The 3-Body Problem Just Got an Upgrade—and You Can Thank Einstein


I have never met a physicist who did not believe in the beauty of the general theory of relativity—said Einstein describing gravity as the curvature of spacetime. After all, it has consistently strengthened a lot of breakthroughs, especially in astrophysics. So when certain cosmic phenomena puzzle scientists, it feels right for them to rely on general relativity to find some answers.

One such mystery, described in a recent paper on The Astrophysical Journal Lettersin relation to circumbinary exoplanets—or rather, the lack thereof—of the current 6,000+ exoplanets confirmed to date. Like the planet Tatooine from the original Star Warscircumbinary exoplanets that orbit a pair of stars, as opposed to one.

Star Wars Tatooine
A still from the original 1977 Star Wars film, featuring a young Luke Skywalker observing a double sunset from the planet Tatooine. Source: Lucasfilm Ltd.

According to the new study, the scarcity of such planets around close binaries (i.e., two stars close to each other) can be partly explained by the effects of general relativity on three-body interaction between the two stars and the planet. The complex gravitational profile will eventually result in the planet’s death or orbital expulsion, according to new research.

In search of a double sunset

Artist's Concept of Kepler 16b
An artist’s concept of Kepler-16b, one of the few exoplanets known to orbit a binary star system. Source: NASA/JPL-Caltech

As such, astronomers believe that binary stars are not necessarily worse than single stars when it comes to forming massive exoplanets; roughly 10% of solitary stars are known to host them. Holding planets, however, can be a different story, as whatever is formed does not always remain stable in the long term. New research is beginning to ask why this is the case and what forces might dislodge—or destroy—those planets over time.

During its run, Kepler observed nearly 3,000 binary star systems. But out of 3,000, astronomers have found only 47 circumbinary planet candidates through transit methodof which only 14 are actually confirmed to exist.

“You have a lack of circumbinary planets in general, and you have a complete desert around binaries with orbital periods of seven days or less,” Mohammad Farhat, the lead author of the study and a postdoctoral researcher at the University of California, Berkeley, said in a statement.

Fly very close to the stars

With his collaborator Jihad Touma, a physicist at the American University of Beirut in Lebanon, Farhat turned to the Old Reliable: general relativity. New research seeks to determine whether the apparent scarcity of exoplanets around binary systems is a product of technological shortcomings or something else, such as the effect of powerful orbital impacts that dislodge planet-like objects over time.

For the study, the researchers performed a mathematical analysis to examine the consequences of the relativistic force around the binary system. As expected, general relativity provides some interesting answers. Specifically, the researchers studied how general relativity affects the orbits of tight binary systems to gradually shift their orientation and change the long-term gravitational environment.

In a binary system, the stars oscillate closer together for tens of millions of years, and their orbital parameters gradually shift and shrink. When a planet—or even the tiniest of planetesimals—enters the mix, its orbit stretches into a thin oval, making its closest and farthest distances from the star even worse.

Binary Star System Orbit Infographic
A step-by-step explanation for why planets orbiting a binary star eventually enter an unstable orbit and disappear from the system. Source: Mohammad Farhat / UC Berkeley

“And along the way, an instability zone was encountered around the binaries, where the three-body effects started in place and gravity removed the zone,” Touma explained.

This could mean one of two things: either the planet flies too close to the stars and becomes smashed by the stars, or the planet flies too far and exits the system entirely, Farhat said. “In both cases, you get the planet.”

Missing or fake?

Again, our detection methods for exoplanets may be inadequate. But assuming the undiscovered looks of Tatooine do exist, the latest analysis sheds some light on why it’s so painful to find. Those 14 circumbinary exoplanets we know of? Truly lucky finds.

On a different note, Farhat and Touma are now wondering if the same approach could shed light on how the relativistic effect influences other unexplained, extreme cosmic phenomena. For example, perhaps the same principle can explain the behavior of stars around binary supermassive black holes or pulsars, they say.



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