Origin and Structures of Solar Eruptions II: Magnetic Modeling (Invited Review)

TL;DR

This review discusses the methods and models used to analyze the three-dimensional magnetic field in the solar atmosphere, which governs solar eruptions like flares and coronal mass ejections.

Contribution

It provides a comprehensive overview of observational techniques, data processing, and modeling approaches for understanding solar magnetic structures and their role in solar activity.

Findings

Vector magnetic fields are routinely observed and processed for modeling.

Various models (force-free, MHD) are used to derive 3D magnetic fields.

Magnetic topology and helicity are key parameters in solar activity analysis.

Abstract

The topology and dynamics of the three-dimensional magnetic field in the solar atmosphere govern various solar eruptive phenomena and activities, such as flares, coronal mass ejections, and filaments/prominences. We have to observe and model the vector magnetic field to understand the structures and physical mechanisms of these solar activities. Vector magnetic fields on the photosphere are routinely observed via the polarized light, and inferred with the inversion of Stokes profiles. To analyze these vector magnetic fields, we need first to remove the 180$^\circ$ ambiguity of the transverse components and correct the projection effect. Then, the vector magnetic field can be served as the boundary conditions for a force-free field modeling after a proper preprocessing. The photospheric velocity field can also be derived from a time sequence of vector magnetic fields. Three-dimensional magnetic field could be derived and studied with theoretical force-free field models, numerical nonlinear force-free field models, magnetohydrostatic models, and magnetohydrodynamic models. Magnetic energy can be computed with three-dimensional magnetic field models or a time series of vector magnetic field. The magnetic topology is analyzed by pinpointing the positions of magnetic null points, bald patches, and quasi-separatrix layers. As a well conserved physical quantity, magnetic helicity can be computed with various methods, such as the finite volume method, discrete flux tube method, and helicity flux integration method. This quantity serves as a promising parameter characterizing the activity level of solar active regions.