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Spins of Black Holes in X-ray Binaries and the Tension with the Gravitational Wave Measurements

This paper reviews the significant tension between the low black hole spins inferred from gravitational wave observations and the high spins typically reported in X-ray binaries, attributing the discrepancy to systematic errors in current X-ray measurement methods and suggesting that the true spin distribution in X-ray binaries may be lower and broader than previously thought.

Original authors: Andrzej A. Zdziarski, Gregoire Marcel, Alexandra Veledina, Aleksandra Olejak, Debora Lancova

Published 2026-02-06

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CC BY 4.0

Original authors: Andrzej A. Zdziarski, Gregoire Marcel, Alexandra Veledina, Aleksandra Olejak, Debora Lancova

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 Great Black Hole Spin-Off: A Tale of Two Measurements

Imagine the universe is a giant dance floor. On one side, you have Black Holes that are about to crash into each other (merging). On the other side, you have Black Holes that are currently eating a star (accreting).

Scientists have been measuring how fast these black holes are spinning (their "spin"). But here is the problem: The two groups of black holes seem to be dancing to completely different rhythms.

Group A (The Mergers): When we listen to the "sound" of black holes crashing together using gravitational waves (like listening to a thunderclap), they seem to be spinning very slowly. They are like lazy dancers, barely turning at all.
Group B (The Eaters): When we look at black holes eating stars using telescopes (light and X-rays), they seem to be spinning incredibly fast. They are like breakdancers spinning at maximum speed, almost reaching the limit of what is physically possible.

This paper is a detective story trying to figure out why these two groups look so different. The authors argue that the "lazy dancers" (Group A) are probably telling the truth, and the "breakdancers" (Group B) are being misjudged because our measurement tools are flawed.

1. The Evidence: Two Different Worlds

The Gravitational Wave Evidence (The "Lazy" Spin)
When two black holes merge, they send out ripples in space-time called gravitational waves. By analyzing these ripples, scientists can tell how fast the black holes were spinning before they hit.

The Finding: The data shows that most merging black holes have very low spins (about 0.1 to 0.2 on a scale of 0 to 1).
The Implication: This suggests that when these black holes were born from dying stars, they were born spinning slowly. It also means that inside massive stars, the "angular momentum" (the spin energy) is transferred very efficiently from the core to the outside, slowing the core down before it collapses.

The X-ray Evidence (The "Fast" Spin)
When a black hole eats a companion star, it creates a hot, swirling disk of gas (an accretion disk) that glows in X-rays. By studying the shape of this light, astronomers try to calculate the spin.

The Finding: Most published measurements say these black holes are spinning very fast (0.7 to 1.0).
The Conflict: This is a huge problem. If the "eater" black holes were born spinning fast, why are the "merger" black holes born spinning slow? And if they were born slow, how did the eaters get so fast?

2. The Suspects: Why the Measurements Might Be Wrong

The authors of this paper believe the "Fast Spin" measurements are likely wrong. They point out that the tools used to measure the spin of eating black holes have some serious "bugs" in the software.

Suspect #1: The Reflection Method (The "Echo" Problem)

One way to measure spin is to look at how the black hole's light bounces off the gas disk, creating an "echo" (reflection).

The Flaw: To measure the spin, scientists have to separate the original light from the reflected light. The paper argues this is like trying to hear a whisper in a noisy room; it's incredibly hard to tell which sound is which.
The Metaphor: Imagine trying to guess how fast a car is going by looking at its reflection in a puddle. If the puddle is wavy or dirty, your guess will be wrong. The paper says the "puddle" (the models used to separate the light) is too wavy and dirty to trust.

Suspect #2: The Continuum Method (The "Unstable Table" Problem)

The other way to measure spin is to look at the temperature and color of the gas disk. This relies on a standard model of how disks work (the "Shakura-Sunyaev" model).

The Flaw: This standard model predicts that the gas disk should be unstable and break apart, like a table with wobbly legs. But when we actually look at the black holes, the disks are rock-solid and stable.
The Metaphor: It's like using a map of a swamp to navigate a solid highway. The map says you should be sinking in mud, but you are driving on pavement. Because the map (the model) is wrong, the speed limit (the spin) calculated from it is also wrong.
The Better Model: The paper suggests using "magnetic" models. Imagine the gas disk is held together by invisible magnetic straws. These models are stable and predict that the gas is hotter than we thought. If the gas is hotter, the math says the black hole must be spinning slower, not faster.

3. Could Accretion (Eating) Speed Them Up?

Maybe the black holes were born slow (like the merger group) but got faster because they ate so much stuff?

The Math: To spin a black hole up from "lazy" to "breakdancer" speed just by eating, it would need to eat a massive amount of material—more than its own weight.
The Problem:
- High-Mass Donors (Big Stars): These systems don't last long enough to eat that much. They run out of time.
- Low-Mass Donors (Small Stars): These could theoretically eat enough, but only if the donor star was originally huge (several times the mass of our Sun). However, the stars we see today look small, suggesting they started small.
- The Conclusion: It is very unlikely that eating alone explains the high spins.

4. The Verdict: What's Really Happening?

The authors propose a solution to the mystery:

The Gravitational Wave Data is Right: Black holes are generally born spinning slowly.
The X-ray Data is Flawed: The high spins we see in eating black holes are an illusion caused by using outdated or incorrect models to interpret the light.
The Real Spin: If we use better, more stable models (like the ones with magnetic support or "warm coronae" of hot gas), the calculated spin of these eating black holes drops down to match the slow spins of the merging black holes.

The "Warm Corona" Analogy:
Imagine you are trying to measure the temperature of a room by looking at a thermometer. But there is a heater blowing hot air right in front of the thermometer. The thermometer reads "Hot!" but the room is actually "Cool."
The paper suggests that the "heater" is a layer of hot gas (a warm corona) sitting above the disk. Previous models ignored this heater, so they thought the disk itself was hotter and spinning faster. When you account for the heater, the disk is actually cooler, and the spin is much lower.

Summary

The paper concludes that the "tension" between the two groups of black holes isn't because they are different types of objects. It's because our rulers are bent. Once we fix the rulers (the models), the "breakdancers" turn out to be "lazy dancers" after all, and the universe makes sense again.

Technical Summary: Spins of Black Holes in X-ray Binaries and the Tension with Gravitational Wave Measurements

Problem Statement
The paper addresses a significant tension in astrophysics regarding the spin parameters ( $a_*$ ) of stellar-mass black holes (BHs). Gravitational wave (GW) observations of merging binary black holes (BBHs) indicate that pre-merger BHs possess low natal spins, with an average dimensionless spin parameter of $a_* \sim 0.1\text{--}0.2$ and 90% having $a_* \lesssim 0.6$ . This suggests efficient angular momentum transport in massive stars and low natal spins. Conversely, electromagnetic (EM) measurements of BHs in X-ray binaries (XRBs), particularly those with high-mass donors (HMXBs) which are potential progenitors of BBHs, consistently yield very high spins ( $a_* \gtrsim 0.7$ , often approaching 1.0). The authors investigate whether this discrepancy arises from physical differences in formation channels or from systematic errors in the EM measurement methodologies.

Methodology
The authors conduct a comprehensive review of observational results and measurement techniques from both GW and EM domains:

GW Analysis: They analyze population statistics from the LIGO-Virgo-KAGRA collaboration (specifically the GWTC-4.0 catalog), focusing on effective spin distributions ( $a_{\text{eff}}$ ) and individual spin components of pre-merger binaries. They consider evolutionary scenarios, including tidal spin-up of the second-born BH and dynamical formation channels.
EM Methodology Review: The paper critically evaluates the two primary methods used to measure BH spins in XRBs:
- Reflection Method: Fitting X-ray spectra including relativistically broadened Fe K $\alpha$ lines. The authors highlight uncertainties in separating incident and reflected spectra, the assumption of a "lamppost" geometry versus extended coronae, and the dependence on ionization parameters and disk density.
- Continuum Fitting Method: Modeling the thermal disk continuum. The authors scrutinize the reliance on standard Shakura-Sunyaev/Novikov-Thorne disk models, which predict thermal and viscous instabilities in radiation-pressure-dominated regimes, despite observations showing stable disks. They also examine the impact of color-correction factors ( $f_{\text{col}}$ ) and the assumption that the disk extends to the Innermost Stable Circular Orbit (ISCO).
Alternative Modeling: The authors explore the effects of "warm coronae" (magnetically supported, geometrically thick disks) and the emission from the plunging region (inside the ISCO) on spectral fits.
Accretion Spin-Up Analysis: They calculate the mass accretion required to spin up a BH from a low natal spin to high values, considering Eddington-limited and hypercritical accretion scenarios for both HMXBs and Low-Mass X-ray Binaries (LMXBs).

Key Contributions and Results

GW Consistency: The GW data robustly supports low natal spins for the first-born BHs in binaries. The distribution of spins in merging binaries peaks near zero, with a secondary peak for the second-born BHs (potentially spun up by tidal interactions) around $a_* \approx 0.3\text{--}0.4$ . The authors note that while some high-spin events exist (e.g., GW231123), they are rare and may require specific formation channels (e.g., hierarchical mergers or accretion in AGN disks) rather than standard isolated binary evolution.
Systematic Errors in EM Measurements: The paper argues that the high spins reported in XRBs are likely artifacts of inadequate modeling:
- Reflection Method: The separation of incident and reflected components is highly uncertain, especially when the incident spectrum is not a simple power law (as often assumed) but a curved Comptonization spectrum.
- Continuum Method: Standard disk models assume stability that does not exist in the radiation-pressure-dominated regime. When using more physically motivated models (e.g., slimbh or bhspec which include radiative transfer) or adding a warm corona component, the fitted spin values drop significantly. For example, including a warm corona in the soft state of Cyg X-1 reduces the fitted spin from $a_* \approx 0.99$ to $a_* \approx 0\text{--}0.1$ .
- Plunging Region Emission: Emission from inside the ISCO, driven by magnetic stresses, can mimic the spectral signature of a high-spin black hole, leading to overestimates when standard models are used.
Accretion Constraints: The authors demonstrate that accretion alone cannot easily explain the high spins in HMXBs. The short lifetimes of HMXBs prevent sufficient mass accretion to spin up a BH to $a_* \sim 1$ unless hypercritical accretion (far exceeding the Eddington limit) occurs, which is physically difficult to sustain and not observed in BBH progenitors. For LMXBs, high spins could be achieved via accretion only if the initial donor masses were significantly higher ( $> \text{several } M_\odot$ ) than typically observed, which conflicts with the initial mass function.
Jet Power Correlation: While powerful transient jets in some LMXBs (e.g., MAXI J1820+070) theoretically require high spins ( $a_* \sim 1$ ) for Blandford-Znajek extraction, the authors note that no correlation has been found between published spin values and ejecta velocities, suggesting the published spins may be unreliable.

Significance and Claims
The paper concludes that the tension between GW and EM spin measurements is likely resolved by recognizing that current EM measurement methods suffer from significant systematic biases. The authors claim that:

The high spins reported for BH HMXBs are likely incorrect and result from the use of unstable standard disk models and oversimplified reflection geometries.
When applying stable, magnetically supported disk models (e.g., "puffy" disks) and including warm coronae, the spins of HMXBs become consistent with the low values inferred from GW observations ( $a_* \ll 1$ ).
For BH LMXBs, the spin distribution is broader; while some may have high spins acquired through accretion from massive donors, many likely possess low spins consistent with GW data.
The most viable path to resolving the discrepancy is the development and application of realistic, stable accretion disk models that account for magnetic fields, radiative transfer, and complex coronal geometries.

The authors do not claim to have definitively measured the true spins of all XRBs but rather provide strong evidence that the current "high spin" paradigm in XRBs is an artifact of modeling limitations, thereby aligning the EM population with the low-spin population revealed by gravitational waves.