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Population III Gamma-Ray Bursts and Breakout Criteria for Accretion-Powered Jets

We investigate the propagation of accretion-powered jets in various types of massive stars such as Wolf-Rayet stars, light Population III (Pop III) stars, and massive Pop III stars, all of which are the progenitor candidates of Gamma-Ray Bursts (GRBs). We perform two dimensional axisymmetric simulations of relativistic hydrodynamics taking into account both the envelope collapse and the jet propagation (i.e., the negative feedback of the jet on the accretion). Based on our hydrodynamic simulations, we show for the first time that the accretion-powered jet can potentially break out relativistically from the outer layers of Pop III progenitors. In our simulations, the accretion rate is estimated by the mass flux going through the inner boundary, and the jet is injected with a fixed accretion-to-jet conversion efficiency $η$. By varying the efficiency $η$ and opening angle $θ_{op}$ for more than 40 models, we find that the jet can make a relativistic breakout from all types of progenitors for GRBs if a simple condition $η\gtrsim 10^{-4} (θ_{op}/8^{\circ})^2$ is satisfied, which is consistent with analytical estimates. Otherwise no explosion or some failed spherical explosions occur.