Among the more than 4,500 known planetary host stars, one surprising pattern stands out. Planets are expected to form around most stars, and many stars exist in pairs, but worlds orbiting both stars are extremely rare.
Of the more than 6,000 exoplanets, or exoplanets, discovered to date (mostly by NASA’s Kepler Space Telescope and the Transiting Exoplanet Survey Satellite (TESS)), only 14 have been confirmed to orbit binary stars. Astronomers believed there must be several hundred, based on their predictions. So where is the real-life version of Tatooine from Star Wars?
Researchers at the University of California, Berkeley and the American University of Beirut now suggest an answer, and they point to Einstein’s theory of general relativity.
How gravity shapes the orbits of binary star systems
In a typical binary star system, two stars of slightly different masses orbit each other in elongated, or elliptical, orbits. A planet orbiting both stars experiences competing gravitational forces, causing it to slowly rotate, or precess, in its orbit, like a teetering top under gravity.
The stars themselves also precess, but for different reasons. Their motion is influenced by general relativity. Over time, tidal forces between the two stars gradually bring them closer together. As the orbit shrinks, the precession of the stars speeds up, but the precession of the planets slows down.
Eventually, these two speeds may coincide in a condition scientists call resonance. When this happens, the planet’s orbit becomes stretched and unstable. At some points it swings farther, at other points it dives even closer.
“Two things can happen: Either the planet gets very close to the binary star and gets engulfed by a tidal disturbance or one of the stars, or its orbit is so disturbed by the binary star that it ends up being ejected from the system,” said Mohammad Farhat, a Miller postdoctoral fellow at the University of California, Berkeley and lead author of the paper. “In either case, you’re removing the earth.”
This does not mean that the binary star is completely devoid of planets. Those that remain tend to orbit much further away and are difficult to detect with the current-passing methods used by Kepler and TESS.
“Planets do exist, they just are difficult to detect with current equipment,” said co-author Jihad Touma, a physics professor at the American University of Beirut.
The team reported the results as follows: Astrophysics Journal Letter.
A planetary “desert” surrounding a dense binary star
Both Kepler and TESS detect planets by measuring small dips in starlight as they pass in front of their stars. Kepler also identified about 3,000 eclipsing binary star systems in which one star periodically passes in front of another.
About 10% of Sun-like stars have large planets, so scientists expected a similar proportion, around 300 systems, around binary stars. Instead, only 47 candidates have been discovered, and only 14 have been confirmed as planets orbiting both stars.
Remarkably, none of these confirmed planets orbit very close binary stars that complete their orbits in less than about seven days.
“Orbiting planets are generally scarce, and there are complete deserts around binary stars with orbits of seven days or less,” Farhat said. “The vast majority of eclipsing binaries are dense binaries, and these are the systems in which we would most expect to find circumbinary stars passing around them.”
Binary star systems also contain what scientists call regions of instability, where the planets’ orbits cannot remain stable. In this zone, the combined gravitational influence of the two stars either knocks the planet out of the system or pulls it in until it is destroyed.
Interestingly, 12 of the 14 known circumbinary planets orbit just outside this unstable region. This suggests that they likely formed further outward and then migrated inward, as they are very difficult to form near boundaries.
“Planets form from the bottom up by sticking together small particles,” he says. “But forming a planet at the edge of an unstable zone is like trying to stick snowflakes together in a hurricane.”
Einstein’s role in cleaning up the planet
Touma had long suspected that general relativity could influence the behavior of planets in binary star systems, but it was unclear how strong that influence would be. As the binary stars slowly spiral closer together over time, relativistic effects become more important.
Using detailed mathematical calculations and computer simulations, the researchers showed that these effects could dramatically reshape planetary systems. Their results show that about 8 out of 10 planets around dense binary stars become unstable, and most of them are eventually destroyed.
The physics behind orbital precession
General relativity, proposed by Albert Einstein in 1915, explains gravity as the bending of spacetime due to mass. This is similar to how a heavy object distorts a stretched surface. One of its earliest confirmations came from Mercury’s orbit, which shifts slightly more than can be explained by Newton’s laws alone.
A similar process occurs with binary stars. These systems often begin with a distant star, but interactions with the surrounding gas gradually bring the star closer over tens of millions of years. Over billions of years, tidal forces continue to shrink their orbit.
As the star approaches, its orbital motion changes more rapidly, including the position of closest approach known as the periastron. On the other hand, planets orbiting both stars also experience precession, but in this case they are driven by classical gravity.
As the binary becomes tighter, the precession of the planets slows down and the precession of the stars speeds up. When the two velocities match, a resonance occurs and the planet’s orbit is stretched further and further.
If the closest point of its orbit enters the instability zone, the planet is either flung outward or pulled inward and destroyed. This process unfolds relatively rapidly on cosmic timescales, and this helps explain why planets around tight binaries are rarely observed.
“We find that the planets caught in the resonance deform their orbits to higher and higher eccentricities, precessing faster and faster in sync with the shrinking binary orbits,” Touma said. “And along that route, it encounters an unstable zone around the binary star, where the three-body effect occurs and gravity sweeps the zone away.”
“The natural way of forming these tight binaries, binaries of less than seven days, allows us to remove the Earth naturally without causing additional disruption from nearby stars or other mechanisms,” Farhat said.
Wider impact on the entire universe
Touma said these same processes could remove multiple planets from a binary system, especially those that were detectable by missions such as Kepler and TESS.
The researchers are now extending their model to investigate how relativity affects star clusters around supermassive black hole pairs. They are also studying whether a similar mechanism could help explain the lack of planets around binary pulsars. Binary pulsars are pairs of rapidly rotating neutron stars that emit regular radio pulses.
The results of this study highlight how Einstein’s theories shape our understanding of the universe, even in systems that were once thought to be fully explained by classical physics.
“Interestingly, almost a century after Einstein’s calculations, computer simulations have shown how relativistic effects saved Mercury from a chaotic spread outside the solar system. Here we see related effects at work that disrupt the planetary system,” Touma said. “General relativity stabilizes the system in some ways, but disturbs it in other ways.”
Farhat is supported by the Miller Institute for Basic Science at the University of California, Berkeley.
