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HD 158259: 6 Planets, Slightly Off-Tune

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.

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{ 18 comments… add one }
  • Enzo April 23, 2020, 18:22

    I just wanted to mention that there’s an article on Scientific American about Proxima C already being imaged :
    https://www.scientificamerican.com/article/astronomers-may-have-captured-the-first-ever-image-of-nearby-exoplanet-proxima-c1/

    The paper referred to in the article is here :
    https://arxiv.org/abs/2004.06685

    • Paul Gilster April 23, 2020, 20:15

      More on Proxima c in tomorrow’s post, which I’m finishing up now.

      • Enzo April 23, 2020, 23:00

        Sorry Paul, I thought it was impossible that you had missed it but it wasn’t particularly new, so I thought I’d mention it.
        Funny world : Proxima C maybe appears while Fomalhaut b disappears !

        • Paul Gilster April 24, 2020, 6:50

          Agreed! Never a dull moment in exoplanet science.

  • Bruce D Mayfield April 23, 2020, 18:42

    Ever since all these multiple planet, tight orbit systems started being discovered I’ve wondered if there might even be numerous additional planets in these systems orbiting out beyond what we’ve been able to detect to date. In the present case, sunlike HD 158259 packs 6 planets well inside our Mercury’s orbit, so what might it’s total tally really be?
    Our system has 8 out to 40 AU, while this one has 6 out to, what, 0.05 AU? That leaves an awful lot of empty potential planetary space, doesn’t it?

    This makes me suspect that the average system contains more, and maybe way more than our measly 8 or 9 planets.

    • Dave Moore April 24, 2020, 15:36

      I was taking a look at the paper and they indicate that they have a pretty good indication that there is a 40 earth-mass planet in a 366 day orbit (about 1 au). There’s also a steady signal for a 80 earth-mass planet at about 5 au (1920 day orbit). And further candidates at 34.5 day and 640 day orbits. So I would say that, assuming another couple of Neptunian giants in the outer system that this system could easily have a dozen planets. And from looking at the gaps between the candidates, I could fit another 3 planets in the system bringing the total to 15.

      • Bruce D Mayfield April 24, 2020, 20:49

        Excellent! Large moons of that planet out at 1 AU could be very interesting.

  • Thomas Mazanec April 23, 2020, 21:45

    Gonna add DMPP to your list?

    • Paul Gilster April 24, 2020, 6:59

      Done.

  • Pranay Patankar April 24, 2020, 4:01

    I think its M type star. However in first it is designated as G type star little more massive than our Sun.

  • James Jason Wentworth April 24, 2020, 6:30

    This reminds me of something. There long was–and still is, to lesser extent today–speculation about the significance, if any, of the Titius-Bode law (also known as Bode’s law: https://en.wikipedia.org/wiki/Titius%E2%80%93Bode_law ). As with the Yagi antenna (which was named for this Japanese physicist because he first published about it in English; it is now called the Yagi-Uda antenna because Dr. Uda actually invented it, although Dr. Yagi contributed to his work), both Titius and Bode developed the “law.”

    Many if not most astronomers think there is nothing to it, but others are not so sure, particularly since many exoplanetary systems have their own Titius-Bode formulae which also predict the spacings of their planets. It could be that the Titius-Bode formulae, like the tip of an iceberg (most of which is submerged), is the uppermost portion of something whose lower depths we can’t understand yet. Also–in connection with the almost-but-not-quite 3:2 orbital resonances:

    Could the differences in mass between the planets perhaps be a factor in this? Using antennas as an example again (organ pipes can also illustrate the following):

    A narrow, Marconi-type wire antenna cut to a quarter-wavelength in length for, say, 1000 kHz (and “worked against” a radio frequency–RF–ground [or alternatively, a dipole antenna consisting of two quarter-wavelength–for 1000 kHz–wire “legs,” resulting in a total dipole length of a half-wavelength, that are “worked against” each other]) will resonate at 1000 kHz, but its bandwidth (the frequency range below and above 1000 kHz at which it will resonate naturally) will be narrow, but:

    In contrast, a quarter-wavelength Marconi antenna–or a half-wavelength dipole antenna–cut to the same lengths, but made of wider conductors (say, 1/2-inch diameter copper pipe, instead of very thin, 26 AWG [American Wire Gauge] “stealth” antenna wire), will have a wider bandwidth. The same is the case for two organ pipes of the same length, but with one being significantly wider than the other one, and:

    With such nearly-resonant (but not quite–having an almost 3:2 orbital resonance, for example) planets, could a wider “mass spread” among them (where the more–or most–massive planet is four or five times as massive as the lesser–or least–massive one) maybe cause an effect like that of a thicker, higher-bandwidth (“surrounding” its length-determined self-resonant frequency) antenna or an organ pipe?

  • Michael Fidler April 24, 2020, 10:57

    There is a lot of ways these planets could of become this close besides migration.
    Warning: Anyone with a closed mind please read no further, it may cause seizures.
    1. Red dwarf in orbit around the G0 star is absorbed by it.
    2. White dwarf in orbit around Go star is ejected from system after exploding leaving its planets behind.
    3. Planets are ejected from stars. (CME)
    4. Planets are ejected from large Jupiter like planets. (what do think the GRS is from)
    5. Go star may show reading of metal-poor hosts because it just ejected planets.

    It will be interesting to see the data from TESS on the earth like planet, will it be large or small? ;-}

  • Mike Serfas April 24, 2020, 14:22

    Are these planets out of tune, or are they “well-tempered”? (Well, alright, I am not aware of any 2:1 resonance to form this octave, nor do they all really have the same numerical ratio, but I’d prefer to hear the music before I cast aspersions on the composer) If only the dark side of one of these worlds were to be habitable, the precedent of http://astrobiology.com/2019/05/the-chaotic-nature-of-trappist-1-planetary-spin-states.html makes me think that whatever dwells there must live and perish according to the musical whimsy of the spheres.

    • Paul Gilster April 24, 2020, 20:28

      ‘Well tempered.’ Well said!

    • andy April 26, 2020, 7:40

      The ratio between b and g is about 3604 cents, which is pretty close to 3 octaves (3600 cents). I had a go at making some music with a microtonal scale based on the orbital periods. I used the periods as-is so this is a non-octave tuning (going up an “octave” increases the pitch by 3604 cents). Here’s the result.

      Another possibility for creating a scale would be to fold the pitches into the near-octave defined by dividing the ratio between b and g by three. This would be somewhat less awkward to work with (I managed to crash the output program in the middle of this because the default “octave” value would result in ultrasound!)

      • Mike Serfas April 28, 2020, 16:00

        What an astounding response! It is as if someone landed a jet plane on my little Cargo Cult airstrip. I had never heard of https://foxdot.org/ and I should try to understand more about how this works; is one of your other videos more tutorial? For example, I don’t understand how the low peaks relate to the series of lines which I assume are the planetary tones.

        I hadn’t noticed that 17.39/2.177 = 7.988. Is there any way that planets so far apart could have influenced one another to form an 8:1 resonance, perhaps based on less-spherical shape?? If that were the case the system would quite literally be a “temperament”, created by nature, yet one that due to the multiple octaves perhaps (I certainly don’t know) centuries of musicians have overlooked.

        • andy April 30, 2020, 16:18

          So far I haven’t done any tutorials for FoxDot, but there is a channel which I found quite useful starting out. It was also useful to see the videos Ryan Kirkbride (creator of FoxDot) made on his channel, although certain features have changed over the course of updates. The best way to learn is to play around with it and see what happens!

          The only thing related to the planetary system in my video is the scale for the notes (the code visible right at the start, which I’d executed immediately before I started recording). I didn’t try to reflect anything else as I’m fairly wary about “sonification”: here’s a pretty amusing takedown of such things. But I was pleasantly surprised at how reasonable the scale ended up being, was expecting it to sound a lot more out-of-tune!

          • Mike Serfas May 1, 2020, 9:57

            I don’t know much about music at all, but my reading took me to http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html and http://www.bikexprt.com/tunings/fibonaci.htm … if I understand this right, then the three-octave series could be collapsed (by dividing the pitches by 2 as needed) to a series of five notes per octave. Notice a lot of “temperament” is needed to make this happen because (3/2)^5 is 0.95, versus 1.01 if you take the twelfth power. The second source points out that this scale exists – with some pushing around of the notes – as the black keys of a piano. I think essentially you’re taking 16 of those keys, changing the tuning a bit, and then the planets are 0, 3, 6, 9, 12, and 15, where 0 and 15 are about an 8:1 ratio so count as the same pitch. (The second link will reward the persistent reader with a link to the messiah of all the guitars)

            Whether the planets have a good musical temperament or are merely “out of tune” depends on details far beyond my comprehension, not to mention aesthetics prone to debate … follow the first author’s link to John Young’s tuning and you’ll see what I mean.

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