Recursive Integer Sequences, Detected in Solar-Cycle Periodicities Measured in Numbers of Rigid Rotations of the Sun

• Published in: Solar physics 2020-06, Vol.295 (6), Article 78
• Main Author: Richard, Jean-Guillaume
• Format: Article
• Language: English
• Subjects: Astrophysics and Astroparticles; Atmospheric Sciences; Fibonacci numbers; Periodicities; Physics; Physics and Astronomy; Sequences; Solar activity; Solar physics; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Sunspot cycle; Sunspots; Symmetry
• ISSN: 0038-0938; 1573-093X
• DOI: 10.1007/s11207-020-01631-1

Consecutive integers in the recursive number sequences, the Fibonacci sequence (F n ) and the Lucas sequence (L n ), are detected in the lengths of solar-activity variations from ≈ 1 yr to ≈ 12 yr, measured in rigid rotations of the Sun at the helioseismologically determined frequency in the radiative zone, 433 ± 3  nHz. One rotation is denoted by the symbol Ω . Firstly, in the new international sunspot-number record (Ri) the most frequent (modal) sunspot-cycle length, which is also the period defined by autocorrelation for the recurrence of sunspot cycles, has been 144 ± ≈ 2 Ω ( F 12 = 144 ). The most frequent length for a descending leg of the cycle has been 89 ± 2 Ω (F = 11 89 ), and for an ascending leg 55 ± 1 Ω (F = 10 55 ). Secondly, there is some observational evidence of Ri spectral peaks at the consecutive L n numbers of Ω : 18 Ω (≈ 1.3 yr), 29 Ω (≈ 2.1 yr), 47 Ω (≈ 3.4 yr), and 76  Ω (≈ 5.6 yr), which are harmonics of the 144 Ω period divided by the first four F > n 1 : 2, 3, 5, and 8. The numbers of Ω : 144, 89, and 55 may be kinematical thresholds in the dynamo process starting at sunspot maximum, when the poles change polarity and the process is re-set. The ratio of two consecutive F n or L n converges to 1 + 5 2 , hence it is suggested that this proportion plays a role in solar behavior over time , described numerically. The length ratio 1 + 5 2 also is characteristic of fivefold symmetry in space . Since the icosahedral group is the link between numerical and spatial expressions of fivefold symmetry, it is proposed that the presence of icosahedral symmetry in the large-scale geometry of the Sun could also be tested.