Mean motion resonances in multiplanetary systems – new study

Posted: March 2, 2015 by oldbrew in Astrophysics
Tags: ,

Exoplanet analysis is a growing field of scientific study as data pours in from the likes of NASA’s successful Kepler probe.

The abstract of a new paper explains its focus on this data:
‘Mean motion resonances and near-resonances up to the outer/inner orbital period ratio’s value of 5 and the denominator 4 are tested for all adjacent exoplanet orbits.’

Without delving into the nuts and bolts of the analysis here, let’s look at the list of results (click on image to view details):

By Marian C. Ghilea (2015)

By Marian C. Ghilea (2015)

The column ‘resonance type’ shows the planet:planet ratios we’re interested in.
Clearly there are many examples, although ‘near resonances’ are also included.

From the author’s concluding remarks:
‘Performing a simple analysis, the resonance or near-resonance states present in all the multiplanetary systems known to date can be found numerically using a computer analysis tool.’

‘The first results, presented in this paper, suggest different resonance or near-resonance distributions for different planet categories. The resonance/near resonance numbers of 2/1 and 3/2 appear to be dominant for the planets with larger masses while the 5/3 resonance seems to be the most common for terrestrial planets and mini neptunes. For giant planets, the 2/1 resonances are dominating at larger distances from the host star while the 3/2 resonance is more common at close distances from it. Resonances for values higher than 5/2 are encountered
only for planets with masses larger than 10 (ME*)’ [*Earth masses].

We can see from this that these ‘near resonances’ crop up regularly in exoplanet systems just as they do in our solar system e.g. Jupiter-Saturn 5:2, Neptune-Pluto 3:2.

Whatever the mechanism(s) involved, the frequency of their appearance can’t be regarded as accidental.

See also the Wikipedia page on orbital resonance

  1. tallbloke says:

    Naturally, ignorant clods like Willis “I’m a cowboy” Eschenbach will write to tell these authors they are cyclomaniac astrologer-numerologists.

    As he’s such an expert on astrophysics.

  2. oldbrew says:

    A closely related paper: ‘The 2 : 1 Resonant Exoplanetary System Orbiting HD 73526’

    Abstract: ‘We report the detection of a second exoplanet orbiting the G6 V dwarf HD 73526. This second planet has an orbital period of 377 days, putting it in a 2 : 1 resonance with the previously known exoplanet, the orbital period for which is updated to 188 days. Dynamical modeling of the combined system allows solution for a self-consistent set of orbital elements for both components. HD 73526 is the fourth exoplanetary system (of a total of 18 systems with two or more components currently known) to have components detected in 2 : 1 resonance. Finding such a large fraction of multiple planets (more than 20%) in 2 : 1 resonance strongly suggests that orbital migration, halted by stabilization in a trapping resonance, plays an important role in the evolution of exoplanets in multiple planet systems.’ [bold added]

    NB this paper appeared in 2006, so a great deal more data has become available since then.

  3. oldbrew says:

    Effects of resonance – example from a NASA-funded study:

    ‘”Our interpretation is that as Jupiter and Saturn migrated, their orbital resonances swept through the asteroid belt, ejecting many more asteroids than is possible with the planets in their current orbits,” Malhotra said. “And the particular pattern of missing asteroids is characteristic of the pattern of Jupiter’s and Saturn’s migration.”

    On BBC2 TV (UK) tonight: ‘the creation of our solar system is a tale of hellfire, chaos and planetary pinball.’

  4. tallbloke says:

    I’ll be sure to watch it on catch-up TV (While it’s still free). 🙂

    Our approach to understanding solar system resonance is vindicated, and Anthony Watts and his ignorant crew are a bunch of know-nothings in this interesting area of science.

    What we need now is for instruments to get good enough to detect the activity cycle frequencies of more of these exo-planet surrounded stars. There are a couple where they think they have managed this.


    The nearly continuous activity record suggests the simultaneous operation of two stellar
    dynamos with cycle periods of 2.95 ± 0.03 years and 12.7 ± 0.3 years,

    documented activity cycles and rotation periods for dozens
    of stars (Saar & Brandenburg 1999). These observations revealed
    two distinct relationships between the activity cycle
    period and the rotation period, with an active “A” sequence including
    stars rotating more than 300 times for each activity cycle,
    and an inactive “I” sequence with stars rotating fewer than
    100 times per activity cycle.

    Some stars in the
    Mount Wilson sample exhibit two distinct cycle periods, suggesting
    that the two dynamos can operate simultaneously.
    The K2V star ǫ Eridani (ǫ Eri ≡ HD 22049, V=3.7,
    B−V=0.88) is a young solar analog with a stellar activity
    record that stretches back to 1968. The first 24 years of observations
    were published in Gray & Baliunas (1995), who
    determined a rotation period of 11.1 days and found evidence
    of a 5 year activity cycle.

    Observations of the variable radial velocity (RV) of ǫ Eri
    were first reported by Campbell et al. (1988). Early claims
    by Walker et al. (1995) of periodic variations were eventually
    corroborated by Cumming et al. (1999), who identified a period
    near 7 years. Hatzes et al. (2000) used additional RV data
    to confirm the ∼7 year period, interpreting it as the reflex motion
    from an eccentric Jovian-mass exoplanet; they ruled out
    stellar activity as the source of the variations from an analysis
    of Mount Wilson data between 1980-1999. The Ca HK observations
    revealed periodic signals near 20 years (the length of
    the data set) and 3 years, but nothing at the orbital period of
    the presumed planet. The planetary nature of the companion
    was later confirmed by Benedict et al. (2006) who measured
    the astrometric orbit using the Hubble Space Telescope, yielding
    an inclination angle i = 30.◦1 ± 3.◦2 (consistent with that
    of an observed dust ring; Greaves et al. 2005) and determining
    the absolute mass of the planet, M = 1.5 MJ. More recent RV
    measurements from the HARPS spectrograph imply that the
    properties of the planet may need to be revised, but still support
    a period near 7 years (Anglada-Escudé & Butler 2012).

    It’s a pity we don’t have better exoplanetary data for this brown dwarf.
    It’s worth noting that 2.95*Phi^3=12.495.

  5. Bruckner8 says:

    Has a single prediction been made with these “harmonic analyses?” So far, all I’ve mustered from this kind of analysis is curious pattern recognition, almost along the lines of “Intelligent Design.” We get lots of “this can’t be accidental” and “this isn’t mere coincidence” but not one single predictive mechanism. It’s all just “Isn’t this beautiful?” (It is…don’t get me wrong…but that’s not science.)

    For once, I”d like to see some real predictive measures, like “When [these ratios] align with [those ratios], and [this Phi-squared situation happens every natural log e years] we can expect another [predicted event, say Maunder Minimum].”

  6. oldbrew says:

    TB: go to and put ‘Eridani’ in name (all 3 words) in the filter box. Then click on the planet name (green text).

    Its orbit period is 2502 days +/ 10 days (about 6.85 years) but as a single planet there’s nothing to relate that to.


  7. oldbrew says:

    TB: the paper you linked to says:

    ‘The long-term behavior of the magnetic activity cycles observed in ǫ Eri qualitatively resembles the interaction of the 11 year solar cycle with the quasi-biennial (∼2 year) variations analyzed by Fletcher et al. (2010, their Fig. 1). The amplitude of the shorter (2.95 year) cycle in ǫ Eri appears to be modulated by the longer (12.7 year) cycle.’

    Eridani b orbit period = 6.85 years
    (6.85 x 3) / 12.7 (long cycle) = 1.61811
    There would be 7 x 2.95y (short cycle) in that period.

  8. Wayne Job says:

    Fear not the Willis ,Tallbloke for the harmony of the spheres will have the last laugh, astrology it is not.

  9. tallbloke says:

    Is Q Eri the same star as Eridani b? I found the paper a little confusing.

  10. tallbloke says:

    Wayne: I don’t fear Willis, though I do fear for the damage he is doing to popular science with his ignorant bullshit.

  11. oldbrew says:

    TB: yes, the paper says ‘The K2V star ǫ Eridani (ǫ Eri ≡ HD 22049, V=3.7, B−V=0.88) is a young solar analog with a stellar activity record that stretches back to 1968’
    [Eridani b is the planet]

  12. oldbrew says:

    Paper: ‘With the solar-like magnetic cycles observed in ǫ Eri, we are now in a better position to
    evaluate the specific property of the Sun that might make it peculiar in the context of other stars. Despite the fact that the Sun rotates less than half as fast as ǫ Eri, the stars each appear to have two interacting dynamos that operate on very similar timescales.’

  13. tchannon says:


    I don’t think prediction is the nature of what is being described.since it is no more than inbuilt to the natural motions. Linking motion to something quite different is a whole different game.

    There is nothing new about “cogging” effects in what is an N-Body issue. Neither do I get why some people seem to think the effect does not exist. Perhaps this is one and the same with jumping to assumptions that there is a direct link with say earth atmospheric variations.

    Perhaps we are looking at a librarian work, cataloguing and classifying.

    However, if the orbital parameters are changing in non-simple ways there are possible surprises. For instance if sun-earth distance is not as stable as assumed by a possibly simplistic assumption, there would be a causal.

    How close to unstable is the current solar system orbital state?

  14. tallbloke says:

    Bruckner8: We’ve been looking at this for two years and we’re starting to understand how the numberspace links to the physics. We’ll start publishing predictions if the ones we’re holding close to our chests pan out OK. Could be some years yet. Plenty of time for you to roll your sleeves up and do some calculating instead of carping, and you might beat us to it. 😉

    Anyway, I already successfully predicted a low solar cycle 24 and a grand minimum in back in 2008 with the barycentric motion theory allied to this resonance theory.

    No-one pays us for doing this stuff, so we have to get on with real lives as well. Why should we jump to other people’s demands? We got rubbished by ‘The most self important climate discussion website in the world ™’ and no-one reads our stuff (apart from the 18,400 PRP downloaders and 3 million Talkshop page visiters), because we’re “pariahs” whose website will “wither and die” according to Anthony Watts, so what’s the hurry?

  15. oldbrew says:

    First ever photograph of light as a particle and a wave.

  16. Wayne Job says:

    Rog, One very clever man outside the scientific circle of closed shop nonsense has a full mechanism that explains why the large planets control the solar cycle. It explains even why the earth is tilted. and many of the other curiosities. Look for his new papers page I think the paper is” what controls the solar cycle”. I do not know how to link but will get you there.

  17. Wayne Job says:

    Thanks old brew my bad, I have been waiting half a century for a real thinker to come along and poke the eye of the standard models.

  18. oldbrew says:

    Another Eridani paper says:

    ‘The analysis of the 2002-2003 MSC data by Handler et al.
    (2004) revealed a variability of µ Eri with a frequency of
    0.616 c/d
    . However, the authors were not able to decide what
    is the origin of this variation: pulsation or rotational modulation.’

  19. Asynsis says:

    Roger, I’m deeply impressed with the tenacity and rigour with which these temporal symmetries are being pursued by you and your collaborative cohort.
    Besides your “Why Phi” intuitions on the Constructal law (with which I continue to concur), I’m also seeing Universality as potentially having a role. It allows systems to be maximally connected for the least energy cost, and is analogous to universal computation behaviours in cellular automata (Wolfram Type 4 Rules 30/110 – Game of Life), edge of Chaos and self-organised criticality regimes.
    These processes can be visualised by a Penrose tiling. Here’s how I connect the dots, starting with E8 theory, working up to consciousness itself. As Above, So Below?
    View story at
    View story at

  20. tallbloke says:

    Nigel: Thanks for the links, I’ll have a look when I get some time. (Hoho)
    Glad you’re keeping an eye on our work (mostly Oldbrew’s until I get a timeout from politics.