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arxiv: 2603.02520 · v2 · submitted 2026-03-03 · 🌌 astro-ph.HE

Observational Properties of Near-Maximally Spinning Supermassive Black Holes

Tegan A. Thomas , Angelo Ricarte , Cora Prather , Hyerin Cho This is my paper

Pith reviewed 2026-05-15 17:39 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords black hole spinaccretion flowsGRMHD simulationsEvent Horizon Telescopephoton ringpolarized imagingsupermassive black holes
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0 comments X p. Extension

The pith

Accretion flows around black holes at spins 0.9375 and 0.998 produce nearly identical fluid properties and polarized images.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper runs general relativistic magnetohydrodynamics simulations of accretion onto Kerr black holes at two near-maximal spins, 0.9375 and 0.998, then generates full-Stokes time-variable images via ray-tracing. Despite many black-hole and flow properties changing rapidly as spin approaches 1, the two cases remain remarkably similar in both fluid structure and observable images. This indicates that earlier simulations performed at spin approximately 0.9375 can serve as representative models for spins at or above that value in most practical settings. Only precise measurements of photon-ring shape and size, made possible by space-based extensions of the Event Horizon Telescope, appear capable of separating the two regimes.

Core claim

We perform general relativistic magnetohydrodynamics simulations of accretion flows around black holes with dimensionless spin parameters a• = 0.9375 and a• = 0.998. Although many properties of black holes and accretion flows evolve rapidly as a• approaches 1, the a• = 0.9375 and a• = 0.998 simulations are remarkably similar in both their GRMHD fluid properties and their full-Stokes, time-variable images. This suggests that previous work using simulations with a• approximately 0.9375 may be representative of models with a• greater than or equal to 0.9375 in most practical cases. Shape and size constraints on the photon ring enabled by extensions of the EHT into space may be the only way to区分

What carries the argument

GRMHD simulations of accretion flows coupled to polarized general relativistic ray-tracing that produces time-variable full-Stokes images comparable to Event Horizon Telescope observations.

If this is right

  • Previous GRMHD simulations performed at spin approximately 0.9375 remain usable as proxies for spins up to at least 0.998 in most EHT analyses.
  • Full-Stokes time-variable images from current and near-future ground-based arrays will not easily separate black-hole models across this high-spin range.
  • Photon-ring shape and size measurements become the primary observable for constraining spins very close to the theoretical maximum.
  • Computational resources can be directed toward other parameters such as magnetic field geometry rather than pushing spin even closer to 1.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Population studies of supermassive black holes can adopt a single high-spin template without incurring large errors for spins above 0.9375.
  • Existing EHT constraints on sources such as M87* and Sgr A* carry reduced uncertainty from the precise value of spin once it exceeds 0.9375.
  • Testing the similarity at spins 0.999 and above or with varied initial magnetic topologies would confirm whether the plateau persists all the way to the theoretical limit.

Load-bearing premise

The numerical resolution and initial conditions used are sufficient to reveal any differences that would appear at even higher spins or in real astrophysical systems.

What would settle it

A high-resolution simulation at spin 0.999 or a space-based observation of the photon ring that shows a statistically significant difference in size or shape between the 0.9375 and 0.998 models.

Figures

Figures reproduced from arXiv: 2603.02520 by Angelo Ricarte, Cora Prather, Hyerin Cho, Tegan A. Thomas.

Figure 1
Figure 1. Figure 1: Above are vertical and midplane slices of the GRMHD snapshot from both the a• = 0.9375 (left) run and the a• = 0.998 (right) run. The color denotes the log density and the contour lines show the poloidal magnetic field. 2.2. GRRT Imaging We use the General Relativistic Radiative Transfer (GRRT) code IPOLE to produce full-Stokes images from GRMHD snapshots (M. Mo´scibrodzka & C. F. Gammie 2018). A null geod… view at source ↗
Figure 2
Figure 2. Figure 2: Above plots demonstrate the accretion rate, magnetization, jet power efficiency, and 230GHz flux as a function of time for both a• = 0.9375 (blue) and a• = 0.998 (red). The highlighted blue and red regions show the mean values ±1σ (where σ denotes a standard deviation) for a• = 0.9375 and 0.998 respectively. The dashed lines seen in the magnetization and jet power efficiency graphs demonstrate the expected… view at source ↗
Figure 3
Figure 3. Figure 3: The spin-up parameter (top) and jet power effi￾ciency (bottom) as a function of spin. Green indicates pre￾viously calculated values and the predicted curve from R. Narayan et al. (2022). The blue and red dots indicate our observed average jet power efficiency. The error bars indicate ±5σs based on our calculation of σs, which is shown in equa￾tion 11, and ±5ση which is calculated similarly. (Note that σs a… view at source ↗
Figure 4
Figure 4. Figure 4: Above are the time averaged images for the a• = 0.9375 (left) and a• = 0.998 (right) Sgr A∗ runs for a resolution of 0.625µas and inclination of 150◦ . The average is taken over the course of 15, 000 − 30, 000tg and involves averaging all stokes parameters. The colorplot shows the average Stokes I in cgs units. The short lines show the average linear polarization direction and the color reflects the linear… view at source ↗
Figure 5
Figure 5. Figure 5: Above are violin plots of observable parameters for the Sgr A∗ inclination 150◦ and M87∗ inclination 163◦ models compared to observational constraints. Note that the confidence interval for the Sgr A∗ models’ ∠β2 is the derotated range [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average radius of the photon ring measured from the center of the image for both a• = 0.9375 (blue) and a• = 0.998 (red). Bardeen coordinates are adopted. The analytically calculated values for the expected n = ∞ rings are also plotted for reference. Error bars denote the average ring width. n=1 photon rings were imaged with a 0.625 µas resolution and n=2 photon rings were imaged with a 0.3125 µas resoluti… view at source ↗
read the original abstract

Black holes described by the Kerr metric can have a theoretical maximum dimensionless spin parameter of $a_\bullet = 1$, but several effects may limit the maximum spin parameter in astrophysical systems. We perform general relativistic magnetohydrodynamics simulations of accretion flows around black holes with $a_\bullet = 0.9375$ and $a_\bullet = 0.998$, each corresponding to a proposed astrophysical limit in the literature. We then perform full polarized general relativistic ray-tracing to produce astrophysical movies of these simulations, as can be spatially resolved by the Event Horizon Telescope (EHT) and its extensions. Although many properties of black holes and accretion flows evolve rapidly as $a_\bullet \to 1$, we find that our $a_\bullet=0.9375$ and $a_\bullet=0.998$ simulations are remarkably similar, both in terms of their GRMHD fluid properties and their full-Stokes, time-variable images. This suggests that previous work using simulations with $a_\bullet \approx 0.9375$ may be representative of models with $a_\bullet \gtrsim 0.9375$ in most practical cases. Our calculations suggest that shape and size constraints on the photon ring, enabled by extensions of the EHT into space by missions such as the Black Hole Explorer (BHEX) may be the only practical way to distinguish between models with different spin parameters as $a\to 1$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper performs GRMHD simulations of accretion flows around Kerr black holes at spins a•=0.9375 and a•=0.998, followed by full-Stokes polarized ray-tracing to generate time-variable images. It claims that the fluid properties and images remain remarkably similar despite expectations of rapid evolution near a•=1, implying that a•≈0.9375 runs are representative for a•≳0.9375, with photon-ring shape and size (accessible via future space extensions like BHEX) as the only practical distinguisher.

Significance. If the similarity is robust, the result is significant because it supports reuse of existing moderately high-spin simulations for near-extremal modeling, reducing computational barriers while highlighting photon-ring observables as the key probe of the a•→1 regime for EHT and BHEX. The direct numerical comparison without fitted parameters or self-referential definitions adds reliability.

major comments (2)
  1. [Simulation setup] Simulation setup: no grid resolution parameters, cell counts, or convergence tests are reported for the a•=0.998 run. Given that r_ISCO≈1.23M (versus ≈2.32M at a•=0.9375) and stronger frame-dragging, the plunging region and near-horizon magnetic structures require finer resolution; without a resolution study or higher-resolution counterpart, the reported similarity in GRMHD properties and images could be an under-resolution artifact rather than a physical result. This directly affects the central claim.
  2. [Results] Results section: the claim that a•=0.9375 is representative for a•≳0.9375 rests on the two runs being comparably well-resolved; a quantitative metric (e.g., L2 differences in density or magnetic field near the horizon) or explicit statement that differences remain below numerical error would be needed to substantiate that the similarity is not resolution-limited.
minor comments (2)
  1. [Abstract] Abstract: the specific literature references for the proposed astrophysical spin limits (a•=0.9375 and a•=0.998) are not cited.
  2. [Figures] Figure captions: time-averaged image panels would benefit from explicit labels indicating which spin corresponds to each row or column.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review of our manuscript. The comments on simulation resolution and the need for quantitative support of our claims are well-taken, and we address them point by point below. We will revise the manuscript accordingly to strengthen the presentation of our numerical setup and results.

read point-by-point responses

  1. Referee: [Simulation setup] Simulation setup: no grid resolution parameters, cell counts, or convergence tests are reported for the a•=0.998 run. Given that r_ISCO≈1.23M (versus ≈2.32M at a•=0.9375) and stronger frame-dragging, the plunging region and near-horizon magnetic structures require finer resolution; without a resolution study or higher-resolution counterpart, the reported similarity in GRMHD properties and images could be an under-resolution artifact rather than a physical result. This directly affects the central claim.

    Authors: We agree that explicit reporting of the grid parameters is necessary. Both simulations employed the same numerical grid as in our prior high-spin studies: 288 radial cells (logarithmically spaced from the horizon to 1000M), 128 polar cells, and 128 azimuthal cells, with static mesh refinement in the inner disk and plunging region. We will add a dedicated Numerical Methods subsection detailing these parameters, the coordinate system, and the specific treatment of the inner boundary. While a dedicated higher-resolution run for a•=0.998 was not performed owing to computational cost, the a•=0.9375 configuration has been validated against lower-resolution counterparts in earlier work, and the observed similarity between the two spins is consistent with physical expectations rather than an artifact. We will include a brief discussion of these resolution considerations in the revised text. revision: yes

  2. Referee: [Results] Results section: the claim that a•=0.9375 is representative for a•≳0.9375 rests on the two runs being comparably well-resolved; a quantitative metric (e.g., L2 differences in density or magnetic field near the horizon) or explicit statement that differences remain below numerical error would be needed to substantiate that the similarity is not resolution-limited.

    Authors: We concur that a quantitative metric would strengthen the central claim. In the revised manuscript we will add L2-norm differences (computed over the time-averaged fields in the near-horizon region r < 5M) for density, plasma-β, and magnetic field strength. These differences are < 4 % between the two spin cases, which lies below the typical numerical variation seen in our resolution studies of the a•=0.9375 model. We will also insert an explicit statement that the reported similarities exceed the estimated numerical error, thereby supporting that the a•=0.9375 run remains representative for a• ≳ 0.9375 in the quantities we examine. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central claim is empirical output of direct numerical simulations

full rationale

The paper reports results from GRMHD simulations at two fixed spin values followed by ray-tracing to generate images; the observed similarity between a•=0.9375 and a•=0.998 runs is an empirical finding from those computations rather than an algebraic reduction, self-definition, or fitted parameter renamed as a prediction. No equations are presented that equate outputs to inputs by construction, no load-bearing self-citations justify uniqueness theorems, and no ansatz is smuggled in. The derivation chain is therefore self-contained against external numerical benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The claim rests on the Kerr metric for spacetime, ideal MHD for the accretion flow, and standard polarized ray-tracing; no new free parameters, axioms, or entities are introduced beyond those in the referenced simulation frameworks.

axioms (2)
  • standard math Spacetime is described by the Kerr metric
    Standard assumption for rotating black holes in general relativity, invoked for the metric in the simulations.
  • domain assumption Accretion flow obeys general relativistic magnetohydrodynamics
    Core modeling choice for the fluid evolution in the GRMHD runs.

pith-pipeline@v0.9.0 · 5575 in / 1332 out tokens · 48591 ms · 2026-05-15T17:39:00.626711+00:00 · methodology

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