Where harmony is at work

In February, astronomers announced the discovery of a nearby star with seven Earth-size planets, and at least some of the planets seemed to be in a zone that could provide cosy conditions for life. The finding of these planets circling the star Trappist-1 40 light-years away came with a bit of mystery. The orbits of the planets are packed tightly, and computer calculations by the discoverers suggested that the gravitational jostling would send the planets colliding with each other or flying apart, some to deep space, others spiraling into the star and destruction.

Now new research provides an explanation for the dynamics of how this planetary system could have formed and remained in stable harmony over billions of years. “It’s actually a very special system,” said Daniel Tamayo, a postdoctoral researcher at the University of Toronto Scarborough, Canada and the lead author of a paper appearing in Astrophysical Journal Letters.

The scientist in the office next door to Daniel found musical inspiration from the Trappist-1 planets. Matt Russo, an
astrophysicist who is also a musician, turned to Daniel’s computer simulations for help turning the orbits into notes, and they have produced a sort of music of the spheres for the 21st century. “I think Trappist is the most musical system we’ll ever discover,” Matt said. “I hope I’m wrong.”


Vastly different

While the planets are roughly the size of Earth, the Trappist-1 system is very different from our solar system. Trappist-1 is a dwarf star that is much smaller and colder than our sun, and all seven of the planets orbit within six million miles of the star. By contrast, Mercury, the innermost planet of our solar system, is 36 million miles from our sun. Earth is nearly 93 million miles away.

Since the Trappist-1 planets are so close to their star, they orbit quickly, and their ‘year’ — the time to complete one orbit — ranges between 1.5 days and 19 days. The original discoverers noted that those orbits were almost exactly in what scientists call ‘resonance’. That is, the second planet completes five orbits in almost exactly the time the first planet makes eight. The third planet completes three orbits for every five orbits of the second planet, and the fourth planet makes two orbits for every three orbits of the third. The other planets are also in resonance.

Yet when they plugged the data into computer simulations, the orbits quickly became unstable, falling apart in less than a million years. Even when they added the effects of tides on the planets, which tend to push planets toward more circular, stable orbits, the system still often fell apart within a few million years, a cosmic instant compared with the estimated age of the Trappist-1 star (3 billion to 8 billion years). “We were missing some physics,” said Amaury HMJ Triaud, an astronomer at the University of Cambridge in England and a member of the team that described the Trappist-1 planets. Also missing: exact information about the shape and tilt of the orbits.


Simulating their paths

Daniel and his colleagues took a different approach. Instead of just looking at the orbits of the planets, they looked at possible ways that the planets got to where they are now. The planets formed out of a disk of gas and dust. After that formation, the remaining disk would have nudged the planets inward, and those nudges tend to push the planets towards the stable resonances.

Daniel offered the analogy of musicians in an orchestra. “It’s not enough for members to merely keep time,” he said. The missing information about orbits is like musicians playing out of tune, he said. “By contrast,” Daniel said, “simulating the formation of the system in its birth disk is analogous to the orchestra tuning itself before playing. When we create these harmonised systems, we find that the majority survive for as long as we can run our supercomputer simulations.”
In more than 300 computer runs, each simulating five million years, the vast majority stayed stable, Daniel said. Then they ran 21 simulations each tracing about 50 million years of orbits, and 17 of those were stable. Each of the longer simulations consumed a week of supercomputer time. That suggests the orbits are stable for several billion years, although it does not provide definitive proof.

The resonant orbits also inspired Matt, who is not only an astrophysicist, but also a guitarist in the indie pop group Rvnners. He and a bandmate, Andrew Santaguida, started playing around with the data. They arbitrarily assigned a particular musical note to the outermost planet. That set the notes for the other planets based on their relative orbital periods, although they are not exactly in tune.

In the musical animation, each planet plays its note each time it passes in front of the Trappist-1 star, with the orbit of the outer planet set at two seconds. In addition, they assigned a specific percussion sound for each time a planet caught up with its neighbour. “It turned out to be very similar to a very natural drum progression,” Matt said. So far, Trappist-1 is the only musically enchanting planetary system in the galaxy. In no other system are the planetary orbits stacked in resonance.