The Sun's Two Pendulums: How Coupled Oscillations Create a 90-Year Rhythm ✎

Original: "Application of Coupled Harmonic Oscillator model to Solar Activity and El Niño Phenomena"

arXiv:1706.09105 · 2017-06-28 · arXiv non-exclusive · independent analysis · 2 min

Solar activity beats like two coupled pendulums, and their slow beat explains the 89-year cycle and the 22-year imprint in Yakushima cedar rings.

Place two pendulums side by side and give one a gentle push; the other will soon pick up the rhythm. This behavior isn't limited to clocks on a shared shelf; it also applies to the plasma inside the Sun. In the star's convection zone, two huge ring-shaped flows circulate: one closer to the surface, the other deeper. Each oscillates with its own period—12.05 and 9.52 years. When the two oscillations overlap, a slow beat emerges: the amplitude swells and fades with a period of 89 years. That's the Gleissberg cycle, which astronomers see in sunspot counts.

Two plasma flows inside the Sun, like two pendulums, exchange energy. The outer one travels from the equator toward the poles at depths of roughly 0.82–0.91 of the star's radius; the inner one at 0.70–0.82. Their interaction follows Lenz's law: the current in one flow damps changes in the other, and together they set a common rhythm.

The same trick works for the ocean. El Niño has two oscillations of its own: 5.35 and 3.55 years. Their sum yields an envelope with a period of 21.5 years. That's exactly the signal found in the rings of the Yakushima cedar—a tree that grew on Yakushima Island since 1924 and even survived the Maunder Minimum, when sunspots nearly vanished. So the 22-year trace in the wood was left not by the Sun but by the warm currents of the Pacific.

The current strength in the outer plasma flow is estimated at 3×$10^{11}$ amperes. This number comes from the magnetic field at the Sun's pole, which is about $10^{-4}$ tesla. In the zone where the two flows converge at a depth of 0.85 of the star's radius, the field can reach 1000 gauss—as much as in sunspots.

Previously, it was unclear why 11- and 22-year periodicities appear in cedar rings even when the Sun quieted for decades. Now the answer is simple: the 89-year cycle arises from the beat of two solar flows, and the 22-year one from the beat of two oceanic ones. Two pendulums in the sky and two in the sea leave a common mark on Earth. The model can serve as a simple tool: take tree-ring data and quickly estimate how much of the climate variability came from the Sun and how much from the ocean.

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The Yakushima cedar, whose rings revealed the 22-year signal, lives on Yakushima Island, where annual precipitation reaches 4000–10000 mm, making it one of the wettest places in Japan.

\psi = \sin(\omega_A t + \alpha) + \sin(\omega_B t) = 2 \sin\left(\frac{\omega_A+\omega_B}{2}t + \frac{\alpha}{2}\right) \cos\left(\frac{\omega_A-\omega_B}{2}t + \frac{\alpha}{2}\right)

The sum of two sinusoids with close frequencies gives an oscillation at the average frequency and a slow envelope at the difference frequency.

B = \frac{\mu I}{2\sqrt{8} R}

The magnetic field at the pole is produced by a toroidal current I flowing at distance R; hence the current is estimated at 3×10^11 A.

Concepts

recharge oscillator model El Niño-Southern Oscillation ENSO Multivariate ENSO Index Jin-Timmermann model La Niña ocean-atmosphere coupling El Niño index solar cycle mixed mode oscillations quasi biennial oscillation seasonal cycle seasonal forcing Indian Ocean capacitor effect TAO/TRITON moorings interannual variability natural variability spring predictability barrier ERSST NOAA CPC

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The Sun's Two Pendulums: How Coupled Oscillations Create a 90-Year Rhythm ✎