Chia-Hsien Lin
Department of Space Science and Engineering, National Central University, Taiwan

Coronal holes (CHs) are regions with unbalanced magnetic flux. They have been associated with open magnetic field (OMF) structures and source regions of high-speed solar wind (HSS). However, significant inconsistency between the CHs and the OMF regions and/or source regions of HSS have been reported^[1,2]. Specifically, Huang et al.^[3] found that some CHs do not intersect with OMF regions, indicating that these CHs do not contain OMF lines.

Figure 1| CR2105 CH magnetic field lines computed from the PFSS model. The background is AIA 193 Å synoptic map. The white contours mark the CH boundaries. The arrows in panel (a) point to the CHs with no open field lines. Different field line types are plotted in different panels in different colors, as indicated. The percentages of their numbers in this Carrington Rotation are: (a) OP1 (open field lines):
20.3%; (b) CL10 (closed field lines extending to bright regions): 27.5%; (c) CL11n (closed field lines confined in the same CH): 51.8%; (d) CL11a (closed field lines connecting two CH): 0.5%.

To investigate why some CHs do not contain open field lines despite being predominantly unipolar, we construct the magnetic structures of the coronal holes using the Potential Field Source Surface (PFSS) model^[4]. The magnetic-field structures of the CHs are represented by the field lines traced from the surface upward. The synoptic maps used for the CH identification are constructed from the line-of-sight magnetograms from Helioseismic and Magnetic Imager (HMI) and 193 Å wavelength band images from the Atmospheric Imaging Assembly (AIA), both onboard the Solar Dynamic Observatory (SDO). The time span is from June 2010 to February 2020, corresponding to the Carrington Rotation (CR) 2099 to 2227. As a parallel comparison to check the effect of the current-free assumption in the PFSS model, we use the thermodynamic MHD model distributed by Predictive Science^[5] to compute a set of synthetic coronal synoptic maps during the same time span, and apply the same procedure to compute the magnetic-field structures of the MHD CHs.

Figure 2| CR2105 CH magnetic field lines computed from the MHD model. The background is the synthetic EUV synoptic map. The white contours mark the CH boundaries. The arrows in panel (a) point to the CHs with no open field lines. Different field line types are plotted in different panels in different colors, as indicated. The percentages of their numbers in this Carrington Rotation are (a) OP1 (open field
lines): 73.1%; (b) CL10 (closed field lines extending to bright regions): 15.6%; (c) CL11n (closed field lines confined in the same CH): 11.1%; (d) CL11a (closed field lines connecting two CH): 0.2%.

The results show that the CH magnetic-field structures constructed from both PFSS and MHD models contain a significant percentage of closed field lines extending beyond the boundary of the CH to either a bright region or another CH, and that there are CHs do not contain OMF lines. As an example, Figure 1 shows the PFSS field lines in the CHs in CR2105. The results from the MHD model are shown in Figure 2. Different field-line types are plotted in different panels in different colors as indicated in the panel titles and explained in the captions. There are three CHs without OMF lines in Figure 1a and two in Figure 2a, as pointed out by the white arrows. Of all CHs studied, the percentage of the CHs do not contain OMF lines is 50% for PFSS magnetic field and 17% for MHD model. Such coronal holes would not intersect with OMF regions, and are unlikely to generate high-speed solar wind.

Our statistical analysis indicate that the boundary-crossing field lines are more likely to be found in the lower latitudes during active times. While they tend to locate slightly closer to the CH boundaries than the non-boundary-crossing ones do, nearly 40% (20%) of them in the PFSS (MHD) CH magnetic fields are sufficiently far away from the boundary regions. The CHs without open field lines are often smaller and less unipolar than those with open field lines. The MHD model indicates higher temperature variations along the boundary-crossing field lines than the non-boundary crossing ones.

More details of this study can be found in https://doi.org/10.3847/1538-4357/ac7786 .

References

[1] Obridko, V. N., & Shelting, B. D. 1999, Solar Phys, 187, 185
[2] Huang, G.-H., Lin, C.-H. & Lee, L. C., 2017, Sci Rep, 7, 9488
[3] Huang, G.-H., Lin, C.-H. & Lee, L. C., 2019, ApJ, 874, 45
[4] Schatten, K. H., Wilcox, J. M. & Ness, N. F., Solar Phys, 6, 442
[5] Lionello, R., Linker, J. A. & Miki´c, Z., 2008, ApJ, 690, 902