Catalog of Simulations of Black Hole Collisions Expands

SXS—Simulating eXtreme Spacetimes—is an ongoing scientific collaboration that has been generating simulations of dramatic events in space, particularly mergers of binary black hole systems, for several decades. Recently, SXS published a paper describing version 3 of its catalog of binary black hole simulations, six years after releasing version 2.

In 2015, LIGO (the Laser Interferometer Gravitational-wave Observatory) first successfully observed gravitational waves—ripples in space-time caused by dramatic celestial events—but the theoretical astrophysicists of the SXS collaboration had already been hard at work over the prior two decades calculating what these waves might look like as they reached Earth.

Gravitational waves are created by a variety of cosmological events, including mergers of neutron stars and black holes, and these waves pass through space and indeed through the Earth. Very sensitive detectors like LIGO record the perturbations made by these gravitational waves as they pass by and then try to determine what sort of celestial event gave rise to them. But it is equally important to take on this challenge from the opposite direction, by calculating what gravitational waveforms would result from different types of celestial events before detections are available. This is what the SXS collaboration does.

Solving Einstein's equations for merging black holes is extremely challenging. "You can take Einstein's equations and write them in a form that's described as hyperbolic, that suits analysis of wave-like phenomena," Keefe Mitman (PhD'24), now a NASA fellow at Cornell University, explains. "This means that if you give these equations some kind of initial data, there is a unique solution for how those data will evolve over time. And as we move to higher-resolution output, we can expect convergence: simulations that come closer and closer to the exact solution you would expect from Einstein's equations."

Today the scientists of SXS and LIGO bounce their data and equations back and forth between one another, pairing predictions to observations and back again. At this point, says Mitman, "we're doing enough and LIGO is just catching up. Up until now, when LIGO has detected something, its astrophysicists can go to the SXS catalog and find a simulation that suggests what is going on with their observations. If they don't find what they need, they can ask SXS for a new simulation with different parameters that might better match their data."

But who knows what the future may bring? In the 1970s and 1980s, theorizing events like black hole mergers via a mathematical technique known as numerical relativity appeared more challenging than simply detecting gravitational waves as they arrived to Earth, and that task appeared to be somewhere between extremely difficult and utterly impossible. And yet in 50 years gravitational-wave detection became a reality.

One day, data may outrace theory, so the researchers of the SXS collaboration continue diligently working to theorize the entire spectrum of possible black hole mergers. They output the waveforms these events would bring to gravitational wave detectors, which now include, in addition to LIGO, the Virgo interferometer near Pisa, Italy, and KAGRA (the Kamioka Gravitational Wave Detector), an interferometer in Gifu Prefecture in Japan, with space-based interferometers such as LISA (the Laser Interferometer Space Antenna) and DECIGO (the DECi-hertz Interferometer Gravitational wave Observatory) soon to come. SXS then publishes its models online where anyone can, so to speak, pull a specific simulation and its accompanying computer code off the library shelf.

The newly released expanded catalog is nearly twice the size it was in its prior release: 3,756 simulations compared to the 2019 catalog. These simulations also take account of a property of gravitational waves predicted by general relativity but which had not previously been included: gravitational-wave memory.

"Normally when you think of waves, for example the expanding concentric waves you get when you throw a rock in a pond, you know that after some time has passed, the waves will disperse and the pond's surface will be flat again," Mitman says. "With gravitational waves, it's a bit different. When a gravitational wave passes through some region of space-time, that space expands and contracts with the peaks and troughs of the gravitational wave. But after the gravitational wave has passed, that region of space does not go back to what it was before. It is permanently changed. That region of space-time remembers what happened, which is why we call it the memory effect."

With the gravitational-wave memory effect now included in SXS's simulations, theoreticians are closing in on ever more precise predictions for black hole mergers. "The catalog is widely used by the worldwide gravitational-wave community, with dozens of papers citing it every year," according to Saul Teukolsky, the Robinson Professor of Theoretical Astrophysics. "For example, waveform models used to search for events in the LIGO data are calibrated against the highly accurate simulations in the catalog. And theoretical ideas about general relativity can be tested against these simulations, which solve the exact equations of Einstein's theory."

"Black hole mergers can only be detected via gravitational waves," Mitman explains, so the work of SXS is vital to pushing the envelope of fundamental physics at the cosmological level.

"The SXS Collaboration's Third Catalog of Binary Black Hole Simulations" was published in Classical and Quantum Gravity. The project received support from the National Science Foundation, NASA, and the European Union's ERC Advanced Grant through the Max Planck Institute.