Measuring monster MBHs: maybe mighty, maybe merely massive

A. Akylas; I. E. Papadakis; J. K. Williams; M. Gliozzi

REVIEW 3 major objections 5 minor 70 references

Measuring monster MBHs: maybe mighty, maybe merely massive

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper argues that the standard single-epoch method overestimates black hole masses in super-Eddington AGN, and that early-universe 'monster' black holes may therefore be merely massive, not overmassive.

desk verdict Useful catalog-offset result, but the high-z X-ray benchmark is thin and one correlation is partly tautological. read the letter →

arxiv 2506.08108 v1 pith:VLMU24LW submitted 2025-06-09 astro-ph.HE astro-ph.GA

M. Gliozzi , A. Akylas , J. K. Williams , I. E. Papadakis This is my paper

classification astro-ph.HEastro-ph.GA

keywords blackholemassessingle-epochmethodX-rayscalingsuper-Eddingtonaccretionhigh-redshiftquasarsAGNcatalogslittlereddotsreverberationmapping

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 whether the optical single-epoch (SE) method, calibrated on nearby moderately accreting AGN, can be trusted when it is extrapolated to distant hyperluminous quasars and highly accreting AGN — the regime where recent JWST-era work has claimed surprisingly massive, 'overmassive' black holes in the early universe. Using an independent X-ray scaling method on 12 X-WISSH quasars and 50 X-HESS AGN, the authors find the two methods agree across a broad range of luminosity, absorption, and Eddington ratio, with two exceptions: heavily absorbed AGN, whose SE masses come out too low, and AGN accreting well above the Eddington limit, whose SE masses come out too high. The paper also shows that a widely used quasar catalog underestimates SE masses by a factor of 2.5, and that using the X-ray masses recovers strong correlations (photon index and bolometric correction versus Eddington ratio, photon index versus soft excess) that vanish with the catalog values. If correct, the work weakens the case that early-universe highly accreting AGN host overmassive black holes, and it warns that automated catalog masses can decide which AGN correlations are found.

What carries the argument

The central instrument is the X-ray scaling method, which estimates an AGN's black hole mass by scaling the dynamically measured mass of a stellar-mass black hole (GX 339-4, GRO J1655-40, or XTE J1550-564) using two quantities from a fit of the bulk Comptonization model BMC to the 2–10 keV spectrum: the photon index $\Gamma$, which selects the spectral state, and the BMC normalization, which fixes the scaling of luminosity to mass, $M_{\mathrm{BH,AGN}} = M_{\mathrm{BH,ref}} \times (N_{\mathrm{BMC,AGN}}/N_{\mathrm{BMC,ref}}) \times (d_{\mathrm{AGN}}^2/d_{\mathrm{ref}}^2)$. Its companion benchmark is the Eddington mass $M_{\mathrm{BH,Edd}} = L_{\mathrm{bol}}/(1.3\times10^{38}\,\mathrm{erg\,s^{-1}})$, obtained by assuming the X-WISSH quasars radiate at $L_{\mathrm{bol}} \approx L_{\mathrm{Edd}}$; this benchmark is what lets the paper verify the X-ray method at high redshift and provides the reference against which SE overestimation at super-Eddington rates is judged.

What would settle it

A decisive check would be to measure black hole masses for a handful of super-Eddington AGN with reverberation mapping or dynamical techniques rather than the SE method: if those independent masses come out close to the SE values instead of lower, the overestimation claim fails, and the catalog bias could be separately tested by remeasuring Hβ widths from the same SDSS spectra to reproduce the 0.111 dex offset.

Watch

Extended reading notes

Core claim

On its own terms, the paper establishes that the X-ray scaling method gives credible black hole masses for distant, highly accreting AGN, and that once a catalog-specific bias is removed, the single-epoch method agrees with it everywhere except for heavily absorbed sources (SE too low) and super-Eddington sources (SE too high). The demonstration proceeds in steps: for the 12 X-WISSH quasars, X-ray masses are consistent with the Eddington benchmark $M_{\mathrm{BH,Edd}} = L_{\mathrm{bol}}/(1.3\times10^{38}\,\mathrm{erg\,s^{-1}})$ (mean maximal ratio 2.61, within method uncertainties), while C IV-based SE masses scatter well off the benchmark and are inconsistent with it at high significance; for the 50 X-HESS AGN, X-ray and SE masses are strongly correlated ($r = 0.74$, $P \approx 10^{-9}$) but offset, and a direct catalog comparison shows the Rakshit et al. (2020) values are low by a factor of 2.5 relative to Wu & Shen (2022). After multiplying the SE values by 2.5, the residual outliers are precisely the absorbed and super-Eddington objects. The paper concludes that super-Eddington SE masses are overestimated — by about an order of magnitude for the most extreme sources — casting doubt on claims of overmassive black holes in highly accreting early-universe AGN and in little red dots.

Load-bearing premise

The load-bearing premise is that the twelve X-WISSH quasars really do accrete near the Eddington limit, because that assumption fixes the benchmark masses used to validate the X-ray method; if those quasars actually accrete at a tenth to a third of Eddington, the X-ray masses would be biased high by the same factor, and the claim that the SE method overestimates super-Eddington masses would lose its footing.

Editorial extensions

If this is right

Claims of overmassive black holes in highly accreting early-universe AGN, including some little red dots, rest on single-epoch masses that the paper argues are overestimated by about an order of magnitude in the most extreme cases, loosening the constraints those claims put on black hole seed models.
The Rakshit et al. (2020) SDSS catalog, a standard source of thousands of AGN masses, should be recalibrated upward by a factor of 2.5; the paper shows its Hβ line widths run systematically 0.111 dex narrow.
Which AGN correlations are found can depend on the mass catalog: the paper recovers strong positive correlations of photon index and X-ray bolometric correction with Eddington ratio, and of photon index with soft-excess strength, that are absent or reversed when the underestimated SE masses are used.
C IV-based SE masses should not be trusted for highly accreting quasars; in the X-WISSH comparison they are inconsistent with the Eddington benchmark at high significance.
Extremely super-Eddington AGN are expected to be X-ray weak with steep spectra, which would make moderately luminous high-redshift sources of this kind practically undetectable by current X-ray observatories — a natural explanation for the X-ray elusiveness of little red dots.

Reading between the lines

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

A testable extension: catalog-wide FWHM comparisons like the one against Wu & Shen (2022) could be run for other automated SDSS pipelines; if the 0.111 dex line-width deficit is a general feature of automated fitting, similar factors of about 2.5 may lurk in other widely used mass catalogs.
The super-Eddington overestimation implies the radius–luminosity relation or the virial factor breaks down in that regime; reverberation mapping of a few super-Eddington AGN would show directly whether the BLR radius deviates from the Bentz et al. (2013) relation.
If the recovered Γ–λ_Edd correlation is as tight as reported, photon index could serve as a mass-independent accretion-state indicator, letting Eddington ratios be estimated from X-ray spectra alone — useful precisely where mass estimates are unreliable.
The same X-ray scaling comparison could in principle be applied to JWST-discovered little red dots once their X-ray spectra reach sufficient quality, directly testing whether their reported extreme black-hole-to-galaxy mass ratios shrink.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, the factor-2.5 offset between the Rakshit et al. (2020) and Wu & Shen (2022) mass catalogs is real and directly demonstrated — a practical result worth having. Second, the claim that single-epoch masses overestimate super-Eddington AGN is plausible and consistent with earlier work, but the paper's quantitative case rests on an X-ray benchmark that is thinner than the prose suggests.

The strongest part is the direct catalog comparison in Fig. 3. The Rakshit catalog's own FWHM offset, noted in the text, points in the same direction, and the shifted fit nearly overlapping the one-to-one line is convincing. Applying the X-ray scaling method to the X-HESS sample is a sensible next step, and the authors handle flagged and Civ-based values carefully. The conclusion that SE overestimates the most extreme super-Eddington sources also aligns with Du et al. (2015, 2018), so the direction of the bias is not new, though this sample provides fresh evidence.

The soft spots are real but not fatal. The 12-object WISSH sanity check assumes L_bol ≈ L_Edd. That is an assumption, not a measurement. The mean max ratio of 2.6 with σ/√n ~0.9 is fully consistent with the X-ray masses being systematically high by a factor 2.5–3, which would shift the high-z comparison and change the magnitude of the super-Eddington bias. The paper's counterargument — that lower accretion rates would imply ~10^11 M⊙ BHs — is a reasonable prior but not a proof. The X-HESS sample includes lower-redshift objects, so the catalog-offset claim is anchored locally, but the high-z, high-accretion extension still leans on that assumption.

Second, the KX vs. λ_Edd correlation in Fig. 7 is largely tautological. From Eq. A.2, MBH,X is proportional to NBMC times d², and at fixed Γ that tracks L_X; hence λ_Edd(X) = L_bol/MBH,X is proportional to KX by construction. Reporting that as a confirmed correlation overstates the evidence. The Γ–λ_Edd correlation is less obviously built-in, but it uses the same λ_Edd values, so it is not fully independent.

Third, the factor 2.5 is a sample-average correction. The scatter in Fig. 2 is large (RMS ~0.6 dex), so treating it as a single multiplier for every object is a modeling choice, not a measurement of individual biases.

This paper is for anyone who uses Rakshit et al. masses or interprets little-red-dot mass estimates. The catalog-offset result deserves to be in the literature on its own. The super-Eddington overestimation claim is worth publishing as a suggestive result, with the X-ray benchmark caveat made more prominent. I would send it to a competent referee; the referee should push on the sanity check and the tautological correlation, but neither kills the paper.

Referee Report

3 major / 5 minor

Summary. The paper uses the X-ray scaling method, which anchors BMC Comptonization-model normalizations to dynamically measured stellar-mass black holes, to estimate black hole masses for 12 hyperluminous X-WISSH quasars and 50 X-HESS AGN, and compares them with single-epoch (SE) virial masses from the Rakshit et al. (2020) catalog. The authors report that the SE method overestimates MBH for sources accreting well above Eddington, underestimates MBH for heavily absorbed sources, and that the Rakshit et al. (2020) catalog systematically underestimates MBH by a factor of 2.5. They further argue that several AGN correlations (Gamma vs. lambda_Edd, KX vs. lambda_Edd, and Gamma vs. soft-excess strength) appear only when X-ray-based masses are used, and they use these results to question claims of overmassive black holes in high-redshift, highly accreting AGN and to speculate about little red dots.

Significance. If the central claims hold, the paper provides a useful methodological caution about single-epoch mass estimates in extreme AGN and a concrete catalog-level correction for Rakshit et al. (2020). The direct catalog comparison in Fig. 3 is a clear, checkable result, and the X-ray scaling method has prior support from local dynamically calibrated samples. The paper also reports its statistical diagnostics transparently. However, the high-redshift validity of the X-ray benchmark rests on a 12-object sanity check that assumes Eddington-level accretion, and one of the reported correlations (KX vs. lambda_Edd) is partially built into the method's definitions. These issues make the headline conclusion about super-Eddington SE overestimation less secure than the paper presents.

major comments (3)

[Section 3.1, Fig. 1] The sanity check does not validate the X-ray method at high redshift as strongly as claimed. The benchmark assumes L_bol approximately L_Edd for the 12 X-WISSH quasars, and the quoted mean max ratio of 2.61 with sigma/sqrt(n)=0.93 means a 68% interval of roughly 1.7-3.5, so a systematic factor-of-2.5 bias in M_BH,X is fully consistent with these data. Applying the 0.65 multiplicative factor improves the mean only to 2.33 with sigma/sqrt(n)=0.62, still not a one-to-one match, so the test is not discriminating. Because the subsequent X-HESS comparison, the 2.5 recalibration, and the super-Eddington overestimation result all use M_BH,X as the reference scale, this weak anchor is load-bearing. Please provide an independent high-z calibration (e.g., dynamical masses from [CII] or CO kinematics, or reverberation mapping of lensed systems) or explicitly restrict the claims to the assumption lambda_Edd approximately 1 and propagate the resulting systematic uncertainty.
[Section 3.3, Fig. 7 (top panel)] The strong KX versus lambda_Edd correlation is largely built into the definitions. From Eq. A.2, M_BH,X is proportional to N_BMC times d^2; for a fixed spectral shape, N_BMC is proportional to the observed flux, so M_BH,X scales approximately with L_X at fixed Gamma. Since lambda_Edd(X)=L_bol/M_BH,X and KX=L_bol/L_X, one obtains lambda_Edd(X) proportional to KX up to scatter in Gamma. The reported Spearman r=0.65 and the fit KX=(2.26+0.59 log lambda_Edd) therefore cannot be used as independent evidence for a physical correlation or as validation of the X-ray masses. This does not by itself invalidate the catalog-offset claim, which has separate support in Fig. 3, but it removes one of the paper's advertised implications and makes the contrast with the SE-based null result less meaningful.
[Section 3.2 and Fig. 4] The factor-2.5 recalibration is applied to the SE masses before the residual discrepancies are identified, and the residuals are then interpreted using lambda_Edd computed from the same X-ray masses. This procedure makes the statement that the only discrepancies are super-Eddington and absorbed sources partly a restatement of the recalibration rather than an independent test. In particular, Fig. 4 color-codes sources by log lambda_Edd(M_BH,X) to define the super-Eddington set, so a systematic error in M_BH,X shifts which sources fall into that set. Please report the residual analysis with lambda_Edd derived from the SE masses (recalibrated or not), or use an external accretion-rate indicator, so that the super-Eddington classification is not tied to the very masses being tested.

minor comments (5)

[Section 3.1] KX is first defined as L_bol/L_Edd, but it should be L_bol/L_X; as written it duplicates lambda_Edd and is inconsistent with Fig. 7 and Table B.1.
[Fig. 2 caption] The caption says the SE method uses the Hbeta line, but the figure includes Hbeta, MgII, and CIV symbols; please clarify the line coverage in the caption.
[Section 4] The text contains a duplicated word, 'source source 54', in the list of CIV-based objects.
[Table B.2] The table header says 'Auxiliary table for Table??' and contains an unresolved placeholder; fix the cross-reference.
[Section 3.2] The reported average Hbeta FWHM offset of 0.111 dex translates to a factor of about 1.7 in M_BH if the width enters quadratically, yet the paper derives a factor of 2.5; the relation between these two numbers should be explained.

Circularity Check

1 steps flagged · score 6.0 of 10

The KX–lambda_Edd correlation is partly built into the X-ray mass definition, but the headline SE-versus-X-ray and catalog-offset findings retain independent support.

self definitional [Section 3.3, Fig. 7 (with Eq. A.2 and Section 2.1 definition of lambda_Edd)]
"Top panel: Logarithm of the X-ray bolometric correction factor log(Lbol/LX) plotted vs. log(lambda_Edd), where the latter is computed using the X-ray scaling method. ... A strong positive correlation is obtained with the X-ray-based values, as confirmed by a Spearman coefficient r=0.65 and relative probability P_S=1.9e-8 and a best fit of K_X=(2.26+/-0.01)+(0.59+/-0.01)xlog(lambda_Edd) (RMS=0.33)."

By Eq. A.2, M_BH,X = M_BH,ref * (N_BMC,AGN/N_BMC,ref) * (d_AGN^2/d_ref^2), and the BMC normalization times distance squared tracks the X-ray luminosity at fixed spectral index, so M_BH,X is proportional to L_X. Since lambda_Edd(X) = L_bol/(1.3e38 * M_BH,X) and K_X = L_bol/L_X, lambda_Edd(X) is proportional to K_X. Plotting log K_X against log lambda_Edd(X) therefore regresses a quantity against a monotone function of itself; the strong positive correlation is produced by the mass definition rather than by independent data. The absence of correlation for SE-based lambda_Edd is likewise expected because SE masses do not share this built-in L_X dependence.

full rationale

The paper's central claim that SE masses are overestimated for super-Eddington AGN rests primarily on the direct SE-versus-X-ray comparison in Figs. 2 and 4, and the Rakshit et al. catalog offset is independently supported by the direct Rakshit-versus-Wu-Shen comparison in Fig. 3. Neither of those central results reduces to the paper's assumptions or to a self-citation. However, the Section 3.3 claim of a strong KX-lambda_Edd correlation (r=0.65) is largely circular: lambda_Edd is computed from M_BH,X, and M_BH,X is proportional to the X-ray luminosity by the scaling relation of Eq. A.2, making lambda_Edd(X) proportional to L_bol/L_X = K_X. The high-redshift sanity check in Section 3.1 also assumes the WISSH quasars accrete at L_bol ~ L_Edd in order to define M_BH,Edd; this is an assumption rather than a circular reduction, but it weakens the claimed verification. Overall, the central derivation is not forced by self-citation or pure definition; only the KX-lambda correlation is a constructed relation, giving a partial circularity score of 6.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claims rest on the X-ray scaling method's calibration to stellar mass black holes and on the assumption that X-WISSH quasars accrete near Eddington. The factor 2.5 correction and the reference source tracks are the main numerical inputs; no new physical entities are introduced.

free parameters (3)

Reference source masses and Gamma-NBMC tracks = Values from Shaposhnikov & Titarchuk 2009 and Gliozzi et al. 2011, not re-derived
Equation A.2 scales all AGN masses linearly from these reference values; an error in the reference masses or tracks propagates directly into every MBH_X.
Factor 2.5 SE mass correction = 2.5
Measured from the Rakshit et al. (2020) versus Wu and Shen (2022) comparison in Fig. 3. It is data-driven rather than fit to the X-ray masses, but the central recalibration depends on it.
Multiplicative factor 0.65 for X-ray masses in the WISSH sanity check = 0.65
Chosen in Section 3.1 by iteratively scaling MBH_X to improve agreement with Eddington masses (mean max ratio drops from 2.61 to 2.33). Diagnostic only; not applied to the main sample.

assumptions (3)

domain assumption The luminosity of any BH accreting system is proportional to MBH, mdot, and eta, and the photon index Gamma is a reliable indicator of accretion state, so matching Gamma between an AGN and a stellar mass BH ensures similar mdot and eta.
Appendix A states this as the foundation of the X-ray scaling method.
ad hoc to paper The 12 X-WISSH quasars used in the sanity check accrete close to the Eddington limit, L_bol ~ L_Edd.
Section 3.1: 'It is reasonable to assume that these sources are accreting around the Eddington level... With this simple assumption, L_bol = L_accr = L_Edd.' Used to validate the X-ray method at high z.
domain assumption The single epoch virial product MBH = f * R_BLR * FWHM^2 / G, with R_BLR from the size luminosity relation calibrated locally, remains valid with the same f at high z.
Section 1: the SE method exploits the R_BLR-L_opt correlation calibrated by Bentz et al. (2013); the paper tests but does not assume this holds blindly, yet the comparison treats SE values as meaningful.

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Cite this review

Pith. "Pith review of Measuring monster MBHs: maybe mighty, maybe merely massive." pith.science (2026). https://pith.science/paper/VLMU24LW

@misc{pith2026250608108,
  author       = {Pith},
  title        = {Pith review of: Measuring monster MBHs: maybe mighty, maybe merely massive},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VLMU24LW}},
  note         = {Machine review of arXiv:2506.08108}
}

read the original abstract

Accurate black hole mass (MBH) measurements in high-z galaxies are difficult yet crucial to constrain the growth of supermassive BHs, and to discriminate between competing BH seed models. Recent studies claimed the detection of massive BHs in very distant AGN, implying extreme growth conditions. However, these estimates are usually obtained by extrapolating indirect methods that are calibrated for moderately accreting, low-luminosity AGN in the local universe. To assess the reliability of the single epoch method (SE) in the distant universe, we compute the MBH for a sample of hyper-luminous distant quasars and a sample of highly accreting AGN using the X-ray scaling method. We first verify that this X-ray method yields reliable MBH values for distant highly accreting objects. Then, we carry out a systematic comparison with the SE method and find that these two indirect methods yield consistent MBH over a broad range of luminosities, intrinsic absorption, and accretion rates. The only discrepancies are associated with AGN that are substantially absorbed (underestimated by the SE method), and AGN accreting well above the Eddington limit (overestimated by the SE method). The latter result casts some doubts on the claim of overmassive BHs in highly accreting AGN in the early universe. Our study also reveals that one of the frequently used AGN catalogs consistently underestimates the MBH values by a factor of 2.5. Although this factor is of the order of the uncertainty generally associated with the SE method, we demonstrate that the use of underestimated values may result in potentially misleading conclusions. Specifically, for this AGN sample we confirm strong positive correlations for Gamma vs. lambda_Edd and for the X-ray bolometric correction vs. lambda_Edd, as well as for Gamma vs. the soft excess strength, at odds with the conclusions inferred using underestimated MBH values.

Figures

Figures reproduced from arXiv: 2506.08108 by the authors.

**Figure 1.** Left panel: MBH obtained with the X-ray scaling method plotted vs. the values corresponding to sources accreting at the Eddington level. Middle panel: MBH obtained with the SE method using the Civ line plotted vs. the Eddington values. Right panel: MBH obtained with the SE method using the Hβ line plotted vs. the Eddington values. The symbols are color coded based on redshift. The continuous black line represents th… view at source ↗

**Figure 2.** Left panel: MBH obtained from the SE method using the Hβ line plotted vs. the values derived with the X-ray scaling method, with color-coded symbols indicating the redshift of the sources. Middle panel: same as the left panel with color-coded symbols illustrating the intrinsic absorption NH in units of 1022 cm−2 . Right panel: same as the left panel with color-coded symbols describing the level of accretion rate, as… view at source ↗

**Figure 3.** [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: Histograms of the log(λEdd) distributions obtained with the X-ray scaling method (red) and the SE method (purple). ¡2:0 ¡1:5 ¡1:0 ¡0:5 0 0:5 1:0 log(¸Edd) 1:5 2:0 2:5 3:0 ¡ [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 4.** Figure 4: Top panel: SE MBH values multiplied by a factor of 2.5 plotted vs. the X-ray-based values, with color-coded symbols indicating the intrinsic absorption NH in units of 1022 cm−2 . Bottom panel: same as the top panel, with color-coded symbols indicating log(λEdd). The s…

**Figure 8.** Figure 8: Photon index plotted vs. the soft excess strength log(SX3) with the best-fit correlation, Γ = (2.75 ± 0.01) + (0.30 ± 0.01) × log(SX3). (19 in our original sample of 50 AGN), when extrapolating the Comptonized model used to fit the hard X-ray spectrum. First of all, we…

**Figure 7.** Figure 7: Top panel: Logarithm of the X-ray bolometric correction factor log(Lbol/LX) plotted vs. log(λEdd), where the latter is computed using the X-ray scaling method. The dashed line represents the best fit including both the X-HESS sample (red diamonds) and WISSH sample (bl…

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