Variation of the sunspot area during the rising and declining phases of the solar cycle supports the toroidal flux loss due to flux emergence

TL;DR

The study tests a nonlinear toroidal flux-loss model for the solar dynamo, predicting larger sunspots in the rising phase and a cycle-strength–independent decline. By analyzing sunspot-group areas across 13 cycles and BMR flux for Cycles 23–24, it shows that the rising phase yields larger, cycle-dependent spots, while the decline phase converges to similar properties irrespective of cycle strength, especially in the last three years. The rising-phase results are complemented by higher mean/median BMR flux in Cycle 23–24, supporting flux emergence as the key loss mechanism. Overall, the findings provide observational support for flux-loss through flux emergence as a fundamental aspect of solar cycle evolution, with implications for space-weather forecasting.

Abstract

Sunspots are obvious observable manifestations of the toroidal magnetic field generated through the dynamo in the convection zone. They appear in different sizes, having a wide distribution in their area. We analyse the sunspot group area of the past 13 cycles and the Bipolar Magnetic Region (BMR) flux for Cycles 23 and 24 to explore their area and flux distributions and connect with the theory. We find that, in general, the group area and BMR flux are statistically larger in the rising phase than in the declining phase of the solar cycle. This implies that the rising phase of the solar cycle is prone to drive more intense space weather. We further show that the mean and median of the area distribution during the rising phase are dependent on cycle strength. However, the distribution mean and median are cycle strength-independent or weakly dependent during the decline phases of the solar cycles, particularly during the last three years when the latitudinal bands of all cycles migrate towards the equator along the same trajectory. These results support the theoretical model of nonlinear flux loss due to flux emergence, which explains why solar cycles rise differently but decay similarly.

Figures (6)

• Figure 1: The mean of the absolute latitudes of sunspot groups in each year ($\lambda_c$) verses the number of sunspot groups in that year. Different curves are for different cycles. One year data at the beginning and at the end of each cycle are excluded in this analysis. Note that a cycle begins with a high value of $\lambda_c$ on the right side of the plot and with the progress of a cycle when sunspot latitude band migrates equatorward, the trajectory moves towards the left. The dashed line (having sunspot number $= 25 \lambda_c - 200$) guides the uniform decay of all cycles. The dark parts of the curves highlight the last three years of each cycle during which all cycles fall at the same rate.
• Figure 2: Distributions of the daily total sunspot areas (in $\mu\mathrm{Hem}$) during the rising (red) and declining (blue) phases of the solar cycle. The rising-phase distribution is best fitted by a Weibull function ($k = 1.335 \pm 0.010$, $\lambda = 1703.14 \pm 12.42\,\mu\mathrm{Hem}$), while the declining-phase distribution is better described by an exponential model ($\lambda = (9.36 \pm 0.06) \times 10^{-4}\,\mu\mathrm{Hem}^{-1}$).
• Figure 3: Scatter plots of the (a) mean and (b) median area of sunspot groups computed over the rising phase verses the same over the decline phase. Cycle numbers are assigned to each data points. The linear Pearson correlation coefficients ($r$) and $p$ values are printed on each subplot.
• Figure 4: Top two panels: Mean area of sunspot groups during the (a) rising phase and (b) declining phase versus the cycle strength (measured by the total group area in $\mu$Hem) for Solar Cycles 12–24. Points are labelled by the cycle number. The dashed line represents the best linear fit to the data. The bottom two panels are the same as the top ones, but for the median area. The linear Pearson correlation value and $p$ are printed on each panel. The Spearman rank correlation coefficients for the four panels are 0.71 ($p = 0.01$), 0.62 ($p = 0.02$), 0.56 ($p = 0.05$), and 0.41 ($p = 0.16$), respectively.
• Figure 5: The same as the bottom panels of Figure \ref{['fig:rd_strength']} but from the sunspot areas during the last 3 years (excluding the final year) of the decline phase of the cycle.