Jie Jiang1, Robert H. Cameron2, & Manfred Schüssler2
1 Key Laboratory of Solar Activity, National Astronomical Observatories, Chinese Academy of Sciences
2 Max-Planck-Institut für Sonnensystemforschung, Germany
The Sun’s current activity Cycle 24 is the weakest in a century, preceded by an unusually deep minimum. Since the strength of a cycle is largely determined by the amplitude of the polar fields (the axial dipole moment) during the preceding minimum1, an explanation for the weakness of Cycle 24 is equivalent to explaining the weak polar field during the minimum of Cycle 23.
Surface flux transport2 (SFT) simulations has so far failed to reproduce the evolution of the polar fields during Cycle 23 unless ad-hoc assumptions (e.g., meridional flow variations) were introduced. An important component, i.e., the random scatter of the magnetic region tilt angles, was not taken into account in these studies. We made a first attempt to simulate the evolution of the large-scale magnetic field during Cycle 23 with a SFT model that includes the actual tilt angles of bipolar regions of Cycle 23 from daily magnetic maps of SoHO/MDI3. For more details, please refer to Ref. .
Figure 1 | Time evolution of the solar axial dipole moment. The curves correspond, respectively, to observed SoHO/MDI magnetic maps (black), a simulation using the actual tilt angles of bipolar magnetic regions (red), and a simulation using tilt angles according to a fitted latitude dependence (Joy’s law; blue).
Figure 2 | Cumulative contributions in latitudinal distance from the equator of magnetic regions to the change of the axial dipole moment since 1996. Results are given assuming tilt angles according to Joy’s law (solid curve) and for the actual individual tilt angles (dashed curve).
The simulation based on the actual tilt angles follows the observed evolution of the axial dipole moment well within the error range. In contrast, employing Joy’s law for the tilt angles leads to a much too strong axial dipole moment in the declining and minimum phases of Cycle 23. The results are displayed in Figure 1. The reason for the weaker axial dipole moment based on the actual tilt angles can be illustrated by the cumulative contributions of magnetic regions to the change of the dipole moment as a function of their emergence latitude, which is shown in Figure 2. The normalized cumulated contribution with the actual tilt angles closely follows that based on Joy’s law above 10 degrees latitude, but diverges near the equator. The actual tilt angles of magnetic regions emerging near the equator statistically deviate strongly from Joy’s law, which causes the total change of the dipole moment since 1996 to be reduced by about 40%.
Figure 3 | SoHO/MDI magnetograms of the active region AR10696 taken on 2004 November 5 (left panel) and 2004 December 2 (right panel, after one solar rotation, then denominated AR10708), respectively. Owing to its near-equator emergence, high tilt, and abnormal polarity orientation in the north/south direction, the region significantly weakened the axial dipole moment.
A typical example is AR10696. It was highly tilted in the north-south direction with the “wrong” orientation, i.e., opposite to the majority of the magnetic regions during Cycle 23. Magnetic maps for this region are shown in Figure 3. Since it emerged near the equator, a large amount of negative flux diffused across the equator, which significantly reduced the axial dipole moment in the descending phase of the cycle5. The polar magnetic flux around activity minima is typically equivalent to only one big bipolar magnetic region. Hence, a few bipolar regions with “wrong” north-south orientation near the equator can have a remarkable impact on the axial dipole field at the minimum.
In summary, our SFT simulations indicate that the deep minimum of Cycle 23 and thus the weak Cycle 24 result from a number of bigger bipolar regions emerging at low latitudes with “wrong” orientation, which impaired the growth of the polar field. The emergence of such bipolar regions appears largely random, which imposes a strong limit on the predictability of solar cycle strength. No reliable prediction can be made until the amplitude of the polar fields is established around solar minimum.
 Cameron, R. H., & Schüssler, M., 2015, Sci, 347, 1333
 Jiang, J., Hathaway, D. H., Cameron, R. H., et al., 2014, SSRv, 186, 491
 Li, J., & Ulrich, R. K., 2012, ApJ, 758, 115
 Jiang, J., Cameron, R. H., & Schüssler, M., 2015, ApJL, 808, L28 (arXiv: 1507.01764)
 Cameron, R. H., Dasi-Espuig, M., Jiang, J., Işık, E., Schmitt, D., & Schüssler, M., 2013, A&A, 557, A141