated at low redshift, with a minimum in merger fraction around M_BH~$10^{7}$ Msun and M_bulge~$10^{10}$ Msun that does not evolve. Random forest regressions identify bulge-to-total ratio as the dominant feature explaining offsets from both relations at all redshifts, with central/satellite status having minor importance, implying environment acts indirectly through morphology.

Load-bearing premise

The ~1 dex cosmic evolution claim rests on the assumption that the cold-gas accretion parameters fSMBH=0.007 and eSB=2.0, manually tuned to the local M_bulge-M_BH normalization, remain a valid extrapolation from z=0 to z=9, and the paper does not test how sensitive the evolution is to those choices.

Editorial extensions

If this is right

  • At fixed stellar mass, high-redshift galaxies should show SMBH masses up to ~1 dex above the local median, so deep surveys at z>4 can distinguish evolving from universal relations.
  • Estimates of SMBH masses from host stellar mass alone will carry large scatter; adding bulge mass or bulge-to-total ratio should markedly improve the inference.
  • The scatter around both relations should grow from z=9 to z=0 by a factor of 2-5, with a stellar-mass-dependent peak around M_star~10^10 Msun at low redshift.
  • Low-mass satellite galaxies should host more massive SMBHs than centrals of the same stellar mass by z=0 (up to ~0.5 dex), but this difference should vanish once morphology is controlled for.
  • The switch from gas-accretion-dominated to merger-dominated SMBH growth around z~4 should be reflected in the demographics of merging and active galaxies.

Reading between the lines

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

  • Extension: If the 1 dex offset is physical, local SMBH mass predictors calibrated at z=0 will systematically underestimate high-redshift SMBH masses; a direct test is to apply the local relations to JWST-discovered z>4 galaxies and compare with independent estimates such as virial or reverberation mapping.
  • Extension: The dominance of morphology in the random forest suggests that merger history (wet versus dry) may be the underlying variable coupling SMBH growth to other galaxy properties; a controlled model experiment that shuffles merger histories at fixed morphology could isolate this.
  • Extension: The model's predicted satellite-central offset below ~10^10 Msun could be probed with upcoming 4MOST AGN surveys overlapping deep environmental metrics; detecting or ruling out the offset would constrain the role of ram-pressure and tidal stripping in SMBH feeding.
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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

2 major / 4 minor

Summary. The paper uses the SHARK v2.0 semi-analytic model, re-calibrated to the Planck-Millennium N-body simulation, to predict the evolution of the M_bulge-M_BH and M_star-M_BH scaling relations from z=9 to z=0. The authors manually retune the cold-gas accretion parameters fSMBH and eSB (Table 2) to reproduce the local M_bulge-M_BH normalisation, and find that the model broadly matches observed BHMFs and scaling relations over the redshift range, predicts a ~1 dex decrease in SMBH mass at fixed stellar mass from z=9 to z=0, a factor of 2-5 increase in scatter toward z=0, and that bulge-to-total ratio is the dominant predictor of scatter in a random forest analysis. They interpret these results as evidence for strong cosmic evolution of the scaling relations and a central role for morphology, with environment playing only an indirect role.

Significance. If robust, the evolution prediction is a valuable, large-volume prediction from an open-source SAM that can be tested with 4MOST and JWST samples; the paper also provides useful qualitative predictions for the morphology-dependence of the relations and for the occupation fraction of low-mass black holes. Strengths include the transparency about primary vs secondary calibration (Section 2.2), the explicit statement that the z=0 normalisation is calibrated rather than predicted (Section 3.1), the test of seed-mass insensitivity (Section 2.1), and the public availability of the code. The high-redshift evolution claim, however, rests on the uncalibrated cold-gas accretion prescription, and the morphology-scatter claim is based on a predictive-correlation analysis rather than a causal decomposition; both caveats need to be addressed before the strong conclusions can be accepted.

major comments (2)
  1. [Section 2.2, Table 2, Eqs. (2)-(3), Section 5] The predicted ~1 dex offset in SMBH mass at fixed stellar mass between z=9 and z=0 is the central claim, and it is anchored at high redshift by the cold-gas accretion channel, which Figure 9 shows dominates SMBH growth at z>~6. This channel is controlled by fSMBH and eSB, which were manually re-tuned from (0.01, 15.0) to (0.007, 2.0) when moving the model to Planck-Millennium (Section 2.2). Because the cold-gas accretion rate in Eq. (3) is proportional to fSMBH/eSB, this retuning changes the high-redshift accretion rate by a factor of 5.25 relative to the L24 values. The paper does not report a sensitivity analysis of the evolution claim to these parameters, so it remains possible that a substantial part of the predicted 1 dex offset is an artifact of this manual adjustment rather than a robust prediction of the model. I request a sensitivity test, such as running the L24 parameter values on the PM trees or varying fSMBH and eSB by factors of order 2, and a discussion of how the z=9-to-z=0 offset responds.
  2. [Section 4.1 and Figure 11] The abstract and conclusions state that galaxy morphology 'alone' explains most of the scatter around both scaling relations, but the evidence presented is random forest feature importance, which is a relative, model-dependent quantity and does not measure the variance in the scatter explained by morphology by itself. Because B/T is correlated with other features (M_bulge, Delta_SFMS, f_M_mergers), the Gini-importance ranking can overstate the unique role of morphology. To support the claim, the authors should quantify the predictive power of a regressor trained on B/T alone (e.g., R^2 or explained variance of the offset) and compare it with the full model, or use permutation importance; they should also phrase the conclusion in terms of predictive association rather than causation.
minor comments (4)
  1. [Introduction, first paragraph] 'as been widely interpreted' should be 'has been widely interpreted'.
  2. [Appendix C, Eqs. (C4)-(C5)] The names SBHMR and SBHMRbulge appear to be swapped, since as written SBHMR uses the M_star,bulge-M_BH fit and SBHMRbulge uses the M_star-M_BH fit, the reverse of the convention in Figure 11.
  3. [Figure 2 caption] 'Inferred SMBH occupation fraction at z~0 from observations show are shown' is grammatically incorrect; it should read 'are shown'.
  4. [Equation (2)] The symbols vSMBH and vvir are used but not defined in the text; please define them explicitly (vSMBH is later mentioned as a free parameter, and vvir is presumably the virial velocity).

Circularity Check

1 steps flagged · score 4.0 of 10

Partial, self-acknowledged circularity: the z=0 scaling-relation normalisation is a manually fitted calibration target, while the headline high-redshift evolution remains an unfitted model prediction.

  1. fitted input called prediction [Section 2.2 (Table 2), Section 3.1, and the Abstract/Conclusions wording]
    "To correct these tensions, we manually re-tuned two parameters: fSMBH and eSB, which control the cold gas accretion into the SMBH (see Equations 2 and 3). With these choices, we treat [...] the normalisation of the z = 0 bulge-SMBH mass relation [...] as secondary observational constraints that we attempt to qualitatively match."

    The z=0 M_bulge-M_BH normalisation is a manual calibration target: fSMBH and eSB in Equations (2)-(3) were re-tuned explicitly to remove offsets in the SMBH mass relations, and Section 3.1 concedes that the resulting z=0 agreement is 'partially by construction'. The Abstract nevertheless lists this agreement as part of the relations 'predicted by shark v2.0' that are in 'good overall agreement' with observations. Thus one component of the validation is a fitted input rather than an independent prediction. The main evolution claim (z=0 versus z=9) is not fitted and therefore has independent content, which is why the circularity is partial and self-acknowledged.

full rationale

The central high-redshift predictions are genuine model extrapolations: the z=9-to-z=0 evolution, the scatter growth, and the morphology trends are not fitted to SMBH observations at high redshift, and the model itself is an open-source SAM with externally stated prescriptions (Kauffmann & Haehnelt 2000; Croton et al. 2006). The paper's reliance on Lagos et al. (2024) and Chandro-Gomez et al. (2025) for the model and merger-tree fixes is normal model provenance, not a circular argument, and no uniqueness theorem or ansatz is smuggled in via self-citation. The one genuine fitted-input issue is the z=0 M_bulge-M_BH normalisation, which is manually tuned via fSMBH and eSB and then presented as part of the overall agreement with observations; the authors explicitly flag this, so it is an acknowledged, bounded circularity rather than a hidden one. The manual retuning of fSMBH/eSB without a sensitivity analysis raises a real correctness risk for the headline evolution, but that is a robustness concern, not a circularity reduction, because the high-z relation is not defined as the calibration target.

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

The model introduces no new physical entities. It relies on several established prescriptions for seeding, gas accretion, and merging, plus a parameter set that is partially re-tuned to local data. The central evolution prediction depends most heavily on the cold gas accretion parameters fSMBH and eSB, which were adjusted to match the z=0 relation normalisation.

free parameters (5)
  • fSMBH = 0.007
    Manually re-tuned in Section 2.2 to correct offsets in the galaxy-SMBH mass relations and AGN bolometric luminosity functions; controls the normalisation of cold gas accretion into SMBHs.
  • eSB = 2.0
    Manually re-tuned in Section 2.2; e-folding parameter controlling the cold gas accretion timescale.
  • M_BH,seed = 1e4 M_sun h^-1
    Chosen seed mass; the paper states tests with 1e2 M_sun h^-1 make little difference, so it is not strongly constraining.
  • Mhalo,seed = 1e10 M_sun h^-1
    Halo mass threshold for seeding SMBHs, retained from prior SHARK implementations; nearly all galaxies above M_star=1e8 M_sun are seeded.
  • kAGN, kjet, Gamma_thresh, tau_reinc, gamma, Mnorm = See Table 2
    Parameters re-tuned with the optim module to match the z=0 and z=1 stellar mass functions of Li and White (2009); these indirectly affect stellar masses and hence the scaling relations.
assumptions (4)
  • domain assumption Every subhalo above Mhalo,seed hosts a seed SMBH of mass M_BH,seed.
    Stated in Section 2.1. This determines the occupation fraction and the low-mass end of the BHMF.
  • domain assumption Cold gas accretion onto SMBHs occurs only during starbursts triggered by mergers or disc instabilities.
    Equation (2)-(3), Section 2.1. This prescription, inherited from Kauffmann and Haehnelt (2000), is the main channel for early SMBH growth and underpins the redshift evolution claim.
  • domain assumption The merger tree numerical artefact fixes of Chandro-Gomez et al. (2025) adequately correct the Planck-Millennium trees.
    Section 2.2 states these fixes are applied; if the corrections are incomplete, the merger-driven SMBH growth and f_M,mergers distributions could be biased.
  • ad hoc to paper Calibration to z=0 and z=1 stellar mass functions is a sufficient primary constraint for the model.
    Section 2.2 describes optimising six parameters to the Li and White (2009) SMFs; this choice shapes the stellar masses that enter the scaling relations.

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Cite this review

Pith. "Pith review of The galaxy-AGN scaling relations over 13 billion years in SHARK v2.0 (I): SMBH masses." pith.science (2026). https://pith.science/paper/XT62SADP

@misc{pith2026250603354,
  author       = {Pith},
  title        = {Pith review of: The galaxy-AGN scaling relations over 13 billion years in SHARK v2.0 (I): SMBH masses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XT62SADP}},
  note         = {Machine review of arXiv:2506.03354}
}
abstract

The presence of strong correlations between super-massive black hole (SMBH) masses and galaxy properties like stellar mass have been well-established in the local Universe, but how these scaling relations evolve with cosmic time is yet to be settled in both observations and theoretical models. Recent works have also highlighted the role of galaxy morphology on the scatter of the SMBH-galaxy mass scaling relations, while the impact of other galaxy properties remains poorly studied, like the role of galaxy environment. We use the state-of-the-art SHARK v2.0 semi-analytic model to explore the evolution of these galaxy-SMBH scaling relations to expand the available predictions from theoretical models to contrast with existing and upcoming observations. We find the relations between SMBH masses and both total and bulge stellar mass predicted by SHARK v2.0 to be in good overall agreement with observational measurements across a wide range of redshift and stellar masses. These scaling relations show a significant evolution as a function of cosmic time in SHARK v2.0, with SMBH masses $\sim1$ dex lower at $z=0$ compared to $z=9$ at fixed stellar mass and the scatter increasing by a factor of $\sim2-5$ towards low redshift. Both relations show a strong dependence with galaxy morphology and the main source for SMBH growth (gas accretion or mergers), with weaker trends with star formation rate, galaxy sizes, and environment. We find that galaxy morphology alone explains most of the scatter around both scaling relations, with other galaxy properties tying to the SMBH scaling relations through their correlations with morphology.

Figures

Figures reproduced from arXiv: 2506.03354 by the authors.

Figure 1
Figure 1. Comparison of the BHMF predicted by shark v2.0 from z = 9 to z = 0 to observational results from the literature. Each panel corresponds to the SMBH mass function at the redshift indicated at the top right corner. The lines show the results from shark v2.0, the total BHMF with the thick black line, the total BHMF with a 0.5 dex scatter applied to M• with the thin (solid) black line, and the contribution of central an… view at source ↗
Figure 2
Figure 2. Fraction of galaxies with M• > 105 M⊙ as a function of M⋆ at different redshifts. Lines coloured by red￾shift, with darker lines for higher redshifts. We note that almost all galaxies (> 99.999%) above M⋆ = 108 M⊙ have a SMBH in the 0 ≤ z ≤ 9 range. Inferred SMBH occupation fraction at z ∼ 0 from observations show are shown with shaded areas: from X-ray data (Miller et al. 2015) in light grey, from dynamical SMBH ma… view at source ↗
Figure 3
Figure 3. Comparison of the predicted M⋆,bulge-M• distribution in shark v2.0 from z = 9 to z = 0 to observational results from the literature. Each panel corresponds to the M⋆,bulge-M• distribution at the redshift indicated at the bottom right corner. The coloured histograms in the background show the overall distribution of shark v2.0 galaxies at each redshift, linearly coloured and with the scale adjusted for maximum contra… view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Similar to [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]
Figure 6
Figure 6. Figure 6: Similar to [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Similar to [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Similar to [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Similar to [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: shows that, while there is an overall trend to an increased contribution of SMBH-SMBH mergers from z = 9 to z = 0, SMBHs with M• ∼ 107 M⊙ show little change on how their mass has been built over ∼ 13 Gyr. We find a similar trend for fM•,mergers as func￾tion of M⋆,bulg…
Figure 11
Figure 11. Figure 11: Relative importance of different galaxy properties in explaining the offset from the M⋆,bulge-M• (left column) and M⋆-M• (right column) relations as a function of redshift, measured as the feature importance from applying Random Forest Regressions to the data at each …
Figure 12
Figure 12. Figure 12: The scatter around the M⋆,bulge-M• and M⋆-M• relations (left and right panels, respectively), as a function of redshift and stellar mass. The scatter is measured as the difference in log-scale of the running 16th and 84th running percentiles. Each line indicates a dif…
Figure 13
Figure 13. Figure 13: Comparison of the M⋆,bulge-M• (top row) and M⋆-M• (bottom row) relations predicted by shark v2.0 at z = 0 to those measured by Graham & Sahu (2023a), including the Chabrier (2003) IMF correction from Graham & Sahu (2024). The solid lines indicated the running median i…
Figure 14
Figure 14. Figure 14: Fit to the M⋆-M• relation used to measure ∆SBHMR used in [PITH_FULL_IMAGE:figures/full_fig_p021_14.png]

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the rapid growth of SMBHs in high-z galaxies: the aftermath of Population III.1 stars

    astro-ph.GA 2025-07 conditional novelty 6.0 of 10

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