Bidya Binay Karak¹, Sudip Mandal², and Dipankar Banerjee²

1. Department of Physics, Indian Institute of Technology (BHU), Varanasi, India
2. Indian Institute of Astrophysics, Bangalore, India

One of the puzzling features of the solar cycle is that most of the cycles (particularly, last three consecutive cycles) have double peaks around their maxima^[1,2]. These peaks are also popularly known as Gnevyshev peaks, and the gap between these two peaks is known as the Gnevyshev gap^[3]. Gnevyshev peaks are not an artifact of observational defects, but real features of the solar cycle. Also, outside the maximum, the solar cycle show occasional spikes and dips^[4]. These features are not correlated in hemispheres as clearly seen in the northern and southern hemisphere sunspot area data (Figure 1).

Figure 1| Demonstrating the double peaks and skipes in the observed solar cycle as measured in the sunspot area data: https://solarscience.msfc.nasa.gov/greenwch.shtml.

In our publication^[5], we have modelled these double peaks and spikes using a kinematic Babcock-Leighton dynamo model. We show that inherent fluctuations in the Babcock-Leighton process (mainly due to the scatters in the sunspot tilts around Joy’s law) can momentarily reduce the polar field. If the decrease of the polar field near the solar minimum is abrupt, then this promotes a double peak in the next cycle. However, if the fluctuations in the polar field occur outside the solar minimum, then these produce spike or dip in the next solar cycle.

By including stochastic fluctuations in the Babcock-Leighton alpha (poloidal source) in our axisymmetric kinematic dynamo model, we successfully reproduce double peaks and spikes similar to those observed in the solar cycle (see Figure 2). These results are robust in a wide range of parameters of the model. However, if the turbulent diffusivity of the magnetic field is increased to a very high value (>5×10¹² cm² s^-1 for the parameters used in the model for Figure 2), then the efficient diffusion tries to smooth out the fluctuations acquired in the polar field and we tend to see infrequent and less prominent double peaks.

Figure 2| Sunspot number obtained from our dynamo model, and reproduced from Ref [5]. Dotted (black), red and blue correspond to the total, northern, and southern hemispheric sunspot numbers, respectively. Cycles are numbered with labels M#.

Finally, we provide an observational support for our theoretical idea by identifying the fluctuations in the Babcock-Leighton process in the observed magnetic field. We show that these abrupt fluctuations in the polar field as seen in the magnetic field data (Figure 3) are the direct cause of the double peaks and spikes in the next cycle. In Figure 3, polar surges as marked by C₁ (the southern hemisphere) and C₂ (northern hemisphere) in cycle 21 possibly caused the double-peaked in cycle 22 around 1990 (Figure 1). Similarly, the fluctuations marked by C₃ and C₄ in the southern and northern hemispheres are the cause of the double peaks in cycle 23. Also a little dip in the polar field of cycle 23 as marked by C₅ in the southern hemisphere produces a halt in the rising phase of sunspot cycle 24 of the same hemisphere.

Figure 3| (a) Surface radial magnetic field obtained from the National Solar Observatory (NSO/KPVT and SOLIS, thanks to Sanjay Gosain for providing the data). The blue and red represent the negative and the positive fields. (b) The mean polar field (from 55° latitude to pole) from the Wilcox Solar Observatory (WSO; data source: http://wso.stanford.edu/Polar.html). Reproduced from Ref. [5].

Based on our understanding, we predict that in the northern hemisphere of the forthcoming solar cycle 25 will have a dip in the rising phase because we already see a prominent opposite polarity surge in the northern hemisphere polar field of cycle 24 (see the label C₁₀ in Figure 3).

In conclusion, we show that double peaks (Gnevyshev peaks), spikes and dips all are caused by the abrupt fluctuations in the Babcock-Leighton process of generating poloidal field as seen in the observations.

References

[1] Norton, A. A., & Gallagher, J. C. 2010, Solar Phys., 261, 193
[2] Georgieva, K. 2011, ISRN Astronomy and Astrophysics, 437838
[3] Gnevyshev, M. N. 1967, Solar Phys., 1, 107
[4] McIntosh, S. W., Leamon, R. J., Krista, L. D., et al. 2015, Nature Comm., 6, 6491
[5] Karak, B. B., Mandal, S., & Banerjee, D. 2018, ApJ, in press: arXiv:1808.03922