The Role of Twist in Kinked Flux Rope Emergence and Delta-spot Formation

It has been observationally well established that the magnetic configurations most favorable for producing energetic flaring events reside in δ-spots, a class of sunspots defined as having opposite-polarity umbrae sharing a common penumbra. They are frequently characterized by extreme compactness, strong rotation, and anti-Hale orientation. Numerous studies have shown that nearly all of the largest solar flares originate in δ-spots, making the understanding of these structures a fundamental step in predicting space weather. Despite their important influence on the space environment, surprisingly little is understood about the origin and behavior of δ-spots. In this paper, we perform a systematic study of the behavior of emerging flux ropes to test a theoretical model for the formation of δ-spots: the kink instability of emerging flux ropes. We simulated the emergence of highly twisted, kink-unstable flux ropes from the convection zone into the corona, and we compared their photospheric properties to those of emerged weakly twisted, kink-stable flux ropes. We show that the photospheric manifestations of the emergence of highly twisted flux ropes closely match the observed properties of δ-spots, and we discuss the resulting implications for observations. Our results strongly support and extend previous theoretical work that suggested that the kink instability of emerging flux ropes is a promising candidate to explain δ-spot formation, as it reproduces their key characteristics very well.