CHEOPS finds unique planetary system tuned in a chain of Laplace resonances

The CHEOPS space telescope detects six planets orbiting the star TOI-178. Five of the planets are trapped in an exceptional chain of Laplace resonances in the 2:4:6:9:12 ratios. This can be visualized as an harmonic rhythm despite very different compositions – a novelty. CHEOPS is a mission of the European Space Agency (ESA) with the participation of Swiss and French laboratories including IMCCE / CNRS / Paris Observatory / PSL University / Sorbonne University.

Musical notes that sound pleasant together can form a harmony. These notes are usually in a special relationship with each other: when expressed as frequencies, their ratios result in simple fractions, such as four-thirds or three-halves. Similarly, a planetary system can also form a kind of harmony when planets, whose orbital period ratios form simple fractions, regularly attract each other with their gravity. When one planet takes three days to orbit its star and its neighbor takes two days, for example. Using the CHEOPS space telescope, scientists, led by astrophysicist Adrien Leleu, former PhD student of IMCCE/Paris Observatory, now a CHEOPS postdoc fellow at Geneva Observatory, found such relationships between five of six planets orbiting the star TOI-178, located over 200 light years away from Earth. The results are published today in the Journal of Astronomy and Astrophysics.

A missing piece in an unexpected puzzle

As was noticed by J. Schneider (Luth/Paris Observatory), observations with the Transiting Exoplanet Survey Satellite (TESS) of NASA pointed toward a three planets system, with two planets orbiting with very close orbital periods, leaving the possibility of co-orbital planets. In search for these co-orbital planets since several years, A. Leleu, P. Robutel (IMCCE/Paris Observatory) and their colleagues therefore observed the system with additional instruments, such as the ground based ESPRESSO spectrograph at the European Southern Observatory (ESO)’s Paranal Observatory in Chile, but the results were inconclusive. When Leleu and his colleagues proposed to investigate the system more closely, they were therefore not sure what they would find. The high precision and target-pointing agility of CHEOPS was required to bring clarity, but that turned out to be more difficult than expected. The team did not find co-orbital planets but the results were still spectacular as there were indeed five planets present with orbital periods of around 2, 3, 6, 10 and 20 days respectively.

While a system with five planets would have been quite a remarkable finding in itself, A. Leleu and his colleagues noticed that there might be more to the story: the system appeared to be trapped in a chain of resonances. “Our theory implied that there could be an additional planet in this harmony; however its orbital period needed to be to a very specific value, near 15 days. If the period were just ten minutes longer or ten minutes shorter than the predicted value, the system would have been chaotic”, Leleu explains. To check if their theory was in fact true, the team scheduled yet another observation with CHEOPS, at the exact time that this missing planet would pass by – if it existed. As Nathan Hara, co-author and astrophysicist from the University of Geneva, and former PhD student at IMCCE, reports. “A few days later, the data clearly indicated the presence of the additional planet and thus confirmed that there are indeed six planets in the TOI-178 system”, Hara explains.

Fig. The TOI-178 6 planets system is a challenge for dynamical studies, which explains why five of the leading authors of the paper are researchers or former PhD students of IMCCE/Paris Observatory. In the above figure made on MesoPSL, the HPC computer center of PSL University, the period of planet g is plotted versus the period of planet f. The actual values are given by the white dotted line (20.71 days for planet g and 15.23 days for planet f). The white dot at the crossing of the two lines represent the state of the TOI-178 system. It is located in a tiny blue island which shows that it is perfectly stable (blue is stable, red is highly chaotic). If the period of planet f were slightly smaller or larger, the system would be in the surrounding red area and thus highly chaotic.

One of the longest chain of resonances in a planetary system

The new research has revealed that the system boasts six exoplanets and that all but the one closest to the star are locked in a chain of resonance. This means that there are patterns that repeat themselves as the planets go around the star, with some planets aligning every few orbits. A similar resonance is observed in the orbits of three of Jupiter’s moons: Io, Europa and Ganymede. Io, the closest of the three to Jupiter, completes four full orbits around Jupiter for every orbit that Ganymede, the furthest away, makes, and two full orbits for every orbit Europa makes.

The five outer exoplanets of the TOI-178 system follow a much more complex chain of resonance (, one of the longest yet discovered in a system of planets. While the three Jupiter moons are in a 4:2:1 resonance, the five outer planets in the TOI-178 system follow a 18:9:6:4:3 chain: while the second planet from the star (the first in the resonance chain) completes 18 orbits, the next planet from the star completes 9 orbits, and so on.

A system that challenges current understanding

Thanks to the precision of CHEOPS’ measurements as well as previous data from the TESS mission, the ESO’s spectrograph ESPRESSO, and others, the scientists could not only measure the periods and sizes of the planets of 1.1 to 3 times the radius of the Earth, but also estimate their densities. With that came another surprise: compared to the harmonic, orderly way the planets orbit around their star, their densities appear to be a wild mixture. In the TOI-178 system, a dense, terrestrial planet like Earth appear to be right next to a very fluffy planet with half the density of Neptune followed by one very similar to Neptune. As Adrien Leleu concludes, “the system therefore turned out to be one that challenges our understanding of the formation and evolution of planetary systems”.

Publication details

Contact at Observatoire de Paris

CHEOPS – in search of potential habitable planets

The CHEOPS mission (CHaracterising ExOPlanet Satellite) is the first of ESA’s newly created “S-class missions” – small-class missions with an ESA budget much smaller than that of large- and medium-size missions, and a shorter timespan from project inception to launch.

CHEOPS is dedicated to characterizing the transits of exoplanets. It measures the changes in the brightness of a star when a planet passes in front of that star. This measured value allows the size of the planet to be derived, and for its density to be determined on the basis of existing data. This provides important information on these planets – for example, whether they are predominantly rocky, are composed of gases, or if they have deep oceans. This, in turn, is an important step in determining whether a planet has conditions that are hospitable to life.

CHEOPS was developed as part of a partnership between the European Space Agency (ESA) and Switzerland. A consortium of more than a hundred scientists and engineers from eleven European states was involved in constructing the satellite over five years, including researchers from Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE)/Observatoire de Paris, IPGP Institut de Physique du Globe de Paris (IPGP), Laboratoire d’Astrophysique de Marseille (LAM), and Institut d’Astrophysique de Paris (IAP).

CHEOPS began its journey into space on Wednesday, December 18, 2019 on board a Soyuz Fregat rocket from the European spaceport in Kourou, French Guiana. Since then, it has been orbiting the Earth on a polar orbit in roughly an hour and a half at an altitude of 700 kilometers following the terminator.

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