Data-driven modeling of solar coronal magnetic field evolution and eruptions

Magnetic fields play a fundamental role in the structure and dynamics of the solar corona. As they are driven by their footpoint motions on the solar surface, which transport energy from the interior of the Sun into its atmosphere, the coronal magnetic fields are stressed continuously with buildup of magnetic nonpotentiality in the form of topology complexity (magnetic helicity) and local electric currents (magnetic free energy). The accumulated nonpotentiality is often released explosively by solar eruptions, manifested as solar flares and coronal mass ejections, during which magnetic energy is converted into mainly kinetic, thermal, and nonthermal energy of the plasma, which can cause adverse space weather. To reveal the physical mechanisms underlying solar eruptions, it is vital to know the three-dimensional (3D) structure and evolution of the coronal magnetic fields. Because of a lack of direct measurements, the 3D coronal magnetic fields are commonly studied using numerical modeling, whereas traditional models mostly aim for a static extrapolation of the coronal field from the observable photospheric magnetic field data. Over the last decade, dynamic models that are driven directly by observation magnetograms have been developed and applied successfully to study solar coronal magnetic field evolution as well as its eruption, which offers a novel avenue for understanding their underlying magnetic topology and mechanism. In this paper, we review the basic methodology of the data-driven coronal models, state-of-the-art developments, their typical applications, and new physics that have been derived using these models. Finally, we provide an outlook for future developments and applications of the data-driven models.