We numerically investigate the jet propagation through a rotating collapsing Wolf-Rayet star with detailed central engine physics constructed based on the neutrino-driven collapsar model. The collapsing star determines the evolution of mass accretion rate, black hole mass and spin, all of which are important ingredients for determining the jet luminosity. We reveal that neutrino-driven jets in rapidly spinning Wolf-Rayet stars are capable of breaking out from the stellar envelope, while those propagating in slower rotating progenitors fail to jet breakout due to insufficient kinetic power. For progenitor models with successful jet breakouts, the kinetic energy accumulated in the cocoon could be as large as ~1051erg and might significantly contribute to the luminosity of the afterglow emission or to the kinetic energy of the accompanying supernova if nickel production takes place. We further analyze the post breakout phase using a simple analytical prescription and conclude that the relativistic jet component could produce events with an isotropic-luminosity Lp(iso) ~1052erg/s and isotropic-energy Ej(iso) ~1054erg. Our findings support the idea of rapidly rotating Wolf-Rayet stars as plausible progenitors of GRBs, while slowly rotational ones could be responsible for low luminosity or failed GRBs.
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