Solve the equations of general relativity for colliding black holes

Again from an inspiration animation of a binary black hole with a 128: 1 mass ratio showing the start of the final burst of gravitational waves. Credit: Carlos Lousto, James Healy, RIT

Final dance of unequal partners of black hole

Scientists at the Rochester Institute of Technology perform the first ever simulation of the large mass ratio black hole merger on Frontera.

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 solutions in sight, Kip Thorne, Nobel Prize 2018 and one of the designers of LIGO, famously wagered 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 groups in NASA and Caltech 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 that it really was from nature and not from introducing our simulation as a test,” said Lousto, now a math professor at 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 this week. It may take decades to confirm the results experimentally, but it still serves as a computational result that will help drive the field of astrophysics forward.

“Modeling pairs of black holes with very different masses is very demanding in terms of calculation due to the need for maintenance precision in a wide range of grid resolutions, “said Pedro Marronetti, program director for gravitational physics at NSF.” The RIT group has performed the world’s most advanced simulations in this area, and each of them brings us closer to understanding of 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 kind of mergers Lousto and Healy have modeled. Their findings show not only what the 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 greater velocities than previously known,” Lousto said. “They can travel at 5,000 kilometers per second. They come out of 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 the Earth – for such mergers, including their 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 that had ever been solved with high accuracy 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’s about putting the black holes, the space between them and the distant observer (us) on a grid or mesh and refining areas of the mesh with more detail where it’s 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 could 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.”

Reference: “Exploring the Small Mass Ratio Binary Black Hole Merger via Zeno’s Dichotomy Approach” by Carlos O. Lousto and James Healy, 5 November 2020, Physical Review Letters.
DOI: 10.1103 / PhysRevLett.125.191102