Magnetic Topology and Loop Statistics in Observed Coronal Holes Using Potential Field Modeling

TL;DR

This work analyzes 702 observed coronal holes using PFSS extrapolations to study magnetic topology and loop statistics and to identify why PFSS sometimes fails to reproduce observed coronal holes. The authors combine CATCH coronal hole boundaries with SDO/HMI photospheric maps and perform high-resolution PFSS modeling with a fixed source surface at $R_s = 2.5R_{\odot}$, tracing loops down to $H \le 3.48\mathrm{Mm}$ and comparing open-field regions to observations via a Jaccard index. They find that low-lying loops in coronal holes are smaller and narrower than in quiet Sun and that the median height of low loops correlates strongly with the mean flux density $|B_s|$; coronal holes also host many high loops that extend far into the corona, complicating their interpretation as open fields under a fixed $R_s$. The results indicate fundamental limitations of universal PFSS parameterization for coronal holes and suggest region-dependent source-surface heights or more sophisticated boundary conditions to improve coronal and heliospheric field models, with implications for space weather forecasting.

Abstract

Potential Field Source Surface (PFSS) models are widely used to study the solar corona and form the basis for solar wind forecasting, yet often fail to reproduce observed properties of coronal holes. We analyze 702 observed coronal holes between 2010 and 2019 and compute corresponding PFSS magnetic field extrapolations to examine their magnetic topology and loop statistics, comparing them with quiet Sun regions. Our goal is to determine how observed coronal holes are represented in a PFSS model and to identify sources of known discrepancies. We find that low-lying loops covering the weak, balanced background field in coronal holes are statistically smaller and narrower than in quiet Sun regions, with a median height strongly correlated to the coronal holes mean magnetic flux density (cc_Pearson = 0.81). This suggests that at low altitudes, the coronal hole magnetic topology is primarily governed by its flux density, unlike in quiet Sun regions. Coronal holes also contain loops extending much higher into the corona than typical quiet Sun loops, although it is unclear if these are truly closed or reflect source surface height limitations. Overall, differences in modeled magnetic structures of coronal holes and quiet Sun regions are evident, even when the PFSS model does not indicate any open fields. These results suggest that observed coronal holes correspond to distinct photospheric magnetic structures, and that discrepancies with PFSS models reflect modeling limitations rather than the absence of coronal holes.

Figures (18)

• Figure 1: Visual overview of the analysis procedure for a selected coronal hole observed on May 29, 2013. The top row shows the extracted coronal hole, and the bottom row shows the corresponding quiet Sun regions. The second column displays open magnetic field lines (black), the third column shows high loops ($H > 3.48$ Mm; blue), and the last column shows low loops ($H \le 3.48$ Mm; red). Cyan contours denote magnetic elements, highlighting the origins of the different loop structures.
• Figure 2: Normalized distribution of the maximum loop height for low (a), high (b) and all loops (c). This is shown for coronal hole loops (green) and quiet Sun loops (orange) with the solid line showing the normalized density (PDF) and the shaded lines showing the cumulative density (CDF). The 80th (P$_{80}$) and 90th (P$_{90}$) percentiles are marked.
• Figure 3: 2D distribution of low-lying loops projected onto the baseline connecting the loop footpoints in polar coordinates. The top panel shows the coronal hole loops, the middle panel the quiet Sun loops and the bottom panel the contour lines from both upper panels. The contour lines correspond to the $60$th, $80$th, $90$th percentiles.
• Figure 4: Same as Figure \ref{['fig:lowloops']} but for high loops instead.
• Figure 5: Median height of low loops ($H \le 3.48$ Mm) as a function of the respective coronal hole (a–c; green) and quiet Sun (d–f; orange) parameters: area ($A$), absolute value of the signed mean magnetic flux density ($|$B$_{\mathrm{s}} |$), and loop fraction ($R_i$). Grey bars indicate the 20th and 80th percentiles of each region. Linear fits are shown for cases with Pearson correlation coefficients exceeding $0.5$.