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REVIEW 4 major objections 5 minor 62 references

Different physical and numerical sources of scatter in the $M_{\star}$-$M_{\mathrm{BH}}$ relation and their connection to galaxy evolution

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

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Pith's one-line read The scatter around the black-hole–stellar-mass relation is a readable signature of black hole feedback physics: simulations with strong quenching produce about 0.1 dex of intrinsic scatter dominated by mergers, while weaker-feedback…

desk verdict The TNG-internal scatter decomposition is a genuinely new and solid result, but the cross-simulation split into accretion versus merging for Illustris and EAGLE rests on an explicitly untested assumption that needs a direct test before the headline claim is fully trusted. read the letter →

arxiv 2502.06203 v2 pith:MQ7GVGII submitted 2025-02-10 astro-ph.GA

Bocheng Zhu , Volker Springel This is my paper · ORCID
classification astro-ph.GA
keywords blackhole-galaxyco-evolutionM_BH-M_starrelationscatterAGNfeedbackhierarchicalmergingcosmologicalhydrodynamicalsimulationssupermassiveholeseedsgalaxyquenching
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

This paper argues that the scatter around the observed relation between supermassive black hole mass and host galaxy stellar mass is not mere noise—it is a diagnostic of how black holes and galaxies co-evolve. Comparing four large cosmological simulations, it finds that at $z=0$ the intrinsic scatter separates simulations into two groups: TNG100 and MillenniumTNG show about $0.1$ dex, dominated by hierarchical merging of quenched galaxies, while Illustris and EAGLE show about $0.3$ dex, dominated by black hole accretion. The paper attributes this difference to how strongly each model's AGN feedback quenches massive galaxies. It also shows that numerical noise is a substantial part of the raw scatter at low redshift, and that variations in black hole seed mass could leave a visible imprint at high redshift but are erased by $z=0$ in TNG-like models. The upshot is that measuring scatter as a function of mass and redshift could discriminate between competing models of black hole seeding and feedback.

What carries the argument

The load-bearing tool is a variance decomposition of logarithmic black hole mass at fixed stellar mass, $\sigma^2_{\mathrm{BH}} \approx \sigma^2_{\mathrm{seed}} + \sigma^2_{\mathrm{Acc\&FB}} + \sigma^2_{\mathrm{HM}} + \sigma^2_{\mathrm{numerical}}$. To isolate the terms, the paper runs five TNG-like boxes with identical initial conditions but different parallel node counts (capturing round-off and stochastic-model noise), and five further boxes with black hole accretion switched off (capturing hierarchical merging plus the same numerical noise). Subtracting these controlled measurements gives separate estimates of the accretion-driven and merger-driven scatter, which are then transferred to Illustris and EAGLE under the assumption that merger-driven scatter is similar across models. The same experiments, plus a run with artificially scattered seed masses, show how seed variations and AGN feedback enter the budget.

What would settle it

Run the paper's controlled no-accretion experiment in Illustris and EAGLE: if the measured merger-driven scatter there differs from the TNG value beyond the quoted uncertainties, the decomposition of their intrinsic scatter into accretion versus merging components fails. A second check would be a higher-resolution measurement of numerical noise in BH mass at $z=0$; if that variance is well above the paper's $\sim0.01$ value, the claimed $\sim0.1$ dex intrinsic scatter in TNG would be largely an artifact.

Watch

Extended reading notes

Core claim

The central claim is that the intrinsic scatter of the $M_{\rm BH}$-$M_\star$ relation at $z=0$ has two physically distinct origins whose relative importance differs between simulation families. In TNG100 and MillenniumTNG the intrinsic scatter is $\sim 0.1$ dex and is dominated by hierarchical merging: massive galaxies are quenched, their black hole growth proceeds mainly by dry mergers, and the relation stays tight. In Illustris and EAGLE the intrinsic scatter is $\sim 0.3$ dex and is dominated by black hole accretion, because those models quench massive galaxies less completely, leaving gas accretion to push black holes away from the relation. The paper reaches this conclusion by decomposing the measured scatter into numerical, merger-driven, and accretion-driven components, and by showing that without AGN feedback the scatter in low-mass galaxies grows to $\gtrsim 0.5$ dex. It also claims that at high redshift the scatter is particularly sensitive to the initial seed mass distribution, making it a promising observational probe of SMBH seed origins.

Load-bearing premise

The paper assumes that hierarchical merging produces the same amount of scatter in Illustris and EAGLE as in TNG, even though their different feedback models could alter merger-driven scatter and post-merger accretion.

Editorial extensions

If this is right

  • At $z\lesssim 1$, BH accretion contributes essentially no scatter in TNG-like models, so the low-redshift relation there is built and maintained by mergers of quenched systems.
  • The observed low-redshift scatter of $\sim 0.29$ dex includes substantial measurement error; if that error is near the high end, galaxies may actually be closer to the TNG prediction than to the Illustris/EAGLE prediction.
  • A $\sim 0.5$ dex spread in seed masses leaves a measurable scatter at high redshift, and the redshift at which that extra scatter disappears depends on feedback; this makes high-redshift scatter a seed-origin probe.
  • Raw simulation scatter cannot be compared directly with observations at $z\lesssim 2$ in TNG-like models, because numerical noise contributes more than half of the raw variance there.

Reading between the lines

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

  • An extension the paper leaves implicit: running its no-accretion experiment in Illustris and EAGLE would directly test the assumption that merger-driven scatter is model-independent, and would either validate or shift the claimed accretion-versus-merging split.
  • If BH mass measurement errors in current observations are overestimated, the true observed scatter could be as low as the TNG value, which would flip the conclusion about which simulation family is favored by data.
  • The same decomposition strategy could be applied to other galaxy formation models, but each would need its own numerical-noise calibration rather than borrowing TNG-based values.
  • High-redshift observations of overmassive black holes with large scatter would point to seed or accretion variations rather than merger-dominated growth, which the paper notes but does not model in detail.
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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 studies the scatter in the M_BH-M_* relation for massive galaxies (M_* > 10^10.5 Msun, sigma > 150 km/s) in the Illustris, TNG100, EAGLE, and MillenniumTNG simulations. Using controlled numerical experiments (five identical-initial-condition TNG boxes with different node counts, and five TNG-like boxes with BH accretion switched off), the authors decompose the measured scatter into numerical noise, hierarchical-merging scatter, BH-accretion scatter, and seed-mass-variation scatter. Their central claims are that at z=0 TNG100 and MTNG have intrinsic scatter ~0.1 dex dominated by hierarchical merging, while Illustris and EAGLE have ~0.3 dex dominated by BH accretion; that accretion-driven scatter becomes negligible at z<1 in TNG-like models; and that scatters at high redshift can constrain SMBH seed scenarios. The paper also relates the lower scatter in TNG/MTNG to more efficient quenching of massive galaxies.

Significance. If the decomposition is correct, the paper offers a new and potentially discriminating diagnostic for BH feedback models and seed formation scenarios: the redshift evolution of the scatter and its split into merging versus accretion components. The authors should be credited for performing dedicated controlled experiments (TNGSeries and NoAcc/NoAccSeries) to isolate numerical and physical scatter, for validating their grouping regression method on the Kormendy-Ho observational sample, and for making the decomposition framework explicit in Eq. (7). The TNG-specific results—especially the time-independent numerical variance and the increasing merger-driven scatter—are useful and strengthen the methodological literature. However, as detailed below, the cross-simulation conclusions for Illustris and EAGLE rely on an untested assumption, and the quoted uncertainties and outlier clipping require more support.

major comments (4)
  1. [Section 3.4, Figure 8] The central comparative claim that Illustris and EAGLE have ~0.3 dex intrinsic scatter dominated by BH accretion while TNG/MTNG have ~0.1 dex dominated by merging rests entirely on the assumption stated in Section 3.4: 'we simply assume that the scatter due to hierarchical merging is similar in these simulations compared to TNG.' This assumption is load-bearing because it converts the measured total scatter into an accretion component via sigma_acc^2 = sigma_int^2 - sigma_HM^2 (Eq. 7 and Figure 8, bottom panel). The authors acknowledge it is 'somewhat less obvious' for Illustris and EAGLE, but provide no quantitative check: no merger-rate comparison, no resolution test, and no no-accretion experiment for those models. Different BH feedback prescriptions (thermal vs kinetic) and the very different sSFR/BHAR trends shown in Figures 11-12 can plausibly change both the merger-driven scatter and the post-merger gas supply, so the universality of sigma_HM is not physically guaranteed. I request a direct test of this assumption—for example, measuring merger rates or the scatter in merger histories in Illustris/EAGLE, or at least a sensitivity test showing that the inferred accretion fraction is stable to plausible variations in sigma_HM. Without such a test, the headline difference between the two groups of simulations is not firmly established for Illustris and EAGLE, even though the TNG-specific decomposition is credible.
  2. [Section 3.2, Figures 5 and 6] The numerical scatter is estimated after removing points outside a 3-sigma region from the distribution of BH-mass deviations among matched subhalos. As shown in the left and right panels of Figure 5, this clipping materially changes the measured variance. The paper justifies the clipping as excluding 'rare extreme deviations' attributed to matching failures, but no independent evidence is given that these outliers are purely technical rather than genuine numerical scatter. Since the numerical variance is subtracted from the total to obtain the intrinsic scatter (Section 3.3), the choice of the 3-sigma threshold directly affects the central results, including the ~0.1 dex intrinsic scatter quoted for TNG at z=0. The authors should demonstrate robustness of their conclusions to the clipping threshold (e.g., 2-sigma, 4-sigma, or no clipping) and, ideally, provide a matching-quality diagnostic to distinguish matching failures from true outliers.
  3. [Figure 7 caption / Section 3.3] The bottom panel of Figure 7 states that 'the statistical uncertainty of the results is ~1e-5', but no derivation or error analysis is provided anywhere in the text. The variance estimates are based on only five matched subhalo sets, with a matching fraction of 60-70% (80% for massive galaxies, Section 3.2), and the variance is then summarized by the median within stellar-mass bins. Sampling noise, matching incompleteness, and binning choices should produce uncertainties far larger than 1e-5 in variance (which corresponds to ~0.003 dex in scatter). The paper should provide a proper error estimate for the decomposed components in Figure 7 and 8, or remove the unsubstantiated precision claim.
  4. [Section 3.3, paragraph after Figure 7] The paper explicitly folds post-merger accretion into the accretion component ('our approach treats such post-merger accretion as part of the accretion-driven component'). This is a definitional choice, but it has systematic consequences: the quantity labeled 'hierarchical merging' (sigma_HM) is not a pure merger statistic but a residual after assigning all accretion-related growth to the accretion term. In particular, gas-rich mergers can enhance accretion, so the NoAcc experiment subtracts only the direct merger contribution, not the merger-induced accretion. This should be discussed as a systematic uncertainty, and it reinforces the need for the robustness tests requested in the first major comment, because the interpretation of the Illustris/EAGLE accretion-dominated scatter depends on this partitioning.
minor comments (5)
  1. [Section 2.2.1] The GMM cleaning of an undermassive-BH satellite population is applied only to MTNG (Figure 1). If a similar population exists in the other simulations at lower abundance, the differing cleaning procedures could introduce a small selection bias in the cross-simulation comparison; a brief discussion of this possibility would be helpful.
  2. [Section 2.3.1] The statement that the Illustris scatter 'decreases from ~0.5 to ~0.35 dex over z=1 to 0, although the latter is not statistically significant based on a t-test' would be clearer if the t-test statistic and p-value were reported.
  3. [Equation (7)] The decomposition ignores the cross-covariance term sigma_cross by assumption; given that accretion and merging are physically coupled (as acknowledged in Section 3.3), a rough estimate of the cross term from the NoAcc and full runs would strengthen confidence that the additive approximation is adequate.
  4. [Section 3.4 / Figure 8] The intrinsic scatter for MTNG is stated to 'appear slightly negative in some cases', which the authors attribute to the numerical noise being approximated from TNG100 rather than measured in MTNG. This is acceptable, but the affected redshift bins should be identified explicitly in the figure or text so that readers do not misinterpret them as unphysical.
  5. [Section 5, bullet list] Minor language issues: 'the scatter scatter' appears in Section 3.3; 'resoluteness' in the final bullet of Section 5 is informal; and the abstract contains formatting artifacts such as '10 10.5' and 'M⊙' spacing. These should be corrected in a final proofreading pass.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; the TNG decomposition is experiment-based, and the Illustris/EAGLE decomposition is an explicitly conditional estimate rather than a circular reduction.

full rationale

The derivation chain is not circular. For TNG, the scatter decomposition is obtained from controlled numerical experiments: five identical TNG boxes run with different node counts isolate numerical/stochastic scatter, and five boxes with BH accretion disabled isolate the merging-plus-numerical contribution; the accretion component is then the difference from the full run. The paper makes this linear combination explicit in Tables 2 and 3, so the TNG-specific results are measured rather than assumed. The extension to Illustris and EAGLE in Section 3.4 does rely on an openly stated assumption: 'we simply assume that the scatter due to hierarchical merging is similar in these simulations compared to TNG.' This is a legitimate correctness/fragility concern, but it is not circularity: the accretion components for Illustris and EAGLE are conditional estimates formed by subtracting the assumed merging term and the numerical term from the measured total scatter. The conclusion that accretion dominates is a contingent consequence of the measured intrinsic scatter being larger than twice the assumed merging scatter, not an equivalence between the input assumption and the output claim. The paper also uses an external measurement (Borrow et al. 2023b) for EAGLE numerical scatter and an external observational benchmark (Kormendy & Ho 2013) to validate the fitting method. There are no load-bearing self-citations or imported uniqueness theorems. Hence no circular step meets the evidentiary standard requiring a specific reduction of the claimed result to its own inputs.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central decomposition rests on four stated assumptions: additivity of variances, similar merger scatter across simulations, similar numerical scatter between TNG and Illustris, and the treatment of extreme outliers as technical noise. The first is explicit in Eq. (7); the second and third are explicit but untested assumptions in Section 3.4; the fourth is a data-cleaning choice in Section 3.2. These are the main liabilities of the analysis.

free parameters (2)
  • SeedVar imposed seed mass scatter = 0.5 dex
    A random 0.5 dex scatter is imposed on BH seed masses in the SeedVar test simulation (Section 3.5) to assess its impact. The value is chosen by hand as a representative amplitude, not derived from data.
  • 3-sigma outlier clipping threshold = 3 sigma
    The numerical scatter estimate in Section 3.2 excludes data points outside a 3-sigma region, a post-hoc choice that reduces the measured numerical variance. The threshold is justified qualitatively as removing technical outliers, but it is not calibrated independently.
assumptions (4)
  • domain assumption Scatter components in Eq. (7) are additive and uncorrelated; cross terms are ignored.
    The paper states 'For simplicity, we ignore cross terms in the following analysis' (Section 3.1). If accretion, merging, and numerical scatter are correlated, the subtraction-based estimates are biased.
  • ad hoc to paper Hierarchical merging scatter is similar in Illustris and EAGLE to that in TNG.
    Section 3.4 says 'we simply assume that the scatter due to hierarchical merging is similar in these simulations compared to TNG', based on conceptually similar BH seeding schemes. No merger-rate comparison is provided.
  • ad hoc to paper Numerical scatter in Illustris is similar to that in TNG.
    Section 3.4 states that since Illustris shares code and model aspects with TNG, the paper 'shall assume the TNG numerical scatter also for Illustris', without a dedicated measurement.
  • domain assumption Numerical variations follow a Gaussian distribution and 3-sigma outliers are technical artifacts.
    Section 3.2 relies on prior work (Genel et al. 2019) and excludes 3-sigma outliers to obtain a clean variance estimate, treating extreme deviations as matching failures or rare anomalies.

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Cite this review

Pith. "Pith review of Different physical and numerical sources of scatter in the $M_{\star}$-$M_{\mathrm{BH}}$ relation and their connection to galaxy evolution." pith.science (2026). https://pith.science/paper/MQ7GVGII

@misc{pith2026250206203,
  author       = {Pith},
  title        = {Pith review of: Different physical and numerical sources of scatter in the $M_\star$-$M_\mathrmBH$ relation and their connection to galaxy evolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MQ7GVGII}},
  note         = {Machine review of arXiv:2502.06203}
}
abstract

Observations have established that the masses of supermassive black holes (SMBHs) correlate tightly with the stellar masses of their host galaxies, albeit with substantial scatter. The magnitude of this scatter as a function of galaxy mass and redshift contains valuable information about the origin of SMBHs and the physical nature of their co-evolution with galaxies. In this work, we highlight this connection by studying the scatter in the $M_{\rm BH}$-$M_\star$ relation for massive galaxies in the Illustris, TNG100, and EAGLE cosmological simulations. We find that TNG100 shows significantly lower scatter than Illustris and EAGLE, reflecting different BH feedback models. Using numerical experiments, we separate different contributions to the scatter, including an intrinsic component. At $z=0$, Illustris and EAGLE show $\sim 0.3$ dex intrinsic scatter dominated by BH accretion, while the smaller scatter in TNG100 is dominated by hierarchical merging, implying more tightly quenched massive galaxies. BH seed mass variations can add scatter, though their impact at $z=0$ depends on the feedback model. Without AGN feedback the scatter is much larger for low-mass galaxies ($\gtrsim 0.5$ dex for $\log M_\star < 10^{10.5},\mathrm{M_\odot}$ at $z=0-3$), underscoring the crucial role of feedback in SMBH-galaxy co-evolution. In contrast, hierarchical merging of quenched systems is the main factor reducing scatter for massive galaxies. Based on our results, we expect that the scatter in the $M_{\rm BH}$-$M_\star$ relation at high redshift could be particularly powerful in providing clues to the origin of SMBHs.

Figures

Figures reproduced from arXiv: 2502.06203 by the authors.

Figure 1
Figure 1. Upper panels: The data samples in MTNG from 𝑧 = 2 to 𝑧 = 0 based on the selection criteria 𝜎 > 150 km s−1 and 𝑀★ > 1010.5 M⊙. Lower panels: The “main sequence” samples in MTNG after discarding outliers with a GMM clustering algorithm. The figure shows that GMM clustering can successfully remove the subpopulation that does not belong to the main relation. We will use the selected part shown in the lower panels for th… view at source ↗
Figure 2
Figure 2. The selected data samples in Illustris, TNG, EAGLE and MTNG from 𝑧 = 3 to 𝑧 = 0, as labeled, with the selection criteria 𝜎 > 150 km s−1 and 𝑀★ > 1010.5 M⊙. The dashed lines show the results of our power-law fits to the relations. The aim of this figure is to illustrate the distribution of selected data samples from the Illustris, TNG, EAGLE, and MTNG simulations, spanning redshifts from 𝑧 = 3 to 𝑧 = 0, with specific… view at source ↗
Figure 4
Figure 4. Upper panel: The time evolution of scatter in the TNG100-1, TNG100-2, and TNG100-3 simulations, obtained by using the fitting proce￾dure described in Section 2.2.2. Lower panel: The time evolution of the slope in the TNG100-1, TNG100-2, and TNG100-3 runs. Different line styles, as labeled, represent the results obtained without data cleaning, with removing data outside 2𝜎, and with removing data outside 3𝜎. The resu… view at source ↗
Figures from the paper (9 more)
Figure 5
Figure 5. Figure 5: Left panel: The standard deviation of the BH mass in the matched subhalos of five identical TNG simulations described in Section 3.2 without any data cleaning. Right panel: The standard deviation of the BH mass in the matched subhalos of five identical TNG simulations …
Figure 6
Figure 6. Figure 6: The time evolution of the variance of the BH mass in matched halos of five identical TNG simulation with and without data cleaning. The figure indicates that after removing data outliers the scatter in the BH mass from numerical origins shows a time-independent behavio…
Figure 7
Figure 7. Figure 7: Upper panel: The time evolution of the scatter of the 𝑀BH − 𝑀★ relation, the intrinsic scatter after correcting for the scatter from numerical origins, the scatter due to hierarchical merging, and the scatter due to BH accretion in the TNG100 simulation. Bottom panel: …
Figure 8
Figure 8. Figure 8: Upper panel:The time evolution of the intrinsic scatter of the 𝑀BH− 𝑀★ relation in TNG100, Illustris, EAGLE, and MTNG. Bottom panel: The time evolution of the fraction of the scatter due to BH accretion with respect to the total scatter in the TNG100, Illustris, EAGLE,…
Figure 9
Figure 9. Figure 9: Top panel: The time evolution of the total and intrinsic scatter in the 𝑀BH − 𝑀★ relation in the TNG100 and SeedVar simulations. The “SeedVar=0.5” simulation imposes a random scatter of 0.5 dex on the BH seed mass in a small TNG-like simulation with box size 25 ℎ −1 cM…
Figure 10
Figure 10. Figure 10: The scatter in the BH mass of galaxies of different stellar mass at different redshifts in the TNG100, Illustris, EAGLE, and MTNG simulations. The black line represents the scatters of BH mass for all galaxies. The blue line gives the scatter only for blue galaxies, w…
Figure 11
Figure 11. Figure 11: Left panels: The median value of the specific SFR as a function of stellar mass at different redshifts in the TNG100, Illustris, EAGLE, and MTNG simulations. Right panels: The median value of the BHAR as a function of stellar mass at different redshifts in TNG100, Ill…
Figure 12
Figure 12. Figure 12: Upper panel: The difference of the sSFR for the stellar mass bins in the ranges 1010−11 M⊙ and 1010.5−11.5 M⊙ in TNG100, Illustris, EAGLE, and MTNG. Lower panel: The difference of the BHAR in units of the Eddington rate for the stellar mass bins in the ranges 1010−11 …
Figure 13
Figure 13. Figure 13: The scatter of the BH masses in galaxies as a function of their stellar mass at different redshifts in our test simulation with no AGN feed￾back. Comparing with the results for our four cosmological simulation, the figure suggest that BH feedback regulates the 𝑀BH − 𝑀…

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Pith tools

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