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Diverse pathways for supermassive black hole-galaxy coevolution

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper finds that the most massive supermassive black holes in the local universe assembled most of their mass before redshift z=2, while lower-mass black holes grew gradually between z=0 and z=2.

desk verdict Useful empirical reconstruction of SMBH growth histories, but the headline result is conditional on an untested Mstar-normalized accretion prescription. read the letter →

arxiv 2411.08838 v1 pith:4WW2KWLP submitted 2024-11-13 astro-ph.GA

Bryan A. Terrazas , James Aird , Alison L. Coil This is my paper · ORCID
classification astro-ph.GA
keywords supermassiveblackholeshole-galaxycoevolutionM_BH-M_starrelationspecificholeaccretionrateAGNempiricalgalaxyformationmodelmassassemblyquenching
open problems Dark Matter
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 asks when supermassive black holes (SMBHs) and their host galaxies actually assembled their masses, and whether there is a single coevolutionary path. The authors construct an empirical model by taking z=0 galaxies from a published galaxy-formation model, assigning each a black hole mass from observed scaling relations that differ for star-forming and quiescent hosts, and then integrating backward to z=2: at each step they subtract the mass implied by observed specific accretion-rate distributions binned by star-formation activity. Their central result is that the most massive SMBHs at z=0 grew very little of their total mass between z=0 and z=2, so these objects must have been largely in place before z=2, while lower-mass SMBHs assembled gradually and often entirely within that window. If this is right, the large scatter in the local SMBH-stellar mass relation is not noise but a record of genuinely different growth histories, and galaxy-formation models need to reproduce both early and late black hole assembly.

What carries the argument

The engine is a backward-time empirical growth model. Starting from z=0, each galaxy in a dark-matter-based empirical galaxy-formation model is assigned a black hole mass from one of two observed $M_\mathrm{BH}$–$M_\mathrm{star}$ relations (quiescent hosts get more massive black holes; scatter 0.65 dex). At every $\sim0.1$ Gyr step back to z=2, the model samples a specific black hole accretion rate ($\lambda_\mathrm{sBHAR}$, the ratio $L_\mathrm{bol}/(1.3\times10^{38}\,\mathrm{erg\,s^{-1}}\times0.002\,M_\mathrm{star}/M_\odot)$) from observed probability distributions binned by distance from the star-forming main sequence, multiplies by two to account for obscured active nuclei, converts the sampled luminosity to a mass accretion rate via $\dot{M}_\mathrm{BH}=(1-\eta)L_\mathrm{bol}/(\eta c^2)$ with $\eta=0.1$, and subtracts that mass from the descendant, apportioning mergers by stellar-mass ratio. The sBHAR distributions plus the z=0 boundary relations are what carry the conclusion: the observed late-time accretion budget is simply too small, relative to their masses, to have built the high-mass end after z=2.

What would settle it

Measure the black hole masses of a representative sample of massive ($M_\mathrm{star}\gtrsim10^{11}\,M_\odot$) quiescent galaxies at z≈2 using dynamical tracers such as ALMA molecular-gas kinematics or JWST IFU stellar kinematics. If typical masses come out well below $10^9\,M_\odot$, the local high-mass population must have grown substantially after z=2, contradicting the paper's central claim; if they already cluster near $10^9$–$10^{10}\,M_\odot$, the early-assembly conclusion is supported.

Watch

Extended reading notes

Core claim

The paper's central discovery is that SMBH assembly is not a single process but is split by mass and star-formation phase. Working backward from the observed z=0 relations, the authors show that the most massive black holes found today — roughly above $10^8\,M_\odot$ — cannot be grown with the accretion rates observed at $z<2$, even when the model is deliberately biased to dump all available accretion onto the most overmassive black holes. Their growth tracks on the $M_\mathrm{BH}$–$M_\mathrm{star}$ plane are flat, meaning stellar mass grows around an already-built black hole. In contrast, lower-mass SMBHs show steep vertical tracks: their entire z=0 mass can be accrued after z=2. The unavoidable consequence is that the $M_\mathrm{BH}$–$M_\mathrm{star}$ relation evolves with redshift, shifting to higher normalization and a shallower slope by z=2, and that the high-redshift relation is dominated by the progenitors of today's quiescent galaxies.

Load-bearing premise

The load-bearing premise is that the factor-of-two correction for black holes hidden from X-ray surveys is accurate — hidden active galaxies are assumed to have the same accretion-rate distribution and live in the same host galaxy types as the X-ray-selected ones — because if hidden accretion is concentrated in the most massive quiet galaxies, the biggest black holes could have grown substantially after z=2.

Editorial extensions

If this is right

  • The high-mass end of the local SMBH population was essentially in place by z=2; successful galaxy-formation models must therefore produce $>10^8\,M_\odot$ black holes before cosmic noon, either through rapid early accretion or heavy seeds.
  • The $M_\mathrm{BH}$–$M_\mathrm{star}$ relation evolves with redshift: by z=2 it has a higher normalization and a shallower slope, and for $M_\mathrm{star}>10^{10}\,M_\odot$ it is populated almost entirely by the ancestors of today's quiescent galaxies.
  • The substantial scatter in the z=0 relation is physically informative; models that assume a single tight $M_\mathrm{BH}$–$M_\mathrm{star}$ relation will miss the diversity of coevolutionary trajectories and under-predict the range of black hole masses at fixed stellar mass at high redshift.
  • A significant fraction of low-mass SMBHs (26% of $M_\mathrm{star}>10^{10}\,M_\odot$ galaxies have zero implied black hole mass at z=2 in the fiducial model) have z=0 masses that can be fully explained by z=0–2 accretion, implying ongoing late-time black hole seeding and growth.
  • Most SMBH mass growth in the model occurs in main-sequence and sub-main-sequence galaxies, with the relatively quiescent phase contributing more total growth than starbursts; this matches X-ray measurements of the declining accretion rate density toward z=0.

Reading between the lines

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

  • If the early-assembly claim is right, dynamical mass measurements of a representative sample of massive quiescent galaxies at z≈2 should already find black holes near $10^9$–$10^{10}\,M_\odot$; the current AGN-selected samples cannot test this because they favor accreting, lower-mass systems.
  • The factor-of-two obscured-AGN correction is the least constrained input; testing it with mid-infrared or radio AGN selection in massive quiescent galaxies would reveal whether hidden accretion could have grown the high-mass end after z=2, which would weaken the central conclusion.
  • The model's population of galaxies with zero reconstructed black hole mass at z=2 suggests that entirely new black holes can form at late times; a targeted search for low-mass active black holes in $z\sim1$–2 star-forming galaxies would test whether this late-seeding channel is real.
  • Because the empirical construction has few physical priors, re-running it with updated accretion-rate distributions from deeper X-ray surveys is a direct route to seeing whether the flat high-mass tracks persist.
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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

3 major / 6 minor

Summary. The paper presents an empirical, post-processing model for SMBH-galaxy coevolution. Using UniverseMachine galaxy catalogs, the authors assign z=0 SMBH masses from the Greene et al. (2020) scaling relations for quiescent and star-forming galaxies, then assign specific accretion rates by randomly sampling the Aird et al. (2019) sBHAR probability distributions in SFR bins at each snapshot, and integrate the growth histories backward in time to z=2. The main findings are that the most massive z=0 SMBHs grow very little of their mass between z=0 and z=2, implying early assembly; lower-mass SMBHs grow more gradually; the MBH-Mstar relation evolves toward higher normalization and shallower slope with redshift; and the scatter in the z=0 relation maps onto diverse growth pathways. Four model variations are presented to test alternative assignments of accretion rates and z=0 boundary conditions.

Significance. If the central conclusion is robust, the paper provides an observationally grounded constraint on SMBH assembly that connects local scaling relations to high-redshift JWST discoveries of overmassive black holes. The framework is transparent and computationally inexpensive, and the paper is explicit that the z=0 relations and sBHAR distributions are reproduced by construction, with the high-z predictions being genuine outputs. The use of observational probability distributions rather than ad hoc subgrid physics is a strength, as is the systematic exploration of model variations. However, the headline result depends on an untested degeneracy in the accretion-rate normalization, so the significance is conditional on whether that degeneracy is resolved.

major comments (3)
  1. [§2.4.2, Eq. (1), Eq. (7)] The central claim that the most massive z=0 SMBHs grew little since z=2 is partly baked into the accretion-rate normalization. In Eq. (1), λ_sBHAR is defined relative to 0.002 Mstar, so for a sampled λ_sBHAR the luminosity, and hence Ṁ_BH in Eq. (7), scales with Mstar. Because the λ_sBHAR probability distributions are sampled independently of MBH, the model imposes Ṁ_BH ∝ Mstar and therefore a fractional growth rate Ṁ_BH/MBH ∝ Mstar/MBH. The galaxies identified as overmassive at z=0 are exactly those with high MBH/Mstar, so their suppressed late growth is a direct consequence of the choice to tie absolute accretion to Mstar rather than to MBH. The observed Aird et al. (2019) constraints are on p(λ_sBHAR), not on p(fEdd); the mapping between the two involves the (evolving) MBH/Mstar distribution, so the same data may be consistent with Eddington-normalized growth that gives overmassive SMBHs substantially more late-time accretion. Model Variations 1 and 2 (§5) only re-rank which galaxies receive the same λ_sBHAR values and leave the Mstar scaling of Ṁ_BH unchanged, so they cannot test this degeneracy. The f0 ≈ 26% population at z=2, whose entire z=0 mass is removed when integrating backward, is a symptom of this choice: low-MBH/Mstar galaxies are assigned effective Eddington ratios far above unity by construction. I request a model variation that instead samples an Eddington-ratio distribution (e.g., using p(λ_sBHAR) with a fixed MBH/Mstar only to derive p(fEdd), then assigning Ṁ_BH ∝ MBH fEdd) to determine whether the early-assembly conclusion survives an alternative, equally plausible normalization.
  2. [§2.4.2, §7.4] The factor-of-two correction for obscured AGN, f_AGN = 2 f_AGN,X, assumes the hidden population has the same sBHAR distribution and occupies the same SFR bins as X-ray-selected AGN. This assumption is load-bearing for the conclusion about massive SMBHs: if obscured accretion is preferentially hosted by massive, quiescent (high) galaxies or has a different λ_sBHAR distribution, the total growth assigned to the most massive SMBHs could increase substantially. The caveat in §7.4 is appropriately explicit, but the paper does not quantify the effect. I suggest adding an extreme model variation that concentrates the factor-of-two hidden population in the quiescent (high) bin or in the highest-MBH/Mstar galaxies, to show the claimed early assembly is not sensitive to this correction.
  3. [§7.4, Fig. 5] The individual growth histories that motivate the 'diverse pathways' conclusion are built on UniverseMachine star formation histories that the authors state are bursty, with ~97% of galaxies switching between star-forming and quiescent classifications multiple times between z=0 and z=2. While coloring by z=0 classification in Fig. 4 mitigates the population mixing, the individual tracks in Fig. 5 still use these unphysical SFHs, so the specific diversity of coevolutionary pathways is not robustly established at the level of individual galaxies. The authors should either test the diversity claim with smoothed or physically motivated SFHs, or explicitly restrict it to ensemble properties.
minor comments (6)
  1. [§1] There is a typo in the Introduction: 'distrubiton' should be 'distribution'.
  2. [§8] In the Conclusions, 'has shown this approach to be a provide a powerful tool' is ungrammatical; it should read 'has shown this approach to provide a powerful tool'.
  3. [§8] The phrase 'serves as a complimentary approach' should be 'complementary approach'.
  4. [§5, Fig. 9] The caption for Fig. 9 says 'similar to Figure 9', which should likely refer to Fig. 4 or another appropriate figure.
  5. [§5, Fig. 5 caption] The sentence 'The black circles are the initial (M_BH, M_star) values that these galaxies have at z=0 before tracking their growth histories backwards in time to lower masses' is confusing because the tracks start at z=0; please rephrase to clarify that the circles mark the z=0 endpoints from which the histories are integrated backward.
  6. [§2.4.2] The truncation of λ_sBHAR sampling to values < 1.0 at z < 1.0 and < 10.0 at z > 1.0 is stated without justification; since the Aird et al. distributions extend beyond these limits, the authors should quantify the resulting bias or explain why the truncation is negligible.

Circularity Check

1 steps flagged · score 6.0 of 10

Mstar-normalized sBHAR prescription partially encodes the headline result; the rest of the paper is transparent about its by-construction inputs.

  1. self definitional [Sec. 2.2 Eq. (1); Sec. 2.4.3 Eqs. (7)-(8); Fig. 2 caption; Secs. 5, 7.3]
    "The calculated L bol values are directly proportional to Mstar, meaning more massive galaxies will host SMBHs with higher L bol for the same λsBHAR. ... The systematic offset in fEdd between quiescent and star-forming galaxies is due to the initial conditions that assign quiescent galaxies more massive SMBHs, and therefore systematically lower Eddington fractions, than star-forming galaxies."

    Eq. (1) defines λ_sBHAR with Lbol normalized by 0.002 Mstar, so Lbol ∝ Mstar. Eq. (7) then makes Mdot_BH ∝ Lbol ∝ Mstar, independent of MBH, and Eq. (8) makes the fractional growth Mdot_BH/MBH ∝ Mstar/MBH. The z=0 boundary (Eq. 2) assigns the most massive BHs to quiescent galaxies with high MBH/Mstar, so their Eddington ratios and fractional growth rates are low by construction, as the Fig. 2 caption concedes. The headline that the most massive z=0 SMBHs grew very little since z=2 is thus largely a restatement of this Mstar-normalized accretion choice rather than an independent measurement of early assembly.

full rationale

The paper is unusually transparent that the z=0 MBH–Mstar relations and the Aird et al. (2019) λ_sBHAR distributions are inputs and that all model variations reproduce them by construction (Secs. 2.4.2, 6, and 8; Fig. 2). Agreement with those constraints is therefore not independent validation, and I do not count that as a hidden circular step. The backward integration from z=0 to z=2 is a genuine forward-calculation using UniverseMachine SFR histories, and the quantitative conclusion does depend on the observed shape of p(λ_sBHAR), the duty cycle fAGN, and the assumed factor-two obscuration correction. However, the qualitative headline ('most massive SMBHs grew very little since z=2') is substantially predetermined by the decision to draw accretion rates from Mstar-normalized λ_sBHAR distributions after assigning high MBH/Mstar to quiescent galaxies at z=0; Eq. (1) plus Eqs. (7)–(8) make Mdot/MBH ∝ Mstar/MBH. The robustness tests reorder λ values but keep the same normalization, so they do not exercise the main alternative where the physical Eddington-ratio distribution is tied to host SFR. The score reflects this partial, disclosed construction rather than a hidden fit or a load-bearing self-citation chain.

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

The central claims rest on three pillars: the observed sBHAR distributions, the observed z=0 scaling relations, and the UniverseMachine galaxy tracks. The paper contributes no new physics but adds a post-processing procedure with a small number of chosen parameters (obscuration factor, SFMS fit, scatter, eta, sampling cutoffs). The main uncertainty is the obscuration correction and the fidelity of the UniverseMachine star formation histories.

free parameters (5)
  • Obscured AGN correction factor = 2.0 (f_AGN = 2 x f_AGN,X)
    Assumes a comparably sized population of heavily obscured AGN with the same sBHAR distribution as X-ray-selected sources (Section 2.4.2). Directly scales the number of accreting black holes and hence total growth.
  • Star-forming main sequence fit = log10 SFR_MS = -7.9 + 0.78 log10 Mstar + 3 log10(1+z)
    Fit to UniverseMachine galaxies to classify them into the five SFR bins used for sBHAR assignment (Section 2.4.1). Affects which accretion rate distribution each galaxy draws from.
  • Intrinsic scatter in z=0 M_BH-M_star relations = epsilon = 0.65 dex
    Adopted from Greene et al. (2020) for both early- and late-type galaxies. This scatter is the key driver of the diversity of growth pathways, a central result.
  • Radiative efficiency = eta = 0.1
    Standard assumption used to convert bolometric luminosity to mass growth rate in Eq. 7; affects the magnitude of derived accretion.
  • sBHAR sampling cutoffs = lambda < 1.0 at z<1, <10 at z>1
    Chosen to avoid assigning super-Eddington accretion rates beyond observed ranges; affects the upper tail of black hole growth.
assumptions (5)
  • domain assumption UniverseMachine provides accurate galaxy stellar masses, SFRs, and assembly histories over z=0-2.
    The growth histories are built on UniverseMachine galaxy tracks (Section 2.1). If its star formation histories are wrong, the SFR classification and stellar mass growth of progenitors are wrong.
  • domain assumption sBHAR probability distributions from Aird et al. (2019) are representative of all galaxies, after the factor-of-two obscuration correction.
    These distributions, measured from Chandra X-ray data in CANDELS/UltraVISTA, supply the accretion rates for every galaxy in every timestep (Sections 2.2, 2.4.2). Selection biases and the obscuration correction directly shape the results.
  • domain assumption The z=0 M_BH-M_star relations from Greene et al. (2020) apply to the full galaxy population at z=0.
    Dynamical SMBH masses are subject to selection effects (Section 1), and the relations for early- and late-type galaxies are used as boundary conditions (Section 2.3).
  • ad hoc to paper Black hole growth is fully described by the assigned accretion (Eq. 8) and mergers with mass proportional to stellar mass (Eq. 9).
    No other growth channels (e.g., seeds, chaotic accretion, black hole mergers with unequal ratios) are included; this defines the growth model (Section 2.4.3).
  • standard math The bolometric correction kbol = 25 and the Eddington-normalized definition of lambda (Eq. 1) apply to all AGN.
    Adopted from Aird et al. (2018) to convert X-ray luminosity to bolometric luminosity and sBHAR (Section 2.2).

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Cite this review

Pith. "Pith review of Diverse pathways for supermassive black hole-galaxy coevolution." pith.science (2026). https://pith.science/paper/4WW2KWLP

@misc{pith2026241108838,
  author       = {Pith},
  title        = {Pith review of: Diverse pathways for supermassive black hole-galaxy coevolution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4WW2KWLP}},
  note         = {Machine review of arXiv:2411.08838}
}
abstract

Supermassive black holes (SMBHs) are observed in diverse galaxy populations across time yet a clear understanding of how they coevolve with their hosts has not been reached. Physically-motivated models of SMBH accretion and feedback vary widely between galaxy formation simulations due to the difficulty of modeling the range of scales important for galactic and SMBH processes. Here we use observational data to build an empirical model for SMBH growth. We apply observed specific accretion rate probability distributions as a function of galaxy star formation rate between $z = 0-2$ to the UniverseMachine galaxy formation model to determine SMBH accretion rates based on galaxy properties. We use observed $z = 0$ SMBH-stellar mass relations for the quiescent and star-forming populations to provide the local boundary conditions for SMBH growth histories. We then track the coevolutionary histories of galaxy stellar mass and their SMBHs backwards in time to $z = 2$. We find that the most massive SMBHs at $z = 0$ have grown very little of their total mass between $z = 0-2$, indicating early SMBH mass assembly for these systems. Conversely, lower mass SMBHs at $z = 0$ assembled their mass gradually across $z = 0-2$. This results in substantial evolution of the SMBH-stellar mass relation, shifting to higher normalization and shallower slope with increasing redshift. We find that the substantial scatter observed in the $z = 0$ SMBH-stellar mass relation results in the diversity of growth pathways found in our model, with some galaxies assembling their stellar mass before their SMBHs and others doing the opposite.

Figures

Figures reproduced from arXiv: 2411.08838 by the authors.

Figure 1
Figure 1. The procedure used for building empirically-motivated SMBH growth histories. We begin with z = 0 galaxies from the UniverseMachine empirical galaxy formation model (Behroozi et al. 2019), splitting them into five populations based on SFR relative to the main sequence (step 1). We then assign SMBH masses to simulated galaxies based on the observed SMBH mass-stellar mass scaling relations for quiescent and star-formin… view at source ↗
Figure 2
Figure 2. The Eddington fraction (fEdd = Lbol LEdd ) as a function of λsBHAR at z = 0 for each SFR classification of simulated galaxies in the UniverseMachine (as indicated by the colors in the legend) following our procedure shown in [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. The evolution of the MBH–Mstar relation for the fiducial model at z = 0, 0.5, 1, and 2. Blue and red contours show the distribution of star-forming and quiescent galaxies at the redshifts shown. There are a significant number of (primarily star-forming) galaxies whose empirically assigned SMBH accretion rates are high enough to account for all their mass growth in the late universe. These are shown as a distribution… view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Similar to [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: Left panel: Individual galaxy growth histories on the MBH–Mstar relation. The z = 0 distributions of star-forming and quiescent galaxies are shown in blue and red contours. Black data points indicate a subset of the UniverseMachine galaxy population at z = 0. The growt…
Figure 6
Figure 6. Figure 6: Top panel: The total SMBH mass growth rate per unit Mpc3 as a function of redshift for each SFR classifica￾tion phase (colors) and for all bins together (black). Bottom panel: The cumulative version of the top panel, showing the growth of SMBH mass over time. straints …
Figure 7
Figure 7. Figure 7: The MBH–Mstar ratio as a function of λsBHAR at z = 0 for the fiducial model and Model Variations 1 and 2, similar to [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 8
Figure 8. Figure 8: Individual galaxy growth histories on the MBH–Mstar relation for our fiducial model (left panel), Model Variation 1 (center panel) and Model Variation 2 (right panel), similar to [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: The z = 0.5 and z = 2 MBH–Mstar relations for the fiducial model and Model Variations 1 and 2, similar to [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: The MBH–Mstar relations at z = 0 for the fiducial model (left panel), Model Variation 3 (center panel), and Model Variation 4 (right panel). Model Variation 3 assumes a strong correlation between MBH, Mstar, and SFR at z = 0. Model Variation 4 assumes a tight correlat…
Figure 11
Figure 11. Figure 11: The MBH–Mstar ratio as a function of λsBHAR at z = 0 for the fiducial model and Model Variations 3 and 4, similar to [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Individual galaxy growth histories on the MBH–Mstar relation for our fiducial model (left panel) compared to Model Variation 3 (center panel) and Model Variation 4 (right panel), similar to [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: The z = 0.5 and z = 2 MBH–Mstar relations for the fiducial model and Model Variations 3 and 4, similar to [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]

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