Abstract The propagation of disturbances in the solar atmosphere is inherently three-dimensional (3D), yet comprehensive studies on the spatial structure and dynamics of 3D wavefronts are scarce. Here we conduct high-resolution 3D numerical simulations to investigate filament eruptions, focusing particularly on the 3D structure and genesis of EUV waves. Our results demonstrate that the EUV wavefront forms a dome-like configuration subdivided into three distinct zones. The foremost zone, preceding the flux rope, consists of fast-mode shock waves that heat the adjacent plasma. Adjacent to either side of the flux rope, the second zone contains expansion waves that cool the nearby plasma. The third zone, at the juncture of the first two, exhibits minimal disturbances. This anisotropic structure of the wavefront stems from the configuration and dynamics of the flux rope, which acts as a 3D piston during eruptions—compressing the plasma ahead to generate fast-mode shocks and evacuating the plasma behind to induce expansion waves. This dynamic results in the observed anisotropic wavefront. Additionally, with synthetic EUV images from simulation data, the EUV waves are observable in Atmospheric Imaging Assembly 193 and 211 $\AA$, which are identified as the fast-mode shocks. The detection of EUV waves varies with the observational perspective: the face-on view reveals EUV waves from the lower to the higher corona, whereas an edge-on view uncovers these waves only in the higher corona.
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