Linking extended and plateau emissions of short gamma-ray bursts

Some short gamma-ray bursts (SGRBs) show a longer lasting emission phase, called extended emission (EE) lasting $\sim 10^{2-3}\,\rm s$, as well as a plateau emission (PE) lasting $\sim10^{4-5}\,\rm s$. While a long-lasting activity of the central engines is a promising explanation for powering both emissions, their physical origin and their emission mechanisms are still uncertain. In this work, we study the properties of the EEs and their connection with the PEs. First, we constrain the minimal Lorentz factor $\Gamma$ of the outflows powering EEs, using compactness arguments and find that the outflows should be relativistic, $\Gamma\gtrsim10$. We propose a consistent scenario for the PEs, where the outflow eventually catches up with the jet responsible for the prompt emission, injecting energy into the forward shock formed by the prior jet, which naturally results in a PE. We also derive the radiation efficiency of EEs and the Lorentz factor of the outflow within our scenario for 10 well-observed SGRBs accompanied by both EE and PE. The efficiency has an average value of $\sim3\,\%$ but shows a broad distribution ranging from $\sim0.01$ to $\sim100\%$. The Lorentz factor is $\sim20-30$, consistent with the compactness arguments. These results suggest that EEs are produced by a slower outflow via more inefficient emission than the faster outflow which causes the prompt emission with a high radiation efficiency.