Spontaneous Generation of δ -sunspots in Convective Magnetohydrodynamic Simulation of Magnetic Flux Emergence

Observations reveal that strong solar flares and coronal mass ejections tend to occur in complex active regions characterized by δ-sunspots, spot rotation, sheared polarity inversion lines (PILs), and magnetic flux ropes. Here we report on the first modeling of spontaneous δ-spot generation as a result of flux emergence from the turbulent convection zone. Utilizing state-of-the-art radiative magnetohydrodynamics code R2D2, we simulate the emergence of a force-free flux tube in the convection zone that stretches down to −140 Mm. Elevated by large-scale convective upflows, the tube appears on the photosphere as two emerging bipoles. The opposite polarities collide against each other due to the subsurface connectivity, and they develop into a pair of closely packed δ-spots. The Lorentz force drives the spot rotation and a strong counter-streaming flow of 10 km s−1 at the PIL in δ-spots, which, in tandem with local convection, strengthens the horizontal field to 4 kG and builds up a highly sheared PIL. In the atmosphere above the PIL, a flux rope structure is created. All these processes follow the multi-buoyant segment theory of the δ-spot formation, and they occur as a natural consequence of interaction between magnetic flux and turbulent convection, suggesting that the generation of δ-spots and the resultant flare eruptions may be a stochastically determined process.