Role of sunspot latitude versus tilt in determining the polar field and amplitude of the next cycle: Cause of the weak Solar Cycle 20

TL;DR

The study addresses how the polar field and the amplitude of the next solar cycle emerge from sunspot properties within the Babcock–Leighton dynamo framework. By analyzing sunspot area, latitude, and tilt data alongside polar-field proxies across Cycles 15–24, it reveals that the polar field is largely linearly related to sunspot area for most cycles, with notable nonlinear quenching in strong cycles such as 19–20 and 4–5. The strongest predictive power comes from area-tilt combinations (e.g., Area×Tilt or Area×Tilt/Latitude), and tilt variation dominates over latitude variation for Cycles 15–22; Cycle 23–24, however, shows exceptions likely due to a few wrongly tilted BMRs at low latitude, underscoring the need for individual BMR tilt measurements. The results imply that tilt quenching is essential for regulating cycle strength, that cycle memory extends only one cycle, and that improved cycle prediction requires accounting for tilt fluctuations beyond cycle averages.

Abstract

One prominent feature of solar cycle is its irregular variation in its cycle strength, making it challenging to predict the amplitude of the next cycle. Studies show that fluctuations and nonlinearity in generating poloidal field throughout the decay and dispersal of tilted sunspots produce variation in the solar cycle. The flux, latitudinal position, and tilt angle of sunspots are the primary parameters that determine the polar field and, thus, the next solar cycle strength. By analysing the observed sunspots and polar field proxy, we show that the nonlinearity in the poloidal field generation becomes important for strong cycles. Except for strong cycles, we can reasonably predict the polar field at the end of the cycle (and thus the next cycle strength) using the total sunspot area alone. Combining the mean tilt angle and latitude positions with the sunspot area, we can predict the polar field of Cycles 15 -- 24 (or the amplitude of sunspot Cycles 16-25) with reasonable accuracy except for Cycle 23 for which the average tilt angle cannot predict the polar field. For Cycles 15--22, we show that the average tilt angle variation dominates over the latitude variation in determining the polar field of a cycle. In particular, the reduction of tilt in Cycle 19 was the primary cause of the following weak cycle (Cycle 20). Thus, we conclude that tilt quenching is essential in regulating the solar cycle strength in the solar dynamo.

Figures (4)

• Figure 1: Solid black line represents the daily calibrated group area as a function of time from Mandal2020. Dashed red line represents the monthly total sunspot number (International Sunspot Number V2) from WDC-SILSO, Royal Observatory of Belgium, Brussels. The cycle numbers are marked on the plot.
• Figure 2: (a) Polar field strength ($A(t)$ index) at the solar minimum plotted against the total sunspot area (strength) of the same solar cycle for Cycles 15--22. (b) Same as (a), but the amplitude of the next solar cycle as measured by the total sunspot area for Cycles 12--23. The cycle numbers are labeled to correspond to the value of $n$ (horizontal axis). The red dashed line shows a polynomial fit, while the blue solid line represents a linear fit excluding the data point for Cycle 19.
• Figure 3: (a) Strength of cycle $n+1$ versus the strength of cycle $n$ as obtained from the sunspot area data. Note, the sunspot area data is available only from Cycle 12 onward. For earlier times, sunspot number data (V2) have been rescaled to match the sunspot area scale, and these points are shown in gray. (b) The same as (a) but for the reconstructed sunspot number from C$^{14}$ data of Usoskin21 and it is for the cycle average number and not the total number. Here we have 85 cycles and we follow the same convention for numbering the cycles as given in Usoskin21. The oval highlights the data points for which the cycle strength of $n+1$ is significantly lower than that of cycle $n$.
• Figure 4: Polar field strength ($A(t)$ index) at the solar minimum vs the (a) total area divided by the mean latitude of sunspots, (b) total area times the mean tilt angle of sunspots, (c) total area times the mean tilt angle of sunspots divided the mean latitude of sunspots of a cycle.