Scientists have used the collision of two black holes to measure and correct the calibration of the detectors that observe them.

The technique was perfected using two exceptionally strong gravitational-wave signals, produced by the collisions of pairs of black holes. These events were so strong that they allowed researchers not only to study the black holes that created them, but also to check how accurately the detectors were recording the signals.

 “We are using black holes to help check the accuracy of our detectors. How cool is that!” said Dr Lilli (Ling) Sun, from the ANU Centre for Gravitational Wave Astronomy, the research School of Physics and ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav).

“By comparing the predicted signal with what we actually record, we can spot tiny mismatches that sometimes reveal the detector wasn’t perfectly calibrated at the time.”

Gravitational waves are produced by some of the most energetic events in the Universe. Despite their violent origins, these ripples in space and time are tiny and have only been detected thanks to the development of the most sensitive instruments ever created.

But because these instruments are so sensitive, their accurate calibration is crucial, and is a major part of the search for gravitational waves.

“As gravitational-wave astronomy moves from discovery to precision science, using the Universe itself to help calibrate our instruments may become an increasingly powerful tool,” Dr Sun said.

The ability to use a measured signal to calibrate the measurement has come about through a calibration between three international facilities: LIGO, in the United States; Virgo, in Europe, and KAGRA in Japan.

Dr Sun and two colleagues from OzGrav, Mallika Sinha, a PhD student at Monash University, and Dr Yi Shuen Christine Lee, a postdoctoral researcher at the University of Melbourne, made important contributions to the analysis and interpretation of the results, which is published in Physical Review Letters.

The LIGO–Virgo–KAGRA collaboration has now confidently detected more than 200 gravitational-wave signals from merging black holes and neutron stars. Each signal carries information about its source and the extreme physics governing these collisions.

Extracting that information requires the detectors to measure gravitational waves with extraordinary precision and to carefully account for any uncertainties in those measurements.

Gravitational waves stretch and squeeze spacetime as they pass through Earth. The detectors measure this by sending laser light down two perpendicular arms and looking for tiny differences in the time it takes the light to travel back and forth. A typical gravitational wave changes the arm length by about one ten-billionth of a billionth of a metre, smaller than the width of a proton.

“Thanks to major upgrades over the past decade, our detectors are now so sensitive that signals from colliding black holes come through loud and clear,” Dr Sun said.

“If Einstein’s theory of general relativity is correct, those signals should follow a very specific pattern.”

Turning those minute measurements into a physical gravitational-wave signal requires a detailed model of the detector’s response. This includes accounting for the complex control systems used to keep the instruments stable. Normally, calibration uncertainties are measured and estimated using auxiliary lasers, sensors, and engineering data.

However, during the detections of events GW240925 and GW250207, the LIGO Hanford detector happened to have a larger calibration error than usual. Because both signals were exceptionally loud, the researchers were able to disentangle the true gravitational-wave signal from the detector’s calibration error, a process known as astrophysical calibration. GW240925 served as a verification case, allowing the team to compare results from astrophysical calibration with data that was later corrected using standard methods.

GW250207, meanwhile, is the second-loudest gravitational-wave event ever observed and provides a unique window into extreme physics. For this event, astrophysical calibration was essential to ensure the data could be trusted at all.

Accurate calibration is critical because even small errors can bias estimates of key source properties, such as the masses of the black holes, whether they are spinning, and where the signal originated in the sky.

“It was simply bad luck that such a loud event was observed while LIGO Hanford was in an unsettled state,” said Ms Sinha. “As our detectors become more sensitive and we observe more events, situations like this will only become more common. Without astrophysical calibration, we might not be able to reliably analyse these interesting events and miss out on some nifty science."

The researchers found that GW240925 was produced by black holes around nine and seven times the mass of the Sun, while GW250207 involved black holes roughly 35 and 30 times the Sun’s mass.

Using three detectors instead of two helps us pinpoint the location of gravitational-wave sources much more precisely, Dr Lee said.

“Better location means we can better understand the physical properties of the sources themselves,” said Dr Lee.

“This successful astrophysical calibration is an exciting step forward for gravitational-wave astronomy. It improves our chances for extracting important astrophysical information from gravitational-wave sources, even when traditional detector calibration methods are not accurate or feasible.”

Because of its strength and position in the sky, GW250207 is considered one of the most promising gravitational-wave signals for future measurements of the Hubble constant. However, many more gravitational-wave signals from black hole mergers that produce no visible light will be needed to resolve the long-standing tension between different cosmological measurements.

Information about OzGrav and gravitational-wave observatories:

The ARC Centre of Excellence for Gravitational Wave Discovery (OzGrav) is funded by the Australian Government through the Australian Research Council Centres of Excellence funding scheme. OzGrav is a partnership between Swinburne University of Technology (host of OzGrav headquarters), the Australian National University, Monash University, University of Adelaide, University of Melbourne, University of Western Australia, University of Queensland, and University of Sydney, along with other collaborating organisations in Australia and overseas.

This material is based upon work supported by NSF’s LIGO Laboratory which is a major facility fully funded by the National Science Foundation. NSF’s LIGO Laboratory is a major facility fully funded by the National Science Foundation and operated by Caltech and MIT, which conceived of LIGO and led the Initial and Advanced LIGO projects. Financial support for the Advanced LIGO project was led by the NSF with Germany (Max Planck Society), the U.K. (Science and Technology Facilities Council) and Australia (Australian Research Council-OzGrav) making significant commitments and contributions to the project. More than 1600 scientists from around the world participate in the effort through the LIGO Scientific Collaboration, which includes the GEO Collaboration. A list of additional partners is available at https://my.ligo.org/census.php.

The Virgo Collaboration is currently composed of approximately 880 members from 152 institutions in 17 different (mainly European) countries. The European Gravitational Observatory (EGO) hosts the Virgo detector near Pisa in Italy, and is funded by Centre National de la Recherche Scientifique (CNRS) in France, the Istituto Nazionale di Fisica Nucleare (INFN) in Italy, and the National Institute for Subatomic Physics (Nikhef) in the Netherlands. A list of the Virgo Collaboration groups can be found at: https://www.virgo-gw.eu/about/scientific-collaboration/. More information is available on the Virgo website at https://www.virgo-gw.eu.

KAGRA is the laser interferometer with 3 km arm-length in Kamioka, Gifu, Japan. The host institute is Institute for Cosmic Ray Research (ICRR), the University of Tokyo, and the project is co-hosted by National Astronomical Observatory of Japan (NAOJ) and High Energy Accelerator Research Organization (KEK). KAGRA collaboration is composed of over 400 members from 128 institutes in 17 countries/regions. KAGRA’s information for general audiences is at the website https://gwcenter.icrr.u-tokyo.ac.jp/en/. Resources for researchers are accessible from http://gwwiki.icrr.u-tokyo.ac.jp/JGWwiki/KAGRA.