Of the more than 4,500 stars known to have planets, one puzzling statistic stands out. Even though nearly all stars are expected to have planets and most stars form in pairs, planets that orbit both stars in a pair are rare.
Of the more than 6,000 extrasolar planets, or exoplanets, confirmed to date - most of them found by NASA's Kepler Space Telescope and the Transiting Exoplanet Survey Satellite (TESS) - only 14 are observed to orbit binary stars. There should be hundreds. Where are all the planets with two suns, like Tatooine in Star Wars?
Astrophysicists at the University of California, Berkeley, and the American University of Beirut have now proposed a reason for this dearth of circumbinary exoplanets - and Einstein's general theory of relativity is to blame.
In most binary star systems, the stars have similar but not identical masses and orbit one another in an egg-shaped or elliptical orbit. If a planet is orbiting the pair of stars, the gravitational tugs from the stars make the planet's orbit precess, meaning the orbital axis rotates similar to the way the axis of a spinning top rotates or precesses in Earth's gravity.
The orbit of the binary stars also precesses, but mainly because of general relativity. Over time, tidal interactions between the binary pair shrink the orbit, which has two effects: The precession rate of the stars increases, but the precession rate of the planet slows. When the two precession rates match, or resonate, the planet's orbit becomes wildly elongated, taking it farther from the star but also nearer at its closest approach.
"Two things can happen: Either the planet gets very, very close to the binary, suffering tidal disruption or being engulfed by one of the stars, or its orbit gets significantly perturbed by the binary to be eventually ejected from the system," said Mohammad Farhat, a Miller Postdoctoral Fellow at UC Berkeley and first author of the paper. "In both cases, you get rid of the planet."
Mohammad Farhat/UC Berkeley
That doesn't mean that binary stars don't have planets, he cautioned. But the only ones that survive this process are too far from the stars for us to detect with transit techniques used by Kepler and TESS.
"There are surely planets out there. It's just that they are difficult to detect with current instruments," said co-author Jihad Touma, a physics professor at the American University of Beirut.
They published their findings Dec. 8 in The Astrophysical Journal Letters.
'An absolute desert'
Both the Kepler and TESS missions searched for exoplanets by looking for a slight dimming of a star as a planet crossed in front of it. But Kepler also found about 3,000 eclipsing binary stars, as one of the pair of stars passed in front of the other. Since about 10% of single sun-like stars were found to have massive planets, astronomers expected to see large planets around about 10% of binaries also - or some 300 stars. Instead, only 47 candidate planets around binary stars were found, and only 14 have been confirmed as transiting circumbinary planets.
None of these 14 exoplanets occur around tight binaries orbiting one another in less than about seven days.
"You have a scarcity of circumbinary planets in general and you have an absolute desert around binaries with orbital periods of seven days or less," Farhat said. "The overwhelming majority of eclipsing binaries are tight binaries and are precisely the systems around which we most expect to find transiting circumbinary planets."
Farhat points out that binaries have an instability zone around them in which no planet can survive. Within that zone, the three-body interactions between the two stars and the planet either expel the planet from the system or pull it close enough to merge with or be shredded by the stars. Peculiarly, 12 of the 14 known transiting exoplanets around tight binaries are just beyond the edge of the instability zone, where they apparently migrated from farther away, since planets would have a hard time forming there.
"Planets form from the bottom up, by sticking small-scale planetesimals together. But forming a planet at the edge of the instability zone would be like trying to stick snowflakes together in a hurricane," he said.
Farhat had previously collaborated with Touma on the formation and evolution of planetary orbits in various star systems, including our own. But Touma also had an interest in the orbits of binary black holes and binary stars. He realized 10 years ago that general relativity should change how planets move around double-star systems, but he didn't know if the effect was strong enough to matter. After digging deeper into exoplanets, however, he suggested that the subtle pushes and pulls from relativity-combined with the stars slowly spiraling closer together-might explain the mystery of the missing planets around tight binaries.
Using mathematical and computer models, Farhat and Touma found that general relativity had a dramatic effect on the fates of circumbinary planets, effectively clearing out any close-in planets. Based on their calculations, general relativistic effects would disrupt eight of every 10 exoplanets around tight binaries, and of those, 75% would be destroyed in the process.
The precession of Mercury's orbit
Proposed by Albert Einstein in 1915, the general theory of relativity interprets gravity as a warping of the fabric of spacetime by a mass, analogous to how a person on a trampoline warps the surface and makes other objects on the trampoline fall inward. Mercury's orbit happens to be closest to the gravitational warp of the sun and, as a result, experiences an orbital precession slightly higher than predicted by the earlier theory of gravity laid out by Isaac Newton. The general relativistic explanation for the additional precession of Mercury's orbit more than a century ago was the first confirmation of Einstein's theory.
NASA's Goddard Space Flight Center
The same effect comes into play when any two objects get close to one another, such as tight-knit binary stars. Binary stars likely begin their lives far apart, but as they interact with surrounding gas during the formation of their star system, it's predicted that many pairs will move closer together over tens of millions of years. When they do, they generate tides in one another that slowly, over billions of years, shrink the orbit even more. Eventually, as they tighten to periods of around a week or less, general-relativistic precession becomes increasingly important. This makes the orbit precess, which means that the point of closest approach, or periastron, also rotates. As the stars get closer and closer, the rate of precession increases.
A circumbinary exoplanet also sees its elliptical axis precess, in this case because of the gravitational tug of the two stars - a strictly Newtonian process. However, as the binaries move closer to one another, their perturbation of the planet gradually weakens and the precession slows down.
As the orbital precession of the binary stars increases and that of the exoplanet decreases, at some point they match and enter a state of resonance. At this point, calculations show, the exoplanet's orbit starts to elongate, taking it farther from the binary at the extreme point of its orbit but closer at periastron. When periastron enters the zone of instability, the exoplanet is either exiled to the far reaches of the system or approaches too close to the binary and is engulfed. Because this disruption occurs quickly, taking a few tens of millions of years within the multibillion-year lifetime of a star, exoplanets around tight binaries end up being very rare.
"A planet caught in resonance finds its orbit deformed to higher and higher eccentricities, precessing faster and faster while staying in tune with the orbit of the binary, which is shrinking," Touma said. "And on the route, it encounters that instability zone around binaries, where three-body effects kick into place and gravitationally clear out the zone."
"Just the natural way you form these tight binaries, these sub-seven-day binaries, you get rid of the planet naturally, without invoking additional disruption from a nearby star or other mechanisms," Farhat said.
According to Touma, the same processes are likely to sweep multiple planets out of binary systems - especially those detectable by Kepler or TESS.
The researchers are employing their models to determine how general relativistic effects impact clusters of stars around pairs of supermassive black holes, and whether, in a more speculative vein, general relativity can partially explain the dearth of planets around binary pulsars - two spinning neutron stars in orbit around one another and emitting precisely timed radio pulses. This work illustrates the major role played by Einstein's revolutionary theory of gravity even in simple systems where Newton's gravitational laws were thought to explain everything.
"Interestingly enough, nearly a century following Einstein's calculations, computer simulations showed how relativistic effects may have saved Mercury from chaotic diffusion out of the solar system. Here we see related effects at work disrupting planetary systems," Touma said. "General relativity is stabilizing systems in some ways and disturbing them in other ways."
Farhat is supported by the Miller Institute for Basic Research in Science at UC Berkeley.
