Tidal triggers and the predictability of solar activity

Abstract

Magneto-Rossby waves in the solar tachocline are currently considered to be one of the main determinants of solar activity. In particular, they can give rise to the quasi-biennial oscillation (QBO). The latter was recently shown to be dominated by a phase-stable period of around 1.7 years. By analyzing 72 ground-level enhancement (GLE) events and 37 S-flares, we determine that this period is close to 1.723 years. This, in turn, is the dominant beat between the periods of the spring tides of the tidally dominant planets Venus, Earth, and Jupiter, which are suspected to synchronize not only the QBO, but also the 11.07-year Schwabe cycle. We demonstrate that recent events, such as the solar storm of 2024 May 10 and the strong X-flare of 2026 February 1, align well with maxima of the tidal forcing. By contrast, the Carrington event (1959 September 1) does not fit this pattern.

Figures (6)

• Figure 1: Analysis of GLE data. (a) Distribution of 72 events (green open circles) observed between 1956 February and 2025 November, as obtained from https://gle.oulu.fi. The abscissa shows the time $t$ in days starting from 1956 January 1. A few event numbers according to Table 1 are indicated. The green curve shows the optimum cosine function $\cos(2 \pi t/626.67 + 1.46)$ that maximizes the correlation coefficient given in Equation (1). The black curve displays $\cos(2 \pi t/629.29 + 2.01)$ that results from the phase optimization when the theoretical period of $T_0=629.29$ days is fixed beforehand. (b) Correlation coefficient $Corr$ of the 72 GLE events with cosine functions with variable periods $T_0$ and phases $\varphi_0$. For each period $T_0$, the vertical extent emerges when using different phases $\varphi_0$ between 0 and $2 \pi$. (c) Zoomed-in version of (b), showing the maximum of $Corr$ appearing for $T_0=626.67$ days and $\varphi_0=1.46$. If the period is fixed beforehand to $T_0=629.29$ days, we obtain a slightly decreased correlation coefficient for an optimum $\varphi_0=2.01$. These periods and phases are used for defining the green and black curves in (a).
• Figure 2: Same as Figure 1, but for the 37 S-flare events since 1978. Here, the red curve shows the optimum cosine function $\cos(2 \pi t/637.92 + 5.05)$ that maximizes $\rm Corr$ given in Equation (1). The light blue curve shows $\cos(2 \pi t/629.29 + 2.96)$ that results from the optimization of the phase when the theoretical period of $T_0=629.29$ days is fixed beforehand.
• Figure 3: Same as Figure 1, but for the merger of the 72 GLE (green open circles) with the 37 S-flare events (red open circles). Here, the violet curve shows the optimum cosine function $\cos(2 \pi t/632.88 + 3.41)$. The gold curve shows $\cos(2 \pi t/629.29 + 2.58)$ that results from the optimization of the phase when the theoretical period of $T_0=629.29$ days is fixed beforehand.
• Figure 4: GLE and S-flare events, $s^2(t)$, and different time averages of it (a,b). The longer beat period of 11.07 years (corresponding to the Schwabe cycle) can be recognized in the varying height of the spikes. Correlation coefficients of the four curves from (a,b) with the solar events in dependence on the time lag (c). The same, but zoomed in on shorter time lags (d).
• Figure 5: The 2026 February 1 event and its potential predictability. (a) GLE and S-flare events since 1977 November together with $s^2(t)$ and the three optimized 629.29-day periodic functions. The strong X-flare of 2026 February 1 is added as a red triangle. (b) Details of (a) with the dates of the maxima of the four curves indicated. (c) Modification of (b) showing the curves with optimized phases $\varphi_0$and periods $T_0$. The dashed green curve with $\varphi_0=2.19$ would result when using the correlation function without denominator. The dotted green line, with the erroneous phase $\varphi_0=1.88$, was given in Stefani2025. The phase difference corresponds to the time shift of 31 day by which the prediction for the early 2026 events was off.