Tropical Timings: solar cycle length analysis – the bi-modality question

This graphic by Timo Niroma was used in our Talkshop post:
Timo Niroma and Ray Tomes on solar cycle lengths and planetary alignments (July 2010).

Tallbloke wrote: It’s widely accepted that the average solar cycle length is just over 11 years. What isn’t so well known is that the actual solar cycle length clusters around two different periods of around 10.38 and 12 years.

Ray Tomes wrote: For some unknown reason, the gravitational oscillations reach maxima at intervals of 10.38 and 12.00 years, whereas best alignments take twice as long.

Timo Niroma’s graphic shows these two maxima of sunspot cycle length. One peak is around the Jupiter orbit period (~11.9 years), the other in the 10.2-10.4 years range and with a higher rate of occurrence.

We can relate this to our post: Jupiter, Earth and Venus’ tropical alignments point to the mean solar cycle length (April 2023). In that post we show that the full period in question is 166*6 = 996 tropical years, which has whole numbers of orbits of Jupiter(84), Earth(996) and Venus(1619) based on tropical orbit periods. It is also the period of 90 mean solar cycles or 45 Hale cycles.

The post also stated:
In 166 tropical years:
Jupiter tropical orbits (J) = 14
Proposed number of mean solar cycles (SC) in the period:
J orbits + 1 = 15

We split the 166 years into its two half cycles of 83 years:
83/7 = 11.857142 tropical years (7 Jupiter orbits in the precessing reference frame)**
83/8 = 10.375 years (9.5 Jupiter-Earth, ~6.5 Earth-Venus, ~16 Jupiter-Venus conjunctions). Note: Ray Tomes said ‘best alignments take twice as long’, i.e. 9.5 and 6.5 are doubled to become whole numbers, and the period is the Hale cycle (= 2 solar cycles).
7+8 = 15 mean solar cycles in 2*83 = 166 tropical years.

By extension, 14 Jupiter-related plus 16*10.375 year related solar cycles = 15*2 SC = 15 Hale cycles in 2*166 tropical years, as a theoretical long-term mean. Detailed information for analysis is restricted to numbered solar cycles 1-25 starting in 1755.

Of course the actual solar cycle periods can vary considerably around the two proposed peaks, but Niroma’s graphical data analysis points to the bi-modal nature of the cycles.

The logic would be that in a theoretical block of 15 solar cycles in 166 tropical years, 8 should fall into the 10.375 years JEV group (11 years or less) and 7 into the ~11.9 years Jupiter group (more than 11 years). Lesser planetary factors can help to account for the broader range of values observed.

By analysing the observed cycle lengths, we can illustrate the foregoing in a simple spreadsheet. The theoretical 8 short (s) plus 7 long (l) solar cycles in a sequential group of 15 occurs 3 times. The average duration of all groups of 15 cycles in the sunspot record is 166.132 years.

It’s of interest to note that the modern end of the range has more shorter cycles, and lower 15 cycle totals. This is consistent with the idea that shorter cycles have higher amplitudes and a greater climatic warming effect.
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Bimodality of the solar cycle (1986) — ‘A persistence of the long-period mode would eventually produce a grand minimum such as the Maunder minimum; a persistence of the short-period mode would produce a grand maximum.’ https://agupubs.onlinelibrary.wiley.com/doi/10.1029/GL013i004p00352

What other researchers say:
Ivanka Charvatova (PRP)

Shows that groups of five shorter cycles appear during the ‘ordered solar inertial motion’ 60 year phase of the José cycle, e.g. 1900 – 1960 with a mean length between 10 and 10.5 years. The following 60 years of ‘disordered motion’ has mixture of predominantly longer cycles.

Ordered ‘Trefoil’ Solar Inertial Motion 1900-1960

Disordered Solar Inertial Motion 1961-2021

Ian Wilson (PRP) — https://tallbloke.wordpress.com/wp-content/uploads/2014/01/prp-1-147-2013.pdf
The Venus–Earth–Jupiter spin–orbit coupling model

‘There is a long-term modulation of the net torque that
has a period of ≈ 166 yr. This 166 yr modulation period results from the fact that 14 sidereal orbital periods of Jupiter (= 166.07 yr) almost equals 15 times the period required for Jupiter to move 90◦ in the Venus–Earth alignment reference frame = 15 × 11.0683 yr (= 166.02 yr).’
(see IW’s Figure 6 and/or our earlier post: Jupiter, Earth and Venus’ tropical alignments point to the mean solar cycle length. Also: search ‘166’ in the PRP paper).

[Talkshop note: we find that 14 Jupiter tropical orbits = 166.0 tropical years, as stated earlier.]

N. Scafetta, A. Bianchini
https://www.mdpi.com/2225-1154/11/4/77
Overview of the Spectral Coherence between Planetary Resonances and Solar and Climate Oscillations

Figure 6(B) ‘Bimodal distribution of the solar cycle lengths. Updated from Scafetta [37].’

‘Thus, including this last cycle, the average of the 13 solar cycle lengths larger than 10.9 years is 11.9±0.7 years, which agrees well with the tidal period associated with the orbit of Jupiter.’

‘We also found that the recurrent pattern (ðœ‚1,ðœ‚2,ðœ‚3)=(32,19,13) = 10.38±0.01 years optimally fulfils the more general condition ðœ‚1·ð‘ƒð‘‰ð½≈ðœ‚2·ð‘ƒð¸ð½≈ðœ‚3·ð‘ƒð‘‰ð¸, when the integers are varied between 1 and 50. Interestingly, a quasi 10.4-year cycle is found in quite a number of climatic records [12,85] and even in meteorite fall records [90].’

(Also: search for ‘10.38’, ‘bimodal’ and ‘recurrent pattern’ in this paper).
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** See Arnholm’s Solar Simulator 2 and/or our tropical alignments post.

Source: https://tallbloke.wordpress.com/2024/10/28/tropical-timings-solar-cycle-length-analysis-the-bi-modality-question/