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

TL;DR

This paper introduces a novel multi-constraint PFSS extrapolation model that integrates 3D coronal loop data to improve magnetic field accuracy while maintaining computational efficiency.

Contribution

It develops a new PFSS-based method incorporating multiple physical constraints from 3D coronal loops, bridging the gap between simple potential models and complex NLFFF approaches.

Findings

Enhanced agreement with observed coronal loops

Maintains computational efficiency with multiple constraints

Better control over divergence and force-freeness

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.