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Numerical Study on Emergence of Kinked Flux Tube for Understanding of Possible Origin of Delta-spot Regions

We carried out a magnetohydrodynamics simulation where a subsurface twisted kink-unstable flux tube emerges from the solar interior to the corona. Unlike the previous expectations based on the bodily emergence of a knotted tube, we found that the kinked tube can spontaneously form a complex quadrupole structure at the photosphere. Due to the development of the kink instability before the emergence, the magnetic twist at the kinked apex of the tube is greatly reduced, although the other parts of the tube is still strongly twisted. This leads to the formation of a complex quadrupole structure: a pair of the coherent, strongly twisted spots and a narrow complex bipolar pair between it. The quadrupole is formed by the submergence of a portion of emerged magnetic fields. This result is relevant for understanding of the origin of the complex multipolar $δ$-spot regions that have a strong magnetic shear and emerge with polarity orientations not following Hale-Nicholson and Joy Laws.