The scientist in the office next door to Dr. Tamayo found musical inspiration from the Trappist-1 planets. Matt Russo, an astrophysicist who is also a musician, turned to Dr. Tamayo’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,” Dr. Russo said. “I hope I’m wrong.”
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 from 1.5 days to 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. (In our solar system, Pluto is in resonance with Neptune, with Pluto making two orbits for every three of Neptune.)
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 (three billion to eight billion years).
“We were missing some physics,” said Amaury H.M.J. 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.
Dr. Tamayo and his colleagues took a different approach.
Instead of just looking at the orbits of the planets today, 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 toward the stable resonances.
Dr. Tamayo 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,” Dr. Tamayo said, “simulating the formation of the system in its birth disk is analogous to the orchestra tuning itself before playing. When we create these harmonized 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, Dr. Tamayo 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.
“That’s basically as long as we can hope to run our simulations,” Dr. Tamayo said.
Jack J. Lissauer, a planetary scientist at the NASA Ames Research Center who works on the space agency’s Kepler planet-finding mission, said the new results fit what was expected. “If the planets are indeed locked in resonances, it’s quite reasonable for them to be stable for very long times,” he said. “This wasn’t a surprise, but it wasn’t shown previously.”
Dr. Triaud said the new results could help refine their observations. “It’s a really beautiful analysis,” he said of Dr. Tamayo’s approach. “We will be looking at our data to see if they match what they propose.”
The resonant orbits also inspired Dr. Russo, 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 — C — 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.
The resonances drift over time, probably because of more complicated gravitational interactions and tidal effects.
“You can tell something is a bit twisted,” Dr. Russo said. “The notes are little wonky.”
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 neighbor. “It turned out to be very similar to a very natural drum progression,” Dr. Russo 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. Dr. Russo did a similar musical treatment of Kepler 90, another star with seven planets. “It’s just horrendous,” Dr. Russo said. “It’s very uncomfortable to listen to.”
That may turn out to indicate something different about how planets form around dwarf stars versus larger stars.
The scientists are releasing the computer software for anyone to explore the music of planetary orbits.