🔭 astrophysics

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

This paper demonstrates that analyzing the position angle of brightness asymmetry in Event Horizon Telescope images, combined with other observables, allows for robust constraints on the spin magnitude, direction, and inclination of black holes like M87* and Sgr A* within general relativistic magnetohydrodynamic models.

Original authors: Nicholas S. Conroy, Michi Bauböck, Vadim Bernshteyn, Paul Tiede, Abhishek V. Joshi, Cora Prather, Charles F. Gammie

Published 2026-06-11

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nicholas S. Conroy, Michi Bauböck, Vadim Bernshteyn, Paul Tiede, Abhishek V. Joshi, Cora Prather, Charles F. Gammie

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Event Horizon Telescope (EHT) as a giant, super-powerful camera that can take pictures of the "shadows" cast by the universe's most massive black holes. When we look at these shadows, they don't look like perfect, dark circles. Instead, they look like glowing rings of light, kind of like a donut that is brighter on one side than the other.

This paper is about figuring out why that ring is brighter on one side and what that tells us about the black hole's spin.

Here is the breakdown of the research using simple analogies:

1. The "Donut" and the "Bright Spot"

When you look at a spinning black hole, the ring of light around it has a "bright spot." Think of it like a spinning carousel at night with a single bright light attached to one of the horses.

The Magnitude ( $a_1$ ): How much brighter is that spot compared to the rest of the ring?
The Position Angle ( $PA_1$ ): Where is that bright spot located? Is it at the top, the bottom, or the side?

The authors wanted to know: If we know exactly where that bright spot is, can we figure out which way the black hole is spinning?

2. The "Spinning Top" Discovery

The researchers ran thousands of computer simulations (like creating a virtual universe) to see how different black holes behave. They found a very consistent rule:

The bright spot almost always appears on the side of the ring that is "coming toward us."

Imagine a spinning top. If you look at it from the side, the part of the top spinning toward your eye moves faster (due to physics called Doppler boosting), making it look brighter. The part spinning away looks dimmer.

The Finding: The bright spot is almost always on the "approaching limb" (the side coming at us).
The Rule: If you find the bright spot, you can draw a line 90 degrees away from it, and that line points roughly in the direction the black hole is spinning.

3. What This Tells Us About M87* (The Giant Black Hole)

M87* is a massive black hole in a distant galaxy. The team looked at pictures taken in 2017 and 2018.

The Spin Direction: They found that the bright spot was in a position that strongly suggests the black hole is spinning away from Earth, not toward it. It's like seeing a spinning top where the top is leaning away from you.
The Speed: The data suggests the black hole isn't spinning very slowly. It's likely spinning at a moderate to fast pace.
The Tilt: The bright spot is perfectly perpendicular to the giant jet of energy shooting out of the black hole. This suggests the "disk" of gas swirling around the black hole is not tilted at a weird angle; it's sitting pretty straight, like a record player on a flat table.

The Future Prediction: The paper predicts that by 2026, the EHT will be able to take a "movie" of M87*. By watching how the bright spot moves in the video, they could tell with about 84% accuracy whether the black hole is spinning in the same direction as its gas disk (prograde) or the opposite way (retrograde).

4. What This Tells Us About Sgr A* (Our Neighbor)

Sgr A* is the black hole right in the center of our own Milky Way galaxy.

The Challenge: It's much smaller and changes its shape much faster than M87*, making it harder to get a clear picture.
The Hope: Even with the blurry, quick snapshots we have so far, the position of the bright spot gives us our first real clue about the direction of Sgr A*'s spin.
The Connection: The direction of the spin seems to line up with other things in our galaxy, like the orbits of nearby stars and flares of light. This suggests the black hole and the stars around it might have formed or evolved together in a coordinated way.

5. The Big Picture: Why Does This Matter?

The authors argue that if we can measure three simple things about any black hole ring in the future:

How big the ring is (tells us the mass).
How bright the spot is (tells us how fast it's spinning).
Where the spot is (tells us which way it's spinning).

...we can solve the mystery of how these black holes grew up. Did they grow slowly by eating gas in one direction (like a child eating a meal)? Or did they grow by smashing into other black holes (like a game of bumper cars)? The direction of the spin is the clue that tells us their "growth history."

Summary

In short, this paper says: "The bright spot on the black hole ring is a compass." By reading where that spot points, we can tell which way the black hole is spinning, how fast it's going, and how it fits into the story of our universe. The EHT is the tool that lets us read this compass.

Technical Summary: Ring Position Angles and Spin in M87 and Sgr A**

Problem Statement
Event Horizon Telescope (EHT) images of supermassive black holes, specifically M87* and Sgr A*, exhibit a ring of emission with a characteristic brightness asymmetry. While previous work established that the magnitude of this asymmetry ( $a_1$ ) depends on black hole spin ( $a_*$ ), the position angle of the peak brightness ( $PA_1$ ) had not been systematically studied as a diagnostic tool. The brightness asymmetry is driven by a complex interplay of Doppler boosting, gravitational lensing, frame dragging, and radiative transfer effects. The central problem addressed is determining the dependence of $PA_1$ on black hole spin, viewing inclination, disk magnetization, and source properties, and evaluating whether $PA_1$ can constrain the spin vector's direction on the sky.

Methodology
The authors utilize a library of synthetic data generated from General Relativistic Magnetohydrodynamic (GRMHD) simulations to compare against EHT observations.

Model Library: The study employs the "Illinois v5" library, spanning 13 spin values ( $a_* \in \{0, \pm0.25, \dots, \pm0.97\}$ ), two magnetization modes (Magnetically Arrested Disk [MAD] and Standard and Normal Evolution [SANE]), and various viewing inclinations ( $i$ ). Electron temperature is modeled using the $R_{high}$ and $R_{low}$ prescriptions.
Simulation: Accretion flow evolution is simulated using the KHARMA code, followed by radiative transfer imaging via the ipole code.
Measurement: The ring asymmetry is quantified using the Comrade and VIDA packages. The geometric model consists of an $m$ -ring (truncated at $m=4$ ) with a Gaussian background. The $m=1$ Fourier component yields the asymmetry magnitude ( $a_1$ ) and position angle ( $PA_1$ ).
Statistical Analysis: To constrain spin, the authors apply a two-sample Kolmogorov-Smirnov (KS) test to the distributions of $a_1$ and $PA_1$ (converted to Cartesian coordinates $a_{1x}, a_{1y}$ to handle circular data). P-values are combined using Fisher's method. For Sgr A*, snapshot geometric modeling results from 2017 are adopted. For M87*, synthetic observations are generated to match 2017–2018 coverage.

Key Results

$PA_1$ Morphology: Across a wide range of parameters (spin, inclination, magnetization, and source), the mean $PA_1$ consistently falls within $1\sigma$ of the black hole's approaching limb (the side of the ring moving toward the observer). Specifically, for high-spin magnitudes ( $a_* > 0.25$ and $a_* \lesssim -0.5$ ), the relationship $PA_{spin} \approx PA_1 - 90^\circ$ holds robustly.
M87 Spin Constraints:*
- Magnitude: Joint analysis of $a_1$ and $PA_1$ from 2017–2018 data mildly disfavors low-magnitude spins ( $|a_*| \lesssim 0.2$ ) and strongly disfavors spin vectors pointing toward Earth ( $a_* \cos i > 0$ ).
- Dynamics: By combining $PA_1$ with the pattern speed ( $\Omega_p$ ) measurable in the upcoming 2026 M87* video data, the EHT can constrain whether M87* is prograde or retrograde with approximately 84% accuracy.
- Tilt: The alignment of $PA_1$ relative to the large-scale jet axis suggests that M87*'s accretion disk does not have a large tilt relative to the spin vector.
Sgr A Spin Constraints:*
- Current 2017 EHT data for Sgr A* provides tentative constraints on the spin vector direction. The inferred direction shows overlap with constraints from NIR flares (GRAVITY collaboration) and the clockwise stellar disk, suggesting potential alignment.
- The paper notes that current constraints are limited by sparse $(u, v)$ coverage and source variability, but future observations could yield the first statistically significant horizon-scale constraints on the Sgr A* spin vector.
Dynamics: $PA_1$ evolves stochastically around a mean value with a correlation timescale ( $\tau_{corr}$ ). While coherent swings in $PA_1$ occur due to bright features propagating around the ring, these are intermittent.

Significance and Claims
The paper claims that $PA_1$ is a robust observable for constraining the black hole spin vector's position angle, independent of the specific source (M87* or Sgr A*) or inclination, provided the spin magnitude is sufficiently high.

M87:* The study provides a statistically significant, model-dependent confirmation that M87* has a spin vector pointing away from Earth and likely possesses a non-zero spin magnitude, consistent with the Blandford-Znajek mechanism for jet launching. The combination of $PA_1$ and pattern speed offers a pathway to determine the prograde/retrograde nature of the system.
Sgr A:* The work demonstrates the potential for EHT data to constrain the galactic center spin vector, potentially linking the spin direction to the near-horizon jet and the surrounding stellar disk.
Future Sources: The authors propose that for future EHT expansions (e.g., the BHEX satellite), a simple set of observables—ring diameter, asymmetry magnitude, and asymmetry angle—could enable robust constraints on black hole mass, spin, and inclination for a dozen or more new sources.

Limitations and Uncertainties
The authors acknowledge that their analysis is model-dependent. Uncertainties arise from:

GRMHD Physics: Boundary conditions, the assumption of ideal fluid dynamics (ignoring kinetic effects), and thermodynamic prescriptions (adiabatic index, electron heating).
Radiative Transfer: Mass density scaling and the "fast-light" approximation (though tests show minimal impact on $PA_1$ ).
Observational Errors: Limited $(u, v)$ coverage, particularly for Sgr A*, introduces significant uncertainty in recovering $PA_1$ . The paper notes that for low-spin models or highly inclined systems, the $m=2$ mode may dominate, complicating the $PA_1$ interpretation.

In conclusion, the paper establishes $PA_1$ as a critical observable that, when combined with asymmetry magnitude and pattern speed, offers a powerful method for inferring black hole spin properties and growth histories, provided future observations improve coverage and model fidelity.