Akash Biswas1, Bidya Binay Karak1, and Robert Cameron2
1 Department of Physics, Indian Institute of Technology (Banaras Hindu University), Varanasi 221005, India
2 Max Planck Institute for Solar System Research, Justus-Von-Liebig-Weg 3, D-37077, Göttingen, Germany
The 11-year activity cycle of the Sun’s magnetic field is one of its most striking features. The space weather conditions of the heliosphere are coupled with the phases of the solar cycles, making it one of the most important topics of research in modern-day astrophysics. The activity of the solar cycles is generally measured by tracking the number of sunspots, dark regions on the solar surface with an enhanced magnetic field concentration. Extreme space weather events, like the coronal mass ejections or solar flares, are very often originated from the regions of the solar surface having sunspot groups.
One obvious feature of the solar cycles is the large variations in the strength of the cycles. The strong cycles rise rapidly and peak early and on the other hand, the weak cycles rise slowly and reach their peaks lately during their evolution. Interestingly, extreme space weather events are as common during the decline of a strong cycle as they are during the decline of a weak cycle.
Long-term observation of the various statistical properties like the central latitude and width of the annual distribution of the sunspots shows that different cycles possess different statistical properties depending on their strengths during their rise phase. However, all the cycles decay with similar statistical properties. This can be clearly seen in Figure 1. The top panel of the figure shows the plots from observational data while the bottom panel presents the results from a simulation which reproduces most of the features of the observational results (top panel). The solar cycles start having sunspots at higher latitudes (right sides of the curves), and as the cycles evolve, the sunspot migrate towards the equator (left sides of the curves). Notice the widely different trajectories of cycles during their rising phase, but the trajectories converge quickly after the cycles reach the peak and all the cycles decline in the same way. Explaining the physical process behind this phenomenon has been a puzzle for many decades since it was first pointed out in 1955 by renowned astronomer M. Waldmeier.
Figure 1| The top panel (a,b) of the plot is from observations , and the bottom panel (c,d) is from dynamo simulations with flux loss mechanism due to magnetic buoyancy . The trajectories of the cycles are represented in terms of (a,c) the annual number of sunspots plotted against the central latitude of the annual sunspot distribution, and in (b,d) the FWHM of the distribution is plotted against the central latitude.
In our study, we propose an adequate solution to this puzzle by using solar dynamo simulations. The solar dynamo is believed to be the underlying mechanism that drives the solar cycles. Generation of strong toroidal magnetic fields in the solar convection zone is one of the important aspects of the dynamo. Once the toroidal fields become sufficiently strong, they become buoyant and start rising through the convection zone eventually piercing out of the solar surface giving birth to sunspots. During this process of sunspot production, a significant amount of magnetic flux is lost from the solar interior.
Incorporating this nonlinear mechanism of toroidal flux loss due to magnetic buoyancy in the dynamo simulations (using the SURYA code), we show that the strong cycles, that rise rapidly having many sunspot eruptions lose significant portion of its toroidal field early in their evolution, however the weaker cycles, that rise slowly having few sunspots deplete its toroidal field at a low pace. This nonlinear mechanism of toroidal flux loss makes sure that all the cycles possess same amount of toroidal flux during their decline phase, hence all the cycles decline in a similar manner.
 Cameron, R. H., & Schussler, M. 2016, Astron. Astrophys., 591, A46
 Biswas A., Karak B. B., Cameron, R. 2022, Phys. Rev. Lett., 129, 24
 Waldmeier, M. 1935, Astronomische Mitteilungen der Eidgenossischen Sternwarte Zurich, 14, 105
 Parker, E. N. 1955, Astrophys. J., 121, 491
 Chatterjee, P., Nandy, D., & Choudhuri, A. R. 2004, Astrophys. J., 427, 1019