M. J. Korpi-Lagg1,3, A. Korpi-Lagg1,2, N. Olspert1, H.-L. Truong1
1. Department of Computer Science, Aalto University, PO Box 15400, FI-00076 Aalto, Finland
2. Max Planck Institute for Solar System Research, Justus-von-Liebig-Weg 3, D-37077 Göttingen, Germany
3. Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, SE-10691 Stockholm, Sweden
Every 11 years the Sun is in a state of minimum magnetic activity. During those quiet phases, the entire solar surface consists of an undisturbed pattern of ~1 Mm2 sized granulation cells with lifetimes in the range of 10 minutes, organized within supergranular, 40 Mm large cells outlined by magnetic fields of kilo-Gauss strength, the so-called network fields. Larger magnetic active regions, which dominate the solar scene during the activity maximum, are absent. But even during solar maximum, more than 90 percent of the solar surface is in the quiet state, apparently indistinguishable from the quiet Sun at solar minimum. In this study we address the question, whether the properties of these quiet regions are really the same throughout the whole activity cycle, or if there are subtle differences. Answering this question sets important constraints on the relative importance of the two dynamo mechanisms believed to operate in the solar convection zone[1,2]: the turbulent small-scale dynamo, responsible for the omnipresent small-scale magnetic fields, and the large-scale dynamo responsible for the solar activity cycle.
The HMI data now cover a time span slightly longer than one activity cycle and provide a unique opportunity to answer this question. We developed a data pipeline which automatically processed the 12-min magnetogram and the 45-sec Dopplergram data. In a first step, the full-disk magnetogram data were tracked for solar rotation and then combined into 8-hr long data cubes. The root-mean-square value of the magnetic field strengths (BRMS) in these cubes was computed on a longitude/latitude grid of 64×64 elements in overlapping patches of 15° in longitude/latitude, containing several supergranular cells including kilo-Gauss network fields at their boundaries. Only the quietest patches of every month, i.e., the ones with the lowest BRMS, located close to disk center, and separated by at least four days were used to populate the plot presented in the left panel of Figure 1.
Figure 1| Left: BRMS computed from the quietest patches including network fields at disk center during Solar Cycle 24. The dots represent the HMI measurements, the solid red lines display the 97% percentile level, the dashed, gray line the mode of a log-normal fit to yearly-binned data moved in a sliding window of 100 days length. Right: Same as left panel, but with BRMS computed for smaller patches excluding the contribution of network fields.
The variation of BRMS computed from those patches with the solar activity cycle is evident. The largest BRMS values occur about 6 months after the maximum of solar activity (April 2014). The rise after 2021 indicates the start of the new Cycle 25. We repeated the analysis for patch sizes of only 1° in longitude/latitude, to exclude the influence of the network fields surrounding the supergranular cells. The resulting plot (right panel of Figure 1) shows no sign of solar cycle variation. The large-scale magnetic fields therefore clearly influence the network fields, whereas the small-scale fields in the center of the supergranular cells are likely to be replenished by the small-scale dynamo.
Figure 2| Butterfly diagram of f-mode energy variations, computed from collapsed ring diagrams. The temporal average has been subtracted from the data, and is shown as the black line in the right panel. Its error bars represent the time-averaged standard deviation of the fluctuations of the f-mode energy around the signal for every bin.
The second aspect addressed in the study relates to the solar cycle variation of the surface gravity waves, the so-called f-mode, computed from the line-of-sight velocity maps. According to theory, the f-mode energy is altered by sub-surface magnetic fields. Therefore, a solar-cycle dependence of the f-mode energy should be a good indicator for the changes of the magnetic field topology in the near-surface shear layer.
We computed the f-mode energy for the quiet 15°-sized patches, presented in Figure 1 (left panel), but this time not only for the patches close to disk center, but also for solar latitudes up to ±60°. This results in a butterfly diagram of the f-mode energy, presented in Figure 2. A variation of the energy is clearly visible: as predicted by theory, the f-mode energy is suppressed during the time of the solar maximum. The highest energy is observed during the minimum in 2010 and 2011, but surprisingly the f-mode energy did not recover to this level at low latitudes during the following minimum around 2020, in contrast to the surface magnetic fields presented in Figure 1 (left panel). This behavior remains enigmatic, and it will be interesting to follow this phenomenon with future HMI measurements.
More details of this study can be found in https://doi.org/10.1051/0004-6361/202243979 .
 Brandenburg, A., & Subramanian, K. 2005, Phys. Rep., 417, 1
 Lites, B. W., Centeno, R., & McIntosh, S. W. 2014, PASJ, 66, S4
 Singh, N. K., Raichur, H., Käpylä, M. J., et al. 2020, Geophys. Astrophys. Fluid Dynam., 114, 196