🔭 astrophysics

S301 and friends: Measuring the spin of Sgr A*

This paper proposes a method to isolate the Lense-Thirring spin signal of Sgr A* from Newtonian precession by using reference stars like S2, S55, and S38 to calibrate and subtract the background gravitational torque, leveraging the distinct dependence of Newtonian and relativistic effects on orbital apocenter and pericenter, respectively.

Original authors: T. Piran, P. Amaro-Seoane, B. Aytac, G. Bourdarot, A. Burkert, D. Calderon, J. Cuadra, F. Eisenhauer, R. Genzel, S. Gillessen, S. Joharle, F. Mang, T. Naab, T. Ott, H. B. Perets, D. C. Ribeiro, M. Sad

Published 2026-07-29

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CC BY 4.0

Original authors: T. Piran, P. Amaro-Seoane, B. Aytac, G. Bourdarot, A. Burkert, D. Calderon, J. Cuadra, F. Eisenhauer, R. Genzel, S. Gillessen, S. Joharle, F. Mang, T. Naab, T. Ott, H. B. Perets, D. C. Ribeiro, M. Sadun Bordoni, R. Sari

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

The Cosmic Dance and the Invisible Spin

Imagine the center of our galaxy, a place so crowded with stars that they are practically bumping into each other. At the very heart of this chaotic ballroom sits a monster: a supermassive black hole called Sgr A*. It's so heavy that it holds the entire neighborhood together with its gravity. For a long time, scientists knew this black hole existed, but they couldn't see how fast it was spinning or which way it was turning. Why does this matter? Because a spinning black hole doesn't just sit there; it drags the very fabric of space and time around with it, like a spoon swirling honey. This effect, called "frame-dragging," twists the paths of any stars that get too close. If we can measure how those stars twist, we can finally figure out the black hole's spin. But there's a catch: the galaxy is full of other stuff—dust, gas, and other stars—that also tugs on the orbiting stars. It's like trying to hear a whisper in a hurricane; the "whisper" is the black hole's spin, and the "hurricane" is the messy gravity of all the other stuff.

The New Star and the Great Cosmic Mix-Up

Enter S301, a newly discovered star that is the perfect detective for this mystery. S301 is a wild card: it zooms incredibly close to the black hole (about 280 times the black hole's radius) and then swings way out, taking about 8.7 years to complete one lap. Because it gets so close, the black hole's spin should make its orbit wobble noticeably. However, the authors of this paper point out a major problem: "Newtonian confusion." Any flat, pancake-shaped cloud of stars or gas around the black hole would also make S301's orbit wobble. It's impossible to tell if the wobble is caused by the black hole's spin or just by this messy cloud of stuff.

The paper proposes a clever solution: use a team of "reference stars" to cancel out the noise. The authors suggest looking at other stars, specifically S2, S55, and S38. These stars are like S301's cousins; they swing out to roughly the same far-away distance (their "apocenters" are all between 31,000 and 50,000 times the black hole's radius), but they never get nearly as close to the black hole as S301 does.

Here is the magic trick: The "messy cloud" (the Newtonian background) affects stars based on how far out they go. Since S301 and S2 swing out to similar distances, the cloud tugs on them almost equally. However, the black hole's spin only affects stars that get very close. Because S301 gets 10 times closer than S2, the spin signal on S301 is about 30 times stronger than on S2. By measuring how much S2, S55, and S38 are wobbling, scientists can calculate exactly how much the "messy cloud" is pushing. Then, they can subtract that push from S301's wobble. What's left over? That should be the pure spin of the black hole.

The Findings and the Future

The authors ran detailed simulations and math checks to see if this plan works. They found that for a wide range of scenarios, the "cloud" tugs on S301 and S2 almost the same amount, while the spin signal on S301 is huge and on S2 is tiny. This means the subtraction method is viable. They also discovered that the "cloud" isn't static; as S301's orbit slowly rotates (due to a different, well-understood effect called Schwarzschild precession), the way the cloud tugs on it changes slightly over time. The spin signal, however, stays constant. This time-variation acts like a fingerprint, helping scientists separate the cloud's noise from the spin's signal even more effectively.

However, the paper is careful not to claim victory just yet. They note that if the "cloud" is made of a few giant, heavy objects (like massive black holes) rather than a smooth mix of stars, the math gets messy and introduces a bit of random "noise" that is hard to predict. This "granularity" might make the measurement harder, but the authors suggest that averaging data over many orbits and many stars should smooth it out.

The conclusion is optimistic but realistic: with the continued help of powerful telescopes like GRAVITY+ and the future Extremely Large Telescope (ELT), we might be able to measure the black hole's spin direction within just a few years (a few orbits of S301). Measuring the full spin vector, however, will take much longer—decades of watching the star's orbit shift. But for the first time, the path to seeing the spin of our galaxy's central monster is clear, provided we can use our friends S2, S55, and S38 to help us tune out the cosmic noise.

Technical Summary: S301 and Friends: Measuring the Spin of Sgr A*

Problem Statement
The discovery of the star S301, with a pericenter distance of $r_p \simeq 280 r_g$ and high eccentricity ( $e \simeq 0.9825$ ), offers a unique opportunity to measure the spin parameter $\chi$ of the supermassive black hole Sgr A* via Lense–Thirring (LT) nodal precession. However, a significant obstacle exists: "Newtonian confusion." Any non-spherical extended mass distribution (e.g., a stellar cusp or dark matter disk) induces nodal precession that mimics the relativistic LT signal. Previous work has established that for stars like S2 ( $r_p \approx 2800 r_g$ ), the Newtonian precession can rival or dominate the relativistic signal, rendering spin detection impossible for such orbits with current instrumentation. The challenge is to disentangle the LT signal, which scales steeply with pericenter distance, from the Newtonian background, which depends on the global mass distribution.

Methodology
The authors propose a "joint stellar strategy" utilizing S301 in conjunction with "apocenter-matched reference stars" (specifically S2, S55, and S38). The core of the methodology relies on a fundamental difference in how Newtonian and relativistic torques scale with orbital parameters:

LT Signal: The LT nodal precession rate scales as $(r_g/r_p)^{3/2}$ , making it highly sensitive to the pericenter distance but largely independent of the apocenter.
Newtonian Torque: For a disk or flattened mass distribution extending beyond the stellar pericenters, the secular Newtonian torque is dominated by the apocenter ( $r_a$ ), not the pericenter.

The authors derive analytic estimates for the secular disk torque using the Gauss planetary equation and validate these with numerical orbit-averaged torque calculations. They compare the precession rates of S301 against reference stars that share comparable apocenters ( $r_a \approx 30,000\text{--}50,000 r_g$ ) but possess significantly larger pericenters.

Key Contributions and Results

Apocenter-Dominance of Newtonian Torque: The paper demonstrates that for orbits embedded in or crossing a disk ( $r_p \lesssim r_{disk} \lesssim r_a$ ), the secular Newtonian nodal precession is controlled by the apocenter. Consequently, S301 and the reference stars (S2, S55, S38) experience comparable Newtonian torques despite their vastly different pericenters.
Signal Separation: While the Newtonian torques are comparable, the LT signals differ by a factor of $\sim 30$ (favoring S301). This allows the reference stars to serve as a calibration for the Newtonian background. By measuring the precession of S2, S55, and S38, the mass and orientation of the extended mass distribution can be constrained and subtracted from S301's total precession, isolating the LT signal.
Geometric Triangulation: A single reference star is insufficient because the disk-induced precession depends on the 3D orientation of the orbit relative to the disk. The mutually misaligned orbital planes of S2, S55, and S38 allow for the triangulation of the disk's orientation and mass, while the wider orbit of S29 anchors the radial profile of the mass distribution.
Numerical Validation: Numerical simulations confirm that for a razor-thin disk (representing a conservative upper limit on Newtonian confusion), the ratio of disk-to-LT precession for S301 is $\sim 1.5$ (for specific orientations), whereas for S2 it is $\sim 14$ . This confirms that S301 is significantly less "confused" by the disk than S2, yet the disk torque on S301 can still be calibrated using S2.
Granularity and Stochasticity: The paper addresses the potential "granularity" of the perturber population (discrete massive objects like stellar-mass black holes). While a smooth disk model provides a deterministic correction, granularity introduces a stochastic floor. However, the authors argue that the steep pericenter concentration of the LT signal persists even in granular scenarios, preserving the viability of the separation strategy, though it may require ensemble averaging over multiple orbits and stars to suppress residual noise.
Time-Variation Discriminant: The authors introduce a secondary discriminant based on the Schwarzschild apsidal advance. As S301's pericenter advances rapidly ( $\sim 1.95^\circ$ per orbit), the geometry of its interaction with the disk changes, causing the Newtonian contribution to vary systematically over time. The LT signal, being fixed by the spin vector, remains constant. This time-dependence aids in separating the two components.

Significance and Claims
The paper claims that with continued astrometry from GRAVITY+ and spectroscopy from the Extremely Large Telescope (ELT), the in-plane projection of the Sgr A* spin vector ( $\chi \sin \beta$ ) is within near-term reach. This measurement can be achieved within a few orbital periods of S301 by leveraging the reference stars to subtract the Newtonian background.

The determination of the full spin vector (including the component parallel to the orbital axis, $\chi \cos \beta$ ) requires measuring the LT apsidal precession. This is a longer-term goal, as the LT apsidal signal is an order of magnitude smaller than the dominant Schwarzschild advance and requires the pericenter to sweep through many orbits to be disentangled.

The authors conclude that the combination of apocenter-matched reference stars (to calibrate the Newtonian mass distribution) and the unique pericenter proximity of S301 (to amplify the relativistic signal) provides a robust pathway to directly measuring both the magnitude and direction of the spin of Sgr A*, a capability unique to the Galactic Center among known black holes.

The Cosmic Dance and the Invisible Spin

The New Star and the Great Cosmic Mix-Up

The Findings and the Future

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