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An optimized tidal-trigger model of the QBO, and some implications for the Carrington event

This paper presents an optimized model linking magneto-Rossby waves in the solar tachocline to planetary tidal forces and the sunspot-derived toroidal magnetic field, achieving a high correlation (up to 0.8) with extreme solar events and offering new insights into historical events like the Carrington event as well as forecasts for solar cycle 25.

Original authors: F. Stefani, G. M. Horstmann, G. Mamatsashvili, T. Weier

Published 2026-06-08

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CC BY 4.0

Original authors: F. Stefani, G. M. Horstmann, G. Mamatsashvili, T. Weier

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: The Sun's "Planetary Alarm Clock"

Imagine the Sun isn't just a ball of fire, but a giant, spinning ocean of gas. Deep inside this ocean, at a specific layer called the tachocline, there are giant waves moving around. Scientists call these "Magneto-Rossby waves." Think of them like massive, invisible ripples in a pond, but instead of water, they are made of magnetic fields and gas.

For a long time, scientists wondered what makes these waves start moving or get stronger. This paper proposes a surprising answer: The planets.

Just as the Moon pulls on Earth's oceans to create tides, the planets Venus, Earth, and Jupiter pull on the Sun's magnetic "ocean." The authors suggest that when these planets line up in specific ways (creating "spring tides"), they give a little nudge to the Sun's waves.

The Problem: The "One-Size-Fits-All" Model Didn't Work Perfectly

In previous studies, scientists tried to predict when the Sun would have massive explosions (called solar flares or "extreme events") by simply adding up these planetary nudges.

The old model: It was like saying, "If the planets push, the Sun explodes."
The result: This worked okay, but it wasn't perfect. It only matched about 40% of the actual explosions. It was like a weather forecast that got the rain right only 4 out of 10 times.

The New Discovery: The Sun's "Magnetic Muscle"

The authors realized that the Sun's waves don't react the same way every time. The strength of the wave depends on how "muscular" the Sun's magnetic field is at that moment.

The Analogy: Imagine a trampoline.
- If the trampoline is loose (weak magnetic field), a small jump (planetary nudge) doesn't do much.
- If the trampoline is tight and bouncy (strong magnetic field), that same jump sends you flying high.
- But there's a catch: If the trampoline is too tight (an extremely strong magnetic field), it becomes stiff and won't bounce at all. The jump gets absorbed.

The authors created a new, "optimized" model that takes this "magnetic muscle" into account. They used the Sunspot Number (a count of dark spots on the Sun) as a proxy for how strong the magnetic field is.

The Results: A Much Better Forecast

By adjusting their model to account for this "Goldilocks" magnetic field (not too weak, not too strong), the predictions improved dramatically.

Old correlation: ~0.4 (40% match).
New correlation: Up to 0.8 (80% match).

This means their new model can predict when extreme solar events will happen with much higher accuracy than just looking at sunspots alone. It suggests that the "planetary clock" is the main trigger, but it only fires the gun when the Sun's magnetic field is in the "sweet spot."

The Carrington Event and 1989: A Historical Echo

The paper looks back at two famous times in history:

The Carrington Event (1859): A massive solar storm that knocked out telegraphs.
The Summer of 1989: A time when many huge solar storms happened in quick succession.

The authors noticed a strange similarity. In both cases, the Sun's magnetic field was slowly getting stronger (the sunspot number was rising), but the "planetary nudges" were staying steady and constant.

The Metaphor: Imagine a bow and arrow. The planets were pulling the string back (building up energy in the waves) while the Sun's magnetic field was slowly tightening the bow. Eventually, the tension got so high that the arrow (the solar storm) was released.
The paper suggests that the 1859 and 1989 events happened because the "planetary nudge" finally hit the Sun at the exact moment the magnetic field was ready to launch a massive explosion.

What About the Future? (Cycle 25)

The authors used their new model to look at the rest of the current solar cycle (Cycle 25).

Even though the Sun is currently "calming down" (sunspots are decreasing), the model predicts that the planetary nudges will still create a few "peaks" of activity.
The Warning: They suggest that we shouldn't be complacent. Just because the Sun is in its "decline phase" doesn't mean it's safe. There are still specific dates in late 2025 and 2026 where the planetary alignment and the magnetic field might line up again, potentially causing strong solar storms.

Summary

This paper argues that the Sun's biggest explosions aren't random. They are likely triggered by the gravitational dance of Venus, Earth, and Jupiter. However, this trigger only works when the Sun's internal magnetic field is in a specific "sweet spot." By accounting for this, the scientists have built a much more accurate "alarm clock" for predicting dangerous space weather.

Technical Summary: An Optimized Tidal-Trigger Model of the QBO and Implications for the Carrington Event

Problem Statement
The paper addresses the physical mechanism driving the quasi-biennial oscillation (QBO) in solar activity and the occurrence of extreme solar events (Ground-Level Enhancements and S-class flares). While magneto-Rossby waves in the solar tachocline are hypothesized to be the underlying cause, previous models utilizing tidal forcing from Venus, Earth, and Jupiter showed only moderate correlations (approx. 0.4) with observed solar events. The central problem is to improve the predictive power of this tidal-trigger model by incorporating the dependence of wave excitation efficiency on the actual strength of the toroidal magnetic field ( $B_\phi$ ) at the tachocline.

Methodology
The authors utilize a dataset comprising 109 extreme solar events (72 GLEs and 37 S-flares) recorded between 1956 and 2025. The analysis relies on a tidal-forcing function, $s(t)$ , defined as the sum of three cosine terms representing the spring tides of the Venus-Jupiter, Earth-Jupiter, and Venus-Earth pairs. The periods correspond to synodic periods of approximately 118, 199, and 292 days, respectively.

To optimize the model, the authors introduce a magnetic-field dependence to the weights ( $A, B, C$ ) of these three tidal components. The toroidal field strength, $B_\phi$ , is inferred from the 13-month smoothed monthly sunspot number (SSN) using a dynamo-scaling relation. The weights are parametrized as functions of $B_\phi$ (Equation 4), incorporating parameters that represent:

Excitation efficiency in the absence of a magnetic field ( $a_0, b_0, c_0$ ).
Sensitivity to field strength ( $a_2, b_2, c_2$ ).
The field strength threshold at which wave excitation breaks down due to suppression ( $a_4, b_4, c_4$ ).

The optimization process involves a look-up table approach to maximize the correlation coefficient ($Corr$) between the squared forcing function $s^2(t)$ (and its time/azimuthal averages) and the timing of the 109 solar events. The correlation is calculated with varying time shifts to account for potential lags.

Key Contributions and Results

Optimization of Correlation: By optimizing the nine parameters governing the magnetic-field dependence, the authors achieved a maximum correlation of approximately 0.8 between the tidal-trigger function and the extreme solar events. This represents a significant improvement over the field-independent model (correlation $\approx 0.4$ ) and the correlation with sunspot numbers alone (correlation $\approx 0.56$ ).
Field Dependence Dynamics: The results indicate that wave excitation is not linearly proportional to the magnetic field. The optimized parameters suggest that excitation can occur even at low field strengths (non-zero $b_0, c_0$ ) but is suppressed at very high field strengths (determined by $a_4, b_4, c_4$ ). This non-monotonic behavior allows the model to predict extreme events occurring far from solar cycle maxima, where the tidal function peaks despite lower sunspot numbers.
The Carrington Event (1859): The model was applied retrospectively to Solar Cycle 10. The analysis reveals that in the 600 days leading up to the September 1, 1859, Carrington event, the sunspot number (and inferred $B_\phi$ ) rose steadily while the tidal-trigger function $s^2(t)$ remained on a relatively constant plateau. The authors propose that this allowed magneto-Rossby waves to build up sufficient amplitude to provide a "final push" to flux tubes once the toroidal field reached its maximum.
Parallel with Cycle 22: A similar pattern of a steady rise in sunspot numbers coupled with a constant tidal plateau was observed in Solar Cycle 22, preceding a massive clustering of extreme solar events in the summer and autumn of 1989.
Forecasts for Cycle 25: Using NOAA predictions for the sunspot number, the model identifies candidate peaks in the tidal-trigger function for the remainder of Solar Cycle 25. Specifically, a peak is predicted around December 5, 2025, with subsequent dates suggesting a possibility of further strong events during the cycle's decline, analogous to patterns seen in Cycles 21 and 23.

Significance and Claims
The paper claims that the optimized model provides a statistically highly significant explanation for the timing of extreme solar events, suggesting that tidally-triggered magneto-Rossby waves are the dominant factor governing their occurrence. The high correlation (0.8) implies that the synchronization of the solar dynamo by planetary tidal forces is a robust physical mechanism.

The authors emphasize that the model explains why extreme events can occur outside the solar maximum: the tidal forcing can reach high values even when the sunspot number (and thus the toroidal field) is relatively low, provided the field is not so strong as to suppress the wave excitation.

Regarding the Carrington event, the paper posits a specific mechanism where the steady accumulation of Rossby wave energy during a period of rising magnetic field, followed by a "kick" at the field's peak, triggers the event. The authors note that while the results are encouraging, the parameterization is a first step and requires further refinement. They explicitly state that forecasts for the remainder of Cycle 25 should be treated with "great caution," acknowledging the inherent uncertainties in predicting the toroidal field evolution. Future work is identified as the need to compute the magnetic field self-consistently within dynamo simulations rather than inferring it from sunspot numbers.