Kuramoto Model with Non-symmetric Coupling Reconstructs Variations of the Solar-Cycle Period

• Published in: Solar physics 2016-03, Vol.291 (3), p.1003-1023
• Main Authors: Blanter, E., Le Mouël, J.-L., Shnirman, M., Courtillot, V.
• Format: Article
• Language: English
• Subjects: Astrophysics and Astroparticles; Asymmetry; Atmospheric Sciences; Magnetic fields; Nonlinear systems; Oscillators; Phase shift; Physics; Physics and Astronomy; Quasi-biennial oscillation; Reconstruction; Solar cycle; Solar cycles; Solar physics; Space Exploration and Astronautics; Space Sciences (including Extraterrestrial Physics; Synchronism
• ISSN: 0038-0938; 1573-093X
• DOI: 10.1007/s11207-016-0867-4

We apply a Kuramoto model with two non-linear, coupled oscillators to the simultaneous reconstruction of the phase difference of the two oscillators and instantaneous period (or length) of the solar cycle. The two long series of sunspot numbers [ R I ] and aa geomagnetic indices are considered as proxies of the toroidal and poloidal components of the solar magnetic field, respectively. Variations in the length of the solar cycle are successfully reconstructed when an asymmetry between coupling coefficients is introduced, corresponding to an asymmetry of the α Ω -mechanisms of solar magnetic-field generation. Application of the Kuramoto model to solar indices and comparison with synthetic data series shows the important role of synchronization in allowing one to estimate solar-cycle length. The Kuramoto model reconstruction reveals a ≈ 30 – 33 year (three solar cycles) quasi-periodicity and the influence of quasi-biennial oscillations present in the aa-index on the determination of solar-cycle length.