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A Cosmic Waltz

By Ria Srivastava

An artist's rendering of six planets orbiting Sun-like star Kepler-11.


Over the past three decades, astronomers have detected hundreds of stars with multiple planets orbiting them scattered in our galaxy. Each one of them is unique. However, the system orbiting the star HD 158259, 88 light years away in the Draco constellation, is truly exceptional.

The star is about the same mass and a bit larger than the sun and is orbited by six planets, a super-Earth, and five mini-Neptunes. After seven years of monitoring, astronomers have discovered that all six planets are in almost perfect orbital resonance. This discovery could help us to better understand the mechanisms of planetary system formation, and how they end up in the configurations we see.

Planets in Rhythm

Orbital resonance is when two orbiting bodies around a parent body exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. In our own solar system, orbital resonance is found mainly among the moons of Jupiter and Saturn, as well as between Pluto and Neptune. These two bodies are in what is described as a 2:3 orbital resonance. For every two laps Pluto makes around the Sun, Neptune makes three.

But each planet orbiting HD 158259 is in an almost 3:2 resonance with the next planet away from the star, which means that as the first planet – the one closest to the star – completes three orbits, the second one completes about two. As this second planet completes three orbits, the third completes about two, and so on.

Using measurements taken using the SOPHIE spectrograph and the TESS space telescope, an international team of researchers from the University of Geneva (UNIGE), led by Nathan Hara, were able to precisely calculate the orbits of each planet.

Starting closest to the star - the super-Earth, revealed by TESS to be around twice the mass of Earth - the orbits are 2.17, 3.4, 5.2, 7.9, 12, and 17.4 days. These produce period ratios of 1.57, 1.51, 1.53, 1.51, and 1.44 between each pair of planets. That's not quite perfect resonance, but close enough, which is what makes the system so special.

CAPTION: In the planetary system HD 158259, all pairs of subsequent planets are close to the 3:2 resonance: the inner one completes about three orbits as the outer completes two.

History of the system

The fact that the planets “almost” complete an orbit as their leading neighbour completes its own orbit hints that the planets which are now slightly out of synchronisation were once in perfect resonance. The breaking of the resonance could have been caused by the planets moving away from synchronicity in unison.

“Several compact systems with several planets in or close to resonances are known, such as TRAPPIST-1 or Kepler-80, and are believed to form far from the star before migrating towards it”, explained astronomer Stephane Udry of the UNIGE.

It is believed that these resonances result when planetary embryos in the protoplanetary disc (a disc, which revolves around a newly formed star), grow and migrate inward to form a resonant chain throughout the system, anchored at the inner edge of the disc. Once the gas dissipates, these resonant chains may become dynamically unstable, which could be the current state of the HD 158259 system.


“With these values on the one hand, and tidal effect models on the other hand, we could constrain the internal structure of the planets in a future study.” said astronomer Nathan Hara. There is something so very magical and beautiful about imagining these planets locked in a rhythmic waltz in a cosmic ballroom.



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