{"id":"0da6ab07-c854-436a-8155-67b2ffc0f9a9","arxiv_id":"2411.08838","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Using observed black hole accretion rates and local scaling relations, an empirical model shows the most massive black holes grew little since z=2 while lower-mass black holes assembled gradually.","lead":"Astronomers built a data-driven model of how supermassive black holes grow inside galaxies from redshift 2 to today. The model finds that the biggest black holes formed early, while smaller ones grew gradually, producing diverse co-evolution paths.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Headline result may be partially baked into the Mstar-normalized accretion prescription, which the robustness tests do not exercise.","rationale":"The paper is a careful empirical reconstruction, and it should be credited for testing four model variations and for consistency with the independent Guetzoyan et al. (2024) analysis. The reader's identified weakest assumption, the factor-of-two obscuration correction, is real but secondary: adjusting the obscured fraction changes the overall normalization of BHAR, yet it does not address whether accretion should be tied to Mstar (sBHAR) or to MBH (Eddington ratio). The central claim concerns exactly the population where these two normalizations diverge most, because overmassive SMBHs have fEdd well below λ_sBHAR under the fiducial assignment. Since every model variation draws λ_sBHAR from distributions independent of MBH, none of them can falsify the possibility that the true Eddington-ratio distribution is the relevant SFR-dependent quantity; the observed p(λ_sBHAR) alone does not uniquely determine growth histories. This is not a claim that the paper is wrong, but it identifies a load-bearing assumption that should be tested explicitly before the headline conclusion is treated as robust. I therefore retain the CONDITIONAL verdict, with the recommended condition expanded to include a direct test of this accretion-normalization degeneracy.","tokens_in":29696,"tokens_out":14896,"duration_ms":145249,"concrete_test":"Within each SFR/redshift bin, replace the fiducial random draw of λ_sBHAR independent of MBH with a draw of fEdd from a distribution p(fEdd | SFR, z) chosen so that the implied λ_sBHAR = fEdd × (MBH/Mstar)/0.002 reproduces the Aird et al. (2019) p(λ_sBHAR) after marginalizing over the model's z=0 MBH–Mstar scatter; recompute the backward growth histories with the same z=0 boundary conditions. If the median fractional z=0–2 growth of z=0 SMBHs above log MBH/Msun ≈ 8.5 shifts by more than roughly 0.1–0.2 dex relative to the fiducial model, the headline claim is sensitive to the Mstar- versus MBH-normalization degeneracy and should be qualified accordingly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.4.2 assigns accretion by drawing λ_sBHAR — defined with a denominator proportional to Mstar (Eq. 1) — from Aird et al. (2019) distributions that depend only on SFR bin and redshift, not on the SMBH mass of the host. Since fEdd = Lbol/LEdd = λ_sBHAR × (0.002 Mstar/MBH), a galaxy with an overmassive SMBH is assigned a systematically low Eddington ratio by construction (Fig. 2). The z=0 SMBHs claimed to grow very little since z=2 are exactly those with high MBH/Mstar, so their suppressed late growth is partly a consequence of the choice to make accretion rates scale with Mstar rather than MBH. Model Variations 1 and 2 only re-rank which galaxies receive the same λ_sBHAR values; they do not change the underlying dependence of absolute growth rate on Mstar versus MBH, and therefore cannot test the main alternative: that the physical Eddington-ratio distribution is the quantity tied to host SFR. The observed p(λ_sBHAR) is a convolution of p(fEdd) with the MBH/Mstar distribution, so the same observational constraint may be consistent with very different growth histories for overmassive SMBHs. The central claim is thus conditional on an untested degeneracy in the accretion-rate normalization, independent of the secondary factor-of-two obscuration uncertainty.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":29921,"tokens_out":6799,"duration_ms":63008,"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":[{"comment":"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.","section":"§2.4.2, Eq. (1), Eq. (7)"},{"comment":"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.","section":"§2.4.2, §7.4"},{"comment":"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.","section":"§7.4, Fig. 5"}],"minor_comments":[{"comment":"There is a typo in the Introduction: 'distrubiton' should be 'distribution'.","section":"§1"},{"comment":"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'.","section":"§8"},{"comment":"The phrase 'serves as a complimentary approach' should be 'complementary approach'.","section":"§8"},{"comment":"The caption for Fig. 9 says 'similar to Figure 9', which should likely refer to Fig. 4 or another appropriate figure.","section":"§5, Fig. 9"},{"comment":"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.","section":"§5, Fig. 5 caption"},{"comment":"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.","section":"§2.4.2"}],"recommendation":"major_revision","confidential_remarks":"The paper is transparent about its construction and the model variations are a strength, but the central claim rests on the assumption that the Mstar-normalized sBHAR distribution is the fundamental quantity driving accretion, rather than the Eddington ratio. The requested alternative-normalization test should be feasible within the same framework and would materially change my assessment of whether the early-assembly conclusion is robust or an artifact of the normalization choice."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe paper builds empirical SMBH growth histories on top of UniverseMachine galaxies and claims the most massive local SMBHs grew very little since z=2. That result is a genuine model output, not a fitted parameter, but it is contingent on an assumption the robustness tests don't reach.\n\nWhat's new and good: This is the first full reconstruction I know of that tracks individual SMBH growth from z=0 back to z=2 in a realistic galaxy model, and it yields a concrete prediction for the evolution of the MBH-Mstar relation—higher normalization, shallower slope. The authors are transparent that the z=0 relations and sBHAR distributions are reproduced by construction. The \"low growth of massive SMBHs\" conclusion survives four variations that change how lambda_sBHAR is assigned and how z=0 masses are set, and it lines up with Guetzoyan et al. (2024). That's real evidence.\n\nThe soft spot: the stress-test note is right. The model assigns accretion using lambda_sBHAR proportional to Lbol/Mstar, not Eddington ratio. Because fEdd = lambda_sBHAR x (0.002 Mstar/MBH), a galaxy with an overmassive SMBH gets a systematically low Eddington ratio by construction. The most massive SMBHs are exactly those with high MBH/Mstar, so their suppressed late growth is partly baked into the choice of normalization. Model Variations 1 and 2 re-rank which galaxies receive the same lambda values; they do not change the underlying dependence of growth rate on Mstar versus MBH. So the central claim depends on an untested degeneracy. The authors note lambda_sBHAR does not equal fEdd in general, but they never test the alternative that the physical Eddington-ratio distribution is the quantity tied to SFR. That is the main reason I scored it conditional.\n\nOther soft spots are minor: the factor-of-two obscuration correction is crude, there are no error bars on the model outputs, and the authors themselves flag the burstiness of UniverseMachine star formation histories. These are addressable and don't break the logic.\n\nWho this is for: anyone working on SMBH-galaxy coevolution, AGN demographics, or empirical models of black hole growth. The method is a useful framework even if the headline conclusion shifts under a different normalization assumption.\n\nRecommendation: send to peer review. The paper deserves serious referee time. A good referee will push for a test that replaces lambda_sBHAR with a physically motivated p(fEdd) and see if the massive-SMBH conclusion survives. That would settle whether the result is real or an artifact of the Mstar normalization.","headline":"Useful empirical reconstruction of SMBH growth histories, but the headline result is conditional on an untested Mstar-normalized accretion prescription.","tokens_in":30542,"tokens_out":5125,"would_cite":true,"duration_ms":168916,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"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.","keywords":["supermassive black holes","black hole-galaxy coevolution","M_BH-M_star relation","specific black hole accretion rate","AGN","empirical galaxy formation model","black hole mass assembly","quenching"],"falsifier":"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.","tokens_in":29394,"feed_emoji":"🕳️","tokens_out":12391,"duration_ms":94138,"temperature":0.7,"pith_summary":"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.","feed_headline":"Most massive black holes were mostly in place by z=2","feed_subtitle":"An empirical reconstruction from z=0 to z=2 shows the biggest SMBHs grew little; smaller ones grew late.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the dark-matter-based empirical galaxy-formation model whose galaxy growth histories and SFRs host the SMBH growth reconstruction.","marker":"Behroozi et al. (2019)"},{"why":"Supplies the observed probability distributions of specific black hole accretion rate as a function of star-formation activity, the input that drives all SMBH mass growth in the model.","marker":"Aird et al. (2019)"},{"why":"Supplies the separate z=0 M_BH-M_star relations for quiescent and star-forming galaxies used as the boundary conditions for the backward integration.","marker":"Greene et al. (2020)"},{"why":"Supplies the observed M_BH-M_star-SFR correlation used in Model Variation 3 to test maximal SFR dependence of z=0 black hole masses.","marker":"Terrazas et al. (2017)"},{"why":"Supplies the single tight M_BH-M_star scaling relation used in Model Variation 4 as the opposite extreme with no SFR dependence.","marker":"Kormendy & Ho (2013)"},{"why":"Provides independent measurements of specific accretion rates in massive galaxies that reach a similar conclusion about limited late-time growth of the most massive black holes.","marker":"Guetzoyan et al. (2024)"},{"why":"Provides observational evidence from broad-line AGN that overmassive black holes grow horizontally and undermassive ones grow vertically on the M_BH-M_star plane, supporting the inferred diversity of pathways.","marker":"Zhuang & Ho (2023)"}],"fun_headline_variants":["Big black holes assembled early, small ones gradually","SMBH growth path depends on black hole mass","Massive black holes built early, smaller ones later","Black hole growth sequences vary by mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Big black holes assembled early, small ones gradually","SMBH growth path depends on black hole mass","Massive black holes built early, smaller ones later","Black hole growth sequences vary by mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001204,"raw_usage":{"total_tokens":5028,"prompt_tokens":1082,"completion_tokens":3946,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":698,"completion_tokens_details":{"reasoning_tokens":3887}},"tokens_in":698,"tokens_out":3946,"duration_ms":29517,"temperature":1.0,"reasoning_tokens":3887,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T21:16:56.931624+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":"X-ray AGN in Bo\\\"otes: The lack of growth of the most massive black holes since z=4","cited_arxiv_id":"2408.14297","evidence_quote":"Provides independent measurements of specific accretion rates in massive galaxies that reach a similar conclusion about limited late-time growth of the most massive black holes."}],"review_version":1}