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A 22-Billion Solar Mass Black Hole in Holmberg 15A with Keck KCWI Spectroscopy and Triaxial Orbit Modeling

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Holmberg 15A hosts one of the two most massive black holes known in the local universe, weighing 22 billion suns.

desk verdict Careful triaxial KCWI measurement gives H15A a 2.16e10 Msun black hole, probably closer to right than the prior MUSE value, but the unresolved kinematic discrepancy means the mass is provisional. read the letter →

arxiv 2501.01493 v1 pith:ZKKK2URF submitted 2025-01-02 astro-ph.GA

Emily R. Liepold , Chung-Pei Ma , Jonelle L. Walsh This is my paper · ORCID
classification astro-ph.GA
keywords supermassiveblackholesgalaxydynamicstriaxialSchwarzschildmodelingHolmberg15Astellarkinematicsintegralfieldspectroscopyscalingrelations
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

Holmberg 15A, the brightest galaxy of the Abell 85 cluster, has an exceptionally dim central core that has made its black hole hard to weigh. This paper reports the most detailed dynamical measurement to date, using Keck KCWI integral-field spectra of 313 spatial bins and triaxial Schwarzschild orbit modeling across roughly 40,000 galaxy models. The authors find a black hole mass of (2.16+0.23-0.18) x $10^{10}$ solar masses, tying NGC 4889 for the most massive black hole known in the local universe. The result matters because it tests how black hole mass scales with galaxy velocity dispersion and stellar mass at the extreme high end, where the scatter is large. It also shows that assuming the galaxy is axisymmetric, rather than triaxial, inflates the inferred black hole mass by about 18 percent.

What carries the argument

The central tool is TriOS, a triaxial Schwarzschild orbit-superposition code. Schwarzschild modeling builds a galaxy model from a library of stellar orbits in a given gravitational potential, then assigns non-negative weights to the orbits so their superposition reproduces the observed light distribution and the first eight Gauss-Hermite moments of the stellar velocity distribution at every spatial bin. The paper also uses the observed misalignment between the photometric and kinematic axes as the kinematic signature that forces a triaxial rather than axisymmetric potential, since symmetry in an axisymmetric galaxy requires the two axes to align. The code simultaneously constrains the black hole mass, the stellar mass-to-light ratio, the dark matter halo mass enclosed within 50 kpc, and the three intrinsic shape parameters.

What would settle it

A re-observation of the inner few arcseconds of H15A with an independent high-resolution spectrograph of comparable or better signal-to-noise, analyzed with both parametric and non-parametric LOSVD fitting, would settle whether the central dispersion drop is real; a flat profile near 335 km/s would falsify the reported black hole mass.

Watch

Extended reading notes

Core claim

Using the first eight Gauss-Hermite moments of the stellar line-of-sight velocity distributions from KCWI as constraints, the paper determines the mass and intrinsic shape of H15A simultaneously. The best-fit triaxial model gives MBH = (2.16+0.23-0.18) x $10^{10}$ M_sun, a luminosity-weighted middle-to-long axis ratio p=0.89 and short-to-long ratio q=0.65, a triaxiality parameter T=0.35, and a stellar mass-to-light ratio M*/L_r' = 4.80 solar units. The galaxy's kinematic axis is misaligned from its photometric major axis by about 62 degrees at large radii, which axisymmetric models cannot reproduce. Re-running the analysis with an axisymmetrized version of the orbit code yields a worse fit and raises MBH to (2.55 ± 0.20) x $10^{10}$ M_sun, still far below the (4.0 ± 0.8) x $10^{10}$ M_sun reported from previous MUSE data with axisymmetric modeling. The paper argues through a series of tests that the KCWI kinematics, particularly the central decline in velocity dispersion from ~340 to ~280-300 km/s at 5 arcseconds, are robust to template choice, spectral fitting parameters, spectral coverage, and parametric versus non-parametric LOSVD extraction.

Load-bearing premise

The central result depends on the KCWI measurement of the central velocity dispersion decline, from about 340 to 280-300 km/s within 5 arcseconds, being unbiased; if the MUSE measurements showing a flat ~335 km/s profile are the true ones, the inferred black hole mass would shift substantially.

Editorial extensions

If this is right

  • H15A joins NGC 4889 as the most massive black holes known in the local universe, and both sit well above the mean MBH–sigma relation: H15A is a factor of 10.1 above the McConnell & Ma (2013) relation, a 3-sigma outlier.
  • The black hole mass is consistent, within 1 sigma, with the MBH–core radius and MBH–bulge mass relations, suggesting that for cored massive ellipticals the stellar core size is a more reliable predictor of MBH than velocity dispersion.
  • Axisymmetric orbit modeling overestimates MBH by about 18 percent for this galaxy when applied to the same KCWI data, and the axisymmetric models fit significantly worse, with chi-square higher by 330.
  • The triaxial intrinsic shape with q=0.65 and T=0.35 rules out both oblate and prolate axisymmetry at high confidence, consistent with the observed kinematic misalignment.

Reading between the lines

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

  • If the KCWI kinematics are correct, the earlier MUSE-based mass of 4.0e10 solar masses is likely biased high by a combination of kinematic differences and the axisymmetry assumption; the paper's own axisymmetric fit to KCWI data (2.55e10) isolates the kinematic contribution as roughly the larger part of the gap.
  • Other ultramassive black hole masses measured with single-aperture or axisymmetric models of cored ellipticals may deserve similar triaxial re-analysis, especially where kinematic misalignment is present or suspected.
  • A triaxial stellar potential implies the gravitational potential is non-axisymmetric, so the dark matter halo may also be triaxial; modeling the halo as triaxial could shift MBH slightly, though the paper's tests suggest the mass parameters change by only about 10 percent when viewing angles move away from best fit.
  • The very low central surface brightness of H15A means the black hole's dynamical signature sits on a faint stellar background; if even deeper spectra become available, the central sigma drop could be measured at higher angular resolution and sharpen the MBH constraint further.
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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

4 major / 6 minor

Summary. This paper presents new Keck KCWI integral-field spectroscopy of the brightest cluster galaxy Holmberg 15A (H15A) covering a roughly 100″ × 100″ contiguous field, binned into 313 spectra from which the first eight Gauss-Hermite moments of the stellar line-of-sight velocity distributions are measured, yielding 2504 kinematic constraints. The authors model these data with the triaxial Schwarzschild code TriOS, running about 40,000 galaxy models over the six-dimensional parameter space of black hole mass MBH, stellar mass-to-light ratio, dark matter mass within 50 kpc, and three intrinsic shape parameters. They infer MBH = (2.16+0.23−0.18) × 10^10 M⊙, luminosity-weighted intrinsic axis ratios p = 0.89 and q = 0.645, a total stellar mass of 2.9 × 10^12 M⊙, and a kinematic axis misaligned by ~62° from the photometric major axis. An axisymmetric reanalysis of the same data gives a worse fit (Δχ2 ≈ 330) and MBH = (2.55 ± 0.20) × 10^10 M⊙. The paper concludes that H15A, along with NGC 4889, hosts one of the two most massive black holes known in the local universe and is a strong outlier relative to the MBH–σ relation, while remaining about a factor of two below the previously reported MUSE-based value of (4.0 ± 0.8) × 10^10 M⊙.

Significance. If the central measurement is correct, this is an important result: H15A would be the first galaxy with a dynamically measured black hole above 2 × 10^10 M⊙ whose mass is determined with a fully triaxial stellar potential, and the mass adds a valuable data point at the extreme high-mass end of the MBH scaling relations. The paper's strengths include the unusually large kinematic dataset (313 bins, eight LOSVD moments), the large orbit-model search (~40,000 models), the split-half consistency test, and the transparency of the comparison with the previous MUSE study. It is a further strength that the orbit-modeling pipeline was validated on simulated galaxies in Pilawa et al. (2024), and that the black-hole mass is derived from a forward model rather than from any scaling relation, so there is no circularity. The paper also honestly quantifies that the assumed symmetry (axisymmetric versus triaxial) changes MBH by only ~18%, isolating stellar kinematics as the dominant source of the disagreement with Mehrgan et al. (2019).

major comments (4)
  1. [Section 5.1 and Figure 7] The central kinematic discrepancy between KCWI and MUSE is the main lever on MBH and is not independently resolved. MUSE finds a flat σ ≈ 335 km/s over the central arcseconds while KCWI declines from ≈340 km/s to 280–300 km/s at R = 5″ (Figure 7), and the MBH constraint comes predominantly from the central LOSVD moments. The tests in Sections 5.1.1–5.1.4 show that the KCWI kinematics are stable to template choice, GH truncation order, spectral coverage, and parametric versus non-parametric extraction, but these tests are all internal to the KCWI data; the red-only experiment in Section 5.1.3 does not reproduce the MUSE measurement from MUSE data. The paper itself concludes that "further tests on MUSE data would be useful." As written, the quoted MBH = (2.16+0.23−0.18) × 10^10 M⊙ contains no systematic term for the alternative, flat central σ profile, so the headline number rests on an unresolved instrument-level discrepancy. I recommend reanalyzing the archival MUSE data with the KCWI-style pipeline and template library, or explicitly adding a systematic error to MBH calibrated to the MUSE profile, or demonstrating quantitatively that MBH is insensitive to the central σ shape.
  2. [Section 4.2] The paper's handling of the low reduced χ2 is qualitative, and the arithmetic does not close the issue. The best-fit χ2 = 1410 with 2504 constraints gives a naive reduced χ2 of 0.57. The paper argues, by analogy with NGC 2693 (Pilawa et al. 2022, 2024), that the effective number of model parameters is about 200, which would raise the reduced χ2 to at most ~0.8 (1410/(2504−200)) — still below unity. A reduced χ2 below 1 indicates that the measurement errors are overestimated, the model is overfitting, or the effective DOF are larger still; in any case the quoted 68% intervals on MBH inherit whatever the resolution is. The split-half test reassures the central value but does not calibrate the uncertainties. The authors should estimate the effective DOF for this specific model and report the resulting reduced χ2, or discuss explicitly how the low χ2 affects the meaning of the quoted intervals.
  3. [Appendix C and Table 2] The MGE light model is fit with the imposed constraint σ′ > 0.96″, and the innermost Gaussian component sits exactly at this lower bound (Table 2). Because the deprojected central luminosity density scales as ν0 ∝ Σ0/σ′, this constraint sets a limit on the central stellar density, and the central stellar density is precisely the mass component that competes with MBH in reproducing the central LOSVD. The paper notes that unconstrained fits produce "exceptionally large and unconstrained central densities," but it does not test how MBH responds to the adopted 0.96″ floor. I request a sensitivity test of MBH to the inner-width bound (e.g., floors of 0.75″ and 1.2″), or an explicit demonstration that the central MGE component is not the driver of the MBH inference.
  4. [Section 4.2, Table 1, Figure 5] The quoted precision on the intrinsic axis ratios is dominated by the boundaries of the allowed parameter region rather than by the data. The best-fit values q = 0.645+0.001−0.002 (99.7% interval) and u > 0.999 sit at the maximal-flattening boundary q = u q′ with u = 1 of the deprojection inequalities. The luminosity-weighted q is therefore essentially pinned by the projected axis ratios, and the sub-percent formal uncertainty is not a meaningful measurement of the intrinsic shape. Since the triaxial shape is a headline result, the text should note explicitly that q and u are prior-limited at the boundary, and that the robust inference is the coarse statement of strong triaxiality (T ≈ 0.35) rather than the precise q value. The authors' own test showing only a 10% change in MBH when the viewing angles are moved >15° away indicates that this does not affect the black hole mass, but the boundary issue is not discussed in Section 4.2.
minor comments (6)
  1. [Throughout] There are several typographical errors: “T able 1” in Table 1; “Give that” should be “Given that” in Section 4.2; “It is is also” in Section 4.2; “T riaxial” and “T riOS” in the title and affiliation line; “W alsh” in the author list; and “T ypeset” in the draft header.
  2. [Figure 10 caption] The caption's final sentence is grammatically incomplete: “then performing dynamic nested sampling that surrogate function” should read “then performing dynamic nested sampling of that surrogate function.”
  3. [Section 5.1.4] The sentence “For these, we find that even at the most negative location in the LOSVD, the mean ratio of the amplitude and the uncertainties at that velocity is only −0.88” should be rephrased to state clearly that this is the mean over the affected bins of (LOSVD value)/(1σ error) at the velocity of the most negative value; as written it is easy to misread.
  4. [Abstract and Section 4.3] The claim that H15A and NGC 4889 are “the galaxies hosting the most massive SMBHs known in the local universe” should be explicitly conditioned on the KCWI kinematics, given that the MUSE-based value of (4.0 ± 0.8) × 10^10 M⊙ from Mehrgan et al. (2019) remains unreconciled; a phrase such as “based on the kinematics adopted here” would prevent overstatement.
  5. [Section 5.1 and elsewhere] The galaxy name is written inconsistently as “H15” in several places in Section 5.1 (e.g., “the central 60″ × 60″ region of H15”) and as “H15A” elsewhere; the paper should use “H15A” consistently.
  6. [Figure 9 caption] The caption states that the data have been point-symmetrized for comparison with the model, but does not specify the symmetry convention for each moment (e.g., V and h3 are antisymmetric while σ and h4 are symmetric under point reflection); specifying this would aid the reader.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the black hole mass is estimated from forward triaxial orbit modeling against independent KCWI stellar kinematics, not derived from a relation or parameter that contains the result.

full rationale

The derivation chain is a standard forward-model parameter estimation: the KCWI spectra are reduced and binned, the LOSVD moments are extracted with pPXF, the galaxy's light distribution is deprojected via an MGE, and TriOS orbit models are fit to the 2500 kinematic constraints with MBH, M*/L, dark matter, and shape parameters as free parameters. The reported MBH = (2.16+0.23-0.18) x 10^10 M_sun is the result of maximizing the likelihood of the orbit superposition against the data, so it is not defined in terms of itself, nor is any fitted quantity renamed as a prediction. The code TriOS is from prior work by the same group (Quenneville et al. 2022), and its accuracy is supported by simulated-galaxy tests in Pilawa et al. (2024); although these are self-citations, they serve as independent benchmarks on mock data and do not smuggle in the H15A result. The paper's own Section 5.1 honestly documents that the MUSE-based kinematics of Mehrgan et al. (2019) disagree with the KCWI sigma profile near the center, and it explicitly notes that further tests on MUSE data would be useful. That unresolved systematic discrepancy is a correctness risk, not a circularity, because the orbit-model likelihood does not incorporate the MUSE measurements or the target MBH as an input. No uniqueness theorem is invoked to forbid alternatives, no ansatz is imported solely by citation, and no known empirical pattern is merely renamed. The circularity score is therefore 0.

Assumptions & free parameters 10 free parameters · 7 assumptions · 0 invented entities

The measurement relies on a standard stellar-dynamical forward model with typical choices for the dark halo and MGE. No new physical entities are introduced, but several modeling choices (halo gamma and rs, MGE inner width, color conversion) are free inputs that can shift the inferred mass if varied outside the tested range.

free parameters (10)
  • MBH = 2.16+0.23-0.18 x 10^10 M_sun
    Central black hole mass, the main result of the orbit modeling.
  • M*/L_r' = 4.80+0.18-0.20 M_sun/L_sun
    Stellar mass-to-light ratio in the r' band, fitted simultaneously with MBH.
  • M50 = 2.56+0.25-0.21 x 10^12 M_sun
    Dark matter mass enclosed within 50 kpc, derived from fitted central density rho0 with fixed rs=150 kpc.
  • p = 0.89 +/- 0.04
    Luminosity-weighted middle-to-long intrinsic axis ratio.
  • q = 0.645 +0.001/-0.002
    Luminosity-weighted short-to-long intrinsic axis ratio.
  • u = >0.999
    Apparent-to-intrinsic long axis ratio, near its maximal allowed value.
  • inclination (axisymmetric run) = 87.0 +/- 0.4 deg
    Inclination in the axisymmetrized TriOS models used for comparison.
  • NFW scale radius rs = 150 kpc (fixed)
    Set to 150 kpc after a coarse search disfavored rs below 50 kpc; data are insensitive to larger rs.
  • MGE inner Gaussian sigma' lower limit = 0.96 arcsec
    Constraint imposed in Appendix C to prevent unphysically large central deprojected densities.
  • V - r' color = 0.5 mag
    Assumed color to convert r'-band to V-band luminosities.
assumptions (7)
  • standard math Schwarzschild orbit superposition models can reproduce the stellar kinematics of a triaxial galaxy in equilibrium.
    Used throughout Section 4; TriOS is an established method validated on simulations.
  • standard math The stellar luminosity density is obtained by deprojecting the MGE surface brightness model.
    Section 3 and Appendix C; requires an assumed orientation and a valid deprojection.
  • domain assumption The stellar mass distribution follows the light with a constant mass-to-light ratio for all MGE components.
    Section 4.1; no radial M/L gradient is modeled.
  • domain assumption The dark matter halo is a generalized NFW profile with gamma=0 and fixed scale radius rs=150 kpc.
    Section 4.1; gamma=0 is chosen to give a finite central density and a flattened inner profile; rs is fixed after a coarse search.
  • domain assumption The observed LOSVD in each bin is fully described by the first eight Gauss-Hermite moments, with h9-h12 set to zero.
    Section 2.3 and Section 4.1; higher moments are constrained to be zero to reduce unphysical LOSVDs.
  • domain assumption The photometric major axis of the MGE is fixed at PA=-34 degrees and the isophotes are described by the seven-component MGE.
    Section 3 and Table 2; PA is uncertain within the central few arcseconds where isophotes are round.
  • ad hoc to paper The MGE fit with the imposed inner-width constraint sigma' > 0.96 arcsec and the outer-component refit is a faithful representation of the light.
    Appendix C introduces these constraints to avoid unphysically large central densities and deprojectability problems; they are not derived from first principles.

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Cite this review

Pith. "Pith review of A 22-Billion Solar Mass Black Hole in Holmberg 15A with Keck KCWI Spectroscopy and Triaxial Orbit Modeling." pith.science (2026). https://pith.science/paper/ZKKK2URF

@misc{pith2026250101493,
  author       = {Pith},
  title        = {Pith review of: A 22-Billion Solar Mass Black Hole in Holmberg 15A with Keck KCWI Spectroscopy and Triaxial Orbit Modeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZKKK2URF}},
  note         = {Machine review of arXiv:2501.01493}
}
abstract

Holmberg 15A (H15A), the brightest cluster galaxy of Abell 85, has an exceptionally low central surface brightness even among local massive elliptical galaxies with distinct stellar cores, making it exceedingly challenging to obtain high-quality spectroscopy to detect a supermassive black hole (SMBH) at its center. Aided by the superb sensitivity and efficiency of KCWI at the Keck II Telescope, we have obtained spatially resolved stellar kinematics over a ${\sim}100''\times 100''$ contiguous field of H15A for this purpose. The velocity field exhibits a low amplitude (${\sim}20\mathrm{~km~s}^{-1}$) rotation along a kinematic axis that is prominently misaligned from the photometric major axis, a strong indicator that H15A is triaxially shaped with unequal lengths for the three principal axes. Using 2500 observed kinematic constraints, we perform extensive calculations of stellar orbits with the triaxial Schwarzschild code, TriOS, and search over ${\sim}$40,000 galaxy models to simultaneously determine the mass and intrinsic 3D shape parameters of H15A. We determine a ratio of $p=0.89$ for the middle-to-long principal axes and $q=0.65$ for the short-to-long principal axes. Our best estimate of the SMBH mass, $M_\mathrm{BH}=(2.16^{+0.23}_{-0.18})\times 10^{10}M_{\odot}$, makes H15A -- along with NGC 4889 -- the galaxies hosting the most massive SMBHs known in the local universe. Both SMBHs lie significantly above the mean $M_\mathrm{BH}-\sigma$ scaling relation. Repeating the orbit modeling with the axisymmetrized version of TriOS produces worse fits to the KCWI kinematics and increases $M_\mathrm{BH}$ to $(2.55\pm 0.20) \times 10^{10}M_{\odot}$, which is still significantly below $M_\mathrm{BH}=(4.0\pm 0.8) \times 10^{10}M_{\odot}$ reported in a prior axisymmetric study of H15A.

Figures

Figures reproduced from arXiv: 2501.01493 by the authors.

Figure 1
Figure 1. Ten representative sky-subtracted KCWI spectra (black curves) of H15A from spatial bins at increasing distance from the galaxy’s center (0.4 ′′ to 31′′ from top to bottom). The inner six spectra are from the KCWI small slicer; the outer four are from the large slicer. Each spectrum is obtained from co-adding spectra from individual KCWI spaxels to meet a S/N threshold. Our observations provide a total of 313 co-adde… view at source ↗
Figure 2
Figure 2. Maps of the first four Gauss-Hermite moments, V, σ, h3, and h4 (left to right), of the stellar LOSVDs of H15A as measured for 313 spatial bins from the Keck KCWI spectra. The top row displays the zoomed-in central 20′′ ×8 ′′ region covered by the KCWI small slicer; the bottom row displays the 60′′ × 60′′ region from the small and large slicer mosaics. North is up and east is left. determined kinematic PA. From R ∼ 2… view at source ↗
Figure 3
Figure 3. Misalignment between the kinematic and pho￾tometric axes of H15A. We model the KCWI velocity field with V (R, Θ) = V1(R) cos [Θ − Θ0(R)] and measure the am￾plitude V1(R) (upper panel) and phase Θ0(R) (lower panel) of the rotation pattern. The phase Θ0 determines the PA of the kinematic axis, PAkin, which varies with increasing radius and reaches PAkin = 28◦ beyond 20′′, leading to a misalign￾ment of 62◦ from the pho… view at source ↗
Figures from the paper (5 more)
Figure 5
Figure 5. Figure 5: and the model parameters are summarized in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 7
Figure 7. Figure 7: Radial profile of the stellar velocity disper￾sion of H15A from KCWI (blue; this work), MUSE (orange; Mehrgan et al. 2019), and a long slit observation (red; PA = −23◦ , Fisher et al. 1995). The top panel shows the inner￾most 5′′; the bottom panel shows all available d…
Figure 8
Figure 8. Figure 8: Posterior distributions of the four parameters in our axisymmetric orbit models of H15A. The mass parame￾ters are the same as in [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]
Figure 9
Figure 9. Figure 9: Radial profiles of the eight Gauss-Hermite moments of the stellar LOSVD for each of the 313 spatial bins of H15A. The black bars denote the values measured from KCWI stellar spectra, while red dots denote the values from the best-fitting triaxial TriOS model. The model…
Figure 10
Figure 10. Figure 10: The marginalized posterior distribution from triaxial Schwarzschild models of H15A (top), the log marginalized posterior (purple, lower), and the χ 2 from in￾dividual TriOS models (black dots) as a function of black hole mass. The marginalized posterior distribution i…

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.