{"id":"21112e14-57ff-4ebd-b27d-57a5ce5b851e","arxiv_id":"2506.22207","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Spin estimates for 33 high-redshift low-luminosity AGNs show a spin-mass correlation that the authors attribute to disk accretion.","lead":"This paper estimates spins, radiative efficiencies, and masses for 33 distant, low-luminosity active galactic nuclei, finding that most have high spin and that spin rises with black hole mass. It matters because it is one of the first attempts to measure spin in this JWST-visible population, though the result is heavily model-dependent.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The spin–mass correlation is largely produced by the estimator itself: Eq. (1) contains M8 explicitly, so recovering a positive a–M relation is not independent evidence for disk-accretion-driven growth.","rationale":"The reader's weakest assumption targets exactly the right link: Eq. (1) plus Eq. (2) makes each recovered spin a deterministic function of the reported M8 and Lbol, so a spin–mass correlation can appear without any physical spin–mass relation. I sharpen this by noting that Eq. (1) contains M8 explicitly, making the sign of the correlation essentially unavoidable, and the inclination loop cannot rescue the inference because it only selects μ to keep ε in the physical range. The paper is transparent about uncertainties and presents the table and distributions clearly, but no amount of per-object caveats removes the need for a null test before claiming that disk accretion dominates SMBH growth. The permutation test is inexpensive and would settle the matter. I therefore agree with the reader's REJECT verdict and recommend no change. My agreement is with the reader's weakest_assumption; the same null-model logic applies to the efficiency–mass correlation in Fig. 11.","tokens_in":7907,"tokens_out":12504,"duration_ms":145150,"concrete_test":"Permutation null test: run the authors' full pipeline (Eqs. 1, 2, 7, 8 and the inclination loop), using the observed line widths and selection rules, on 1000 datasets in which the observed M8 values are kept and the observed Lbol values are randomly permuted, breaking the physical Lbol–M8 covariance. Fit a vs log M* and record r and slope. If the observed r≈0.72 and slope≈0.65 fall within the null distribution, Fig. 12 is an artifact of the estimator; if they are far outside it, part of the signal may be physical. A secondary check is to re-derive Table 1 from the verbatim Trakhtenbrot (2014) formula, since Eq. (1) as printed is dimensionally inconsistent.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (Fig. 12, Section 5: a = (0.65±0.11) log M − 4.12, r=0.72) is not an independent spin measurement. Eq. (1) inserts M8 linearly into ε, and Eq. (2) makes Lopt a deterministic function of Lbol alone. For fixed inclination, the recovered ε is therefore ε ∝ M8 × Lbol^(−1/2) × BC(Lbol)^(3/2), an algebraic function of exactly the two quantities whose correlation is then reported (BC is the Eq. (2) correction factor). Because the sample already has Lbol ∝ M^0.73 with r=0.83, the estimator forces a positive ε–M relation, which maps through the Bardeen relation (Eq. 8) into a steep a–M correlation. The per-object inclination adjustment (Section 3) does not add astrophysical information; it only finds a μ that keeps ε in [0.039,0.324], so the reported relation survives that filter by construction. A permutation test on (Lbol, M8) pairings would show whether any residual correlation remains when the physical covariance is destroyed. Until such a null test is done, the conclusion that disk accretion dominates mass growth is not supported; the same caveat applies to the efficiency–mass relation in Fig. 11. The paper's transparent caveats (Section 4) acknowledge per-object limitations but do not address this built-in functional dependence. As a separate note, Eq. (1) as printed has units (erg/s)^(−1/2) unless constants carry hidden dimensions; a check against Trakhtenbrot (2014) is warranted.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript estimates radiative efficiency, spin, and black-hole mass for 33 distant low-luminosity AGNs drawn from the JADES survey (Juodzbalis et al. 2025). The method combines the Trakhtenbrot (2014) efficiency formula with the Hopkins et al. (2007) bolometric correction and an adaptive inclination angle. The authors report a strong correlation between the estimated spin and estimated mass (a = (0.65 ± 0.11) log(M/M_sun) - 4.12, r = 0.72), which they interpret as evidence that disk accretion is the dominant mass-growth mechanism. They also present distributions of spin, mass, Eddington ratio, and comparisons with other AGN samples.","tokens_in":8256,"tokens_out":8842,"duration_ms":91493,"significance":"If the spin–mass correlation were astrophysically genuine, the result would be a useful constraint on SMBH growth at high redshift and would complement spin measurements from X-ray reflection. The paper is transparent about several per-object limitations and uses a plausible, published efficiency model. However, the central claim is compromised because the efficiency estimator explicitly contains the black-hole mass, and the paper does not provide a null test that would separate an astrophysical signal from a mathematical consequence of the method. The comparison samples are processed with the same estimator, so they do not resolve this concern.","major_comments":[{"comment":"The estimated efficiency ε is a deterministic function of Lbol and M8 for fixed μ: substituting Eq. (2) into Eq. (1) gives ε ∝ M8 Lbol^(-1/2) BC(Lbol)^(3/2), where BC is the bolometric correction factor. Because the sample already has a strong Lbol–M8 correlation (r = 0.83, reported in Section 2), the positive ε–M8 and a–M8 correlations in Figs. 11 and 12 are expected even in the absence of any intrinsic spin–mass relation. The authors must demonstrate that their correlation is not an artifact of this functional dependence, for example by a permutation test that randomizes the (Lbol, M8) pairings while preserving the individual distributions, or by using a spin estimator that does not contain M8 explicitly. Without such a null test, the conclusion in Section 5 that disk accretion is the main growth mechanism is not supported.","section":"Section 3, Eqs. (1)–(2)"},{"comment":"The adaptive inclination procedure (starting at i = 30° and adjusting in ±5° steps until ε falls in [0.039, 0.324]) acts as a selection filter that can bias the sample toward specific ε values and can create or amplify correlations between ε and M8. The paper should report how many objects required i ≠ 30°, how many adjustment steps were needed, and how the results in Figs. 11–12 change if all objects are processed at a fixed inclination without the validity filter. This would test whether the reported correlations are robust to the filtering.","section":"Section 3, inclination adjustment"},{"comment":"The statement that the estimates 'cannot be considered as exact values for each individual object' but 'have statistical significance for the entire sample as a whole' does not address the built-in functional dependence of the estimator. The statistical significance of the sample correlation is exactly the quantity that is biased by Eq. (1). The authors should either provide a control sample of objects with no known spin–mass relation processed through the same pipeline, or explicitly reframe the result as a property of the estimator rather than as an astrophysical measurement.","section":"Section 4, caveat"}],"minor_comments":[{"comment":"The sentence 'In Su et al. (2017) authors showed' should read 'Su et al. (2017) showed'.","section":"Section 1"},{"comment":"The statement that the redshift distribution 'appears to be close to log-normal, so we can conclude that there are no significant differences from a random distribution' is unclear: a log-normal distribution is not a random (uniform) distribution, and the inference does not follow.","section":"Section 2"},{"comment":"Consider adding the original catalog identifiers from Juodzbalis et al. (2025) to make the objects traceable; the current short names (e.g., GS-30148179) are not self-explanatory.","section":"Table 1"},{"comment":"The fit line is drawn over the combined sample of three datasets; it would be clearer to show the fit for the LLAGN sample alone and to distinguish the three samples in the legend.","section":"Figure 12"}],"recommendation":"reject","confidential_remarks":"The central claim of the paper appears to be a mathematical consequence of Eq. (1) combined with the Lbol–M8 correlation in the input sample. A permutation null test could in principle be added, but if the correlation persists after such a test it would still reflect the explicit M8 dependence in the estimator; if it disappears, the paper's main conclusion would need to be withdrawn. Since the manuscript as submitted does not include any such test and the main interpretation rests on this correlation, I do not see how the paper can be accepted in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know: this paper estimates spins for 33 JADES low-luminosity AGNs using the Trakhtenbrot (2014) efficiency formula and reports a strong spin–mass correlation (r=0.72) that they interpret as evidence for disk accretion growth. The sample is new, and the paper is transparent about its limitations. But the headline result is not trustworthy: the estimator explicitly contains M8 (Eq. 1), and the bolometric correction (Eq. 2) makes Lopt a deterministic function of Lbol, so ε (and hence a) is a mathematical function of M8 and Lbol. Given the already strong Lbol–M8 correlation in the sample (r=0.83), a positive ε–M relation and therefore a positive a–M relation are largely built in. No null test (e.g., permuting Lbol across M8 values) is presented, so the central claim is unsupported.\n\nWhat is new: the 33 objects are from JADES, a population not previously probed this way. The table with derived values is useful, and the distributions and comparisons with other samples are clearly presented. The lack of a spin–redshift correlation is a reasonable null result, and the authors are careful to call their values statistical rather than per-object. Credit is due for the clear presentation and honest caveats.\n\nThe soft spots: the main one is circularity. The paper acknowledges method limitations but never addresses the fact that the spin estimator directly inherits M8. The per-object inclination adjustment only widens the acceptance range and cannot add astrophysical signal. The fit slope is close to what the formula alone would produce. There is also a minor units issue in Eq. (1) (dimensions don't balance unless constants carry hidden units) that should be checked against Trakhtenbrot. These issues mean the paper's principal interpretation is not yet justified.\n\nBottom line: this is a useful dataset and a good cautionary example, but the spin–mass correlation as evidence for disk accretion does not hold up. A serious referee should ask for a permutation test and a demonstration that any residual correlation survives after removing the functional dependence. As is, I would not accept the claim. But I would not desk-reject the manuscript; it deserves review because the sample is valuable and the flaw is fixable with additional analysis.\n\nRecommendation: send to peer review, but expect major revision and require the null test. If I were the reviewer, I'd reject the current version.","headline":"The new JADES LLAGN sample is welcome, but the reported spin–mass correlation is largely a consequence of the estimator, not of disk accretion physics.","tokens_in":8786,"tokens_out":4365,"would_cite":false,"duration_ms":43658,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"For 33 distant low-luminosity AGNs, estimated black hole spin rises steeply with mass, a correlation the authors attribute to disk accretion.","keywords":["supermassive black holes","black hole spin","low-luminosity AGN","radiative efficiency","disk accretion","high-redshift AGN","JWST"],"falsifier":"Compute spins for the same 33 objects with an independent technique that does not use the Trakhtenbrot efficiency formula, such as X-ray reflection (Fe K$\\alpha$) fitting or optical/UV continuum fitting, and check whether the $a$--$M_{\\rm BH}$ correlation with slope near 0.65 and $r\\approx0.7$ survives.","tokens_in":7725,"feed_emoji":"🕳️","tokens_out":9416,"duration_ms":88321,"temperature":0.7,"pith_summary":"The paper estimates radiative efficiencies, spins, and black hole masses for 33 distant low-luminosity active galactic nuclei drawn from a recent JWST-based sample. Its central result is a strong correlation between estimated spin and estimated mass, $a=(0.65\\pm0.11)\\log(M_{\\rm BH}/M_\\odot)-(4.12\\pm0.82)$ with Pearson $r=0.72$: the more massive black holes in this sample spin fastest. The authors interpret this as evidence that the main mass-growth mechanism in this population is disk accretion, which spins the black hole up, rather than chaotic accretion or mergers. If correct, the result carries the spin-driven growth picture into a distant, low-luminosity regime and suggests these objects are not qualitatively different from other AGN types.","feed_headline":"Distant faint black holes spin faster when more massive","feed_subtitle":"Spin estimates for 33 JWST-era AGNs rise steeply with mass, pointing to disk accretion as the growth engine.","key_machinery":"The argument is carried by the radiative-efficiency-to-spin conversion. From the Shakura--Sunyaev thin-disk model, the efficiency $\\varepsilon(a)$ is tied to the spin through the radius of the innermost stable circular orbit, using the Bardeen et al. (1972) formula (Eqs. 8--9). The efficiency for each object is obtained from the Trakhtenbrot (2014) formula (Eq. 1), which takes bolometric luminosity, optical luminosity at 4400 \\AA, and black hole mass as inputs, with the optical luminosity derived from the Hopkins et al. (2007) bolometric correction (Eq. 2). Black hole masses are re-derived self-consistently from the broad-line region radius--luminosity relation, and the inclination angle is adjusted in $5^\\circ$ steps whenever the standard $i=30^\\circ$ does not give a physical solution. This chain converts the two observed quantities $L_{\\rm bol}$ and $M_{\\rm BH}$ into a spin estimate for every object.","core_discovery":"The central discovery is that, for a sample of 33 distant low-luminosity AGNs with redshifts $z\\approx2.3$--$8.9$, the dimensionless spin parameter $a$ estimated from radiative efficiency increases steeply with estimated black hole mass, following $a=(0.65\\pm0.11)\\log(M_{\\rm BH}/M_\\odot)-(4.12\\pm0.82)$ with Pearson $r=0.72$, and most objects have $a>0.8$. The authors take this steep spin--mass relation as a signature that these supermassive black holes grow mainly through coherent disk accretion, which transfers angular momentum and spins the hole up, rather than through randomized accretion episodes or mergers that would leave lower, more scattered spins. They also report no significant correlation between spin and redshift ($r=0.16$) and no qualitative difference in the spin distribution compared with red quasars, local Seyferts, and other AGN samples.","pith_inferences":["Because each spin value in this method is a deterministic function of the same bolometric luminosity and black hole mass used to build the correlation, part of the reported $r=0.72$ may be built into the assumed formulas rather than coming from independent astrophysics.","An independent check using X-ray reflection or continuum-fitting spin measurements on the same 33 objects would test whether the steep spin--mass trend survives outside the Trakhtenbrot (2014) framework.","The procedure of adjusting inclination until a physical spin is obtained could bias the sample toward higher spins and toward a steeper spin--mass relation; quantifying that bias would sharpen the interpretation.","If the spin--mass relation is real, the highest-mass faint AGNs should show the most relativistic reflection signatures, a prediction that future X-ray observations with the same sample could test."],"forward_implications":["The steep spin--mass relation indicates that disk accretion, not chaotic accretion or mergers, dominates the mass growth of supermassive black holes in this distant low-luminosity population.","The prevalence of $a>0.8$ among most objects suggests these black holes have been efficiently spun up by their accretion history.","The absence of a spin--redshift correlation in the sample, if selection effects are properly accounted for, implies no strong spin evolution across $z\\approx2$--$9$ in this luminosity regime.","Similarity of the spin distribution to those of red quasars and local AGNs points toward a common spin-growth physics across very different AGN classes.","The authors caution that individual spin values are not exact and that the result should be read as a statistical property of the whole sample rather than a measurement of any single object."],"supporting_citations":[{"why":"Supplies the initial JWST-based sample of 34 distant low-luminosity AGNs with redshifts, black hole masses, and bolometric luminosities; one object is excluded for large errors.","marker":"Juodzbalis et al. (2025)"},{"why":"Provides Eq. (1), the radiative-efficiency formula designed for distant AGNs that converts luminosity and mass into efficiency.","marker":"Trakhtenbrot (2014)"},{"why":"Provides Eq. (2), the bolometric correction linking $L_{\\rm opt}$ to $L_{\\rm bol}$ that feeds the efficiency estimate.","marker":"Hopkins et al. (2007)"},{"why":"Supplies the ISCO-based relation between radiative efficiency and spin used in the numerical spin computation.","marker":"Bardeen et al. (1972)"},{"why":"Gives the broad-line region radius--luminosity relation used to recompute black hole masses self-consistently.","marker":"Bentz et al. (2013)"},{"why":"Supplies the $L_{5100}$ bolometric correction used in the mass and luminosity conversions.","marker":"Richards et al. (2006)"},{"why":"Provides the comparison efficiency--mass relation shown in the paper's Fig. 11 and the wider range of efficiencies against which the new sample is compared.","marker":"Davis & Laor (2011)"}],"fun_headline_variants":["Distant AGN spins rise steeply with black hole mass","Faint AGNs hint: black hole mass drives spin-up","Spin-mass trend in distant AGNs points to disk accretion","Massive distant black holes spin fastest in AGN sample","High spins in far-off AGNs correlate with mass"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole result stands or falls on the assumption that the adopted radiative-efficiency formula, fed with bolometric luminosity and black hole mass, returns a true spin for each object; if that formula is wrong, the spin-mass correlation is an artifact rather than an astrophysical signal.","fun_headline_variants_meta":{"raw":{"variants":["Distant AGN spins rise steeply with black hole mass","Faint AGNs hint: black hole mass drives spin-up","Spin-mass trend in distant AGNs points to disk accretion","Massive distant black holes spin fastest in AGN sample","High spins in far-off AGNs correlate with mass"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000704,"raw_usage":{"total_tokens":3122,"prompt_tokens":838,"completion_tokens":2284,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":454,"completion_tokens_details":{"reasoning_tokens":2202}},"tokens_in":454,"tokens_out":2284,"duration_ms":16168,"temperature":1.0,"reasoning_tokens":2202,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T22:08:57.804540+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute spins for the same 33 objects with an independent technique that does not use the Trakhtenbrot efficiency formula, such as X-ray reflection (Fe K$\\alpha$) fitting or optical/UV continuum fitting, and check whether the $a$--$M_{\\rm BH}$ correlation with slope near 0.65 and $r\\approx0.7$ survives.","supporting_citations":[{"cited_title":"2014, ApJ, 789, L9 4, 5, 6","cited_arxiv_id":null,"evidence_quote":"Provides Eq. (1), the radiative-efficiency formula designed for distant AGNs that converts luminosity and mass into efficiency."},{"cited_title":"M., Press, W","cited_arxiv_id":null,"evidence_quote":"Supplies the ISCO-based relation between radiative efficiency and spin used in the numerical spin computation."},{"cited_title":"C., Denney, K","cited_arxiv_id":null,"evidence_quote":"Gives the broad-line region radius--luminosity relation used to recompute black hole masses self-consistently."},{"cited_title":"T., Lacy, M., Storrie-Lombardi, L","cited_arxiv_id":null,"evidence_quote":"Supplies the $L_{5100}$ bolometric correction used in the mass and luminosity conversions."},{"cited_title":"W., & Laor, A","cited_arxiv_id":null,"evidence_quote":"Provides the comparison efficiency--mass relation shown in the paper's Fig. 11 and the wider range of efficiencies against which the new sample is compared."}],"review_version":1}