Why Phi? – modelling the solar cycle

Posted: August 27, 2016 by oldbrew in solar system dynamics
Tags: ,
Credit: cherishthescientist.net

Credit: cherishthescientist.net

We’re familiar with the idea of the solar cycle, e.g.:
‘The solar cycle or solar magnetic activity cycle is the nearly periodic 11-year change in the Sun’s activity (including changes in the levels of solar radiation and ejection of solar material) and appearance (changes in the number of sunspots, flares, and other manifestations).

They have been observed (by changes in the sun’s appearance and by changes seen on Earth, such as auroras) for centuries.’

Here we’ll try a bit of pattern-hunting, so to speak.

This post stems from comments on an earlier Talkshop thread e.g.:
H/T Paul Vaughan for the Hale cycle/Jupiter-Saturn/phi connection.

Theory: an average solar (Hale) cycle is about 22.14 years.
It consists of one North and one South ’11 year’ magnetic cycle, due to magnetic reversal.
Paper: Synchronized Helicity Oscillations: A Link Between Planetary Tides and the Solar Cycle? [Aug.2016]
Quote: ‘we recover a 22.14-year cycle of the solar dynamo.’

Click to access 1511.09335.pdf

Jupiter-Saturn axial period is 8.456146 years.
That’s when the sum of J and S orbital movement in the conjunction period = 1, as shown here:
J-S conjunction period = 19.865036 years
(19.865036 / J orbit period) + (19.865036 / S orbit period) = 2.3491832
19.865036 / 2.3491832 = 8.456146 years
(8.456146 / J orbit period) + (8.456146 / S orbit period) = 1
Data (Sidereal Orbit Period) : http://ssd.jpl.nasa.gov/?planet_phys_par

If we assume two axial periods plus a remainder period:
22.14 – (2 x 8.456146y) = 5.227~y (= remainder)
8.456146 / 5.227 = 1.61778~ = ~Phi
22.14 / 8.456146 = 2.6182~ = ~Phi²
22.14 / 5.227 = 4.2357~ = ~Phi³

If we break the 22.14 years up into those parts like this:
8.456146 + 5.227 + 8.456146 = ~22.14y
it is equivalent to saying, in terms of a model:
1/Phi²(0.382) + 1/Phi³(0.236) + 1/Phi²(0.382) = 1 (Hale cycle)

Timo Niroma’s solar cycle analysis shows the min./max. periods of solar cycles.

From: Timo Niroma and Ray Tomes on solar cycle lengths and planetary alignments
Sunspot cycles: Min. = 8.7 years, max. = 13.9 years
8.7 is about 1/4 of a year more than 8.456146y
13.9 is about 1/4 of a year more than 8.456146 + 5.227y (= 13.683y)
13.9 – 8.7 = 5.2, matches to 5.227 (the ‘remainder’)

Very close to the phi pattern (above).

The variability of a single solar cycle lies within the 5.2 year period (1/Phi³) in the middle of the Hale cycle. The question as always is: what lies behind the observed variability?

Note: J-S axial period / Hale cycle = 1/Phi²

  1. oldbrew says:

    Abstract of the linked paper (see above):
    Recent years have seen an increased interest in the question of whether
    the gravitational action of planets could have an influence on the solar dynamo.
    Without discussing the observational validity of the claimed correlations, we
    ask for a possible physical mechanism that might link the weak planetary forces
    with solar dynamo action. We focus on the helicity oscillations that were recently
    found in simulations of the current-driven, kink-type Tayler instability, which is
    characterized by an m = 1 azimuthal dependence. We show how these helicity
    oscillations can be resonantly excited by some m = 2 perturbation that reflects
    a tidal oscillation. Specifically, we speculate that the 11.07 years tidal oscillation
    induced by the Venus–Earth–Jupiter system may lead to a 1:1 resonant excitation
    of the oscillation of the α-effect. Finally, in the framework of a reduced,
    zero-dimensional α–Ω dynamo model we recover a 22.14-year cycle of the solar

    Keywords: Solar cycle, Models Helicity, Theory
    See also:
    Ian Wilson: Venus-Earth-Jupiter Spin-Orbit Coupling Model

    Ian Wilson: How planets could be modulating solar activity – The VEJ Torquing Model

  2. oldbrew says:

    The 2016 paper mentions several researchers familiar to Talkshop readers:

    ‘Somewhat disconnected from that main road of solar-dynamo research, a few
    studies were devoted to the theoretical possibility that the motion of planets
    could have an influence on the solar magnetic field (Abreu et al., 2012; Charvatova,
    1997; Jose, 1965; Hung, 2007; Palus et al., 2000; Scafetta, 2014; Wilson,
    2013). A recent example is the article by Abreu et al. (2012) who had found
    synchronized cycles in proxies of the solar activity and the planetary torques,
    with periodicities that remain phase-locked over 9400 years. Given the immense
    relevance of a putative planetary influence on the solar dynamo and, perhaps,
    on the Earth’s climate and its predictability (see Figure 9 in Scafetta (2014)) via
    several proposed mechanisms (Svensmark and Friis-Christensen, 1997; Scafetta,
    2010; Gray et al., 2010), it is not surprising that those claims are vigorously

    ‘Although the empirical correlation of the solar cycle with the Venus–Earth–
    Jupiter conjunction cycle seems amazingly persuasive (see Figure 1 of Bollinger
    (1952), Figures 1 and 2 of Wood (1972), and Figure 3 of Okhlopkov (2014)),
    we will abstain here from any judgment of empirical correlations, in particular
    with regard to longer periodicities as discussed by Abreu et al. (2012) and in the
    reactions to that article.

    Instead, the aim of this investigation is to explore whether a specific mechanism
    could indeed lead to synchronization of the solar dynamo with planetary

  3. oldbrew says:

    The authors of the paper (Stefani et al.) note:
    ‘An interesting and non-trivial next step would be to check if also longer periods of the solar dynamo,
    like the ≈ 87-year Gleissberg cycle, the ≈ 210-year Suess-de-Vries cycle, and the ≈ 2300-year Hallstatt cycle, can be explained somehow in the framework of the present model.’

    There are many interesting blog posts on the Talkshop and elsewhere about such matters.

  4. Ian Wilson says:

    Yes – specifically:

    Wilson, I.R.G.: 2013, The Venus-Earth-Jupiter spin-orbit coupling model. Pattern Recogn.
    Phys. 1, 147 DOI.

    Which can be accessed here:


    [reply] absolutely 🙂

  5. Paul Vaughan says:

    Let me help simplify….
    …because reader intuition won’t be helped by this arrangement:

    OB wrote:

    Jupiter-Saturn axial period is 8.456146 years.
    That’s when the sum of J and S orbital movement in the conjunction period = 1, as shown here:
    J-S conjunction period = 19.865036 years
    (19.865036 / J orbit period) + (19.865036 / S orbit period) = 2.3491832
    19.865036 / 2.3491832 = 8.456146 years
    (8.456146 / J orbit period) + (8.456146 / S orbit period) = 1

    …Also, the conjunction period has nothing to do with 8.456145629.
    A blend is not a contrast. I’ll keep repeating that for the community!

    – –


    (29.447498)*(11.862615) / (29.447498 + 11.862615) = 8.456145629

    8.456145629 / 11.862615 = 0.712839929
    8.456145629 / 29.447498 = 0.287160071

    0.712839929 + 0.287160071 = 1

    What this says is simple:

    Say Jupiter and Saturn are coworkers doing clean-up.
    Their work area is shaped like a circle.
    They have to sweep it.
    Jupiter moves faster than Saturn.
    If they combine efforts to sweep the circle it will take them 8.456145629 to finish the job.
    Fraction of sweeping done by faster Jupiter = 8.456145629 / 11.862615 = 0.712839929
    Fraction of sweeping done by slower Saturn = 8.456145629 / 29.447498 = 0.287160071
    Together they got the whole job done:
    0.712839929 + 0.287160071 = 1

    J & S combine their efforts to sweep out a circle and it takes 8.456145629.
    Faster J does 71.2839929% of the work while slower S does 28.7160071%.

    Simple harmony.

    Nothing to do with conjunctions whatsoever. That’s another matter. Conjunctions are contrasts whereas axial periods and harmonic means are blends. Knowing a blend does NOT tell you a contrast and vice versa. This FUNDAMENTAL point can be underscored as many times as necessary

    ….For their skeptic-lukewarmist conversion campaign custom-tailored to support a clinton dynasty, California Lukes need suckers to blindly / naively / unconsciously believe knowing a blend informs of the contrast (playing up global averages as if they specify spatial pattern), but that’s mathematically STRICTLY FALSE.

    It’s simple…

    Draw a line:
    A blend is not a contrast.

    That’s it.

    International nature-lovers can harmonize to sweep up the californian mess with simple harmonic means …getting the whole job done faster by each taking a piece.

  6. Paul Vaughan says:

    One thing I don’t understand is why people keep pointing to that Timo Niroma plot. It’s grossly inadequate. It’s a temporally-global summary; it doesn’t even have the cycle lengths ordered chronologically. A marginal summary like that jumps all over the place with minor variations in cycle length measurement method. As some may recall I ran lots of diagnostics on this a few years ago. Much better can — and has been — done. (There has been some kind of a communication break-down on this one.)

    I noticed an error in the paper to which OB linked. It’s a repeat of an error in Bollinger on 44.77 or whatever. It’s not a Hale subharmonic. (“Close” implies drift. Only exact doesn’t slip.)

    More generally I think a different tone needs to be taken in papers like that one. It’s too apologetic. No one needs to apologize for exploring.

    ….Having said that, I hasten to add: It’s good to see authors with interest in an interesting topic.

  7. oldbrew says:

    PV: note that I’m only using Niroma for the shortest and longest recorded solar cycles, nothing else.

  8. tallbloke says:

    I think Niroma’s summary is useful in several pedagogical respects, despite the fact that it’s not chronological.

    It shows that the solar cycle length tends to cluster around two distinct periodicities rather than near the average 11.07

    It shows that those periods are close to the JEV 10.38 and the Jupiter orbital 11.86.

    It points up the phi relationship that OB sets out to elucidate in this post by looking at the envelope as well as the clustering.

    It’s also worth remembering,as Landscheidt observed, that the solar cycle does on average split into rising and falling sections that are themselves in the golden (phi) ratio.

    Discovering exact relationships is equally important of course.

  9. Paul Vaughan says:

    Sobriety Call:

    I was just looking at the 3 links OB gave to the old discussion thread and I suggest some realism:

    There’s not a snowball’s chance in h*ll we could ever get mainstream climate scientists to acknowledge something so fundamental and simple as what I outlined there:

    https://tallbloke.wordpress.com/2015/12/21/why-phi-an-orbital-parameters-test/comment-page-2/#comment-113885 (February 20, 2016 at 10:14 am)

    It won’t register for them at all. There’s no chance. The capacity doesn’t even exist.

  10. Paul Vaughan says:

    The histogram isn’t stable.
    Minor changes in aggregation criteria reshape it.

    If it is treated as a probability distribution (as OB suggested at 1 of the 3 links), that’s based on a false assumption, as the distribution isn’t random in time.

    If the goal is to provoke people to do better than Landscheidt & Niroma, you have my applause …but I’m not saying they got it right.

  11. oldbrew says:

    Ian Wilson was discussing the 44.77 year period here:

    28 × SVE = 44.763 years
    69 × SVJ = 44.770 years
    41 × SEJ = 44.774 years
    20 × SMJ = 44.704 years

    SVJ = synodic period of Venus/Jupiter
    SEJ = synodic period of Earth/Jupiter
    SMJ = synodic period of Mars/Jupiter
    This means that these four planets return to the same relative orbital configuration once every 44.77 years.

    Ian Wilson: Linking the Orbital Configuration of Jupiter, Saturn, Venus & Earth to Lunar Tides & Earth’s Climate

    Which reminds me of something else about lunar tides, maybe another post.

  12. Paul Vaughan says:

    Here is my suggestion for anyone who thinks there’s something special about the aggregation criteria used by Niroma:

    Vary the aggregation criteria to explore how the histogram shape dances wildly (…with even minor variations in aggregation criteria).

    Let us know if you discover some specific criteria for tuning the aggregation criteria systematically.

    But as for the notion that there’s no temporal autocorrelation in cycle length estimates: forget it. The cycle lengths don’t arise from a lottery that’s independent of time (…as suggested by plotting the cycle lengths in a histogram without an accompanying timeplot acknowledging the nonrandom chronological order).

    As for Landscheidt:
    I see nothing on the record suggesting he was aware of FRI. His devotion to a time-only approach — ignoring of the SPATIAL organization of ENSO — defined the brick wall he hit with his temporal explorations of SPATIOtemporal phenomena.

  13. oldbrew says:

    Re axial periods: we also know that Jupiter+Neptune = 11.066~ years = about half a solar Hale cycle or one ‘sunspot cycle’ (i.e. 11.066 / J plus 11.066 / N = 1)

  14. oldbrew says:

    The paper also mentions the Babcock-Leighton mechanism [see: 3. Synchronizing the Solar Dynamo, and 4. Conclusions and Outlook].

    ‘The Babcock Model describes a mechanism which can explain magnetic and sunspot patterns observed on the Sun.’
    The authors say: ‘Most notable in the context of our work is that the 22-year (Hale) cycle is basically set by the velocity of the meridional circulation (Charbonneau and Dikpati, 2000).’

    They admit: ‘Perhaps the most significant problem of our model is the complete omission of rotation and gravity.’

    NB the word ‘spatial’ is used 4 times in the paper.

  15. Paul Vaughan says:

    Just like 44.77 isn’t a Hale subharmonic, J+N slips on Hale …and the Hale Core Model would fall apart if it didn’t!

    If 2 things cannot mathematically exist simultaneously, wishing for their simultaneous existence isn’t the answer.

  16. oldbrew says:

    We also have J+U = 10.3949y. For whatever reason (or no reason) that period sits in the middle of the main peak in Niroma’s solar cycle length distribution chart.

    Could axial periods be like boundaries? Obviously individual Hale cycles can vary in duration but mean/min/max are more or less known.

  17. oldbrew says:

    PV says: ‘I noticed an error in the paper to which OB linked. It’s a repeat of an error in Bollinger on 44.77 or whatever. It’s not a Hale subharmonic. (“Close” implies drift. Only exact doesn’t slip.)’

    Agree. But note that 4 x 44.77 is just over 179 years.

    ‘the 179-year cycle in the Sun’s motion’
    See section 2 here: http://www.john-daly.com/theodor/DecadalEnso.htm

    Prolonged minima and the 179-yr cycle of the solar inertial motion
    Authors: Fairbridge, Rhodes W.; Shirley, James H.

  18. Paul Vaughan says:

    To put it loosely:

    It’s not about cycles; it’s about aggregation criteria.

    That statement — to be thorough and a lot more clear — would require extensive elaboration.

    There’s no time. We have MUCH higher priorities over the next several months. Any volunteers ready to move with a sense of urgency on a problem that matters in REAL time, see where we’re going on Suggestions-20. The clock is ticking AND IT WILL RUN OUT. We’ll be ready OR WE WON’T.

    Let me tell you something: I’m not going to fail on an important mission because of a luxurious addiction to phi. Human beings will rediscover phi at their leisure a billion times over if necessary. It’s not any kind of real risk in the here and now. Perspective: It has ZERO impact in the here-and-now. You could discover the smoking holy grail with phi AND NO ONE WOULD RECOGNIZE IT!

    [ :

    How’s that for a smiley?

    : ]

    A flipping smiley — in GOOD humor!

    Sometimes you just have to have a sense of humor friends.

    I’m boycotting phi for the next several months.

    On Suggestions-20:
    explosive volcanism….
    (even the mainstream is going there with a vengeance…. there’s just one group offside….)


    [mod] wordpress only handles a limited set of ‘smileys’ 😕