2018ApJ...852..136L

Central engines of gamma-ray bursts (GRBs) may be intermittent and launch several episodes of ejecta separated by a long quiescent interval. In this scenario, an external shock is formed due to the propagation of the first launched ejecta into the circum-burst medium and the later launched ejecta may interact with the external shock at a later period. Owing to the internal dissipation, the later launched ejecta may be observed at a later time (t_jet). In this paper, we study the relation of t_b and t_jet, where t_b is the collision time of the later launched ejecta with the formed external shock. It is found that the relation of t_b and t_jet depends on the bulk Lorentz factor (Γ_jet) of the later launched ejecta and the density (ρ) of the circum-burst medium. If the value of Γ_jet or ρ is low, the t_b would be significantly larger than t_jet. However, the t_b ∼ t_jet can be found if the value of Γ_jet or ρ is significantly large. Our results can explain the large lag of the optical emission relative to the γ-ray/X-ray emission in GRBs, e.g., GRB 111209A. For GRBs with a precursor, our results suggest that the energy injection into the external shock and thus more than one external-reverse shock may appear in the main prompt emission phase. According to our model, we estimate the Lorentz factor of the second launched ejecta in GRB 160625B.