Scientists at the international LIGO, Virgo and KAGRA (LVK) gravitational wave observatory collaboration have employed the technique, which they call astrophysical calibration, to use gravitational-wave signals to measure the response of their incredibly sensitive instruments.
It enables them to ensure that they can clearly ‘hear’ the sounds of colossal cosmic events like the collision of black holes, even when one gravitational wave detector is slightly out of tune. This is crucial to accurately interpret the signals and find their source location.
By combining signals from other detectors with precise predictions from the laws of gravity, researchers can identify and account for subtle distortions in the data. The process is similar to how music-production software such as Auto-Tune can correct a singer’s errant pitch to meet the intended note in a melody.
In a new paper published as a preprint on the arXiv ahead of publication in the journal Physical Review Letters, LVK researchers demonstrate how they turned the challenge of analysing data collected from two gravitational wave signals detected when LIGO Hanford was up and running, but performing below its usual standard, into an opportunity to improve the collaboration’s ability to analyse data.
The results could help future observing runs of the international network of LVK detectors in the USA, Italy and Japan ensure that they produce the most reliable results even when the circumstances of the detection are less than ideal.
Dr Christopher Berry, of the University of Glasgow’s Institute for Gravitational Research, is part of the LVK collaboration and an author of the paper. He said: “Gravitational waves are ripples in spacetime that stretch and squeeze space. They are tiny by the time that they reach the Earth, millions of years after the events that first created them.
“They are not something which we can hear, but our detectors can output the signals as waveforms that we can increase in pitch to listen to, with each signal producing their own distinctive chirp. Those chirps encode a wealth of information we can analyse to learn about their sources—their masses, spins, distance, and location.”
The gravitational-wave signals that the team used to develop their astrophysical calibration technique are among the loudest ever detected by the collaboration. The first signal, picked up on 25th September 2024 and named GW240925, was produced by the merger of two black holes between nine and seven times the mass of our sun more than a billion light-years away.
The second signal, on 7th February 2025 and named GW250207, was the second-loudest signal in the nearly 200 detected by the collaboration in the decade since the first detection in 2015. It was produced by the collision of two black holes between 35 and 30 times the mass of our sun around 600 million light-years from Earth.
The LVK collaboration can be confident of their results because of the work they did to overcome initial uncertainties introduced by problems with the US National Science Foundation Laser Interferometer Gravitational-Wave Observatory’s (NSF LIGO) detector in Hanford, Washington. For GW240925, there was a temporary error with the calibration—this was monitored and later corrected, enabling scientists to check the performance of astrophysical calibration for a case with a known miscalibration. For GW250207, the detector was just coming online, so not all monitoring systems were up and running.
The paper’s editorial chair, Dr Ling Sun of the Australian National University, said: “The loudness of these signals was remarkable, with very high signal-to-noise ratios compared to many of our other detections. These are exactly the types of signals you want to be recorded by all of our detectors.
“However, given the technical hitches with LIGO Hanford, we might have had to throw out the detector’s results altogether, losing a large chunk of the signal strength and our ability to precisely locate these events in the sky. By first verifying astrophysical calibration with the analysis of the September 2024 detection, we were much more prepared to deal with the more significant problems with the February 2025 data.”
The astrophysical calibration technique works because the telltale chirp of a black hole merger signal is well predicted by the theory of general relativity, Einstein’s theory of gravity.
By comparing the predicted and observed signals, the researchers were able to make accurate inferences about how the LIGO Hanford detector was distorting the data picked up at the same time by the LIGO’s Livingston detector in Louisiana and the Virgo detector in Italy. For GW240925, this method matched known calibration errors measured on-site. For GW250207, however, it was essential to use astrophysical calibration because reliable onsite calibration measurements were unavailable.
Having accurately calibrated data is essential to accurately characterise the signal and its source. By including the potential to auto-tune the detector data, using the signal as a reference, as part of the analysis, the team can avoid introducing errors into their results. Using the corrected calibration for the LIGO Hanford detector, the team measured the black hole masses, distances, and spins more accurately and significantly improved the precision of the sky location. Sky location depends critically on the number of detectors observing and improves significantly going from two to three detectors.
Dr Daniel Williams from the University of Glasgow’s Institute for Gravitational Research said: “These discoveries demonstrate that, over our decade of work since the first detection, we have developed a comprehensive understanding of our entire analysis pipeline, from the signals themselves to the detector behaviour. In the rare instance that something goes wrong with one detector, we now have robust backup methods to compensate and leverage data from the other detectors to give us the best-quality results.”
Cardiff University’s Professor Stephen Fairhurst, who is the LIGO Scientific Collaboration’s spokesperson, said, “It’s remarkable that these massive cosmic events can not only be measured by our instruments but actually used to check our measurements. Being able to use astrophysical calibration so successfully during our fourth observing run is a demonstration of the maturation of the detector’s capabilities and our ability to get the most out of every detection. Improving the quality of our results on sky localisation will also help us test key concepts like the expansion rate of the universe, a value which is still being debated by scientists.
“We’re moving from the era of first discoveries to the era of precision gravitational wave astronomy. We can be confident that our next observing runs will continue to build our rapidly growing catalogue of gravitational-wave discoveries and expand our understanding of the Universe.”
The team’s paper, titled ‘GW240925 and GW250207: Astrophysical Calibration of Gravitational-wave Detectors’, is accepted in Physical Review Letters.
The publication comes 10 years after the publication of the first observation of gravitational waves in Physical Review Letters, a discovery that was recognised with the Nobel Prize for Physics.
