⚛️ phenomenology

No Evidence for Superradiant Axions in LIGO-Virgo-KAGRA GWTC-5 Binary Black Hole Spins

Using spin measurements from the LIGO-Virgo-KAGRA GWTC-5 catalog of 257 binary black hole mergers, this study finds no evidence for superradiant axion clouds, thereby excluding axion masses between $1.7 \times 10^{-14}$ and $3.3 \times 10^{-12}$ eV at 95% confidence and providing one of the most robust lower bounds on the QCD axion mass to date.

Original authors: Orion Ning, Benjamin R. Safdi, Catherine Welch

Published 2026-07-03

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CC BY 4.0

Original authors: Orion Ning, Benjamin R. Safdi, Catherine Welch

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 Big Idea: Hunting for Invisible Ghosts with Spinning Black Holes

Imagine the universe is filled with a mysterious, invisible substance called axions. Scientists think these particles might make up "dark matter," the stuff that holds galaxies together but that we can't see. The problem is, axions are so light and interact so weakly with normal matter that catching one in a lab is like trying to hear a whisper in a hurricane.

However, nature has a way of amplifying these whispers. This paper uses spinning black holes as giant, cosmic amplifiers to see if axions exist.

The Mechanism: The "Cosmic Whirlpool"

Think of a spinning black hole as a massive, fast-spinning top. If axions exist and have a specific weight (mass), they behave like a fluid that gets caught in the black hole's spin.

The Trap: Just like a whirlpool pulls in water, the spinning black hole pulls in these axion particles.
The Cloud: The axions form a giant, invisible cloud around the black hole, similar to how water swirls around a drain.
The Drain: As the cloud grows, it steals energy and spin from the black hole. It's like a child on a spinning merry-go-round grabbing onto a rope and slowing the ride down.
The Result: If axions exist, the black hole should spin much slower than it was born with. In fact, there would be a "forbidden zone" in the universe: you wouldn't find any black holes spinning too fast if they were heavy enough to trap axions.

The Investigation: Checking the "Speedometer" of 257 Black Holes

The scientists (Orion Ning, Benjamin Safdi, and Catherine Welch) looked at the most recent and largest list of black hole collisions ever recorded, called the GWTC-5 catalog. This list contains 257 events detected by the LIGO, Virgo, and KAGRA observatories.

The Old Way: Previous studies tried to measure black hole spins using X-rays (light) from gas swirling around them. However, this is like trying to measure a car's speed by looking at the dust it kicks up; the dust cloud is messy, and the math to figure out the speed is full of guesswork and errors.
The New Way: This team used gravitational waves (ripples in space-time caused by the collision). This is like measuring a car's speed by listening to the engine's pitch as it passes. It's much cleaner and doesn't rely on messy gas clouds.

They took the mass and spin data for all 257 black holes and asked: "Do these spins match what we expect if axions are stealing their energy?"

The Findings: The "Whisper" Wasn't There

The scientists ran a massive computer simulation to see what the universe would look like if axions existed in a wide range of weights.

The Prediction: If axions existed, the data should show a "hole" or a gap. There should be no fast-spinning black holes in a specific weight range because the axion cloud would have slowed them all down.
The Reality: The data showed no gap. The black holes were spinning at all sorts of speeds, exactly as if no invisible axion clouds were stealing their energy.

The Conclusion: They found no evidence for axions in the mass range they tested. Specifically, they ruled out axions with masses between roughly 1.7 × 10⁻¹⁴ eV and 3.3 × 10⁻¹² eV.

Why This Matters

This is a big deal for two reasons:

It's a Stronger Ruling: Previous studies using X-rays had to make many assumptions about messy gas clouds, leaving room for error. This study used the clean gravitational wave data, making their "no axions found" result much more reliable. It's one of the strongest "lower bounds" (rules out the lightest possible axions) we have so far.
It Narrows the Search: By proving axions don't exist in this specific weight range, it tells other scientists where not to look. It effectively closes the door on the lightest part of the "QCD axion" parameter space, forcing experiments on Earth to focus on heavier axions or different theories.

Summary Analogy

Imagine you are a detective trying to find a thief who steals energy from spinning tops.

Previous detectives looked at the dust kicked up by the tops and guessed the thief was there because some tops were spinning slowly. But the dust was confusing, so they weren't 100% sure.
These detectives listened to the sound of the tops spinning. They checked 257 tops. They found that the tops were spinning exactly as fast as they should be, with no energy missing.
The Verdict: In the specific weight range they tested, the thief (the axion) does not exist. The universe is quiet, and the black holes are spinning freely.

Technical Summary: No Evidence for Superradiant Axions in LIGO-Virgo-KAGRA GWTC-5 Binary Black Hole Spins

Problem Statement
The Quantum Chromodynamics (QCD) axion and axion-like particles (ALPs) are well-motivated dark matter candidates that solve the Strong CP problem and arise generically in string theory compactifications. While terrestrial experiments are scaling up to search for axions with masses $m_a \lesssim 20$ meV, they struggle to detect masses below roughly $0.5$ neV due to ultra-feeble interaction strengths. Conversely, axion-induced black hole (BH) superradiance (SR) offers a promising astrophysical mechanism to probe the lowest portion of the theoretically viable axion mass range (potentially up to $m_a \sim 10^{-11}$ eV or higher).

The SR mechanism posits that when the Compton wavelength of an ultralight boson is comparable to the gravitational radius of a spinning Kerr BH, a classical wave amplification process forms a hydrogen-like bound cloud. This cloud extracts angular momentum from the BH, depleting its spin to a critical value $\chi_c(m_a, M)$ until the instability shuts off. Consequently, a "forbidden region" exists in the BH mass-spin (Regge) plane where BHs cannot persist on observationally relevant timescales; any BH born with a spin above the critical curve should be rapidly spun down.

Prior constraints on axions in this mass range have been derived from X-ray measurements of stellar-mass and supermassive BH spins. However, these constraints are fundamentally limited by substantial modeling systematics inherent in continuum-fitting and Fe K $\alpha$ reflection-spectroscopy methods, which require detailed modeling of inner accretion disks. Recent analyses suggest that some high-spin BHs driving X-ray-based exclusions may suffer from systematic mismodeling, potentially biasing spin measurements toward higher values.

Methodology
This work performs a hierarchical Bayesian analysis to constrain ultralight axions using the binary black hole (BBH) spin measurements from the LIGO-Virgo-KAGRA (LVK) GWTC-5 catalog. This catalog is the most extensive public BBH catalog to date, containing $N=257$ merger events with BH masses spanning roughly $5\text{--}135\,M_\odot$ from observing runs O1 through O4b.

The analysis proceeds as follows:

Population Modeling: The natal spin distribution of BHs is modeled as a Beta distribution, $p(\chi | \alpha, \beta) \propto \chi^{\alpha-1}(1-\chi)^{\beta-1}$ , where $\alpha$ and $\beta$ are hyperparameters. This allows for flexibility in capturing populations ranging from high-spin peaked to low-spin peaked (the latter favored by current LVK inferences).
Superradiance Physics: For a given axion mass $m_a$ , the model incorporates the SR spin-down effect. BHs born with spins above the critical curve $\chi_{\text{sat}}(m_a, M, \tau_m)$ are spun down to the saturation curve, while those below retain their natal spins. The time between BH formation and merger, $\tau_m$ , is treated as a nuisance parameter drawn from a log-uniform delay-time distribution (DTD) $p(\tau_m) \propto \tau_m^{-1}$ over $[10^7, \tau_H]$ years, accounting for both isolated and dynamically assembled binary scenarios.
Hierarchical Likelihood: The joint posterior over population hyperparameters $\Lambda = (m_a, \alpha, \beta, \tau_{m,1}, \dots)$ is computed using the LVK parameter estimation (PE) posterior samples for each event. The analysis preserves the per-event correlations between primary and secondary component masses and spins.
Hypothesis Testing: The study compares the axion-signal hypothesis ( $H_B$ ) against the null hypothesis ( $H_A$ , no axion). The analysis includes modes up to $m=6$ and utilizes numerical solutions for SR equations at higher couplings ( $\alpha \gtrsim 0.5$ ) to ensure robustness, though perturbative solutions dominate the fiducial analysis.
Data Selection: Events are selected with median component masses $M_{1,2}^{\text{med}} \geq 3\,M_\odot$ to exclude neutron star candidates, resulting in the final sample of 257 BBHs.

Key Results

Exclusion Limits: The analysis finds no evidence for axions across more than two decades in mass. At 95% confidence, the study excludes axion masses in the range:
$1.7 \times 10^{-14} \, \text{eV} \lesssim m_a \lesssim 3.3 \times 10^{-12} \, \text{eV}$
This corresponds to a decay constant range of roughly $10^{17} \text{--} 10^{19}$ GeV for the QCD axion.
Bayesian Evidence: The Bayes factor between the axion-signal and null hypotheses is $\log B^B_A = 0.22 \pm 0.06$ , which is consistent with no evidence for the axion hypothesis.
Population Inference: Simultaneously, the analysis infers the BH natal-spin population, yielding posterior medians of $\alpha = 0.69^{+0.21}_{-0.12}$ and $\beta = 2.28^{+0.62}_{-0.43}$ . This favors a low-spin natal population ( $\alpha < \beta$ ), consistent with broader LVK population inferences.
Robustness: The exclusion region is robust to variations in the prior on $m_a$ (including a non-informative Jeffreys prior), the delay-time distribution, and alternate natal spin parameterizations (e.g., truncated Gaussian, Beta-mixture models).

Significance and Claims
The authors claim this result represents one of the strongest robust lower bounds on the QCD axion mass to date. Unlike previous X-ray-based constraints, this analysis relies on gravitational wave data where spin inference is derived solely from inspiral-merger-ringdown waveforms, avoiding the accretion-disk modeling systematics that plague X-ray measurements.

By excluding the mass range $1.7 \times 10^{-14} \text{ eV} \lesssim m_a \lesssim 3.3 \times 10^{-12} \text{ eV}$ , the work effectively eliminates the lowest-mass part of the QCD axion parameter space targeted by terrestrial experiments such as CASPEr. Furthermore, the results constrain axion-like particles and ultra-light scalars in this mass range, impacting string axiverse constructions that predict near log-uniform distributed particle masses.

The paper notes that these constraints are expected to improve substantially with future LVK observing runs (O4c, O5) and third-generation detectors (Cosmic Explorer, Einstein Telescope), which will provide tighter natal-spin inferences, higher signal-to-noise ratios, and access to a broader mass range, potentially extending sensitivity to axion masses above $10^{-11}$ eV.