AI Reveals New Math Behind The Search For Exoplanets
New planets orbiting other stars can be discovered using general relativity theory, which relies on connections buried in sophisticated mathematics.
AI algorithms that have been trained on real astronomical observations are now better than astronomers at sorting through huge amounts of data to find new exploding stars, new types of galaxies, and the mergers of massive stars. This is speeding up the rate of new discoveries in astronomy, the oldest science in the world.
Researchers at Berkeley’s Institute for Computational Astronomy and Astrophysics (ICAA) found that AI, also known as machine learning, can uncover something deeper: previously unknown relationships in the complicated mathematics deriving from general relativity.
In a paper published this week in the journal Nature Astronomy, the researchers explain how an AI algorithm they made to find exoplanets faster when they pass in front of a background star and briefly brighten it (a process called gravitational microlensing) showed that the decades-old theories used to explain these observations are woefully incomplete.
In 1936, Albert Einstein used his new general relativity theory to demonstrate how the gravity of a foreground star can bend the light from a distant star, not only brightening it as seen from Earth, but also splitting it into multiple points of light or distorting it into a ring, now known as an Einstein ring. This is like how a hand lens can bring light from the sun into focus and make it stronger.
But the light curve is more complicated when the object in the foreground is a star with a planet. Furthermore, there are frequently numerous planetary orbits that can as well explain a given light curve, known as degeneracies. Humans simplified math and ignored the big picture.
The AI algorithm, on the other hand, pointed to a mathematical way to unify the two major types of degeneracy in interpreting what telescopes detect during microlensing, demonstrating that the two “theories” are really special cases of a broader theory that is likely still incomplete, according to the researchers.
When Joshua Bloom uploaded the paper to the arXiv preprint server last year, he wrote in a blog post that “A machine learning inference algorithm we previously developed led us to discover something new and fundamental about the equations that govern the general relativistic effect of light- bending by two massive bodies.” Bloom is a UC Berkeley astronomy professor and department chair.
He linked the discovery by UC Berkeley graduate student Keming Zhang to recent links found by Google’s AI team, DeepMind, between two fields of mathematics. These examples demonstrate that AI systems can uncover fundamental relationships that humans miss.
“I argue that they constitute one of the first, if not the first time that AI has been used to directly yield new theoretical insight in math and astronomy,” Bloom said. “Just as Steve Jobs suggested computers could be the bicycles of the mind, we’ve been seeking an AI framework to serve as an intellectual rocket ship for scientists.”
“This is kind of a milestone in AI and machine learning,” said co-author Scott Gaudi, an astronomy professor at The Ohio State University and a pioneer in the use of gravitational microlensing to find exoplanets. “KKeming’s machine learning algorithm uncovered this degeneracy that had been missed by experts in the field toiling with data for decades. This is suggestive of how research is going to go in the future when it is aided by machine learning, which is really exciting .”
Microlensing for exoplanet discovery
More than 5,000 extrasolar planets, or exoplanets, have been found around stars in the Milky Way. However, few have been seen with a telescope because they are too dim. Most have been discovered because they induce a Doppler effect in the movements of their host stars or because they dim the light from the host star as they pass in front of it — transits that NASA’s Kepler mission was designed to study. Microlensing, a third technique, has revealed slightly more than a hundred.
Microlensing is one of the primary goals of NASA’s Nancy Grace Roman Space Telescope, which is scheduled to launch in 2027. The approach has an advantage over Doppler and transit in that it can discover lower-mass planets, such as those the size of Earth, that are far from their stars, at a distance comparable to Jupiter or Saturn in our solar system.
Bloom, Zhang, and their colleagues began working on an AI program to evaluate microlensing data more quickly in order to establish the stellar and planetary masses of these planetary systems, as well as the distances the planets orbit their stars, two years ago. An algorithm like this would speed up the examination of the hundreds of thousands of events that the Roman telescope is anticipated to detect in order to locate the 1% or fewer that are triggered by exoplanetary systems.
However, one issue that astronomers face is that the measured signal can be unclear. When a single foreground star travels in front of a background star, the brightness of the background stars grows smoothly to a peak before symmetrically falling down to its original brightness. It’s simple to comprehend both mathematically and visually.
If a planet orbits the foreground star, the planet forms a distinct brightness peak within the star’s peak. General relativity typically offers two or more so-called degenerate solutions to explain the findings when trying to rebuild the orbital configuration of the exoplanet that created the signal.
According to Gaudi, astronomers have traditionally dealt with these degeneracies in a simplistic and artificially separate manner. If distant starlight passes close to the star, the observations could be interpreted as either a wide or close orbit for the planet — an ambiguity that astronomers can usually clarify with other data. When background starlight passes close to the planet, a second sort of degeneracy arises. However, in this example, the two distinct planetary orbit solutions are just marginally different.
Gaudi says that these two simplified versions of two-body gravitational microlensing are usually enough to figure out the real masses and distances between orbits. In fact, Zhang, Bloom, Gaudi, and two other UC Berkeley co-authors, astronomy professor Jessica Lu and graduate student Casey Lam, proposed a new AI method that does not rely on knowledge of these interpretations at all in a study published last year. The system substantially reduces the amount of time it takes to analyze microlensing observations, delivering conclusions in minutes rather than days.
Zhang then used the new AI technique to microlensing light curves from hundreds of different star and planetary orbital configurations and discovered something unusual: the two interpretations failed to account for other ambiguities. He came to the conclusion that the popular explanations of microlensing were simply particular cases of a larger theory that explains the complete range of ambiguity in microlensing events.
“The two previous theories of degeneracy deal with cases where the background star appears to pass close to the foreground star or the foreground planet,” Zhang explained. “The AI algorithm showed us hundreds of examples from not only these two cases, but also situations where the star doesn’t pass close to either the star or planet and cannot be explained by either previous theory. That was key to us proposing the new unifying theory .”
Gaudi was initially doubtful, but changed his mind after Zhang presented numerous examples in which the prior two theories failed to explain observations and the new theory did. Zhang examined data from two dozen prior studies describing the identification of exoplanets by microlensing and discovered that the new theory fit the data better in every case than the previous theories.
“People were seeing these microlensing events, which actually were exhibiting this new degeneracy but just didn’t realize it,” Gaudi explained. “It was really just the machine learning looking at thousands of events where it became impossible to miss,” says the researcher.
Zhang and Gaudi have published a new work that thoroughly covers the new general relativity mathematics and investigates the theory in microlensing conditions when several exoplanets orbit a star.
Technically, the new theory makes it harder to figure out what microlensing observations mean because there are now more ways to describe the observations. However, the theory shows that watching the identical microlensing event from two angles — for example, from Earth and from the orbit of the Roman Space Telescope — makes determining the proper orbits and masses much easier. According to Gaudi, astronomers are currently planning to accomplish just that.
“TThe AI suggested a way to look at the lens equation in a new light and uncover something really deep about the mathematics of it,” Bloom added. “AI is sort of emerging as not just this kind of blunt tool that’s in our toolbox, but as something that’s actually quite clever. Alongside an expert like Keming, the two were able to do something pretty fundamental.”
Image Credit: Berkeley
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