What an exceptional system the one around HD 158259 is! Here we have six planets, uncovered with the SOPHIE spectrograph at the Haute-Provence Observatory in the south of France, with the innermost world also confirmed through space-based TESS observations. Multiple things jump out about this system. For one thing, all six planets are close to, but not quite in, a 3:2 resonance. That ‘close to’ tells the tale, for researchers believe there are clues to the formation history of the system within their observations of this resonance.

Image: 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. Credit & Copyright: UNIGE/NASA.

The primary, HD 158259, is itself interesting, in that it’s a G-class star about 88 light years out, an object just a little more massive than our Sun. But tucked well within the distance of Mercury from the Sun we find all six of the thus far discovered planets. In fact, the outermost planet orbits at a distance 2.6 times smaller than Mercury’s, making this a compact arrangement indeed. Five of the planets are considered ‘mini-Neptunes’, while the sixth is a ‘super-Earth.’

The innermost world masses about twice the mass of Earth, while the five outer planets weigh in at about six times Earth’s mass each. The 3:2 resonance detected here runs through the entire set of planets, so that as the planet closest to the star completes three orbits, the next one out completes two, or close to it (remember, this is an ‘almost resonant’ situation). And so on — the second planet completes three orbits while the third completes about two.

Nathan Hara (University of Geneva), who led the study, likens the resonance to music, saying “This is comparable to several musicians beating distinct rhythms, yet who beat at the same time at the beginning of each bar.” The researchers involved (who used, by the way, the same telescope deployed by Michel Mayor and Didier Queloz in their ground-breaking detection of 51 Pegasi b in 1995, though with added help from SOPHIE) believe that the ‘almost resonances’ here suggest that what had been a tight resonance was disrupted by synchronous migration.

In other words, the six planets would have formed further out from the star and then moved inward together. As Hara puts it:

“Here, ‘about’ is important. Besides the ubiquity of the 3:2 period ratio, this constitutes the originality of the system. Furthermore, the current departure of the period ratios from 3:2 contains a wealth of information. 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. In summary, the current state of the system gives us a window on its formation.”

And here’s how the paper deals with the issue;

…period ratios so close to 3:2 are very unlikely to stem from pure randomness. It is therefore probable that the planets underwent migration in the protoplanetary disk, during which each consecutive pair of planets was locked in 3:2 MMR [mean-motion orbital resonance]. The observed departure of the ratio of periods of two subsequent planets from exact commensurability might be explained by tidal dissipation, as was already proposed for similar Kepler systems (e.g., Delisle & Laskar 2014). Stellar and planet mass changes have also been suggested as a possible cause of resonance breaking (Matsumoto & Ogihara 2020). The reasons behind the absence of three-body resonances, which are seen in other resembling systems (e.g., Kepler-80, MacDonald et al. 2016), are to be explored.

It’s interesting that while other systems with compact planets in near-resonance conditions have been detected (TRAPPIST-1 is the outstanding example, I suppose, but as we see above, Kepler-80 also fits the bill), this is the first to have been found through radial velocity methods. According to the authors, the method demands a high number of data points and accurate accounting of possible instrumental or stellar noise in the signal. In this work, 290 radial velocity measurements were taken, and supplemented by the TESS transit data on the inner planet.

Compact systems with multiple planets on close orbits do not appear only among M-dwarfs like HD 158259. Kepler-223, for example, is a G-class star with four known planets. Here the orbital periods are 7, 10, 15 and 20 days respectively. The Dispersed Matter Planet Project (DMPP) has turned up data on an F-class star (HD 38677) with four massive planets with orbital periods ranging from 2.9 to 19 days. The ancient Kepler-444 is a K-class star with five evidently rocky worlds orbiting the star in less than ten days.

Rather than the size of the star, at least one recent paper argues that metallicity is a key factor in producing compact systems (Brewer et al., (2018) “Compact multi-planet systems are more common around metal-poor hosts,” Astrophys J 867:L3). Clearly we have much to learn about planet formation and migration in compact systems. Such systems are near or below the current detection limits of radial velocity surveys — this is where the work on HD 158259 truly stands out — but they are good targets for transit studies. It will be instructive to see what TESS comes up with as it continues its work.

The paper is Hara et al., “The SOPHIE search for northern extrasolar planets. XVI. HD 158259: A compact planetary system in a near-3:2 mean motion resonance chain,” Astronomy & Astrophysics Vol. 636, L6 (April 2020). Abstract / preprint.