Black holes speeding in the middle of galaxies like balls in billiards

Black holes are special objects in the universe. We have little knowledge of them, partly because they do not emit light of their own. Until a few years ago, our main source of information about the universe was light. In 2015, however, LIGO detected gravitational waves from a black hole collision for the first time.

In the present research, nine physicists from all over the world worked together. Three of them are Hungarians, all of whom have connections with the ELTE Faculty of Science: Imre Bartos (the University of Florida, former ELTE student), Zoltán Haiman (Columbia University, New York, former György Békésy postdoctoral research fellow at ELTE), and Bence Kocsis (Oxford University, former student and assistant professor at ELTE, and currently an external supervisor). An important element has been discovered in this cosmic puzzle that could solve the big open question about the origin of unusual gravitational waves.

But why is it surprising that two black holes are not moving around each other in circular orbits? “This is due to the fundamental nature of gravitational waves. The orbits of the radiant black holes become circular relatively quickly due to the gravitational waves, long before they collide,” explained Zoltán Haiman. Previous research has shown that non-circular orbits are very rare. This raises the question: Why could an already exceptional black hole collision occur on such an elliptical orbit?

Imre Bartos (on the left) is a professor at the University of Florida. He gained his M.Sc. degree in physics from ELTE, and then his Ph.D. from Columbia University. He researches gravitational waves and is a member of the LIGO, LISA, and IceCube collaborations. Zoltán Haiman (in the middle) is a cosmologist and astrophysicist at Columbia University in New York. He studied at Mihály Fazekas Secondary Grammar School in Budapest and continued his studies at MIT, Cambridge University, and Harvard University. He won a György Békésy postdoctoral fellowship for a period of three years and did his research partly at ELTE. His current research interests include the formation of the first black holes, the properties of black hole binaries, and the study of dark energy and dark matter through the gravitational lens effect. Bence Kocsis (on the right) is a professor at Oxford University. He also studied at Mihály Fazekas Secondary Grammar School in Budapest, then obtained a M.Sc. degree and doctorate from ELTE and was the supervisor of the GALNUC ERC Starting Grant project. His research is focused on gravitational dynamics systems, and he investigates the astrophysical origin of gravitational waves.

The possible answer lies in the centre of galaxies with a huge black hole millions of times heavier than the sun in the middle and a flat, disc-shaped cloud of gas swirling around it.

“In this disc, there are a large number of minor black holes and they are moving at such a high speed that

due to their gravitational interaction, the black holes bounce between each other like balls in billiards.

Under such circumstances, double circles cannot exist,” pointed out Bence Kocsis. “The presence of a giant central black hole is not enough in itself to create such an environment. Together with Ákos Szölgyén and Gergő Máthé, doctoral candidates at ELTE, we previously found that the black holes are arranged in a thick disk due to their weight. However, frequent collisions require an even thinner structure than that.

Together with Hiromichi Tagawa, a former postdoctoral research fellow at ELTE, we have demonstrated that the necessary conditions can develop in galactic nuclei where there is also a gas cloud. This is because the distribution of black holes becomes nearly two-dimensional due to the gas and they start moving towards the centre. Then, as they approach each other randomly, the black holes can merge into a close binary system as a result of the gas dissipation. These objects often collide with a third black hole in a chaotic dance”.

Two-dimensional black hole billiards

Calculations have so far suggested that the interaction between black holes takes place in three dimensions, which is true in most cases, but then mostly circular binaries are formed.

“We started thinking about what would happen if the black holes could only move within a flat cloud of gas, which corresponds to a two-dimensional environment. Surprisingly, we found that in this case, the formation of non-circular orbits increases dramatically, by up to 100 times compared to the three-dimensional case. This theory corresponds well to the 2019 observation that all the special features of the GW190521 collision can be explained by the fact that the process took place in a flat gas cloud in the core of a distant galaxy near a huge black hole,” explains Johan Samsing. This discovery also reveals a lot about the three-body problem, a problem in mechanics going back to hundreds of years.

This process also plays a critical role in how black holes collide in hidden corners of the universe.

“It is very interesting that the structure created by the black holes is in many ways similar to a completely different physical system, which I studied as an ELTE student together with József Cserti and Gergely Palla. In the quantum billiard problem, electrons bounce in a two-dimensional configuration; we observed how quantum mechanics makes an order in chaos. The black holes may have collided in a configuration reminiscent of this,” said Bence Kocsis.

Black hole collisions in flat gas clouds

In addition to eccentricity, the theory of flat gas clouds automatically explains two other surprising properties of the GW190521 collision. The large mass of black holes is caused by the fact that many smaller black holes crammed into the cloud of gas undergo multiple collisions, each collision increasing the mass of the resulting black hole. These successive collisions also accelerate the spin of the black holes.

This is just the beginning. “Researchers have long been trying to understand the properties of dense, flat gas clouds, but that is a complex problem. The result depends very much on the properties of the gas clouds and how exactly the black holes move in them. Black hole collisions similar to the GW190521 source open up a new way to study gas clouds. The research must be continued, which may lead to further unexpected discoveries,” concludes Zoltán Haiman.