Living for billions and billions of years, it is no simple task to figure out how old a star is. Fortunately, despite appearances, earthquake-like pulsations cause stars like our Sun to vibrate, imprinting fluctuations in the light they emit and leaving clues for how they evolved over the course of their lives.

But using those oscillations to determine the properties of a star was so far an extremely difficult and time-consuming task, requiring tens of thousands of supercomputing hours to study a single star. An interdisciplinary team of computer scientists and astrophysicists led by Earl Bellinger at the Max Planck Institute for Solar System Research (MPS) in Gottingen have now dramatically improved the process.

Their study, published this week in the Astrophysical Journal, called upon machine learning techniques to help characterize stars and their exoplanets up to a million times faster. The artificial intelligence that they developed was able to discover formulas that take only seconds to connect the pulsation patterns seen in starlight to the properties of a star such as its age, mass, and radius. Their work will help identify which planetary systems are old enough to potentially host life, and help researchers to understand how the Galaxy has evolved over time.

As the old saying goes - the flame that burns twice as bright lives half as long. The same is true for stars in the night sky. Bigger and brighter stars have shorter lives than smaller and dimmer stars, with more massive stars rapidly burning through their nuclear fuel in order to generate enough pressure to oppose their powerful inward gravity. Stars hundreds of times more massive than the Sun may live for 'only' a few 100,000s of years, whereas those half the mass of our Sun are predicted to keep burning for more time than the current age of the Universe.

How bright a star appears does not much limit the possibilities of how old it could be. Without peering into a star's interior and gauging how much nuclear fuel is left, it is very difficult to figure out the age of a star.

But thanks to the field of asteroseismology-the study of pulsations in stars-as well as dedicated space missions such as NASA's Kepler spacecraft, it is now possible to do just that. Based not just on the brightness of a star, but the periodic changes in a star's brightness caused by vibrations of the star, asteroseismology allows astronomers to actually look inside of stars and extract the information that is needed to figure out just how old they are.

"The physics of the structure and evolution of stars dictate that a star at a given age and mass will pulsate with a particular pattern," says lead author Earl Bellinger, a Ph.D. student in the Stellar Ages and Galactic Evolution (SAGE) research group at the Max Planck Institute for Solar System Research and the Department of Astronomy at Yale University. "Studying these pulsations thus enables a star's 'seismic age' to be inferred."

Although there are already methods for performing seismic aging, they can be slow. Usually, to determine the age of a star, astrophysicists calculate mathematical models that best match a given set of observations.

The age calculated in the model is then attributed to the star. The likely match can be found either by searching through millions of precomputed models of stars-ones that are limited in their sophistication-or by refining more complex models, which can take tens of thousands of supercomputing hours per star.

Rather than searching for the model that fits the observations, Bellinger and his team are calling on the help of artificial intelligence (A.I.) to flip the problem on its head. Using a machine learning approach called random forest regression, they train a computer to learn the direct relationships between the pulsations we can observe and the kinds of stars that give rise to them.

These relationships, which are far too complex for a person to derive by hand, enable a star to be characterized in mere seconds, which allows the researchers to include much more sophisticated physics in their models than previous methods.

The team has applied their method to several test cases, including 34 well-studied stars that are known to host exoplanets. So far, the machine has passed every test thrown at it. "The results are in excellent agreement with other approaches to astronomical dating, such as the radioactive dating that is used to measure the age of the Sun," Bellinger says, "and it works very quickly, so it can be used on a lot of stars. We are rapidly developing the capability to characterize entire stellar catalogues for the next generation of Galactic surveys."

There will be more A.I.-assisted stellar dating to come in the future. The method is currently only applicable to main-sequence stars, which are those stars that burn hydrogen in their core.

"The method appears to be quite powerful and robust. We are looking forward to seeing how we can apply it to learn about other types of stars," says Bellinger. "This will enable us to date stars all throughout our Galaxy, which will ultimately allow us understand how the Milky Way itself developed." The study was published in the Astrophysical Journal.

Earl P. Bellinger et al: Fundamental parameters of main-sequence stars in an instant with machine learning. The Astrophysical Journal, 830:31 (20pp), 2016 October 10