Jul 14 2020
Researchers are clueless about how planetary systems—similar to the solar system or the multi-planet systems surrounding other stars—arrange themselves, and why collision does not occur more often between the planets.
While three planets have been detected in the Kepler-431 system, little is known about their orbits. On the left are a large number of superimposed orbits for each planet that are consistent with observations. On the right, a computer model (SPOCK) from Princeton’s Daniel Tamayo has removed the unstable configurations that would have already collided. Doing this with previous methods would take over a year of computer time. With SPOCK, it takes 14 minutes. Image Credit: Daniel Tamayo.
Of all of the potential ways planets are likely to orbit, researchers are not aware of the number of configurations that will continue to remain steady across the billions of years of the life cycle of a star.
Ruling out the wide range of unstable prospects—the entire configurations that would result in collisions—would provide a clearer picture of the planetary systems surrounding other types of stars; however, it is not as simple as it sounds.
“Separating the stable from the unstable configurations turns out to be a fascinating and brutally hard problem,” stated Daniel Tamayo, a NASA Hubble Fellowship Program Sagan Fellow in astrophysical sciences at Princeton University.
To ensure that a planetary system remains stable, astronomers have to estimate the movements of numerous interacting planets across billions of years and assess every potential configuration for stability, an undertaking that is computationally prohibitive.
Since the time of Isaac Newton, astronomers have struggled with the issue of orbital stability, and although the struggle contributed to several mathematical revolutions, such as chaos theory and calculus, none has identified a method to forecast stable configurations at the theoretical level. Today’s astronomers continue to “brute-force” the calculations, but they use supercomputers rather than slide or abaci rules.
Tamayo noted that the process could be expedited by integrating simplified models of the dynamical interactions of planets with machine learning techniques. With this approach, the large swaths of unstable orbital configurations can be eliminated rapidly—in other words, calculations that would have taken an infinite number of hours can now be performed in minutes.
Tamayo is the lead author of the study that describes the method in Proceedings of the National Academy of Sciences. The study’s co-authors include Miles Cranmer, a graduate student, and David Spergel, Princeton University’s Charles A. Young Professor of Astronomy on the Class of 1897 Foundation, Emeritus.
For a majority of the multi-planet systems, several orbital configurations are considering the present-day observational information, of which not all will be stable. Several orbital configurations that are hypothetically viable would “quickly” destabilize into a web of crossing orbits, that is, in not too many millions of years. The aim was to discard those supposed “fast instabilities.”
We can’t categorically say ‘This system will be OK, but that one will blow up soon’. The goal instead is, for a given system, to rule out all the unstable possibilities that would have already collided and couldn’t exist at the present day.
Daniel Tamayo, NASA Hubble Fellowship Program Sagan Fellow, Department of Astrophysical Sciences, Princeton University
Rather than replicating a specified configuration for a billion orbits—the conventional brute-force method, which would take around 10 hours—Tamayo’s new model rather replicates for 10,000 orbits, which takes just a fraction of a second.
From this brief snippet, the researchers were able to estimate 10 summary metrics that record the resonant dynamics of the system. The scientists ultimately trained a machine-learning algorithm to forecast from these 10 traits whether the configuration would continue to stay stable if they allow it to keep going out to one billion orbits.
We called the model SPOCK—Stability of Planetary Orbital Configurations Klassifier—partly because the model determines whether systems will ‘live long and prosper.
Daniel Tamayo, NASA Hubble Fellowship Program Sagan Fellow, Department of Astrophysical Sciences, Princeton University
The SPOCK model establishes the long-term stability of planetary configurations approximately 100,000 times faster when compared to the earlier method, overcoming the computational bottleneck.
Tamayo, however, warned that while he and his collaborator are yet to “solve” the general issue of planetary stability, the SPOCK model indeed detects the rapid instabilities in compact systems in a reliable manner, and according to the researchers, such systems are the most significant in attempting to do stability limited characterization.
“This new method will provide a clearer window into the orbital architectures of planetary systems beyond our own,” added Tamayo.
But How Many Planetary Systems are There? Is the Solar System the Only One?
Over the past 25 years, astronomers have detected over 4000 planets circling other stars, of which nearly 50% is in multi-planet systems. However, since small exoplanets are quite difficult to identify, their orbital configurations still do not give a complete picture.
More than 700 stars are now known to have two or more planets orbiting around them. Dan and his colleagues have found a fundamentally new way to explore the dynamics of these multi-planet systems, speeding up the computer time needed to make models by factors of 100,000. With this, we can hope to understand in detail the full range of solar system architectures that nature allows.
Michael Strauss, Professor and Chair, Department of Astrophysical Sciences, Princeton University
The SPOCK model is particularly helpful for deciphering some of the feeble, distantly located planetary systems that were recently detected by the Kepler telescope, stated Jessie Christiansen, an astrophysicist with the NASA Exoplanet Archive. Christiansen was not part of this study.
“It’s hard to constrain their properties with our current instruments,” Christiansen added. “Are they rocky planets, ice giants, or gas giants? Or something new? This new tool will allow us to rule out potential planet compositions and configurations that would be dynamically unstable—and it lets us do it more precisely and on a substantially larger scale than was previously available.”
The study titled “Predicting the long-term stability of compact multi-planet systems” was penned 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.
Tamayo’s study was funded by the NASA Hubble Fellowship (grant HST-HF2-51423.001-A) awarded by the Space Telescope Science Institute.