Graduate Institute of Space Science, National Central University, Taoyuan, Taiwan
Solar open magnetic flux (OMF) regions are the regions with magnetic field lines extending far away from the Sun. They represent the largest-scale magnetic-field structure of the Sun. Their “open” magnetic field configuration allows plasma to flow into the interplanetary space. Therefore, they are major source regions for high-speed solar wind streams (HSS), which can cause significant geomagnetic activity at the Earth. Observed in soft X-ray and certain extreme ultraviolet (EUV) wavelength, OMF regions often appear dark, and are called coronal holes.
Figure 1| Panels (a)–(c) are the time maps of unsigned OMF, outward OMF and inward OMF, respectively. Panel (d) shows the sunspot butterfly diagram. Panel (e) compares the total unsigned OMF area with sunspot number (SSN). Panel (f) compares the low-latitude unsigned OMF area with SSN.
Huang et al.  aims to examine the solar-cycle variation of the area and polarities of OMF regions at different latitudes. The data are the radial-field synoptic maps from May 1976 to December 2014 (Carrington Rotation 2099 to 2158) from Wilcox Solar Observatory (WSO). The OMF regions are identified by (1) constructing a 3D coronal magnetic field using Potential Field Source Surface (PFSS) model, and (2) identifying the OMF regions as the footpoints of the magnetic field lines that extend beyond 2.5R⊙ from the Sun’s center. After the OMF regions are identified in all synoptic maps, they construct the unsigned, outward and inward OMF maps by summing the area of the unsigned, outward and inward open magnetic field over longitude in each Carrington Rotation. The maps are shown in Figure 1(a) – (c). The sunspot number (SSN) time curve is compared with the total area of unsigned OMF area in panel (e) and with the low-latitude area in panel (f). Comparing the OMF maps with the SSN time curve, we can see that during the sunspot rising phase, the outward and inward open fluxes perform pole-to-pole trans-equatorial (PPTE) migrations in opposite directions, leading to the polarity reversal in the two hemispheres.
Figure 2| Panel (a) is the time map of the outward OMF area. The black arrows indicate the direction of 4 solar cycle evolution. The blue circle marks an example of locally generated open flux area. Total area of outward OMF area in different latitudinal ranges as a function of time are plotted in panels (b)–(c). Red and blue curves represent northern and southern hemispheres, respectively. Dashed and solid lines are to distinguish the curves before and after crossing the equator in each solar cycle. The maximum total area in each hemisphere in each solar cycle is printed above the corresponding peak.
The cause of the migration pattern can be better understood by examining Figure 2, which uses the outward OMF map as an example to show the temporal variation of the area in different latitude ranges. The black arrows in panel (a) indicate the direction of solar cycle evolution. The maximum total area in each hemisphere in each solar cycle is printed above the corresponding peak. We can deduce from Figure 2 that the PPTE migration consists of three parts: (1) open flux area migrating across the equator; (2) new open flux areas generated in the low latitude and migrating poleward; and (3) new open flux areas locally generated in the polar region. The comparisons in Figure 1(e) and (f) show that SSN profile is negatively correlated with the total OMF area but is positively correlated with the low-latitude OMF area.
 Krieger, A. S., Timothy, A. F. & Roelof, E. C., 1973, Solar Physics, 29, 505
 Obridko, V. N. & Shelting, B. D., 1999, Solar Physics, 187, 185
 Huang, G.-H., Lin, C.-H. & Lee, L. C., 2017, Scientific Reports , 7, 9488