Recently, the National Space Science Center of the Chinese Academy of Sciences has conducted research on the problem of determining the surface geometric parameters of the coronal magnetic field source. It analyzed the forward and inverse problems of the potential field source surface model (PFSS) from the perspective of free boundary problems and shape optimization, and combined with the near-solar in-situ observations of the PSP satellite to construct a source surface radius optimization algorithm. This study used ACE satellite observations for independent verification to reveal the overall trend of optimal source surface radius changes with solar activity and the trade-off relationship between different observation indicators.
The PFSS model is a commonly used model for large-scale coronal magnetic field research. The source surface serves as the outer boundary of the model's solution domain, where the magnetic field is constrained to be radial, thereby approximately describing the magnetic field lines open to the heliosphere. The source surface radius is a key geometric parameter of the PFSS model, which affects the open magnetic flux, coronal hole boundary, heliosphere current sheet structure and solar wind source region position given by the model. Traditional research usually uses 2.5 solar radius, but more and more observations show that the optimal values corresponding to different solar activity stages, different magnetic maps and different evaluation indicators are different. Therefore, it is necessary to study the optimal value and establish a corresponding optimization algorithm.
Based on the in-situ magnetic field and solar wind speed observations during the first 19 perihelions of the PSP, the research team constructed a numerical optimization algorithm for the source surface radius. In the 25th solar cycle, the optimal source surface radius obtained by PSP observation and inversion generally shows an increasing trend in the radius value during the rising stage in low solar activity years. The source surface radius evolution obtained by the ACE satellite near the Sun-Earth L1 point and the PSP results show a similar overall trend, achieving a generalization test of the algorithm. In addition, the optimal source surface radius does not change monotonically with solar activity, and the results corresponding to some PSP Encounters are lower than those in adjacent periods. These local deviations are related to transient activities such as current sheet structures or coronal mass ejections.
In order to explain the optimization results, the team introduced indicators such as open magnetic flux and magnetic field polarity accuracy, and used a multi-objective optimization algorithm to analyze the trade-off relationship between different objectives. In years of low solar activity, the PFSS model's underestimate of open magnetic flux is more prominent. At this time, the objective function is more sensitive to amplitude differences, and the optimization results are mainly driven by the open flux consistency dominance. As solar activity enters the rising phase, the role of magnetic field polarity prediction accuracy in parameter selection increases accordingly.
This work combines coronal magnetic field modeling, free boundary problems, optimization algorithms based on in-situ observations, and multi-objective optimization to provide a mathematically interpretable modeling and optimization method for the observation constraints of key geometric parameters of the PFSS model, and is expected to be extended to well-posed research on the inverse problem of the coronal magnetic field under some observation constraints.
Relevant research results were published inJournal of Geophysical Research: Machine Learning and Computationsuperior. The research work is supported by the National Natural Science Foundation of China and the National Key Research and Development Program.
Source: https://www.cas.cn/syky/202608/t20260825_5118969.shtml