⚛️ general relativity

Toward a complete understanding of the properties of GW190521

This paper presents a comprehensive reanalysis of the gravitational wave event GW190521 using diverse waveform models, revealing that the source was highly eccentric and that previously inferred spin precession was largely an artifact of eccentricity-spin degeneracies, while confirming a high probability that the primary black hole resides within the pair-instability supernova mass gap.

Original authors: Aasim Jan, Sophia Nicolella, Aaron Zimmerman, Deirdre Shoemaker, Katerina Chatziioannou, Richard O'Shaughnessy, Muhammed Saleem

Published 2026-10-08

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CC BY 4.0

Original authors: Aasim Jan, Sophia Nicolella, Aaron Zimmerman, Deirdre Shoemaker, Katerina Chatziioannou, Richard O'Shaughnessy, Muhammed Saleem

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

In the quiet depths of space, two massive objects can spiral toward each other, tightening their orbit until they collide in a violent merger. When these objects are black holes, their collision sends ripples through the fabric of space-time itself, known as gravitational waves. Detectors on Earth, sensitive enough to measure changes smaller than a single atom, listen for these ripples. One such event, detected in May 2019, was unlike any other seen before. It came from two black holes so heavy that their combined mass was nearly 150 times that of our Sun, creating a single, even more massive black hole. This event was so massive that the signal it sent to Earth was incredibly brief, lasting only a fraction of a second, with the detectors capturing just a handful of the waves before the signal faded. Because the signal was so short, scientists faced a difficult puzzle: the brief data contained many different possible explanations for what the black holes were doing, and the standard tools used to interpret the data were struggling to tell them apart.

A team of researchers has now returned to this mysterious event to solve the puzzle, using a new set of tools designed to look for a specific, often overlooked feature: orbital eccentricity. In a perfectly smooth orbit, two objects circle each other in a circle. However, if the orbit is stretched into an oval shape, it is called eccentric. For decades, scientists assumed that black holes merging in the quiet isolation of space would have circular orbits. But if black holes form in crowded star clusters where they bump into one another, they might be thrown into oval-shaped paths before they collide. The researchers re-analyzed the data from the 2019 event using waveform models that could account for these oval orbits, as well as the wobbling motion caused by the black holes' spins. They found that the data strongly supports the idea that the black holes were indeed moving in a highly eccentric, oval-shaped orbit. The analysis suggests that at the moment the signal began, the orbit was stretched to a degree of 0.81, a value indicating a very distinct oval shape rather than a circle.

The study reveals that previous confusion about this event arose because the standard models used by scientists were not allowed to look at these highly oval possibilities. When the researchers restricted their search to only low levels of eccentricity, the models failed to find the true shape of the orbit, leaving the data looking flat and uninformative. However, once they allowed the models to explore the full range of possible oval shapes, the data clearly pointed to a highly eccentric system. This discovery also resolved a second mystery: earlier studies had suggested the black holes were wobbling wildly as they spiraled inward. The new analysis shows that this apparent wobble was actually an illusion. The models had been trying to explain the oval shape of the orbit by inventing a wobble instead. When the oval shape was included in the calculation, the need for the wobble disappeared, and the data showed no significant evidence of spin-induced precession.

The researchers also examined the masses of the two black holes. Their analysis confirms that the larger black hole almost certainly lies within a theoretical "mass gap," a range of weights where stars are thought to be unable to form black holes naturally. The probability that the primary black hole falls in this gap is at least 97 percent. The status of the smaller black hole is less certain and depends on which specific model is used, but the most robust models suggest it is also likely to be in this unusual mass range. To ensure their findings were not just a result of the math, the team performed a series of tests. They created fake signals that mimicked the real event, injecting them into the analysis software to see if the models could correctly identify the source. When they fed the software a fake signal with a highly oval orbit but no wobble, the standard models that ignored the oval shape incorrectly invented a wobble to explain the data. Conversely, when they fed the software a signal with a real wobble but a circular orbit, the models correctly identified the wobble and did not invent an oval shape. This confirmed that the models were working correctly and that the real event was indeed highly eccentric.

Finally, the team tested their most advanced model against real computer simulations of colliding black holes that were known to be highly eccentric. They found that the model could successfully reproduce the shape of the waves from these simulations, even though the simulations were more extreme than anything the model had been previously tested against. This gives them confidence that their interpretation of the real event is solid. The study concludes that the 2019 event was a collision of two black holes in a highly stretched, oval orbit, likely formed in a crowded stellar environment. This finding changes our understanding of how these massive objects behave and explains why earlier attempts to describe the event led to conflicting results. By allowing the data to speak for itself without forcing it into a circular shape, the researchers have uncovered a clearer picture of one of the most massive and energetic events ever recorded in the history of gravitational-wave astronomy.

Technical Summary: Toward a complete understanding of the properties of GW190521

Problem Statement
The gravitational-wave event GW190521, detected by the LIGO–Virgo–KAGRA (LVK) collaboration, presents a unique challenge for parameter estimation due to its exceptionally high total mass. The signal contains only a few observable cycles within the detectors' sensitive frequency band, rendering the inference highly sensitive to waveform-modeling assumptions. Previous analyses have yielded conflicting conclusions regarding the event's physical properties, particularly concerning orbital eccentricity and spin precession. While some studies suggested a highly eccentric source, others found no evidence for eccentricity or favored spin-precessing, quasicircular configurations. These discrepancies are attributed to degeneracies between eccentricity and spin precession, as well as the limited prior ranges on eccentricity used in various models. The paper aims to resolve these tensions through a comprehensive reanalysis using state-of-the-art waveform models that include both eccentricity and spin precession.

Methodology
The authors performed a Bayesian reanalysis of GW190521 using the RIFT parameter-estimation algorithm. The analysis utilized 4 seconds of data from the LIGO Hanford, LIGO Livingston, and Virgo observatories, evaluating the likelihood over the 20–224 Hz frequency range.

Key methodological components include:

Waveform Models: The study employed multiple waveform families to test physical hypotheses:
- Eccentric Models: TEOBResumS (incorporating generic spin orientations), IMRPhenomTEHM, and SEOBNRv5EHM (restricted to aligned spins).
- Spin-Precessing Models: TEOBResumS, IMRPhenomTPHM, IMRPhenomXPHM, NRSur7dq4, and SEOBNRv5PHM.
- Combined Models: TEOBResumS was used to test configurations combining eccentricity and spin precession (-E+P).
Priors: Uniform priors were applied to detector-frame masses, sky location, and luminosity distance. For eccentricity ( $e_5$ at 5 Hz), uniform priors were generally set over $[0.0, 0.9]$ , though SEOBNRv5EHM was restricted to $[0.0, 0.4]$ due to waveform generation failures at higher eccentricities.
Validation Studies:
- Zero-Noise Injection: The authors injected synthetic signals based on the maximum-likelihood parameters of GW190521 (both highly eccentric and highly spin-precessing) to test model recovery capabilities and identify sources of systematics.
- Numerical Relativity (NR) Recovery: Highly eccentric NR waveforms (RIT eBBH 1637 and 1639) were injected and recovered using TEOBResumS-E+P to validate the model's performance in the high-eccentricity regime favored by the GW190521 analysis.

Key Contributions and Results

Evidence for High Eccentricity:
Analyses using TEOBResumS and IMRPhenomTEHM with broad eccentricity priors ( $e_5 \in [0.0, 0.9]$ ) robustly infer a highly eccentric source, with $e_5 \approx 0.81^{+0.05}_{-0.01}$ . In contrast, SEOBNRv5EHM and restricted-range analyses ( $e_5 \le 0.4$ ) yield uninformative or flat posteriors. The authors demonstrate that the lack of eccentricity evidence in previous studies arises because restricting the prior below the high-likelihood region ( $e_5 > 0.8$ ) prevents the posterior from accessing the true solution. The full-range analysis is favored over the restricted range by a log Bayes factor of $\ln \mathcal{B} \approx 4.9$ .
Eccentricity–Spin-Precession Degeneracy:
When eccentricity is included in the analysis (TEOBResumS-E+P), the inferred effective precession spin parameter ( $\chi_p$ ) shifts significantly toward lower values compared to quasicircular spin-precessing models. While quasicircular models favor moderate-to-large $\chi_p$ ( $\sim 0.6$ ), the eccentric analysis yields $\chi_p \approx 0.31$ . This indicates that the apparent spin precession in quasicircular analyses is partially driven by the models' attempt to accommodate unmodeled eccentric features. The data show no significant indication of spin precession when eccentricity is properly accounted for.
Mass Ratio and PISN Gap:
All waveform models favor a comparable-mass binary ( $q \approx 0.7$ ). However, some models (e.g., IMRPhenomXPHM) exhibit a secondary mode at highly asymmetric masses ( $q \sim 0.2$ ). Regarding the Pair-Instability Supernova (PISN) mass gap ( $\sim 60\text{--}130 M_\odot$ ):
- The primary black hole lies within the gap with a robust probability ( $\ge 97\%$ ) across all models.
- The probability for the secondary depends on the model and the eccentricity prior. The full eccentricity range analysis increases the probability of the secondary being in the gap to $\sim 92\%$ , whereas restricted ranges or specific models yield lower probabilities.
Origin of Waveform Systematics:
Zero-noise injection studies reveal that the waveform-model systematics observed in the real GW190521 analysis (discrepancies in mass, spin, and eccentricity posteriors) arise primarily from the response of quasicircular models to unmodeled eccentricity. When a highly eccentric signal is analyzed with quasicircular models, they spuriously infer significant spin precession and exhibit model-dependent mass ratios. Conversely, when a genuinely spin-precessing, quasicircular signal is analyzed, different models yield consistent results.
Model Validation:
Recovery of highly eccentric NR waveforms using TEOBResumS-E+P demonstrates that the model can reproduce the overall waveform morphology and recover injected masses and spins. However, the recovery of eccentricity is not always unique; one injection was correctly identified as highly eccentric, while another yielded a multimodal posterior including support for zero eccentricity. This highlights the difficulty of uniquely identifying high eccentricity in short signals.

Significance and Claims
The paper claims that a complete understanding of GW190521 requires waveform models that explicitly include orbital eccentricity. The authors conclude that GW190521 is most likely a highly eccentric binary black hole merger. This interpretation resolves the tension between previous studies by showing that non-eccentric results stem from insufficient exploration of the eccentric parameter space. Furthermore, the study establishes that the previously inferred spin precession is likely an artifact of the eccentricity–spin-precession degeneracy.

The authors emphasize that restricting the physical content of waveform models (e.g., assuming quasicircularity) can lead to qualitatively different interpretations of short, high-mass gravitational-wave signals. While the results strongly favor an eccentric interpretation, the authors note that astrophysical inferences regarding formation channels must be tempered by the rarity of such high eccentricities and the need to combine Bayesian evidence with astrophysical prior odds. The work underscores the necessity of broadening the parameter space in waveform modeling to avoid systematic biases in future gravitational-wave astronomy.

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