When a gravitational wave passes through Earth, the LIGO, Virgo, and KAGRA detectors are ready to detect it. However, their sensitivity depends on many factors, and it is possible that a detector is not operating nominally at the time of the wave's passage. In such situations, it is important to be able to process the data collected by that detector to improve its quality. The network now has an effective tool to achieve this: astrophysical calibration.
Gravitational waves deform spacetime, stretching and compressing it as they pass. This effect on the detectors' arms is on the order of 10⁻¹⁹ meters, much smaller than the diameter of a proton! To be sensitive to such minuscule variations, the detectors are calibrated in real time using feedback control circuits and a precise procedure that models their response to waves, while taking into account the effects generated by the control circuits themselves. If calibration is not optimal, the "reading" of the signal — and therefore the interpretation of the cosmic phenomenon that generated it — is compromised.
Image: Carl Knox - OzGrav, Swinburne University Of Technology Retroactively recalibrating collected data
However, if the detected gravitational signal is sufficiently intense (i.e., it clearly stands out from the background noise), it is possible to retroactively recalibrate the data collected by a poorly calibrated detector by comparing its signal to the predictions of general relativity, as well as to the signals observed by other detectors. Theoretical models here play a role similar to musical scores, which indicate the expected shape of the signal (the "notes" it should "play"). Combined with data from well-calibrated detectors, they allow correcting spurious effects in the data from the poorly calibrated detector. The process is comparable to how music production software corrects a singer's off-key notes to align them with a melody.
"Gravitational waves are ripples in spacetime that stretch and compress space," explains Christopher Berry, researcher at the "
Institute for Gravitational Research" of the University of Glasgow. "They are extremely faint when they reach Earth, millions of years after the events that produced them. We cannot hear them directly, but our detectors can convert their signals into sound waves, whose frequency we increase to listen to them. Each signal then produces a characteristic 'chirp,' rich in information about their sources: masses, spins, distance, and location. In the specific case of two black holes merging, the astrophysical calibration technique works because the signal's 'chirp' is described with extreme precision by Einstein's theory of general relativity."
Test on two particularly intense and interesting signals
In an article to be published in
Physical Review Letters, researchers from the LVK collaboration demonstrate how this technique was applied to two particularly intense and interesting signals: GW240925 and GW250207 (the names of the signals indicating their detection dates, in September 2024 and February 2025, respectively). At the time these signals were captured, the LIGO Hanford detector (Washington State, USA) was not in optimal conditions, making the interpretation of its data particularly difficult.
At the time the two studied signals were captured, the Hanford detector suffered from instability, while those in Livingston and Virgo were operating nominally.
Image: collaboration Virgo By comparing the signals predicted by theory with the signals observed simultaneously by the LIGO Livingston detector (in Louisiana) and Virgo (in Italy), the researchers were able to draw precise conclusions about how the LIGO Hanford detector had distorted the collected data. For GW240925, this method confirmed calibration errors already measured on site. For GW250207, however, it was essential to resort to astrophysical calibration, as no reliable calibration measurement was available on site.
Thanks to the corrected calibration of the LIGO Hanford detector, LVK researchers determined that GW240925 was generated by the merger of two black holes with masses of 9 and 7 times that of the Sun, located about 350 megaparsecs (about 1.14 billion light-years) from Earth, while GW250207 came from two black holes of 35 and 30 solar masses, about 200 megaparsecs (about 652 million light-years) away. Without a rigorous accounting of calibration uncertainties, these estimates could have been biased toward incorrect values.
Precision gravitational astronomy
"These discoveries show that after more than a decade of work since the first detection, we have developed a deep understanding of the entire analysis chain, from the signals themselves to the behavior of the detectors. In the rare case where a detector malfunctions, we now have robust methods to exploit data from other detectors to obtain the best possible results. This information is crucial for distinguishing false deviations from general relativity, which could arise from unmodeled detector behavior," rejoices Elisa Maggio, researcher at the Italian National Institute of Nuclear Physics (INFN) and former postdoctoral fellow and Marie Curie fellow at the Max Planck Institute (Albert Einstein Institute) in Potsdam.
"It is remarkable that these colossal cosmic events can not only be measured by our instruments, but also serve to validate our measurements. The fact that we have succeeded in using astrophysical calibration demonstrates the maturity of gravitational wave detector capabilities. We are moving from the era of first discoveries to that of precision gravitational astronomy. Moreover, the catalog of gravitational wave detections continues to grow, and in a few weeks we will publish a new chapter, with new observations that will further deepen and broaden our understanding of the Universe and its most violent phenomena," concludes Benoît Revenu, researcher at the Subatech laboratory (CNRS, IMT Atlantique, Nantes University) in Nantes and responsible for cosmological analysis for these two very special events.