| Summary: | Strong flares and coronal mass ejections (CMEs), launched from <inline-formula><math display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-sunspots, are the most catastrophic energy-releasing events in the solar system. The formations of <inline-formula><math display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-sunspots and relevant polarity inversion lines (PILs) are crucial for the understanding of flare eruptions and CMEs. In this work, the kink-stable, spot-spot-type <inline-formula><math display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-sunspots induced by flux emergence are simulated, under different subphotospheric initial conditions of magnetic field strength, radius, twist, and depth. The time evolution of various plasma variables of the <inline-formula><math display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-sunspots are simulated and compared with the observation data, including magnetic bipolar structures, relevant PILs, and temperature. The simulation results show that magnetic polarities display switchbacks at a certain stage and then split into numerous fragments. The simulated fragmentation phenomenon in some <inline-formula><math display="inline"><semantics><mi>δ</mi></semantics></math></inline-formula>-sunspots may provide leads for future observations in the field.
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