Addressing the open flux problem with a non-spherical solar coronal magnetic field model

Abstract

The coronal magnetic field plays a fundamental role in governing coronal activities, driving space-weather events, and shaping the heliosphere. Due to a lack of direct observations, extrapolation models such as the Potential Field Source Surface (PFSS) model become the primary method to obtain the three-dimensional magnetic field distribution in the corona. However, the PFSS model cannot solve the long-standing open-flux problem, in which the extrapolated open magnetic flux is significantly lower than that inferred from in-situ measurements. To address this issue, we develop an innovative Non-Spherical Potential Field (NSPF) model. The model introduces a Non-Spherical Source Surface (NSSS) defined as an isosurface of the total magnetic field. The NSSS naturally forms concave structures beneath external current sheets, enabling the model to generate substantially more open magnetic flux while yielding a physically plausible distribution of open field regions. As a result, the NSPF model successfully reproduces complex coronal magnetic topologies, interplanetary magnetic field properties, and solar wind source mappings. Our refined coronal magnetic model provides a proper foundation for future research on solar and heliospheric magnetic coupling.

Figures (6)

• Figure 1: The structure of the NSPF model. The model comprises three concentric layers: (1) a potential field layer; (2) a current sheet layer; (3) an interplanetary layer. The interface between the potential field and current sheet layers is the non-spherical source surface, while the interface between the current sheet and interplanetary layers is the exit sphere (located at 10$R_\odot$). Magnetic field lines and layer boundaries are labeled.
• Figure 2: Illustration of the workflow of the NSPF model. (a) extraction of the NSSS from a potential field-layer magnetic field computed with a spherical source surface; (b) recalculation of the potential field-layer magnetic field under the NSSS; (c) computation of the magnetic field in the current sheet layer and the IMF; and (d) optional iteration of the NSSS to match the observed open magnetic flux.
• Figure 3: Model results compared with coronagraph observations. Panels (a–c) show NSPF models with initial source surface radii of 3.0 $R_{\odot}$, 2.5 $R_{\odot}$, and 2.2 $R_{\odot}$, respectively. Panels (d–f) show PFSS+PFCS models with source surface radii of 2.5 $R_{\odot}$, 2.0 $R_{\odot}$, and 1.5 $R_{\odot}$. In each panel, background images are from SDO/AIA 171 $\AA$ and SOHO/LASCO C2, taken on 2024 March 28 at 02:04 UT. The colors of magnetic field lines indicate their polarities. The silver curves represent the boundary of the source surface projected on the image plane. Panel (i) shows the background images, the yellow arc and arrows highlight the face-on HCS and separated streamers, respectively. The yellow arrows in panels (a-f) also refer to the separated streamers.
• Figure 4: Comparison between the modeled open-field maps and the SDO/AIA Carrington map. The background image is taken from the SDO/AIA 193 $\AA$ Carrington map dataset SDO_AIA_CAR_MAP. Red and blue shading indicate positive and negative open-field regions derived from the models, respectively. Panels (a–c) show NSPF models with the initial source surface radii of 3.0 $R_{\odot}$, 2.5 $R_{\odot}$, and 2.2 $R_{\odot}$, while panels (d–f) show PFSS + PFCS models with source surface radii of 2.5 $R_{\odot}$, 2.0 $R_{\odot}$, and 1.5 $R_{\odot}$.
• Figure 5: Comparison between the modeled IMF and PSP's in-situ measurements. (a) NSPF models vs. observations. (b) PFSS+PFCS models vs. observations. (c) PFSS models vs. observations. In each panel, the black solid line denotes the observed IMF, while the colored dashed lines represent the modeled IMF obtained from models with different (initial) source surface heights, as indicated in the legend. The text annotations indicate the performance metrics for each model.