The cycle in question is the 11-year cycle of solar magnetic activity, and one of the fundamental challenges in solar physics is to understand what leads to its irregularity. It is well-known that the strength of an upcoming cycle is quite well predicted by the strength of the Sun’s polar magnetic field at the preceding activity minimum, or by proxies thereto . But no-one has yet found a reliable way of making predictions earlier in the preceding cycle. Now research is suggesting that this effort may be futile: random fluctuations at the level of individual active regions may be enough to cause the observed variations in polar-field strength at minimum. Earlier predictions may be effectively impossible.
Forming the polar field
Active regions are important here because the net polar field at activity minimum can be traced back to the contributions of many decaying active regions during the preceding cycle. Their magnetic flux is transported poleward through a combination of supergranular convection (gradually breaking up and tearing the strong regions apart) and poleward meridional flow. This process is captured in numerical simulations of surface flux transport (Figure 1; see  for a review).
Active regions tend to contain both positive and negative magnetic polarities roughly equally. It is when these polarities are separated in latitude — so that the region has an axial dipole moment — that a particular active region makes a net contribution to the polar field, of one polarity or the other. In the movie (Figure 1) you can see this process taking place, and you can also see that the polar fields are gradually weakened, because there is a dominant polarity in each hemisphere (the trailing polarity) which is being transported from the activity belt towards the poles. During cycle 24, net positive flux is being transported to the north pole, and net negative flux to the south pole. However, our point here is that this is only a net tendency: individual active regions are often observed to have an axial dipole moment of the “wrong” sign. A good example of this comes from some of our recent work.
Rogue active regions
We used flux transport simulations in  to determine the origin of a particular polar surge observed during cycle 24 (Figure 2). This surge represents the poleward transport of a significant amount of negative, or “wrong polarity” magnetic flux, slowing the reversal of the polar field. By “origin”, we wanted to determine which active regions were the source of this magnetic flux. The simulations (Figure 1) proved ideal for this task, enabling us to repeat the simulation omitting each active region one-at-a-time, so as to isolate its contribution to the polar surge.
The findings were striking: a single active region caused the surge. It emerged at rather high latitude, but most notably had a strongly negative dipole moment. As shown in Figure 2, its two main polarity regions were aligned almost directly north-south, in a highly abnormal orientation. The poleward transport of its northernmost part caused the negative surge. With its extreme opposite dipole moment, we might call this a “rogue” active region.
A lasting contribution?
However, a word of caution is due. Although our rogue region had a significant short-term impact on the polar field, we went on to predict that it will have little effect on the all-important end-of-cycle polar field. This is because, although the region emerged with a strong negative dipole moment, it also emerged at high latitude. As shown in Figure 3, our region would make a much greater net contribution to the polar field if it emerged nearer the equator. This is because producing a net polar field in the northern hemisphere requires an equal amount of opposite polarity flux to be lost across the equator. This important point was first noted (we believe) by R. Giovanelli in the 1980s . The negative surge from our high-latitude region will produce only a transient contribution to the polar field, before the other polarity also arrives at the pole and cancels it out.
What this does suggest, however, is that rogue regions emerging nearer to the equator could very well have a significant influence on the polar field at the following cycle minimum. And indeed, this very theory has been put forward in a recent letter by Jiang et al. . They suggest that a (small) number of low-latitude active regions with the “wrong” orientation were responsible for the very low polar field at the end of cycle 23, compared to cycles 21 and 22.
In summary, the evidence is pointing to a limit for how early we can make cycle predictions. We may simply have to wait for most of the active regions to emerge in a given cycle, before we can be sure that no more rogue regions will emerge and change the outcome. It is rather reminiscent of the perils of long-range weather forecasting; perhaps the butterfly diagram and the butterfly effect have more in common than you might think.
We acknowledge the Leverhulme Trust for funding the ‘Probing the Sun: inside and out’ project upon which this research is based.
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