Multiwavelength Campaign Observations of a Young Solar-type Star, EK Draconis. II. Understanding Prominence Eruption through Data-Driven Modeling and Observed Magnetic Environment

EK Draconis, a nearby young solar-type star (G1.5V, 50-120 Myr), is known as one of the best proxies for inferring the environmental conditions of the young Sun. The star frequently produces superflares and Paper I presented the first evidence of an associated gigantic prominence eruption observed as a blueshifted H$\alpha$ Balmer line emission. In this paper, we present the results of dynamical modeling of the stellar eruption and examine its relationship to the surface starspots and large-scale magnetic fields observed concurrently with the event. By performing a one-dimensional free-fall dynamical model and a one dimensional hydrodynamic simulation of the flow along the expanding magnetic loop, we found that the prominence eruption likely occurred near the stellar limb (12$^{+5}_{-5}$-16$^{+7}_{-7}$ degrees from the limb) and was ejected at an angle of 15$^{+6}_{-5}$-24$^{+6}_{-6}$ degrees relative to the line of sight, and the magnetic structures can expand into a coronal mass ejection (CME). The observed prominence displayed a terminal velocity of $\sim$0 km s$^{-1}$ prior to disappearance, complicating the interpretation of its dynamics in Paper I. The models in this paper suggest that prominence's H$\alpha$ intensity diminishes at around or before its expected maximum height, explaining the puzzling time evolution in observations. The TESS light curve modeling and (Zeeman) Doppler Imaging revealed large mid-latitude spots with polarity inversion lines and one polar spot with dominant single polarity, all near the stellar limb during the eruption. This suggests that mid-latitude spots could be the source of the pre-existing gigantic prominence we reported in Paper I. These results provide valuable insights into the dynamic processes that likely influenced the environments of early Earth, Mars, Venus, and young exoplanets.