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The XRISM measurements of the black-hole spin in Cyg X-1 are highly model-dependent

XRISM observations of Cyg X-1 reveal that the black hole's spin measurement is highly model-dependent, yielding near-maximal values with simple reflection models but low values with improved Comptonization-based models, suggesting a low-spin scenario consistent with gravitational wave constraints and an outflowing disk corona geometry.

Original authors: Andrzej A. Zdziarski, Swadesh Chand, Michal Szanecki, Gulab Dewangan, Barbara De Marco

Published 2026-05-26

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CC BY 4.0

Original authors: Andrzej A. Zdziarski, Swadesh Chand, Michal Szanecki, Gulab Dewangan, Barbara De Marco

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 Mystery of the Spinning Black Hole

Imagine Cyg X-1 as a cosmic dance partner: a massive black hole and a giant star. For decades, astronomers have been trying to figure out how fast the black hole is spinning. Think of the spin like a figure skater. Some skaters spin slowly, while others spin so fast they blur.

For a long time, scientists thought Cyg X-1's black hole was spinning at maximum speed, like a skater in a blur. However, a new study using the latest space telescopes suggests the story is much more complicated. The answer depends entirely on how you ask the question.

The New Tools: XRISM, NICER, and NuSTAR

The researchers used three powerful "cameras" in space to take a picture of this black hole system:

XRISM: A high-definition camera that sees fine details in X-rays (like a 4K camera).
NICER: A camera good at seeing the "soft" or lower-energy X-rays.
NuSTAR: A camera that sees the "hard" or high-energy X-rays.

They looked at the light bouncing off the swirling disk of gas around the black hole. This light is like a reflection in a funhouse mirror; the shape of the reflection tells us how fast the mirror (the black hole) is spinning.

The Great Disagreement: It Depends on the Model

The core finding of this paper is that the result changes based on the mathematical "recipe" (model) the scientists use to interpret the data.

The Old Recipe (relxill): When the team used the simplest, most common recipe, the data said: "The black hole is spinning as fast as physically possible!" (Almost 100% speed). This matched what previous studies had found.
The New, Sophisticated Recipe (relxillCp & reflkerrD): When they used more advanced recipes that better account for how the gas gets heated and how the light bounces, the data said: "The black hole is spinning very slowly." (Close to 0% speed).

The Analogy: Imagine you are trying to guess the speed of a car by looking at its shadow.

If you use a simple shadow model, you might think the car is a race car going 200 mph.
If you use a complex model that accounts for the sun's angle, the road's bumps, and the car's suspension, you realize it's actually a slow-moving truck.
The paper argues that the "complex model" is the correct one for Cyg X-1.

Why the Slow Spin Makes Sense

The paper points out that a slow spin fits better with other clues:

The Angle: The simple recipe suggested the black hole was tilted at a weird angle that didn't match the known tilt of the star system. The complex recipe gave an angle that matches perfectly.
The Cosmic Census: When we look at black holes that crash into each other (detected by gravitational waves), they are almost always slow-spinners. If Cyg X-1 is a "first-born" black hole, it should be slow, not fast.
The Physics: To spin a black hole up to maximum speed, it needs to eat a massive amount of matter very quickly. The paper argues that Cyg X-1 isn't eating fast enough to spin up that much.

The "Truncated" Disk Puzzle

There is another mystery: How close does the gas disk get to the black hole?

If the black hole spins fast, the disk can get very close.
If it spins slow, the disk should stop further away.

The data shows the disk gets very close (within about 10 times the size of the black hole). This is consistent with a slow-spinning black hole where the disk reaches all the way down. If the black hole were spinning fast, the disk would have to be "cut off" (truncated) further out, which the data doesn't strongly support.

The "Outflowing Corona" Explanation

The paper suggests a specific shape for the hot gas (corona) surrounding the black hole. Instead of a static cloud sitting on top, they propose it is an outflowing wind, like a fountain spraying upward.

This explains why the X-ray light is polarized (shining in a specific direction).
It explains why the disk isn't getting blasted with as much energy as expected (the wind blows the energy away).
It fits the observation that the "thermal reverberation" (the echo of light bouncing off the disk) is very weak.

The Bottom Line

The paper concludes that the spin of Cyg X-1 is highly model-dependent.

If you use the old, simple math, you get a fast spin.
If you use the new, complex math that fits the physics better, you get a slow spin.

The authors argue that the slow spin is the correct answer. It aligns with gravitational wave data, matches the tilt of the star system, and fits the physical behavior of the gas around the black hole. The "fast spin" result was likely an illusion caused by using a simplified tool to measure a complex object.

Technical Summary: The XRISM Measurements of the Black-Hole Spin in Cyg X-1 are Highly Model-Dependent

Problem Statement
The black hole (BH) spin parameter ( $a_*$ ) of the archetypal high-mass X-ray binary Cyg X-1 remains a subject of significant uncertainty, with measurements yielding conflicting results. Recent analyses of XRISM Resolve data in the hard spectral state by Draghis et al. (2025b, hereafter D25) using the relativistic reflection model relxill suggested a near-maximal spin ( $a_* \approx 0.99$ ). This result stands in tension with gravitational wave observations of merging BHs, which generally indicate low natal spins ( $a_* \lesssim 0.57$ ), and with evolutionary models predicting efficient angular momentum transport in massive stars. Furthermore, previous spectral fitting of Cyg X-1 has yielded a wide range of disk inclinations, some of which are inconsistent with the binary's orbital inclination. The authors investigate whether the high spin derived by D25 is a robust physical result or an artifact of the specific spectral model employed.

Methodology
The authors re-analyzed the same XRISM Resolve observation of Cyg X-1 used by D25, conducted in the hard spectral state, alongside simultaneous observations by NICER and NuSTAR. To avoid complications from strong stellar wind absorption, they selected a 42-hour interval of the observation (phases 0.67–0.95).

The spectral analysis was performed using XSPEC with $\chi^2$ statistics. The study employed a comparative approach using three distinct relativistic reflection models:

relxill: The standard model assuming an e-folded power-law incident spectrum and fixed disk density ( $n=10^{15}$ cm $^{-3}$ ).
relxillCp: An improved model utilizing a thermal Comptonization spectrum (Zdziarski et al. 1996) as the incident seed and allowing for variable disk density.
reflkerrD: A model using the Poutanen & Svensson (1996) Comptonization model for the incident spectrum, noted for higher accuracy in the hard state.

The authors fitted the XRISM data alone and then performed joint spectral fitting with NICER (0.5–10 keV) and NuSTAR (9–79 keV, later extended to 3–79 keV) data. They tested models with single and double Comptonization components, including disk blackbody (diskbb) emission, and investigated the effects of disk truncation (varying the inner disk radius, $R_{in}$ ).

Key Contributions and Results

Model Dependence of Spin: The study confirms that the derived spin parameter is strongly dependent on the choice of the reflection model.
- Fitting the XRISM Resolve data alone with relxill yields a high spin ( $a_* = 0.988^{+0.003}_{-0.008}$ ) and a high disk inclination ( $i \approx 70^\circ$ ), consistent with D25.
- However, fitting the same data with the more physically motivated relxillCp yields a low spin ( $a_* = 0.0^{+0.17}$ ) and an inclination ( $i = 33^{+1}_{-2}^\circ$ ) consistent with the binary's orbital inclination.
- Similarly, the reflkerrD model yields a low spin ( $a_* = 0.18^{+0.10}_{-0.18}$ ) and an inclination ( $i = 36^{+1}_{-4}^\circ$ ).
Broadband Spectral Fitting: Joint fitting of NICER, NuSTAR, and XRISM data reveals that a single Comptonization component cannot adequately reproduce the spectrum, particularly the Fe K complex.
- Models requiring two Comptonization components (representing distinct coronal regions) and a disk blackbody component provide a significantly better fit ( $\Delta \chi^2 \approx -47$ ).
- In these broadband models, the spin parameter becomes largely unconstrained ( $a_* = 0.18^{+0.82}_{-0.18}$ ).
- When the full NuSTAR energy range (3–79 keV) is included, the fit constrains the spin to be low ( $a_* = 0.10^{+0.19}_{-0.10}$ ), though this introduces calibration discrepancies in the Fe K region between instruments.
Disk Geometry and Truncation:
- All models constrain the inner disk radius to $R_{in} \lesssim 10 R_g$ (gravitational radii).
- For relxillCp and reflkerrD, the data are consistent with a disk extending to the ISCO of a slowly spinning BH ( $a_* \approx 0$ ) or a modestly truncated disk for a fast-spinning BH.
- The authors rule out a disk extending to the ISCO of a maximally rotating BH ( $a_* \approx 1$ ) based on the derived inner radius constraints.
Source Geometry and Energetics:
- The derived low reflection fractions and the hard spectral slope ( $\Gamma \sim 1.7$ ) are inconsistent with a static corona.
- The results support a geometry of an outflowing disk corona, which aligns with X-ray polarization measurements showing the polarization angle aligned with the jet.
- The weak soft X-ray reverberation lags observed in Cyg X-1 are explained by the specific geometry of the source and the dilution of the thermal disk component by the coronal emission.

Significance
The paper concludes that the high spin value previously reported for Cyg X-1 is not a robust physical measurement but a consequence of using the relxill model with an e-folded power-law incident spectrum, which is less suitable for the hard state of this source. By employing Comptonization-based reflection models (relxillCp and reflkerrD), the authors find that low spin values are consistent with the data, aligning with gravitational wave constraints and stellar evolution models.

The study emphasizes that the spin of Cyg X-1 is strongly model-dependent. While the data do not uniquely determine a single spin value, the low-spin solutions are physically consistent with independent constraints (binary inclination, gravitational wave statistics, and polarization data). The authors propose that the source geometry involves an outflowing corona illuminating a disk that extends to $\sim 10 R_g$ , consistent with the ISCO of a slowly rotating black hole. This finding resolves the tension between X-ray binary spin measurements and gravitational wave observations for this specific system, suggesting that the apparent high spin was an artifact of modeling assumptions rather than a physical reality.