“Islands” of regularity discovered in the famous chaotic three-body problem

When three massive objects meet in space, they influence each other’s gravity in unpredictable ways. In a word: chaos. This is the conventional understanding. Now, a University of Copenhagen researcher has discovered that such encounters often avoid chaos and instead follow regular patterns, in which one of the objects is quickly kicked out of the system. This new idea could prove vital to our understanding of gravitational waves and many other aspects of the universe.

One of the most popular shows on Netflix right now is the sci-fi series 3-Body Problem. Based on a series of Chinese novels by Liu Cixin, the series involves a menagerie of characters, time periods and even extraterrestrial visitors. But the central principle concerns a star system in which three stars orbit each other.

Such a system, in which three objects influence each other, has fascinated scientists since the “father of gravity,” Isaac Newton, first described it. While the interaction between two objects meeting in space is predictable, the introduction of a third massive object makes the triadic encounter not only complex, but chaotic.

“The three-body problem is one of the most famous intractable problems in mathematics and theoretical physics. The theory states that when three objects meet, their interaction evolves chaotically, without regularity and completely detached from the starting point” , explains Alessandro Alberto Trani of the Niels Bohr Institute at the University of Copenhagen.

“But our millions of simulations demonstrate that there are gaps in this chaos – ‘islands of regularity’ – that depend directly on how the three objects are positioned relative to each other when they meet, as well as of their speed and angle of approach.”

Trani hopes this discovery will pave the way for improved astrophysical models, because the three-body problem is not just a theoretical challenge. The encounter of three objects in the universe is a common phenomenon and its understanding is crucial. The research is published in the journal Astronomy and astrophysics.

“If we want to understand the gravitational waves emitted by black holes and other massive moving objects, the interactions of black holes as they meet and merge are essential. Immense forces are at play, especially when three of them Therefore, our understanding of such encounters could be the key to understanding phenomena such as gravitational waves, gravity itself and many other fundamental mysteries of the universe,” explains the researcher.

A tsunami of simulations

To study the phenomenon, Trani coded his own software, Tsunami, capable of calculating the movements of astronomical objects based on the knowledge we have about the laws of nature, such as Newton’s gravity and General Relativity. Einstein. Trani set it up to run millions of three-body dating simulations within certain defined parameters.

The initial parameters of the simulations were the positions of two of the objects in their mutual orbit, that is, their phase along a 360 degree axis. Then, the angle of approach of the third object – varying from 90 degrees.

The millions of simulations were distributed according to the different possible combinations in this framework. Taken together, the results form a rough map of every conceivable outcome, like a vast tapestry woven from the threads of the initial configurations. This is where the islands of regularity appear.

The colors represent the object that is ultimately ejected from the system after the encounter. In most cases, it is the object with the lowest mass.

“If the three-body problem were purely chaotic, we would see only a chaotic mixture of indistinguishable points, with the three outcomes mixing together without any discernible order. Instead, regular “islands” emerge from this chaotic sea, where the system behaves in a predictable manner, leading to uniform results and therefore uniform colors,” explains Trani.

Two steps forward, one step back

This discovery holds great promise for a deeper understanding of an otherwise impossible phenomenon. In the short term, however, this represents a challenge for researchers. Pure chaos is something they already know how to calculate using statistical methods, but when the chaos is interrupted by regularities, the calculations become more complex.

“When certain regions of this map of possible outcomes suddenly become regular, this disrupts statistical probability calculations, leading to inaccurate predictions. Our challenge now is to learn how to combine statistical methods with so-called numerical calculations, which offer great accuracy when the system behaves consistently,” says Trani.

“In this sense, my results take us back to square one, but at the same time they hold out hope for a whole new level of understanding in the long term,” he says.