The ancient notion of the ‘music of the spheres’ sounds primitive until you learn something about planetary dynamics. Gravity is wondrous and can nudge planets in a given system into orbits that show an obvious mathematical ratio. Two planets in resonance can emerge, for instance, in a 2:1 ratio, where one goes around its star twice in the time it takes the second to orbit it once. Such linkages might seem almost coincidental to the casual observer until the coincidences begin to pile up.
In the exoplanet system at HD 110067, for example, resonance flourishes, so much so that we have six planets moving in a ‘resonance chain.’ No coincidence here, just gravity at work, although an actual coincidence is that just when I finished a post highlighting system dynamics in closely packed environments like TRAPPIST-1 as a ‘brake’ on inbound comets, an international team should reveal HD 110067’s resonance chain. It’s a beauty, for all six planets not only move in harmonic rhythm but also turn out to be transiting worlds. An orbital dance this complex is rare, but even more so is the ability to study such worlds thanks to the happenstance of our viewing angle.
Transits allow us to extract information, and plenty of it, including analysis of planetary atmospheres as light from the central star passes through them. Because complex resonances are in some sense ‘self-correcting,’ they tell us something about the history of the system, for planet migration during the period when the resonance is being established influences the final state of the system. In HD 110067 we have a mother lode of system harmonics around a star that, usefully enough, is fifty times brighter than TRAPPIST-1, where we have seven rocky planets in a resonant chain.
HD 110067 offers up all of this for that highly interesting category of planets called ‘sub-Neptunes,’ about which we’d like to know a lot more. 100 light years away in the constellation Coma Berenices, HD 110067’s resonance chain is obviously complex. The innermost planet makes three orbital revolutions as the second world makes two – a 3:2 resonance. But the chain continues: 3:2, 3:2, 3:2, 4:3, and 4:3, with the innermost planet making six orbits as the outermost planet completes one.
Image: A rare family of six exoplanets has been unlocked with the help of ESA’s Cheops mission. The planets in this family are all smaller than Neptune and revolve around their star HD110067 in a very precise waltz. When the closest planet to the star makes three full revolutions around it, the second one makes exactly two during the same time. This is called a 3:2 resonance. The six planets form a resonant chain in pairs of 3:2, 3:2, 3:2, 4:3, and 4:3, resulting in the closest planet completing six orbits while the outermost planet does one. CHEOPS confirmed the orbital period of the third planet in the system, which was the key to unlocking the rhythm of the entire system. This is the second planetary system in orbital resonance that CHEOPS has helped reveal. The first one is called TOI-178. Credit and copyright: ESA.
Untangling this particular chain was not easy. The astronomers used data from both ESA’s CHEOPS mission and the TESS space observatory to nail down the system architecture. Data from TESS determined the orbital periods of the innermost worlds to be 9 and 14 days. Observations from CHEOPS tagged planet d at 20.5 days and thus demonstrated that while the innermost planet revolves 9 times around the star, the second revolves six, and the third planet four times. The periods of the three outer planets could then be deduced as 31, 41 and 55 days respectively, with further analysis of the TESS data showing that no solution other than the 3:2, 3:2, 3:2, 4:3, 4:3 chain would work. Ground-based observations supplemented the TESS and CHEOPS data.
The analysis was led by Rafael Luque (University of Chicago) and published in Nature. Says Luque:
“This discovery is going to become a benchmark system to study how sub-Neptunes, the most common type of planets outside of the solar system, form, evolve, what are they made of, and if they possess the right conditions to support the existence of liquid water in their surfaces.”
TOI-178 offers a five-planet resonance chain that may include a sixth world in this system of transiting planets in the constellation Sculptor, some 200 light years out. The paper on HD 110067 takes note of the fact that resonant architectures like these imply a situation that has remained unchanged since the birth of the system, making them useful laboratories for planet formation and evolution. The planetary radii at HD 110067 range from 1.94 that of Earth to 2.85 times as large (1.94R⊕ to 2.85R⊕), and the low densities found in the three planets whose mass has been measured point to the likelihood of large atmospheres dominated by hydrogen.
Image: Tracing a link between two neighbor planets at regular time intervals along their orbits creates a pattern unique to each couple. The six planets of the HD110067 system create together a mesmerizing geometric pattern due to their resonance-chain. © CC BY-NC-SA 4.0, Thibaut Roger/NCCR PlanetS.
Ann Egger (a graduate student at the University of Bern and a co-author of the paper on this work) notes what is ahead in the study of this system:
“The sub-Neptune planets of the HD110067 system appear to have low masses, suggesting they may be gas- or water-rich. Future observations, for example with the James Webb Space Telescope (JWST), of these planetary atmospheres could determine whether the planets have rocky or water-rich interior structures.”
The sheer beauty of the HD 110067 system comes across in the animation below:
Image: To-scale animation of the orbits of the six resonant planets in the HD110067 system. The pitch of the notes played when each planet transits matches the resonant change in orbital frequencies between each subsequent planet. The relative sizes of the planets is accurate, although their true size compared to the star is much smaller. Also available at https://www.youtube.com/watch?v=2rrODAG7nmI.
The paper is Luque et al., “A resonant sextuplet of sub-Neptunes transiting the bright star HD 110067,” Nature 623 (November 29, 2023), 932-937 (abstract).