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arxiv: 2606.11322 · v1 · pith:XS2XV6IFnew · submitted 2026-06-09 · 🌌 astro-ph.HE

Ring Position Angles and Spin in M87* and Sgr A*

Nicholas S. Conroy , Michi Baub\"ock , Vadim Bernshteyn , Paul Tiede , Abhishek V. Joshi , Cora Prather , Charles F. Gammie This is my paper

Pith reviewed 2026-06-27 11:55 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords black hole spinM87*Sgr A*GRMHD modelsevent horizon telescopering asymmetryposition angleaccretion flow
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The pith

The position angle of peak brightness asymmetry in black hole rings aligns with the approaching limb for high spin magnitudes.

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

The paper studies the position angle PA1 of the brightest part of the ring asymmetry in GRMHD models of M87* and Sgr A*. It finds that for larger spin values, whether positive or strongly negative, the average PA1 stays within 1 sigma of the approaching side of the black hole no matter the viewing angle or disk strength. Matching the observed spread of asymmetry magnitude and angle in M87* data against the models lets observers mildly rule out small spins and strongly rule out any spin vector aimed at Earth. The same alignment also hints that M87* lacks a large disk tilt relative to its jet and opens a path to constrain Sgr A* spin with future detections.

Core claim

In GRMHD models, for black hole spins a* > 0 and a* ≲ -0.5 the mean PA1 falls within 1σ of the approaching limb independent of inclination, disk magnetization, or source. Direct comparison of the (a1, PA1) distribution measured in M87* images with these models mildly disfavors low-magnitude spins and strongly disfavors all spin vectors that point toward Earth. Alignment of PA1 with the large-scale jet axis suggests M87* lacks a large disk tilt, while PA1 combined with pattern speed could distinguish prograde from retrograde spin at roughly 84 percent accuracy; a future detection in Sgr A* would similarly constrain its spin magnitude and direction.

What carries the argument

The mean position angle PA1 of the peak brightness asymmetry, which tracks the approaching limb in high-spin models.

If this is right

  • Alignment of PA1 with the jet axis implies M87* does not have a large disk tilt.
  • PA1 together with pattern speed can distinguish prograde from retrograde spin in M87* at about 84 percent accuracy under 2026 video conditions.
  • A detection of (a1, PA1) in Sgr A* would constrain both the magnitude and direction of its spin vector.
  • With a larger sample of horizon-scale sources, the combination of ring diameter, asymmetry magnitude, and asymmetry angle could constrain mass, spin, and inclination.

Where Pith is reading between the lines

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

  • The same PA1 observable could be applied to additional black holes once EHT arrays expand.
  • If the alignment persists across varied models, PA1 offers a spin diagnostic that is relatively insensitive to exact disk magnetization.
  • Repeated measurements over time could test whether spin vectors in active galactic nuclei show preferred orientations relative to their jets.

Load-bearing premise

The GRMHD models used are representative enough of real accretion flows that differences in observed (a1, PA1) can be attributed to spin rather than missing physics such as disk tilt or emission details.

What would settle it

A measured PA1 in M87* that lies outside the 1σ range of all high-spin model predictions would show that the claimed alignment does not hold under actual conditions.

Figures

Figures reproduced from arXiv: 2606.11322 by Abhishek V. Joshi, Charles F. Gammie, Cora Prather, Michi Baub\"ock, Nicholas S. Conroy, Paul Tiede, Vadim Bernshteyn.

Figure 1
Figure 1. Figure 1: — Mean MAD model images (averaging over time, Rlow, and Rhigh, and blurred using a 10 µas full width at half maximum Gaussian kernel) across spin and inclination, for both M87* (i = 17◦) and Sgr A* (i = 30, 50, 90◦). White wedges shows the measured circular standard deviation σ in PA1 about the circular mean. Images are oriented so that disk angular momentum vectors project along PA = 0, prograde spin vect… view at source ↗
Figure 2
Figure 2. Figure 2: — Distributions of PA1 for M87* (left) and Sgr A* (right). Lines correspond to the circular mean µ and colored bands correspond to the circular standard deviation σ of the distribution. Images are oriented so that disk angular momentum vectors project along PA = 0, prograde spin vectors project along PA = 0, and retrograde spin vectors project along PA = 180◦. Across all high-spin models, PA1 falls within … view at source ↗
Figure 3
Figure 3. Figure 3: — Timeseries of PA1 for a fiducial MAD spin-zero model (left) and the corresponding distribution density (right). The distribution evolves stochastically about the circular mean µ (dashed black line) with a circular standard deviation σ (purple dashed line) and correlation time τcorr. Right, we fit a von Mises distribution (yellow line) as an approximation of the circular Gaussian distribution. -0.97 -0.94… view at source ↗
Figure 4
Figure 4. Figure 4: — A “pizza plot” showing constraints based on the recovered asymmetry magnitude and position angle of M87* in 2017 and 2018. Subplot rows correspond to MAD and SANE, subplots columns correspond to inclination, radial position correspond to Rhigh (marginalizing across Rlow), and azimuthal position correspond to spin. Models are disfavored when grey or red, for p-value ≲ 0.05. Here, the asymmetry favors spin… view at source ↗
Figure 5
Figure 5. Figure 5: — Constraints on the sign of M87* models’ inclination and spin, based on model videos with realistic duration. We measure the direction of the pattern speed and whether PA1 occurs above or below the jet axis (i.e. the sign of sin ∆PA for ∆PA ≡ PA1 − PAjet). We recover the correct sign of the spin using cos idisk and cos ispin ∼ 84% of the time (for inclination to the accretion disk angular momentum vector … view at source ↗
Figure 6
Figure 6. Figure 6: — The asymmetry magnitude distribution in Sgr A* MAD models across spin at i = 30◦ (yellow), 50◦ (purple), and 90◦ (blue). Lines and surrounding shaded regions show the mode µ and standard deviation σ respectively for the fitted truncated Normal distribution, without observational error from limited (u, v) coverage. For observations, the dashed gray line shows the mean from snapshot geometric modeling with… view at source ↗
Figure 7
Figure 7. Figure 7: — The direction of various galactic center L⃗ vectors as viewed from Earth, as a function of PA (horizontal axis) and i (vertical axis). Shaded regions illustrate approximate 1σ uncertainties. Constraints on the Sgr A* spin vector (this work) using April 6-7 EHT data are shown in yellow, although we emphasize these constraints are tentative due to limited (u, v) coverage. Other galactic center angular mome… view at source ↗
Figure 8
Figure 8. Figure 8: — Left: the density of the m = 1 position angles for M87* MAD models measured in the image domain (PA1,I ) and (u, v) domain (PA1,UV ) assuming 2018 M87* (u, v) coverage, calculated using Gaussian kernel density estimation. The dashed red line corresponds to PA1,UV = PA1,I . Right: The density of position angle measurements across PA1,UV − PA1,I , with 1σ (for circular standard deviation σ), 90%, and 99% b… view at source ↗
Figure 9
Figure 9. Figure 9: — As in [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
read the original abstract

Event Horizon Telescope (EHT) images of black holes appear as rings with a brightness asymmetry. Here, we expand on our previous study of the asymmetry magnitude $a_1$ to study the position angle of the peak brightness asymmetry $\mathrm{PA}_1$ in general relativistic magnetohydrodynamic (GRMHD) models. For larger spin magnitudes ($a_{*}>0$ and $a_{*}\lesssim-0.5$), the mean $\mathrm{PA}_1$ falls within $1\sigma$ of the approaching limb of the black hole, regardless of viewing inclination, disk magnetization, or source. By comparing the $(a_1, \mathrm{PA}_1)$ distribution in M87* observations with models, we demonstrate that we can mildly disfavor low-magnitude spins and strongly disfavor all spin vectors that point toward Earth. The alignment of $\mathrm{PA}_1$ relative to the large-scale jet axis may suggest that M87*'s disk does not have a large tilt. By combining $\mathrm{PA}_1$ with the pattern speed measured in optimistic 2026 M87* video conditions, the EHT can constrain whether M87* is prograde or retrograde with $\sim 84\%$ accuracy. In Sgr A*, we show that a detection of $(a_1, \mathrm{PA}_1)$ could constrain the magnitude and direction of the galactic center spin vector. Finally, if future EHT expansions increase the sample of horizon-scale sources, a simple set of observables (ring diameter, asymmetry magnitude, and asymmetry angle) could enable robust constraints on black hole mass, spin, and inclination.

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

3 major / 2 minor

Summary. The paper extends prior work on the brightness asymmetry magnitude a1 in EHT ring images to the position angle PA1 of the peak asymmetry in a library of GRMHD simulations. It reports that for |a*| ≳ 0.5 the mean PA1 lies within 1σ of the approaching limb independent of inclination, magnetization, and source; compares the observed (a1, PA1) distribution in M87* to the models to mildly disfavor low-magnitude spins and strongly disfavor Earth-pointing spin vectors; and argues that PA1 plus future pattern-speed measurements can distinguish prograde/retrograde rotation at ~84% accuracy while also offering constraints for Sgr A*.

Significance. If the sampled GRMHD library is representative, the result supplies a new, relatively simple observable (PA1) that can be combined with a1 and ring diameter to place statistical limits on black-hole spin vector orientation. The explicit comparison of simulated versus observed (a1, PA1) distributions and the forward-looking statements about 2026 video data constitute concrete, falsifiable predictions that strengthen the manuscript's utility for EHT analysis.

major comments (3)
  1. [Results section on PA1 alignment (likely §3–4)] The central claim that mean PA1 falls within 1σ of the approaching limb for a* > 0 and a* ≲ −0.5 (independent of inclination, magnetization, and source) is load-bearing for the subsequent statistical disfavoring of spin vectors. The manuscript does not appear to include tilted-disk GRMHD runs; a tilt ≳ 10° can rotate the effective Doppler pattern and shift the PA1 distribution by tens of degrees, directly eroding the claimed 1σ alignment and the exclusion of Earth-pointing spins.
  2. [Comparison with M87* observations (likely §5)] The statement that the (a1, PA1) distribution in M87* observations “mildly disfavors low-magnitude spins and strongly disfavors all spin vectors that point toward Earth” rests on a direct comparison whose statistical details (sample size per (a*, i, σ) bin, exact definition of the 1σ contour, treatment of observational uncertainties) are not provided in sufficient detail to verify the quoted confidence levels.
  3. [Discussion of future EHT video data] The ~84% accuracy claim for distinguishing prograde versus retrograde rotation when PA1 is combined with future pattern-speed measurements assumes that the optimistic 2026 video conditions will yield an independent pattern-speed measurement whose uncertainty does not correlate with the PA1 measurement; this joint-error budget is not quantified.
minor comments (2)
  1. [Introduction] Notation: the symbols a1 and PA1 are introduced without an explicit reminder of their definitions from the prior a1 paper; a one-sentence recap would aid readability.
  2. [Figure captions] Figure captions should state the number of GRMHD snapshots or runs contributing to each histogram so that the reader can judge the robustness of the reported means and 1σ intervals.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have identified important areas for clarification and improvement. We respond to each major comment below.

read point-by-point responses

  1. Referee: The central claim that mean PA1 falls within 1σ of the approaching limb for a* > 0 and a* ≲ −0.5 (independent of inclination, magnetization, and source) is load-bearing for the subsequent statistical disfavoring of spin vectors. The manuscript does not appear to include tilted-disk GRMHD runs; a tilt ≳ 10° can rotate the effective Doppler pattern and shift the PA1 distribution by tens of degrees, directly eroding the claimed 1σ alignment and the exclusion of Earth-pointing spins.

    Authors: We agree that the GRMHD library used consists exclusively of untilted, aligned disks. The independence claimed is with respect to inclination, magnetization, and source within that library, but does not extend to tilted configurations. We will revise the manuscript to explicitly state this scope and to discuss tilted disks as a limitation that could affect PA1, with plans to address tilted models in future work. revision: yes

  2. Referee: The statement that the (a1, PA1) distribution in M87* observations “mildly disfavors low-magnitude spins and strongly disfavors all spin vectors that point toward Earth” rests on a direct comparison whose statistical details (sample size per (a*, i, σ) bin, exact definition of the 1σ contour, treatment of observational uncertainties) are not provided in sufficient detail to verify the quoted confidence levels.

    Authors: We acknowledge that additional statistical details are required for full verification. In the revised manuscript we will expand the relevant sections to report sample sizes per bin, the precise definition of the 1σ contours, and the treatment of EHT observational uncertainties in the comparison. revision: yes

  3. Referee: The ~84% accuracy claim for distinguishing prograde versus retrograde rotation when PA1 is combined with future pattern-speed measurements assumes that the optimistic 2026 video conditions will yield an independent pattern-speed measurement whose uncertainty does not correlate with the PA1 measurement; this joint-error budget is not quantified.

    Authors: The quoted accuracy is an estimate derived under the optimistic 2026 conditions with the assumption of independent measurements. We will revise the text to make this assumption explicit and to note that a complete joint-error analysis would require further modeling beyond the present scope. revision: partial

Circularity Check

0 steps flagged

Minor self-citation present but central comparison is independent

full rationale

The derivation compares simulated (a1, PA1) distributions from GRMHD models directly to M87* observations to constrain spin, with no reduction of predictions to fitted inputs or self-definitional loops. The abstract notes expansion on a prior study of a1, constituting one minor self-citation that is not load-bearing for the spin disfavoring claims. No uniqueness theorems, ansatzes smuggled via citation, or renaming of known results appear in the provided text. The result remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no extractable free parameters, axioms, or invented entities; all such details reside in the unreviewed full manuscript.

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Works this paper leans on

66 extracted references · 66 canonical work pages

  1. [1]

    2025, Living Reviews in Relativity, 28, 4, doi:10.1007/s41114-025-00057-0

    Ayzenberg, D., Blackburn, L., Brito, R., et al. 2025, Living Reviews in Relativity, 28, 4, doi:10.1007/s41114-025-00057-0

    work page doi:10.1007/s41114-025-00057-0 2025

  2. [2]

    E., et al

    Backes, M., Müller, C., Conway, J. E., et al. 2016, in The 4th Annual Conference on High Energy Astrophysics in Southern Africa (HEASA 2016), 29, doi:10.22323/1.275.0029

    work page doi:10.22323/1.275.0029 2016

  3. [3]

    K., et al

    Bartko, H., Martins, F., Fritz, T. K., et al. 2009, ApJ, 697, 1741, doi:10.1088/0004-637X/697/2/1741

    work page doi:10.1088/0004-637x/697/2/1741 2009

  4. [4]

    2010, ApJ, 708, 834, doi:10.1088/0004-637X/708/1/834

    Bartko, H., Martins, F., Trippe, S., et al. 2010, ApJ, 708, 834, doi:10.1088/0004-637X/708/1/834

    work page doi:10.1088/0004-637x/708/1/834 2010

  5. [5]

    S., Dubois, Y., Volonteri, M., et al

    Beckmann, R. S., Dubois, Y., Volonteri, M., et al. 2025, MNRAS, 536, 1838, doi:10.1093/mnras/stae2595

    work page doi:10.1093/mnras/stae2595 2025

  6. [6]

    M., Levin, Y., Eisenhauer, F., et al

    Beloborodov, A. M., Levin, Y., Eisenhauer, F., et al. 2006, ApJ, 648, 405, doi:10.1086/504279

    work page doi:10.1086/504279 2006

  7. [7]

    S., Bauböck, M., et al

    Bernshteyn, V., Conroy, N. S., Bauböck, M., et al. 2026, arXiv e-prints, arXiv:2601.00394, doi:10.48550/arXiv.2601.00394

    work page doi:10.48550/arxiv.2601.00394 2026

  8. [8]

    S., & Ruzmaikin, A

    Bisnovatyi-Kogan, G. S., & Ruzmaikin, A. A. 1974, Ap&SS, 28, 45, doi:10.1007/BF00642237

    work page doi:10.1007/bf00642237 1974

  9. [9]

    D., & Znajek, R

    Blandford, R. D., & Znajek, R. L. 1977, MNRAS, 179, 433, doi:10.1093/mnras/179.3.433

    work page doi:10.1093/mnras/179.3.433 1977

  10. [10]

    E., Fish, V

    Broderick, A. E., Fish, V. L., Johnson, M. D., et al. 2016, ApJ, 820, 137, doi:10.3847/0004-637X/820/2/137

    work page doi:10.3847/0004-637x/820/2/137 2016

  11. [11]

    2025, MNRAS, 537, 2496, doi:10.1093/mnras/staf200

    Chael, A. 2025, MNRAS, 537, 2496, doi:10.1093/mnras/staf200

    work page doi:10.1093/mnras/staf200 2025

  12. [12]

    N., & Quataert, E

    Chael, A., Lupsasca, A., Wong, G. N., & Quataert, E. 2023, arXiv e-prints, arXiv:2307.06372, doi:10.48550/arXiv.2307.06372

    work page doi:10.48550/arxiv.2307.06372 2023

  13. [13]

    D., Bouman, K

    Chael, A. A., Johnson, M. D., Bouman, K. L., et al. 2018, ApJ, 857, 23, doi:10.3847/1538-4357/aab6a8

    work page doi:10.3847/1538-4357/aab6a8 2018

  14. [14]

    2020, MNRAS, 499, 362, doi:10.1093/mnras/staa2718

    Chatterjee, K., Younsi, Z., Liska, M., et al. 2020, MNRAS, 499, 362, doi:10.1093/mnras/staa2718

    work page doi:10.1093/mnras/staa2718 2020

  15. [15]

    S., Bauböck, M., Dhruv, V., et al

    Conroy, N. S., Bauböck, M., Dhruv, V., et al. 2025, arXiv e-prints, arXiv:2510.08848, doi:10.48550/arXiv.2510.08848

    work page doi:10.48550/arxiv.2510.08848 2025

  16. [16]

    S., Bauböck, M., Dhruv, V., et al

    Conroy, N. S., Bauböck, M., Dhruv, V., et al. 2023, The Astrophysical Journal, 951, 46, doi:10.3847/1538-4357/acd2c8

    work page doi:10.3847/1538-4357/acd2c8 2023

  17. [17]

    2023, Nature, 621, 711, doi:10.1038/s41586-023-06479-6

    Cui, Y., Hada, K., Kawashima, T., et al. 2023, Nature, 621, 711, doi:10.1038/s41586-023-06479-6

    work page doi:10.1038/s41586-023-06479-6 2023

  18. [18]

    V., & Gammie, C

    Dhruv, V., Prather, B., Chandra, M., Joshi, A. V., & Gammie, C. F. 2025, ApJ, 993, L33, doi:10.3847/2041-8213/ae1236

    work page doi:10.3847/2041-8213/ae1236 2025

  19. [19]

    Dhruv, V., Prather, B., Wong, G., & Gammie, C. F. 2024, arXiv e-prints, arXiv:2411.12647, doi:10.48550/arXiv.2411.12647 Position Angles in M87* and Sgr A* 13 TABLE 1 Circular Gaussian Fits to the Brightness Asymmetry Position AnglePA1 Source MAD/SANE Spin inclination [deg]R high Rlow µ[deg]σ[deg]M o[deg] M87* MAD−0.97 17All All269 20 270 M87* MAD−0.9375 1...

    work page doi:10.48550/arxiv.2411.12647 2024

  20. [20]

    S., Barrett, J., Blackburn, L., et al

    Doeleman, S. S., Barrett, J., Blackburn, L., et al. 2023, Galaxies, 11, 107, doi:10.3390/galaxies11050107

    work page doi:10.3390/galaxies11050107 2023

  21. [21]

    2006, A&A, 455, 1, doi:10.1051/0004-6361:20064948 Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., et al

    Eckart, A., Schödel, R., Meyer, L., et al. 2006, A&A, 455, 1, doi:10.1051/0004-6361:20064948 Event Horizon Telescope Collaboration, Akiyama, K., Alberdi, A., et al. 2019a, ApJ, 875, L1, doi:10.3847/2041-8213/ab0ec7 —. 2019b, ApJ, 875, L5, doi:10.3847/2041-8213/ab0f43 Event Horizon Telescope Collaboration, Akiyama, K., Algaba, J. C., et al. 2021, ApJ, 910,...

    work page doi:10.1051/0004-6361:20064948 2006

  22. [22]

    G., & Moncrief, V

    Fishbone, L. G., & Moncrief, V. 1976, ApJ, 207, 962, doi:10.1086/154565

    work page doi:10.1086/154565 1976

  23. [23]

    2023, ApJ, 957, 103, doi:10.3847/1538-4357/acfa77 14 Conroy et al

    Galishnikova, A., Philippov, A., & Quataert, E. 2023, ApJ, 957, 103, doi:10.3847/1538-4357/acfa77 14 Conroy et al

    work page doi:10.3847/1538-4357/acfa77 2023

  24. [24]

    Gammie, C. F. 2025, ApJ, 980, 193, doi:10.3847/1538-4357/adaea3

    work page doi:10.3847/1538-4357/adaea3 2025

  25. [25]

    F., McKinney, J

    Gammie, C. F., McKinney, J. C., & Tóth, G. 2003, ApJ, 589, 444, doi:10.1086/374594

    work page doi:10.1086/374594 2003

  26. [26]

    2010, Reviews of Modern Physics, 82, 3121, doi: 10.1103/RevModPhys.82.3121

    Genzel, R., Eisenhauer, F., & Gillessen, S. 2010, Reviews of Modern Physics, 82, 3121, doi:10.1103/RevModPhys.82.3121

    work page doi:10.1103/revmodphys.82.3121 2010

  27. [27]

    L., & Syrovatskii, S

    Ginzburg, V. L., & Syrovatskii, S. I. 1965, ARA&A, 3, 297, doi:10.1146/annurev.aa.03.090165.001501 GRAVITY Collaboration, Abuter, R., Amorim, A., et al. 2018, A&A, 618, L10, doi:10.1051/0004-6361/201834294 GRAVITY Collaboration, Bauböck, M., Dexter, J., et al. 2020, A&A, 635, A143, doi:10.1051/0004-6361/201937233 Gravity Collaboration, Abuter, R., Aimar, ...

    work page doi:10.1146/annurev.aa.03.090165.001501 1965

  28. [28]

    V., Narayan, R., & Abramowicz, M

    Igumenshchev, I. V., Narayan, R., & Abramowicz, M. A. 2003, ApJ, 592, 1042, doi:10.1086/375769

    work page doi:10.1086/375769 2003

  29. [29]

    M., Geis, N., Genzel, R., et al

    Jackson, J. M., Geis, N., Genzel, R., et al. 1993, ApJ, 402, 173, doi:10.1086/172120

    work page doi:10.1086/172120 1993

  30. [30]

    Jeter, B., & Broderick, A. E. 2021, ApJ, 908, 139, doi:10.3847/1538-4357/abda3d

    work page doi:10.3847/1538-4357/abda3d 2021

  31. [31]

    M., & Nathanail, A

    Jiang, H.-X., Mizuno, Y., Fromm, C. M., & Nathanail, A. 2023, MNRAS, 522, 2307, doi:10.1093/mnras/stad1106

    work page doi:10.1093/mnras/stad1106 2023

  32. [32]

    D., Akiyama, K., Blackburn, L., et al

    Johnson, M. D., Akiyama, K., Blackburn, L., et al. 2023a, Galaxies, 11, 61, doi:10.3390/galaxies11030061 —. 2023b, Galaxies, 11, 61, doi:10.3390/galaxies11030061

    work page doi:10.3390/galaxies11030061

  33. [33]

    D., Akiyama, K., Baturin, R., et al

    Johnson, M. D., Akiyama, K., Baturin, R., et al. 2024, arXiv e-prints, arXiv:2406.12917, doi:10.48550/arXiv.2406.12917 La Bella, N., Issaoun, S., Roelofs, F., Fromm, C., & Falcke, H. 2023, A&A, 672, A16, doi:10.1051/0004-6361/202245344

    work page doi:10.48550/arxiv.2406.12917 2024

  34. [34]

    H., Achtermann, J

    Lacy, J. H., Achtermann, J. M., & Serabyn, E. 1991, ApJ, 380, L71, doi:10.1086/186176

    work page doi:10.1086/186176 1991

  35. [35]

    2024, ApJ, 975, 278, doi:10.3847/1538-4357/ad81f5

    Levin, Y. 2024, ApJ, 975, 278, doi:10.3847/1538-4357/ad81f5

    work page doi:10.3847/1538-4357/ad81f5 2024

  36. [36]

    Levin, Y., & Beloborodov, A. M. 2003, ApJ, 590, L33, doi:10.1086/376675

    work page doi:10.1086/376675 2003

  37. [37]

    R., & Baganoff, F

    Li, Z., Morris, M. R., & Baganoff, F. K. 2013, ApJ, 779, 154, doi:10.1088/0004-637X/779/2/154

    work page doi:10.1088/0004-637x/779/2/154 2013

  38. [38]

    2017, Monthly Notices of the Royal Astronomical Society: Letters, 474, L81, doi:10.1093/mnrasl/slx174

    Liska, M., Hesp, C., Tchekhovskoy, A., et al. 2017, Monthly Notices of the Royal Astronomical Society: Letters, 474, L81, doi:10.1093/mnrasl/slx174

    work page doi:10.1093/mnrasl/slx174 2017

  39. [39]

    Liszt, H. S. 2003, A&A, 408, 1009, doi:10.1051/0004-6361:20031033

    work page doi:10.1051/0004-6361:20031033 2003

  40. [40]

    R., Ghez, A

    Lu, J. R., Ghez, A. M., Hornstein, S. D., et al. 2009, ApJ, 690, 1463, doi:10.1088/0004-637X/690/2/1463

    work page doi:10.1088/0004-637x/690/2/1463 2009

  41. [41]

    M., Chen, A

    Mehlhaff, J. M., Chen, A. Y., Luepker, M., & Yuan, Y. 2026, arXiv e-prints, arXiv:2602.22168, doi:10.48550/arXiv.2602.22168 Mościbrodzka, M., Falcke, H., & Shiokawa, H. 2016, A&A, 586, A38, doi:10.1051/0004-6361/201526630 Mościbrodzka, M., & Gammie, C. F. 2018, MNRAS, 475, 43, doi:10.1093/mnras/stx3162

    work page doi:10.48550/arxiv.2602.22168 2026

  42. [42]

    Starck, J. L. 2008, ApJ, 673, 251, doi:10.1086/521641 Mužić, K., Eckart, A., Schödel, R., et al. 2010, A&A, 521, A13, doi:10.1051/0004-6361/200913087 Mužić, K., Eckart, A., Schödel, R., Meyer, L., & Zensus, A. 2007, A&A, 469, 993, doi:10.1051/0004-6361:20066265

    work page doi:10.1086/521641 2008

  43. [43]

    V., & Abramowicz, M

    Narayan, R., Igumenshchev, I. V., & Abramowicz, M. A. 2003, PASJ, 55, L69, doi:10.1093/pasj/55.6.L69

    work page doi:10.1093/pasj/55.6.l69 2003

  44. [44]

    D., 2012, @doi [ ] 10.1111/j.1365-2966.2012.21871.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.426.3282M 426, 3282

    Narayan, R., SÄ dowski, A., Penna, R. F., & Kulkarni, A. K. 2012, MNRAS, 426, 3241, doi:10.1111/j.1365-2966.2012.22002.x

    work page doi:10.1111/j.1365-2966.2012.22002.x 2012

  45. [45]

    Palumbo, D. C. M., Wong, G. N., & Prather, B. S. 2020, ApJ, 894, 156, doi:10.3847/1538-4357/ab86ac

    work page doi:10.3847/1538-4357/ab86ac 2020

  46. [46]

    2004, A&A, 426, 81, doi:10.1051/0004-6361:20034209

    Paumard, T., Maillard, J.-P., & Morris, M. 2004, A&A, 426, 81, doi:10.1051/0004-6361:20034209

    work page doi:10.1051/0004-6361:20034209 2004

  47. [47]

    W., Palumbo, D

    Pesce, D. W., Palumbo, D. C. M., Ricarte, A., et al. 2022, Galaxies, 10, 109, doi:10.3390/galaxies10060109

    work page doi:10.3390/galaxies10060109 2022

  48. [48]

    Prather, B. S. 2025, in New Frontiers in GRMHD Simulations, ed. C. Bambi, Y. Mizuno, S. Shashank, & F. Yuan, 167–201, doi:10.1007/978-981-97-8522-3_5

    work page doi:10.1007/978-981-97-8522-3_5 2025

  49. [49]

    2023, Galaxies, 11, 15, doi:10.3390/galaxies11010015

    Ramakrishnan, V., Nagar, N., Arratia, V., et al. 2023, Galaxies, 11, 15, doi:10.3390/galaxies11010015

    work page doi:10.3390/galaxies11010015 2023

  50. [50]

    M., White, C

    Ressler, S. M., White, C. J., Quataert, E., & Stone, J. M. 2020, ApJ, 896, L6, doi:10.3847/2041-8213/ab9532

    work page doi:10.3847/2041-8213/ab9532 2020

  51. [51]

    S., Wielgus, M., et al

    Ricarte, A., Conroy, N. S., Wielgus, M., et al. 2025, ApJ, 987, 152, doi:10.3847/1538-4357/add729

    work page doi:10.3847/1538-4357/add729 2025

  52. [52]

    2024, A&A, 685, A92, doi:10.1051/0004-6361/202348925

    Sala, L., Valentini, M., Biffi, V., & Dolag, K. 2024, A&A, 685, A92, doi:10.1051/0004-6361/202348925

    work page doi:10.1051/0004-6361/202348925 2024

  53. [53]

    Salas, L. D. S., Liska, M. T. P., Markoff, S. B., et al. 2025, MNRAS, 538, 698, doi:10.1093/mnras/staf240

    work page doi:10.1093/mnras/staf240 2025

  54. [54]

    , keywords =

    Shapiro, S. L., Lightman, A. P., & Eardley, D. M. 1976, ApJ, 204, 187, doi:10.1086/154162 Sądowski, A., Narayan, R., Penna, R., & Zhu, Y. 2013, MNRAS, 436, 3856, doi:10.1093/mnras/stt1881

    work page doi:10.1086/154162 1976

  55. [55]

    1989, ApJ, 341, L47, doi:10.1086/185454

    Sofue, Y., Reich, W., & Reich, P. 1989, ApJ, 341, L47, doi:10.1086/185454

    work page doi:10.1086/185454 1989

  56. [56]

    Su, M., & Finkbeiner, D. P. 2012, ApJ, 753, 61, doi:10.1088/0004-637X/753/1/61 The Event Horizon Telescope Collaboration. 2024, arXiv e-prints, arXiv:2410.02986, doi:10.48550/arXiv.2410.02986

    work page doi:10.1088/0004-637x/753/1/61 2012

  57. [57]

    2022, The Journal of Open Source Software, 7, 4457, doi:10.21105/joss.04457

    Tiede, P. 2022, The Journal of Open Source Software, 7, 4457, doi:10.21105/joss.04457

    work page doi:10.21105/joss.04457 2022

  58. [58]

    E., & Palumbo, D

    Tiede, P., Broderick, A. E., & Palumbo, D. C. M. 2022, ApJ, 925, 122, doi:10.3847/1538-4357/ac3a6b von Fellenberg, S. D., Gillessen, S., Stadler, J., et al. 2022, ApJ, 932, L6, doi:10.3847/2041-8213/ac68ef

    work page doi:10.3847/1538-4357/ac3a6b 2022

  59. [59]

    C., Hardee, P

    Walker, R. C., Hardee, P. E., Davies, F. B., Ly, C., & Junor, W. 2018, ApJ, 855, 128, doi:10.3847/1538-4357/aaafcc

    work page doi:10.3847/1538-4357/aaafcc 2018

  60. [60]

    2024, Nature Astronomy, 8, 1592, doi:10.1038/s41550-024-02358-w

    Wang, Y., & Zhang, B. 2024, Nature Astronomy, 8, 1592, doi:10.1038/s41550-024-02358-w

    work page doi:10.1038/s41550-024-02358-w 2024

  61. [61]

    1992, Nature, 357, 308, doi:10.1038/357308a0

    Wardle, M., & Yusef-Zadeh, F. 1992, Nature, 357, 308, doi:10.1038/357308a0

    work page doi:10.1038/357308a0 1992

  62. [62]

    2022, ApJ, 930, L19, doi:10.3847/2041-8213/ac6428

    Wielgus, M., Marchili, N., Martí-Vidal, I., et al. 2022, ApJ, 930, L19, doi:10.3847/2041-8213/ac6428

    work page doi:10.3847/2041-8213/ac6428 2022

  63. [63]

    N., Prather, B

    Wong, G. N., Prather, B. S., Dhruv, V., et al. 2022, ApJS, 259, 64, doi:10.3847/1538-4365/ac582e

    work page doi:10.3847/1538-4365/ac582e 2022

  64. [64]

    B., & Nelson, G

    Yusef-Zadeh, F., Morris, M., Slee, O. B., & Nelson, G. J. 1986, ApJ, 300, L47, doi:10.1086/184600

    work page doi:10.1086/184600 1986

  65. [65]

    2012, ApJ, 758, L11, doi:10.1088/2041-8205/758/1/L11

    Yusef-Zadeh, F., Arendt, R., Bushouse, H., et al. 2012, ApJ, 758, L11, doi:10.1088/2041-8205/758/1/L11

    work page doi:10.1088/2041-8205/758/1/l11 2012

  66. [66]

    R., Goss, W

    Zhao, J.-H., Morris, M. R., Goss, W. M., & An, T. 2009, ApJ, 699, 186, doi:10.1088/0004-637X/699/1/186

    work page doi:10.1088/0004-637x/699/1/186 2009