While three planets have been detected in the Kepler-431 system, little is known about the shapes of their orbits. To the left are a large number of overlapping orbits for each planet that are consistent with the observations. An international team of astrophysicists led by Princeton’s Daniel Tamayo removed all unstable configurations that would have already collided and were not visible today. Doing this with previous methods would take more than a year of computer time. With his new SPOCK model, it takes 14 minutes. Credit: Image by Daniel Tamayo.
Why don’t planets collide more often? How are planetary systems like our solar system or multi-planet systems organized around other stars? Of all the possible ways that planets could orbit, how many configurations will remain stable for billions of years in a star’s life cycle?
Rejecting the wide range of unstable possibilities, all the settings that would lead to collisions, would leave a sharper view of the planetary systems around other stars, but it’s not as easy as it sounds.
“Separating stable from unstable configurations turns out to be a fascinating and brutally difficult problem,” said Daniel Tamayo, a POT Hubble Sagan Fellow Scholarship Program in Astrophysical Sciences at Princeton. To ensure that a planetary system is stable, astronomers need to calculate the motions of multiple planets interacting over billions of years and verify the stability of every possible configuration, a computationally prohibitive task.
Astronomers since Isaac Newton have struggled with the problem of orbital stability, but while the fight contributed to many mathematical revolutions, including calculus and chaos theory, no one has found a way to theoretically predict stable configurations. Modern astronomers have yet to “force” the calculations, albeit with supercomputers instead of abaci or slide rules.
Tamayo realized that he could speed up the process by combining simplified models of dynamic planet interactions with machine learning methods. This allows you to quickly eliminate large swaths of unstable orbital configurations – calculations that would have taken tens of thousands of hours can now be done in minutes. He is the lead author of an article detailing the focus on the procedures of the National Academy of Sciences. Co-authors include graduate student Miles Cranmer and David Spergel, professor of astronomy Charles A. Young of Princeton at the Class of 1897 Foundation, Emeritus.
For most multi-planet systems, there are many orbital configurations that are possible given current observational data, of which not all will be stable. Many configurations that are theoretically possible would destabilize “quickly”, that is, in not many millions of years, in a tangle of crossed orbits. The goal was to rule out so-called “rapid instabilities”.
“We cannot say categorically ‘This system will be fine, but it will explode soon,'” Tamayo said. “The goal, instead, is, for a given system, to rule out all unstable possibilities that would have already collided and could not exist today.”
Instead of simulating a given configuration for one billion orbits, the traditional brute force approach, which would take approximately 10 hours, the Tamayo model instead simulates 10,000 orbits, which only takes a fraction of a second. From this short snippet, they calculate 10 summary metrics that capture the resonant dynamics of the system. Finally, they train a machine learning algorithm to predict from these 10 features whether the configuration would remain stable if it were to be released to a billion orbits.
“We call the model SPOCK – Stability of Klassifier Planetary Orbital Configurations – in part because the model determines whether the systems will ‘live and prosper,'” Tamayo said.
SPOCK determines the long-term stability of planetary configurations approximately 100,000 times faster than the previous approach, breaking the computational bottleneck. Tamayo cautioned that while he and his colleagues have not “solved” the overall problem of planetary stability, SPOCK reliably identifies rapid instabilities in compact systems, which they say are the most important in trying to make a characterization of restricted stability.
“This new method will provide a clearer window to the orbital architectures of planetary systems beyond ours,” said Tamayo.
But how many planetary systems are there? Isn’t our solar system the only one?
In the past 25 years, astronomers have found more than 4,000 planets orbiting other stars, of which nearly half are in multi-planet systems. But since small exoplanets are extremely difficult to detect, we still have an incomplete picture of their orbital configurations.
“It is now known that more than 700 stars have two or more planets orbiting around them,” said Professor Michael Strauss, chairman of the Princeton Department of Astrophysical Sciences. “Dan and his colleagues have found a fundamentally new way to explore the dynamics of these multi-planetary systems, speeding up the computer time needed to model by factors of 100,000. With this, we can hope to understand in detail the full range of solar system architectures that nature allows. ”
SPOCK is especially helpful in making sense of some of the faint and distant distant planetary systems recently detected by the Kepler telescope, said Jessie Christiansen, an astrophysicist at the NASA Exoplanet Archive who was not involved in this research. “It is difficult to restrict their properties with our current instruments,” she said. Are they rocky planets, ice giants, or gas giants? Or something new? This new tool will allow us to rule out possible planetary compositions and configurations that would be dynamically unstable, and allow us to do so with greater precision and on a substantially larger scale than was previously available. ”
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Reference: “Predicting long-term stability of compact multi-planet systems” by Daniel Tamayo, Miles Cranmer, Samuel Hadden, Hanno Rein, Peter Battaglia, Alysa Obertas, Philip J. Armitage, Shirley Ho, David Spergel, Christian Gilbertson, Naireen Hussain, Ari Silburt, Daniel Jontof-Hutter and Kristen Menou, July 13, 2020, procedures of the National Academy of Sciences.
DOI: 10.1073 / pnas.2001258117
Tamayo’s research was supported by the NASA Hubble Fellowship (HST-HF2-51423.001-A grant) awarded by the Space Telescope Science Institute.
