Short GRBs: opening angles, local neutron star merger rate and off-axis events for GRB/GW association

The jet breaks in the afterglow lightcurves of short gamma-ray bursts (SGRBs), rarely detected so far, are crucial for estimating the half-opening angles of the ejecta ($\theta_{\rm j}$) and hence the neutron star merger rate. In this work we report the detection of jet decline behaviors in GRB 150424A and GRB 160821B and find $\theta_{\rm j}\sim 0.1$ rad. Together with five events reported before 2015 and other three "identified" recently (GRB 050709, GRB 060614 and GRB 140903A), we have a sample consisting of nine SGRBs and one long-short GRB with reasonably estimated $\theta_{\rm j}$. In particular, three {\it Swift} bursts in the sample have redshifts $z\leq 0.2$, with which we estimate the local neutron star merger rate density {to be $\sim 1109^{+1432}_{-657}~{\rm Gpc^{-3}~yr^{-1}}$ or $162^{+140}_{-83} {\rm Gpc^{-3}yr^{-1}}$ if the narrowly-beamed GRB 061201 is excluded}. Inspired by the typical $\theta_{\rm j}\sim 0.1$ rad found currently, we further investigate whether the off-beam GRBs (in the uniform jet model) or the off-axis events (in the structured jet model) can significantly enhance the GRB/GW association or not. For the former the enhancement is at most moderate, while for the latter the enhancement can be much greater and a high GRB/GW association probability of $\sim 10\%$ is possible. We also show that the data of GRB 160821B may contain a macronova/kilonova emission component with a temperature of $\sim 3100$ K at $\sim 3.6$ days after the burst and more data are needed to ultimately clarify.