http://arxiv.org/abs/1712.01077
Central engine 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 later period. Owing to the internal dissipation, the later launched ejecta may be observed at a later time ($t_{\rm{jet}}$). In this paper, we study the relation of $t_{\rm{b}}$ and $t_{\rm{jet}}$, where $t_{\rm{b}}$ is the collision time of the later launched ejecta with the formed external shock. It is found that the relation of $t_{\rm{b}}$ and $t_{\rm{jet}}$ depends on the bulk Lorentz factor ($\Gamma_{\rm{jet}}$) of the later launched ejecta and the density ($\rho$) of the circum-burst medium. If the value of $\Gamma_{\rm{jet}}$ or $\rho$ is low, the $t_{\rm{b}}$ would be significantly larger than $t_{\rm{jet}}$. However, the $t_{\rm{b}}\sim t_{\rm{jet}}$ can be found if the value of $\Gamma_{\rm{jet}}$ or $\rho$ is significantly large. Our results can explain the large lag of the optical emission relative to the $\gamma$-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.
D. Lin, B. Huang, T. Liu, et. al.
Tue, 5 Dec 17
35/96
Comments: 10 pages, 4 figures, accepted for publication in ApJ
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