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We present the results of 3D hydrodynamic simulations of gamma-ray burst(GRB) jet emanating from a massive star with a particular focus on theformation of high-velocity quasi-spherical ejecta and the jet-induced chemicalmixing. Recent early-time optical observations of supernovae associated withGRBs (e.g., GRB 171205A/SN 2017iuk) indicate a considerable amount of heavymetals in the high-velocity outer layers of the ejecta. Using our jetsimulations, we show that the density and chemical structure of the outerejecta implied by observations can be naturally reproduced by a powerful jetpenetrating the progenitor star. We consider three representative jet modelswith a stripped massive star, a standard jet, a weak jet, and a jet choked byan extended circumstellar medium, to clarify the differences in the dynamicalevolution and the chemical properties of the ejected materials. The standardjet successfully penetrates the progenitor star and creates a quasi-sphericalejecta component (cocoon). The jet-induced mixing significantly contaminatesthe cocoon with heavy elements that have been otherwise embedded in the innerlayer of the ejecta. The weak and choked jet models fail to produce anultra-relativistic jet but produce a quasi-spherical cocoon with differentchemical properties. We discuss the impact of the different jet-starinteractions on the expected early-time electromagnetic signatures of long GRBsand how to probe the jet dynamics from observations.

Chemical stratification in a long gamma-ray burst cocoon and early-time spectral signatures of supernovae associated with gamma-ray bursts