A study by AEI researchers reveals how even the most advanced waveform
models can introduce systematic errors when used to measure key
properties of black holes.
To the point:
- Researchers use state-of-the-art waveform models to infer the masses, spins, and location of black holes from simulated gravitational-wave events in order to prepare for future observations.
- The models often misestimate these values, particularly when one or both black holes are processing similar to a spinning top, or when their masses differ significantly.
- These inaccuracies can mislead our understanding of how black hole systems form and evolve, and they may affect measurements used to estimate the expansion rate of the Universe.
Gravitational waves from binary black hole coalescences can help answer important
astrophysical, cosmological, and fundamental physics questions. How are
black holes born, and how do they evolve? How fast is our Universe
expanding? Is Einstein’s theory of general relativity still valid in the
strong gravity regime?
When analyzing data from these
coalescences, researchers employ the most advanced waveform models to
simulate the complex dynamics of these systems and match them to
observational data. But how do scientists know their waveform models are
accurate and which parameters influence the models’ accuracy? As
detectors become more sensitive, researchers have to rely more than ever
on the high accuracy of their waveform templates to correctly interpret
the data. As they prepare for future observing runs of facilities such
as LIGO, Virgo, KAGRA and the upcoming Cosmic Explorer and Einstein
Telescope, the reliability of these models becomes increasingly
important.
In a new study, researchers from the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) in the Potsdam Science Park found that state-of-the art approximate gravitational waveform models used to infer the properties of coalescing black holes and neutron stars can introduce systematic errors that significantly skew estimates of key astrophysical parameters. These parameters include the masses, spins, and distances of merging objects, as well as the inferred value of the Hubble constant, which is a fundamental measure of how fast the Universe is expanding. The study shows that, although the cutting-edge waveform models are trying to capture the complexity of real astrophysical systems, they still don’t provide an accurate enough description for the very precise observations we expect to make in the future.
“Even the most advanced models are not sufficiently accurate for upcoming observing runs,” says Arnab Dhani, a postdoctoral scientist in the Astrophysical and Cosmological Relativity department at the AEI and the lead author of the study. “Biased estimates of black hole properties occur, in particular, when the component masses in a binary are highly unequal and one or both black holes are rapidly spinning. Such biases can mislead our understanding of how black hole systems form and evolve,” he adds. "Reliably predicting these biases across state-of-the-art waveform models required crucial improvements to existing data analysis techniques,"says Sebastian Völkel, also a postdoctoral scientist from the same department and co-author of the study.
In a new study, researchers from the Max Planck Institute for Gravitational Physics (Albert Einstein Institute, AEI) in the Potsdam Science Park found that state-of-the art approximate gravitational waveform models used to infer the properties of coalescing black holes and neutron stars can introduce systematic errors that significantly skew estimates of key astrophysical parameters. These parameters include the masses, spins, and distances of merging objects, as well as the inferred value of the Hubble constant, which is a fundamental measure of how fast the Universe is expanding. The study shows that, although the cutting-edge waveform models are trying to capture the complexity of real astrophysical systems, they still don’t provide an accurate enough description for the very precise observations we expect to make in the future.
“Even the most advanced models are not sufficiently accurate for upcoming observing runs,” says Arnab Dhani, a postdoctoral scientist in the Astrophysical and Cosmological Relativity department at the AEI and the lead author of the study. “Biased estimates of black hole properties occur, in particular, when the component masses in a binary are highly unequal and one or both black holes are rapidly spinning. Such biases can mislead our understanding of how black hole systems form and evolve,” he adds. "Reliably predicting these biases across state-of-the-art waveform models required crucial improvements to existing data analysis techniques,"says Sebastian Völkel, also a postdoctoral scientist from the same department and co-author of the study.
Impact on cosmology
The biases also can have profound implications for the so-called “Hubble tension” – the growing discrepancy between different, independent measurements of the Hubble constant. Some methods based on the cosmic microwave background suggest a slower expansion rate than methods using supernovae. Observations of gravitational-wave standard sirens provide a third independent measurement, enticing the possibility of resolving the conflict. However, it requires accurate measurements of the distance and the location of the event in the sky to identify the galaxy hosting the event. The researchers demonstrate, using an example, how current waveform models can lead to inaccurate localization of the event impacting our measurement (see figure 1).
These results imply that errors in gravitational-wave modeling could significantly contribute to the Hubble tension, which could undermine the credibility of the standard siren method. “The standard siren method in gravitational-wave astronomy holds immense promise for cosmology, but its success depends on the accuracy of our waveform models,” explains Alessandra Buonanno, co-author of the publication and director of the Astrophysical and Cosmological Relativity department. “If we don’t account for spin, tidal deformations, or asymmetric mass ratios, we’re not just making small errors – we’re potentially misreading the expansion history of the Universe.”
These results imply that errors in gravitational-wave modeling could significantly contribute to the Hubble tension, which could undermine the credibility of the standard siren method. “The standard siren method in gravitational-wave astronomy holds immense promise for cosmology, but its success depends on the accuracy of our waveform models,” explains Alessandra Buonanno, co-author of the publication and director of the Astrophysical and Cosmological Relativity department. “If we don’t account for spin, tidal deformations, or asymmetric mass ratios, we’re not just making small errors – we’re potentially misreading the expansion history of the Universe.”
Neutron stars or black holes?
Biased gravitational-wave observation may also impact nuclear physics. Neutron star mergers are the only astrophysical phenomena in which scientists have observed the formation of heavy elements such as gold and uranium. An accurate measurement of the maximum neutron star mass would expand our understanding of nuclear matter at densities that cannot be attained in human experiments on Earth. The researchers found that inaccurate measurements of masses can lead to black holes being identified as neutron stars, thereby misleading our understanding of nuclear matter.
Testing Einstein’s theory
Binary black hole mergers provide one of the most extreme conditions in which to test Einstein’s theory of general relativity. The theory precisely predicts the amount of energy released in such collisions, as well as the mass of the remaining black hole. However, the researchers found that model inaccuracies can lead to incorrect predictions of these quantities, resulting in apparent inconsistencies with the observed data. Quantifying the relevance of systematic effects is crucial for assessing whether possible future tests claiming deviations from general relativity are really due to new physics beyond Einstein’s theory, which would be revolutionary.
More accurate waveform models for future observing runs
Future observing runs at current facilities, such as LIGO, Virgo, and KAGRA are expected to detect thousands of binary black hole mergers. Next-generation observatories, such as the Cosmic Explorer and Einstein Telescope, will detect almost all stellar-origin binary black hole merger in the Universe, totaling millions. Accurately estimating black hole properties is essential to achieve the promising scientific goals of gravitational-wave astronomy. By identifying the most problematic regions in black hole parameter space, the researchers provide a roadmap for improving waveform accuracy in the future. The ERC Synergy Grant “Making Sense of the Unexpected in the Gravitational-Wave Sky” aims to address this accuracy challenge, making it possible to infer properties of gravitational-wave sources limited only by measurement uncertainty.
Media contact:
Dr. Elke Müller
Press Officer AEI Potsdam, Scientific Coordinator
Tel: +49 331 567-7303
elke.mueller@aei.mpg.de
Science contacts:
Prof. Dr. Alessandra Buonanno
Director
Tel: +49 331 567-7220
Fax: +49 331 567-7298
alessandra.buonanno@aei.mpg.de
Dr. Arnab Dhani
Junior Scientist/Postdoc
Tel: +49 331 567-7236
arnab.dhani@aei.mpg.de
Dr. Héctor Estellés
Research Scientist
hestelles@ice.csic.es
Institute of Space Sciences, Barcelona
Dr. Jonathan Gair
Group Leader
Tel: +49 331 567-7306
Fax: +49 331 567-7298
jonathan.gair@aei.mpg.de
Prof. Harald Pfeiffer
Group Leader
Tel: +49 331 567-7328
Fax: +49 331 567-7298
harald.pfeiffer@aei.mpg.de
Dr. Lorenzo Pompili
Research Fellow
Lorenzo.Pompili@nottingham.ac.uk
University of Nottingham, School of Mathematical Sciences
Dr. Alexandre Toubiana
Assistant Professor
alexandre.toubiana@unimib.it
University of Milano-Biccoca
Dr. Sebastian Völkel
Senior Scientist/Leibniz Fellow
Tel: +49 331 567-7199
sebastian.voelkel@aei.mpg.de
Publication:
Arnab Dhani, Sebastian H. Völkel, Alessandra Buonanno, Hector Estelles, Jonathan Gair, Harald P. Pfeiffer, Lorenzo Pompili, and Alexandre Toubiana
Systematic Biases in Estimating the Properties of Black Holes Due to Inaccurate Gravitational-Wave ModelsPhys. Rev. X 15, 031036 (2025)
Source | DOI
Further information:
Homepage of the “Astrophysical and Cosmological Relativity” department GWSky
GWSky is an ERC Synergy Grant project led by Enrico Barausse (SISSA), Zvi Bern (University of California, Los Angeles (UCLA), Alessandra Buonanno (AEI), and Maarten van de Meent (NBI).
