Bidya Binay Karak¹ & Mark Miesch²
1. Indian Institute of Technology (BHU), Varanasi, India
2. High Altitude Observatory, NCAR, Boulder, CO 80301, USA

The solar magnetic cycle is not regular, and the individual cycle strength and duration vary cycle-to-cycle. The extreme example of this irregularity is the Maunder minimum in the 17th century when sunspot cycle went to a very low value. We explore the cause of this solar cycle irregularities using a novel 3D kinematic Babcock–Leighton dynamo model^[1]. This model is an updated version of the original model developed by M. Miesch and his colleagues^[2]. In this updated model, based on the toroidal flux at the base of the convection zone, bipolar magnetic regions (BMRs) are produced with statistical properties obtained from observed distributions.

Figure 1| Result from a dynamo simulation with Gaussian tilt scatter of σ_δ = 15° around Joy’s law (Ref. 1): BMR tilts versus latitudes (λ) shown only from the northern hemisphere data. The solid, dashed, and dotted lines respectively show the actual Joy’s law: δ = 35°sin λ, the mean BMR tilts in each latitudes, and the zero line. Note that the dashed line deviates from Joy’s law (solid line) due to the non- linear quenching introduced in it.

We find that a little quenching in the BMR tilt, as shown in Figure 1, is sufficient to stabilize the dynamo growth. The randomness and nonlinearity in the BMR emergences make the poloidal field unequal and cause some variability in the solar cycle (Figure 2a). However, when observed Gaussian scatter of BMR tilts around Joy’s law³ with a standard deviation (σ_δ) of 15° is considered, our model produces a variation in the solar cycle, including north-south asymmetry comparable to the observations (Figure 2b).

Figure 2| Time series of the monthly sunspot number (which is same as the BMR number) from the simulation (a) without tilt scatter (Ref. 1), with Gaussian scatter of (b) σ_δ = 15° (Run B10), and (c) σ_δ = 30° (Run B11). The horizontal line shows the mean of peaks of the monthly BMRs obtained for last 13 observed solar cycles. Arrows in (c) represent the locations of grand minima.

The morphology of magnetic fields closely resembles observations (Figure 3), in particular, the surface radial field possesses a more mixed polarity field that is a consequence of the wrong tilt (Figures 1 and 3). The magnetic field is largely antisymmetric across the equator (dipolar) only near the solar minimum (Figure 3). The mean parity of surface radial field deviates most strongly from the antisymmetric mode during cycle maxima. This is again consistent with the solar data⁴.

Figure 3| Results from simulation with σ_δ = 15° (Run B10 of Ref. 1): temporal variations of (a) azimuthal-averaged surface radial field ⟨B_r(R,θ,φ)⟩_φ, and (b) latitudes of BMRs; red points show the wrongly tilted BMRs; green/solid and blue/dashed lines show symmetric parities, computed over the four years of surface B_r and the bottom B_φ, respectively.

Observed scatter also produces grand minima. In 11,650 years of simulation, 17 grand minima are detected and 11% of its time the model remained in these grand minima, while these numbers for the Sun are 27 and 17%, respectively^[5]. When we double the tilt scatter, the model produces more variability in the solar cycle (Figure 2c) and also produces correct statistics of grand minima. A downward magnetic pumping of speed about 20 m s⁻¹ in the upper convection zone suppress the horizontal magnetic field through the surface and thereby helps to achieve 11-year magnetic cycle using the observed BMR flux distribution, even at the high diffusivity (∼ 10¹² cm² s⁻¹).

References

[1] Karak, B. B., & Miesch, M. S., 2017, ApJ, 847, 69
[2] Miesch, M. S., & Teweldebirhan, K. 2016, SSRv
[3] Stenflo, J. O., & Kosovichev, A. G. 2012, ApJ, 745, 129
[4] DeRosa, M. L., Brun, A. S., & Hoeksema, J. T. 2012, ApJ, 757, 96
[5] Usoskin, I. G., Solanki, S. K., & Kovaltsov, G. A. 2007, A&A, 471, 301