New estimates of the spin and accretion rate of the black hole M87*

Brett A. Patterson; Derek Ward-Thompson; Joshua S. Stanway; Michael Drew; Timothy J. Walton

REVIEW 4 major objections 4 minor 19 references

New estimates of the spin and accretion rate of the black hole M87*

T0 review · 4 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Analyzing the brightness asymmetry in the Event Horizon Telescope ring, the paper derives a disk rotation speed of about $0.14c$ and a black hole spin of $a\sim0.8$, a lower limit.

desk verdict A transparent but fatally flawed attempt to measure M87*'s spin from Doppler beaming; the angle between the disk velocity and the line of sight is misidentified, so the central estimate does not stand. read the letter →

arxiv 2505.17035 v1 pith:L4WFJNDY submitted 2025-05-07 astro-ph.HE

Michael Drew , Joshua S. Stanway , Brett A. Patterson , Timothy J. Walton , Derek Ward-Thompson This is my paper · ORCID

classification astro-ph.HE

keywords M87*blackholespindimensionlessparameterDopplerbeamingaccretiondiskraterelativisticjetsEventHorizonTelescope

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 sets out to show that the Event Horizon Telescope images of M87* already contain the information needed to measure the black hole's spin. By interpreting the persistent bright spot on the ring as Doppler beaming from plasma rotating at about $0.14c$, and by identifying the ring radius with the innermost stable circular orbit at roughly three Schwarzschild radii, the authors obtain a dimensionless spin parameter $a\sim0.8$. They argue this is a lower limit, because Schwarzschild and Kerr metric corrections push the value toward $0.998$. Using the measured polarization angle as a tracer of the inward spiral, they also infer an accretion velocity of about $0.23c$ and an accretion rate of roughly $4\times10^{-5}$ to $0.4$ solar masses per year. The authors conclude that M87* is a rapidly spinning black hole whose accretion power is sufficient to drive its jet.

What carries the argument

The load-bearing mechanism is the relativistic Doppler beaming ratio, $[D_{\rm app}/D_{\rm rec}]^3\approx2.25$, read off the EHT ring's brightness cross-section; with $\cos\theta=0.96$ this fixes the inner-disk rotation speed at about $V_R\approx0.14c$. The spin then comes from the formula $a=V_R R_{\rm ISCO} c/(G M_{\rm BH})$, where $R_{\rm ISCO}$ is identified with the measured ring radius of about $20\,\mu$arcsec ($\sim3$ Schwarzschild radii). For the accretion rate, the polarization angle $\alpha\approx58.5^\circ$ is used as the angle between the magnetic field and the tangent, so the inward velocity is $V_A=V_R\tan\alpha\approx0.23c$, and the accretion rate is estimated by integrating the mass flux over a thin or thick annular disk sector at $R_{\rm ISCO}$.

What would settle it

Measure the projected velocities of the approaching and receding sides of the ring directly, for instance with submillimeter VLBI spectral-line or polarimetric mapping of M87*, and check whether they differ by the $0.14c$ implied by a Doppler ratio of 2.25; an independent velocity or a brightness ratio that changes with frequency or epoch would show the asymmetry is not pure beaming, and the spin estimate would need revision.

Watch

Extended reading notes

Core claim

The central discovery is that the dimensionless spin parameter of M87* is about $a\sim0.8$, and that this is probably a lower limit. The argument starts from the ring's brightness asymmetry, which the paper interprets as the Doppler factor between approaching and receding disk material: a measured brightness ratio of about $2.25$ yields an orbital velocity $V_R\approx0.14c$ at the inner edge of the disk. Taking that edge to be the innermost stable circular orbit at $R_{\rm ISCO}\sim5.5\times10^{13}$ m (about three Schwarzschild radii) and conserving angular momentum down to the horizon gives $J=M_{\rm BH}V_R R_{\rm ISCO}$ and hence $a=Jc/GM_{\rm BH}^2\sim0.8$. The authors note that using Schwarzschild or Kerr metrics instead of flat spacetime raises the inferred spin toward $0.998$, so $a\sim0.8$ is stated as a lower limit.

Load-bearing premise

The load-bearing assumption is that the ring's brightness asymmetry is entirely Doppler beaming and that the orbiting material's motion makes the same 17-degree angle to our line of sight as the jet; if that angle is actually much larger for a nearly face-on disk, the derived rotation speed and spin change dramatically.

Editorial extensions

If this is right

If $a\sim0.8$ is a lower limit, M87* is a rapidly spinning black hole and low-spin models in the lower part of the previously estimated range would be ruled out.
The inferred accretion power, roughly $10^{34}$ to $10^{38}$ J/s, overlaps the estimated jet power, so the jet can be powered directly by accretion without an additional energy source.
The accretion rate of about $4\times10^{-5}$ to $0.4\,M_\odot\,{\rm yr}^{-1}$ is orders of magnitude below the Eddington limit, placing M87* in a quiescent accretion state.
A single brightness asymmetry measurement, combined with an assumed ISCO radius, is enough to estimate spin, which opens the same method to other horizon-resolved black holes.

Reading between the lines

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

A re-derivation not given in the paper: for a nearly face-on disk with the line of sight at 17 degrees to the jet axis, an orbital velocity vector in the disk plane makes an angle of at least about 73 degrees with the line of sight, so $\cos\theta$ should be near 0.29 rather than 0.96; inserting $\cos\theta=0.29$ into the paper's own equations would raise the inferred rotation speed and push the s
The method's dependence on the brightness ratio means a second-epoch or multi-frequency check of the ring's asymmetry would directly test whether the bright spot is stable Doppler beaming or partly jet variability.
Applied to Sgr A*, whose inclination may be better constrained, the same beaming-ratio route would provide an independent spin estimate and test whether the assumed geometry generalizes.

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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

Dear colleague,

This paper is a clean, readable attempt to extract the spin of M87* from the EHT ring asymmetry. The idea—use the Doppler beaming ratio to get the rotation speed—is worth trying, and the authors are unusually honest about their assumptions. The writing is clear and the caveats are mostly acknowledged. But the central result, a ~ 0.8, rests on a simple geometric mistake, so I would not trust the number.

The problem is in Eqs. (1)–(4). The authors take the angle θ between the emitting matter's velocity and our line of sight to be 17°, i.e., cosθ = 0.96, citing M87* Paper VI. That 17° is the inclination of the jet/disk axis to the line of sight, not the angle between an orbital velocity vector and the line of sight. For a near-face-on disk, the orbital velocity lies in the disk plane, nearly transverse to the line of sight; the angle ranges from about 73° to 107°, so cosθ is at most ±0.29. Using cosθ ≈ 0.29 in the same ratio gives V_R ≈ 0.4c instead of 0.14c, and a very different spin. The observed ring asymmetry may also include lensing or absorption contributions, not pure Doppler, but the geometry error alone is fatal.

The ISCO argument is also internally inconsistent. They measure the ring radius at ~3 Schwarzschild radii, which is the ISCO for a Schwarzschild (a=0) hole, yet they derive a=0.8, whose ISCO is near 1.4 Schwarzschild radii. The ring is a lensed image, not a direct measure of the ISCO. Appendix A.3 compounds this by starting from a=0.8 and recovering a≈1.0; that's circular.

The accretion rate section is weaker: the range spans four orders of magnitude, the density is an upper limit, and the polarization-angle method ignores GR effects on the polarization pattern. It does not rescue the paper.

What is genuinely positive: the paper lays out its method step by step, does not hide its uncertainties, and is honest that the spin is model-dependent. It also makes an attempt to connect accretion power to jet power, which is a reasonable check. But the load-bearing geometric assumption is wrong.

For a reader working on M87* or EHT image modeling, this is a useful cautionary example, not a source of numbers. I would not cite it. If you are editing, send it to a referee if you want the geometry error on record; a competent referee will stop at the angle issue. The verdict should be rejection.

Best, [Your name]

Referee Report

4 major / 4 minor

Summary. The paper uses Event Horizon Telescope images of M87* to estimate the rotation velocity of the inner accretion disk, the dimensionless black-hole spin, the accretion velocity, and the accretion rate. From the observed brightness asymmetry of the ring (a Doppler ratio of about 2.25) and an assumed ring radius of 20 μas (≈3 Schwarzschild radii), the authors derive a rotation velocity V_R≈0.14c and, via angular-momentum conservation from the ISCO to the horizon, a spin a≈0.8, which they argue is a lower limit. Using the EHT polarization angle as a proxy for the velocity direction, they obtain an accretion velocity V_A≈0.23c and an accretion rate in the range ≈4×10⁻⁵–4×10⁻¹ M_☉ yr⁻¹, with a corresponding accretion power ≈10³⁴–10³⁸ J/s that overlaps the jet power. The main result is the spin estimate, with the accretion-rate range presented as a consistency check.

Significance. If correct, the method would provide a direct observational route to black-hole spin using only EHT imaging, bypassing spectral fitting. The paper is transparent about its assumptions and includes explicit calculations for Minkowski, Schwarzschild, and Kerr metrics. However, the central spin estimate rests on a misapplication of the Doppler formula: the angle between the orbital velocity of disk gas and the line of sight is not the jet inclination angle of 17°, and the resulting spin value is inconsistent with the assumed ISCO radius. The paper does not ship machine-checked proofs or code, but the derivations are straightforward and reproducible once the geometry is corrected. The accretion-rate estimate is explicitly acknowledged to span four orders of magnitude, so it is not a strong constraint by itself.

major comments (4)

[Section 2.1, Eqs. (1)–(4)] The Doppler factor is evaluated with cosθ≈0.96, obtained by taking θ≈17° from the jet inclination. This is the wrong angle for the Doppler formula. For material orbiting in a disk whose plane is viewed at inclination i≈17° (i.e., the angle between the disk normal and the line of sight), the angle between an orbital velocity vector and the line of sight has cosθ in the range ±sin i ≈ ±0.29, not 0.96. Using cosθ=0.29 in the same brightness ratio (D_app/D_rec)³=2.25 gives V_R≈0.46c instead of 0.14c, which changes the spin estimate in Eq. (6) dramatically. The claimed value a≈0.8 therefore depends critically on an incorrect geometric assignment.
[Section 2.2, Eq. (6)] The assumption that R_ISCO is measured directly from the observed ring radius is internally inconsistent with the derived spin. The paper takes R_ISCO≈3 Schwarzschild radii and then derives a≈0.8. However, for a Kerr black hole with a=0.8, the prograde ISCO radius is approximately 2.9 GM/c² ≈1.45 Schwarzschild radii, not 3. A radius of 3 Schwarzschild radii corresponds to a non-spinning (a=0) spacetime. Additionally, the observed EHT ring is a lensed image of the photon ring and emission region, not a direct image of the ISCO, so the measured angular radius cannot be interpreted as R_ISCO without a self-consistent lensing model. The spin estimate is therefore not self-consistent with its own radius assumption.
[Appendix A.3 and A.4] The Kerr-metric calculation is circular. The authors state 'in order to estimate the Kerr spin we have to start from a value of 0.8', and then the calculation returns a≈1.00. This is not an independent estimate; it presumes the quantity being derived. Consequently, the conclusion in A.4 that 'regardless of the spacetime model ... spin of at least 0.8' is not supported by the Kerr case, since the Kerr result is essentially an artifact of the input a=0.8.
[Section 2.3 and Appendix B] The accretion-rate estimate is extremely weakly constrained, spanning four orders of magnitude (≈4×10⁻⁵ to ≈4×10⁻¹ M_☉ yr⁻¹), with the uncertainty dominated by the assumed disk opening angle (α≈60° vs α≈6°) and the plasma density (n_e from 10⁷ down to 10⁴ cm⁻³). More importantly, the use of the polarization angle α as the pitch angle of the velocity assumes that the magnetic field direction exactly corresponds to the plasma velocity direction in a highly ionized accretion disk; this is a strong assumption not justified in the text and is generally not true in MHD accretion flows. While this issue does not directly invalidate the spin calculation, it means the accretion-rate range should not be presented as a new measurement.

minor comments (4)

[Appendix A.1] Appendix A.1 states that θ=π/2 is set (source in the equatorial plane), but then immediately uses cosθ=0.96, which corresponds to θ≈17°. These two choices are mutually inconsistent and should be reconciled.
[Section 2, paragraph 3] The sentence 'This has been shown to be a valid calculation, even when the disk is close to edge-on, as in this case' is inconsistent with the near-face-on geometry (i≈17°) used in the rest of the paper; the Doppler-beaming calculation is later performed with a nearly face-on disk.
[Throughout] The term 'Schwarzchild' is used repeatedly (e.g., Sections 2.2 and 3, and Appendix A), but the correct spelling is 'Schwarzschild'.
[Section 2.1] The brightness ratio is taken from only one cross-cut through the ring in each reconstruction method; given the variability between reconstruction algorithms, it would be helpful to specify how the 2.1±0.1 and 2.4±0.2 values are averaged and whether the quoted uncertainty includes systematic differences between the three methods.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the spin and accretion estimates are computed directly from observed EHT brightness asymmetry, ring size, and external mass/density inputs; no fitted parameter is relabeled as a prediction.

full rationale

The paper's central spin estimate is not circular. The observed brightness ratio (D_app/D_rec)^3 ≈ 2.25 is taken from EHT images (Section 2.1), the ring radius R_ISCO ≈ 20 μas is measured from the same images (Section 2.2), and the black hole mass is adopted from M87* Paper I. The Doppler factor equations (1)–(4) then yield V_R ≈ 0.14c, and Equation (6) evaluates the dimensionless spin parameter directly from these measured inputs. No parameter is fitted to a target spin; the quoted a ~ 0.8 is a computed consequence of the assumed geometry and measured brightness asymmetry. Although the assumption that the observed asymmetry is entirely due to Doppler beaming is physically debatable, it is a modeling assumption, not a circular reduction. Similarly, the accretion velocity V_A = V_R tan(58.5°) follows from the measured polarization angle, and the accretion rate is computed from V_A, R_ISCO, and an adopted density range; these are not fitted to match the jet power. The only self-referential element is the Kerr-metric correction in Appendix A.3, which states 'in order to estimate the Kerr spin we have to start from a value of 0.8,' but the paper openly acknowledges this starting-value dependence and does not use the Kerr iteration as the basis for its central claim; the a ~ 0.8 result stands on the Minkowski-space calculation from Section 2. Thus, there is no load-bearing circularity. The paper's weaknesses lie in the validity of the geometric assumptions (e.g., using θ ≈ 17° for the orbital velocity angle and equating the observed ring radius with the ISCO radius), which are correctness risks, not circularity risks.

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

The central spin claim rests on the adopted Doppler geometry and the ISCO identification. The accretion rate depends on arbitrary disk thickness and density assumptions. No new physical entities are introduced.

free parameters (2)

disk opening angle for accretion rate = 60 degrees (thick) or 6 degrees (thin)
Chosen by hand to bracket the accretion rate; not derived from data, and acknowledged as extremely uncertain.
plasma density n_e = 1e7 cm^-3 (upper limit)
Taken from M87* Paper VIII as an upper limit; lower estimates are up to three orders of magnitude smaller, producing the wide accretion rate range.

assumptions (5)

domain assumption The inner edge of the accretion disk is at the ISCO, and the ring radius measured in the EHT image directly gives R_ISCO with negligible gravitational lensing.
Stated in Section 2.2; if lensing is significant, the observed ring radius is not the ISCO radius.
domain assumption The brightness asymmetry in the ring is entirely due to relativistic Doppler beaming, and the SED is flat near the EHT bands.
Stated as a caveat in Section 2; other contributions such as the jet base or varying absorption would affect the ratio.
domain assumption The accreting plasma is 100% ionized and tied to the magnetic field, so the measured polarization angle gives the direction of the total velocity.
Section 2.3; if the field is not frozen into the plasma, V_A = V_R tan alpha is invalid.
domain assumption Angular momentum is conserved inside R_ISCO, giving J = M_BH V_R R_ISCO.
Section 2.2; ignores pressure and magnetic stresses that could alter the angular momentum inside the ISCO.
ad hoc to paper The angle theta in the Doppler factor is 17 degrees, the inclination of the jet to the line of sight, rather than the angle between the orbital velocity and the line of sight.
Section 2.1; for a near face-on disk this is geometrically incorrect, as the orbital velocity cannot be aligned with the line of sight more than about 73 degrees.

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Cite this review

Pith. "Pith review of New estimates of the spin and accretion rate of the black hole M87*." pith.science (2026). https://pith.science/paper/L4WFJNDY

@misc{pith2026250517035,
  author       = {Pith},
  title        = {Pith review of: New estimates of the spin and accretion rate of the black hole M87*},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L4WFJNDY}},
  note         = {Machine review of arXiv:2505.17035}
}

abstract

In this paper we use the imaging results of M87* from the EHT to calculate the rotational velocity of the inner edge of the accretion disk and find a value of $\sim$0.14c. We then calculate the dimensionless spin parameter, $a$, of the black hole, obtaining a value of $a \sim 0.8$. We deduce that this is probably a lower limit. We go on to use the results of the EHT polarization study of the magnetic field direction in the accretion disk of M87* as a proxy for the direction of motion of the spiralling accreting matter in this highly ionized disk. This direction is defined by the vector sum of the tangential rotation velocity and the inward radial accretion velocity. We thus calculate the accretion velocity to be $\sim$ (7 $\pm$ 0.7) $\times$ $10^7$~ms$^{-1}$. We go on to estimate a range of values for the accretion rate from the inner disk to be $\sim$4 $\times$ 10$^{{-5}}$ to $\sim$4 $\times$ 10$^{-1}$ M$_{\odot}$yr$^{-1}$, and a range of values for the accretion power to be $\sim$10$^{34}$ to 10$^{38}$ J/s. This is the same range as the power of the jet, making it consistent with accretion-driven jet models.

Figures

Figures reproduced from arXiv: 2505.17035 by the authors.

**Figure 2.** A cross section of brightness vs relative position of each side of the ring (in µarcsec) for each of the three main EHT image reconstruction methods, as applied to the 2017 data. Image credit: M87∗ Paper IV fig. 37. follows: Dapp = γ 1 − v cos θ c −1 , (1) Drec = γ 1 + v cos θ c −1 , (2) where v is the velocity of the matter, γ is the Lorentz factor, which is given by (1−v 2/c2 ) −1/2 , and the angle of … view at source ↗

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

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M., Press, W

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