{"id":"60853be9-5a9e-4ded-8b75-158663b05978","arxiv_id":"2505.17035","paper_version":1,"verdict":"REJECT","confidence":"LOW","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Using Doppler beaming of the EHT image of M87*, the authors derive a spin parameter a ~ 0.8 and an accretion rate between 4e-5 and 4e-1 solar masses per year.","lead":"The authors use Event Horizon Telescope images of the black hole M87* to estimate that its accretion disk rotates at about 14% of light speed, and use that to infer a black hole spin of about 0.8. They then use the polarization angle of the disk to estimate the infall speed and accretion rate, finding that the accretion power is comparable to the jet power.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Doppler beaming geometry likely misapplied: the paper uses cosθ≈0.96 for a near face-on disk, but the orbital velocity of the inner disk is nearly transverse to the line of sight.","rationale":"The reader's verdict identified the same geometric flaw as the weakest assumption. The concern is load-bearing because the spin estimate is directly derived from the Doppler beaming ratio; if the angle-to-line-of-sight is ~73° rather than 17°, the implied velocity and spin change by large factors and likely become unphysical. The internal inconsistency between the assumed ISCO radius (3 Schwarzschild radii, appropriate for a=0) and the claimed a≈0.8 (ISCO at ~1.5 Schwarzschild radii) further weakens the central claim. The Kerr correction in Appendix A.3 is circular: it assumes a=0.8 to find a≈1.0, and both are inconsistent with the direct ISCO measurement assumption. The paper is transparent and honest about uncertainties, which is a credit, but the load-bearing geometry is incorrect. The accretion rate and power claims inherit the velocity error and are also extremely wide, but the spin claim alone justifies rejection as stated.","tokens_in":8197,"tokens_out":1619,"duration_ms":12938,"concrete_test":"Recompute Section 2.1 using the correct geometry: for a face-on disk with inclination i = 17°, set cosθ = sin(i) cosφ for the approaching side with φ−φ0 chosen to maximize the projected velocity; i.e., use cosθ ≈ 0.29 instead of 0.96 in Eqs. 3-4. Determine what V_R and a are required to reproduce the observed brightness ratio (D_app/D_rec)^3 = 2.25. If V_R exceeds ~0.4c or if a becomes >1, the spin estimate of 0.8 is not supported.","verdict_should_be":"REJECT","load_bearing_attack":"The central spin estimate hinges on identifying the observed crescent brightness asymmetry purely with Doppler beaming of orbital motion in the disk plane (Section 2.1, Eqs. 1-4). The paper takes θ ≈ 17° as the angle between the matter velocity and the line of sight, citing M87* Paper VI. However, 17° is the viewing angle of the jet/disk axis, not the angle between an orbital velocity vector and the line of sight. For a disk with inclination i ≈ 17° (near face-on), the angle between an azimuthal orbital velocity vector and the line of sight ranges from 90° − i to 90° + i, i.e., around 73° to 107°, so cosθ ≈ ±0.29, not 0.96. Using cosθ ≈ 0.29 in Eqs. 3-4 with the observed brightness ratio (D_app/D_rec)^3 ≈ 2.25 yields V_R ≈ 0.4c (or more if the observed asymmetry is partially lensed/absorbed), changing the inferred spin drastically. The paper also treats the ISCO radius as directly measurable from the ring diameter (20 ± 2 μas ≈ 3 Schwarzschild radii), but the observed ring is dominated by photon-ring and lensing effects and is not a direct measure of ISCO; moreover, a spin of 0.8 has ISCO at ≈1.5 Schwarzschild radii, not 3, so the assumed ISCO radius and derived spin are internally inconsistent. The Appendix A.3 compounds this by 'correcting' to a Kerr metric starting from a=0.8 and recovering a≈1.0, which is circular. The accretion rate estimate is also extremely weakly constrained (four orders of magnitude), but the spin value is the central claim, and it rests on the geometric misapplication.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":8550,"tokens_out":7094,"duration_ms":70493,"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":[{"comment":"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":"Section 2.1, Eqs. (1)–(4)"},{"comment":"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.","section":"Section 2.2, Eq. (6)"},{"comment":"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":"Appendix A.3 and A.4"},{"comment":"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.","section":"Section 2.3 and Appendix B"}],"minor_comments":[{"comment":"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":"Appendix A.1"},{"comment":"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.","section":"Section 2, paragraph 3"},{"comment":"The term 'Schwarzchild' is used repeatedly (e.g., Sections 2.2 and 3, and Appendix A), but the correct spelling is 'Schwarzschild'.","section":"Throughout"},{"comment":"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.","section":"Section 2.1"}],"recommendation":"reject","confidential_remarks":"The central claim of the paper, a spin of about 0.8 for M87*, is built on a misapplication of the Doppler factor geometry and an internally inconsistent mapping of the observed ring radius to the ISCO. These are load-bearing errors that cannot be fixed by local edits; a corrected treatment would require re-deriving the velocity and spin with the proper line-of-sight projection and a self-consistent Kerr spacetime model. The accretion-rate estimate is also too weakly constrained to stand as a meaningful new result. I see no indication of plagiarism or citation manipulation; the rejection is based solely on the scientific validity of the main result."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThis 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.\n\nThe 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.\n\nThe 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.\n\nThe 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.\n\nWhat 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.\n\nFor 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.\n\nBest,\n[Your name]","headline":"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.","tokens_in":9084,"tokens_out":5166,"would_cite":false,"duration_ms":48775,"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":"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.","keywords":["M87*","black hole spin","dimensionless spin parameter","Doppler beaming","accretion disk","accretion rate","relativistic jets","Event Horizon Telescope"],"falsifier":"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.","tokens_in":7958,"feed_emoji":"🕳️","tokens_out":12606,"duration_ms":113397,"temperature":0.7,"pith_summary":"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.","feed_headline":"M87* spins at about 80 percent of the black-hole maximum","feed_subtitle":"A Doppler-beamed ring in the Event Horizon Telescope image gives spin ~0.8 and a jet-scale accretion power.","key_machinery":"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 $R_{\\rm ISCO}$.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Supplies the 2017 EHT image of M87* and the black hole mass $6.5\\times10^9\\,M_\\odot$ used in the spin calculation.","marker":"EHTC et al. 2019a"},{"why":"Provides the 17-degree inclination angle that sets $\\cos\\theta=0.96$ in the Doppler factor.","marker":"EHTC et al. 2019b"},{"why":"Provides the brightness cross-sections of the ring from which the Doppler ratio of about 2.25 is measured.","marker":"EHTC et al. 2019c"},{"why":"Supplies the polarization angle measurements used to fix the direction of the inflowing plasma, giving $V_A=V_R\\tan\\alpha$.","marker":"EHTC et al. 2021a"},{"why":"Supplies the electron density upper limit $n_e\\sim10^7\\,{\\rm cm}^{-3}$ used to bound the accretion rate.","marker":"EHTC et al. 2021b"},{"why":"Establishes the range of innermost stable circular orbit radii for a Kerr black hole against which $R_{\\rm ISCO}\\sim3R_S$ is assessed.","marker":"Bardeen et al. 1972"},{"why":"Supplies the spin-up timescale argument and the $a=0.998$ upper limit that frame the claim that $a\\sim0.8$ is a lower limit.","marker":"Thorne 1974"},{"why":"Supports applying the Doppler beaming calculation to a near edge-on disk, as assumed for M87*.","marker":"Medeiros et al. 2022"}],"fun_headline_variants":["M87* spins at least 80% of max, maybe more","M87* spin a~0.8, lower limit, near 0.998?","M87*: fast spin and jet-powering accretion","M87* spin estimate: 0.8, possibly near maximal","M87* black hole spins quick: a≥0.8"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["M87* spins at least 80% of max, maybe more","M87* spin a~0.8, lower limit, near 0.998?","M87*: fast spin and jet-powering accretion","M87* spin estimate: 0.8, possibly near maximal","M87* black hole spins quick: a≥0.8"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000787,"raw_usage":{"total_tokens":3508,"prompt_tokens":1016,"completion_tokens":2492,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":632,"completion_tokens_details":{"reasoning_tokens":2395}},"tokens_in":632,"tokens_out":2492,"duration_ms":16271,"temperature":1.0,"reasoning_tokens":2395,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T23:19:56.917725+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[],"review_version":1}