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REVIEW 3 major objections 4 minor 29 references

Spins of SMBHs in distant low luminosity AGNs

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read For 33 distant low-luminosity AGNs, estimated black hole spin rises steeply with mass, a correlation the authors attribute to disk accretion.

desk verdict 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. read the letter →

arxiv 2506.22207 v1 pith:RNZ7WNGQ submitted 2025-06-27 astro-ph.HE astro-ph.GA

M.Yu. Piotrovich , S.D. Buliga , T.M. Natsvlishvili This is my paper · ORCID
classification astro-ph.HEastro-ph.GA
keywords supermassiveblackholesholespinlow-luminosityAGNradiativeefficiencydiskaccretionhigh-redshiftJWST
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

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.

What carries the argument

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.

What would settle it

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.

Watch

Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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 / 4 minor

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.

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 (3)
  1. [Section 3, Eqs. (1)–(2)] 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.
  2. [Section 3, inclination adjustment] 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.
  3. [Section 4, caveat] 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.
minor comments (4)
  1. [Section 1] The sentence 'In Su et al. (2017) authors showed' should read 'Su et al. (2017) showed'.
  2. [Section 2] 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.
  3. [Table 1] 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.
  4. [Figure 12] 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.

Circularity Check

2 steps flagged · score 7.0 of 10

The spin–mass correlation is largely constructed by the estimator: Eq. (1) injects M8 directly into ε, so the reported a–log M relation is a deterministic consequence of the already strong Lbol–M correlation rather than independent evidence for disk accretion.

  1. self definitional [Section 3, Eq. (1) and Eq. (2); Section 5 / Fig. 12]
    "ε (a) = 0.073 ( Lbol /10^46 erg/s ) ( Lopt /10^45 erg/s )^-1.5 × (4400 Å /5100 Å)^-2 M8 μ^1.5 ... The dependence of the estimated spin values on the estimated SMBH masses shows strong correlation between them (Pearson correlation coefficient is 0.72). Linear fitting by least squares method gives us a = (0.65 ± 0.11) log(MBH/M⊙) − (4.12 ± 0.82)."

    Through Eq. (2), Lopt is a fixed function of Lbol alone, so Eq. (1) makes ε a deterministic algebraic function of exactly the two quantities whose correlation is then reported: ε ∝ M8 × Lbol^-0.5 × BC(Lbol)^1.5. The paper's own Fig. 5 shows log Lbol = (0.73 ± 0.09) log MBH + const with r = 0.83; inserting this covariance into the estimator produces a positive ε–M relation even if the spins carry no independent astrophysical signal. Eq. (8) then maps that forced ε–M trend into the steep a–log M relation of Fig. 12. The disk-accretion interpretation is therefore not independent of the estimator's built-in M8 scaling; no permutation or null test separates the astrophysical correlation from the mathematical consequence of the adopted formula.

  2. self citation load bearing [Section 4, Fig. 11 discussion]
    "In our work Piotrovich et al. (2024) we obtain very similar (within error limits) relation for red quasars."

    This corroborating comparison is made with the authors' own previous red-quasar sample, which the present paper states was analyzed 'for consistency with our previous work' using the same Hopkins et al. (2007) bolometric correction and the same style of M8-dependent estimator. Since the same M8-carrying formula is applied to both samples, similarity between the two spin–mass relations is expected by construction and does not provide independent support for the disk-accretion conclusion.

full rationale

The central derivation is not self-contained in the way a measurement-driven relation should be. Eq. (1) already contains M8 linearly, and Eq. (2) removes Lopt as an independent variable, so the estimated ε (and hence a) is an algebraic transform of (Lbol, MBH). The sample's strong Lbol–MBH correlation (r = 0.83, slope 0.73) therefore forces a positive spin–mass correlation before any astrophysical spin-up mechanism is invoked. The per-object inclination adjustment adds a further free parameter that keeps ε within the allowed band, so the quoted distribution is the result of a search procedure rather than independent measurement. The paper's own caveats (Section 4: estimates 'cannot be considered as exact values for each individual object') do not address this built-in functional dependence. The comparison with the authors' earlier red-quasar work is also not an external check because it relies on the same estimator. These issues make the headline claim (disk accretion as the main mass-growth mechanism, inferred from Fig. 12) largely a consequence of the chosen estimator plus the input Lbol–M correlation; however, the estimator itself is an externally cited empirical formula and the Bardeen mapping is nonlinear, so the paper is not wholly reducible to a definition. Score 7 reflects strong partial circularity rather than complete tautology.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The analysis rests on the Shakura-Sunyaev disk model, the Trakhtenbrot (2014) efficiency formula, the Hopkins et al. (2007) bolometric correction, virial mass estimators, and the input catalog from Juodzbalis et al. (2025). The only free parameter is the inclination angle, tuned per object. No new physical entities are introduced.

free parameters (2)
  • Inclination angle i = 30° for most objects; 25°, 35°, 55° for 7 objects (Table 1)
    Adjusted per object until the derived efficiency falls in the physically allowed range 0.039-0.324; not independently measured.
  • Efficiency acceptance range = [0.039, 0.324]
    Used to accept an inclination solution; from Thorne (1974), but the search procedure biases the spin distribution.
assumptions (5)
  • domain assumption Shakura-Sunyaev thin disk model applies to these high-z LLAGNs
    Invoked in Section 3 to justify using Eq (1); the paper acknowledges the model's shortcomings.
  • domain assumption Trakhtenbrot (2014) efficiency formula (Eq 1) is valid for distant low-luminosity AGNs
    The formula is designed for distant quasars; its applicability to JWST-selected LLAGNs is assumed without direct verification.
  • domain assumption Hopkins et al. (2007) bolometric correction (Eq 2) maps Lbol to Lopt for these objects
    Lopt is derived from Lbol via Eq (2), so the efficiency is effectively a function of Lbol and M8; the correction's validity at high z is assumed.
  • domain assumption Virial mass estimators (Decarli et al. 2008; Bentz et al. 2013) hold at high redshift
    Used to recompute M*_BH; assumes RBLR-L5100 relation and the f factor are valid for these objects.
  • domain assumption Input masses and luminosities from Juodzbalis et al. (2025) are accurate
    The entire analysis inputs the catalog values without independent verification; one object was excluded due to large errors.

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Cite this review

Pith. "Pith review of Spins of SMBHs in distant low luminosity AGNs." pith.science (2026). https://pith.science/paper/RNZ7WNGQ

@misc{pith2026250622207,
  author       = {Pith},
  title        = {Pith review of: Spins of SMBHs in distant low luminosity AGNs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RNZ7WNGQ}},
  note         = {Machine review of arXiv:2506.22207}
}
read the original abstract

We estimated radiative efficiency, spin and SMBH mass values for sample of 33 distant low luminosity AGNs. The distribution of the estimated spin values (majority of objects have a spin greater than 0.8) is fairly typical for many types of AGNs. The dependence of the estimated spin values on the estimated SMBH masses shows strong correlation between them, which suggests a rapid increase in spin with mass, i.e. that the main mechanism of mass growth in this case is disk accretion. We did not find any significant qualitative differences in the spin characteristics between our objects and objects of other types considered in the paper.

Figures

Figures reproduced from arXiv: 2506.22207 by the authors.

Figure 1
Figure 1. Distribution of the cosmological redshift for the initial sample. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Distribution of the SMBH mass for the initial sample. [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Distribution of the bolometric luminosity for the initial sample. [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Distribution of the Eddington ratio for the initial sample. [PITH_FULL_IMAGE:figures/full_fig_p003_4.png]
Figure 5
Figure 5. Figure 5: Dependence of the bolometric luminosity on the SMBH mass for the initial sample, for sample [PITH_FULL_IMAGE:figures/full_fig_p004_5.png]
Figure 6
Figure 6. Figure 6: Radiative efficiency coefficient as the function of the spin value. [PITH_FULL_IMAGE:figures/full_fig_p005_6.png]
Figure 7
Figure 7. Figure 7: Normalized distribution of the estimated spin values for our sample, for sample of red quasars [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]
Figure 8
Figure 8. Figure 8: Distribution of the estimated SMBH masses. [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: Dependence of the estimated spin values on the cosmological redshift. [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: Dependence of the estimated SMBH masses on the cosmological redshift. [PITH_FULL_IMAGE:figures/full_fig_p009_10.png]
Figure 11
Figure 11. Figure 11: Dependence of the estimated radiative efficiency on the estimated SMBH masses. Solid line is [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 12
Figure 12. Figure 12: Dependence of the estimated spin values on the estimated SMBH masses for our sample, for [PITH_FULL_IMAGE:figures/full_fig_p010_12.png]

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Reference graph

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