M. Švanda1,2, A. S. Brun3, Th. Roudier4, & L. Jouve4,3
1 Astronomical Institute, Academy of Sciences of the Czech Republic, Ondřejov, Czech Republic
2 Astronomical Institute, Charles University in Prague, Czech Republic
3 CEA Saclay, France
4 IRAP, Université de Toulouse, France
The properties and origin of the solar cycle are still not well understood. They are nevertheless well described by a class of dynamo models that utilize the redistribution of magnetic flux due to systematic plasma flows, such as convection, differential rotation, supergranular diffusion, and meridional flows. These so called Babcock-Leighton-type (BL) dynamos1,2 have been successful in reproducing the features of solar cycle, including the reversal of the global magnetic field occurring every 11 years, and the propagation of solar activity toward the equator as the cycle progresses. BL dynamos rest entirely on the presence of tilted bipolar magnetic fields, where sunspots usually appear. Grand minima (such as Maunder minimum 1645-1715) are an issue for this class of models, since the needed source terms vanish. There is evidence, however, that solar cycles were present even during these periods3 when almost no spots were seen.
Observers in the Maunder minimum era mostly used smaller refractors, with an estimated angular resolution of 2” at best. Taking into account the seeing, we estimated the resolving power to be around 5”. Therefore they were probably unable to see the tiny spots, i.e., pores. Moreover, there is evidence of a recent secular decrease of solar activity4 when small sunspots become more frequent whereas large spots become rarer5.
So here is an idea: what if during weak cycles during Maunder minimum the photospheric activity was dominated by tiny sunspots — pores — in agreements with ref. 5? The pores would practically be invisible to the observers then and yet, they could serve as agents for the bipolar magnetic regions needed by BL dynamos.
We performed the following test6. We removed all active regions with sunspots (SARs) from observations, leaving in only the pores. We used these pores as proxies for the magnetic field and studied whether there is enough flux to cause global reversal. If these pores do contribute to the reversal, they should follow the solar cycle and display a significant net flux.
Using an automated pipeline, we processed all SOHO/MDI observations and almost all available SDO/HMI observations. We used intensity images to automatically search for the pores outside SARs and magnetograms to assess their magnetic field.
Figure 1 | Top: Magnetic butterfly diagram from MDI and HMI synoptic maps shows the prevailing polarity of the magnetic field in polar caps, reversals of the global magnetic field and the flux transported to the polar regions from the relics of the active regions. Bottom: Magnetic butterfly diagram of the pores outside active regions. At the top and the bottom the polar cap from magnetic butterfly from above is inserted. The intensity of the average magnetic field in the inserts is boosted by the factor of 5 to make them visible. This figure clearly shows that the pores follow the cycle. The inset in the lower panel demonstrates the mixed polarity in magnification.
We found that the pores outside SARs do follow the solar cycle (Figure 1). They seem to broaden the activity belt. At first glance, their polarity seems to be mixed and with no obvious bias — such bias appears only after averaging in time. There is a net magnetic flux of ~1021 Mx per hemisphere in those pores alone, which (if transported towards poles) is almost sufficient to cause a reversal of polar caps in a weak cycle. The hemispheric polarity bias was the right one to contribute to the reversal.
Figure 2 | Binned index of match of the flux polarity in pores and their closest SAR as a function of distance from the closest SAR and time. One can see that the pores in the intermediate distances 40–100 Mm from closest SAR depict systematically opposite polarity to that SAR.
We further investigated the origin of these pores. We found that those with polarity bias are located at distances 40 to 100 (possibly up to 140) Mm from the flux-weighted center of the closest SARs (Figure 2). We further found that a vast majority of these pores form in weaker bipolar active regions located to the west of the closest SARs (hence closer to their trailing parts). The locations of the pores do not necessarily coincide with previously existing, strong SARs (within 4 rotations).
We speculate that these pores originate from “failed” emergence of sub-surface flux ropes, which either did not reach the surface or only partly reached the surface. They were then dispersed to the neighborhood by large-scale convection, e.g., giant cells. This would explain their typical distance (40 to 100 Mm) from the closest SARs.
We therefore speculate that during the grand-minima, a weak source term akin to a BL mechanism was possibly operating, as there were organized magnetic fields present on the Sun.
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 Švanda, M., Brun, A. S., Roudier, Th., & Jouve, L., 2016, A&A, in press, arXiv: 1511.06894