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A New Multi-Constraint Potential Field Source Surface (PFSS) Extrapolation Model

C. Antonio, I. Chifu, R. Gafeira, J. J. G. Lima

Abstract

The Potential Field Source Surface (PFSS) model is the most used approach for extrapolating the global coronal magnetic field, offering efficiency and strong performance at large scales. However, PFSS assumes a potential coronal field, so it cannot account for distortions from electric currents. More advanced methods, such as nonlinear force-free field (NLFFF) models, can represent these effects but are much more computationally intensive. Recent observational techniques also allow 3D reconstruction of coronal loops, which trace solar magnetic field geometry. This work develops a new approach that constrains the PFSS model using 3D coronal loop information, improving agreement with observations while keeping efficiency. The model is based on PFSS field constraints from photospheric data but allows magnetic field deviations from the potential state within loop-influenced regions, maintaining control over divergence and force-freeness. We adapted NLFFF optimization to the PFSS framework, enabling multiple physical constraints. Our functional includes up to three terms: divergence-free, loop geometry, and force-free. The resulting Python algorithm was tested with synthetic loops, using Carrington rotation 2284 as the lower boundary. This method yields magnetic field solutions that better match the geometry of included loops and controls divergence and force-freeness. Our results show that 3D coronal loop information can be incorporated into PFSS, largely preserving computational efficiency even with many loops. This approach lets PFSS better reflect observed coronal structures without significant computational cost.

A New Multi-Constraint Potential Field Source Surface (PFSS) Extrapolation Model

Abstract

The Potential Field Source Surface (PFSS) model is the most used approach for extrapolating the global coronal magnetic field, offering efficiency and strong performance at large scales. However, PFSS assumes a potential coronal field, so it cannot account for distortions from electric currents. More advanced methods, such as nonlinear force-free field (NLFFF) models, can represent these effects but are much more computationally intensive. Recent observational techniques also allow 3D reconstruction of coronal loops, which trace solar magnetic field geometry. This work develops a new approach that constrains the PFSS model using 3D coronal loop information, improving agreement with observations while keeping efficiency. The model is based on PFSS field constraints from photospheric data but allows magnetic field deviations from the potential state within loop-influenced regions, maintaining control over divergence and force-freeness. We adapted NLFFF optimization to the PFSS framework, enabling multiple physical constraints. Our functional includes up to three terms: divergence-free, loop geometry, and force-free. The resulting Python algorithm was tested with synthetic loops, using Carrington rotation 2284 as the lower boundary. This method yields magnetic field solutions that better match the geometry of included loops and controls divergence and force-freeness. Our results show that 3D coronal loop information can be incorporated into PFSS, largely preserving computational efficiency even with many loops. This approach lets PFSS better reflect observed coronal structures without significant computational cost.
Paper Structure (9 sections, 11 equations, 15 figures, 1 table)

This paper contains 9 sections, 11 equations, 15 figures, 1 table.

Table of Contents

  1. Introduction
  2. The Multi-Constrained PFSS Model
  3. Data
  4. Results and Discussion
  5. Setup I: $N=2$ Followed by a $L_2$ Switch Off
  6. Setup II: $N=3$ Followed by a $L_2$ Switch Off
  7. Finding the Optimal $\xi_2$
  8. Conclusions
  9. Effect of Switching $L_2$ On/Off on the Local $L_1$ and $L_3$

Figures (15)

  • Figure 1: GONG radial magnetic field CR 2284 synoptic map. The map is used as a lower boundary condition for the pfsspy.
  • Figure 2: Contour plot of the pfsspy output radial magnetic field at some height reference equal to r=1.15 R$_{\odot}$.
  • Figure 3: Projection of the selected PFSS loops traced using the pfsspy output magnetic field onto the CR 2284 map radial photospheric magnetic field.
  • Figure 4: Projection of the selected (non-modified) traced loops on SDO/AIA 193 $\AA$ image taken on 2024 May 16 at 13:00 UT.
  • Figure 5: Projection of the modified loops on the SDO/AIA 193 $\AA$ EUV image taken on 2024 May 16 at 13:00 UT. The modified loops, shown in yellow, correspond to those in Fig. \ref{['aia-pfss-original-selected-loops']} whose heights were artificially increased by a factor of 1.4.
  • ...and 10 more figures