Why Phi? – solar rotation notes

Posted: February 6, 2016 by oldbrew in Fibonacci, Phi, solar system dynamics

Carrington Rotations = CarRots [credit: dreamstime.com]

Carrington Rotations = CarRots [credit: dreamstime.com]

Tallbloke recently acquired a book by Hartmut Warm called ‘Signature of the Celestial Spheres: Discovering Order in the Solar System’ which offers this gem:
588 solar Carrington rotations (CarRots) = 587 lunar sidereal months
We’ll call this the HW cycle, about 43.91 years.

‘Richard Christopher Carrington determined the solar rotation rate from low latitude sunspots in the 1850s and arrived at 25.38 days for the sidereal rotation period. Sidereal rotation is measured relative to the stars, but because the Earth is orbiting the Sun, we see this period as 27.2753 days.’ – Wikipedia

Picking this ball up and running with it, we find there are 308 CarRots (27.2753 d) per 331 solar sidereal days (25.38 d) in 23 years (331 – 308). This period, or a multiple of it, can be found in certain identified solar-planetary cycles (as discussed below).

To connect these two observations, we first break them down.
308 = 11 x 28 CarRots
588 = 21 x 28 CarRots

5 x 11 x 28 = 55 x 28 CarRots = 23 years x 5 = 115 years
So 1 HW cycle x phi² (or 55/21) = 115 years
11 HW cycles = 483 years = 23y x 21

115 years will be at or very near a whole number of:
* Carrington rotations (1540 = 55 x 28 or 308 x 5)
* Solar sidereal days (1655 = 1540 + 115 or 331 x 5)

It’s also about 5 days short of 13 lunar apsidal cycles and 2 days more than 102 (34×3) full moon cycles. These periods (56 of them per 339 Metonic-year cycle) are analysed in more detail in the ‘quarter precession’ post :

So here we have a close correlation between solar, lunar and Earth periods with multiples of Fibonacci numbers (3, 13, 34, 55) to the fore.

If we increase the 115 year period by a factor of 5 to 575 years, the Jupiter-Saturn axial period is in play.

J+S axial = (J x S) orbit periods / (J + S) = 8.4561455 years
(In this context the axial is a period where the sum of the number of orbits of each planet in that time is 1. Or: half the harmonic mean.)
575y / 8.4561455 = 67.997883 J+S = ~68 (99.997% match)
68 = 34 x 2 (both Fibonacci numbers)

Research evidence

Turning to the possible significance of some of these periods:
‘Multi-scale harmonic model’ [etc.] – Nicola Scafetta

Scafetta identifies the 115-year period:
‘The major beat periods occur at about 115, 61 and 130 years, plus a quasi-millennial large beat cycle around 983 years.’

‘The quasi-secular beat oscillations hindcast reasonably well the known prolonged periods of low solar activity during the last millennium such as the Oort, Wolf, Spörer, Maunder and Dalton minima as well as the seventeen ~115-year long oscillations found in a detailed temperature reconstruction of the Northern Hemisphere covering the last 2000 years.’

‘The model forecasts a new prolonged solar minimum during 2020–2040, which is stressed by the minima of both the 61 and 115-year reconstructed cycles.’

Chinese scientists have also found this period:
Periodic oscillations in millennial global-mean temperature and their causes

‘The three long-term periods of the Medieval Warm Period (MWP), Little Ice Age (LIA) and recent Global Warming Period (GWP) were distinct in the temperature series. 21-year, 65-year, 115-year and 200-year oscillations were derived from the temperature series after removing three long-term climatic temperatures.’

Ian Wilson often refers to the Hallstatt cycle, thought to be around 2300 years, in his science papers and blog posts.
(2300 = 115y x 20 or 23y x 100)
‘The VEJ Tidal Torquing Model can explain many of the long-term changes in the level of solar activity.’ – Ian Wilson
II. The 2300 year Hallstatt Cycle 

‘Solar activity levels in 2100’ – Clilverd et al

‘The residue 14C is then seen to oscillate about zero with an apparent period known as the Hallstatt cycle (Damon and Jirikowic 1992). The lower panel shows a sine wave with a Hallstatt period of 2300 years (solid line). The times of minima in the Hallstatt cycle (indicated by arrows) appear to coincide with significant solar activity minima such as the Maunder Minimum of around 1700. Century-scale oscillations during these periods have been linked to solar activity (Damon and Jirikowic 1992). It is thus possible that the recovery of solar activity from significant minima such as the Maunder Minimum is repeatable over time scales of about 2300 years.’

For how long will the current grand maximum of solar activity persist?
Authors: J. A. Abreu, J. Beer, F. Steinhilber, S. M. Tobias, N. O. Weiss

This paper says: ‘It is apparent that there are many grand minima and maxima in this record. Frequency analysis reveals the presence of a number of significant periodicities, namely around 200 years (de Vries) and 2300 years (Hallstatt) [Tobias et al., 2004].’

Note: 23 x 21 x 5 = 2415 = 115 years more than the 2300 year sine wave period.
‘The ∼ 2400-year cycle in atmospheric radiocarbon concentration:
bispectrum of 14C data over the last 8000 years’

S. S. Vasiliev and V. A. Dergachev

The authors say: ‘The epochs of fluctuations with high amplitude are repeated each 2300–2500 years.’ [see fig. 2]

  1. ulriclyons says:

    There is a good Earth-Mercury-Ceres resonance at 23 sidereal years.
    Scafetta’s theoretical 115yr cycle is too long, solar minima occur on average every ten cycles, with a long term astronomical mean of around 108yrs, close to Leif’s 107yrs.

  2. oldbrew says:

    Scafetta’s paper says: ‘The correlation coefficient is r0=0.3 for 200 points, which indicates that the 115-year cycles in the two curves are well correlated (P(|r|≥r0)<0.1%). The 115-year cycle reached a maximum in 1980.5 and will reach a new minimum in 2037.9 A.D.'

    A prediction – only 21 years away 😉

  3. ulriclyons says:

    I have a planetary model of solar cycles and solar minima, that accounts for the variability in timing and duration of each solar minimum, so it plots exactly which cycles are weaker in each minimum. From the start of the Gleissberg Minimum (SC12) to SC24 is 12 cycles, while from SC5 at the start of Dalton to SC12 is only 7 cycles, so the minima wander considerably, but average at around every ten cycles. And this minimum is looking short like the last two, effecting mostly cycles 24&25.

  4. You say: To connect these two observations, we first break them down.
    308 = 11 x 28 CarRots
    588 = 21 x 28 CarRots

    Readers may note that 11 & 21 approximate the periods of the Schwabe & Hale sunspot cycles.

    The Extended Cycle of Solar Activity and the Sun’s 22-Year Magnetic Cycle, E.W. Cliver

  5. oldbrew says:

    Re: ‘The Extended Cycle of Solar Activity and the Sun’s 22-Year Magnetic Cycle, E.W. Cliver’

    No magnetism without electricity (excluding manufactured bar magnets and the like).

    Hartmut Warm’s 43.91 year period is close to 2 solar magnetic cycles, but a bit short of the supposed average.

  6. oldbrew says:

    Re: 308 = 11 x 28 CarRots
    588 = 21 x 28 CarRots

    Common factor: 28 CarRots
    19 x 28 CarRots = 2 Jupiter-Saturn conjunctions (> 99.99% match)

    So 42 J-S = ~19 HW cycles

    Here we derived a model based on 42 J-S x 3 = 126 J-S:

  7. tallbloke says:

    Vuk finds the period to be 107.5

    It is a fundamental period in these graphs of mine.
    (118+97)/2 =107.5

  8. oldbrew says:

    TB: from the Roger Andrews post you linked to in the latest NOAA thread…

    ‘a recent paper by Komitov et al. (http://arxiv.org/ftp/arxiv/papers/1011/1011.0347.pdf) conveniently identifies a 110-120 year cycle in the solar record over the last few hundred years.’

    From the abstract of the paper:
    ‘On the other hand a strong and stable quasi 110-120 years and ~200-year cycles are obtained in all of these series except in Ri. In the last series a strong mean oscillation of ~ 95 years is found, which is absent in the other data sets.’

    110-120 and 95 are in the ballpark of Vuk’s numbers, but 95 only shows up in one data set.

  9. tallbloke says:

    Also looking good for Scafetta’s 115yr period

  10. oldbrew says:

    Yes, and the Chinese paper comes to a similar conclusion as Scafetta:

    ’21-year, 65-year, 115-year and 200-year oscillations were derived from the temperature series after removing three long-term climatic temperatures.’

    ‘Based on the long-term trend during the GWP and the four periodic oscillations, global-mean temperature is expected to drop to a new cool period in the 2030s and then a rising trend would be towards to a new warm period in the 2060s.’

  11. oldbrew says:

    27 HW periods looks interesting. We get exactly 134 (27 x 5, -1) lunar apsidal cycles .

    That’s confirmed by: 27 HW = 15715 lunar anomalistic months = 15849 lunar tropical months (exact match).
    15849 (587 x 27) – 15715 (582 x 27, +1) = 134.

    The number of CarRots is 15849 + 27 = 15876 (588 x 27) = 126²
    126 = 21 x 3 x 2 (Fibonacci numbers).

  12. ulriclyons says:

    My heliocentric planetary model gives solar minima starting from around; 1018, 1117, 1217, 1320, 1428, 1550, 1670, 1805, 1881, and 2015. Maunder didn’t begin 1645 temperature wise, the 1650’s and 1660’s saw many very warm years. Note that Sporer is actually two minima, from the 1430’s, and from the 1550’s.

  13. oldbrew says:

    Edward R Cook of the US Lamont-Doherty Earth Observatory also found an amplitude modulation period of 115 years in his US drought research.

    That’s a slide from a presentation in 2003. Can’t find a link to the document I downloaded in 2014, at the moment.
    The analysis went back to 800 AD.

  14. oldbrew says:

    Btw the same Dr. Ed. Cook wrote a ‘Climategate’ e-mail:

    ‘Climategate 2.0: ‘We know f***-all’

    Columbia dendrologist Ed Cook knows how much Michael Mann et al. knows — and ever will know — about historic global temperatures.’

  15. ulriclyons says:

    Solar minima can be at 7 cycles apart, like from SC5 to SC12, or at 12 cycles apart, like from SC12 to SC24. What is causing them therefore has nothing to do with any hypothetical 115yr cycle, as it couldn’t possibly account for the variation in length. 115yrs is definitely more than the average frequency of solar minima too.

  16. oldbrew says:

    Komitov et al found a mean cycle of 55-60 years. Two of those = 115 years +/- 5y.

  17. ulriclyons says:

    I cannot see why two of what they found would be making solar minima, whatever it is that they found, and it won’t explain the large variations in the intervals between solar minima.

  18. oldbrew says:

    Ulric: see Scafetta’s paper e.g. Figure 7. He talks about a three-frequency model.

    ‘Fig. 7. Modulated three-frequency harmonic model, Eq. (8), (which represents an ideal solar activity variation) versus the Northern Hemisphere proxy temperature reconstruction by Ljungqvist (2010). Note the good timing matching between the millenarian cycle and the seventeen 115-year cycles between the two records. The Roman Warm Period (RWP), Dark Age Cold Period (DACP), Medieval Warm Period (MWP), Little Ice Age (LIA) and Current Warm Period (CWP) are indicated in the figure. At the bottom: the model harmonic (blue) with period P12=114.783 and phase T12=1980.528 calculated by means of regression; the 165-year smooth residual of the temperature signal. The correlation coefficient is r0=0.3 for 200 points, which indicates that the 115-year cycles in the two curves are well correlated (P(|r|≥r0)<0.1%). The 115-year cycle reached a maximum in 1980.5 and will reach a new minimum in 2037.9 A.D.'

    If you don't agree, so be it but that's what he said.

  19. oldbrew says:

    23 years / lunar nodal cycle = ~2/Phi or 2 x ~0.61784

  20. oldbrew says:

    The beat period of the Saros cycle and the draconic year (both are eclipse-related periods) lines up with 575 tropical years = 5 x 115 TY.

    The number of beats is 574, i.e. one beat is only slightly more than a tropical year (by about 15.27 hours).

    The beat period of the lunar nodal cycle and the Saros is just over 575 years (per beat i.e 575 – 574 = 1).
    The beat period of the lunar nodal cycle and the draconic year is the tropical year.