Final dance of unequal partners of black holes

Solving the equations of general relativity for colliding black holes is not easy.

Physicists started using supercomputers to come up with solutions to this famous difficult problem in the 1960s. In 2000, with no solution in sight, Kip Thorne, 2018 Nobel laureate and one of LIGO’s designers, famously bet that there would be an observation of gravitational waves before a numerical solution was reached.

He lost that bet when, in 2005, Carlos Lousto, then at the University of Texas at Brownsville, and his team generated a solution using the Lonestar supercomputer at the Texas Advanced Computing Center. (At the same time, the NASA and Caltech groups have derived independent solutions.)

In 2015, when the Laser Interferometer Gravitational-Wave Observatory (LIGO) first observed such waves, Lousto was in shock.

“It took us two weeks to realize it really was from nature and not from introducing our simulation as a test,” said Lousto, now a math professor at the Rochester Institute of Technology (RIT). “The comparison with our simulations was so obvious. You could see with your naked eyes that it was the merger of two black holes.”

Lousto is back again with a new milestone in numerical relativity, this time simulating the merger of black holes where the ratio of the mass of the largest to the smallest black hole is 128 to 1 – a scientific problem bordering on that. which is computational possible. Its secret weapon: the Frontera supercomputer at TACC, the eighth most powerful supercomputer in the world and the fastest in any university.

His research with collaborator James Healy, supported by the National Science Foundation (NSF), was published in Physical Review Letters [journals.aps.org/prl/abstract/ … ysRevLett.125.191102] this week. It may take decades to confirm the results experimentally, but nonetheless serves as a computational result that will help guide the field of astrophysics forward.

“Modeling pairs of black holes with very different masses is very computationally challenging due to the need to maintain accuracy across a wide range of grid resolutions,” said Pedro Marronetti, program director for the gravitational physics at NSF. “The RIT team has performed the world’s most advanced simulations in this area, and each of them brings us closer to understanding the observations that gravitational wave detectors will provide in the near future.”

LIGO can only detect gravitational waves caused by small and intermediate mass black holes of approximately equal size. It will take 100 times more sensitive observers to detect the type of mergers that Lousto and Healy have modeled. Their findings show not only what gravitational waves caused by a 128: 1 fusion would look like to an observer on Earth, but also the characteristics of the last fused black hole including its final mass, spin, and recoil velocity. This led to some surprises.

“These merged black holes can have much faster speeds than previously known,” Lousto said. “They can travel at 5,000 kilometers per second. They depart from a galaxy and roam the universe. This is another interesting prediction.”

The researchers also calculated the gravitational waveforms, the signal that would be perceived near Earth, for such mergers, including the peak frequency, amplitude and brightness. Comparing these values ​​with the predictions of existing scientific models, their simulations were within 2% of the expected results.

Previously, the largest mass ratio ever solved with high precision was 16 to 1, eight times less extreme than the Lousto simulation. The challenge of simulating larger mass ratios is that it requires resolving the dynamics of interacting systems at additional scales.

Like computer models in many fields, Lousto uses a method called adaptive mesh refinement to obtain precise models of the dynamics of interacting black holes. It involves putting the black holes, the space between them and the distant observer (us) on a grid or mesh and refine the areas of the mesh with more detail where it is needed.

Lousto’s team approached the problem with a methodology that compares to Zeno’s first paradox. By halving and halving the mass ratio and adding levels of internal grid refinement, they were able to shift from 32: 1 black hole mass ratios to 128: 1 binary systems that undergo 13 orbits before merging. On Frontera, it took seven months of constant calculations.

“Frontera was the perfect tool for the job,” Lousto said. “Our problem requires high performance processors, communications and memory, and Frontera has all three.”

Simulation is not the end of the road. Black holes can have a variety of rotations and configurations, which affect the amplitude and frequency of the gravitational waves produced by their merger. Lousto would like to solve the equations 11 more times to get a good first range of possible “models” to compare against future findings.

The findings will help designers of future ground and space gravitational wave detectors plan their instruments. These include advanced third-generation ground-based gravitational wave detectors and the Laser Interferometer Space Antenna (LISA), which is slated for launch in the mid-2030s.

The research may also help answer fundamental mysteries about black holes, such as how some can grow so large, millions of times the mass of the Sun.

“Supercomputers help us answer these questions,” Lousto said. “And the problems inspire new research and pass the baton to the next generation of students.”