EP240414a: Off-axis View of a Jet-Cocoon System from an Expanded Progenitor Star

When a relativistic jet is launched following the core-collapse of a star, its interaction with the stellar envelope leads to the formation of a hot cocoon, which produces various viewing-angle-dependent observational phenomena following the breakout from the surface. We study the observational signatures of fast X-ray transient (FXT) EP240414a, which may originate from a jet-cocoon system viewed slightly off-axis. In our model, (1) the prompt X-ray emission lasting $\sim\! 100\,{\rm{s}}$ is attributed to the cooling emission from the inner cocoon (shocked jet material); (2) the $\sim\! 0.1\,{\rm{d}}$ X-ray emission comes from the inner cocoon's afterglow; (3) the $\sim\! 0.4\,{\rm{d}}$ thermal-dominated optical emission arises from the cooling of the outer cocoon (shocked stellar material); (4) the $\sim\! 3\,{\rm{d}}$ non-thermal optical component and subsequent radio emission can be explained by the afterglow from a jet with a viewing angle of $10^{\circ}\lesssim \theta_{\rm{v}}\lesssim15^\circ$; and (5) the associated broad-lined Type Ic supernova only dominates the optical emission after $\sim\! 7\rm\, d$. Both the jet inferred from the off-axis afterglow and the inner cocoon constrained by the cooling emission are found to have similar kinetic energies, on the order of $10^{51}\,{\rm{erg}}$. We find that the progenitor's radius is $\sim3\,R_\odot$ as constrained by the { inner cocoon's} cooling emissions, indicating that the pre-explosion star may be a massive helium star that is slightly inflated. More FXTs associated with off-axis jets and supernovae will be further examined by the Einstein Probe, leading to a deeper understanding of jet-cocoon systems.