Propagation of Relativistic, Hydrodynamic, Intermittent Jets in a Rotating, Collapsing GRB Progenitor Star

The prompt emission of gamma-ray bursts (GRBs) is characterized by rapid variabilities, which may be a direct reflection of the unsteady central engine. We perform a series of axisymmetric 2.5-dimensional simulations to study the propagation of relativistic, hydrodynamic, intermittent jets through the envelope of a GRB progenitor star. A realistic rapidly rotating star is incorporated as the background of jet propagation, and the star is allowed to collapse due to the gravity of the central black hole. By modeling the intermittent jets with constant-luminosity pulses with equal on and off durations, we investigate how the half-period, $T$, affects the jet dynamics. For relatively small $T$ values (e.g. 0.2 s), the jet breakout time $t_{\rm bo}$ depends on the opening angle of the jet, with narrower jets more penetrating and reaching the surface at shorter times. For $T \leq 1$ s, the reverse shock crosses each pulse before the jet penetrates through the stellar envelope. As a result, after the breakout of the first group of pulses at $t_{\rm bo}$, several subsequent pulses vanish before penetrating the star, causing a quiescent gap. For larger half-periods ($T=2.0, 4.0$ s), all the pulses can successfully penetrate through the envelope, since each pulse can propagate through the star before the reverse shock crosses the shell. Our results may interpret the existence of a weak precursor in many long GRBs, given that the GRB central engine injects intermittent pulses with half-period $T \leq 1$ s. The observational data seem to be consistent with such a possibility.