Solar filament eruptions, flares, and coronal mass ejections (CMEs) are manifestations of drastic releases of energy in the magnetic field, which are related to many eruptive phenomena, from the Earth’s magnetosphere to black hole accretion disks. With the availability of high-resolution magnetograms on the solar surface, observational data-based modeling is a promising way to quantitatively study the underlying physical mechanisms behind observations. By incorporating thermal conduction and radiation losses in the energy equation, we develop a new data-driven radiative magnetohydrodynamic model, which has the capability of capturing the thermodynamic evolution compared to our previous zero-β model. Our numerical results reproduce the major observational characteristics of the X1.0 flare on 2021 October 28 in NOAA active region 12887, including the morphology of the eruption, the kinematics of the flare ribbons, extreme ultraviolet (EUV) radiations, and the two components of the EUV waves predicted by the magnetic stretching model, i.e., a fast-mode shock wave and a slower apparent wave, due to successive stretching of the magnetic field lines. Moreover, some intriguing phenomena are revealed in the simulation. We find that flare ribbons separate initially and ultimately stop at the outer stationary quasi-separatrix layers (QSLs). Such outer QSLs correspond to the border of the filament channel and determine the final positions of flare ribbons, which can be used to predict the size and the lifetime of a flare before it occurs. In addition, the side views of the synthesized EUV and white-light images exhibit typical three-part structures of CMEs, where the bright leading front is roughly cospatial with the nonwave component of the EUV wave, reinforcing the use of the magnetic stretching model for the slow component of EUV waves.
Solar filaments are cold and dense materials situated in magnetic dips, which show distinct radiation characteristics compared to the surrounding coronal plasma. They are associated with coronal sheared and twisted magnetic field lines. However, the exact magnetic configuration supporting a filament material is not easy to ascertain because of the absence of routine observations of the magnetic field inside filaments. Since many filaments lie above weak-field regions, it is nearly impossible to extrapolate their coronal magnetic structures by applying the traditional methods to noisy photospheric magnetograms, in particular the horizontal components. In this paper, we construct magnetic structures for some filaments with the regularized Biot–Savart laws and calculate their magnetic twists. Moreover, we make a parameter survey for the flux ropes of the Titov–Démoulin-modified model to explore the factors affecting the twist of a force-free magnetic flux rope. It is found that the twist of a force-free flux rope, ∣ T w ¯ ∣ , is proportional to its ratio of axial length to minor radius, L/a, and is basically independent of the overlying background magnetic field strength. Thus, we infer that long quiescent filaments are likely to be supported by more twisted flux ropes than short active-region filaments, which is consistent with observations.
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