The unexpected mathematics behind the search for exoplanets

The unexpected connections hidden in the complex mathematics behind how to apply general relativity to find new planets around other stars.

In a paper published this week in Nature Astronomy, Berkeley researchers describe how a machine learning algorithm was developed to detect exoplanets more quickly when such planetary systems pass in front of a background star and briefly illuminate it – a process called microgravity – revealing that theories The old ones now used to explain these notes are woefully incomplete.

In 1936, Albert Einstein himself used his new theory of general relativity to show how light from a distant star could be deflected by the gravitational pull of a star in the foreground, illuminating it as seen from Earth, but often splitting it into several light points. . Light it or distort it into a ring, now called an Einstein ring. This is similar to the way a magnifying glass can focus and intensify sunlight.

But when the foreground body is a star with a planet, the brightness over time, the curve of light, is more complex. Also, there are often multiple planetary orbits that can explain a given light curve well, which are called atomizations. This is where humans have simplified the math and missed the big picture.

However, the new algorithm suggested a mathematical way to unify the two main types of degeneracy by interpreting what telescopes detect during microlensing, showing that the two “theories” are really special cases of a larger theory that the researchers admit may still be incomplete.

“Our previously developed machine learning inference algorithm led us to discover something new and fundamental about the equations that govern the general relativistic effect of the bending of light by two massive objects,” Joshua Bloom wrote in a statement. Article to arXiv preprint server. Bloom is professor of astronomy at the University of California, Berkeley and chair of the department.

UC Berkeley graduate student Kiming Zhang’s discovery compared the connections recently made by Google’s artificial intelligence team, DeepMind, between two different areas of mathematics. Taken together, these examples show that AI systems can reveal essential connections that humans miss.

“I assert that it constitutes one of the first, if not the first, times that artificial intelligence has been used to directly produce new theoretical knowledge in mathematics and astronomy,” Bloom said. “Just as Steve Jobs suggested that computers can be bikes of the mind, we were looking for an AI framework that would serve as an intellectual rocket for scientists.”

“This is a milestone in artificial intelligence and machine learning,” said co-author Scott Gaudi, a professor of astronomy at Ohio State University and one of the pioneers in using microgravity to discover exoplanets. “Keming’s machine learning algorithm revealed this degeneracy that experts in the field who have been working with data for decades have missed. This indicates what future research will look like when machine learning helps it, which is really exciting.”

Zhang and Gaudi present a new paper that accurately describes new mathematics based on general relativity and explores the theory in the exact lens positions as more than one exoplanet orbits a star.

Technically, the new theory makes the interpretation of fine-lens observations more ambiguous, as there are more decadent solutions to describing the observations. But the theory also shows that observing the same exact lensing event from two perspectives, from Earth and from the orbit of the Roman Space Telescope, for example, would make it easier to determine the correct orbits and masses. That’s what astronomers are currently planning to do, Gaudi said.